Readings for the Financial Risk Manager Volume 2
Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding. The Wiley Finance series contains books written specifically for finance and investment professionals as well as sophisticated individual investors and their financial advisors. Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation, and financial instrument analysis as well as much more. For a list of available titles, visit our web site at www.WileyFinance.com.
Readings for the Financial Risk Manager Volume 2
RENÉ M. STULZ, EDITOR RICH APOSTOLIK, EDITOR GLOBAL ASSOCIATION OF RISK PROFESSIONALS, INC.
John Wiley & Sons, Inc.
Copyright © 2005 by Global Association of Risk Professionals, Inc. All rights reserved. Please see Credits for additional copyright and source information. In all instances, permission credits and source information appear directly on any reprinted chapter. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com. ISBN-13 978-0-471-78297-1 ISBN-10 0-471-78297-1 Printed in the United States of America.
Contents
Editors’ Note Acknowledgments READING 57
Computing Value-at-Risk Philippe Jorion Reproduced with permission from Value at Risk, 2nd ed. (New York: McGraw-Hill, 2001): 107–128.
READING 58
VaR Methods Philippe Jorion Reproduced with permission from Value at Risk, 2nd ed. (New York: McGraw-Hill, 2001): 205–230.
READING 59
Liquidity Risk Philippe Jorion Reproduced with permission from Value at Risk, 2nd ed. (New York: McGraw-Hill, 2001): 339–357.
READING 60
Credit Risks and Credit Derivatives René M. Stulz Reproduced with permission from Risk Management and Derivatives (Mason, Ohio: South-Western, 2003): 571–604.
READING 61
Extending the VaR Approach to Operational Risk Linda Allen, Jacob Boudoukh, and Anthony Saunders Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value at Risk Approach (Oxford: Blackwell Publishing, 2004): 158–199.
v
vi
READINGS FOR THE FINANCIAL RISK MANAGER
READING 62
Case Studies Reto Gallati Reproduced with permission from Risk Management and Capital Adequacy (New York: McGraw-Hill, 2003): 441–493.
READING 63
What Is Operational Risk? Douglas G. Hoffman Reproduced with permission from Managing Operational Risk (New York: John Wiley & Sons, 2002): 29–55.
READING 64
Risk Assessment Strategies Douglas G. Hoffman Reproduced with permission from Managing Operational Risk (New York: John Wiley & Sons, 2002): 181–212.
READING 65
Operational Risk Analysis and Measurement: Practical Building Blocks Douglas G. Hoffman Reproduced with permission from Managing Operational Risk (New York: John Wiley & Sons, 2002): 257–304.
READING 66
Economic Risk Capital Modeling Douglas G. Hoffman Reproduced with permission from Managing Operational Risk (New York: John Wiley & Sons, 2002): 375–403.
READING 67
Capital Allocation and Performance Measurement Michel Crouhy, Dan Galai, and Robert Mark Reproduced with permission from Risk Management (New York: McGraw-Hill, 2001): 529–578.
Contents
READING 68
The Capital Asset Pricing Model and Its Application to Performance Measurement Noël Amenc and Véronique Le Sourd Reproduced with permission from Portfolio Theory and Performance Analysis (West Sussex: John Wiley & Sons, 2003): 95–102, 108–116.
READING 69
Multi-Factor Models and Their Application to Performance Measurement Noël Amenc and Véronique Le Sourd Reproduced with permission from Portfolio Theory and Performance Analysis (West Sussex: John Wiley & Sons, 2003): 149–194.
READING 70
Fixed Income Security Investment Noël Amenc and Véronique Le Sourd Reproduced with permission from Portfolio Theory and Performance Analysis (West Sussex: John Wiley & Sons, 2003): 229–252.
READING 71
Funds of Hedge Funds Jaffer Sohail Reproduced with permission. Lars Jaeger, ed., The New Generation of Risk Management for Hedge Funds and Private Equity Investments (London: Euromoney Books, 2003): 88–107.
READING 72
Style Drifts: Monitoring, Detection and Control Pierre-Yves Moix Reproduced with permission. Lars Jaeger, ed., The New Generation of Risk Management for Hedge Funds and Private Equity Investments (London: Euromoney Books, 2003): 387–398.
vii
viii
READINGS FOR THE FINANCIAL RISK MANAGER
READING 73
Risk Control Strategies: The Manager’s Perspective Pierre-Yves Moix and Stefan Scholz Reproduced with permission. Jaffer Sohail, ed., Funds of Hedge Funds (London: Euromoney Books, 2003): 219–233.
APPENDIX
FRM Suggested Readings for Further Study Credits About the CD-ROM
Editors’ Note
he objective of this volume is to provide core readings recommended by the Global Association of Risk Professionals’ Financial Risk Manager (FRM®) Committee for the 2005 exam that are not available on the first Readings for the Financial Risk Manager CD-ROM. The FRM Committee, which oversees the selection of reading materials for the FRM Exam, suggests 100 readings for those registered for the FRM Exam and any other risk professionals interested in the critical knowledge essential to their profession. Fifty-five of these recommended readings appear on the Readings for the Financial Risk Manager CD-ROM* and 17 appear on this CD-ROM. While every attempt has been made by GARP to obtain permissions from authors and their respective publishers to reprint all materials on the FRM Committee’s recommended reading list, not all readings were available for reprinting. A list of those readings that are not reprinted on either the Readings for the Financial Risk Manager CD-ROM or this CD-ROM can be found in the Appendix of this CD-ROM. In every instance, full bibliographic information is provided for those interested in referencing these materials for study, citing them in their own research, or ultimately acquiring the volumes in which the readings first appeared for their own risk management libraries. GARP thanks all authors and publishers mentioned—particularly those who graciously agreed to allow their materials to be reprinted here as a companion text to the Financial Risk Manager Handbook, Third Edition, by Philippe Jorion. We hope these books of readings prove to be of great convenience and use to all risk professionals, including those enrolled for the FRM Exam.
T
*The Editors note that Reading 56, which appears on the first Readings for the Financial Risk Manager CD-ROM, is not on the suggested reading list for the 2005 FRM Exam. To avoid confusion, we have labeled the first reading on Volume 2 as Reading 57, so that each suggested reading, whether current or dormant, has its own unique assigned number.
ix
Acknowledgments
his second volume of Readings for the Financial Risk Manager was made possible through the work of the Global Association of Risk Professionals’ FRM Committee. To choose the readings for the FRM Exam, the Committee reviewed an extremely large number of published works. The readings selected were chosen because they meet high expositional standards and together provide coverage of the issues the Committee expects candidates to master. GARP’s FRM Exam has attained global benchmark status in large part because of the hard work and dedication of this core group of risk management professionals. These highly regarded professionals have volunteered their time to develop, without a historical road map, the minimum standards that risk managers must meet. The challenge to successfully implement this approach on a global basis cannot be overstated. GARP’s FRM Committee meets regularly via e-mail, through conference calls, and in person to identify and discuss financial risk management trends and theories. Its objective is to ensure that what is tested each year in the FRM Exam is timely, comprehensive, and relevant. The results of these discussions are memorialized in the FRM Study Guide. The Study Guide, which is revised annually, clearly delineates in a topical outline the base level of knowledge that a financial risk manager should possess in order to provide competent financial risk management advice to a firm’s senior management and directors. FRM Committee members represent some of the industry’s most knowledgeable financial risk professionals. The following individuals were the Committee members responsible for developing the 2005 FRM Study Guide:
T
Dr. René Stulz (Chairman) Richard Apostolik Juan Carlos Garcia Cespedes Dr. Marcelo Cruz Dr. James Gutman Kai Leifert Steve Lerit, CFA
x
Ohio State University Global Association of Risk Professionals Banco Bilbao Vizcaya Argentaria Risk Maths, Inc. Goldman Sachs International Credit Suisse Asset Management New York Life Investment Management
xi
Acknowledgments
Michelle McCarthy Dr. Susan Mangiero Michael B. Miller Peter Nerby Dr. Victor Ng Dr. Elliot Noma Gadi Pickholz Robert Scanlon Omer Tareen Alan Weindorf
Washington Mutual Bank BVA, LLC Fortress Investment Group Moody’s Investors Service Goldman Sachs & Co. Asset Alliance Corporation Ben Gurion University of the Negev Standard Chartered Bank Microsoft Corporation Starbucks Coffee Company
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 107 nd
CHAPTER
5
Computing Value at Risk
The Daily Earnings at Risk (DEaR) estimate for our combined trading activities averaged approximately $15 million. J.P. Morgan 1994 Annual Report
P
erhaps the greatest advantage of value at risk (VAR) is that it summarizes in a single, easy to understand number the downside risk of an institution due to financial market variables. No doubt this explains why VAR is fast becoming an essential tool for conveying trading risks to senior management, directors, and shareholders. J.P. Morgan, for example, was one of the first users of VAR. It revealed in its 1994 Annual Report that its trading VAR was an average of $15 million at the 95 percent level over 1 day. Shareholders can then assess whether they are comfortable with this level of risk. Before such figures were released, shareholders had only a vague idea of the extent of trading activities assumed by the bank. This chapter turns to a formal definition of value at risk (VAR). VAR assumes that the portfolio is “frozen” over the horizon or, more generally, that the risk profile of the institution remains constant. In addition, VAR assumes that the current portfolio will be marked-to-market on the target horizon. Section 5.1 shows how to derive VAR figures from probability distributions. This can be done in two ways, either from considering the actual empirical distribution or by approximating the distribution by a parametric approximation, such as the normal distribution, in which case VAR is derived from the standard deviation. Section 5.2 then discusses the choice of the quantitative factors, the confidence level and the horizon. Criteria for this choice should be guided by the use of the VAR number. If VAR is simply a benchmark for risk, 107
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 108 nd
108
PART 2 Building Blocks
the choice is totally arbitrary. In contrast, if VAR is used to set equity capital, the choice is quite delicate. Criteria for parameter selection are also explained in the context of the Basel Accord rules. The next section turns to an important and often ignored issue, which is the precision of the reported VAR number. Due to normal sampling variation, there is some inherent imprecision in VAR numbers. Thus, observing changes in VAR numbers for different estimation windows is perfectly normal. Section 5.3 provides a framework for analyzing normal sampling variation in VAR and discusses methods to improve the accuracy of VAR figures. Finally, Section 5.4 provides some concluding thoughts. 5.1 COMPUTING VAR
With all the requisite tools in place, we can now formally define the value at risk (VAR) of a portfolio. VAR summarizes the expected maximum loss (or worst loss) over a target horizon within a given confidence interval. Initially, we take the quantitative factors, the horizon and confidence level, as given.
5.1.1 Steps in Constructing VAR Assume, for instance, that we need to measure the VAR of a $100 million equity portfolio over 10 days at the 99 percent confidence level. The following steps are required to compute VAR: ■ ■
■
■
■
Mark-to-market of the current portfolio (e.g., $100 million). Measure the variability of the risk factors(s) (e.g., 15 percent per annum). Set the time horizon, or the holding period (e.g., adjust to 10 business days). Set the confidence level (e.g., 99 percent, which yields a 2.33 factor assuming a normal distribution). Report the worst loss by processing all the preceding information (e.g., a $7 million VAR).
These steps are illustrated in Figure 5–1. The precise detail of the computation is described next.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 109 nd
CHAPTER 5 Computing Value at Risk
FIGURE
109
5–1
Steps in constructing VAR.
Mark position to market
Measure Set variability of time risk factors horizon
Set confidence level
Report potential loss
Value
Value
Frequency
Value
VAR σ
10 days Time
−α
Horizon
Horizon
Sample computation: $100M
x
15%
x
(10/252)
x
2.33
=
$7M
5.1.2 VAR for General Distributions To compute the VAR of a portfolio, define W0 as the initial investment and R as its rate of return. The portfolio value at the end of the target horizon is W W0 (1 R). As before, the expected return and volatility of R are and . Define now the lowest portfolio value at the given confidence level c as W* W0 (1 R*). The relative VAR is defined as the dollar loss relative to the mean: VAR(mean) E(W) W* W0 (R* )
(5.1)
Sometimes VAR is defined as the absolute VAR, that is, the dollar loss relative to zero or without reference to the expected value: VAR(zero) W0 W* W0R*
(5.2)
In both cases, finding VAR is equivalent to identifying the minimum value W* or the cutoff return R*. If the horizon is short, the mean return could be small, in which case both methods will give similar results. Otherwise, relative VAR is conceptually more appropriate because it views risk in terms of a deviation
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 110 nd
110
PART 2 Building Blocks
from the mean, or “budget,” on the target date, appropriately accounting for the time value of money. This approach is also more conservative if the mean value is positive. Its only drawback is that the mean return is sometimes difficult to estimate. In its most general form, VAR can be derived from the probability distribution of the future portfolio value f(w). At a given confidence level c, we wish to find the worst possible realization W* such that the probability of exceeding this value is c: c
∞
f(w) dw
(5.3)
W*
or such that the probability of a value lower than W*, p P(w W*), is 1 c: 1c
W*
∞
f(w) dw P(w W*) p
(5.4)
In other words, the area from ∞ to W* must sum to p 1 c, for instance, 5 percent. The number W* is called the quantile of the distribution, which is the cutoff value with a fixed probability of being exceeded. Note that we did not use the standard deviation to find the VAR. This specification is valid for any distribution, discrete or continuous, fat- or thin-tailed. Figure 5–2, for instance, reports J.P. Morgan’s distribution of daily revenues in 1994. To compute VAR, assume that daily revenues are identically and independently distributed. We can then derive the VAR at the 95 percent confidence level from the 5 percent left-side “losing tail” from the histogram. From this graph, the average revenue is about $5.1 million. There is a total of 254 observations; therefore, we would like to find W* such that the number of observations to its left is 254 5 percent 12.7. We have 11 observations to the left of $10 million and 15 to the left of $9 million. Interpolating, we find W* $9.6 million. The VAR of daily revenues, measured relative to the mean, is VAR E(W) W* $5.1 million ($9.6 million) $14.7 million. If one wishes to measure VAR in terms of absolute dollar loss, VAR is then $9.6 million.
5.1.3 VAR for Parametric Distributions The VAR computation can be simplified considerably if the distribution can be assumed to belong to a parametric family, such as the normal dis-
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 111 nd
CHAPTER 5 Computing Value at Risk
FIGURE
111
5–2
Distribution of daily revenues. 20
Number of days VAR=$15 million
Average=$5 million
5% of Occurrences 15
10
5
0
<-25
-20
-15
-10
-5 0 5 10 15 Daily revenue ($ million)
20
tribution. When this is the case, the VAR figure can be derived directly from the portfolio standard deviation using a multiplicative factor that depends on the confidence level. This approach is sometimes called parametric because it involves estimation of parameters, such as the standard deviation, instead of just reading the quantile off the empirical distribution. This method is simple and convenient and, as we shall see later, produces more accurate measures of VAR. The issue is whether the normal approximation is realistic. If not, another distribution may fit the data better. First, we need to translate the general distribution f(w) into a standard normal distribution ( ), where has mean zero and standard deviation of unity. We associate W* with the cutoff return R* such that W* W0(1 R*). Generally, R* is negative and also can be written as |R*|.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 112 nd
112
PART 2 Building Blocks
Further, we can associate R* with a standard normal deviate 0 by setting |R*|
(5.5)
It is equivalent to set 1c
W*
∞
f(w) dw
|R*|
∞
f(r) dr
∞
( ) d
(5.6)
Thus the problem of finding a VAR is equivalent to finding the deviate such that the area to the left of it is equal to 1 c. This is made possible by turning to tables of the cumulative standard normal distribution function, which is the area to the left of a standard normal variable with value equal to d: N(d)
d
∞
( ) d
(5.7)
This function also plays a key role in the Black-Scholes option pricing model. Figure 5–3 graphs the cumulative density function N(d ), which increases monotonically from 0 (for d ∞) to 1 (for d ∞), going through 0.5 as d passes through 0. To find the VAR of a standard normal variable, select the desired left-tail confidence level on the vertical axis, say, 5 percent. This corresponds to a value of 1.65 below 0. We then retrace our steps, back from the we just found to the cutoff return R* and VAR. From Equation (5.5), the cutoff return is R*
(5.8)
For more generality, assume now that the parameters and are expressed on an annual basis. The time interval considered is t, in years. We can use the time aggregation results developed in the preceding chapter, which assume uncorrelated returns. Using Equation (5.1), we find the VAR below the mean as VAR(mean) W0(R* ) W0 t
(5.9)
In other words, the VAR figure is simply a multiple of the standard deviation of the distribution times an adjustment factor that is directly related to the confidence level and horizon.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 113 nd
CHAPTER 5 Computing Value at Risk
FIGURE
113
5–3
Cumulative normal probability distribution. 1
N(d)
1.65σ 0.5
c = 5% confidence level 0.05 0
-3
-2
-1 0 1 d=Standard normal variable
2
3
When VAR is defined as an absolute dollar loss, we have t) VAR(zero) W0R* W0( t
(5.10)
This method generalizes to other cumulative probability functions (cdf) as well as the normal, as long as all the uncertainty is contained in . Other distributions will entail different values of . The normal distribution is just particularly easy to deal with because it adequately represents many empirical distributions. This is especially true for large, welldiversified portfolios but certainly not for portfolios with heavy option components and exposures to a small number of financial risks.
5.1.4 Comparison of Approaches How well does this approximation work? For some distributions, the fit can be quite good. Consider, for instance, the daily revenues in Figure 5–2. The standard deviation of the distribution is $9.2 million. According
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 114 nd
114
PART 2 Building Blocks
FIGURE
5–4
Comparison of cumulative distributions. 1
Cumulative probability
0.5
Normal distribution Actual distribution 5% 0
<-25
-20
-15
-10
-5 0 5 10 15 Daily revenue ($ million)
20
to Equation (5.9), the normal-distribution VAR is (W0) 1.65 $9.2 million $15.2 million. Note that this number is very close to the VAR obtained from the general distribution, which was $14.7 million. Indeed, Figure 5–4 presents the cumulative distribution functions (cdf) obtained from the histogram in Figure 5–2 and from its normal approximation. The actual cdf is obtained from summing, starting from the left, all numbers of occurrences in Figure 5–2 and then scaling by the total number of observations. The normal cdf is the same as that in Figure 5–3, with the horizontal axis scaled back into dollar revenues using Equation (5.8). The two lines are generally very close, suggesting that the normal approximation provides a good fit to the actual data.
5.1.5 VAR as a Risk Measure VAR’s heritage can be traced to Markowitz’s (1952) seminal work on portfolio choice. He noted that “you should be interested in risk as well as
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 115 nd
CHAPTER 5 Computing Value at Risk
115
return” and advocated the use of the standard deviation as an intuitive measure of dispersion. Much of Markowitz’s work was devoted to studying the tradeoff between expected return and risk in the mean-variance framework, which is appropriate when either returns are normally distributed or investors have quadratic utility functions. Perhaps the first mention of confidence-based risk measures can be traced to Roy (1952), who presented a “safety first” criterion for portfolio selection. He advocated choosing portfolios that minimize the probability of a loss greater than a disaster level. Baumol (1963) also proposed a risk measurement criterion based on a lower confidence limit at some probability level: L
(5.11)
which is an early description of Equation (5.10). Other measures of risk have also been proposed, including semideviation, which counts only deviations below a target value, and lower partial moments, which apply to a wider range of utility functions. More recently, Artzner et al. (1999) list four desirable properties for risk measures for capital adequacy purposes. A risk measure can be viewed as a function of the distribution of portfolio value W, which is summarized into a single number (W): ■
■
■
■
Monotonicity: If W1 W2, (W1) (W2), or if a portfolio has systematically lower returns than another for all states of the world, its risk must be greater. Translation invariance. (W k) (W) k, or adding cash k to a portfolio should reduce its risk by k. Homogeneity. (bW) b(W), or increasing the size of a portfolio by b should simply scale its risk by the same factor (this rules out liquidity effects for large portfolios, however). Subadditivity. (W1 W2) (W1) (W2), or merging portfolios cannot increase risk.
Artzner et al. (1999) show that the quantile-based VAR measure fails to satisfy the last property. Indeed, one can come up with pathologic examples of short option positions that can create large losses with a low probability and hence have low VAR yet combine to create portfolios with larger VAR. One can also show that the shortfall measure E(X|X VAR),
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 116 nd
116
PART 2 Building Blocks
which is the expected loss conditional on exceeding VAR, satisfies these desirable “coherence” properties. When returns are normally distributed, however, the standard deviation–based VAR satisfies the last property, (W1 W2) (W1) (W2). Indeed, as Markowitz had shown, the volatility of a portfolio is less than the sum of volatilities. Of course, the preceding discussion does not consider another essential component for portfolio comparisons: expected returns. In practice, one obviously would want to balance increasing risk against increasing expected returns. The great benefit of VAR, however, is that it brings attention and transparency to the measure of risk, a component of the decision process that is not intuitive and as a result too often ignored. 5.2 CHOICE OF QUANTITATIVE FACTORS
We now turn to the choice of two quantitative factors: the length of the holding horizon and the confidence level. In general, VAR will increase with either a longer horizon or a greater confidence level. Under certain conditions, increasing one or the other factor produces equivalent VAR numbers. This section provides guidance on the choice of c and t, which should depend on the use of the VAR number.
5.2.1 VAR as a Benchmark Measure The first, most general use of VAR is simply to provide a companywide yardstick to compare risks across different markets. In this situation, the choice of the factors is arbitrary. Bankers Trust, for instance, has long used a 99 percent VAR over an annual horizon to compare the risks of various units. Assuming a normal distribution, we show later that it is easy to convert disparate bank measures into a common number. The focus here is on cross-sectional or time differences in VAR. For instance, the institution wants to know if a trading unit has greater risk than another. Or whether today’s VAR is in line with yesterday’s. If not, the institution should “drill down” into its risk reports and find whether today’s higher VAR is due to increased volatility or larger bets. For this purpose, the choice of the confidence level and horizon does not matter much as long as consistency is maintained.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 117 nd
CHAPTER 5 Computing Value at Risk
117
5.2.2 VAR as a Potential Loss Measure Another application of VAR is to give a broad idea of the worst loss an institution can incur. If so, the horizon should be determined by the nature of the portfolio. A first interpretation is that the horizon is defined by the liquidation period. Commercial banks currently report their trading VAR over a daily horizon because of the liquidity and rapid turnover in their portfolios. In contrast, investment portfolios such as pension funds generally invest in less liquid assets and adjust their risk exposures only slowly, which is why a 1-month horizon is generally chosen for investment purposes. Since the holding period should correspond to the longest period needed for an orderly portfolio liquidation, the horizon should be related to the liquidity of the securities, defined in terms of the length of time needed for normal transaction volumes. A related interpretation is that the horizon represents the time required to hedge the market risks. An opposite view is that the horizon corresponds to the period over which the portfolio remains relatively constant. Since VAR assumes that the portfolio is frozen over the horizon, this measure gradually loses significance as the horizon extends. However, perhaps the main reason for banks to choose a daily VAR is that this is consistent with their daily profit and loss (P&L) measures. This allows an easy comparison between the daily VAR and the subsequent P&L number. For this application, the choice of the confidence level is relatively arbitrary. Users should recognize that VAR does not describe the worst-ever loss but is rather a probabilistic measure that should be exceeded with some frequency. Higher confidence levels will generate higher VAR figures.
5.2.3 VAR as Equity Capital On the other hand, the choice of the factors is crucial if the VAR number is used directly to set a capital cushion for the institution. If so, a loss exceeding the VAR would wipe out the equity capital, leading to bankruptcy. For this purpose, however, we must assume that the VAR measure adequately captures all the risks facing an institution, which may be a stretch. Thus the risk measure should encompass market risk, credit risk, operational risk, and other risks.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 118 nd
118
PART 2 Building Blocks
The choice of the confidence level should reflect the degree of risk aversion of the company and the cost of a loss exceeding VAR. Higher risk aversion or greater cost implies that a greater amount of capital should cover possible losses, thus leading to a higher confidence level. At the same time, the choice of the horizon should correspond to the time required for corrective action as losses start to develop. Corrective action can take the form of reducing the risk profile of the institution or raising new capital. To illustrate, assume that the institution determines its risk profile by targeting a particular credit rating. The expected default rate then can be converted directly into a confidence level. Higher credit ratings should lead to a higher VAR confidence level. Table 5–1, for instance, shows that to maintain a Baa investment-grade credit rating, the institution should have a default probability of 0.17 percent over the next year. It therefore should carry enough capital to cover its annual VAR at the 99.83 percent confidence level, or 100 0.17 percent. Longer horizons, with a constant risk profile, inevitably lead to higher default frequencies. Institutions with an initial Baa credit rating have a default frequency of 10.50 percent over the next 10 years. The same credit rating can be achieved by extending the horizon or decreasing the confidence level appropriately. These two factors are intimately related.
T A B L E 5–1
Credit Rating and Default Rates
Default Frequency Desired Rating
1 Year
10 Years
Aaa Aa A Baa Ba B
0.02% 0.05% 0.09% 0.17% 0.77% 2.32%
1.49% 3.24% 5.65% 10.50% 21.24% 37.98%
Source: Adapted from Moody’s default rates from 1920–1998.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 119 nd
CHAPTER 5 Computing Value at Risk
119
5.2.4 Criteria for Backtesting The choice of the quantitative factors is also important for backtesting considerations. Model backtesting involves systematic comparisons of VAR with the subsequently realized P&L in an attempt to detect biases in the reported VAR figures and is described in a later chapter. The goal should be to set up the tests so as to maximize the likelihood of catching biases in VAR forecasts. Longer horizons reduce the number of independent observations and thus the power of the tests. For instance, using a 2-week VAR horizon means that we have only 26 independent observations per year. A 1-day VAR horizon, in contrast, will have about 252 observations over the same year. Hence a shorter horizon is preferable to increase the power of the tests. This explains why the Basel Committee performs backtesting over a 1-day horizon, even though the horizon is 10 business days for capital adequacy purposes. Likewise, the choice of the confidence level should be such that it leads to powerful tests. Too high a confidence level reduces the expected number of observations in the tail and thus the power of the tests. Take, for instance, a 95 percent level. We know that, just by chance, we expect a loss worse than the VAR figure in 1 day out of 20. If we had chosen a 99 percent confidence level, we would have to wait, on average, 100 days to confirm that the model conforms to reality. Hence, for backtesting purposes, the confidence level should not be set too high. In practice, a 95 percent level performs well for backtesting purposes.
5.2.5 Application: The Basel Parameters One illustration of the use of VAR as equity capital is the internal models approach of the Basel Committee, which imposes a 99 percent confidence level over a 10-business-day horizon. The resulting VAR is then multiplied by a safety factor of 3 to provide the minimum capital requirement for regulatory purposes. Presumably, the Basel Committee chose a 10-day period because it reflects the tradeoff between the costs of frequent monitoring and the benefits of early detection of potential problems. Presumably also, the Basel Committee chose a 99 percent confidence level that reflects the tradeoff between the desire of regulators to ensure a safe and sound financial system and the adverse effect of capital requirements on bank returns.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 120 nd
120
PART 2 Building Blocks
Even so, a loss worse than the VAR estimate will occur about 1 percent of the time, on average, or once every 4 years. It would be unthinkable for regulators to allow major banks to fail so often. This explains the multiplicative factor k 3, which should provide near absolute insurance against bankruptcy. At this point, the choice of parameters for the capital charge should appear quite arbitrary. There are many combinations of the confidence level, the horizon, and the multiplicative factor that would yield the same capital charge. The origin of the factor k also looks rather mysterious. Presumably, the multiplicative factor also accounts for a host of additional risks not modeled by the usual application of VAR that fall under the category of model risk. For example, the bank may be understating its risk due to a short sample period, to unstable correlation, or simply to the fact that it uses a normal approximation to a distribution that really has more observations in the tail. Stahl (1997) justifies the choice of k based on Chebyshev’s inequality. For any random variable x with finite variance, the probability of falling outside a specified interval is P(|x | r) 1/r2
(5.12)
assuming that we know the true standard deviation . Suppose now that the distribution is symmetrical. For values of x below the mean, P[(x ) r] 12 1/r2
(5.13)
We now set the right-hand side of this inequality to the desired level of 1 percent. This yields r(99%) 7.071. The maximum VAR is therefore VARmax r(99%). Say that the bank reports its 99 percent VAR using a normal distribution. Using the quantile of the standard normal distribution, we have VARN (99%) 2.326
(5.14)
If the true distribution is misspecified, the correction factor is then VARmax 7.071 k
3.03 VARN 2.326
(5.15)
which happens to justify the correction factor applied by the Basel Committee.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 121 nd
CHAPTER 5 Computing Value at Risk
121
5.2.6 Conversion of VAR Parameters Using a parametric distribution such as the normal distribution is particularly convenient because it allows conversion to different confidence lev) is els (which define ). Conversion across horizons (expressed as t also feasible if we assume a constant risk profile, that is, portfolio positions and volatilities. Formally, the portfolio returns need to be (1) independently distributed, (2) normally distributed, and (3) with constant parameters. As an example, we can convert the RiskMetrics risk measures into the Basel Committee internal models measures. RiskMetrics provides a 95 percent confidence interval (1.65) over 1 day. The Basel Committee rules define a 99 percent confidence interval (2.33) over 10 days. The adjustment takes the following form: 2.33 4.45VARRM VARBC VARRM
10 1.65 Therefore, the VAR under the Basel Committee rules is more than four times the VAR from the RiskMetrics system. More generally, Table 5–2 shows how the Basel Committee parameters translate into combinations of confidence levels and horizons, taking an annual volatility of 12 percent, which is typical of the DM/$ T A B L E 5–2
Equivalence Between Horizon and Confidence Level, Normal Distribution, Annual Risk 12 Percent (Basel Parameters: 99 Percent Confidence over 2 Weeks)
Confidence Level c
Number of S.D.
Baseline 99% 57.56% 81.89% 86.78% 95% 99% 99.95% 99.99997%
2.326 0.456 0.911 1.116 1.645 2.326 3.290 7.153
Horizon t
2 1 3 2 4 2 1 1
weeks year months months weeks weeks week day
Actual S.D. t
Cutoff Value t
2.35 12.00 6.00 4.90 3.32 2.35 1.66 0.76
5.47 5.47 5.47 5.47 5.47 5.47 5.47 5.47
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 122 nd
122
PART 2 Building Blocks
exchange rate (now the euro/$ rate). These combinations are such that t. For instance, a 99 percent they all produce the same value for confidence level over 2 weeks produces the same VAR as a 95 percent confidence level over 4 weeks. Or conversion into a weekly horizon requires a confidence level of 99.95 percent. 5.3 ASSESSING VAR PRECISION
This chapter has shown how to estimate essential parameters for the measurement of VAR, means, standard deviations, and quantiles from actual data. These estimates, however, should not be taken for granted entirely. They are affected by estimation error, which is the natural sampling variability due to limited sample size. Users should beware of the limited precision behind the reported VAR numbers.
5.3.1 The Problem of Measurement Errors From the viewpoint of VAR users, it is important to assess the degree of precision in the reported VAR. In a previous example, the daily VAR was $15 million. The question is: How confident is management in this estimate? Could we say, for example, that management is highly confident in this figure or that it is 95 percent sure that the true estimate is in a $14 million to $16 million range? Or is it the case that the range is $5 million to $25 million. The two confidence bands give quite a different picture of VAR. The first is very precise; the second is rather uninformative (although it tells us that it is not in the hundreds of millions of dollars). This is why it is useful to examine measurement errors in VAR figures. Consider a situation where VAR is obtained from the historical simulation method, which uses a historical window of T days to measure risk. The problem is that the reported VAR measure is only an estimate of the true value and is affected by sampling variability. In other words, different choices of the window T will lead to different VAR figures. One possible interpretation of the estimates (the view of “frequen^ ^ and are samples from an untist” statisticians) is that these estimates derlying distribution with unknown parameters and . With an infinite number of observations T → ∞ and a perfectly stable system, the estimates should converge to the true values. In practice, sample sizes are limited, either because some series, like emerging markets, are relatively recent or because structural changes make it meaningless to go back too
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 123 nd
CHAPTER 5 Computing Value at Risk
123
far in time. Since some estimation error may remain, the natural dispersion of values can be measured by the sampling distribution for the pa^ ^ and . We now turn to a description of the distribution of starameters tistics on which VAR measures are based.
5.3.2 Estimation Errors in Means and Variances When the underlying distribution is normal, the exact distribution of the ^ is distributed sample mean and variance is known. The estimated mean normally around the true mean ^ N(, 2/T )
(5.16)
where T is the number of independent observations in the sample. Note that the standard error in the estimated mean converges toward 0 at a rate as T increases. of 1/T As for the estimated variance ^ 2, the following ratio has a chi-square distribution with (T 1) degrees of freedom: (T 1) ^ 2
2(T 1) 2
(5.17)
In practice, if the sample size T is large enough (e.g., above 20), the chisquare distribution converges rapidly to a normal distribution, which is easier to handle:
2 ^ 2 N 2, 4
T1
(5.18)
As for the sample standard deviation, its standard error in large samples is se(^ )
2T 1
(5.19)
For instance, consider monthly returns on the DM/$ rate from 1973 ^ 0.15 percent, ^ 3.39 percent, to 1998. Sample parameters are with T 312 observations. The standard error of the estimate indicates how confident we are about the sample value; the smaller the error, the ^ ^ is se( ) ^ 1/T more confident we are. One standard error in ^ 0.19 percent. Therefore, the point estimate of 0.15 3.39 1/312 percent is less than one standard error away from 0. Even with 26 years of data, is measured very imprecisely.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 124 nd
124
PART 2 Building Blocks
In contrast, one standard error for ^ is se(^ ) ^ 1/2T 3.39 0.14 percent. Since this number is much smaller than the es1/624 timate of 3.39 percent, we can conclude that the volatility is estimated with much greater accuracy than the expected return—giving some confidence in the use of VAR systems. As the sample size increases, so does the precision of the estimate. To illustrate this point, Figure 5–5 depicts 95 percent confidence bands around the estimate of volatility for various sample sizes, assuming a true daily volatility of 1 percent. With 5 trading days, the band is rather imprecise, with upper and lower values set at [0.41%, 1.60%]. After 1 year, the band is [0.91%, 1.08%]. As the number of days increases, the confidence bands shrink to the point where, after 10 years, the interval narrows to [0.97%, 1.03%]. Thus, as the observation interval lengthens, the estimate should become arbitrarily close to the true value.
FIGURE
5–5
Confidence bands for sample volatility.
Daily volatility (%) 1.5
1
0.5
5
10
20
30 60 90 126 252 Observation interval (days)
504 1260 2520
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 125 nd
CHAPTER 5 Computing Value at Risk
125
Finally, ^ can be used to estimate any quantile (an example is shown in Section 5.1.4). Since the normal distribution is fully characterized by two parameters only, the standard deviation contains all the information necessary to build measures of dispersion. Any -based quantile can be derived as q^ ^
(5.20)
At the 95 percent confidence level, for instance, we simply multiply the estimated value of ^ by 1.65 to find the 5 percent left-tail quantile. Of course, this method will be strictly valid if the underlying distribution is closely approximated by the normal. When the distribution is suspected to be strongly nonnormal, other methods, such as kernel estimation, also provide estimates of the quantile based on the full distribution.1
5.3.3 Estimation Error in Sample Quantiles For arbitrary distributions, the cth quantile can be determined empirically from the historical distribution as q^ (c) (as shown in Section 5.1.2). There is, as before, some sampling error associated with the statistic. Kendall (1994) reports that the asymptotic standard error of q^ is se(q^ )
c(1 c)
T f(q)2
(5.21)
where T is the sample size, and f() is the probability distribution function evaluated at the quantile q. The effect of estimation error is illustrated in Figure 5–6, where the expected quantile and 95 percent confidence bands are plotted for quantiles from the normal distribution. For the normal distribution, the 5 percent left-tailed interval is centered at 1.65. With T 100, the confidence band is [1.24, 2.04], which is quite large. With 250 observations, which correspond to 1 year of trading days, the band is still [1.38, 1.91]. With T 1250, or 5 years of data, the interval shrinks to [1.52, 1.76]. These intervals widen substantially as one moves to more extreme quantiles. The expected value of the 1 percent quantile is 2.33. With 1 year of data, the band is [1.85, 2.80]. The interval of uncertainty is about 1. Kernel estimation smoothes the empirical distribution by a weighted sum of local distributions. For a further description of kernel estimation methods, see Scott (1992). Butler and Schachter (1998) apply this method to the estimation of VAR.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 126 nd
126
PART 2 Building Blocks
FIGURE
5–6
Confidence bands for sample quantiles. 3
Quantile-normal distribution Expected
T=100
T=250
T=1250
2
1
1%
5% Left-tail probability
10%
twice that at the 5 percent interval. Thus sample quantiles are increasingly unreliable as one goes farther in the left tail. As expected, there is more imprecision as one moves to lower lefttail probabilities because fewer observations are involved. This is why VAR measures with very high confidence levels should be interpreted with extreme caution.
5.3.4 Comparison of Methods So far we have developed two approaches for measuring a distribution’s VAR: (1) by directly reading the quantile from the distribution q^ and (2) by calculating the standard deviation and then scaling by the appropriate factor ^ . The issue is: Is any method superior to the other? Intuitively, we may expect the -based approach to be more precise. Indeed, ^ uses information about the whole distribution (in terms of all
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 127 nd
CHAPTER 5 Computing Value at Risk
127
T A B L E 5–3
Confidence Bands for VAR Estimates, Normal Distribution, T 250 VAR Confidence Level c
Exact quantile Confidence band Sample qˆ -Based, ˆ
99%
95%
2.33
1.65
[1.85, 2.80] [2.24, 2.42]
[1.38, 1.91] [1.50, 1.78]
squared deviations around the mean), whereas a quantile uses only the ranking of observations and the two observations around the estimated value. And in the case of the normal distribution, we know exactly how to transform ^ into an estimated quantile using . For other distributions, the value of may be different, but we should still expect a performance improvement because the standard deviation uses all the sample information. Table 5–3 compares 95 percent confidence bands for the two meth2 ods. The -based method leads to substantial efficiency gains relative to the sample quantile. For instance, at the 95 percent VAR confidence level, the interval around 1.65 is [1.38, 1.91] for the sample quantile; this is reduced to [1.50, 1.78] for ^ , which is much narrower than the previous interval. A number of important conclusions can be derived from these numbers. First, there is substantial estimation error in the estimated quantiles, especially for high confidence levels, which are associated with rare events and hence difficult to verify. Second, parametric methods provide a substantial increase in precision, since the sample standard deviation contains far more information than sample quantiles. Returning to the $15.2 million VAR figure at the beginning of this chapter, we can now assess the precision of this number. Using the parametric approach based on a normal distribution, the standard error of this ) number is se(q^ ) se(^ ) 1.65 $9.2 million 1/(2254 $0.67. Therefore, a two-standard-error confidence band around the VAR 2. For extensions to other distributions such as the Student, see Jorion (1996).
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.05 7/19/00 3:34 PM Page 128 nd
128
PART 2 Building Blocks
estimate is [$13.8 million, $16.6 million]. This narrow interval should provide reassurance that the VAR estimate is indeed meaningful. 5.4 CONCLUSIONS
In this chapter we have seen how to measure VAR using two alternative methodologies. The general approach is based on the empirical distribution and its sample quantile. The parametric approach, in contrast, attempts to fit a parametric distribution such as the normal to the data. VAR is then measured directly from the standard deviation. Systems such as RiskMetrics are based on a parametric approach. The advantage of such methods is that they are much easier to use and create more precise estimates of VAR. The disadvantage is that they may not approximate well the actual distribution of profits and losses. Users who want to measure VAR from empirical quantiles, however, should be aware of the effect of sampling variation or imprecision in their VAR number. This chapter also has discussed criteria for selection of the confidence level and horizon. On the one hand, if VAR is used simply as a benchmark risk measure, the choice is arbitrary and only needs to be consistent. On the other hand, if VAR is used to decide on the amount of equity capital to hold, the choice is extremely important and can be guided, for instance, by default frequencies for the targeted credit rating.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 205 nd
CHAPTER
9
VAR Methods
In practice, this works, but how about in theory? Attributed to a French mathematician
Value at risk (VAR) has become an essential component in the toolkit of risk managers because it provides a quantitative measure of downside risk. In practice, the objective should be to provide a reasonably accurate estimate of risk at a reasonable cost. This involves choosing among the various industry standards a method that is most appropriate for the portfolio at hand. To help with this selection, this chapter presents and critically evaluates various approaches to VAR. Approaches to VAR basically can be classified into two groups. The first group uses local valuation. Local-valuation methods measure risk by valuing the portfolio once, at the initial position, and using local derivatives to infer possible movements. The delta-normal method uses linear, or delta, derivatives and assumes normal distributions. Because the deltanormal approach is easy to implement, a variant, called the “Greeks,’’ is sometimes used. This method consists of analytical approximations to first- and second-order derivatives and is most appropriate for portfolios with limited sources of risk. The second group uses full valuation. Fullvaluation methods measure risk by fully repricing the portfolio over a range of scenarios. The pros and cons of local versus full valuation are discussed in Section 9.1. Initially, we consider a simple portfolio that is driven by one risk factor only. This chapter then turns to VAR methods for large portfolios. The best example of local valuation is the delta-normal method, which is explained in Section 9.2. Full valuation is implemented in the historical 205
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 206 nd
206
PART 3 Value-at-Risk Systems
simulation method and the Monte Carlo simulation method, which are discussed in Sections 9.3 and 9.4. This classification reflects a fundamental tradeoff between speed and accuracy. Speed is important for large portfolios exposed to many risk factors, which involve a large number of correlations. These are handled most easily in the delta-normal approach. Accuracy may be more important, however, when the portfolio has substantial nonlinear components. An in-depth analysis of the delta-normal and simulation VAR methods is presented in following chapters, as well as a related method, stress testing. Section 9.5 presents some empirical comparisons. Finally, Section 9.6 summarizes the pros and cons of each method. 9.1 LOCAL VERSUS FULL VALUATION
9.1.1 Delta-Normal Valuation Local-valuation methods usually rely on the normality assumption for the driving risk factors. This assumption is particularly convenient because of the invariance property of normal variables: Portfolios of normal variables are themselves normally distributed. We initially focus on delta valuation, which considers only the first derivatives. To illustrate the approaches, take an instrument whose value depends on a single underlying risk factor S. The first step consists of valuing the portfolio at the initial point V0 V(S0)
(9.1)
along with analytical or numerical derivatives. Define 0 as the first partial derivative, or the portfolio sensitivity to changes in prices, evaluated at the current position V0. This would be called modified duration for a fixed-income portfolio or delta for a derivative. For instance, with an atthe-money call, 0.5, and a long position in one option is simply replaced by a 50 percent position in one unit of underlying asset. The portfolio simply can be computed as the sum of individual deltas. The potential loss in value dV is then computed as V dV 0 dS 0 dS S
(9.2)
which involves the potential change in prices dS. Because this is a linear relationship, the worst loss for V is attained for an extreme value of S.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 207 nd
CHAPTER 9 VAR Methods
207
If the distribution is normal, the portfolio VAR can be derived from the product of the exposure and the VAR of the underlying variable: VAR 0 VARS 0 (S0)
(9.3)
where is the standard normal deviate corresponding to the specified confidence level, e.g., 1.645 for a 95 percent confidence level. Here, we take (dS/S) as the standard deviation of rates of changes in the price. The assumption is that rates of changes are normally distributed. Because VAR is obtained as a closed-form solution, this method is called analytical. Note that VAR was measured by computing the portfolio value only once, at the current position V0. For a fixed-income portfolio, the risk factor is the yield y, and the price-yield relationship is dV D*V dy
(9.4)
where D* is the modified duration. In this case, the portfolio VAR is VAR (D*V ) ()
(9.5)
where (dy) is now the volatility of changes in the level of yield. The assumption is that changes in yields are normally distributed, although this is ultimately an empirical issue. This method is illustrated in Figure 9–1, where the profit payoff is a linear function of the underlying spot price and is displayed at the upper left side; the price itself is normally distributed, as shown in the right panel. As a result, the profit itself is normally distributed, as shown at the bottom of the figure. The VAR for the profit can be found from the exposure and the VAR for the underlying price. There is a one-to-one mapping between the two VAR measures. How good is this approximation? It depends on the “optionality’’ of the portfolio as well as the horizon. Consider, for instance, a simple case of a long position in a call option. In this case, we can easily describe the distribution of option values. This is so because there is a one-to-one relationship between V and S. In other words, given the pricing function, any value for S can be translated into a value for V, and vice versa. This is illustrated in Figure 9–2, which shows how the distribution of the spot price is translated into a distribution for the option value (in the left panel). Note that the option distribution has a long right tail, due to the upside potential, whereas the downside is limited to the option premium. This shift is due to the nonlinear payoff on the option.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 208 nd
208
PART 3 Value-at-Risk Systems
FIGURE
9–1
Distribution with linear exposures.
Payoff
Frequency
Spot price
Spot price
Frequency
VAR Payoff
Here, the cth quantile for V is simply the function evaluated at the cth quantile of S. For the long-call option, the worst loss for V at a given confidence level will be achieved at S* S0 S0, and VAR V(S0) V(S0 S0)
(9.6)
The nonlinearity effect is not obvious, though. It also depends on the maturity of the option and on the range of spot prices over the horizon. The option illustrated here is a call option with 3 months to expiration. To obtain a visible shift in the shape of the option distribution, the volatility was set at 20 percent per annum and the VAR horizon at 2 months, which is rather long. The figure also shows thinner distributions that correspond to a VAR horizon of 2 weeks. Here, the option distribution is indistinguishable from the normal. In other words, the mere presence of options does not necessarily invalidate the delta-normal approach. The quality of the approximation depends on the extent of nonlinearities, which is a function of the
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 209 nd
CHAPTER 9 VAR Methods
FIGURE
209
9–2
Transformation of distributions.
Option value
Spot price
Distribution of option values
2 weeks
Distribution of spot prices
2 months
type of options, of their maturities, as well as of the volatility of risk factors and VAR horizon. The shorter the VAR horizon, the better is the deltanormal approximation.
9.1.2 Full Valuation In some situations, the delta-normal approach is totally inadequate. This is the case, for instance, when the worst loss may not be obtained for extreme realizations of the underlying spot rate. Also, options that are near expiration and at-the-money have unstable deltas, which translate into asymmetrical payoff distributions. An example of this problem is that of a long straddle, which involves the purchase of a call and a put. The worst payoff, which is the sum of the premiums, will be realized if the spot rate does not move at all. In general, it is not sufficient to evaluate the portfolio at the two extremes. All intermediate values must be checked.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 210 nd
210
PART 3 Value-at-Risk Systems
The full-valuation approach considers the portfolio value for a wide range of price levels: dV V(S1) V(S0)
(9.7)
The new values S1 can be generated by simulation methods. The Monte Carlo simulation approach relies on prespecified distributions. For instance, the realizations can be drawn from a normal distribution, dS/S N(0, 2)
(9.8)
Alternatively, the historical simulation approach simply samples from recent historical data. For each of these draws, the portfolio is priced on the target date using a full-valuation method. This method is potentially the most accurate because it accounts for nonlinearities, income payments, and even timedecay effects that are usually ignored in the delta-normal approach. VAR is then calculated from the percentiles of the full distribution of payoffs. Computationally, this approach is quite demanding because it requires marking-to-market the whole portfolio over a large number of realizations of underlying random variables. To illustrate the result of nonlinear exposures, Figure 9–3 displays the payoff function for a short straddle that is highly nonlinear. The resulting distribution is severely skewed to the left. Further, there is no direct way to relate the VAR of the portfolio to that of the underlying asset. The problem is that these simulation methods require substantial computing time when applied to large portfolios. As a result, methods have been developed to speed up the computations. One example is the grid Monte Carlo approach, which starts by an exact valuation of the portfolio over a limited number of grid points.1 For each simulation, the portfolio value is then approximated using a linear interpolation from the exact values at the adjoining grid points. This approach is especially efficient if exact valuation of the instrument is complex. Take, for instance, a portfolio with one risk factor for which we require 1000 values V(S1). With the grid Monte Carlo method, 10 full valuations at the grid points may be sufficient. In contrast, the full Monte Carlo method would require 1000 full valuations. 1. Picoult (1997) describes this method in more detail.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 211 nd
CHAPTER 9 VAR Methods
FIGURE
211
9–3
Distribution with nonlinear exposures.
Payoff
Frequency
Spot price
Spot price
Frequency
VAR
Payoff
9.1.3 Delta-Gamma Approximations (the “Greeks’’) It may be possible to extend the analytical tractability of the delta-normal method with higher-order terms. We can improve the quality of the linear approximation by adding terms in the Taylor expansion of the valuation function: V 1 2V V dV dS dS2 dt S 2 S2 t 1 dS dS2 dt 2
(9.9)
where is now the second derivative of the portfolio value, and is the time drift, which is deterministic.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 212 nd
212
PART 3 Value-at-Risk Systems
For a fixed-income portfolio, the price-yield relationship is now 1 dV (D*V) dy (CV) dy2 2
(9.10)
where the second-order coefficient C is called convexity and is akin to . Figure 9–4 describes the approximation for a simple position, a long position in a European call option. It shows that the linear model is valid only for small movements around the initial value. For larger movements, the delta-gamma approximation creates a better fit. We use the Taylor expansion to compute VAR for the long-call option in Equation (9.6), which yields VAR V(S0) V(S0 S0) V(S0) [V(S0) ( S) 1/2 ( S)2] (9.11) (S) 1/2 (S)2 This formula is actually valid for long and short positions in calls and puts. If is positive, which corresponds to a net long position in options, the second term will decrease the linear VAR. Indeed, Figure 9–4 FIGURE
9–4
Delta-gamma approximation for a long call.
Current value of option
10
Actual price
5 Delta+gamma estimate Delta estimate
0 90
100 Current price of underlying asset
110
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 213 nd
CHAPTER 9 VAR Methods
213
shows that the downside risk for the option is less than that given by the delta approximation. If is negative, which corresponds to a net short position in options, VAR is increased. This transformation does not apply, unfortunately, to more complex functions V(S), so we have to go back to the Taylor expansion [Equation (9.9)]. The question now is how to deal with the random variables dS and dS2. The simplest method is called the delta-gamma-delta method. Taking the variance of both sides of the quadratic approximation [Equation (9.9)], we obtain 2(dV) 22(dS) (1/2 )22(dS2) 2(1/2 ) cov(dS, dS2)
(9.12)
If the variable dS is normally distributed, all its odd moments are zero, and the last term in the equation vanishes. Under the same assumption, one can show that V(dS2) 2V(dS)2, and the variance simplifies to 2(dV) 22(dS) 1/2[ 2(dS)]2
(9.13)
Assume now that the variables dS and dS2 are jointly normally distributed. Then dV is normally distributed, with VAR given by VAR (S)2
1/2 ( S22 )2
(9.14)
This is, of course, only an approximation. Even if dS was normal, its square dS2 could not possibly also be normally distributed. Rather, it is a chi-squared variable. A further improvement can be obtained by accounting for the skewness coefficient , as defined in Chapter 4.2 The corrected VAR, using the so-called Cornish-Fisher expansion, is then obtained by replacing in Equation (9.14) by 1⁄6(2 1)
(9.15)
There is no correction under a normal distribution, for which skewness is zero. When there is negative skewness (i.e., a long left tail), VAR is increased.3 The second method is the delta-gamma–Monte Carlo method, which creates random simulations of the risk factors S and then uses the Taylor 2. Skewness can be computed as [E(dV3) 3E(dV2)E(dV) 2E(dV)3]/3(dV) using the third moment of dV, which is E(dV3) (9/2)2 S 44 (15/8) 3S 66. 3. See also Zangari (1996).
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 214 nd
214
PART 3 Value-at-Risk Systems
approximation to create simulated movements in the option value. This method is also known as a partial-simulation approach. Note that this is still a local-valuation method because the portfolio is fully valued at the initial point V0 only. The VAR can then be found from the empirical distribution of the portfolio value. In theory, the delta-gamma method could be generalized to many sources of risk. In a multivariate framework, the Taylor expansion is dV(S) dS 1/2(dS) (dS)
(9.16)
where dS is now a vector of N changes in market prices, is a vector of N deltas, and is an N by N symmetrical matrix of gammas with respect to the various risk factors. While the diagonal components are conventional gamma measures, the off-diagonal terms are cross-gammas, or i,j 2V/SiSj. For instance, the delta of options also depends on the implied volatility, which creates a cross-effect. Unfortunately, the delta-gamma method is not practical with many sources of risk because the amount of data required increases geometrically. For instance, with N 100, we need 100 estimates of , 5050 estimates for the covariance matrix , and an additional 5050 for the matrix , which includes second derivatives of each position with respect to each source of risk. In practice, only the diagonal components are considered. Even so, a full Monte Carlo method provides a more direct route to VAR measurement for large portfolios.
9.1.4 Comparison of Methods To summarize, Table 9–1 classifies the various VAR methods. Overall, each of these methods is best adapted to a different environment: ■
■
■
For large portfolios where optionality is not a dominant factor, the delta-normal method provides a fast and efficient method for measuring VAR. For portfolios exposed to a few sources of risk and with substantial option components, the “Greeks’’ method provides increased precision at a low computational cost. For portfolios with substantial option components (such as mortgages) or longer horizons, a full-valuation method may be required.
It should be noted that the linear/nonlinear dichotomy also has implications for the choice of the VAR horizon. With linear models, as we
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 215 nd
CHAPTER 9 VAR Methods
215
T A B L E 9–1
Comparison of VAR Methods
Valuation Method Risk Factor Distribution Analytical Simulated
Local Valuation Delta-normal Delta-gamma-delta Delta-gamma-MC
Full Valuation Not used Monte Carlo (MC) Grid MC Historical
have seen in Chapter 4, daily VAR can be adjusted easily to other periods by simple scaling by a square root of time factor. This adjustment assumes that the position is constant and that daily returns are independent and identically distributed. This time adjustment, however, is not valid for options positions. Since options can be replicated by dynamically changing positions in the underlying assets, the risk of options positions can be dramatically different from the scaled measure of daily risk. Therefore, adjustments of daily volatility to longer horizons using the square root of time factor are valid only when positions are constant and when optionality in the portfolio is negligible. For portfolios with substantial options components, the full-valuation method must be implemented over the desired horizon instead of scaling a daily VAR measure.
9.1.5 An Example: Leeson’s Straddle The Barings’ story provides a good illustration of these various methods. In addition to the long futures positions described in Chapter 7, Leeson also sold options, about 35,000 calls and puts each on Nikkei futures. This position is known as a short straddle and is about delta-neutral because the positive delta from the call is offset by a negative delta from the put, assuming most of the options were at-the-money. Leeson did not deal in small amounts. With a multiplier of 500 yen for the options contract and a 100-yen/$ exchange rate, the dollar exposure of the call options to the Nikkei was delta times $0.175 million. Initially, the market value of the position was zero. The position was
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 216 nd
216
PART 3 Value-at-Risk Systems
FIGURE
9–5
Leeson’s straddle.
Payoff ($ millions)
0
Delta estimate
-50
Exact value
-100
Delta+gamma estimate
-150 17,000
18,000
19,000
20,000
21,000
Nikkei index
designed to turn in a profit if the Nikkei remained stable. Unfortunately, it also had an unlimited potential for large losses. Figure 9–5 displays the payoffs from the straddle, using a BlackScholes model with a 20 percent annual volatility. We assume that the options have a maturity of 3 months. At the current index value of 19,000, the delta VAR for this position is close to zero. Of course, reporting a zero delta-normal VAR is highly misleading. Any move up or down has the potential to create a large loss. A drop in the index to 17,000, for instance, would lead to an immediate loss of about $150 million. The graph also shows that the delta-gamma approximation provides increased accuracy. How do we compute the potential loss over a horizon of, say, 1 month? The risks involved are described in Figure 9–6, which plots the frequency distribution of payoffs on the straddle using a full Monte Carlo simulation with 10,000 replications. This distribution is obtained from a revaluation of the portfolio after a month over a range of values for the Nikkei. Each replication uses full valuation with a remaining maturity of
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 217 nd
CHAPTER 9 VAR Methods
FIGURE
217
9–6
Distribution of 1-month payoff for straddle.
Frequency
VAR
-300
-200
-100
0
Payoff ($ millions)
2 months (the 3-month original maturity minus the 1-month VAR horizon). The distribution looks highly skewed to the left. Its mean is $1 million, and the 95th percentile is $139 million. Hence the 1-month 95 percent VAR is $138 million. How does the “Greeks’’ method fare for this portfolio? First, let us examine the delta-gamma-delta approximation. The total gamma of the position is the exposure times the sum of gamma for a call and put, or $0.175 million 0.000422 $0.0000739 million. Over a 1-month horizon, the standard deviation of the Nikkei is S 19,000 20 percent/12 1089. Ignoring the time drift, the VAR is, from Equation (9.13), [ (S) ] 1.65 ($0.00 00739 million 1089 ) 1.65 $62 million $102 million
VAR
1 2
2 2
1 2
2 2
This is substantially better than the delta-normal VAR of zero, which could have fooled us into believing the position was riskless. Using the Cornish-Fisher expansion and a skewness coefficient of 2.83, we obtain a correction factor of 1.65 16 (1.652 1)( 2.83)
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 218 nd
218
PART 3 Value-at-Risk Systems
2.45. The refined VAR measure is then 2.45 $62 million $152 million, much closer to the true value of $138 million. Finally, we can turn to the delta-gamma–Monte Carlo approach, which consists of using the simulations of S but valuing the portfolio on the target date using only the partial derivatives. This yields a VAR of $128 million, not too far from the true value. This variety of methods shows that the straddle had substantial downside risk. And indeed the options position contributed to Barings’ fall. As January 1995 began, the historical volatility on the Japanese market was very low, around 10 percent. At the time, the Nikkei was hovering around 19,000. The options position would have been profitable if the market had been stable. Unfortunately, this was not so. The Kobe earthquake struck Japan on January 17 and led to a drop in the Nikkei to 18,000, shown in Figure 9–7. To make things worse, options became more expensive as market volatility increased. Both the long futures and the straddle positions lost money. As losses ballooned, Leeson increased his exposure in a desperate attempt to recoup the losses, but to no avail. On February 27, the Nikkei dropped further to 17,000. Unable to meet the mounting margin calls, Barings went bust. FIGURE
9–7
The Nikkei’s fall.
Nikkei index 20,000
Kobe earthquake Barings collapse
19,000
18,000
17,000
16,000 Jan
Feb
Mar
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 219 nd
CHAPTER 9 VAR Methods
219
9.2 DELTA-NORMAL METHOD
9.2.1 Implementation If the portfolio consisted of only securities with jointly normal distributions, the measurement of VAR would be relatively simple. The portfolio return is N
Rp,t 1 wi,tRi,t 1
(9.17)
i1
where the weights wi,t are indexed by time to recognize the dynamic nature of trading portfolios. Since the portfolio return is a linear combination of normal variables, it is also normally distributed. Using matrix notations, the portfolio variance is given by 2(Rp,t 1) wt t 1wt
(9.18)
where t 1 is the forecast of the covariance matrix over the VAR horizon. The problem is that VAR must be measured for large and complex portfolios that evolve over time. The delta-normal method, which is explained in much greater detail in a subsequent chapter, simplifies the process by ■ ■
■ ■ ■
Specifying a list of risk factors Mapping the linear exposure of all instruments in the portfolio onto these risk factors Aggregating these exposures across instruments Estimating the covariance matrix of the risk factors Computing the total portfolio risk
This mapping produces a set of exposures xi,t aggregated across all instruments for each risk factor and measured in dollars. The portfolio VAR is then xt t 1 xt VAR
(9.19)
Within this class of models, two methods can be used to measure the variance-covariance matrix . It can be solely based on historical data using, for example, a model that allows for time variation in risk. Alternatively, it can include implied risk measures from options. Or it can
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 220 nd
220
PART 3 Value-at-Risk Systems
FIGURE
9–8
Delta-normal method. Historical data
Option data
Volatility, correlation model
Option model
Estimated future volatilities, correlations
Securities delta model
Delta valuation
Delta positions
Estimated value changes
use a combination of both. As we saw in the preceding chapter, optionsimplied measures of risk are superior to historical data but are not available for every asset, let alone for pairs of assets. Figure 9–8 details the steps involved in this approach.
9.2.2 Advantages The delta-normal method is particularly easy to implement because it involves a simple matrix multiplication. It is also computationally fast, even with a very large number of assets, because it replaces each position by its linear exposure. As a parametric approach, VAR is easily amenable to analysis, since measures of marginal and incremental risk are a by-product of the VAR computation.
9.2.3 Problems The delta-normal method can be subject to a number of criticisms. A first problem is the existence of fat tails in the distribution of returns on most financial assets. These fat tails are particularly worrisome precisely because VAR attempts to capture the behavior of the portfolio return in the
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 221 nd
CHAPTER 9 VAR Methods
221
left tail. In this situation, a model based on a normal distribution would underestimate the proportion of outliers and hence the true value at risk. As discussed in Chapter 8, some of these fat tails can be explained in terms of time variation in risk. However, even after adjustment, there are still too many observations in the tails. A simple ad hoc adjustment consists of increasing the parameter to compensate, as is explained in Chapter 5. Another problem is that the method inadequately measures the risk of nonlinear instruments, such as options or mortgages. Under the deltanormal method, options positions are represented by their “deltas’’ relative to the underlying asset. As we have seen in the preceding section, asymmetries in the distribution of options are not captured by the deltanormal VAR. Lest we lead you into thinking that this method is inferior, we will now show that alternative methods are no panacea because they involve a quantum leap in difficulty. The delta-normal method is computationally easy to implement. It only requires the market values and exposures of current positions, combined with risk data. Also, in many situations, the delta-normal method provides adequate measurement of market risks. 9.3 HISTORICAL SIMULATION METHOD
9.3.1 Implementation The historical simulation method provides a straightforward implementation of full valuation (Figure 9–9). It consists of going back in time, such as over the last 250 days, and applying current weights to a time-series of historical asset returns: N
Rp,k wi,tRi,k
k 1, . . ., t
(9.20)
i1
Note that the weights wt are kept at their current values. This return does not represent an actual portfolio but rather reconstructs the history of a hypothetical portfolio using the current position. The approach is sometimes called bootstrapping because it involves using the actual distribution of recent historical data (without replacement). More generally, full valuation requires a set of complete prices, such as yield curves, instead of just returns. Hypothetical future prices for scenario k are obtained from applying historical changes in prices to the current level of prices: S*i,k Si,0 Si,k
i 1, . . ., N
(9.21)
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 222 nd
222
PART 3 Value-at-Risk Systems
FIGURE
9–9
Historical simulation method. Historical returns
Securities model
Full valuation
Portfolio positions
Distribution of values
A new portfolio value V*p,k is then computed from the full set of hypothetical prices, perhaps incorporating nonlinear relationships V*k V(S*i,k). Note that to capture vega risk, due to changing volatilities, the set of prices can incorporate implied volatility measures. This creates the hypothetical return corresponding to simulation k: V*k V0 Rp,k V0
(9.22)
VAR is then obtained from the entire distribution of hypothetical returns, where each historical scenario is assigned the same weight of (1/t). As always, the choice of the sample period reflects a tradeoff between using longer and shorter sample sizes. Longer intervals increase the accuracy of estimates but could use irrelevant data, thereby missing important changes in the underlying process.
9.3.2 Advantages This method is relatively simple to implement if historical data have been collected in-house for daily marking-to-market. The same data can then be stored for later reuse in estimating VAR.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 223 nd
CHAPTER 9 VAR Methods
223
Historical simulation also short-circuits the need to estimate a covariance matrix. This simplifies the computations in cases of portfolios with a large number of assets and short sample periods. All that is needed is the time series of the aggregate portfolio return. The method also deals directly with the choice of horizon for measuring VAR. Returns are simply measured over intervals that correspond to the length of the horizon. For instance, to obtain a monthly VAR, the user would reconstruct historical monthly portfolio returns over, say, the last 5 years. By relying on actual prices, the method allows nonlinearities and nonnormal distributions. Full valuation is obtained in the simplest fashion: from historical data. The method captures gamma, vega risk, and correlations. It does not rely on specific assumptions about valuation models or the underlying stochastic structure of the market. Perhaps most important, it can account for fat tails and, because it does not rely on valuation models, is not prone to model risk. The method is robust and intuitive and, as such, is perhaps the most widely used method to compute VAR.
9.3.3 Problems On the other hand, the historical simulation method has a number of drawbacks. First, it assumes that we do have a sufficient history of price changes. To obtain 1000 independent simulations of a 1-day move, we require 4 years of continuous data. Some assets may have short histories, or there may not be a record of an asset’s history. Only one sample path is used. The assumption is that the past represents the immediate future fairly. If the window omits important events, the tails will not be well represented. Vice versa, the sample may contain events that will not reappear in the future. And as we have demonstrated in Chapter 8, risk contains significant and predictable time variation. The simple historical simulation method presented here will miss situations with temporarily elevated volatility.4 Worse, historical simulation will be very slow to incorporate structural breaks, which are handled more easily with an analytical methods such as RiskMetrics. 4. A simple method to allow time variation in risk proceeds as follows: First, fit a time-series model to the conditional volatility and construct historical scaled residuals. Second, perform a historical simulation on these residuals. Third, apply the most recent volatility forecast to the scaled portfolio volatility. For applications, see Hull and White (1998).
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 224 nd
224
PART 3 Value-at-Risk Systems
This approach is also subject to the same criticisms as the movingwindow estimation of variances. The method puts the same weight on all observations in the window, including old data points. The measure of risk can change significantly after an old observation is dropped from the window.5 Likewise, the sampling variation of the historical simulation VAR will be much greater than for an analytical method. As is pointed out in Chapter 5, VAR is only a statistical estimate and may be subject to much estimation error if the sample size is too short. For instance, a 99 percent daily VAR estimated over a window of 100 days produces only one observation in the tail, which necessarily leads to an imprecise VAR measure. Thus very long sample paths are required to obtain meaningful quantiles. The dilemma is that this may involve observations that are not relevant. A final drawback is that the method quickly becomes cumbersome for large portfolios with complicated structures. In practice, users adopt simplifications such as grouping interest rate payoffs into bands, which considerably increases the speed of computation. Regulators also have adopted such a “bucketing’’ approach. But if too many simplifications are carried out, such as replacing assets by their delta equivalents, the benefits of full valuation can be lost. 9.4 MONTE CARLO SIMULATION METHOD
9.4.1 Implementation Monte Carlo (MC) simulations cover a wide range of possible values in financial variables and fully account for correlations. MC simulation is developed in more detail in a later chapter. In brief, the method proceeds in two steps. First, the risk manager specifies a stochastic process for financial variables as well as process parameters; parameters such as risk and correlations can be derived from historical or options data. Second, fictitious price paths are simulated for all variables of interest. At each horizon considered, the portfolio is marked-to-market using full valuation as in the historical simulation method, V*k V(S*i,k). Each of these “pseudo’’ realizations is then used to compile a distribution of returns, 5. To alleviate this problem, Boudoukh et al. (1998) propose a scheme whereby each observation Rk is assigned a weight wk that declines as it ages. The distribution is then obtained from ranking the Rk and cumulating the associated weights to find the selected confidence level.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 225 nd
CHAPTER 9 VAR Methods
FIGURE
225
9–10
Monte Carlo method. Historical/implied data Model parameters
Stochastic model
Future rates
Securities model
Full valuation
Portfolio positions
Distribution of values
from which a VAR figure can be measured. The method is summarized in Figure 9–10. The Monte Carlo method is thus similar to the historical simulation method, except that the hypothetical changes in prices Si for asset i in Equation (9.20) are created by random draws from a prespecified stochastic process instead of sampled from historical data.
9.4.2 Advantages Monte Carlo analysis is by far the most powerful method to compute VAR. It can account for a wide range of exposures and risks, including nonlinear price risk, volatility risk, and even model risk. It is flexible enough to incorporate time variation in volatility, fat tails, and extreme scenarios. Simulations generate the entire pdf, not just one quantile, and can be used to examine, for instance, the expected loss beyond a particular VAR. MC simulation also can incorporate the passage of time, which will create structural changes in the portfolio. This includes the time decay of options; the daily settlement of fixed, floating, or contractually specified cash flows; or the effect of prespecified trading or hedging strategies.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 226 nd
226
PART 3 Value-at-Risk Systems
These effects are especially important as the time horizon lengthens, which is the case for the measurement of credit risk.
9.4.3 Problems The biggest drawback of this method is its computational time. If 1000 sample paths are generated with a portfolio of 1000 assets, the total number of valuations amounts to 1 million. In addition, if the valuation of assets on the target date involves itself a simulation, the method requires a “simulation within a simulation.’’ This quickly becomes too onerous to implement on a frequent basis. This method is the most expensive to implement in terms of systems infrastructure and intellectual development. The MC simulation method is relatively onerous to develop from scratch, despite rapidly falling prices for hardware. Perhaps, then, it should be purchased from outside vendors. On the other hand, when the institution already has in place a system to model complex structures using simulations, implementing MC simulation is less costly because the required expertise is in place. Also, these are situations where proper risk management of complex positions is absolutely necessary. Another potential weakness of the method is model risk. MC relies on specific stochastic processes for the underlying risk factors as well as pricing models for securities such as options or mortgages. Therefore, it is subject to the risk that the models are wrong. To check if the results are robust to changes in the model, simulation results should be complemented by some sensitivity analysis. Finally, VAR estimates from MC simulation are subject to sampling variation, which is due to the limited number of replications. Consider, for instance, a case where the risk factors are jointly normal and all payoffs linear. The delta-normal method will then provide the correct measure of VAR, in one easy step. MC simulations based on the same covariance matrix will give only an approximation, albeit increasingly good as the number of replications increases. Overall, this method is probably the most comprehensive approach to measuring market risk if modeling is done correctly. To some extent, the method can even handle credit risks. This is why a full chapter is devoted to the implementation of Monte Carlo simulation methods.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 227 nd
CHAPTER 9 VAR Methods
227
9.5 EMPIRICAL COMPARISONS
It is instructive to compare the VAR numbers obtained from the three methods discussed. Hendricks (1996), for instance, calculated 1-day VARs for randomly selected foreign currency portfolios using a delta-normal method based on fixed windows of equal weights and exponential weights as well as a historical simulation method. Table 9–2 summarizes the results, which are compared in terms of percentage of outcomes falling within the VAR forecast. The middle column shows that all methods give a coverage that is very close to the ideal number, which is the 95 percent confidence level. At the 99 percent confidence level, however, the delta-normal methods seem to underestimate VAR slightly, since their coverage falls short of the ideal 99 percent. Hendricks also reports that the delta-normal VAR measures should be increased by about 9 to 15 percent to achieve correct coverage. In other words, the fat tails in the data could be modeled by choosing a
T A B L E 9–2
Empirical Comparison of VAR Methods: Fraction of Outcomes Covered
Method Delta-normal Equal weights over 50 days 250 days 1250 days Delta-normal Exponential weights: 0.94 0.97 0.99 Historical simulation Equal weights over 125 days 250 days 1250 days
95% VAR
99% VAR
95.1% 95.3% 95.4%
98.4% 98.4% 98.5%
94.7% 95.0% 95.4%
98.2% 98.4% 98.5%
94.4% 94.9% 95.1%
98.3% 98.8% 99.0%
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 228 nd
228
PART 3 Value-at-Risk Systems
distribution with a greater parameter. A Student t distribution with four to six degrees of freedom, for example, would be appropriate. As important, when the VAR number is exceeded, the tail event is, on average, 30 to 40 percent greater than the risk measure. In some instances, it is several times greater. As Hendricks states, “This makes it clear that VAR measures—even at the 99th percentile—do not bound possible losses.’’ This empirical analysis, however, examined positions with linear risk profiles. The delta-normal methods could prove less accurate with options positions, although it should be much faster. Pritsker (1997) examines the tradeoff between speed and accuracy for a portfolio of options. Table 9–3 reports the accuracy of various methods, measured as the mean absolute percentage error in VAR, as well as their computational times. The table shows that the delta method, as expected, has the highest average absolute error, at 5.34 percent of the true VAR. It is also by far the fastest method, with an execution time of 0.08 seconds. At the other end, the most accurate method is the full Monte Carlo, which comes arbitrarily close to the true VAR, but with an average run time of 66 seconds. In between, the delta-gamma-delta, delta-gamma–Monte Carlo, and grid Monte Carlo methods offer a tradeoff between accuracy and speed. An interesting but still unresolved issue is, How would these approximations work in the context of large, diversified bank portfolios? There is very little evidence on this point. The industry initially seemed to prefer the analytical covariance approach due to its simplicity. With the rapidly decreasing cost of computing power, however, there is now T A B L E 9–3
Accuracy and Speed of VAR Methods: 99 Percent VAR for Option Portfolios
Method Delta Delta-gamma-delta Delta-gamma-MC Grid Monte Carlo Full Monto Carlo
Accuracy: Mean Absolute Error in VAR (%)
Speed: Computation Time, s
5.34 4.72 3.08 3.07 0
0.08 1.17 3.88 32.19 66.27
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 229 nd
CHAPTER 9 VAR Methods
229
a marked trend toward the generalized use of historical simulation methods. 9.6 SUMMARY
We can distinguish a number of different methods to measure VAR. At the most fundamental level, they separate into local (or analytical) valuation and full valuation. This separation reflects a tradeoff between speed of computation and accuracy of valuation. Delta models can use parameters based on historical data, such as those implemented by RiskMetrics, or on implied data, where volatilities are derived from options. Both methods generate a covariance matrix, to which the “delta’’ or linear positions are applied to find the portfolio VAR. Among full-valuation models, the historical simulation method is the easiest to implement. It simply relies on historical data for securities valuation and applies the most current weight to historical prices. Finally, the most complete model, but also the most difficult to implement, is the Monte Carlo simulation approach, which imposes a particular stochastic process on the financial variables of interest, from which various sample paths are simulated. Full valuation for each sample path generates a distribution of portfolio values. Table 9–4 describes the pros and cons of each method. The choice of the method largely depends on the composition of the portfolio. For portfolios with no options (nor embedded options) and whose distributions are close to the normal pdf, the delta-normal method may well be the best choice. VAR will be relatively easy to compute, fast, and accurate. In addition, it is not too prone to model risk (due to faulty assumptions or computations). The resulting VAR is easy to explain to management and to the public. Because the method is analytical, it allows easy analysis of the VAR results using marginal and component VAR measures. For portfolios with options positions, however, the method may not be appropriate. Instead, users should turn to a full-valuation method. The second method, historical simulation, is also relatively easy to implement and uses actual, full valuation of all securities. However, its typical implementation does not account for time variation in risk, and the method relies on a narrow window only. In theory, the Monte Carlo approach can alleviate all these technical difficulties. It can incorporate nonlinear positions, nonnormal distributions, implied parameters, and even user-defined scenarios. The price to pay for this flexibility, however, is heavy. Computer and data require-
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.09 7/19/00 3:38 PM Page 230 nd
230
PART 3 Value-at-Risk Systems
T A B L E 9–4
Comparison of Approaches to VAR
Features Positions Valuation Distribution Shape Time-varying Implied data Extreme events Use correlations VAR precision Implementation Ease of computation Accuracy Communicability VAR analysis Major pitfalls
Delta-Normal
Historical Simulation
Monto Carlo Simulation
Linear
Full
Full
Normal Yes Possible Low probability Yes Excellent
Actual Possible No In recent data Yes Poor with short window
General Yes Possible Possible Yes Good with many iterations
Yes Depends on portfolio Easy Easy, analytical Nonlinearities, fat tails
Intermediate Yes
No Yes
Easy More difficult Time-variation in risk, unusual events
Difficult More difficult Model risk
ments are a quantum step above the other two approaches, model risk looms large, and value at risk loses its intuitive appeal. As the price of computing power continues to fall, however, this method is bound to take on increasing importance. In practice, all these methods are used. A recent survey by Britain’s Financial Services Authority has revealed that 42 percent of banks use the covariance matrix approach, 31 percent use historical simulation, and 23 percent use the Monte Carlo approach. The delta-normal method, which is the easiest to implement, appears to be the most widespread. All these methods present some advantages. They are also related. Monte Carlo analysis of linear positions with normal returns, for instance, should yield the same result as the delta-normal method. Perhaps the best lesson from this chapter is to check VAR measures with different methodologies and then to analyze the sources of differences.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 339 nd
CHAPTER
14
Liquidity Risk
LTCM then faced severe market liquidity problems when its investments began losing value and the fund attempted to unwind some of its positions. President’s Working Group on Financial Markets, 1999
T
raditional value at risk (VAR) models rely on market prices, since marking-to-market is widely viewed as the ultimate discipline. VAR, however, assumes that the portfolio is “frozen” over the horizon and that market prices represent achievable transaction prices. This marking-to-market approach is adequate to quantify and control risk but may be more questionable if VAR is supposed to represent the worst loss over a liquidation period. The question is how VAR can be adapted to deal with liquidity considerations. As we saw in Chapter 1, liquidity risk can be grouped into asset liquidity and funding liquidity risk. The former relates to the risk that the liquidation value of the assets differs significantly from the current mark-to-market value. The latter refers to the risk that an institution could run out of cash and is unable to raise new funds to meet its payment obligations, which could lead to formal default. Thus liquidity considerations should be viewed in the context of liabilities. This chapter discusses recent developments that adapt traditional VAR measures to liquidity considerations. First, Section 14.1 analyzes asset and funding liquidity risk in some detail. Asset liquidity risk can be evaluated by the price impact of the liquidation. Funding liquidity risk, in contrast, deals with cash resources as well as potential cash requirements. Next, Section 14.2 provides insight into asset liquidity risk by comparing liquidation strategies. One strategy is immediate liquidation, which 339
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 340 nd
340
PART 3 Value-at-Risk Systems
may incur very large costs due to the price impact but insulates the portfolio from price volatility risk. Another strategy is that of liquidation at a constant rate, which minimizes trading costs but leaves the portfolio exposed to volatility risk. Optimal execution strategies best balance these low-cost and volatility requirements. Section 14.3 then discusses measures of funding liquidity risk proposed by the Counterparty Risk Management Policy Group (CRMPG). These measures show that even though an institution can have zero traditional VAR, different swap credit terms can generate very different cash requirements. Next, Section 14.4 is devoted to an analysis of the Long-Term Capital Management (LTCM) debacle. LTCM failed because of its lack of diversification and funding liquidity risk and asset liquidity risk, which were simply due to its sheer size. Finally, Section 14.5 provides some concluding comments.
14.1 DEFINING LIQUIDITY RISK
14.1.1 Asset Liquidity Risk Asset liquidity risk, sometimes called market/product liquidity risk, arises when a transaction cannot be conducted at prevailing market prices due to the size of the position relative to normal trading lots. Liquidity can be measured by a price-quantity function. This is also known as the market impact effect. Highly liquid assets, such as major currencies or Treasury bonds, are characterized by deep markets, where positions can be offset with very little price impact. Thin markets, such as exotic OTC derivatives contracts or emerging market equities, are those where any transaction can quickly affect prices. This price function is illustrated in Figure 14–1.1 The starting point is the current mid price, which is the average of the bid and ask quotes and is generally used to mark the portfolio to market. The bid-ask spread is $0.25, valid up to some limit, say, 10,000 shares. This is sometimes called the normal market size. For quantities beyond this point, however, the sale price is a decreasing function of the quantity, reflecting the price pressure required to clear the market. Conversely for the purchase price. 1. In what follows, we ignore the fixed component of trading costs, i.e., commissions and taxes.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 341 nd
CHAPTER 14 Liquidity Risk
FIGURE
341
14–1
Price-quantity function.
Price $100.5
Ask price $100.0
Bid price
$99.5
0 10,000
50,000 Quantity transacted
100,000
The relationship is assumed to be linear, although it could take another shape with parameters that vary across assets and, possibly, across time. In this case, selling 100,000 shares would incur a cost of about 60 basis points per share. In practice, the size of the sale would have to be measured relative to some metric such as the median daily trading volume. For a widely traded stock such as IBM, for instance, selling 4 percent of the daily trading volume incurs a cost of about 60 basis points. Here, liquidity can be measured usefully by the price-quantity function combined with the existing position of the institution. If the position is below 10,000 shares, then market liquidity is not a major issue. In contrast, if the institution holds a number of shares worth several days of normal trading volume, liquidity should be of primary concern. In addition to varying across assets, liquidity is also a function of prevailing market conditions. This is more worrying, because markets seem to go through regular bouts of liquidity crises. Most notably, liquidity in bond markets dried up during the summer of 1998 as uncertainty about defaults led to a “flight to quality,” i.e., increases in the prices of Treasuries relative to those of other bonds. A similar experience occurred
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 342 nd
342
PART 3 Value-at-Risk Systems
during the 1994 bond market debacle, at which time it became quite difficult to deal in eurobonds or mortgage-backed securities. Traditionally, asset liquidity risk has been controlled through position limits. The goal of position limits is to limit the exposure to a single instrument, even if it provides diversification of market risk, in order to avoid a large market impact in case of forced liquidation.
14.1.2 Funding Liquidity Risk Cash-flow/funding liquidity risk refers to the inability to meet payment obligations when the institution runs out of cash and is unable to raise additional funds. Often, this forces unwanted liquidation of the portfolio. It should be noted that funding risk arises from the use of leverage, whereby institutions borrow to expand their assets. This type of risk must be analyzed in the context of the asset and liability structure of the institution. Looking at the asset side, potential demands on cash resources depend on ■ ■
■
Variation margin requirements, due to marking-to-market Mismatch in the timing of collateral payments, due to the fact that even if an institution is perfectly matched in terms of market risk, it may be forced to make a payment on a position without having yet received an offsetting payment on a hedge Changes in collateral requirements, due to requests by lenders to increase the amount of collateral they require
Here, some words of explanation are in order. An example of mismatch in cash flows is an institution that has two economically hedged positions structured with different credit terms, such as a one-way markto-market swap and a two-way mark-to-market swap. In the former, the institution is required to make payments if the position loses money; it will not, however, receive intermediate payments if the position gains. In contrast, under two-way swaps, payments can be made or received if the position loses or gains money. Because of the asymmetry in the hedge, the institution will be subject to mismatches in the timing of collateral payments if the first swap loses money. Even with two-way mark-tomarket agreements, there can be some uncertainty in the cash-flow payments due to operational errors or discrepancies in the valuation of the swaps.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 343 nd
CHAPTER 14 Liquidity Risk
343
Next, changes in collateral requirements can arise due to requests by lenders to raise their haircuts. Normally, brokers require collateral that is worth slightly more than the cash loaned, by an amount known as a haircut, designed to provide a buffer against decreases in the collateral value. Unless contract terms forbid it, brokers can raise their haircuts if the market becomes more volatile, creating demands on cash. These examples provide yet another illustration of the complex interaction between different types of risks. Marking-to-market has been developed primarily to control credit risk. The problem is that it may create another risk, cash-flow risk. Further, if the institution does not carry enough cash to meet its margin calls, it may be forced to liquidate holdings at depressed prices, thereby creating asset liquidity risk. Looking at the liability side is also important, however. The institution may be able to meet margin calls by raising funds from another source, such as a line of credit or new equity issues. The problem is that it may be difficult to raise new funds precisely when the institution is faring badly and needing it most. Conversely, the institution also must evaluate the likelihood of redemptions, or cash requests from equity holders or debt holders. However, this is most likely to occur when the institution appears most vulnerable, thereby transforming what could be a minor problem into a crisis. It is also important to avoid debt covenants or options that contain “triggers” that would force early redemption of the borrowed funds. 14.2 DEALING WITH ASSET LIQUIDITY RISK
Trading returns typically are measured from midmarket prices. This may be adequate for measuring daily profit and loss (P&L) but may not represent the actual fall in value if a large portfolio were to be liquidated. The question is how to measure risk more properly, which can give insights into how to manage this risk. Traditional adjustments are done on an ad hoc basis. Liquidity risk can be loosely factored into VAR measures by ensuring that the horizon is at least greater than an orderly liquidation period. Generally, the same horizon is applied to all asset classes, even though some may be more liquid than others. Sometimes, longer liquidation periods for some assets are taken into account by artificially increasing the volatility. For instance, one could mix a large position in the dollar/yen with another one in the dollar/Polish
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 344 nd
344
PART 3 Value-at-Risk Systems
zloty, both of which have an annual volatility of 10 percent, by artificially increasing the second volatility in the VAR computations.
14.2.1 Bid-Ask Spread Cost More formally, one can focus on the various components of liquidation costs. The first and most easily measurable is the quoted bid-ask spread, defined in relative terms, that is, [P(ask) P(bid)] S P(mid)
(14.1)
Table 14–1 provides typical spreads. We see that spreads vary from a low of about 0.05 percent for major currencies, large U.S. stocks, and onthe-run Treasuries to much higher values when dealing with less liquid currencies, stocks, and bonds. Treasury bills are in a class of their own, with extremely low spreads. These spreads are only indicative, since they depend on market conditions. Also, marketmakers may be willing to trade within the spread. T A B L E 14–1
Typical Spreads and Volatility
Volatility, % Asset Currencies Major (euro, yen, etc.) Emerging (floating) Bonds On-the-run Treasuries Off-the-run Treasuries Corporates Treasury bills Stocks U.S. Average, NYSE Average, all countries
Spread, % (Bid-Ask)
Daily
Annual
0.05–0.20 0.50–1.00
0.3–1.0 0.3–1.9
5–15 5–30
0.03 0.06–0.20 0.10–1.00 0.003–0.02
0.0–0.7 0.0–0.7 0.0–0.7 0.0–0.1
0–11 0–11 0–11 0–11
0.05–5.00 0.20 0.40
1.3–3.8 1.0 1.0–1.9
20–60 15 15–30
Note: Author’s calculations. Cost of trades excludes broker commissions and fees. See also Institutional Investor (November 1999).
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 345 nd
CHAPTER 14 Liquidity Risk
345
At this point, it is useful to review briefly the drivers of these spreads. According to market microstructure theory, spreads reflect three different types of costs: order-processing costs, asymmetric information costs, and inventory-carrying costs. Order-processing costs cover the cost of providing liquidity services and reflect the cost of trading, the volume of transaction, the state of technology, and competition. With fixed operating costs, these orderprocessing costs should decrease with transaction volumes. Asymmetric information costs reflect the fact that some orders may come from informed traders, at the expense of marketmakers who can somewhat protect themselves by increasing the spread. Finally, inventory-carrying costs are due to the cost of maintaining open positions, which increases with higher price volatility, higher interest rate carrying costs, and lower trading activity or turnover. If the spread were fixed, one could simply construct a liquidityadjusted VAR from the traditional VAR by adding a term: LVAR VAR L1 (W) 1/2(WS)
(14.2)
where W is the initial wealth, or portfolio value. For instance, if we have $1 million invested in a typical stock, with a daily volatility of 1 percent and spread of S 0.25 percent, the 1-day LVAR at the 95 percent confidence level would be LVAR ($1 million 1.645 0.01) 1/2($1 million 0.0025) $16,450 $1250 $17,700 Here, the correction factor is relatively small, accounting for 7 percent of the total. This adjustment can be repeated for all assets in the portfolio, leading to a series of add-ons, 1⁄2 i | Wi | Si. This sequence of positive terms increases linearly with the number of assets, while the usual VAR benefits from diversification effects. Thus the relative importance of the correction factor will be greater for large portfolios. A slightly more general approach is proposed by Bangia et al. (1999), who consider the uncertainty in the spread. They characterize the distribution by its mean S and standard deviation S. The adjustment considers the worst increase in the spread at some confidence level: 1 S)] LVAR VAR L2 (W) [W(S 2
(14.3)
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 346 nd
346
PART 3 Value-at-Risk Systems
At the portfolio level, one could theoretically take into account correlations between spreads. In practice, summing the individual worst spreads provides a conservative measure of the portfolio worst spread. Although this approach has the merit of considering some transaction costs, it is not totally satisfactory. It only looks at the bid-ask spread component of these costs, which may be appropriate for a small portfolio but certainly not when liquidation can affect market prices. Also, if the decision is taken to liquidate the portfolio immediately, the VAR horizon should be very short. What is needed is a model that takes into account the cost and benefit of trading strategies.
14.2.2 Trading Strategies The extension based on bid-ask spreads, while an improvement over traditional VAR calculation, very much ignores the market impact factor, which can be significant. To some extent, this can be mitigated by suitable execution strategies. These should be taken into account when computing a liquidity-adjusted VAR. To simplify, let us assume a linear price-quantity function. For a sale, P(q) P0(1 kq)
(14.4)
7
Assume that P0 $100 and k 0.5 10 . Say that we start with a position of 1 million shares of the stock. If we liquidate all at once, the price drop will be P0 kq $100 (0.5 107) 1,000,000 $5, leading to a total price impact of $5 million. In contrast, we could decide to work the order through at a constant rate of 200,000 shares over 5 days. Define n as the number of days to liquidation. In the absence of other price movements, the price drop will be $1.0, leading to a total price impact of $1 million, much less than before. Immediate liquidation creates quadratic costs: C1(W ) q [P0 P(q)] kq2P0
(14.5)
whereas uniform liquidation creates lower costs: C2(W ) q [P0 P(q/n)] k(q2/n)P0
(14.6)
The drawback of liquidating more slowly is that the portfolio remains exposed to price risks over a longer period. The position profiles are illustrated in Figure 14–2. Under the immediate sale, the position is liquidated before the end of the next day, leading to a high cost but min-
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 347 nd
CHAPTER 14 Liquidity Risk
FIGURE
347
14–2
Profile of execution strategies. 1,000,000
Position
Uniform sales: minimum impact 500,000
Minimum L-VAR Immediate sale: minimum risk 0
0
1
2 3 4 Calendar time (days)
5
6
imum risk. Under the uniform sale, the position is sold off in equal-sized lots, leading to low costs but high risk. The key is to choose a strategy that offers the best cost-risk tradeoff. To analyze the risk profile of these strategies, define as the daily volatility of the share price, in dollars. We assume that sales are executed at the close of the business day, in one block. Hence, for the immediate sale, the price risk or variance of wealth is zero, V1(W ) 0. For the uniform sale, the portfolio variance can be computed assuming independent returns over n days as
1 V2(W ) 2q2 1 n
2
2
1 2 1 (n 1) n 1 1 1 2q2 n 1 1 (14.7) 3 n 2n
1 1 2 n
For example, with n 5, the correction factor between braces is 1.20. Thus constant liquidation over 5 days is equivalent to the markingto-market risk of a position held over 1.2 days. It is interesting to note
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 348 nd
348
PART 3 Value-at-Risk Systems
that the 10-day fixed horizon dictated by the Basel Committee is equivalent to a constant liquidation over 31 days. Execution strategies need not be limited to these two extreme cases. More generally, we can choose a strategy x that leads to an optimal tradeoff between execution costs and price risk: minx[Cx(W ) Vx(W )]
(14.8)
where reflects the aversion to price risk. Lawrence and Robinson (1997), for instance, propose a simple solution, which is to minimize over n, using Equations (14.7) and (14.6). Almgren and Chriss (1999) provide a more complete closed-form solution for efficient execution strategies in the cost-risk plane. An optimal trajectory is described in Figure 14–2. Note that the strategy can be described by its half-life, which is the time required to liquidate half the portfolio. For the optimal strategy here, this takes 1 day. This leads to the concept of liquidity-adjusted VAR, or implementation shortfall, which is ) C(W ) LVAR V(W
(14.9)
where corresponds to the confidence level c. In other words, this LVAR measure takes into account not only liquidation costs but also the best execution strategy such that LVAR will not be exceeded more than a fraction c of the time. Figure 14–3 compares various VAR measures for different speeds of execution. The “static” 1-day and 5-day VARs correspond to the usual mark-to-market VAR measures with 30 percent annual volatility. Under these conditions, the daily volatility is 1.9 percent, and the 1-day VAR is $3.1 million for this $100 million portfolio. With a 25-basis-point spread and no market impact, the spread adjustment is small, at $125,000 only. This, however, ignores price impact. Instead, the LVAR measure incorporates the total execution cost and price risk components in a consistent fashion. As we extend the length of liquidation, the execution cost component decreases, but the price risk component increases. Here, the total LVAR is minimized at a half-life of 1 day. In this case, a 5-day static VAR would provide a conservative measure of liquidation VAR. The real benefit of this approach is that it draws attention to market impact effects in portfolio liquidation. It also illustrates that execution strategies should account for the tradeoff between execution costs and price volatility.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 349 nd
CHAPTER 14 Liquidity Risk
FIGURE
349
14–3
Liquidity-adjusted VAR. 10
VAR ($ millions)
9 8
Static-5 days
7 6 5
LVAR
4 3 2
Price risk
1
Execution cost
Static-1 day
0
0
1
10 Length of liquidation (half-life, in days)
For instance, there are other ways to implement the liquidation. In the case of stock portfolios, for example, the portfolio manager could cut its price risk by immediately putting in place a hedge with stock index futures. In this case, the remaining price risk is “specific” to the security. Orders to sell could then be transmitted so as to minimize their price impact.
14.2.3 Practical Issues In practice, the computational requirements to adjust the conventional VAR numbers are formidable. The method requires a price-quantity function for all securities in the portfolio. Combined with the portfolio position, this yields an estimate of the price impact of a liquidation, as well as the optimal time to liquidation. Table 14–2 provides an example of such an analysis, as provided by Morgan Stanley (MS) for a four-country $50 million equity portfolio. The data for Switzerland are expanded at the individual stock level. To estimate the total impact cost, we need information about the historical bid-ask spreads, the median trading volume, and recent volatility. The
350
Source: Morgan Stanley (1999).
France Germany Switzerland Novartis Swatch Nestle CS Group U.K. Total
Asset 19,300,182 19,492,570 19,300,182 5,351,851 64,678 1,752,009 1,165,797 5,860,371 50,004,974
Value (US$)
Market Impact Cost Report
T A B L E 14–2
184,063 322,550 9,355 1,630 400 935 6,390 424,373 940,341
Shares Held
Portfolio
104.9 60.4 572.1 1,453.6 161.7 1,873.8 182.4 13.8 53.2
Price 19.9 26.1 12.5 11.7 32.9 6.4 22.2 20.2 21.6
Spread (bp)
123,554 42,559 76,004 978,168
Median Volume
Cost Analysis
1.3% 2.5% 1.1% 1.3% 0.9% 1.2% 0.7% 0.6% 1.7%
Shares/ Volume
18.2 29.3 9.5 8.8 15.5 7.3 14.1 17.6 21.5
Impact Cost (bp)
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 350 nd
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 351 nd
CHAPTER 14 Liquidity Risk
351
portfolio relative size is then defined as the number of shares held as a percentage of median trading volume. MS then computes the total impact cost as a function of half the bid-ask spread and of this size variable. Here, the total cost of immediate (1-day) liquidation is estimated to be 21.5 basis points. This can be compared to the daily markingto-market volatility of this portfolio, which is 110 basis points. Thus, if the portfolio were to be liquidated at the end of the next day, the worst LVAR loss at the 95 percent confidence level would be about $50 million (1.65 1.1 percent 0.22 percent) $50 million 2.0 percent $1.0 million. The relative importance of liquidity would no doubt be much greater for a larger portfolio. In addition, the framework presented in the preceding section allows the investor to evaluate the cost and risk of various trading strategies. 14.3 GAUGING FUNDING LIQUIDITY RISK
Measuring funding liquidity risk involves examining the asset-liability structure of the institution and comparing potential demands on cash with the available supply of equivalent instruments. Some lessons are available from the Counterparty Risk Management Policy Group (CRMPG), which was established in the wake of the LTCM near failure to strengthen practices related to the management of market, counterparty credit, and liquidity risk.2 The CRMPG proposes to evaluate funding risk by comparing the amount of cash an institution has at hand with to what it could need to meet payment obligations. It defines cash liquidity as the ratio of cash equivalent over the potential decline in the value of positions that may create cash-flow needs. Table 14–3 illustrates an example of an institution that has a position in two offsetting swaps. Since it is perfectly hedged, it has zero traditional VAR, or market risk. Yet different swap credit terms create funding risk. In the case where the two swaps are both marked-to-market, any cash payment in one swap must be offset by a receipt on the other leg. The only risk is that of a delay in the receipt. Assume the worst move on a $100 million swap at the 99 percent level over 1 day is $1.1 million. 2. The CRMPG consists of senior-level practitioners from the financial industry, including many banks that provided funding to LTCM.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 352 nd
352
PART 3 Value-at-Risk Systems
T A B L E 14–3
Computing Funding Liquidity Ratio
Case 1 Assets Cash Liabilities Equity Derivatives Long 10-year swap Short 10-year swap Cash equivalent Funding VAR Ratio
Case 2
$5
$5
$5
$5
$100, two-way marked-to-market $100, two-way marked-to-market $5 $1.1 (1-day) 4.5
$100, unsecured $100, two-way marked-to-market $5 $3.5 (10-day) 1.4
Let us consider this is the worst cash need. The funding ratio is then $5/$1.1 4.5, rather high, which indicates sufficient cash coverage. In the case where one of the swaps is not secured by markingto-market, the risk is that of a decrease in the value of the mark-to-market swap, which would not be offset by a cash receipt on the other leg until settlement. We now need to consider a longer horizon VAR, say, 10 days, which gives $3.5, for a funding ratio of 1.4. This seems barely enough to provide protection against funding risk. Thus some of the elements of traditional VAR can be used to compute funding risk, which can be quite different from market risk when the institution is highly leveraged. 14.4 LESSONS FROM LTCM3
The story of Long-Term Capital Management (LTCM) provides a number of lessons in liquidity risk. LTCM was founded by Meriwether in 1994, who left Salomon Brothers after the 1991 bond scandal. Meriwether took with him a group of traders and academics and set up a hedge fund that tried to take advantage of “relative value” or “convergence arbitrage” trades, betting on differences in prices, or spreads, among closely related securities. 3. This draws on Philippe Jorion, “How Long-Term Lost Its Capital,” Risk (September 1999).
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 353 nd
CHAPTER 14 Liquidity Risk
353
14.4.1 LTCM’s Leverage Since such strategies tend to generate tiny profits, leverage has to be used to create attractive returns. By December 1997, the total equity in the fund was $5 billion. LTCM’s balance sheet was about $125 billion. This represented an astonishing leverage ratio of 25:1. Even more astonishing was the off-balance-sheet position, including swaps, options, and other derivatives, that added up to a notional amount of $1.25 trillion. This represents the total of gross positions, measured as the sum of the absolute value of the trade’s notional principals. To give an idea of the magnitude of these positions, the BIS reported a total swap market of $29 trillion in 1998. Hence LTCM’s swap positions accounted for 2.4 percent of the global swap market. Many of these trades, however, were offsetting each other, so this notional amount is practically meaningless. What mattered was the net risk of the fund. LTCM, however, failed to appreciate that these gross positions were so large that attempts to liquidate them would provoke large market moves.
14.4.2 LTCM’s “Bulletproofing” LTCM was able to leverage its balance sheet through sale-repurchase agreements (repos) with commercial and investment banks. Under repo agreements, the fund sold some of its assets in exchange for cash and a promise to purchase them back at a fixed price on some future date. Normally, brokers require collateral that is worth slightly more than the cash loaned, by an amount known as a haircut, designed to provide a buffer against decreases in the collateral value. LTCM, however, was able to obtain unusually good financing conditions, with next-to-zero haircuts, since it was widely viewed as “safe” by its lenders. In addition, the swaps were subject to two-way marking-to-market. On the supply side, LTCM also had “bulletproofed” itself against a liquidity squeeze. LTCM initially had required investors to keep their money in the fund for a minimum of 3 years. The purpose of this socalled lockup clause, which was very unusual in the hedge fund industry, was to avoid forced sales in case of poor performance. LTCM also secured a $900 million credit line from Chase Manhattan and other banks. Even though LTCM had some protection against funding liquidity risk, it was still exposed to market risk and asset liquidity risk.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 354 nd
354
PART 3 Value-at-Risk Systems
FIGURE
14–4
LTCM’s returns. 60%
(Percent after fees)
40% 20% 0% -20% -40%
LTCM Fund
-60%
U.S. Stocks LTCM, cumulative, 1998
-80% -100% 1994 1995 1996 1997 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
14.4.3 LTCM’s Downfall LTCM’s strategy profited handsomely from the narrowing of credit spreads during the early years, leading to after-fees returns above 40 percent, as shown in Figure 14–4. Troubles began in May and June of 1998. A downturn in the mortgage-backed securities market led to a 16 percent loss in LTCM’s capital. Then came August 17. Russia announced that it was “restructuring” its bond payments—de facto defaulting on its debt. This bombshell led to a reassessment of credit and sovereign risks across all financial markets. Credit spreads, risk premia, and liquidity spreads jumped up sharply. Stock markets dived. LTCM lost $550 million on August 21 alone. By August, the fund had lost 52 percent of its December 31 value. With assets still at $126 billion, the leverage ratio had increased from 28:1 to 55:1. LTCM badly needed new capital. It desperately tried to find new investors, but there were no takers. In September, the portfolio’s losses accelerated. Bear Stearns, LTCM’s prime broker, faced a large margin call from a losing LTCM
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 355 nd
CHAPTER 14 Liquidity Risk
355
T-bond futures position. It then required increased collateral, which depleted the fund’s liquid resources. LTCM was now caught in a squeeze between funding risk, as its reserves dwindled, and asset risk, as the size of its positions made it impractical to liquidate assets. From the viewpoint of the brokers, a liquidation of the fund would have forced them to sell off tens of billions of dollars of securities and to cover their numerous derivatives trades with LTCM. Because lenders had required next-to-zero haircuts, there was a potential for losses to accrue while the collateral was being liquidated. The potential disruption in financial markets was such that the New York Federal Reserve felt compelled to act. On September 23, it organized a bailout of LTCM, encouraging 14 banks to invest $3.6 billion in return for a 90 percent stake in the firm. These fresh funds came just in time to avoid meltdown. By September 28, the fund’s value had dropped to $400 million only. Investors had lost a whopping 92 percent of their year-to-date investment.
14.4.4 LTCM’s Liquidity LTCM failed because of its inability to measure, control, and manage its risk. This was due in no small part to the fact that LTCM’s trades were rather undiversified. LTCM was reported to have lost about $1.5 billion from interest rate swaps positions and a similar amount from short positions on equity volatility. As we show later, this was a result of an ill-fated attempt to manage risk through portfolio optimization. Table 14–4 describes the exposure of various reported trades to fundamental risk factors. All the trades were exposed to increased market volatility. Most were exposed to liquidity risk (which is itself positively correlated with volatility). Many were exposed to default risk. To illustrate the driving factor behind LTCM’s risks, Figure 14–5 plots the monthly returns against monthly changes in credit spreads. The fit is remarkably good, indicating that a single risk factor would explain 90 percent of the variation up to the September bailout. Thus there was little diversification across risk factors. In addition, LTCM was a victim of both asset and funding liquidity risk. Although it had taken some precautions against withdrawal of funds, it did not foresee that it would be unable to raise new funds as its performance dived. The very size of the fund made it difficult to organize an orderly portfolio liquidation.
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 356 nd
356
PART 3 Value-at-Risk Systems
T A B L E 14–4
Exposure of LTCM’s Portfolio to Risk Factors
Loss If Risk Factor Increases Trade
Volatility
Default
Illiquidity
Yes Yes
Yes
Yes
Long interest rate swap Short equity options Long off-the-run/short on-the-run Treasuries Long mortgage-backed securities (hedged) Long sovereign debt
FIGURE
Yes Yes Yes
Yes Yes
Yes
14–5
Explaining LTCM returns. 60%
Return after fees
40% 20% Jul
0%
May
Jun
-20% -40%
To Sep-98
-60%
After bail-out
Aug
-80%
Sep
-100% -0.4
-0.2
0
0.2
Change in corporate bond spread
0.4
0.6
This chapter with has been reproducedfrom with permission from Value at Risk, 2 Ed. byJorion. Philippe© Jorion, by McGraw-Hill , New Reproduced permission Value at Risk, 2nd ed., by Philippe 2001published The McGraw-Hill Companies, York 2001 (© McGraw-Hill, all rights reserved). Inc. 9706.Ch.14 7/19/00 3:42 PM Page 357 nd
CHAPTER 14 Liquidity Risk
357
The episode also raised questions about the soundness of the brokers’ risk-management systems. The brokers lulled themselves into thinking that they were protected because their loans were “fully collateralized.” Even so, their loans carried no haircuts and were exposed to the risk that LTCM could default at the same time as the collateral lost value. One of the lessons of this near disaster was to accelerate the integration of credit and market risk management. 14.5 CONCLUSIONS
This chapter has shown how to account for liquidity risk. Originally, the implicit assumption behind VAR was that the assets can be liquidated before they have moved by more than the amount estimated. In practice, this concept can be refined to account for liquidity risk. Asset liquidity risk can be traced to the price impact of the liquidation of a large position relative to normal market sizes. We have seen that different execution strategies can be compared on the basis of a liquidityadjusted VAR, which requires an estimate of the price impact function. Funding liquidity risk, in contrast, considers the available supply of cash equivalents as well as potential claims that may arise due to leverage. Here again, the VAR concept can be altered to estimate the risk that a portfolio could run out of cash. Whether liquidity risk is relevant very much depends on the liability structure of the investment. Consider, for instance, an investment in “illiquid” assets such as exotic collateralized mortgage obligations. If the investment is funded by short-term borrowing, the investor runs a liquidity risk and should mark the investment at its liquidation value. In contrast, if the investment is funded by unleveraged equity, marking-tomarket is an appropriate measure of risk. As for other applications of VAR, the main benefit of these analyses is not so much to come up with one summary risk number but rather to provide a systematic framework to think about alternative execution strategies or marking-to-market arrangements. While LVAR may be somewhat difficult to measure, some rules of thumb are useful. We do know that bid-ask spreads are positively correlated with volatility. A position in illiquid assets will incur greater execution costs as volatility increases. Thus liquidity risk can be mitigated by taking offsetting positions in assets, or businesses, that benefit from increased volatility or have positive vega.
At the end of this chapter, you will:
1. Understand the main approaches to price risky debt. 2. Know how to evaluate credit risks quantitatively for individual credits and for portfolios.
3. Have learned what credit derivatives are and how to use them.
4. Have tools to assess the credit risks of derivatives.
From Risk Management and Derivatives, 1st edition, by René M. Stulz. © 2003. Reproduced with permission ofThis South-Western, division of Thomson www.thomsonrights.com. Fax 800 chapter has beenareproduced with permission from Riskby Management and Derivatives, René M. 730-2215. Stulz, by of From Risk Management and Derivatives, 1st Learning: edition, René M. Stulz. © 2003. by Reprinted with published permission Thomson South-Western, Mason, Ohio 2003 (© Thomson South-Western, all rights reserved). South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215. From Risk Management and Derivatives, 1st edition, by René M. Stulz. © 2003. Reproduced with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
Part 3
Beyond Plain Vanilla Rirk Munagemmt
Consider Credit Bank Corp. It makes loans to corporations. For each loan, there is some risk that the borrower will default, in which case Credit will not receive all the payments the borrower promised to make. Credit has to understand the risk of the individual loans it makes, but it must also be able to quantify the overall risk of its loan portfolio. Credit has a high franchise value and wants to protect that franchise value by making sure that the risk of default on its loans does not make its probability of financial distress too high. Though Credit knows how to compute VaR for its trading portfolio, it cannot use these techniques directly to compute the risk of its loan portfolio. Loans are like bonds-credit never receives more from a borrower than the amounts the borrower promised to pay. Consequently, the distribution of the payments received by borrowers cannot be lognormal. To manage the risk of its loans, Credit must know how to quantify the risk of default and of the losses it makes in the event of default both for individual loans and for its portfolio of loans. At the end of this chapter, you will know the techniques that Credit can use for this task. We will see that the Black-Scholes formula is useful to understand the risks of individual loans. Recently, a number of firms have developed models to analyze the risks of portfolios of loans and bonds. For example, J.I? Morgan has developed CreditMetricsTM along the lines of its product kskMetricsTM. We discuss this model in some detail.
A credit risk is the risk that someone who owes money might fail to make promised payments. Credit risks play two important roles in risk management. First, credit risks represent part of the risks a firm tries to manage in a risk management program. If a firm wants to avoid lower tail outcomes in its income, it must carefully evaluate the riskiness of the debt claims it holds against third parties and determine whether it can hedge these claims and how. Second, the firm holds positions in derivatives for the express purpose of risk management. The counterparties on these derivatives can default, in which case the firm does not get the payoffs it expects on its derivatives. A firm taking a posirion in a derivative must therefore evaluate the riskiness of the counterparty in the position and be able to assess how the riskiness of the counterparty affects the value of its derivatives positions. Credit derivatives are one of the newest and most dynamic growth areas in the derivatives industry. At the end of 2000, the total notional amount of credit derivatives was estimated to be $8 10 billion; it was only $180 billion two years before. Credit derivatives have payoffs that depend on the realization of credit risks. For example, a credit derivative could promise to pay some amount if Citibank defaults and nothing otherwise; or a credit derivative could pay the holder of Citibank debt the shortfall that occurs if Citibank defaults on its debt. Thus firms can use credit derivatives to hedge credit risks.
18. I. Credit risks as options Following Black and Scholes (1973), option pricing theory has been used to evaluate default-risky debt in many different situations. The basic model to value risky debt using option pricing theory is the Merton (1974) model. To understand this approach, consider a levered firm that has only one debt issue and pays
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
Credit Ri~ksand Credit Deriva~iver
no dividends. Financial markets are assumed to be perfect. There are no taxes and no bankruptcy costs, and contracts can be enforced costlessly. Only debt holders and equity holders have claims against the firm and the value of the firm is equal to the sum of the value of debt and the value of equity. The debt has no coupons and matures at T. At date T, the firm has to pay the principal amount of the debt, F. If the firm cannot pay the principal amount at T, it is bankrupt, equity has no value, and the firm belongs to the debt holders. If the firm can pay the principal at T, any dollar of firm value in excess of the principal belongs to the equity holders. Suppose the firm has issued debt that requires it to make a payment of $100 million to debt holders at maturity and that the firm has no other creditors. If the total value of the firm at maturity is $120 million, the debt holders receive their promised payment, and the equity holders have $20 million. If the total value of the firm at maturity is $80 million, the equity holders receive nothing and the debt holders receive $80 million. Since the equity holders receive something only if firm value exceeds the face value of the debt, they receive VT - F if that amount is positive and zero otherwise. This is equivalent to the payoff of a call option on the value of the firm. Let VT be the value of the firm and ST be the value of equity at date T. We have at date T:
To see that this works for our example, note that when firm value is $120 million, we have ST equal to Max($l20M - $100M, 0), or $20 million, and when firm value is $80 million, we have ST equal to Max($80M -$100M, 0), or $0. Figure 18.1 graphs the payoff of the debt and of the equity as a function of the value of the firm. If the debt were riskless, its payoff would be the same for any value of the firm and would be equal to F. Since the debt is risky, when the value of the firm falls below F, the debt holders receive less than F by an amount equal to F - VT. The amount F - VT paid ifVT is smaller than F, Max(F - VT, O), corresponds to the payoff of a put option on VT with exercise price F. We can therefore think of the debt as paying F for sure minus the payoff of a put option on the firm with exercise price F:
where DT is the value of the debt at date T. Equation (18.2) therefore tells us that the payoff of risky debt is equal to the payoff of a long position in a risk-free zerocoupon bond with face value F and a short position on a put option on firm value with exercise price F. This means that holders of risky debt effectively buy riskfree debt but write a put option on the value of the firm with exercise price equal to the face value of the debt. Alternatively, we can say that debt holders receive the value of the firm, VT, minus the value of equity, ST. Since the payoff of equity is the payoff of a call option, the payoff of debt is the value of the firm minus the payoff of a call option with exercise price equal to the principal amount of the debt.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
"7-7-
e .-.-Ts .-
'iF@we 18.1
-r---w--
=-----%-T.w?-?+..% Debt and equity payoffs when debt is risky 7-
- ~ ~ - - - % . m 7 = , . - %
----aF---.--T+y=
--
F is the debt prlnc~palamount andV(T) 1s the value of the flrm at date T.
To price the equity and the debt using the Black-Scholes formula for the pricing of a European call option, we require that the value of the firm follow a lognormal distribution with a constant volatility o, the interest rate r be constant, trading take place continuously, and financial markets be perfect. We do not require that there is a security that trades continuously with value V. All we need is a portfolio strategy such that the portfolio has the same value as the firm at any particular time. We use this portfolio to hedge options on firm value, so that we can price such options by arbitrage. We can write the value of equity as S(V, F, T, I-) and use the formula to price a call option to obtain: Merton's formula for the value of equity
Let S(V, F, T, t ) be the value of equity at date t, V the value of the firm, F the face value of the firm's only zero-coupon debt maturing at T, (T the volatility of the value of the firm, P,(T) the price at t of a zero-coupon bond that pays $1 at T, and lV(d) the cumulative distribution function evaluated at d. With this notation, the value of equity is:
yv, F, T, t ) = V N ( ~ )- P ~ ( T ) F N -( ~O K )
When V is $120 million, F is $100 million, T is equal to t + 5, P,(T) is $0.6065, and o is 20 percent, the value of equity is $60.385 million. From our understanding of the determinants of the value of a call option, we know that equity increases in value when the value of the firm increases, when firm volatility in-
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
Credit Risks and Credit Derivatives
creases, when time to maturity increases, when the interest rate increases, and when the face value amount of the debt falls. Debt can be priced in two different ways. First, we can use the fact that the payoff of risky debt is equal to the payoff of risk-free debt minus the payoff of a put option on the firm with exercise price equal to the face value of the debt:
where p(V, F, T, t ) is the price of a put with exercise price F on firm value V. F is $100 million and P,(T) is $0.6065, so P,(T)F is $60.65 million. A put on the value of the firm with exercise price of $100 million is worth $1.035 million. The value of the debt is therefore $60.65M - $1.035M, or $59.615 million. The second approach to value the debt involves subtracting the value of equity from the value of the firm:
We subtract $60.385 million from $120 million, which gives us $59.615 million. The value of the debt is, for a given value of the firm, a decreasing function of the value of equity, which is the value of a call option on the value of the firm. Everything else equal, therefore, the value of the debt falls if the volatility of the firm increases, if the interest rate rises, if the principal amount of the debt falls, and if the debt's time to maturity lengthens. To understand the effect of the value of the firm on the value of the debt, note that a $1 increase in the value of the firm affects the right-hand side of equation (18.5) as follows: It increases V by $1 and the call option by $6, where 6 is the call option delta. 1 - 6 is positive, so that the impact of a $1 increase in the value of the firm on the value of the debt is positive and equal to $1 - $6. 6 increases as the call option gets more in the money. Here, the call option corresponding to equity is more in the money as the value of the firm increases, so that the impact of an increase in firm value on debt value falls as the value of the firm increases. Investors pay a lot of attention to credit spreads. The credit spread is the difference between the yield on the risky debt and the yield on risk-free debt of same maturity. If corporate bonds with an A rating have a yield of 8 percent while Tbonds of the same maturity have a yield of 7 percent, the credit spread for A-rated debt is 1 percentage point. An investor can look at credit spreads for different ratings to see how the yields differ across ratings classes. An explicit formula for the credit spread is: Credit spread
=
- ( T1t ) l n ( F ) -
where r is the risk-free rate. For our example, the risk-free rate (implied by the zero-coupon bond price we use) is 10 percent. The yield on the debt is 10.35 percent, so the credit spread is 35 basis points. Not surprisingly, the credit spread falls as the value of the debt rises. The logarithm of D/F in equation (18.6) is
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyond Plain Vanilla Risk Management
multiplied by -[l/(T - t ) ] .An increase in the value of debt increases D/F, but since the logarithm of D/F is multiplied by a negative number, the credit spread falls. With debt, the most we can receive at maturity is par. As time to maturity lengthens, it becomes more likely that we will receive less than par. However, if the value of the debt is low enough to start with, there is more of a chance that the value of the debt will be higher as the debt reaches maturity if time to maturity is longer. Consequently, if the debt is highly rated, the spread widens as time to maturity gets longer. For sufficiently risky debt, the spread can narrow as time to maturity gets longer. This is shown in Figure 18.2. Helwege and Turner (1999) show that credit spreads widen with time to maturity for low-rated public debt, so that even low-rated debt is not risky enough to lead to credit spreads that narrow with time to maturity. It is important to note that credit spreads depend on interest rates. The expected value of the firm at maturity increases with the risk-free rate, so there is less risk that the firm will default. As a result, credit spreads narrow as interest rates increase.
18.1.1. Finding firm value and firm value volatility Suppose a firm, Supplier Inc., has one large debt claim. The firm sells a plant to a very risky third party, In-The-Mail Inc., and instead of receiving cash it receives a promise from In-The-Mail Inc. that it will pay $100 million in five years. We want to value this debt claim. IfV,, 5 is the value of In-The-Mail Inc. at maturity of the debt, we know that the debt pays F - Max(F - V,. 5, 0) or V, 5 Max(V,+ 5 - F, 0). If it were possible to trade claims on the value of In-The-Mad Inc., pricing the debt would be straightforward. We could simply compute the value of a put -onIn-The-Mail Inc. with the appropriate exercise price. In general, we cannot directly trade a portfolio of securities that represents a claim to the whole firm; In-The-Mail Inc.'s debt is not a traded security, +
The fact that a firm has some nontraded securities creates two problems. First, we cannot observe firm value directly and, second, we cannot trade the firm to hedge a claim whose value depends on the value of the firm. We can solve both problems. Remember that with Merton's model the only random variable that affects the value of claims on the firm is the total value of the firm. Since equity is a call option on firm value, it is a portfolio consisting of 6 units of firm value plus a short position in the risk-free asset. The return on equity is perfectly correlated with the return on the value of the firm for small changes in the value of the firm because a small change in firm value of AV changes equity by 6AV. We can therefore use equity and the risk-free asset to construct a portfolio that replicates the firm as a whole, and we can deduce firm value from the value of traded claims on the value of the firm. To do that, however, we need to estimate the 8 of equity. To compute the 6 of equity from Merton's formula, we need to know firm value V, the volatility of firm value, the promised debt payment, the risk-free interest rate, and the maturity of the debt. If we have this information, computing delta is straightforward. Otherwise, we can estimate these variables using information we have. If we have an estimate of 6 and we know the value of the firm's equity, then we can solve for firm value and the volatility of firm value as long as we know the promised debt payment and the maturity of the debt. This is be-
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Credit Rrskj and Credif Derivatzves
Chapter 18
I*"wFFW -
'
..-.yvm*w---.-IUT
.p7irpa-nw--^LIP?I*q
, ' ~ r e c a d stime , to maturity, and i n r e r e s w
Thure
18.2
Panel A has firm value of $50 million, volatility of 20 percent, and debt with face value of $150 million. Panel B differs only in that firm value is $200 million. Panel A
Time to maturity
2/0 -\
'-4'
30
Panel B
Decimal
Interest Time to maturity
30
cause, in this case, we have two unknowns, firm volatility and firm value, and two equations, the Merton equation for the value of equity and the Merton equation for the equity's delta. We can solve these equations to find firm volatility and the value of the firm. Having these values, we can then solve for the value of the debt. (In practical applications, the Merton model is often used for more complicated capital structures. In this case, the promised debt payment is an estimate of the amount of firm value over some period of time such that if firm value falls below that amount, the firm will be in default and have to file for bankruptcy.) Suppose we do not know 6. One way to find 8 is as follows. We assume Inthe-Mail Inc. has traded equity and that its only debt is the debt it owes to
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyotld Plain Vanilla Risk Management
Supplier Inc. The value of the debt claim in million dollars is D(V, 100, t + 5, t ) . The value of a share is $14.10 and there are 5 million shares. T h e value of the firm's equity is therefore $70.5 million. The interest rate is 10 percent per year. Consequently, in million dollars, we have:
We know that equity is a call option on the value of the firm, so that S(V, 100, t + 5 , t ) = c(V, 100, t +5, t ) .We cannot trade V because it is the sum of the debt we own and the value of equity. Since the return to V is perfectly correlated with the return on equity, we can form a dynamic portfolio strategy that pays V,, 5 at t + 5. We will see the details of the strategy later, but for now we assume it can be done. If we know V, we can use equation (18.7) to obtain the firm's implied volatility, but the equation has two unknowns: V and the volatility of the value of the firm, o.To solve for the two unknowns, we have to find an additional equation so that we have two equations and two unknowns. Suppose that there are options traded on the firnl's equity. Suppose further that a call option on one share with exercise price of $10 and maturity of one year is worth $6.72. We could use the option pricing formula to get the volatility of equity and deduce the volatility of the firm from the volatility of equity. After all, the option and the equity both depend on the same random variable, the value of the firm. The difficulty with this is that the Black-Scholes formula does not apply to the call option in our example because it is a call option on equity, which itself is an option when the firm is levered. We therefore have an option on an option, or what is called a compound option. The Black-Scholes formula applies when equity has constant volatility, but the equity in our example cannot have constant volatility if firm value has constant volatility. For a levered firm where firm value has constant volatility, equity is more volatile when firm value is low than when it is high, so that volatility falls as firm value increases. This is because, in percentage terms, an increas; in firm value has more of an impact on equity ;hen the value of equity is extremely low than when it is extremely high-even though the equity's 6 increases as firm value increases.
A compound call option gives its holder the right to buy an option for a given exercise price. Geske (1979) derives a pricing formula for a compound option that we can use. Geske's formula assumes that firm value follows a lognormal distribution with constant volatility. Therefore, if we know the value of equity, we can use Geske's formula to obtain the value of firm volatility This formula is presented in Technical Box 18.1, Compound option formula.
18.1.2. Pricing the debt of In-The-Mail Inc. We now have two equations that we can use to solve for V and a: the equation for the value of equity (the Black-Scholes formula), and the equation for the value of an option on equity (the compound option formula of Technical Box 18.1). These two equations have only two unknowns. We proceed by iteration. Suppose we pick a firm value per share of $25 and a volatility of 50 percent. With this, we find that equity should be worth $15.50 and that the call price should be $6.0349. Consequently, the value of equity is too high and the value
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
Credit risk^ and Credit Dmivativa
"\'
iat, for I
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyond Plain Valzilla Rijk Management
of the call is too low. Reducing the assumed firm value reduces both the value of equity and the value of rhe call, so that it brings us closer to the value of equity we want but farther from the value of the call we want. We therefore need to change both firm value and some other variable, taking advantage of the fact that equity and a call option on equity have different greeks. Reducing our assumed firm value reduces the value of equityas well as the value of the call, and increases volatility, which increases the value of equity and the value of the call. In this case, we find an option value of $7.03 and a value of equity of $13.30. Now, the value of equity is too low and the value of the option is too high. This suggests that we have gone too far with our reduction in firm value and increase in volatility. A value of the firm of $21 per share and a volatility of 68.36 percent yield the right values for equity and for the option on equity. Consequently, the value of the debt per share is $6.90. The value of the firm is therefore $105 million. It is divided between debt of $34.5 million and equity of $70.5 million. Once we have the value of the firm and its volatility, we can use the formula for the value of equity to create a portfolio whose value is equal to the value of the firm and thus can replicate dynamically the value of the firm just using the risk-free asset and equity. Remember that the value of the firm's equity is given by a call option on the value of the firm. Using the Black-Scholes formula, we have:
Inverting this formula, the value of the firm is equal to:
Note that we know all the terms on the right-hand side of this e uation. Hence, an investment of 1/ N ( d )of the firm's equity and of N (d- a T - t)FIN(d) units of the zero-coupon bond is equal to the value of the firm per share. Adjusting this portfolio dynamically over time insures that we have V(T) at maturity of the debt. We can scale this portfolio so that it pays off the value of the firm per share. With our example, the portfolio that pays off the value of the firm per share has an investment of 1.15 shares, and an investment in zero-coupon bonds worth $7.9 1.
?
18.1.3. Subordinated debt In principle, subordinated debt receives a payment in the event of bankruptcy only after senior debt has been paid in full. Consequently, when a firm is in poor financial condition, subordinated debt is unlikely to be paid in full and is more like an equity claim than a debt claim. In this case, an increase in firm volatility makes it more likely that subordinated debt will be aid off and hence increases the value of subordinated debt. Senior debt always falls in value when firm volatility increases.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
Credit Riskj and Credit Derivatives
To understand the determinants of the value of the subordinated debt, consider then the case where the senior debt and the subordinated debt mature at the same date. F is the face value of the senior debt and U is the face value of the subordinated debt. Equity is an option on the value of the firm with exercise price U + F since the shareholders receive nothing unless the value of the firm exceeds U + F. Figure 18.3 shows the payoff of subordinated debt as a function of the value of the firm. In this case, the value of the firm is:
D denotes senior debt, SD subordinated debt, and S equity. The value of equity is given by the call option pricing formula:
By definition, shareholders and subordinated debt holders receive collectively the excess of firm value over the face value of the senior debt, F, if that excess is positive. Consequently, they have a call option on V with exercise price equal to F. This implies that the value of the senior debt is the value of the firm V minus the value of the option held by equity and subordinated debt holders:
Having priced the equity and the senior debt, we can then obtain the subordinated debt by subtracting the value of the equity and of the senior debt from the value of the firm:
Both debt claims are zero-coupon bonds.They mature at the same tirne.The subordinated debt has face value U and the senior debt has face value F. Firm value isV(T).
/ Equity
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyond Plain Vanilla Risk Management
With this formula, the value of subordinated debt is the difference between the value of an option on the value of the firm with exercise price F + U and an option on the value of the firm with exercise price F. Consider a firm with value of $1 20 million. It has junior debt maturing in five years with face value of $50 million and senior debt maturing in five years with face value of $100 million. The interest rate is 10 percent and the volatility is 20 percent. In this case, we have F = $100 million and U = $50 million. The first call option is worth $60.385 million. It is sin~plythe equity in the absence of subordinated debt, which we computed before. T h e second call option is worth $36.56 million. The value of the subordinated debt is therefore $60.385M - $36.56M = $23.825 million. Using our formula for the credit spread, we find that the spread on subordinated debt is 4.83 percent, which is more than 10 times the spread on senior debt of 35 basis points. The fact that the value of subordinated debt corresponds to the difference between the value of two options means that an increase in firm volatility has an ambiguous effect on subordinated debt value. As shown in Figure 18.4, an increase in firm volatility can increase the value of subordinated debt. Subordinated debt is a portfolio that has a long position in a call option that increases in value with volatility and a short position in a call option that becomes more costly as volatility increases. If the subordinated debt is unlikely to pay off, the short position in the call is economically unimportant. Consequently, subordinated debt is almost similar to equity and its value is an increasing function of the volatility of the firm. Alternatively, if the firm is unlikely to ever be in default, then the subordinated debt is effectively like senior debt and inherits the characteristics of senior debt. The value of subordinated debt can fall as time to maturity decreases. If firm value is low, the value of the debt increases as time to maturity increases because there is a better chance that it will pay something at maturity. If firm value is high and debt has low risk, it behaves more like senior debt. Similarly, a rise in interest rates can increase the value of subordinated debt. As the interest rate rises, the value of senior debt falls so that what is left for the subordinated debt holders and equity increases. For low firm values, equity gets little out of the interest rate increase because equity is unlikely to receive anything at maturity, so the value of subordinated debt increases. For high firm values, the probability that the principal will be paid is high, so the subordinated debt is almost risk-free, and its value necessarily falls as the interest rate increases.
118.1.4. The pricing of debt when interest rates change randomly Unanticipated changes in interest rates can affect debt value through two channels. First, an increase in interest rates reduces the present value of promised coupon payments absent credit risk, and hence reduces the value of the debt. Second, an increase in interest rates can affect firm value. Empirical evidence suggests that stock prices are negatively correlated with interest rates. Hence, an increase in interest rates generally reduces the value of debt both because of the sensitivity of debt to interest rates and because on average it is associated wi.th an adverse shock to firm values. When we want to hedge a debt position, we therefore have to take into account the interaction between interest rate changes and firm value changes.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Credit Rrsks and Cvedrt Deriuatrves
Chapter 18
~
-
~
m
%
v
~
-
~
-
~
~
.
>
-
- T ~:-.--~-l
w
9-=--
~
-
-
, -~ --%--
Subordinated debt, firm value, and volatility
- - ,-.*<--
rnF>*,-
-- .? -*-.---..-" -
We consider subordinated debt with face value of $50 million and senior debt with face value of $100 million. The two debt issues mature in five years.The risk-free rate is I 0 percent. Panel A. Firm value is $20 million.
Value of subordinated debt
(.*-.$--tz"*rsr
6
Panel 0. Firm value is $200 million.
Value of subordinated debt
maturity 30
We consider the pricing of risky debt when the spot interest rate follows the Vasicek model discussed in Chapter 14. The change in.the spot interest rate over a period of length At is:
where r , is the current spot interest rate and E, is a random shock. When A is positive, the interest rate reverts to a long-run mean of k. With equation (18.14) describing how the interest rate evolves, the price of a zero-coupon bond at t that pays $1 at T, Pt(T),is given by the Vasicek model.
-7.
*qx < ,
'Figtr,~18.4
.,
Part 3
Beyond Pkain Vanilla Rirk Management
Suppose value and interest rate changes are correlated. Shimko, Tejima, and van Deventer (1993) show that with these interest rate dynamics the value of risky dcbt is:
To see how interest rate changes affect the price of debt, we price debt of face value of $100 million maturing in 5 years on a firm worth $120 million as we did before. When we assumed a fixed interest rate of 10 percent and a firm volatility of 20 percent, we found that the value of the debt was $59.6 15 million in section 18.1. We choose the parameters of the Vasicek model to be such that, with a spot interest rate of 10 percent, the price of a zero-coupon bond that pays $1 in 5 years is the same as with a fixed interest rate of I0 percent. This requires us to assume k to be 14.21 percent, the interest rate volatility 10 percent, and the mean reversion parameter 0.25. The volatility of firm value is 20 percent as before and the correlation between firm value changes and interest rate changes is -0.2. With these assumptions, the debt is then $57.301 1 million. Figure 18.5 shows how the various parameters of interest rate dynamics affect the price of the debt. We choose a firm value of $50 million, so that the firm could not repay the debt if it matured immediately. In Panel A, the value of the debt falls as the correlation between firm value and interest rate shocks increases. In this case, firm value is higher when the interest rate is high, so that the impact of an increase in firm value on the value of the debt is more likely to be dampened by a simultaneous interest rate increase. In Panel B, an increase in interest rate volatility and an increase in the speed of mean reversion reduce debt value. With high mean reversion, the interest rate does not diverge for very long from its long-run mean, so that we are closer to the case of fixed interest rates. However, with our assumptions, the long-run mean is higher than the current interest rate. Figure 18.6 shows that the debt's interest rate sensitivity depends on the volatility of interest rates. At highly volatile interest rates, the value of the debt is less sensitive to changes in interest rate. Consequently, if we were to hedge debt against changes in interest rates, the hedge ratio would depend on the parameters of the dynamics of interest rates.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Credzt Risks and Credit Derivatzves
Chapter 18
-. -- -. ,* - .-- - .--.--.., v<.-.-. .----. , ....Debt value and interest rate dynamics -
.. , *
,--r .$ ..
n-iv
r.,
r
l :
i-
,
-
-
-*
-'"*
.r*r
..,,--
.
-+
.,?-)*--.
.+
- %&TP
,ciViV. iViViViViV
*
18:6%
In the base case,firm value o f $50 million, the promised debt payment is $100 million, the maturity o f the debt is 5 years, the interest rate is set at I 0 percent, the speed of mean reversion parameter is 0.25, the volatility of the interest rate is I 0 percent, the correlation between firm value and the interest rate is -0.2. Panel A
Debt
Correlation
Panel B
0.1
Mean reversion parameter
Interest rate
0.4 0.5
1 8.1.5. VaR and credit risks Once we have a pricing model for the valuation of default-risky debt held by the firm, we can incorporate credit risk into the computation of firm-wide risk. Suppose we use the Merton model. Default-risky debt depends on firm value, which itself is perfectly correlated with the debtor's stock price. This makes the debtor's equity one additional risk factor. Suppose we want to compute a VaR measure for the firm, and the firm has just one risky asset: its risky debt. One way is to cornpute the deha-VaR by transforming the risky debt into a portfolio of the risk-free
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyond Plain VanzLla R ~ s kManagemenr
-T -=. - =- r T >* m - - T =v 5.-
+. v
v*,
*
---v
r
-s
2-
%. p- s.2
'W.
a>--*-
.-, -:-,-
T-".-"-s-T
*-
,"
%"-
--<*-.
q?c
lnterest rate sensitivity of debt
Firm value is $50 million, the promised debt payment is $100 million, the maturity of the debt is 5 years, the speed of mean reversion parameter is 0.25, the correlation between firm value and the interest rate is -0.2.
Debt value
45 42.5 40
37.5 Interest rate
Decimal interest rate
0.15 0.20
bond and of the debtor's equity if we are computing a VaR for a short period of time. A second way is to compute the Monte Carlo VaR by simulating equity returns and valuing the debt for these equity returns. If the firm has other assets, we must consider the correlations among the asset returns. Conceptually, the inclusion of credit risks in computations of VaR does not present serious difficulties. All the difficulties are in the implementation-but they are serious. The complexities of firm capital structures create important obstacles to valuing debt, and often debt is issued by firms with no traded equity, There are thus alternative approaches to debt pricing.
18.2. Beyond the Met-ton model Corporations generally have many different types of debt with different maturities, and most debt makes coupon payments when not in default. T h e Merton model approach can be used to price any type of debt. Jones, Mason, and Rosenfeld (1984) test this approach for a panel of firms that include investment-grade firms as well as firms below investment grade. They find that a naive model predicting that debt is riskless works better for investment-grade debt than the Merton model. In contrast, the Merton model works better than the naive model for debt below investment grade. As ~ o i n t e dout by Kim, Ramaswamy, and Sundaresan (1993), however, Merton's model fails to predict credit spreads large enough to match empirical data. They point out that from 1926 to 1986, AAA spreads ranged from 15 to 215 basis points, with an average of 77, while BAA spreads ranged from 5 1 to 787 basis points, with an average of 198. Yet they show that Merton's model cannot generate spreads in excess of 120 basis points. There are important difficulties in implementing the Merton model when debt makes coupon payments or a firm has multiple debt issues that mature at
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
Cvedil Risks and Credit Derivatrves
different dates. Consider the simple case where debt makes one coupon payment u at t' and pays F + u at T. We know how to value the coupon payment u since it is equivalent to a risky zero-coupon debt payment at t'. Valuing the right to F + u to be received at T is harder because it is contingent on the firm paying u at t ' .Taking the viewpoint of the equity holders simplifies the analysis. After the equity holders have paid the coupon at t', their claim on the firm is the same as the claim they have in our analysis in section 18.1, namely a call option on the firm with maturity at T with exercise price equal to the promised payment to the debt holders (which here is F + u). Consequently, by paying the coupon at t' the equity holders acquire a call option on the value of the firm at T with exercise price F + u. The value of equity at t is the present value of the call option equity holders acquire at t' if they pay the coupon. This is the present value of the payoff of a European call option maturing at t', since they get Max(S,q - u, 0), where St#is the value of equity at t'. Hence, at t, the equity holders have a call option on the equity value at t' with exercise price u-they have an option on an option, or a compound option. The value of debt at t is firm value minus a compound option. If we had an additional coupon at t", so that t' < t" < T, we would have to subtract from V at t a n option on an option on an option. This creates a considerable computational burden in computing debt value. This burden can be surmounted, but it is not trivial to do so. In practice, this difficulty is compounded by the difficulty that one does not know V because of nontraded debt. Another difficulty with the Merton model is that default is too predictable. Remember that to obtain prices of debt in that model, we make the Black-Scholes assumptions. We know that with these assumptions firm value cannot jump. As a result, default cannot occur unless firm value is infinitesimally close to the point where default occurs. In the real world, default is often more surprising. For instance, a run on a bank could make its equity worthless even though before the run its equity value was not close to zero. These problems have led to the development of a different class of models that take as their departure point a probabil& of default that evolves over time according to a well-defined process. Under this approach, the probability of default can be posirive even when firm value significantly exceeds the face value of the debt-this is the case if firm value can .jump. . The economics of default are modeled as a black box. Default either happens over an interval of time or it does not. Upon default, the debt holder receives a fraction of the promised claim. 'l'he recovery rate is the fraction of the principal recovered in the event of default. This recovery rate can be random or certain. Let's look at the simplest case and assume that the process for the probability of default is not correlated with the interest rate process and recovery in the event of default is a fixed fraction of the principal amount, 0, which does not depend on time. The bond value next period is D,, A , + u if the bond is not in default, where u is the coupon. If the debt is in default, its value is OF. In the absence of arbitrage opportunities, the bond price today, D,, is simply the expected value of the bond next period computed using risk-neutral probabilities discounted at the risk-free rate. Using qas the risk-neutral probability of default, it must be the case that:
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyond Plain Vanilla Risk Manugemcnt
In this equation, the value of the nondefaulted debt today depends on the value of the nondefaulted debt tomorrow. To solve this problem, we therefore start From the last period. In the last period, the value of the debt is equal to the principal amount plus the last coupon payment, F + u, or to OF. We then work backward to the next-to-the-last period, where we have:
If we know q and 0, we can price the debt in the next-to-the-last period and continue to keep worlung backward to get the debt value. How can we obtain the probability of default and the amount recovered in the event of default? If the firm has publicly traded debt, we can infer these parameters from the price of the debt. Alternatively, we can infer risk-neutral probabilities of default and recovery rates from spreads on debt with various ratings. Different applications of this approach can allow for random recovery rates as well as for correlations between recovery rates and interest rates or correlations between default rates and interesr rates. The empirical evidence shows that this approach works well to price swap spreads and bank subordinated debt.
18.3. Credit risk models There are several differences between measuring the risk of a portfolio of debt claims and measuring the risk of a portfolio of other financial assets. First, because credit instruments typically do not trade on liquid markets where we can observe prices, we cannot generally rely on historical data on individual credit instruments to measure risk. Second, the distribution of returns differs. We cannot assume that continuously compounded returns on debt follow a normal distribution. The return of a debt claim is bounded by the fact that investors cannot receive more than the principal payment and the coupon payments. In statistical terms, this means that the returns to equity are generally symmetric, while the returns to debt are skewed-unless the debt is deeply discounted. . The third difference is that firms often have debt issued by creditors with no
traded equity. A fourth difference is that typically debt is not marked to market in contrast to traded securities. When debt is not marked to market, a loss is recognized only if default takes place. Consequently, when debt is not marked to market, a firm must be able to assess the probability of default and the loss made in the event of default.
A number of credit risk models resolve some of the difficulties associated with debt portfolios. Some models focus only on default and on the recovery in the event of default. The most popular model of this type is CreditRisk+, from Credit Suisse Financial Products. It is based on techniques borrowed from the insurance industry for the modeling of extreme events. Other models are based on the marked-to-market value of debt claims. CreditMetricsTM is a risk model built on the same principles as those of RiskMetrics-. The purpose of this risk model is to provide the distribution of the value of a portfolio of debt claims, which leads to a VaR measure for the portfolio. The KMV model is in many ways quite similar to the CreditMetricsTM model, except that it makes direct use of the Merton
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Credit Risks and Credit Derivatives
Chapter 18
model in computing the probability of default.' All these models can be used to compute the risk of portfolios that include other payoffs besides those of pure debt contracts. For example, they call illclude swap contracts. As a result, these models talk about estimating the risk of obligors-all those who have legal obligations-to the firm-rather than debtors. To see how we can use the Merton model for default prediction, remember that it assumes that firm value is lognormally distributed Gith constant volatility and that the firm has one zero-coupon debt issue. If firm value exceeds the face value of debt at maturity, the firm is not in default. We want to compute the probability that firm value will be below the face value of debt at maturity of the debt becaise we are interested in forecasting the likelihood of a default. ib cornpute this probability, we have to Isnow the expected rate of return of the firm since the higher that expected rate of return, the less likely it is that the firm will be in default. Let p, be the expected rate of return of the firm value. In this case, the probability of default is simply:
i
Probability of default = N
ln(F) -in(\/)
-
p(T - t)
+ 0.502(T -
0llT-t
"1
where N denotes the cumulative normal distribution, F is the face value of the debt, V the value of the firm, T the maturity date of the debt, and o the volatility of the rate of change of V. Consider the case where a firm has value of $120 million, debt with face value of $100 million and maturity of five years, the expected rate of change of firm value is 20 percent, the volatility is 20 percent, and the interest rate is 5 percent. The probability that the firm will default is 0.78 percent. Figure 18.7 shows how the probability of default is related to volatility and firm value. As volatility increases, the probability of default increases. It can be substantial even for large firm values compared to the face value of the debt when volatility is high. We use the same approach to compute the firm's expected loss if default occurs. The loss if default occurs is often called loss given default or LGD. Since default occurs when firm value is Jess than the face value of the debt, we have to compute the expected value of V given that it is smaller than F. The solution is: Expected loss
FN
ln(F)
- ln(V)
- -(T - t ) + 0 . 5 0 2 ( ~-
(18.191
0.JT-t
1 Oldrich A. Vas~cek,Credit Valuat~on,KMV Corporation, 1984
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
,-.&-P-W..fi p
;
y .
'FGure
-----.
18.7
.
,
Beyond Plain Vanzlku Risk Manngmnent
.
-
7
u
,
- .-
-
-
. z *,-..
= - -
Probability of default
. - ., '
. ..
*
.- -
.
- - - .-,
The firm has debt with face value of $100 million due in five years.The firm's expected rate of return is 20 percent.
Firm value
501-.
The expected loss is $1 00,6 14. Figure 18.8 shows how the expected loss depends on firm value and its volatility.
18.3.1. CreditRisk+ CreditRisk+ allows only two outcomes for each firm over the risk measurement period: default and no default. If default occurs, the creditor experiences a loss of fixed size. The probability of default for an obligor depends on its rating, the realization of K risk factors, and the sensitivity of the obligor to the risk factors. The risk factors are common across all obligors, but sensitivity to the risk factors differs across obligors. Defaults across obligors covary only because of the K risk factors. Conditional on the risk factors, defaults are uncorrelated across obligors. The conditional probability of default for an obligor is the probability of default given the realizations of the risk factors, while the unconditional pobability of default is the probability obtained if we do not know the realizations of the risk factors. For example, if there is only one risk factor, say, macroeconomic activity, we would expect the conditional probability of default to be higher when macroeconomic activity is poorer. The unconditional probability of default in this case is the probability when we do not know whether macroeconomic activity is poor or not.
I f p i ( x ) is the probability of default for the ith obligor conditional on the realizations of the risk factors, and x is the vector of risk factor realizations, the model specifies that:
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
Credzt Rzsk~and Credzt Dertvatiues
,
- -
The expected loss and its dependence on volatility
> - < . , -
..
?=~;trr.rvc18.8
The firm has value of $120 million, the face value o f the debt is $100 million, the expected rate of change of firm value is 20 percent, and the interest rate is I 0 percent.
.4 F i r m volatility
where ~ q ; is the ) unconditional probability of default for obligor i given that it belongs to grade G. A natural choice of the grade of an obligor would be its public debt rating if it has one. Often, obligors may not have a rating, or the rating of the company may not reflect the riskiness of the debt. Bank debt has different covenants than public debt, which makes it easier for banks to intervene when the obligor becomes riskier. As a result, bank debt is less risky than otherwise comparable public debt. The bank internal evaluation system often grades loans on a scale from one to ten. A bank internal grading system could be used to grade obligors.
'The risk factors can take only positive values and are scaled so that they have a mean of one. 'l'he model also assumes that the risk factors follow a specific statistical distribution (the gamma distribution). If the kth risk factor has a realization above one, this increases the probability of default of firm i in proportion to the obligor's exposure to that risk factor measured by w;k. Once we have computed the probability of default for all the obligors, we can get the distribution of the total number of defaults in the portfolio. The relevant distribution is the distribution of losses. The model expresses the loss upon default for each loan in standardized units. A standardized unit could be $1 million. The exposure to the ith obligor, v ( i ) , would be an exposure of v(i) standardized units. A mathematical function gives the unconditional probability of a loss of n standardized units for each value of n. We can also get the volatility of the probabi1i.t~of a loss of n standardized units since an unexpectedly high realization of the vector of risk factors will lead to a higher than expected loss. The Creditask+ model is easy to use, largely because of some carefully chosen assumptions about the formulation of the probability of default and the distribution of the risk factors. The statistical assumptions of the model are such that
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyomd Plu~nVanilla Risk Manngenzeni
an increase in the volatility of the risk factor has a large impact on the tail of the distribution of the risk factor. Gordy (2000) provides simulation evidence on the CreditRisk+ model. His base case has 5,000 obligors and a volatility of the risk factor of 1. The distribution of grades for obligors is structured to correspond to the typical distribution for a large bank according to Federal Reserve Board statistics. He assumes that the loss upon default is equal to 30 percent of the loan for all loans. Losses are calculated as a percentage of outstanding loans. For a lowquality portfolio (the model rating is BB), the expected loss is 1.872 percent and its volatility is 0.565 percent. The distribution of losses is skewed, so the median of 0.769 percent is much lower than the expected loss. There is a 0.5 percent probability that the loss will exceed 3.320 percent. As the volatility of the risk factor is quadrupled, the mean and standard deviation of losses are essentially unchanged, but there is a 0.5 percent probability that the loss will exceed 4.504 percent.
18.3.2. CreditMetricsTM J.R Morgan's CreditMetrics-
offers an approach to evaluate the risk of large portfolios of debt claims on firms with realistic capital structures. To see how the CreditMetricsTMapproach works, we start from a single debt claim, show how we can measure the risk of the claim with the approach, and then extend the analysis to a portfolio of debt claims.2 Consider a debt claim on Almost Iffy Inc. We would like to measure the risk of the value of the debt claim in one year using VaR. To do that, we need to know the fifth quantile of the distribution of the value of the debt claim if we use a 5 percent VaR.
Our first step in using the CreditMetricsTM approach is to figure out a rating class for the debt claim. Say that we decide the claim should have a rating BBB. Almost I f v s debt could remain at that rating, could improve if the firm does better, or could worsen if default becomes more likely. There is a historical probability distribution that a claim with a BBB rating will move to some other rating. Across claims of all ratings, the rating transition matrix presented in Table 18.1 gives us the probability that a credit will migrate from one rating to another over one year. Such matrices are estimated and made available by rating agencies. For a debt claim rated BBB, there is a 1.17 percent probability that the debt claim will have a B rating next year. To obtain the distribution of the value of the debt claim, we compute the value we expect the claim to have for each rating in one year. Using the term structure of bond yields for each rating category, we can get today's price of a zero-coupon bond for a forward contract to mature in one year. Table 18.2 provides an example of one-year forward zero curves. The rows of the table give us the one-year forward discount rates that apply to zero-coupon bonds maturing in the following four years. We assume coupons are promised to be paid exactly in one year and at the end of each of the four subsequent years. Say that the coupon is $6. We can use the
2 The CreditMetricsTM Technical Manual, available on RiskMetrics website, analyzes the example used here in much greater detail. The data used here is obtained from that manual.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Credzt Rzsks and Cvedzt Dertvatives
Chapter 18
Initial rating- AAA -
Rating at yeafiend (%)
AA
A
BBB
BB
B
CCC
Default
AAA AA A
90.8 1
8.33
0.68
0.06
0.12
0
0.70
90.65
7.79
0.64
0.06
0.14
0 0.02
0 0
0.09
2.27
9 1.05
5.52
0.70
0.26
0.0 1
0.06
BBB
0.02
0.33
5.95
86.93
5.30
1.17
0.12
0.18
0
0.1 I
0.24
0.43
6.48
83.46
4.07
5.20
0.22
0
0.22
1.30
2.38
1 1.24
64.86
19.79
B
CCC
forward zero curves to compute the value of the bond for each possible rating next year. For example, using Table 18.2, if the bond migrates to a RB rating, the present value of the coupon to be paid two years from now as of next year is $6 discounted at the rate of 5.55 percent. If the bond defaults, we need a recovery rate, which is the amount received in the event of default as a fraction of the principal. Suppose that the bond is a senior unsecured bond. Using historical data, the recovery rate for this type of bond is 5 1.13 percent. We can compute the value of the bond for each rating class next year and assign a probability that the bond will end up in each one of these rating classes. Table 18.3 shows the result of such calculations. A typical VaR measure would use the fifth percentile of the bond price distribution, which is a BB rating and a value of $102.02. The mean value of the bond is $107.09, so that the fifth percentile is $5.07 below the mean. Say that the price today is $108. There is a 5 percent chance we will lose at least $5.98.
---
-
---- ----, One-year forward zero curves f o r various rating classes (%)
7
Rating class AAA
-rr-
? --lr-.-*..---r.c"r----.
Year I
Year 2
Year 3
Year 4
3.60
4.17
4.73
AA
3.65
4.22
4.78
5.12 5.17
A BBB BB B CCC
3.72
4.32
4.93
5.32
4.10
4.67
5.25
5.63
5.55
6.02
6.78
7.27
6.05
7.02
8.03
8.52
15.05
15.02
14.03
13.52
------rrm
-IF-
-.- --
%bLe
---.". 18.2 n-
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Tvmw,,
iTglh".m~~,F,lRy-TF--~~.v----mymm**rr-
Table 78.2
Beyond Plain Vanzlla RtsR Managanmt
nt-,
r---v-..
+----
- . - .-- --
-,?e"-." -.,-.+.
-->*"
z:=v
--
-V"q,
-r
7-
,.-.
vz-.-.
The value of the debt claim across rati classes and associated probabilities Y e a ~ e n dratine
AAA AA A BBB BB
B
CCC Default
Probability (?A)
0.02 0.33 5.95 86.93 5.30 1.17 0.12 0.18
Bond value plus coupon($)
109.37 1 09.19 108.66 107.55 102.02 98.10 83.64 51.13
If we have many claims, we have to make an assumption about the correlations among the various claims. If we know the correlations, we can measure the risk of a portfolio of debt claims using the distribution of the portfolio value. For example, suppose that we have an AAA bond and a B bond whose migration probabilities are independent. That is, knowing that the B bond migrates from a B rating to a BB rating provides no information about the likelihood that the AAA bond will migrate to an AA rating. We compute the probabilities of the transitions for each bond independently and multiply them to obtain the joint probability. Using the transition probability matrix in Table 18.1, we know that the probability of a B bond moving to a BB rating is 6.48 percent and that the probability of an AAA bond moving to an AA rating is 8.33 percent. The probability of these two events happening at the same time is the product of the probabilities of the individual events, 0.0648 x 0.0833 = 0.0054, or 0.54 percent. We can compute the value of the portfolio for that outcome. Once we have computed the value of the portfolio for each possible outcome as well as the probability of each outcome, we have a distribution for the value of the portfolio, and we can compute the fifth percentile to obtain a VaR measure. If the probabilities of the two bonds moving to a particular rating are not independent, the probability that the B bond moves to BB given that the AAA bond moves to AA is not the product of the probability of the B bond moving to BB and the probability of the AAA bond moving to AA. We have to know the probability that the two bonds will move that way. In other words, we need to know the joint distribution of bond migrations. Note that the values of the portfolio for each possible outcome are the same whether the bond migrations are independent or not. The probabilities of the various outcomes differ depending on the migration correlations. Once we know the probabilities of each outcome, we can compute a distribution for the bond portfolio and again compute its VaR. The major difficulty using the CreditMetricsTM approach is computing the joint distribution of the migrations of the bonds in the portfolio. One way is to use historical estimates for the joint probabilities of bond migrations. In other words, we could figure how often AAA bonds move to an AA rating and B bonds
Chapter 18
Credid Rijks and Credij Derivatives
move to a BB rating. This historical frequency would give us an estimate of the probability that we seek. Once we have the joint probability distribution of transitions for the bonds in the portfolio, we can compute the probability distribution of the portfolio. In general, though, the historical record of rating migrations will not be enough. The correlation among the rating migrations of two bonds depends on other factors. For example, firms in the same industry are more likely to migrate together. To improve on the historical approach, CreditMetricsTM proposes an approach based on stock returns. Suppose that a firm has a given stock price, and we want to estimate its credit risk. From the rating transition matrices, we know the probability of the firm moving to various ratings. Using the distribution of the stock return, we can compute ranges of returns corresponding to the various ratings-if there is a 5 percent probability of default, a default event corresponds to all stock returns that have a probability of at least 95 percent of being exceeded over the period over which credit risk is computed. Proceeding this way we can produce stock returns corresponding to the various rating outcomes for each firm whose credit is in the portfolio. The correlations between stock returns can then be used to compute probabilities of various rating outcomes for the credits. For instance, if we have rwo stocks, we can compute [he probability that one stock will be in the BB rating range and the other in the AA rating range. With a large number of credits, using stock returns to compute the joint distribution of outcomes is time-consuming. To simplify the computation, CreditMetricsTM recommends using a factor modej in which stock returns depend on country and industry indices as well as on unsystematic risk. The CreditMetricsTM technical manual shows how to implement such a model.
18.3.3. The KMV model KMV derives default probabilities using the "Expected Default Frequency" for each obligor from an extension of equation (18.18). KMV computes similar probabilities of default, but assumes a slightly more complicated capital structure in doing so. With KMV's model, the capital structure includes equity, short-term debt, long-term debt, and convertible debt. KMV then solves for the firm value and volatility. One advantage of the KMV approach is that probabilities of default are obtained using the current equity value, so that any event that affects firm value translates directly into a ching; in the probability bf default. Ratings change only with a lag. Another advantage is that probabilities of default change continually rather than only when ratiigs chang;. An increase in equity value reduces thk probability of default. In the CreditMetricsTM approach, the value of the firm can ;hang substantially, but the probability of d e f d t may remain the same because the firm's rating does not change.
KMV uses an approach inspired by the CAPM to obtain the expected growth of firm values that is required to implement equation (18.18) and uses a factor model to simplify the correlation structure of firm returns. The assumptions used imply an analytical solution for the loss distribution, so that simulation is not needed to compute a credit VaR with the KMV model.
--
Part 3
Beyorid Plain Vanrllcl Rirk Management
18.3.4. Some difficulties with credit portfolio models The credit portfolio models just discussed present an important advance in measuring credit risk. At the same time, however, the models as presented have obvious limitations. Some have addressed some of these limitations in implementing the models and other models have been developed trying to avoid some of these limitations, but these models as described are the most popular. Models in their most common implementations do not take into account changes in interest rates or credit spreads. Yet, we know that the value of a portfolio of debt can change both because of changes in default risk and changes in interest rates or credit spreads. Nor do the models do much to take into account current economic conditions. As the economy moves from expansion to recession, the distribution of defaults changes dramatically. For example, default numbers reached a peak in 199 1, a recession year, then fell before reaching another peak in 2001, another recession year. Further, the transition correlations increase in recessions. Models that use historical transition matrices cannot take into accounc changing economic conditions.
1 8.4. Credit derivatives Credit derivatives are financial instruments whose payoffs are contingent on credit risk realizations. For most credit derivatives, the payoff depends on the occurrence of a "credit event" for a reference entity. Generally, a credit event is (1) failure to make a required payment, (2) restr;cturing that makes any creditor worse off, (3) invocation of cross-default clause, and (4) bankruptcy. Generally, the required payment or the amount defaulted will have to exceed-a minimum value (e.g., $10 million) for the credit event to occur.3 Credit derivatives are designed as hedging instruments for credit risks. Consider a bank that has credit exposure to many obligors. Before the advent of loan sales and credit derivatives, banks managed their credit risk mostly through diversification. The problem with that approach to managing credit risk is that it forces a bank to turn down customers with which it has valuable relationships. With a credit derivative, a bank can make a loan to a customer and then hedge part or all of this loan by buying a credit derivative. A highly visible example of such a way to use credit derivatives is discussed in Box 18.2, Citigroup and Enron. Except for a futures contract discussed later, credit derivatives are not traded on exchanges. They are over-the-counter instruments. However, firms can also issue securities publicly that provide them with credit protection. The simplest credit derivative is a put that pays the loss on debt due to default at maturity. A put on the firm value with the same maturity as the debt and with an exercise price equal to the face value of the debt is a credit derivative, called a credit default put, that compensates its holder for che loss due to default if such a loss occurs. The put gives its holder the option to receive the exercise price in exchange of the debt claim. Since the put pays the loss incurred by the debt holder if default takes place, a portfolio of the risky debt and the put option is
3 For a description of the documentation of a credit derivative trade, see "Inside a credit trade," Derivatives Strategy, 1998 (December), 24-28.
Credit Risks and Credzt Derivatives
Chapter 18
derable e'xposure Citigroup h 1 in 200(1. At tha t time, % was a successful company. It had equity capitafization in excess. of $50 billion ar the start of the year. Its net income for the year was $979 milliofi. Eriron's senior unsecured debt's rating was upgraded, m that it finished the year rated, -. . BAA1 by Moody's and BBB+ by Standard and 'Poor's. Despite all rhis, group chose to issue securities for $1.4 billion from August 2000 to May t h a ~effectively hedged Citigroup's exposure to Enrom.
,
Enron's senior unsecured debt kept its ratings until October 2001. In December 2001, Enron's rating was a D; it was bankrupt. Citigroup had a loan exposure of $1.2 billion. It also had some insurance-related obligations. It had c dlaterd for about Ihalf of the loan -exposure. Most likiely, its p 1 :losses we1re covereld by the securities it had i,ssued.
.
. TL,llr;ac ,, ,*..".*.,,. a, r;uuluco
- .
vvorked' as fol.lows. C i t i b a n ~uadccd a trust. 1m a L ~LbLL 13sued five-year notes with.fixed interest paymenrs. The proceeds were iri\irested in high-quality debt. If Ehron did not go bankrupt, the investors would rt:ceive A- principal after five yeax. Tf Enron did " go bankrupt, Citigroup had the ,.:,-At " swap En1:on's deb t tk Citigyoup for the secu rities in Ithe trust. 'A
7.
1
~ of 7.37 percel~ tAt Citigrou]3 prom is^ed a c o uJon . the: time, B1 were promising 8.07 percent. However, according to a presentation by EI~ron's treasurer to. Standard and Poor's in 2000, Enron debt was trading above iits rating, which-led him to pitch a rating of AA. At the same time, he explaineii that the off-balance sheet debt was not material to E n ~ o n . Source Daniel Altman,"How C~t~group hedged bets on Enron," New York T~mes,February 8,2002
equivalent to holding default-free debt since the risk of the debt is offset by the purchase of the put. We already priced such a put when we valued In-The-Mail's deb.t, since that debt was worth risk-free debt minus a put. The holder of In-TheMail debt was short a put on firm value; by buying the credit default put, the holder of the debt eliminates his credit risk by acquiring an offsetting position in the same put. The most popular credit derivatives involve swap contracts.* One type of contract is called a credit default swap. With this swap, party A makes a fixed annual payment to party B, while party B pays the amount lost if a credit event occurs. For example, if Supplier Inc. in our example wants to get rid of the credit risk of In-The-Mail Inc., it can enter a credit default swap with a bank. It makes fixed payments to the bank. If In-The-Mail Inc. defaults at maturity, the bank pays Supplier Inc. the shortfall due to default (face value minus fair value of the debt at the time of default). The credit default swap for Supplier Inc. is effectively equivalent to buying a credit default put but paying for it by installment. Note
4
Dominrc Baldwin, "Business is boom~ng," Credrt Risk Spec~alReport,
Risk, April 1999, 8.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyo~zdPlain Vanilla Risk Manngement
that the debt will in general require interest payments before maturity and covenants to be respected. If the obligor fails in fulfilling its obligations under the debt contract, there is a credit event. With the credit event, the default payment becomes due. The credit default swap can have physical delivery, so that Supplier Inc. would sign over the loan to the bank in the event of a default and would receive a fixed payment. Physical delivery is crucial for loans that do not have a secondary market, but physical delivery of loans involves tricky and time-consuming issues. Borrowers often object to having their loans signed over. The settlement period for a credit default swap with physical delivery tends to be longer than for a bond trade. If the transfer of a loan faces objections from the borrower, the settlement might extend beyond 30 days.5 A credit default exchange swap requires each party to pay the default shortfall on a different reference asset. Two banks might enter a credit default exchange swap for Bank A to pay the shortfall on debt from Widget Inc. and Bank B to pay the shortfall on debt from In-The-Mail Inc. This way, BankA reduces its exposure to In-The-Mail Inc. and Bank B reduces its exposure to Widget Inc. Another popular structure is the total return swap. The party seeking to buy insurance against credit risks receives the return on a risk-free investment and pays the return on an investment with default risk. Suppose a bank, the protection buyer, owns a debt claim worth $80 million today that pays interest of $6 million twice a year in the absence of default for the next five years. In a total return swap, the bank pays what it receives from the debt claim every six months. Assuming that the issuer of the debt claim is not in default, the bank pays $6 million every six months. If the issuer does not pay interest at some due date, then the bank pays nothing. In return, the bank might receive six-month LIBOR on $80 million. At maturity, the obligor repays the principal if he is not in default. Suppose the principal is $100 million. In this case, the bank gets a payment at maturity of $20 million corresponding to the final payment of $100 million minus the initial value of $80 million to the swap counterparty. Or, if the obligor is in default and pays only $50 million, the protection buyer receives from the swap counterparty $80 million minus $50 million, or $30 million. This total return swap guarantees to the bank the cash flows equivalent to the cash flows of a risk-free investment of $80 million. Pricing a total return swap is straightforward, since it is effectively the exchange of a risky bond for a default-free bond. At initiation, the two bonds have to have the same value. Another credit derivative is a futures contract. The Chicago Mercantile Exchange Quarterly Bankruptcy Index (QBI) futures contract has been traded since April 1998. The QBI is the total of bankruptcy filings in U.S. courts over a quarter. Most bankruptcies are filed by individuals, which makes the contract appropriate to hedge portfolios of consumer debts, such as credit card debt. The contract is cash settled and the index level is the number of bankruptcy filings in thousands during the quarter preceding contract expiration. At matu-
5
Dwight Case, "The dev~l'sIn the details," Risk, August 2000, 26-28.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
rity, the futures price equals the index level. The settlement variation is the change in the futures price times $1,000. The minimum increment in the futures price is $0.025.
18.5. Credit risks of derivatives Since the value of an option is never negative whereas a swap can alternate beween positive and negative values, it is not surprising thar the credit risks of options are easier to evaluate than the credit risks of swaps. An option with default risk is called a d n e r a b l e option. At maturity, the holder of an option receives the promised payment only if the writer can make the payment, Suppose rhe writer is a firm with value V and the option is a European call on a stock with price S. The exercise price of the call is K. Without dehull: 'isk, the option holder receives Max(S - K, 0 ) at maturity. With a vulnerable oprion, the holder receives the promised payment only if it is smaller than V, so that the payoff of the call is: Max[Min(V, S - Kl, 01
(18.21)
The current value of the call with default risk is just the present value of this payment. There is no closed-form solution for su& an optLon, but it is not diffi;cdt to evaluate its value using a Monte Carlo simulation. The cotrelacion between the value of the fum and the value of the option's underlying asset plays an extremely important role in valuation of the vulnerable option. Suppose that V and S are strbngly negatively correlated. In this case, it could be that the option has lictle value because V is low when the option pays off. I f V and S are strongly positively correlated, the option might have almost no credit risk because V is always high when S is high. If an option has credit risk, it becomes straightforward to write an option contract that eliminates that credit risk. The appropriate credit derivative is one that & pays. the difference between a call without default risk and the vulnerable call:
If we can price the vulnerable call, we can also price the credit derivative that insures the call.
An alternative approach is to compute the probability of default and apply a recovery rate if default occurs. In this case, the option is a weighted average of an option without defaulc risk and of rhc present value of the payoff if default occurs. Say that the option can default only at maturity and do& ;o with probability p. If default occurs, the holder receives a fraction z of the vaIue of the option. In this case, the value of the option today is (1 - p) c + pzc, where c is the value of the option without default risk. This approach provides a rather simple way to incorporate credit risk in the value of the option when the probability of default is independent of the value of the underlying asset of the option. Say that the probability of default is 0.05 and the recovery rate is 50 percent. In this case, the vulnerable call is worth
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Beyond Plain Vanilla Risk Managonat
- 0.05) c +
0.05 x 0.5 x c, which is 97.5 percent of the value of the call without default risk.
(I
As we saw in Chapter 16, it is often the case that the counterparties to a swap enter margin arrangements to reduce default risk. Nevertheless, swaps can entail default risk for both counterparties. Netting means that the payments between the two counterparties are netted out, so that only a net payment has to be made. We assume that netting takes place and that the swap is treated like a debt claim. If the counterparty due to receive net payments is in default, that counterparty still receives the net payments. This is called the full two-way payment covenant. In a limited two-way payment covenant, the obligations of the counterparties are abrogated if one party is in default. With these assumptions, the analysis is straightforward when the swap has only one payment. Suppose a market maker enters a swap with a risky credit. The risky credit receives a fixed amount F at maturity of the swap-the fixed leg of the swap-and pays S. S could be the value of equity in an equity swap or could be a floating rate payment determined on some index value at some point after the swap's inception. Let V be the value of the risky credit net of all the debt that is senior to the swap. In this case, the market maker receives S-F in the absence of default risk. This amount can be positive or negative. If the amount is negative, the market maker pays F-S to the risky credit for sure. If the amount is positive, the market maker receives S-F if that amount is less than V, The swap's payoff to the market maker is:
The payment that the risk-free counterparty has to make, F, is chosen so that the swap has no value at inception. Since the risk-free counterparty bears the default risk, in that it may not receive the promised payment, it reduces F to take into account the default risk. To find F, we have to compute the present value of the swap payoff to the market maker. The first term in equation (18.23) is minus the value of a put with exercise price F on the underlying asset whose value is S. The second term is the present value of an option on the minimum of two risky assets. Both options can be priced. The correlation between V a ~ l dS plays a crucial role. As this correlation falls, the value of the put is unaffected, but the value of the option on the minimum of two risky assets falls because for a low correlation it will almost always be the case that one of the assets has a low value. Swaps generally have multiple payments, however, so this approach will work only for the last period of the swap, which is the payment at T, At the payment date before the last payment date, T - At, we can apply our approach. At T - 2A t, however, the market maker receives the promised payment at that dare plus the promise of two more payments: the payment at T - At and the payment at T. The payment at T - A t corresponds to the option portfolio of equation (18.23), but at T - At the market maker also has an option on the payment of date T which is itself a portfolio of options. In this case, rather than having a compound option, we have an option on a portfolio of options. Valuation of an option on a
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Cvedit Rixkx and Creclit Derivatives
Chapter 18
-
portfolio of options is difficult to handle analytically, but as long as we know the dynamics that govern the swap payments in the default-free case as well as when default occurs, we can use Monte Carlo analysis.
18.6. Summary We have developed merhods to evaluate credit risks for individual risky claims, for portfolios of risky claims, and for derivatives. The Merton model allows us to price risky debt by viewing it as risk-free debt minus a put written on the firm issuing the debt. The Merton model is practical mostly for simple capital structures with one debt issue that has no coupons. ,Other approaches to pricing risky debt model the probability of default and then discount the risky cash flows from debt using a risk-neutral distribution of the probability of default. Credit risk models such as the ~ r e d i t ~ i s kmodel, + the CreditMetricsTM model, and the KMV model provide approaches to estimating the VaR for a portfolio of credits. Credit derivatives can be used to hedge credit risks.
credit default swap, 597 credit event, 596 credit risk, 572 credit spread, 575 CreditMetricsTM,588 KMV model, 595
?&died
loss given default (LGD), 5 89 obligors, 589 rating transition matrix, 592 recovery rate, 593 vulnerable option, 599
@estio~s
1. Vlrhy is equity an option? 2. Why are you doing the equivalent of writing a put when you buy risky debt?
3. What is Merton's model for the pricing of debt?
4. What is a compound option? 5. How can you use the risk-neutral distribution of default to price coupon debt?
6. Why is it not reasonable to estimate the VaR of a portfolio of debt using 1.65 times the volatility of the return of the portfolio?
7. What is CreditRisk+? 8. What is CreditMetricsm?
9. What is a credit-default swap? 10. Why is it more difficult to evaluate the credit risk of a swap than to evaluate the credit risk of a risky zero-coupon bond?
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
@----
Part 3
Beyond Plain Vanilla Rirk Managnnent
1 . Debt can be priced using the Merton model. You are told that an increase in the volatility of firm value can increase the value of senior discount debt on the firm because in some cases debt is like equity and equity increases in value as firm volatility increases. Is this argument correct? 2. Consider a firm with a debt payment due in five years. The debt is not traded, so that firin value does not correspond to a traded asset. The assumptions that make the Merton model work hold. The longest maturity option traded on the firm's equity matures in one year. Assume that you know the volatility of the return of the firm and you know the firm value. How could you form a portfolio strategy that pays the same amount as the debt in five years? Extra credit: Provide portfolio weights if firm value volatility is 50 percent, interest rate is constant at 5 percent, firm value is $1 billion, and face value of debt is $1.2 billion.
3. Given your answer in question 2, what are the implications for your portfolio strategy of an unexpected increase in the firm's stock price caused by an increase in firm value? Extra credit: Using the data of the previous question, show how the portfolio changes if equity value increases by 10 percent because of a change in firm value.
4. Assume again that the assumptions that make the Merton model work hold, except that the firm pays a known dividend before maturity of its only debt, which is discount debt. How can you quantify the impact of a known future dividend payment on the value of discount debt? Extra credit: Using the data in the extra credit portion of question 3, assume a dividend payment of $1 00 million in three years. Wliat is the impact of that payment on firm value?
5. Suppose that you compute a one-year VaR of a portfolio using the deltaVaR approach. The assumptions that make the Merton model work hold. You want to include in your VaR computation discount debt that matures in sixteen months. Somebody points out to you that your VaR computation has a significant probability that the discount debt will pay more than par. Is that right?
6 . Attending a conference on credit risk, an attendee tells you that he computes the-probability of default for a firm as the cumulative normal that multiplies P,(T)F in equation (18.3). Has he discovered a better mousetrap or does he have a biased estimate of the probability of default? If he has a biased estimate, what is the bias? Extra credit: Using the data from question 3, compute the probability of default and the expected loss for the debt. How does your answer differ from the one proposed by the conference attendee?
7. At the same conference, you find an old friend. She emphatically declares that, since her firm does not mark loans to market, she uses CreditRisk+
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Chapter 18
Credit R i s b and Credit Deriuutzver
because CreditMetricsTM would be useless for her. What arguments could you make for her to use CreditMetricsm?
8. You are told by your boss that there is no reason for your balk to use a credit risk model because the bank has thousands of obligors, so that default risk is diversifiable. Is this argument correct if Merton's model applies to each of the obligors?
9. In an advertisement for credit derivatives, it is argued that the benefit of a credit default swap for the protection seller is that he "earns investment income with no funding cost."6 How would you analyze the impact on a bank of selling credit protection through a credit default swap?
10. You want to enter a swap with a bank. The bank does not want to make the trade because their credit risk model implies that the swap has too much credit risk. The bank agrees to enter the swap if it is marked to market, but your boss objects to such an arrangement. Why does the bank find such an arrangement more agreeable than a swap that is not marked to market? What arguments could your boss have to reject the arrangement?
Black and Sclioles (1 973) had a brief discussion of the pricing of risky debt. Merton (1974) provides a detailed analysis of the pricing of risky debt using the Black-Scholes approach. Black and Cox (1976) derive additional results, including the pricing of subordinated debt and the pricing of debt with some covenants. Geske (1977) demonstrates how to price coupon debt using the compound option approach. Stulz and Johnson (1985) show the pricing of secured debt. Longstaff and Schwartz (1995) extend the model so that default takes place if firm value falls below some threshold.. Their model takes into account interest rate risk as well as the possibility that strict priority rules will not be respected. Arnin and Jarrow (1992) price risky debt in the presence of interest rates changing randomly using the Black-Scholes approach with a version of the HeathJarrow-Morton model. Duffie and Singleton (1999) provide a detailed overview and extensions of the approaches that model the probability of default. Applications of this approach show that it generally works quite well. Perhaps the easiest application to follow is the work of Das and Tufano (1996). They extract probabilities of default from historical data on changes in credit ratings. Armed with these probabilities and with historical evidence on recovery rates and their correlations with interest rates, they price corporate debt. lnstead of using historical estimates of default probabilities and recovery rates, they could have extracted .ihese parameters from credit spreads and their study discusses how this could be done. Jarrow and Turnbull (1995) build an arbitrage model of risky debt where the probability of default can be obtained from the firm's credit spread curve. Jarrow, Lando, and Turnbull (1997) provide a general approach using credit ratings. Another
6 Barclays Cap~tal,"Applying credit derivatives to emerging markets," Cred~tR ~ s kSpecial Report, Advertising Supplement, Risk, November 1998.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
Part 3
Beyond Plaifz Vanilla Risk Manage?nent
interesting application is Duffie and Singleton (1997), who use this approach to price credit spreads embedded in swaps. Madan and Unal (1998) price securities of savings and loan associations. They show how firm-specific information can bc incorporated in the default probabilities. These various approaches to pricing risky claims have rather weak corporate finance underpinnings. They ignore the fact that firms act differently when their value falls and that they can bargain with creditors. Several recent papers take strategic actions of the debtor into account. Leland (1994) models the firm in an intertemporal setting taking into account taxes and the ability to change volatility. Anderson and Sundaresan (1996) take into account the ability of firms to renegotiate on the value of the debt. Deviations from the doctrine of absolute priority by the courts are described in Eberhart, Moore, and Roenfeldt (1990). Crouhy, Galai, and Mark (2000) provide an extensive comparative analysis of the CreditRisk+, CreditMetricsm, and KMV models. Gordy (2000) provides evidence on the performance of the first two of these models. Jarrow and Turnbull (2000) critique these models and develop an alternative. Johnson and Stulz (1987) were the first to analyze vulnerable options. A number of papers provide formulas and approaches to analyzing the credit risk of derivatives. Jarrow and Turnbull (1995) provide an approach consistent with the use of the HJM model. Jarrow and Turnbull (1997) show how the approach can be implemented to price the risks of swaps. The CME-QBT contract is discussed in Arditti and Curran (1998). Longstaff and Schwartz (1995) show how to value credit derivatives.
From From Risk Risk Management Management andand Derivatives, Derivatives, 1st1st edition, edition, by by René René M.M. Stulz. Stulz. © 2003. © 2003. Reprinted Reproduced with with permission permission of South-Western, of South-Western, a division a division of Thomson of Thomson Learning: Learning: www.thomsonrights.com. www.thomsonrights.com. Fax 800 Fax730-2215. 800 730-2215.
This chapter has permission been reproduced with permission from Market, Understanding Market, Credit and Operational Risk: The At Reproduced with from Understanding Credit and Operational Risk: The Value Value at Risk Approach, by Linda Allen, Jacob Boudoukh and Anthony Saunders, published by Blackwell Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. Publishing, Oxford 2004 (© Blackwell Publishing, all rights reserved).
EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
5.1 Top-Down Approaches to Operational Risk Measurement 5.1.1 Top-down vs. bottom-up models 5.1.2 Data requirements 5.1.3 Top-down models 5.2 Bottom-Up Approaches to Operational Risk Measurement 5.2.1 Process approaches 5.2.2 Actuarial approaches 5.2.3 Proprietary operational risk models 5.3 Hedging Operational Risk 5.3.1 Insurance 5.3.2 Self -insurance 5.3.3 Hedging using derivatives 5.3.4 Limitations to operational risk hedging 5.4 Summary Appendix 5.1 Copula Functions
All business enterprises, but financial institutions in particular, are vulnerable to losses resulting from operational failures that undermine the public's trust and erode customer confidence. The list of cases involving catastrophic consequences of procedural and operational lapses is long and unfortunately growing. To see the implications of operational risk events one need only look at the devastating loss of reputation of Arthur Andersen in the wake of the Enron scandal, the loss of independence of Barings Bank as a result of Nick Leesonrs rogue trading operation, or UBS' loss of US$100 million due to a trader's
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
159
error, just to name a few examples.' One highly visible operational risk event can suddenly end the life of an institution. Moreover, many, almost invisible individual pinpricks of recurring operational risk events over a period of time can drain the resources of the firm. Whereas a fundamentally strong institution can often recover from market risk and credit risk events, it may be almost impossible to recover from certain operational risk events. Marshall (2001) reports that the aggregate operational losses over the past 20 years in the financial services industry total approximately US$200 billion, with individual institutions losing more than US$500 million each in over 50 instances and over US$1 billion in each of over 30 cases of operational f a i l ~ r e sI.f~anything, the magnitude of potential operational risk losses will increase in the future as global financial institutions specialize in volatile new products that are heavily dependent on technology. Icingsley et al. (1998) define operational risk to be the "risk of loss caused by failures in operational processes or the systems that support them, including those adversely affecting reputation, legal enforcement of contracts and claims" (p. 3). Often this definition includes both strategic risk and business risk. That is, operational risk arises from breakdowns of people, processes, and systems (usually, but not limited to technology) within the organization. Strategic and business risk originate outside of the firm and emanate from external causes such as political upheavals, changes in regulatory or government policy, tax regime changes, mergers and acquisitions, changes in market conditions, etc. Table 5.1 presents a list of operational risks found in retail banking. Operational risk events can be divided into high frequencyllow severity (HFLS) events that occur regularly, in which each event individually exposes the firm to low levels of losses. In contrast, low frequencylhigh severity (LFHS) operational risk events are quite rare, but the losses to the organization are enormous upon occurrence. An operational risk measurement model must incorporate both HFLS and LFHS risk events. As shown in figure 5.1, there is an inverse relationship between frequency and severity so that high severity risk events are quite rare, whereas low severity risk events occur rather frequently. In order to calculate expected operational losses (EL),one must have data on the likelihood of occurrence of operational loss events (PE) and the loss severity (loss given event, LGE), such that EL = PE x LGE. Expected losses measure the anticipated operational losses from HFLS events. VaR techniques can be used to measure unexpected losses.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing.
Table 5.1 Operational risk categories Process risk Pre-transaction: marketing risks, selling risks, new connection, model risk Transaction: error, fraud, contract risk, product complexity, capacity risk Management information Erroneous disclosure risk People risk Integrity: fraud, collusion, malice, unauthorized use of information, rogue trading Competency Management Key personnel Health and safety Systems risk Data corruption Programming errorslfraud Security breach Capacity risks System suitability Compatibility risks System failure Strategic risks (platformlsupplier) Business strategy risk Change management Project management Strategy Political External environmental risk Outsourcing/external supplier risk Physical security Money laundering Compliance Financial reporting Tax Legal (litigation) Natural disaster Terrorist threat Strike risk Source: Rachlin (1998), p. 127.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
161
123 276 623 1,406 3,885 10,73736,365 123,163 51 1,184 2,600,000
.c
I
4
Empirical distribution
I
+
Fit to model distribution
I
+
Fit using EVT
Severity of loss events ($'000)in logorithrnic scale
Figure 5.1 Frequency and severity of loss events Source: Ceske and Hernandez (1999), p. 19.
However, LFHS events typically fall in the area of the extreme tail (the area fit using extreme value theory (EVT) shown in figure 5.1). Analysis of operational risk requires all three measures. The typical risk assessment period in these operational risk measurement models is assumed to be one year.
5.1 TOP-DOWN APPROACHES TO OPERATIONAL RISK MEASUREMENT Financial institutions have long articulated the truism that "reputation is e~erything."~ Particularly in businesses that deal with intangibles that require public trust and customer confidence, such as banking, loss of reputation may spell the end of the institution. Despite this recognition (unfortunately often limited to the firm's advertising campaign), banks and other financial institutions have been slow at internalizing operational risk measurement and management tools to protect their reputational capital. As backward as financial firms have been in this area, nonfinancial firms are often even less sophisticated in assessing potential operational weaknesses.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 162
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
5.1 .I
Top-down vs. bottom-up models
Historically, operational risk techniques, when they existed, utilized a "top-down" approach. The top-down approach levies an overall cost of operational risk to the entire firm (or to particular business lines within the firm). This overall cost may be determined using past data on internal operational failures and the costs involved. Alternatively, industry data may be used to assess the overall severity of operational risk events for similar-sized firms as well as the likelihood that the events will occur. The top-down approach aggregates across different risk events and does not distinguish between HFLS and LFHS operational risk events. In a top-down model, operational risk exposure is usually calculated as the variance in a target variable (such as revenues or costs) that is unexplained by external market and credit risk factors. The primary advantage of the top-down approach is its simplicity and low data input requirements. However, it is a rather unsophisticated way to determine a capital cushion for aggregate operational losses that may not be covered by insurance. Nonetheless, top-down operational risk measurement techniques may be appropriate for the determination of overall economic capital levels for the firm. However, top-down operational risk techniques tend to be of little use in designing procedures to reduce operational risk in any particularly vulnerable area of the firm. That is, they do not incorporate any adjustment for the implementation of operational risk controls, nor can they advise management about specific weak points in the production process. They over-aggregate the firm's processes and procedures and are thus poor diagnostic tools. Top-down techniques are also backward looking and cannot incorporate changes in the risk environment that might affect the operational loss distribution over time. In contrast to top-down operational risk methodologies, more modern techniques employ a "bottom-up" approach. As the name implies, the bottom-up approach analyzes operational risk from the perspective of the individual business activities that make up the bank's or firm's "output." That is, individual processes and procedures are mapped to a combination of risk factors and loss events that are used to generate probabilities of future scenariosr o c ~ u r r e n c e HFLS .~ risk events are distinguished from LFHS risk events. Potential changes in risk factors and events are simulated, so as to generate a loss distribution that incorporates correlations between events and processes. Standard
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS 163
Table 5.2 Top -down and bottom-up operational risk measurement models Operational risk problem
Primarily use top-down or bottom-up model
Operational risk model recommended
Control Mitigation Prevention Economic capital
Bottom-up Bottom-up Bottom-up Top-down
Regulatory capital Efficiency optimization
Top-down Top-down and bottom-up
Process approach Process approach Process approach Multi-factor, scenario analysis Risk profiling Risk profiling and process approach
Source: Adapted from Doerig (2000), p. 95.
VaR and extreme value theory are then used to represent the expected and unexpected losses from operational risk exposure. Bottom-up models are useful to many constituencies within the firm - from the internal risk auditor to the line area middle managers to the operations staff. Results of the analysis may be utilized to correct weaknesses in the organization's operational procedures. Thus, bottomup models are forward looking in contrast to the more backward looking top-down models. The primary disadvantages of bottom-up models are their complexity and data requirements. Detailed data about specific losses in all areas of the institution must be collected so as to perform the analysis. Industry data are required to assess frequencies both for LFHS and HFLS events. Moreover, by overly disaggregating the firm's operations, bottom-up models may lose sight of some of the interdependencies across business lines and processes. Therefore, neglecting correlations may lead to inaccurate results since many of the operational risk factors have a systematic component. Most firms that have operational risk measurement programs use both top-down and bottom-up operational risk measurement model^.^ Table 5.2 shows how both top-down and bottom-up models can be used to address different operational risk problems.
5.1.2
Data requirements
The operational risk measurement methodology that is chosen is often determined by data availability. Senior (1999) interviewed top
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 164
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
managers at financial firms and found that the biggest impediment to the implementation of precise operational risk measurement models is the absence of accurate data on operational risk events. Ceske and Hernandez (1999) present four choices for obtaining data inputs: internal collection of data, external data, simulating data using educated estimates, and extrapolating data based on limited samples. Internal data are most applicable to the individual institution and are therefore the most useful in determining the firm's operational loss distribution. However, internal data are biased toward HFLS events. It is likely that there will be no LFHS events at all in the internal database, simply because many firms do not survive the catastrophic losses associated with this type of operational risk events. Moreover, it is extremely costly and time-consuming to develop a historical internal database on operational risk events. Thus, internal data should be supplemented with external data obtained from other institutions. This expands the database to include more LFHS events, particularly if the scope of the external database is industry-wide. However, external data must be scaled and adjusted to reflect institutional differences in business unit mix, activity level, geography and risk control mechanisms across firms. Moreover, competing firms are reluctant to release sensitive and detailed information about their internal processes and procedures to competitors. Ceske and Hernandez (1999) advocate the creation of a data consortium for financial insti~ tutions along the lines of the insurance and energy i n d ~ s t r i e s ."The database would contain information on non-public, internal, operational loss events, with the sources of the losses concealed. This would help financial institutions to learn the lessons from operational risk failures at other institutions" (Ceske and Hernandez, 1999, p. 18). Thus, individual firm confidentiality would be preserved while minimizing the cost of developing a comprehensive database on operational risk events for financial institution^.^ However, Ong (1998) argues against this emphasis on data collection because it would only encourage "follow the pack" decision making that would not necessarily improve risk management. Another source of data is obtained from management-generated loss scenarios. These scenarios emanate from either educated estimates by operational line managers or from extrapolation from smaller databases. Using either of these methods, management must construct frequency and severity estimates from individual operational risk events across individual business lines using bootstrapping and
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
,
165
jackknife methodologies in order to construct "synthetic data points."' The operational risk loss distribution is then obtained by considering all possible imaginable scenarios. The distribution can be specified using either parametric models or may be based on non-parametric, empirical distributions. Empirical distributions may not be representative and the results may be driven by outliers. In practice, loss severity is typically modeled using lognormal, gamma or Pareto distributions, although the uniform, exponential, Weibull, binomial and beta distributions are sometimes used.9 For catastrophic losses (in the fat tails of the distribution), extreme value theory is used. Loss frequency parametric distributions such as Poisson, beta, binomial, and negative binomial are most often used (see discussion in section 5.2.2.2). However, the current state of data availability still does not permit long run backtesting and validation of most operational risk measurement models.
5.1.3 Top-down models The data requirements of top-down models are less onerous than for bottom-up models.1° Top-down models first identify a target variable, such as earnings, profitability or expenses. Then the external risk (e.g., market and credit risk) factors that impact the target variable are modeled, most commonly using a linear regression model in which the target variable is the dependent variable and the market and credit risk factors are the independent variable. Operational risk is then calculated as the variance in value of the target variable that is unexplained by the market and credit risk factors (i.e., the variance in the residual of the regression that is unexplained by the independent variables). Sometimes operational risk factors are directly modeled in the regression analysis. Then operational risk is calculated as the portion of the target variable's variance explained by the operational risk independent variable.
5.1.3.1 Multi-factor models One top-down model that can be estimated for publicly traded firms is the multi-factor model. A multi-factor stock return generating function is estimated as follows:
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 166
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
where R, is the rate of return on firm i's equity; I,,, I,,, and I,, are the external risk factor indices (i.e., the change in each market and credit risk factor at time t); PIi, P2i and p,, are firm its sensitivity to changes in each external risk factor; and is the residual term. The risk factors are external to the firm and include as many market and credit risk factors as possible (i.e., interest rate fluctuations, stock price movements, macroeconomic effects, etc.). The multi-factor model measures operational risk as 0;= (1 - R2)c: where of is the variance of firm irs equity return from equation (5.1) and R, is the regression's explanatory power. The multi-factor model is easy and inexpensive to estimate for publicly traded firms. However, as in most top-down models, it cannot be used as a diagnostic tool because it does not identify specific risk exposures. More importantly, however, the multi-factor model is useful in estimating the firm's stock price reaction to HFLS operational risk events only. In contrast, LFHS events often have a catastrophic impact on the firm (often leading to bankruptcy or forced merger) as opposed to the marginal decline in equity returns resulting from the HFLS operational risk events that are measured by equation (5.1). Thus, the multi-factor model does not perform well when large scale events (such as mergers or catastrophic operational risk events) break the continuity of equity returns.', 5.1.3.2
Income-based models
Also known as Earnings at Risk models, income-based models extract market and credit risk from historical income volatility, leaving the residual volatility as the measure of operational risk. A regression model similar to equation (5.1) is constructed in which the dependent variable is historical earnings or revenues. Since long time series of historical data are often unavailable, income-based models can be estimated using monthly earnings data, in which annualized earnings are inferred under that assumption that earnings follow a Wiener process. Thus, monthly earnings volatility can be annualized by multiplying the monthly result by 'lt where t = 12. Since earnings for individual business lines can be used in the incomebased model, this methodology permits some diagnosis of concentrations of operational risk exposure. Diversification across business lines can also be incorporated. However, there is no measure of opportunity cost or reputation risk effects. Moreover, this methodology is sensitive to HFLS operational risk events, but cannot measure LFHS risk events that do not show up in historical data.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
5.1.3.3
167
Expense-based models
The simplest models are expense-based approaches that measure operational risk as fluctuations in historical expenses. Historical expense data are normalized to account for any structural changes in the organization.13Unexpected operational losses are calculated as the volatility of adjusted expenses. The primary disadvantage of expensebased models is that they ignore all operational risk events that do not involve expenses, e.g., reputational risk, opportunity costs, or risks that reduce revenues. Moreover, improving the operational risk control environment may entail increased expenses. Thus, expense-based models would consider the implementation of costly risk control mechanisms as an increase, rather than a decrease in operational risk exposure. Finally, since organizational changes are factored out of the analysis, expense-based models do not consider structural operational risk exposure (e.g., the operational risks of new business ventures).
5.1.3.4
Operating leverage models
A class of models that joins both the income-based and expense-based
approaches is the operating leverage model. Operating leverage measures the relationship between operating expenses (variable costs) and total assets. Marshall (2001) reports that one bank estimated its operating leverage to be 10 percent multiplied by the fixed assets plus 25 percent multiplied by three months of operating expenses. Another bank calculated its operating leverage to be 2.5 times the monthly fixed expenses for each line of business. Operating leverage risk results from fluctuations from these steady state levels of operating leverage because of increases in operating expenses that are relatively larger than the size of the asset base. Data are readily available and thus the model is easy to estimate. However, as is the case with income-based and expense-based models, the operational risk measure does not measure nonpecuniary risk effects, such as the loss of reputation or opportunity costs.
5.1.3.5
Scenario analysis
Scenario analysis requires management to imagine catastrophic operational shocks and estimate the impact on firm value. These scenarios focus on internal operations and try to estimate the impact of LFHS operational risk events, such as a critical systems failure, major
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 168
UNDERSTAND!NG MARKET, CREDIT, AND OPERATIONAL RISK
regulatory changes, losses of key personnel, or legal action. Marshall (2001) enumerates some possible scenarios: (i) the bank's inability to reconcile a new settlement system with the original system, thereby preventing its implementation (such as in the case of the TAURUS system cancellation by the London Stock Exchange in 1993 resulting in a US$700 million loss); (ii) a class action suit alleging incomplete disclosure (such as in Merrill Lynch's exposure to allegations about conflicts of interest affecting the accuracy of its stock recommendations resulting in a US$100 million fine plus pending legal action); (iii) a significant political event (such as the overthrow and reinstatement of Venezuela's president); (iv) massive technology failure (such as eBayrs internet auction failure that reduced market value by US$5 billion in 1999); (v) non-authorized trading (such as Barings Bank's losses of US$1.6 billion in 1995); and many others. The enumeration of scenarios is only limited by management's imagination.14 The primary advantage of scenario analysis is its incorporation of LFHS operational risk events that may not have transpired as of yet. This is also the model's primary disadvantage, however. Scenario analysis is by its very nature subjective and highly dependent on management's subjective assessment of loss severity for each operational risk scenario. Moreover, it comprises a laundry list of operational risk events without attaching a likelihood estimate to each event. Thus, scenario analysis is often used to sensitize management to risk possibilities, rather than strictly as an operational risk measure.
5.1.3.6
Risk profiling models
Risk profiling models directly track operational risk indicators. Thus, they do not use income or expenses as proxies for operational risk, but rather measure the incidence of risk events directly. For example, commonly used operational risk indicators are: trading volume, the number of mishandling errors or losses, the number of transaction fails or cancellations, the staff turnover rate, the percentage of staff vacancies, the number of incident reports, the amount of overtime, the ratio of supervisors to staff, the pass-fail rate in licensing exams for the staff, the number of limit violations, the number of process "fails," the number of personnel errors, the average years of staff experience, backlog levels, etc. Risk indicators can be divided into two categories: performance indicators and control indicators. Performance indicators (such as the number of failed trades, staff turnover rates, volume and systems downtime) monitor operational efficiency. Control indicators
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
169
Training expenditure Employee errors as a % of trade volume
p
.-
150
-; roo I-
1
Customer complaints asasof trade volume Mar
Jun
Sep
Dec
Mar
Jun
Sep
98
98
98
98
99
99
99
Quarter
Figure 5.2 Composite risk indicators: training dollars vs. employee error rate vs. customer complaints Source: Taylor and Hoffman (1999), p. 15.
measure the effectiveness of controls, e.g., the number of audit exceptions and the number of outstanding confirmations. Risk profiling models can track operational risk changes over time. The results can be used as a diagnostic tool to target operational risk weaknesses. The results can be incorporated into an operational risk scorecard (see discussion in section 5.2.1.1 ) .I5 However, risk profiling models assume that there is a direct relationship between operational risk indicators and target variables such as staff turnover rate. If this is not true, then the risk indicators may not be relevant measures of operational risk. Moreover, risk profiling may concentrate on the symptom (say, increased overtime), not the root cause of the operational risk problem. Finally, risk profiling models should analyze the relationships among different indicator variables to test for cross correlations that might yield confounding results. For example, figure 5.2 shows the inverse relationship between training expenditures and employee errors and employee complaints. A composite risk indicator can be determined using, say, the average expenditure required to reduce errors or customer complaints by 1 percent. Thus, a risk profiling model will examine several different risk indicators in order to obtain a risk profile for the company. Doerig (2000) states that each business unit uses approximately 10-1 5 risk indicators to assess its operational risk exposure.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 170
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RlSK
It is a matter of judgment, however, which risk indicators are most relevant to the overall operational risk exposure of the firm.16
5.2 BOTTOM-UP APPROACHES TO OPERATIONAL RlSK MEASUREMENT Top-down models use various statistical techniques (e.g., regression analysis) to take a "bird's eye view" of the firm's operational risk. Bottom-up models may use the same techniques, but instead apply them to the nuts and bolts of the firm's operational processes and procedures. Thus, bottom-up models are more precise and targeted to the measurement of specific operational risk problems, but at the same time, are more complicated and difficult to estimate than are top-down models. Bottom-up models use two different approaches to estimate the operational risk of a particular business line or activity: (i) the process approach and (ii) the actuarial approach.17 The process approach focuses on a step-by-step analysis of the procedures used in any activity. This can be used to identify operational risk exposures at critical stages of the process. In contrast, the actuarial approach concentrates on the entire distribution of operational losses, comprised of the severity of loss events and their frequency. Thus, the actuarial approach does not identify specific operational risk sources, but rather identifies the entire range of possible operational losses taking into account correlations across risk events.
5.2.1
Process approaches
The process approach maps the firm's processes to each of the component operational activities,'' Thus, resources are allocated to causes of operational losses, rather than to where the loss is realized, thereby emphasizing risk prevention. There are three process models: causal networks or scorecards, connectivity and reliability analysis. 5.2.1.1
Causalnetworks orscorecards
Causal networks, also known as scorecards, break down complex systems into simple component parts to evaluate their operational risk exposure. Then data are matched with each step of the process map
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS 171
Figure 5.3 Process map for a transaction settlement Source: Srnithson (2000), p. 58.
to identify possible behavioral lapses. Data are obtained using incident reports, direct observation and empirical proxies. For example, figure 5.3 shows a process map for a transaction settlement. The transaction is broken into four steps. Then data regarding the number of days needed to complete the step is integrated into the process map to identify potential weak points in the operational cycle. Scorecards require a great deal of knowledge about the nuts and bolts of each activity. However, the level of detail in the process map is a matter of judgment. If the process map contains too much detail, it may become unwieldy and provide extraneous data, detracting from the main focus of the analysis. Thus, the process map should identify the high risk steps of the operational process that are the focus of managerial concern. Then all events and factors that impact each high risk step are identified through interviews with employees and observation. For example, the high risk steps in the transaction settlement process map shown in figure 5.3 relate to customer interaction and communication. Thus, the process map focuses on the customer-directed steps, i.e., detailing the steps required to get customer confirmation, settlement instructions and payment notification. In contrast, the steps required to verify the price and position are not viewed by management as particularly high in operational risk and thus are summarized in the first box of the process map shown in figure 5.3. Mapping the procedures is only the first step in the causal network model. Data on the relationship between high risk steps and component risk factors must be integrated into the process map. In the process map shown in figure 5.3, the major operational risk factor is
-
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 172
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
Time progression Event Event occurrence detection
External event occurs
Response implementation Response identification
Staff detects Staff correctly Staff implements appropriate Success diagnoses response event response Staff implements inappropriate Failure response Staff misdiagnoses response Staff fails to detect event.
Figure 5.4
Outcome
Failure Failure
Generic event tree
Source: Marsha11 (2001), p. 259.
assumed to be time to completion. Thus, data on completion times for each stage of the process are collected and input into the process map in figure 5.3. In terms of the number of days required to complete each task, figure 5.3 shows that most of the operational risk is contained in the last two steps of the process - settlement instructions and payment notification. However, there may be several different component risk factors for any particular process. If another operational risk factor were used, say the number of fails and errors at each stage of the process, then the major source of operational risk would be at another point of the process, say the position reconciliation stage. Another technique used in causal networks is the event tree. The event tree evaluates each risk events' direct and indirect impacts to determine a sequence of actions that may lead to an undesirable outcome. For example, figure 5.4 shows a generic event tree triggered by some external event. As an example, we can apply the generic event tree to Arthur Andersen's operational risk in the wake of the external event of Enron's bankruptcy declaration and the resulting SEC investigation into Enron's financial reporting. One can argue that Arthur Andersen employees, while detecting the event, failed to correctly interpret its significance for Arthur Andersen's reputation as Enron's auditor. In directing employees to shred documents, the staff misdiagnosed the appropriate response, resulting in a failed outcome. Event trees are particularly useful when there are long time lags between an event's occurrence and the ultimate outcome. They help identify chronological dependencies within complex processes. However,
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
173
both event trees and process maps are somewhat subjective. Management has to identify the critical risk factors, break down the process into the appropriate level of detail and apply the correct data proxies. Moreover, by focusing on individual processes at the microlevel, the analysis omits macrolevel interdependencies that may result from a single failed activity that produces many failed processes. Moreover, there is no analysis of the likelihood of each external risk event.19 5.2.1.2
Connectivity models
Connectivity models are similar to causal networks, but they focus on cause rather than effect. That is, they identify the connections between the components in a process with an emphasis on finding where failure in a critical step may spread throughout the procedure. Marshall (2001) shows that one technique used in connectivity models is fishbone analysis. Each potential problem in a process map is represented as an arrow. Each problem is then broken down into contributing problems. An example of fishbone analysis for errors in a settlement instruction is shown in figure 5.5. The root cause of
Safekeeping error
Broker error
Error in message content Incorrect lSlN
Free-text error
Security error
Figure 5.5 Example of a fishbone diagram for errors in a settlement instruction Source: Marshall (2001),p. 252.
w
.., Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 174
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
( Late settlement
E lw Staff error
Missing
System failure
confirmation
Telecom failure
Human error
Booking error
\
/
<
)/I
R
Counterparty 1
complexity
Figure 5.6 Causal structure of late settlement losses Source: Marshall (2001),p. 95.
the error message is traced to either a safekeeping error, a broker error, a free-text error, or a security error. Within each of these possible problems, the specific cause of the error is identified. Another technique used in connectivity models is fault tree analysis. A fault tree integrates an event tree with fishbone analysis in that it links errors to individual steps in the production process. Management specifies an operational risk event to trigger the analysis. Then errors are identified at each stage of the process. In both fishbone and fault tree analysis, as well as for causal networks, care should be taken to avoid over-disaggregation which will make the analysis unnecessarily complex, thereby losing its focus. Connectivity models suffer from some of the same disadvantages as do causal networks. They are subjective and do not assess probabilities for each risk event. However, when combined with a scorecard to assess subjective probabilities, one obtains the fault tree shown in figure 5.6. This is taken from Marshall's (2001) example of the analysis of late
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
175
settlement losses for a financial institution. As shown in figure 5.6, late settlement occurs because of late confirmation (with a 40 percent probability), staff error (5 percent probability) or telecom failure (5 percent probability); the remainder of the cause of the late settlement operational risk event is the result of unknown factors (occurring with However, late confirmations themselves can a 50 percent pr~bability).~' be the result of several errors: missing trades, system failures, human errors, booking errors, or counterparty errors. Each of these operational risk events is assigned a probability in figure 5.6. Finally, the booking error cause can be the result of product complexity or product volume. Thus, the fault tree measures the extent of interdependencies across steps that make up complex processes.
5.2.1.3
Reliability models
Reliability models use statistical quality control techniques to control for both the impact and the likelihood of operational risk events. They differ from causal networks and connectivity models in that they focus on the likelihood that a risk event will occur. Reliability models estimate the times between events rather than their frequency (the event failure rate).21This methodology is similar to intensity-based models of credit risk measurement (see chapter 4, section 4.2.2). If p(t) is the probability that a particular operational risk event will occur at time t, then the time between events, denoted h(t), can be calculated as follows:
Thus, the reliability of a system is the probability that it will function without failure over a period of time t, which can be expressed as:
External as well as internal data are needed to estimate the reliability function R(t). Thus, the data requirements may be daunting. Moreover, the model must be estimated separately for LFHS events in contrast to HFLS events. However, by focusing only on frequency
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
and not on impact, reliability models do not measure the severity of the risk event.
5.2.2 Actuarial approaches The actuarial approach combines estimation of loss severity and frequency in order to construct operational loss distributions. Thus, the actuarial approach is closest to the VaR models discussed in the remainder of this book. There are three actuarial approaches: empirical loss distributions, explicit parametric loss distributions and extreme value theory.
5.2.2.1 Empirical loss distributions Both internal and external data on operational losses are plotted in a histogram in order to draw the empirical loss distribution. External industry-wide data are important so as to include both LFHS and HFLS operational risk events. The relationship shown in figure 5.1 represents an empirical loss distribution. This model assumes that the historical operational loss distribution is a good proxy for the future loss distribution. Gaps in the data can be filled in using Monte Carlo simulation techniques. Empirical loss distribution models do not require the specification of a particular distributional form, thereby avoiding potential errors that impact models that make parametric distributional assumptions. However, they tend to understate tail events and overstate the importance of each firm's idiosyncratic operational loss history. Moreover, there is still insufficient data available to backtest and validate empirical loss distributions.
5.2.2.2 Parametric loss distributions Examining the empirical loss distribution in figure 5.1 shows that in certain ranges of the histogram, the model can be fit to a parametric loss distribution such as the exponential, Weibull or the beta distribution. In contrast to the methodology used in market risk rnea~urement,~~ parametric operational loss distributions are often obtained using different assumptions of functional form for the frequency of losses and for the severity of operational losses. Typically, the frequency of operational risk events is assumed to follow a Poisson distribution. The distribution of operational loss severity is assumed to be either
1
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
177
Events
Figure 5.7(a) Distribution of mishandling events per day Source: Laycock (1998),p. 138.
lognormal or Weibull in most studies. The two distributions are then combined into a single parametric operational loss distribution using a process called convolution. An example of the procedure used to fit actual data2' to empirical distributions is given by Laycock (1998), who analyzes mishandling losses and processing errors that occur because of late settlement of cash or securities in financial transactions. Figure 5.7 (a) shows that the likelihood of daily mishandling events can be modeled as a Poisson distribution, with the caveat that actual events are more likely to be correlated than those represented by the theoretical distribution. That is, when it is a bad day, many mishandling events will be bunched together (as shown i n the extreme right tail region of the data observations which lies above the Poisson distribution values). Moreover, there are more no-event days than would be expected using the Poisson distribution (as shown by the higher probability density for the observed data in the extreme low-event section of the distributions). Laycock (1998) then plots the loss severity distribution for mishandling events and finds that the Weibull distribution is a "good" fit, as shown in figure 5.7(b). Finally, the likelihood and severity distributions are brought together to obtain the distribution of daily losses shown in figure 5.7(c). Separating the data into likelihood and severity distributions allows risk managers to ascertain whether operational losses from mishandling stem from infrequent, large value losses
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 178
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
Size of losses
Figure 5.7(b) Mishandling loss severity distribution Source: Laycock (1998), p. 139.
Size of losses
Figure 5.7(c) Distribution of daily mishandling operational losses Source: Laycock (1998), p. 140.
or from frequent, small value losses. However, the data required to conduct this exercise are quite difficult to obtain. Moreover, this must be repeated for every process within the firm. Even if the operational loss distribution can be estimated for a specific business unit or risk variable, there may be interdependencies across risks within the firm. Therefore, operational losses cannot be simply
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
179
aggregated in bottom-up models across the entire firm. For example, Ceske and Hernandez (1999) offer the simplified example of measuring the operational risk on a trading desk comprised of operational losses on foreign exchange (denoted X) and operational losses on precious ~ and Y are independent, then S = X + Y can metals (denoted Y ) . If~ X be represented as:
where F denotes distribution functions and f,(Y) is the probability density function for the random variable Y. However, X and Y are generally not independent. Thus, one must specify the interdependencies between the two random variables in order to specify the (joint) operational loss distribution. This requires a large amount of information that is generally unavailable. Ceske and Hernandez (1999) suggest the use of a copula function that represents the joint distribution as a function of a set of marginal distributions. The copula function can be traced out using Monte Carlo simulation to aggregate correlated losses. (See Appendix 5.1 for a discussion of copula functions.)
5.2.2.3
Extreme value theory
As shown in figure 5.1, it is often the case that the area in the extreme tail of the operational loss distribution tends to be greater than would be expected using standard distributional assumptions (e.g., lognormal or Weibull). However, if management is concerned about catastrophic operational risks, then additional analysis must be performed on the tails of loss distributions (whether parametric or empirical) comprised almost entirely of LFHS operational risk events. Put another way, the distribution of losses on LFHS operational risk events tends to be quite different from the distribution of losses on HFLS events. The Generalized Pareto Distribution (GPD) is most often used to represent the distribution of losses on LFHS operational risk events.25As will be shown below, using the same distributional assumptions for LFHS events as for HFLS events results in understating operational risk exposure. The Generalized Pareto Distribution (GPD) is a two parameter distribution with the following functional form:
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 180
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
r
0 Mean
$4.93 $6.97 $22.23 $53.53
t
95% VaR normal dist.
t
f
E
t
S
99% 99% VaR VaR Mean of normal GPD ~?xtmne dist. losses beyond the 99th percentile VaR under the GPD
Figure 5.8 Estimating unexpected losses using Extreme Value Theory (ES = the expected shortfall assuming a Generalized Pareto Distribution (GPD) with fat tails)
The two parameters that describe the GPD are 5 (the shape parameter) and p (the scaling parameter). If 5 > 0,then the GPD is characterized by fat tails.26 Figure 5.8 depicts the size of losses when catastrophic events Suppose that the GPD describes the distribution of LFHS operational losses that exceed the 95th percentile VaR, whereas a normal distribution best describes the distribution of values for the HFLS operational risk events up to the 95th percentile, denoted as the "threshold value" u, shown to be equal to US$4.93 million in the example presented in figure 5.8.28The threshold value is obtained using the assumption that losses are normally distributed. In practice, we observe that loss distributions are skewed and have fat tails that are
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
181
inconsistent with the assumptions of normality. That is, even if the HFLS operational losses that make up 95 percent of the loss distribution are normally distributed, it is unlikely that the LFHS events in the tail of the operational loss distribution will be normally distributed. To examine this region, we use extreme value theory. Suppose we had 10,000 data observations of operational losses, denoted n = 10,000. The 95th percentile threshold is set by the 500 observations with the largest operational losses; that is (10,000 500)/10,000 = 95%; denoted as Nu= 500. Suppose that fitting the GPD parameters to the data yields 6 = 0.5 and P = 7.29McNeil (1999) shows that the estimate of a VaR beyond the 95th percentile,taking into account the heaviness of the tails in the GPD (denoted VaR,) can be calcillated as follows:
Substituting in the parameters of this example for the 99th percentile yields: VaR, or
m,.,,,
That is, in this example, the 99th percentile VaR for the GPD, denoted -
VaR,,,, is US$22.23 million. However, VaR,,, does not measure the severity of catastrophic losses beyond the 99th percentile; that is, in the bottom 1 percent tail of the loss distribution. This is the primary area of concern, however, when measuring the impact of LFHS operational risk events. Thus, extreme value theory can be used to calculate the Expected Shortfall to further evaluate the potential for losses in the extreme tail of the loss distribution. The Expected Shortfall, denoted mO.,,, is calculated as the mean of the excess distribution of unexpected losses beyond the threshold $22.23 million VaR,.,,. McNeil (1999) shows that the expected shortfall (i.e., the mean of the LFHS operational losses exceeding VaR,.,,) can be estimated as follows: -
ES, =
(VaR,/(l - 5)) + (B - c ~ ) l (-l 5).
where q is set equal to the 99th percentile. Thus, in our example, -
ES, = (($22.23)/0.5)+ (7 - 0.5(4.93))/0.5= US$53.53 million to obtain the values shown in figure 5.8. As can be seen, the ratio of the extreme (shortfall) loss to the 99th percentile loss is quite high:
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk182 Approach, by Linda Allen, JacobCREDIT, Boudoukh, Anthony Saunders. UNDERSTANDING MARKET, AND OPERATIONAL RISK © 2004 Blackwell Publishing.
This means that nearly 2'12 times more capital would be needed to secure the bank against catastrophic operational risk losses compared to (unexpected) losses occurring up to the 99th percentile level, even when allowing for fat tails in the VaR,.,, measure. Put another way, coverage for catastrophic operational risk would be considerably underestimated using standard VaR methodologies. The Expected Shortfall would be the capital charge to cover the mean of the most extreme LFHS operational risk events (i.e., those in the 1 percent tail of the distribution). As such, the amount can be viewed as the capital charge that would incorporate risks posed by extreme or catastrophic operational risk events, or alternatively, a capital charge that internally incorporates an extreme, catastrophic stress-test multiplier. Since the GPD is fat tailed, the increase in losses is quite large at high confidence levels; that is, the extreme values of E S , (i.e., for high values of q, where q is a risk percentile) correspond to extremely rare catastrophic events that result in enormous losses.30
mO.,,
5.2.3
Proprietary operational risk models31
The leading32proprietary operational risk model currently available is OpVar, offered by OpVantage which was formed in April 2001 by a strategic alliance between NetRisk, Inc. and PricewaterhouseCoopers (PwC). OpVar integrates NetRisk's Risk Ops product with an operational risk event database originally developed by PwC to support its in-house operational risk measurement product. The operational loss database currently contains more than 7,000 publicly disclosed operational risk events, each amounting to a loss of over US$1 million for a total of US$272 billion in operational losses. In addition, the database contains over 2,000 smaller operational risk events amounting to less than US$1 million each. The data cover a period exceeding 10 years, with semiannual updates that add approximately 500 new large operational risk events to the database each half year. Figure 5.9(a) shows the distribution of operational risk events by cause. Clients, products and business practices overwhelmingly account for the majority (71 percent) of all operational losses in the OpVar database. However, this database may not be relevant for a particular financial institution with distinctive characteristics and thus OpVar's accuracy hinges on its ability to scale the external data and create a customized database for each financial firm. OpVar is currently installed at more than 20 financial institutions throughout the world,
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing.
Clients, products and business practices 71% H External fraud 7% El Execution, delivery and process management 3% @ Internal I fraud 10% Damage to physical assets 5% H Employment practices and workplace safety 2% H Business disruption and system failures 2%
Figure 5.9(a) Total operational losses by cause amount Source: www.opvantage.com
Commercial banking 16% fl Retail brokerage 8% Ed Trading and sales 21% B4. Asset management 4% H Institutional brokerage 3% H Corporate finance 3% H Insurance 18% Retail banking 23% Agency services 3% Other 1%
. I .
t.l
.
' ,,"
&me5.9(b)
Total operation losses by business uriit type
Source: www.opvantage.com
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, byUNDERSTANDING Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 184 MARKET, CREDIT, AND OPERATIONAL RISK
including Bank of America, Banco Sabadell, CIBC, ING, Sanwa, Societe Generale and Swiss Re. Figure 5.9(b) shows that most operational losses originate in the banking sector (16 percent in commercial banking and 22 percent in retail banking). OpVar is a bottom-up model that uses several different methodologies. It features multiple curve fitting techniques employing both parametric (e.g., lognormal) and empirical models of severity distributions, frequencies, and operational losses. Moreover, OpVar uses actuarial methods and Monte Carlo simulation to fill in gaps in the data. Graphical displays of causes and effects of operational risk events incorporate the process approach through the analysis of fault trees, causal networks, and risk profiles. Another major proprietary operational risk measurement model, Algorithmics Algo OpRisk, consists of three components: Algo Watchdog, Algo OpData, and Algo 0pCapita1.~~ Algo Watchdog is a bottom-up factor model that uses simulations and Bayesian analysis to predict the sensitivity of operational losses to risk events. AIgo OpData provides a flexible framework to store internal data on operational losses. The database is two-dimensional in that each operational risk event (or near miss) is sorted by organizational unit and by risk category. For financial firms, there are nine organizational units (corporate finance, merchant banking, Treasury, sales, market making, retail banking, card services, custody, and corporate agency services)34and five risk categories (two categories of employee fraud: collusion and embezzlement and three categories of systems failure: network, software, and hardware). Finally, OpCapital calculates operational risk capital on both an economic and a regulatory basis (following BIS I1 proposals; see discussion in section 6.3) using an actuarial approach that estimates loss frequency and severity distributions ~ e p a r a t e l y . ~ ~ Another proprietary model called 6 Sigma, developed by General Electric for the measurement of manufacturing firms' operational risk, has been adapted and applied to the operational risk of financial firms by Citigroup and GE Capital. This model primarily utilizes a topdown approach, focusing on variability in outcomes of risk indicator variables, such as the total number of customer complaints, reconciliations, earnings volatility, etc. However, because of the shortcomings of top-down models, 6 Sigma has added a bottom-up component to the model that constructs process maps, fault trees, and causal networks. Several companies offer automated operational risk scorecard models that assist middle managers in using bottom-up process approaches
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
185
to create causal networks or fault trees. JP Morgan Chase's Horizon (marketed jointly with Ernst 6 Young) and Accenture's operational risk management framework focus on key risk indicators identified by the financial institution. These models essentially massage manual data inputs into graphs and charts that assist the manager in visualizing each process's operational risk exposure. Capital requirements (either economic or regulatory) are also computed using the data input into the model. However, if the data inputs are subjective and inaccurate, then the outputs will yield flawed operational risk measures. The pressure to develop more proprietary models of operational risk measurement has been increased by the BIS I1 consideration of an operational risk component in international bank capital requirements (see section 6.3). Moreover, in June 2005, the US is scheduled to move to a T + 1 settlement standard, such that all securities transactions will be cleared by one day after the trade. The Securities Industry Association conducted a survey and found that only 61 percent of equity transactions at US asset management firrns and 87 percent of equity transactions at US brokerage houses comply with the straightthrough-processing standards required to meet the T + 1 requirement. The compliance levels in the fixed income markets were considerably lower: only 34 percent of asset managers and 63 percent of brokerage houses in the US were capable of straight-through-processing(see Bravard and David, 2001). Compliance with T + 1 standards will require an estimated investment of US$8 billion with an annual cost saving of approximately US$2.7 billion. Failure to meet the standard would therefore put firms at a considerable competitive disadvantage. Thus, the opportunity for operational losses, as well as gains through better control of operational risk, will expand considerably.
5.3 HEDGING OPERATIONAL RISK Catastrophic losses, particularly resulting from LFHS operational risk events, can mean the end of the life of a firm. The greater the degree of financial leverage (or conversely, the lower its capital), the smaller the level of operational losses that the firm can withstand before it becomes insolvent. Thus, many highly levered firms utilize external institutions, markets, and/or internal insurance techniques to better manage their operational risk exposures. Such risk management can take the form of the purchase of insurance, the use of self-insurance, or hedging using derivatives.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 186
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
5.3.1
Insurance
Insurance contracts can be purchased to transfer some of the firm's operational risk to an insurance company. The insurance company can profitably sell these policies and absorb firm-specific risk because of its ability to diversify the firm's idiosyncratic risk across the policies sold to many other companies. The most common forms of insurance contract sold to financial firms are: fidelity insurance, electronic computer crime insurance, professional indemnity, directors' and officers' insurance, legal expense insurance, and stockbrokers' indemnity. Fidelity insurance covers the firm against dishonest or fraudulent acts committed by employees. Electronic computer crime insurance covers both intentional and unintentional errors involving computer operations, communications, and transmissions. Professional indemnity insurance covers liabilities to third parties for claims arising out of employee negligence. Directors' and officers' insurance covers any legal expenses associated with lawsuits involving the discharge of directors' and officers' fiduciary responsibilities to the firm's stakeholders. Stockbrokersfindemnity insurance protects against stockbrokersf losses resulting from the regular course of operations such as the loss of securities and/or cash, forgery by employees, and any legal liability arising out of permissible transactions. All insurance contracts suffer from the problem of moral hazard; that is, the mere presence of an insurance policy may induce the insured to engage in risky behavior because the insured does not have to bear the financial consequences of that risky behavior. For example, the existence of directors' insurance limiting the directors' personal liability may cause directors to invest less effort in monitoring the firm's activities, thereby undermining their responsibility in controlling the firm's risk taking and questionable activities. Thus, insurance contracts are not written to fully cover all operational losses. There is a deductible, or co-insurance feature which gives the firm some incentive to control its own risk taking activities because it bears some of the costs of operational failures. The impact of insurance, therefore, is to protect the firm from catastrophic losses that would cause the firm to become insolvent, not to protect the firm from all operational risk. To better align the interests of the insured and the insurer, losses are borne by both parties in the case of an operational risk event. Figure 5.10 shows how operational losses are typically distributed. Small losses fall entirely under the size of the deductible and are thus completely absorbed by the firm (together with the cost of the insurance prem i ~ m )Once . ~ ~the deductible is met, any further operational losses
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
1
2
3
4
5
6
7
8
187
9 10 11 12 13 14 15 16 17 18 19 20 Operational losses
Figure 5.10 The typical payout structure on an operational risk insurance policy
are covered by the policy up until the policy limit is met. The firm is entirely responsible for operational losses beyond the policy limit. The higher (lower) the deductible and the lower (higher) the policy limit, the lower (higher) the cost of the insurance premium and the lower (higher) the insurance coverage area on the policy. Thus, the firm can choose its desired level of risk reduction by varying the deductible and policy limit of each operational risk insurance policy. Despite their role as outsiders to the inner workings of insured firms, -insurance companies have a comparative advantage in absorbing risks. Insurance companies diversify risks by holding large portfolios of.policies. Moreover, insurance companies have access to actuarial information and data obtained from past loss experience to better assess operational risk exposure. This expertise can also be used to advise their clients about internal risk management procedures to prevent operational losses. Finally, insurance companies spread risk among themselves using the wholesale reinsurance market.37 The primary disadvantage of insurance as a risk management tool is the limitation of policy coverage. Hoffman (1998) estimates that insurance policies cover only 10-30 percent of possible operational losses. Large potential losses may be uninsurable. Moreover, there may be ambiguity in the degree of coverage that results in delays in settling claims, with potentially disastrous impacts on firm solvency.38Large claims may threaten the solvency of the insurance companies themselves, as
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 188
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
evidenced by the problems suffered after Hurricane Andrew in 1992 (which resulted in insured losses of US$19.6 billion) and the terrorist attacks on the World Trade Center on September 11, 2001. Although estimates of losses to the insurance industry resulting from the September 11 attacks range from US$30 billion to US$70 billion, it is clear that this will be the most expensive catastrophic loss event ever recorded in the history of the insurance industry. Insurance premium costs have gone up and policy coverage narrowed in the wake of the terrorist attacks. Moreover, US property-liability insurers responded to large losses (such as Hurricane Andrew and the Northridge earthquake) by significantly increasing their capital from US$0.88 in equity per dollar of incurred losses in 1991 to US$1.56 in 1997. Thus, Cummins, Doherty, and Lo (2002) find that 92.8 percent of the US property-liability insurance industry could cover a catastrophe of US$100 billion. However, Niehaus (2002) contends that a major disaster would seriously disrupt the insurance industry, particularly since many propertylcasualty insurers lost money in 2002. Even without considering the cost of major catastrophes, insurance coverage is expensive. The Surety Association of America estimates that less than 65 percent of all bank insurance policy premiums have been paid out in the form of settlements (see Hoffman, 1998, and Marshall, 2001). Thus, the firm's overall insurance program must be carefully monitored to target the areas in which the firm is most exposed to operational risk so as to economize on insurance premium payments. The firm may obtain economies of scope in its operational risk insurance coverage by using integrated, combined or basket policies. These policies are similar in that they aggregate several sources of risk under a single contract. For example, Swiss Re's Financial Institutions Operational Risk Insurance product provides immediate payout in the event of a wide variety of operational risk incidents. To price such a comprehensive policy, the insurance company often sets very high deductibles, often as high as US$100 million. In exchange for this, the firm receives a wide range of insurance coverage at a relatively low premium cost.
5.3.2 Self-insurance The firm can reduce the cost of insurance coverage by self-insuring. Indeed, the presence of a deductible and a policy limit amounts to a form of self-insurance. The most common form of self-insurance is
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
189
the capital provision held as a cushion against operational losses. Regulatory capital requirements set minimum levels of equity capital using some measure of the firm's operational risk exposure (see discussion in section 6.3 for the BIS proposals on operational risk capital req~irernents).~~ However, capital requirements may be an exceedingly costly form of self-insurance to protect the firm against operational risk losses because equity capital is the most expensive source of funds available to the financial institution. Indeed, Leyden (2002) suggests that internal market risk models that economize on capital requirements have a return on investment of up to 50 percent. Alternatively, the firm could set aside a portfolio of liquid assets, such as marketable securities, as a cushion against operational losses. Moreover, the firm could obtain a line of credit that precommits external financing to be available in the event of losses. Thus, the firm allocates some of its debt capacity to covering losses resulting from operational risk events. Finally, some firms self-insure through a wholly owned insurance subsidiary, often incorporated in an offshore location such as Bermuda or the Cayman Islands, known as a captive insurer.40This allows the firm to obtain the preferential tax treatment accorded to insurance companies. That is, the insurance company can deduct the discounted value of incurred losses, whereas the firm would only be able to deduct the actual losses that were paid out during the year. Suppose that the firm experiences a catastrophic operational risk event that results in a loss of reputation that will take an estimated three years to recover. Under current US tax law, the firm can reduce its tax liabilities (thereby regaining some of the operational losses through tax savings) only by the amount of out-of-pocket expenses actually incurred during the tax year. Operational losses realized in subsequent tax years are deductible in those years, assuming that the firm survives until then. In contrast, a captive insurer can deduct the present value of all future operational losses covered by the policy immediately in the current tax year. Thus, the formation of a captive insurer allows the firm to co-insure with the relevant tax authorities. Risk prevention and control can be viewed as a form of selfinsurance. The firm invests resources to construct risk mitigation techniques in the form of risk identification, monitoring, reporting requirements, external validation, and incentives to promote activities that control operational risk. Of course, these techniques must themselves be credible since operational risk problems may be pervasive and may even infect the risk monitoring and management apparatus.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 190
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
Self-insurance tends to be less costly than external insurance when the firm has control over its risk exposure. Thus, routine, predictable losses that can be controlled using internal management and monitoring techniques are most often self-insured. If the risk is unique to a particular firm, and thus cannot be diversified by an insurance company, then it is more efficient for the firm to self-insure. The very largest catastrophic operational risks, most subject to moral hazard considerations, are often uninsurable and thus the firm has no choice but to self-insure in these cases. Thus, the costs of external and selfinsurance must be compared for each source of operational risk exposure to determine the optimal insurance program. Doerig (2000) presents a hierarchy of insurance strategies such that catastrophic losses (exceeding US$100 million) should be insured using captive insurance companies and external insurance if possible. Significant losses (US$51 to US$100 million) should be covered using a combination of insurance, self-insurance, and captive insurimce. Small operational losses (US$ll million to US$50 million) can be self-insured or externally insured. The smallest HFLS operational losses (less than US$10 million) can be fully self-insured. Doerig (2000) cites a 1998 McKinsey study that estimates that 20 percent of all operational risk is self-insured (including captive insurance), with the expectation that it will double to 40 percent in the near future.
5.3.3
Hedging using derivatives
Derivatives can be viewed as a form of insurance that is available directly through financial markets rather than through specialized firms called insurance companies. Swaps, forwards, and options can all be designed to transfer operational risk as well as other sources of risk (e.g., interest rate, exchange rate, and credit risk exposures). In recent years, there has been an explosive growth in the use of derivatives. For example, as of December 2000, the total (on-balance-sheet)assets for all US banks was US$5 trillion and for Euro area banks over US$13 trillion. The value of non-government debt and bond markets worldwide was almost US$12 trillion. In contrast, global derivatives markets exceeded US$84 trillion in notional value (see Rule, 2001). BIS data show that the market for interest rate derivatives totalled $65 trillion (in terms of notional principal), foreign exchange rate derivatives exceeded $16 trillion, and equities almost $2 trilli~n.~' The
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
young and still growing credit derivatives market has been estimated at US$1 trillion as of June 2001.42 By comparison to these other derivatives markets, the market for operational risk derivatives is still in its infancy.
5.3.3.1
Catastrophe options
In 1992, the Chicago Board of Trade (CBOT) introduced catastrophe futures contracts that were based on an index of underwriting losses experienced by a large pool of property insurance policies written by 22 insurers. Futures contracts were written on both national and regional indices. Because the contracts were based on an industry index, moral hazard concerns associated with the actions of any particular insurer were reduced and more complete shifting of aggregate risk became possible (see Niehaus and Mann, 1992). However, the CBOT futures contracts contained significant amounts of basis risk for insurers who bought them to hedge their catastrophe risk because the payoffs were not tied to any particular insurer's losses. Thus, the CBOT replaced the futures contract with an options contract in 1994. Options can be written on any observable future outcome whether it is a catastrophic loss of a company's reputation, the outcome of a lawsuit, an earthquake, or simply the weather. Catastrophe options trade the risk of many diverse events. Catastrophe ("cat") options, introduced in 1994 on the Chicago Board of Trade (CBOT), are linked to the Property and Claims Services Office (PCS) national index of catastrophic loss claims that dates back to 1949. To limit credit risk exposure, the CBOT cat option trades like a catastrophe call spread, combining a long call position with a short call at a higher exercise If the settlement value of the PCS index falls within the range of the exercise prices of the call options, then the holder receives a positive payoff. The payoff structure on the cat option mirrors that of the catastrophe insurance policy shown in figure 5.10. Niehaus (2002) claims that the trading volume in cat options is still (six years after their introduction) surprisingly small, given their potential usefulness to insurers concerned about hedging their exposure to catastrophic risk? Cat options are valuable to investors other than insurance companies because they show no correlation with the S6P500 equity index, making them highly valuable as a diversification tool for investors. Cruz (1999) cites a study by Guy Carpenter 6 Co. that finds that if 5 percent cat risk is added to a
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 192
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
portfolio comprised of 60 percent equities and 40 percent bonds, (say, by allocating a portion of the bond portfolio to cat bonds; see section 5.3.3.2), then the return on the portfolio would increase by 1.25 percent and the standard deviation would decrease by 0.25 percent, thereby increasing return while also decreasing the risk of the portfolio. In recent years, the market for a particular cat option, weather derivatives, has been steadily growing. Cao and Wei (2000) state that about US$1 trillion of the US$7 trillion US economy is affected by the weather. However, the market's growth has been hampered by the absence of a widely accepted pricing Note that this market is characterized by wide bidlask spreads despite the presence of detailed amounts of daily temperature data. Clearly, the pricingldata problems are much more daunting for other operational risk options. The most common weather derivatives are daily heating degree day (HDD) and cooling degree day (CDD) options written on a cumulative excess of temperatures over a one month or a predetermined seasonal period of time. That is, the intrinsic value of the HDDICDD weather options is: daily HDD = max (65°F - daily average temperature, O), daily CDD = max (daily average temperature - 65"F, 0). The daily average temperature is computed over the chosen time period (e.g., a month or a season) for each weather option. Cao and Wei (2000) find that the estimate of daily temperature patterns is subject to autocorrelation (lagged over three days) and is a function of a long range weather forecast. Because a closed form solution is not available, they use several simulation approaches. One approach, similar to VaR calculations, estimates the average value of the HDDICDD contract as if it were written every year over the period for which data are available. The temperature pattern distribution is then obtained by equally weighting each year's outcome. This method, referred to as the "burn rate" method, equally weights extreme outcomes without considering their reduced likelihood of occurrence, thereby increasing the simulated variability in temperature patterns and overstating the option's value. Cao and Wei (2000) suggest using long-range US National Weather Service forecasts (even if the forecast only predicts seasonal levels, rather than daily temperatures) to shape the simulated distribution. Unfortunately, the US National Weather Service does not forecast other operational risk factors.
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
5.3.3.2
193
Cat bonds
Sometimes options are embedded into debt financing in order to provide operational risk hedging through the issuance of structured debt. For example, in 1997, the US Automobile Association (USAA) issued US$477 million of bonds that stipulated that all interest and principal payments would cease in the event of a hurricane in the Gulf of Mexico or along the eastern seaboard of the US. That would allow the USAA to use the debt payments to service any claims that would arise from hurricane damage. This was the first of a series of catastrophe-linked or "cat" bonds. Since its inception, the market has grown to an annual volume of approximately US$1 billion.46Most cat bonds put both interest and principal at risk and thus, 96 percent of the bonds issued between April 2000 and March 2001 were rated below investment grade (see Schochlin, 2002). Early issues (81 percent of those issued before March 1998) had maturities under 12 months, but currently 11 percent of new issues (between April 2000 and March 2001) have maturities over 60 months, with approximately one-third having maturities under 12 months and another third having maturities between 24 to 36 months. There are three types of cat bonds: indemnified notes, indexed notes and parametric notes. The cash flows (compensation payments) on indemnified notes are triggered by particular events within the firm's activities. In contrast, payments on indexed notes are triggered by industry-wide losses as measured by a specified index, such as the PCS. In the case of parametric notes, the cash flows are determined by the magnitude of a given risk event according to some predetermined formula; that is, the compensation payment may be some multiple of the reading on the Richter scale for a cat bond linked to earthquakes. Indemnified notes are subject to moral hazard and information asymmetry problems because they require analysis of the firm's internal operations to assess the catastrophe risk exposure. Indexed and parametric notes, on the other hand, are more transparent and less subject to moral hazard risk taking by individual firms. Thus, although indemnified notes offer the firm more complete operational risk hedging, the trend in the market has been away from indemnified notes. From April 1998 to March 1999, 99 percent of the cat bonds that were issued were in the form of indemnified notes. During April 1998 to March 1999, the fraction of indemnified notes dropped to 55 percent and further to 35 percent during April 2000 to March 2001 (see Schochlin, 2002).
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, Linda Allen, Jacob Boudoukh, Saunders.RISK © 2004 Blackwell Publishing. MARKET, CREDIT,Anthony AND OPERATIONAL 194 byUNDERSTANDING
The earliest cat bonds were typically linked to a single risk. However, currently more than 65 percent of all new issues link payoffs to a portfolio of catastrophes. During April 2000 to March 2001, 11 percent of all newly issued cat bonds had sublimits that limited the maximum compensation payment per type of risk or per single catastrophe within the portfolio. Despite this limitation, the introduction of cat bonds allows access to a capital market that has the liquidity to absorb operational risk that is beyond the capacity of traditional insurance and self-insurance vehicles. Since cat bonds are privately placed Rule 144A instruments, most investors were either mutual fundslinvestment advisors or proprietarylhedge funds, accounting for 50 percent of the market in terms of dollar commitments at the time of primary distribution (see Schochlin, 2002). The remainder of the investors consisted of reinsurerslfinancial intermediaries (21 percent), banks (8 percent), non-life insurers (4 percent) and life insurers (17 percent of the new issues market). Cat bonds would be impractical if the cost of the catastrophic risk hedge embedded in the bond was prohibitively expensive. Cruz (1999) shows that this is not the case. For a pure discount bond47with a yield of 5 percent, the added annual cost for approximately $26.8 million worth of operational loss insurance (at the 1 percent VaR level) would be 1 percent, for a total borrowing cost of 6 percent per annum. Cruz (1999) compares that cost to an insurance policy issued to protect a large investment bank against fraud (limited to a single trading desk for losses up to $300 million) that had a premium of 10 percent." As an illustration of the order of magnitude on cat bond pricing, consider a five year zero coupon, plain vanilla default risk free bond with a $100 par value yielding 5 percent p.a. The price would be calculated as: 10011.05~= $78.35. However, if the bond were a cat bond, then the price would be calculated as: (100(1- a))/1.05' where a denotes the probability of occurrence of an operational loss event's o c ~ u r r e n c eAlternatively, .~~ the cat bond could be priced as: 1001(1 + 0.05 + ORS)' where ORS is 1 percent p.a. (the operational risk spread estimated by Cruz, 1999). Substituting ORS = 0.0 1 into the pricing formula, the price of the cat bond would be $74.73. This corresponds to an a of only 4.6 percent over the five-year life of the cat bond. The cost of the cat bond may be reduced because of the bonds' attractiveness to investors interested in improving portfolio efficiency who are attracted to the bond's diversification properties resulting from the low (zero) correlation between market risk and catastrophic risk.50Thus, cat bonds may provide a low cost method for firms to manage their
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
195
operational risk exposure. Furthermore, not only does the cat bond provide operational loss insurance at a significantly lower cost, but the firm does not have to wait for the insurance company to pay off on the policy in the event of a triggering event, since the proceeds from the bond issue are already held by the firm.51Similarly, a new product, equity based securitization (or "insuritization"), entails the issuance of a contingent claim on equity markets such that equity is raised if a large operational loss is realized.52
5.3.4
Limitations to operational risk hedging
Operational risk management presents extremely difficult risk control challenges when compared to the management of other sources of risk exposure, such as market risk, liquidity risk, and credit risk. The internal nature of the exposure makes both measurement and management difficult. Young ( 1999) states that "open socio-technical systems have an infinite number of ways of failing. . . . The complexity of human behavior prevents errors from being pre-specified and reduced to a simple numerical representation" (p. 10). Operational risk is embedded in a firm and cannot be easily separated out. Thus, even if a hedge performs as designed, the firm will be negatively impacted in terms of damage to reputation or disruption of business as a result of an LFHS operational risk event. Assessing operational risk can be highly subjective. For example, a key sponsor of operational risk reports, books, and conferences, as well as an operational risk measurement product was the accounting firm Arthur Andersen. However, when it came to assessing its own operational risk exposure, key partners in the accounting firm made critical errors in judgment that compromised the entire firm's reputation. Thus, the culture of a firm and the incentive structure in place yields unanticipated cross correlations in risk taking across different business units of the firm. One unit's operational problems can bring down other, even unrelated units, thereby requiring complex operational risk analysis undertaking an all encompassing approach to the firm, rather than a decentralized approach that breaks risk down into measurable pieces. The data problems discussed in chapter 4 in reference to credit risk measurement are even more difficult to overcome when it comes to operational risk measurement models. Data are usually unavailable, and when available are highly subjective and non-uniform in both form and function. Since each firm is individual and since operational risk
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 196
UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
is so dependent on individual firm cultural characteristics, data from one firm are not easily applicable to other firms. Moreover, simply extrapolating from the past is unlikely to provide useful predictions of the future. Most firms are allotted only one catastrophic risk event in their lifetime. The observation that a catastrophic operational risk event has not yet occurred is no indication that it will not occur in the future. All of these challenges highlight the considerable work remaining before we can understand and effectively hedge this important source of risk exposure.
5.4 SUMMARY Operational risk is particularly difficult to measure given its nature as the residual risk remaining after consideration of market and credit risk exposures. In this chapter, top-down techniques are contrasted with bottom-up models of operational risk. Top-down techniques measure the overall operational risk exposure using a macrolevel risk indicator such as earnings volatility, cost volatility, the number of customer complaints, etc. Top-down techniques tend to be easy to implement, but they are unable to diagnose weaknesses in the firm's risk control mechanisms and tend to be backward looking. More forward looking bottom-up techniques map each process individually, concentrating on potential operational errors at each stage of the process. This enables the firm to diagnose potential weaknesses, but requires large amounts of data that are typically unavailable within the firm. Industry-wide data are used to supplement internal data, although there are problems of consistency and relevance. Operational risk hedging can be accomplished through external insurance, self-insurance (using economic or regulatory capital or through risk mitigation and control within the firm), and derivatives such as catastrophe options and catastrophe bonds. However, the development of our understanding of operational risk measurement and management is far behind that of credit risk and market risk measurement and management techniques.
APPENDIX 5.1 COPULA FUNCTIONS Contrary to the old nursery rhyme, "all the Icing's horses and all the King's men" could have put Humpty Dumpty together again if they had been familiar with copula functions.53If marginal probability
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS
197
distributions can be derived from a joint probability distribution, can the process be reversed? That is, if one knows the marginal probability distributions, can they be rejoined to formulate the joint probability distribution? Copula functions have been used in actuarial work for life insurance companies and for reliability studies to recreate the joint distribution from the marginal distributions. However, the resulting joint probability distribution is not unique and the process requires several important assumptions. To reconstitute a joint probability distribution, one must specify the marginal distributions, the correlation structure, and the form of the copula function. We consider each of these inputs in turn.
5.A1 The marginal distributions Suppose that the time until the occurrence of a specified risk event is denoted T.54Then the distribution function of T is F(t) = Pr[T I t] where t 2 0, denoting the probability that the risk event occurs within t years (or periods).55Conversely, the survival function is S(t) = 1 - F(t) = Pr[T 2 t], where t 2 0, denoting that S(t) is the probability that the risk event has not occurred as of time t. The conditional event probability is defined to be ,qx = Pr[T - x I tlt > x] where T 2 x is the probability that an event will occur within t years (or periods) conditional on the firm's survival without a risk event until time x. The probability density function can be obtained by differentiating the cumulative probability distribution such that f(t) = F'(t) = -Sf(t) = lim A+O
Pr [t I T c t + A] A
The hazard rate function, denoted h(x), can be obtained as follows:
and is interpreted as the conditional probability density function of T at exact age x given survival to that time. Thus, the conditional event probability can be restated as:
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. 198 UNDERSTANDING MARKET, CREDIT, AND OPERATIONAL RISK
These functions must be specified for each process, security, and firm in the portfolio.
5.A2 The correlation structure The event correlation can be defined as:
This is a general specification of the survival time correlation and has no limits on the length of time used to calculate correlations. Indeed, the correlation structure can be expected to be time varying, perhaps in relation to macroeconomic conditions (see Allen and Saunders (2002) for a survey of cyclical effects in credit risk correlations). Since the general correlation structure is usually not available in practice, the discrete event correlation is typically calculated over a fixed period of time, such as one year. For example, as shown in section 4.3.2.2, CreditMetrics calculates asset correlations using equity returns.
5.A3 The form of the copula function Li (2000) describes three copula functions commonly used in biostatistics and actuarial science. They are presented in bivariate form for random 1, 0 < v I 1). variables U and V defined over areas {u,v)10 < u I
Frank copula
1
(eau- 1)(eav- 1)
a
where -= < a < =.
(5.A5)
Bivariate normal copula C , ) = 2 ( 1 ( u ) l, ( v ) , p) where -1 I p I 1
(5.A6)
where @, is the bivariate normal distribution function with the correlation coefficient p and a-' is the inverse of a univariate normal
Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value At Risk Approach, by Linda Allen, Jacob Boudoukh, Anthony Saunders. © 2004 Blackwell Publishing. EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS 199
distribution function. This is the specification used by CreditMetrics, assuming a one-year asset correlation, in order to obtain the bivariate normal density function. As an illustration of how the density function could be derived using the bivariate normal copula function, substitute the marginal distributions for a one-year risk event probability (say, default for CreditMetrics) random variables TAand TBinto equation (5.A6) such that:
where FA and FB are cumulative distribution functions for TA and TB,respectively. If the one-year asset correlation p is substituted for y, equation (4.10) is obtained.
Biva riate mixture copula A new copula function can be formed using two copula functions. As a simple example, if the two random variables are independent, then the copula function C(u,v) = UV. If the two random variables are perfectly correlated, then C(u,v)= min(u,v).The polar cases of uncorrelated and perfectly correlated random variables can be seen as special cases of the more general specification. That is, the general mixing copula function can be obtained by mixing the two random variables using the correlation term as a mixing coefficient p such that:
where 8(x) = 1 if x 2 0 and 8(x) = 0 if x c 0 Once the copula function is obtained, Li (2000) demonstrates how it can be used to price credit default swaps and first-to-default contracts. Similar applications to operational risk derivatives are possible.
2/27/03with 9:14 AM Page 441 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER
6
Case Studies
6.1 STRUCTURE OF STUDIES
A
t present, there are standard industry-accepted definitions for market, credit, and systemic risk, but no such definition for operational risk. (The BIS definition of operational risk is not accepted throughout the industry.) For these case studies, therefore, we use the definitions and framework from Chapter 5 and verify case by case the extent to which the structure of this approach can be applied. The first section of each case study describes the causal events and contributory factors leading to losses at a given financial institution. The following section outlines the effect of the causal events and contributory factors in order to clearly separate the causes, symptoms, and main and side effects. The final section allocates the different findings to the risk areas being affected. This section is key and will highlight to which areas the losses have to be allocated and why management and/or regulatory controls failed.
6.2
OVERVIEW OF CASES
The list of crises, near collapses, and effective collapses involving financial institutions is endless. However, some cases catch the attention of the regulators, and especially the media, and thus drive developments and trigger the implementation of new regulations. This in turn forces the industry to develop new approaches and new processes. Table 6-1 provides an overview of recent incidents in the market. Other cases, such as the losses and consequent shutdown of the London-based Griffin Trading 441
Overview of Recent Incidents in Financial Institutions
Institution
Date
Cause
Effect
Banco Ambrosiano
1982
Money laundering; fraud; conspiracy leading to multiple murders; complex networking of criminal elements including P2 members, Vatican officials, and high-ranking politicians in many countries.3
Loss of $1.4 billion
Bankers Trust
October 27, 1994
Material misrepresentations and omissions to client; lawsuits filed by Procter & Gamble and Gibson Greetings.4
$195 million damage; bankruptcy as clients moved business to other banks; takeover in 1999 through Deutsche Bank
Barings
February 23, 1995
Unauthorized trading; failure of controls; lack of understanding of the business, particularly in futures; carelessness in the internal audit department.
Loss of $1.328 billion; bankruptcy (takeover)
BCCI
1991
Weak credit analysis process; missing or incomplete loan documentation; concealment and fraud across the institution; money laundering.5
Collapse; $500 billion in estimated damage to taxpayers
Bre-X
November 5, 1997
Deliberate stock manipulation through false claims of gold discovery.6
Loss of $120 million
Credit Lyonnais
1994
Inadequate supervision and deregulation supported fraud; loan mismanagement; money laundering; fraud; complex networking of politicians, bankers, and new owners.7
Loss of accumulated $24.22 billion; collapse without governmental support
Daiwa
July 1995
Unauthorized trading of U.S. bonds and accumulated losses over 12 years.8
Loss of $1.1 billion
2/27/03with 9:14 AM Page 442 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published Companies, by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Inc.
442
T A B L E 6-1
February 9, 1990
Growth and profit were tied to the junk bond market Drexel had created and that crashed. The company was highly leveraged with substantial unsecured short-term borrowing at holding company. Drexel did not and could not obtain committed bank lines of credit to support the unsecured borrowing positions.
$1.3 billion global settlement case; $200 million criminal fine; $400 million civil restitution fund with SEC; bankruptcy
Jardine Fleming
July 1995
Lax controls; fraud; insider trading; selective deal allocations to client account.9
Compensation of $19.3 million to client with impacted performance from selective deal allocation; $2.2 million missing from client account
Kidder Peabody
April 1994
Phony profits; superiors did not understand trades; no questions asked because profits were being produced; inadequate supervision; promotion of superstar culture; employment references not checked; payment of bogus bonuses.10
Loss of $350 million
LTCM
September 1998
Growth and profit were tied to leverage and large exposures to illiquid emerging market exposures. The company was highly leveraged with substantial unsecured short-term borrowing at holding company. No questions were asked because profits were being produced. Inadequate supervision; promotion of superstar culture (including Nobel Prize winners). LTCM did not and could not sell illiquid positions to support the unsecured borrowing positions as the market went down and investors sold shares of LTCM.
Loss of $3.5 billion; investment of additional $1 million by syndicate of borrowers to avoid crash and systemic crisis; retirement of chairman of UBS
443
2/27/03with 9:14 AM Page 443 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published Companies, by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Inc.
Drexel Burnham Lambert
Overview of Recent Incidents in Financial Institutions (Continued )
Institution
Date
Cause
Effect
Metallgesellschaft
December 1993
Hedge strategies for oil prices; incorrect economic assumptions. Liquidation of positions failed, strategies led to fraud.
Loss of $1.5 billion
Morgan Grenfell
September 2, 1996
Inadequate supervision; promotion of superstar culture; no questioning of profits and instruments used.11
Loss of $260 million
Nasdaq
May 1994
Between 1989 and 1994, several brokers kept spread above unnaturally high levels and generated excessive profits for themselves and their institutions. Article in Journal of Finance disclosed excess profits from spread and initiated SEC investigation.12
Payment by clients of a spread kept at unnaturally high levels
NatWest
1996
Rogue trading; fraud.13
Loss of £90.3 million
Orange County, California
December 1994
Illegal use of state funds; losses from bond trading; false and misleading financial statements; fraud.14
Loss of $164 million; bankruptcy
Sumitomo
June 13, 1995
Copper trading errors; failure to segregate duties; no questions asked because profits were produced; inadequate supervision; promotion of superstar culture.
Loss of $2.6 billion
2/27/03with 9:14 AM Page 444 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published Companies, by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Inc.
444 T A B L E 6-1
2/27/03with 9:14 AM Page 445 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
445
company1 and of Cendant,2 or fraud charges against Martin Frankel, are not analyzed. The cases of Metallgesellschaft, Sumitomo, LTCM, and Barings have been selected for detailed analysis.
6.3
METALLGESELLSCHAFT 6.3.1 Background
Starting in 1991, Metallgesellschaft began offering fixed-price contracts with terms of up to 10 years to supply heating oil and gasoline to independent wholesalers and retailers.15 Firm-fixed contracts supplied the end user with a fixed volume per month for a fixed price over a 5- or 10-year period. The contracts were based on the average price of futures maturing over the next 12 months plus a fixed premium of $3 to $5 per barrel.16 The same price was offered for the 5- and 10-year contracts, without regard for the time value of credit. Participating firms could also exit the contract if the spot price rose above the contract price. The two parties would then split the difference in the prices. Later, Metallgesellschaft began writing in a mandatory exit if the spot price was higher than the contract price, so that Metallgesellschaft could reduce its exposure to rising oil prices. In 1993, Metallgesellschaft began offering firm-flexible contracts. These contracts were set at a higher price than the firm-fixed contracts. Under these contracts, a firm could exit and receive the entire difference between the spot price and the contract price multiplied by the remaining barrels in the contract. Metallgesellschaft negotiated most of its contracts in the summer of 1993.17 Metallgesellschaft sought to offset the exposure resulting from its delivery commitments by buying a combination of short-dated oil swaps and futures contracts as part of a strategy known as a stack-and-roll hedge. A stack-and-roll hedge involves repeatedly buying a bundle, or stack, of shortdated futures or forward contracts to hedge a longer-term exposure. Each stack is rolled over just before expiration by selling the existing contracts while buying another stack of contracts for a more distant delivery date; thus the term stack-and-roll. Metallgesellschaft implemented its hedging strategy by maintaining long positions in a wide variety of contract months, which it shifted between contracts for different oil products (crude oil, gasoline, and heating oil) in a manner intended to minimize the costs of rolling over its positions. Metallgesellschaft used short-dated contracts because the futures markets for most commodities have relatively little liquidity beyond the first few contract dates. The gains and losses on each side of the forward and futures transactions should have offset each other. By September 1993, Metallgesellschaft had committed to sell forward the equivalent of over 150 million barrels of oil for delivery at fixed prices, with most contracts containing 10-year terms. Energy prices were
2/27/03with 9:14 AM Page 446 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
446
CHAPTER 6
relatively low by recent historical standards during this period and were continuing to fall. As long as oil prices kept falling, or at least did not rise appreciably, Metallgesellschaft stood to make a handsome profit from this marketing arrangement. But a significant increase in energy prices could have exposed the firm to massive losses unless it hedged its exposure. In December 1993, it was revealed that Refining and Marketing, Inc., a subsidiary of the German conglomerate Metallgesellschaft AG, had experienced losses of approximately $1.5 billion in connection with implementing a hedging strategy in the petroleum futures market.18 In 1992, the subsidiary had begun a new strategy to sell petroleum to independent retailers, on a monthly basis, at fixed prices above the prevailing market price for periods of up to 5 and even 10 years. To lock in the profits and protect against the risk of rising prices, Metallgesellschaft employed a great many short-term derivative contracts such as swaps and futures on crude oil, heating oil, and gasoline on several exchanges and markets in an attempt to hedge its forward positions with retailers. This led to a timing (maturity) mismatch between the short-term hedges and the long-term liability and also resulted in overhedging (see Table 6-2). While the strategy protected against large price fluctuations, it ignored other risks, including basis risk, dealing risk, liquidity risk, and credit risk. The strategy relied on the prevailing condition of normal backwardation, where the spot price is greater than the futures price. However, due to a sudden large drop in oil prices in the fall of 1993 (due to OPEC’s problems sticking to its quotas), the market condition changed into one of contango, where the futures price is greater than the spot price. This had the effect of significantly increasing the costs of Metallgesellschaft’s hedging strategy, finally resulting in a loss of $1.5 billion. Although the petroleum market during that time period was deviating from its historical norm, Metallgesellschaft’s problem was with cash flow. Metallgesellschaft entered agreements to supply a defined total volume of heating oil and gasoline to companies over a 5- to 10-year period for a fixed rate. The fixed rate was calculated as a simple 12-month average of the futures prices plus a set premium and did not take into account contract maturity.19 Metallgesellschaft’s customers were obligated to accept monthly delivery of a specified amount of oil or gas for the fixed rate. This arrangement provided customers with an effective means to reduce exposure to oil price volatility risk. In addition, customers were given the option of exiting the contract if the nearest month futures price listed on the New York Mercantile Exchange (NYMEX) was greater than the fixed price defined in the contract. When this option was exercised, Metallgesellschaft made a cash payment to the company for half the difference between the futures price and the fixed price. A company might choose to exercise this option in the event of financial difficulties or if it did not need the product.
Cash Flow Deficit Created by a Maturity-Mismatched Hedge
Supply Contracts
Near Month Futures Price, $/Barrel
Next Month Futures Price, $/Barrel
March
20.16
20.30
April
20.22
20.42
May
19.51
19.83
June
18.68
18.90
Month
Futures Stack
Net Position
Net Receipts, $ Million
Size of Stack, Millions of Barrels
—
—
154.00
—
—
1.28
1.00
152.70
(12.30)
(11.30)
(11.30)
1.28
1.90
151.40
(139.00)
(137.10)
(148.40)
1.28
3.10
150.20
(189.30)
(186.20)
(334.60)
Deliveries, Millions of Barrels
Monthly Settlement, $ Million
Net Cash Flow, $ Million
Accumulated Net Cash Flow, $ Million —
July
17.67
17.92
1.28
4.30
148.90
(184.70)
(180.40)
(515.00)
August
17.86
18.30
1.28
4.00
147.60
(8.90)
(4.90)
(519.90)
September
16.86
17.24
1.28
5.30
146.30
212.50
(207.20)
(727.10)
October
18.27
18.38
1.28
3.50
145.00
150.70
154.20
(572.90)
November
16.76
17.06
1.28
5.40
143.70
234.90
(229.50)
(802.40)
December
14.41
14.80
1.28
8.50
142.50
380.90
(372.40)
(1174.80)
SOURCE:
Antonio S. Mello and John E. Parsons, “Maturity Structure of a Hedge Matters: Lessons from the Metallgesellschaft Debacle,” Journal of Applied Finance, 8/1 (1995), 106–120. Reproduced with permission of The Financial Management Association International.
447
2/27/03with 9:14 AM Page 447 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published Companies, by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Inc.
T A B L E 6-2
2/27/03with 9:14 AM Page 448 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
448
6.3.2 Cause In the fall of 1993, Metallgesellschaft went long on approximately 55 million barrels of gasoline and heating oil futures. At that time, the average trading volume for unleaded gas was only between 15,000 and 30,000 barrels. By December of that year, Metallgesellschaft had long positions in energy derivatives equivalent to 185 million barrels of oil. As oil prices fell, Metallgesellschaft was forced to pay the difference, and, by the end of December 1993, losses were just over $1 billion. In addition to the direct losses, rolling over the contracts cost the firm a total of $88 million in October and November alone. Problems arose because Metallgesellschaft’s volume was too high to act as an effective hedge. The company owned so many futures that it had trouble liquidating them. Also, contango caused Metallgesellschaft to perpetually roll into higher futures prices even as the spot prices were falling. In addition, because futures get marked to market each day so that as the price falls, the futures value drops, margin calls were initiated. As these contracts matured, Metallgesellschaft was forced to make large payments to its counterparties, putting further pressure on its cash flows. At the same time, most offsetting gains on its forward delivery commitments were deferred. Had oil prices risen, the accompanying gain in the value of Metallgesellschaft’s hedge would have produced positive cash flows that would have offset losses stemming from its commitments to deliver oil at below-market prices. As it happened, however, oil prices fell even further in late 1993 (see Figure 6-1). 6.3.2.1 Hedging Strategy The hedging strategies used by Metallgesellschaft were very misleading, going from a less appropriate method to final speculative hedging.20 •
•
Short forward. In 1991, Metallgesellschaft wrote forward contracts of up to 10 years. This strategy was based on Arthur Benson’s unproven theory that these contracts were profitable because they guaranteed a price over the cash oil price. There was no certainty that in such a market this situation could continue. Metallgesellschaft’s 10-year forward contracts seemed like an action taken by a risk minimizer; however, given 10 years’ worth of uncertain market price movement, it would be extremely risky to fix future cash flows for such a long time and ignore the importance of the real value of future cash flows. If Metallgesellschaft expected future cash flows to fund its future operations, the shrinking value of these cash flows would prove insufficient. Forward with option. Of immediate interest was the sell-back option included in the forward contracts. If we assume the short
2/27/03with 9:14 AM Page 449 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
449
F I G U R E 6-1
Oil Prices Between January 1993 and December 1994. (Data source: Bloomberg Professional.) 22
18
16
14
12
12/94
11/94
9/94
10/94
8/94
7/94
6/94
5/94
4/94
3/94
2/94
1/94
12/93
11/93
9/93
10/93
8/93
7/93
6/93
5/93
4/93
3/93
2/93
10 1/93
WTI cushion ($/barrel)
20
$/barrel
•
forward strategy to be a risk minimizer, then the sell-back option cast some doubt on it. The sell-back occurred month by month based on the scenario that the front-month NYMEX futures contract price was greater than the fixed price at which Metallgesellschaft was selling its oil products. Metallgesellschaft did not hedge its entire future products price, and, after canceling those forward obligations, it had to pay 50 percent of the difference in cash. There is no benefit from such a cash outflow given that Metallgesellschaft never received cash inflow from the counterparties and that it would never benefit after canceling the forward contracts. In a price swing market, this position could create continuing and enormous cash obligations for Metallgesellschaft. The option items moved Metallgesellschaft from a simple hedger to a market maker, a position that conflicted with its fundamental role. Futures and swaps. Metallgesellschaft used another strategy to hedge the risk of upward price movements: it entered into huge positions in the futures market for each month, then stacked and rolled over these contracts every month. Thus, contrary to the characteristics of its large forward, Metallgesellschaft entered
2/27/03with 9:14 AM Page 450 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
450
CHAPTER 6
another market, which was marking to market daily, rolling over all 10-year contracts together every month, with constant risk of margin call and cash requirement due to basis risk in a contango market. As Metallgesellschaft built large positions in the futures market, it had to respond to the obligation from the market price swing and short-term cash responsibility and to the 10-year long-term responsibility, while the theoretical gain from the short 10-year forward would not materialize at that time. The credit risk created thus far led to Metallgesellschaft’s final liquidation and loss of $1.5 billion. The notional gain from the short forward did not make up for the loss in futures, and these notional gains could disappear given such a long cycle in the financial market. It is very hard to understand how such a double hedging strategy was allowed. 6.3.2.2 Effect Moreover, declines in spot and near-term oil futures and forward prices significantly exceeded declines in long-term forward prices. As a result, realized losses from the hedge appeared to exceed any potential offsetting gains accruing to Metallgesellschaft’s long-term forward commitments. It was both contango and margin calls that created a major cash crunch for Metallgesellschaft. German accounting methods made Metallgesellschaft show the futures losses but did not allow the company to show the not yet realized gains from the forward contracts. This caused panic, and Metallgesellschaft’s credit rating plummeted. In response to these developments, NYMEX raised its margin requirements for the firm.21 This action, which was intended to protect the exchange in case of a default, further exacerbated Metallgesellschaft’s funding problems. Rumors of the firm’s financial difficulties led many of its OTC counterparties to begin terminating their contracts. Others began demanding that it post collateral to secure contract performance. In December 1993, Benson entered into put positions just as the price of crude oil bottomed out.22 By the fourth quarter of 1993, Metallgesellschaft’s U.S. division needed $1 billion in additional funding and received it even though its credit was faltering. After dismissing the firm’s executive chairman, Dr. Heinz Schimmelbusch, Metallgesellschaft’s new chairman (turnaround specialist Dr. Kajo Neukirchen) began liquidating the hedge and entering into negotiations to cancel long-term contracts with the company’s customers. NYMEX withdrew its hedging exemption once Metallgesellschaft announced the end of its hedging program. The loss of the hedging exemption forced Metallgesellschaft to reduce its positions in energy futures still further. Metallgesellschaft’s board of supervisors was forced to negotiate a $1.9 billion rescue package with the firm’s 120 creditor banks.
2/27/03with 9:14 AM Page 451 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
451
Metallgesellschaft’s strategy of paying a floating volatile price in exchange for a fixed price meant the company needed an effective means to manage the price risk. If Metallgesellschaft were to deliver on the contract by purchasing oil on the spot market, the company would be exposed to losses when oil prices increased. Table 6-3 shows that when the spot oil price increased, Metallgesellschaft would incur losses on the delivery of the contract. To manage the risk of increasing prices, Metallgesellschaft purchased short-term futures contracts for gas and oil on the NYMEX. Normally the markets for oil and gas commodities were in backwardation, which means that the futures prices were less than the current spot prices. By purchasing forward contracts in a backwardation market equal to the amount to be delivered, Metallgesellschaft was able to increase profits when the spot price decreased or to decrease losses when the spot price increased (see Table 6-4). The historical backwardation term structure of the oil and gas futures markets also presented an opportunity for Metallgesellschaft to earn a profit by hedging. As maturity approaches, the futures and spot prices will normally converge. If the futures price increases as the two prices converge, then the value of the futures contract also increases. A long position established a few months before maturity could then be closed out the month prior to maturity by selling a short position, which generates a net profit. Taking a new long position in a futures contract maturing in a few months, called a rollover, extends the hedge. Additional leverage, and thus profit, can be achieved by entering into more contracts.23 T A B L E 6-3
Three Scenarios for the Amount of Profit Generated per Barrel of Oil on a Six-Month Contract Supplied by Purchasing Oil on the Spot Market Stable Spot Price
Declining Spot Price
Increasing Spot Price
Date
Spot
Profit
Spot
Profit
Spot
Profit
4/1/01
32.50
0.3331
32.50
0.3331
32.50
0.3331
5/1/01
32.50
0.3331
32.18
0.6581
32.83
0.0081
6/1/01
32.50
0.3331
31.85
0.9799
33.15
−0.3201
7/1/01
32.50
0.3331
31.53
1.2984
33.48
−0.6517
8/1/01
32.50
0.3331
31.22
1.6138
33.82
−0.9865
9/1/01
32.50
0.3331
30.91
1.9260
34.16
−1.3247
Delivery profit per barrel
$2.00
$6.81
$(2.94)
The assumption is made that prices increase or decrease by 1 percent per month. Formula: Profit = spot price − fixed price.
In a Normal Backwardation Market, Futures Contracts Purchased One Month Before Physical Delivery Increase Profit or Decrease Loss per Barrel.
Stable Spot Price
Declining Spot Price
Increasing Spot Price
Profit
Spot
Futures 1 Month Before Delivery
Profit
Spot
Futures 1 Month Before Delivery
Profit
Date
Spot
Futures 1 Month Before Delivery
4/1/01
32.50
32.18
0.66
32.50
32.18
0.66
32.50
32.18
0.66
5/1/01
32.50
32.18
0.66
32.18
31.85
0.98
32.83
32.50
0.34
6/1/01
32.50
32.18
0.66
31.85
31.93
1.30
33.15
32.82
0.01
7/1/01
32.50
32.18
0.66
31.53
31.22
1.61
33.48
33.15
−0.32
8/1/01
32.50
32.18
0.66
31.22
30.91
1.93
33.82
33.48
−0.65
9/1/01
32.50
32.18
0.66
30.91
30.60
2.24
34.16
33.82
−0.98
Delivery profit per barrel
$3.95
$8.71
$(0.94)
The assumption is made that the futures contract price with a one-month expiration is 1 percent less than the eventual spot price. Formula: Profit = futures price − fixed price.
2/27/03with 9:14 AM Page 452 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published Companies, by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Inc.
452 T A B L E 6-4
2/27/03with 9:14 AM Page 453 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
453
The strategy of taking a position in several futures contracts with identical maturities, holding, and then taking an offsetting position before maturity is called a stack hedge strategy. A stack hedge is created when a position in futures contracts for a specific maturity is established, but then an offsetting position is taken shortly before maturity. A profit or loss is earned if the futures price increases or decreases.24 As long as the spot prices for oil and gas remain relatively stable or increase over the one-month holding period of the stack hedge contracts and the market is in backwardation, then a profit is earned using this strategy. However, if the spot price drops significantly, then losses will be incurred. In the event the spot price drops to less than the futures prices, the market is said to be contango. Entering a long-position stack hedge in a contango market can generate a profit only if spot and futures prices diverge or if spot prices increase while the basis spread does not decrease by an equal amount (i.e., if futures prices increase). Table 6-5 shows the results of holding a long position in futures contracts during a contango and backwardation where the spot price remains stable but the futures price converges. We will assume that if the spot price decreases during backwardation or increases during contango, the futures price remains stable so that the two converge and zero net profit is earned. The benefits of using a long-position stack hedge when the spot price remains relatively stable or increases can be seen in Table 6-6. As long as the market stays in backwardation, a profit can be earned almost regardless of the direction in which the spot price moves.
T A B L E 6-5
Results of Holding a Long Position in Futures Contracts During a Contango and Backwardation Date
Rollover
Profit (Loss)
Futures Contract
Buy
Sell
Contango
Backwardation
5/01
3/1/01
4/1/01
−0.20
0.20
6/01
4/1/01
5/1/01
−0.20
0.20
7/01
5/1/01
6/1/01
−0.20
0.20
8/01
6/1/01
7/1/01
−0.20
0.20
9/01
7/1/01
8/1/01
Rollover profit per contract
−0.20
0.20
$(1.00)
$1.00
The assumption is made that the price of the oil futures contract either increases (backwardation) or decreases (contango) by $0.20 per barrel during the one-month holding period of the contract. The calculation is based on rollover of only one contract.
2/27/03with 9:14 AM Page 454 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
454
T A B L E 6-6
Summary of Total Profit Expected Under Each of the Three Scenarios in a Backwardation Market Using 1 and 10 Rollover Contracts
Spot Price
Backwardation Market 1 rollover contract
10 rollover contracts
Stable
Declining
Increasing
$8.71
$(0.94)
Delivery profit
$3.95
Rollover profit
$1.00
—
$1.00
Total profit
$4.95
$8.71
$0.06
Delivery profit
$3.95
$8.71
$(0.94)
Rollover profit
$10.00
—
$10.00
Total profit
$13.95
$8.71
$9.06
The assumption is made that when the spot price decreases, the futures price remains relatively stable.
The term basis refers to the difference between the spot price of an item and its futures price. Metallgesellschaft’s stack-and-roll hedging strategy exposed it to basis risk—the risk that the price behavior of its stack of short-dated oil contracts might diverge from that of its long-term forward commitments. Because the forward price equals the spot price plus the cost of carry minus the convenience yield, if the convenience yield is high enough to offset the cost of carry, then the forward price is lower than the spot price. This is known as backwardation. A stack-androll strategy appeared to offer a means of avoiding carrying costs because short-dated futures markets for oil products have historically tended to exhibit backwardation. In markets that exhibit persistent backwardation, a strategy of rolling over a stack of expiring contracts every month can generate profits. However, a long-dated exposure hedged with a stack of short-dated instruments leaves exposure to curve or contango risk. Buyers of futures and forward contracts should pay a premium for deferred delivery. This premium is known as contango. With contango, the hedge cannot be rolled without a net loss. In 1993, short-term energy futures exhibited a pattern of contango rather than backwardation for most of the year. Once near-dated energy futures and forward markets began to exhibit contango, Metallgesellschaft was forced to pay a premium to roll over each stack of shortterm contracts as they expired. This, however, was only a minor addition to Metallgesellschaft’s dilemma.25 Metallgesellschaft’s financial difficulties were not attributable solely to its use of derivatives; the company had accumulated a heavy debt load in previous years. Metallgesellschaft reported losses of DM 1.8 billion on its operations for the fiscal year ending September 30, 1993, in addition to
2/27/03with 9:14 AM Page 455 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
455
the DM 1.5 billion loss auditors attributed to its hedging program during the same time frame. The parent firm already had accumulated a cash flow deficit of DM 5.65 billion between 1988 and 1993, which had been financed largely by bank loans. Because of the potential funding risk, Metallgesellschaft should have mitigated the impact by requiring periodic cash settlements from its customers on the forwards. This would have limited the risk of customer default as well as reduced the potential of a cash drain. Also, the firm should have arranged for expanded credit lines to be collateralized by the net value of its forward contracts.26 Metallgesellschaft had been using the historical backwardation of the oil market to earn rollover profits, but at the end of 1993 the situation changed to one of contango. The catalyst for this situation was the OPEC cartel, which instituted production quotas that kept spot prices high. Without the production quotas, OPEC countries would have increased oil production, causing spot prices to drop.27 Since the contracts Metallgesellschaft had entered into to supply oil were at a fixed rate, the value of these contracts had increased. However, the unexpected move to a contango market caused losses in Metallgesellschaft’s long futures. Table 6-7 details three scenarios showing what could have happened to the futures contracts that Metallgesellschaft held to maturity to meet delivery requirements during the contango market. Under the declining spot price scenario, which most closely matches what actually occurred, Metallgesellschaft would earn only $4.91 per barrel in a contango market rather than $8.71 per barrel in a backwardation market (Table 6-6). Although Metallgesellschaft lost money on each long futures contract purchased in the contango market, the losses on the contracts held to maturity were offset by the increase in the fixed-floating spread. The major problem Metallgesellschaft faced in the contango market resulted from losses on the stacked hedge. Since the stacked hedge was long oil futures, Metallgesellschaft lost money each time a rollover was made. Table 6-8 shows how the rollover losses could have affected the total profit earned by Metallgesellschaft. The losses were exacerbated by the large positions that Metallgesellschaft had in the market, totaling approximately 160 million barrels of oil. In all, Metallgesellschaft lost about $1.5 billion due to the stack hedge and its rollover. Metallgesellschaft had obviously not anticipated the spot price decrease and the switch to the contango market. It seems that the company’s management, led by Arthur Benson, was either speculating that spot prices would not decrease or did not fully understand the company’s derivative position. When the spot price fell, it created the need for large amounts of cash to cover the margin calls on the long futures positions. Metallgesellschaft could have easily managed the risk of falling prices by purchasing put options—a move that was not made until December 1993. The spot decrease also had the positive effect of increasing the value of the fixed-rate contracts by an amount equal to the losses in the long futures.
In a Contango Market Using Futures Contracts Purchased One Month in Advance of Physical Asset Delivery, Oil Costs More than If Purchased on the Spot Market
Stable Spot Price
Declining Spot Price
Increasing Spot Price
Date
Spot
Futures 1 Month Before Delivery
4/1/01
32.50
32.83
0.01
32.50
32.83
0.01
32.50
32.83
0.01
5/1/01
32.50
32.83
0.01
32.18
32.50
0.34
32.83
33.15
−0.32
6/1/01
32.50
32.83
0.01
31.85
32.17
0.66
33.15
33.48
−0.65
7/1/01
32.50
32.83
0.01
31.53
31.85
0.98
33.48
33.82
−0.99
Profit
Spot
Futures 1 Month Before Delivery
Profit
Spot
Futures 1 Month Before Delivery
Profit
8/1/01
32.50
32.83
0.01
31.22
31.53
1.30
33.82
34.16
−1.32
9/1/01
32.50
32.83
0.01
30.91
31.22
1.62
34.16
34.50
−1.67
Delivery profit per barrel
$0.05
$4.91
The assumption is made that futures contract price one-month expiration is 1 percent greater than the eventual spot price. Formula: Profit = Futures price − Fixed price.
$(4.94)
2/27/03with 9:14 AM Page 456 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published Companies, by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Inc.
456 T A B L E 6-7
2/27/03with 9:14 AM Page 457 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
457
T A B L E 6-8
Summary of Total Profit Expected Under Each of the Three Scenarios in a Contango Market Using 1 and 10 Rollover Contracts Spot Price Contango Market
Stable
1 rollover contract
10 rollover contracts
Declining
Increasing
Delivery profit
$0.05
$4.91
Rollover profit
$(1.00)
$(1.00)
—
Total profit
$(0.95)
$3.91
$(4.94)
Delivery profit
$0.05
$4.91
$(4.94)
Rollover profit
$(10.00)
$(10.00)
—
$(9.95)
$(5.09)
$(4.94)
Total profit
$(4.94)
The assumption is made that when the spot price increases in a contango market, the futures price remains relatively stable.
However, the daily margin calls required Metallgesellschaft to ask for more than $1.8 billion in loans from its German parent company during the fourth quarter of 1993 to cover the large number of long futures.28 Although Metallgesellschaft was having a cash flow crisis due to trying to cover the margin calls, a larger public relations crisis resulted from German accounting requirements. Under the U.S. accounting system for a hedge fund, Metallgesellschaft could have netted out the losses in long futures with the gains in fixed-rate contracts and actually shown a profit.29 However, using the German rules, Metallgesellschaft could not realize the gains on the fixed-rate forwards. Thus huge losses had to be reported, which caused counterparties to lose confidence. In conclusion, it seems that management was directly responsible for the financial catastrophe at Metallgesellschaft. If managers had not taken such a large position in long futures, or if they had at least used put options as a hedge for their position, then the magnitude of the cash flow problem could have been reduced. The overall strategy was sound, and, had a little more effort been made by management to analyze worst-case scenarios, the situation could have turned out differently. 6.3.3 Risk Areas Affected 6.3.3.1 Market Risk The accepted wisdom is that the flaw in Metallgesellschaft’s strategy was the mismatch between the short-term hedge and the long-term liability. Merton Miller, a Nobel Prize winner from the University of Chicago, and
2/27/03with 9:14 AM Page 458 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
458
Christopher Culp, a consultant, argue that the accepted wisdom is wrong. The so-called stacked hedge used by Metallgesellschaft would have protected the company fully against fluctuations in oil prices. However, regardless of inputs into simulation models and the soundness of the strategy, there were several risks the company’s management did not address: •
Basis risk. Metallgesellschaft had entered into stacked futures positions in the front-month contracts, which were rolled over at the expiration of each contract (see Table 6-9). The company became exposed to the basis risk because the market moved from the state of normal backwardation to contango. In the contango market, the spot price decreased more than the futures prices. This created rollover losses that were unrecoverable, and, as long as the market stayed in contango, Metallgesellschaft continued to lose on the rollover. This shift in the market to contango mode did not make the hedge bad, it just magnified the cash flow problems.
T A B L E 6-9
Valuation of Contracts, Unhedged and Hedged with a Running Stack
Inputs to simulation model Duration of contract
10 years
Total delivery obligation
150 million barrels
Monthly delivery
1.25 million barrels
Fixed contract delivery price
$20/barrel
Cost of delivery
$2/barrel
Initial spot price of oil
$17/barrel
Annual interest rate
7%
Annual convenience yield less cost of storage
7%
Cost of external financing $1 million/month
0 basis points
$10 million/month
0.2 basis points
$50 million/month
2.2 basis points
Results Present value of contract
$63.6 million
Cost of financing, unhedged
$4.4 million
Net value of contract, unhedged
$59.2 million
Cost of financing, rolling stack
$28.5 million
Net value of contract, rolling stack
$35.1 million
2/27/03with 9:14 AM Page 459 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
•
•
459
Dealing risk. Metallgesellschaft had such a huge position in the market that it would have taken 10 days to liquidate. The position was the equivalent of the entire oil output of Kuwait over a period of 85 days. Such a huge position exposed Metallgesellschaft to dealing risk. The company could not get out of its position immediately if things went bad. The trading volume in the heating oil and unleaded gasoline pits usually averaged from 15,000 to 30,000 contracts per day; Metallgesellschaft’s reported position was 55,000 contracts. To liquidate this position without influencing the market price would take Metallgesellschaft anywhere from 20 to 55 days. The risk was so large that it became a systemic risk. Liquidity risk. Metallgesellschaft failed to take into account the huge cash flow problem that would result almost immediately from its strategy. The problem was that the maturity structures of the derivatives were mismatched with the initial forward contracts. Thus, in the event of daily oil price variations, the futures positions would have to be settled due to the markto-market feature of this derivative instrument. Meanwhile, the unrealized gains from the forward positions would not translate into cash flow in the near term, as they would only be realized when the contracts expired. Thus, when oil prices decreased because OPEC had problems holding to its quota, Metallgesellschaft was unable to meet margin calls without assistance from its creditors. Even though the cash flows would have balanced out over the life of the hedge, the timing of the cash flows became a very serious problem for Metallgesellschaft. Another complicating issue at the time was the short-term liquidity crisis of the parent company, which had experienced several down years and was forced to sell off assets to meet liquidity needs. Employment had decreased by some 30 percent, to 43,000 employees, and the company was planning on forgoing the next dividend. The subsidiaries were informed that they could not expect to be easily financed by the parent company. Thus Metallgesellschaft chose a particularly poor time to run into funding problems, as its parent could not be of assistance.
6.3.3.2 Credit Risk The futures and swap positions Metallgesellschaft entered into introduced significant credit risk for the company. The majority of the credit risk was counterparty/settlement risk. If Metallgesellschaft had been subject to banking law, a substantial fraction of capital would have been blocked in regulatory capital. The extraordinary risk concentration might have become obvious and public before the blow-up through banking law auditors and business reports, which require disclosure of the major risks and concentrations.
2/27/03with 9:14 AM Page 460 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
460
CHAPTER 6
6.3.3.3 Operational Risk The company was subject to major operational risk, of which the fraud element is not covered in this analysis: accounting standards contributed substantially to the crisis. Another factor that compounded the problem (and made it possible to “hide” the losses) was the difference between the accounting standards in Germany and the United States. Operating from Germany and processing all accounting transactions and losses according to German accounting standards became a structural operational risk. The German standard required that Metallgesellschaft report its current losses without recognizing the gains on its fixed-rate forwards until they were effectively realized. Thus the company was exposed to a temporary paper loss, which would affect its credit risk, prompting its creditors to require additional margins well above the standard. The banks’ panic prevented Metallgesellschaft from rolling over its positions until the long-term delivery contracts expired, which would have left the company with a profit rather than a loss. According to U.S. accounting standards, Metallgesellschaft would have been showing a profit on its strategy, but the lack of foresight to address this issue through a subsidiary or other means left the company vulnerable to a change in market conditions. 6.3.3.4 Systemic Risk See comments in Section 6.3.3.1 regarding the size of dealing risk leading to systemic risk. 6.3.3.5 Additivity of Risk Management Framework In this case the BIS framework failed, as Metallgesellschaft is not subject to banking regulation. Internal risk management failed, as positions were reported to management very late in the crisis and hedging activity became more and more speculative. Unless information about rogue trading is known, any regulatory framework will be useless. The management framework failed to recognize the mismatch between the maturity of the original oil contracts and the instruments used to hedge adverse price movements (model risk); to recognize the liquidity impact from the potential cash flows absorbed to cover the margin calls; to recognize the positions in the accounting system; and to supervise employees, given the lack of dual control. The crisis was triggered by incorrect maturity and cash flow assumptions contained in the investment strategy (model risk) and subsequently not reported as additional operational risk factors contributing to the crisis. It is interesting that market participants knew about the substantial positions and the behavior of Arthur Benson, but top management was not aware of these facts. Stress testing would have been especially helpful in such a situation, as it would have indicated the substantial potential losses of Metallgesellschaft leading to funding problems.
2/27/03with 9:14 AM Page 461 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
461
Had Metallgesellschaft been subject to the BIS and local German banking regulations—apart from management actions—the capital requirements would have been substantially higher. Metallgesellschaft could not have entered the exposures without the capital required by regulations. Stress testing would have indicated that variations in oil prices would break confidence levels and would have shown capital to be inadequate in relation to the risk exposures.
6.4 SUMITOMO 6.4.1 Background Yasuo Hamanaka was a rogue trader with Sumitomo responsible for the risk management of the company’s copper portfolio. Sumitomo, with global assets of $50 billion, maintained a dominant role in copper trading with about 8 percent of the world’s supplies of the metal, excluding what is held in the former Eastern Bloc nations and China. The company, which had been in business since the seventeenth century, bought 800,000 tons of copper a year, selling it to affiliates and to the booming market in Southeast Asia. Most of that trading was done by Hamanaka, known as Mr. Five Percent because he and his team controlled at least that share of the world copper market. Nonetheless, the copper market was relatively small, and this provided Hamanaka with an opportunity to exercise his strategy of capitalizing on copper spot price increases in an effort to corner the market. The strategy failed to minimize its risk against downside risks of falling copper prices. In June 1996, exposure of Hamanaka’s illegal transactions sent the price of copper plummeting, resulting in a loss of $2.6 billion. Following the plummeting prices, Sumitomo was able to unwind some of the positions, placing the company in a losing position. Hamanaka was fired and subsequently jailed for his actions in trying to manipulate the price of copper. 6.4.2 Cause The strategy implemented by Yasuo Hamanaka was quite simple. He worked with brokerage firms such as Merrill Lynch, J. P. Morgan, and Chase to acquire funds to support his transactions. The funds were used to secure a dominant position in copper futures with the purchase of warrants. Hamanaka would buy up physical copper, store it in London Metal Exchange (LME) warehouses, and watch demand drive up the price. His intention was to push up the price of copper and corner the market by acquiring all the deliverable copper in LME warehouses. Since Hamanaka increased his huge long position, it would have been extremely vulnerable to short sales. Peter Hollands, president of Bloomsbury Minerals Economics Ltd. in London, says that was probably the strategy that left Sumitomo
2/27/03with 9:14 AM Page 462 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
462
CHAPTER 6
so vulnerable and so determined to buy physical copper to boost world copper prices. Hamanaka was convinced he could drive prices up at will using his huge physical position and sold over-the-counter put options to get cash on the premiums. Put options give their holders the right to sell copper at a predetermined price. Thus, as long as prices were on the upswing, Hamanaka could keep the premiums that the holders paid on the put options. But when copper prices started tumbling, the put holders exercised their puts and Hamanaka had to pay the difference between the strike price and the spot price of copper. His biggest exposure was in a falling spot price.30 Given an unusual degree of autonomy within the Sumitomo organization, Hamanaka’s intention was to drive up the price of copper to corner the market by acquiring all the deliverable copper in LME warehouses. Implementing the strategy was made easier as he was given the ability to grant power of attorney to brokerage firms to consummate transactions on behalf of Sumitomo without appropriate approval. The lack of oversight apparently allowed Hamanaka to keep two sets of trading books, one reportedly showing big profits for Sumitomo in the buying and selling of copper and copper futures and options and the other a secret account that recorded a dismal tale of billion-dollar losses. Hamanaka’s double-dealing began to unravel in December 1995, when the U.S. Commodity Futures Trading Commission and Britain’s Securities and Investments Board, which oversee commodity markets in New York City and London, asked Sumitomo to cooperate in an investigation of suspected price manipulation. Sumitomo later started an inhouse investigation of its own. According to CEO Tomiichi Akiyama, in early May 1996 a company auditor uncovered an unauthorized April transaction, the funds for which had passed through an unnamed foreign bank. The trade, which was described as “small in value,” led to Hamanaka’s office door on the third floor of Sumitomo’s headquarters near the Imperial Palace. On May 9, Hamanaka was abruptly reassigned to the post of assistant to the general manager of the Non-Ferrous Metals Division, in what Sumitomo characterized at the time as a promotion. Within days, traders around the world began to realize something was wrong at Sumitomo. In mid-May, a phalanx of commodities firms unloaded their copper holdings in anticipation that Sumitomo would do the same. Prices dropped 15 percent in four days (see Figure 6-2), leaving the international market in an uproar. 6.4.2.1 Intervention by the Commodity Futures Trading Commission Yasuo Hamanaka’s strategy to corner the copper market was most notable not because of his use of derivatives but because his plan included outright fraud and illegal trading practices. Because Sumitomo’s positions in the
2/27/03with 9:14 AM Page 463 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
463
F I G U R E 6-2
LME Copper Prices in 1996. (Data source: Bloomberg Professional.) 3100
2900
2700
$/metric ton copper
2500
2300
2100
1900
1700
12/96
11/96
10/96
9/96
8/96
7/96
6/96
5/96
4/96
3/96
2/96
1/96
1500
LME Copper price (LMCADY) $/metric ton
various copper markets artificially manipulated prices and were not related to a “legitimate commercial purpose,” Sumitomo was in violation of several sections of the Commodity Exchange Act (CEA).31 Ultimately, Sumitomo entered into a settlement agreement with the Commodities and Futures Trading Commission (CFTC), agreeing to pay $150 million in fines.32 Because the futures market can be manipulated to the detriment of producers or consumers of commodities, Congress expressly prohibits manipulative activity in Sections 6(a), 6(d), and 9(a)(2) of the CEA.33 While the statutes do not define words like manipulation, corner, or squeeze, the courts have designed a commonsense approach to interpretation. In Cargill Inc., v. Hardin,34 the court enumerated the following elements that indicate manipulation: (1) the market participant had the ability to influence market prices; (2) the market participant specifically intended to influence market prices; (3) artificial prices existed; and (4) the market participant created an artificial price.35 Essentially, when intentional conduct has been engaged in, and that conduct has resulted in a price that does not reflect the basic forces of supply and demand, the courts will presume that manipulation has taken place.36 Hamanaka needed a method to generate profits, presumably to offset large losses accumulated as a result of trading in the cash markets.37 In
2/27/03with 9:14 AM Page 464 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
464
analyzing the market actions of Sumitomo, the CFTC concluded that as a result of the company’s huge physical inventory and its corresponding dominating long futures position, Sumitomo had “expressly [created] artificially high absolute prices and distorted premium of nearby prices over future prices.”38 Furthermore, “Sumitomo deliberately exploited its market dominance [in the futures and physical markets] in order to profit when market prices became artificially high, as Sumitomo had foreseen and planned.” Because these positions were not related to Sumitomo’s legitimate commercial needs, the resulting price impacts were necessarily artificial and thus in violation of the CEA.39 6.4.3
Effect
The effect of the Sumitomo case is typical for disasters triggered by operational risk, with the consequence that the deficiencies in information systems or internal controls will result in unexpected loss. The risk is associated with human error, system failures, and inadequate procedures and controls. The prevention of an event such as the Sumitomo debacle should include proper internal control measures as well as better portfolio diversification to protect against downside risk. Controls must be in place to prevent such occurrences within an organization. Segregation of duties is vital to proper management of transactions and prevention of fraudulent activities within an organization. Sumitomo should have had a control procedure limiting the ability of copper traders to grant power of attorney to brokerage firms. Such an action on behalf of a company should have appropriate prior approval by senior management. Transactions with a brokerage firm exceeding a certain limit should have multiple approvals by senior management. Senior managers should not allow cash transactions by a trader without appropriate approval from management within the trader’s department. Implementing these preventive measures could have prevented some of the transactions that led to huge losses and subsequent civil proceedings. 6.4.4 Risk Areas Affected 6.4.4.1 Market Risk Put options allow producers the right to sell copper at a set price. As long as the prices were on the upswing, Hamanaka made money and producers lost only the premium on the put options. But when copper prices started tumbling in mid-May and again in June, producers exercised their puts, and Sumitomo swallowed even more losses. This compounded Sumitomo’s inability to thwart short sellers due to the company’s own desperate sale of long positions, which also drove down prices. Hamanaka underestimated gamma risk. Gamma measures the parabolic curvature of delta sensitivity. The gamma effect means that position
2/27/03with 9:14 AM Page 465 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
465
deltas move as the asset price moves, and predictions of revaluation profit and loss based on position deltas are therefore not accurate, except for small moves. Gamma measures the response of an option’s delta to changes in rates (gamma = change in delta / change in underlying asset). 6.4.4.2 Credit Risk Sumitomo dealt with over-the-counter forwards and swaps, where there is a lot of room for subjectivity. Hamanaka was able to sell large quantities of over-the-counter options cheaply, and also financed his positions through large credit lines and prepayment swaps with major banks. Credit risk in the form of counterparty risk was substantially underestimated, as the concentration in copper trading with a few counterparties was not appropriately recognized and reported to management. 6.4.4.3 Operational Risk Sumitomo suffered serious control and supervision problems: •
•
•
Lack of management supervision. Hamanaka was given limitless freedom in handling the copper trade, creating brokerage accounts and bank accounts, executing loan documents, and authorizing cash payments. There was virtually no check on his functional activity. Hamanaka granted power of attorney over Sumitomo trading accounts to brokers. These brokerage firms with power of attorney were doing transactions on margin, which leveraged the position of Sumitomo even higher. It is quite obvious that upper management didn’t have the knowledge base to understand these complex transactions. Lack of risk management. There was no risk management culture at Sumitomo, and even if it had existed, there were a lot of loose ends. Brokerage firms with power of attorney were doing highly leveraged transactions in Sumitomo’s name, while Sumitomo thought it was trading cash and futures with the brokerage company. Failure to control the market. Hamanaka tried to control the market by buying up physical copper, storing it in LME warehouses, and watching demand drive up the price. It’s believed that Hamanaka held off huge short sells by purchasing the other side of those short positions.
6.4.4.4 Systemic Risk Due to fear of facing the market, Hamanaka apparently could not bring himself to accept the fact that even the most successful market manipulator must experience an occasional downward market swing. Rather than sell some of his copper at a loss, he chose to play double or nothing, try-
2/27/03with 9:14 AM Page 466 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
466
ing to repeat his initial success by driving prices ever higher, leading to disaster. 6.4.4.5 Additivity of Risk Management Framework In this case, the BIS framework and internal risk management framework failed, as the positions were unknown to management and undetected by the accounting system until the last minute. Unless information about rogue trading is known, any regulatory framework will be useless. The management framework failed to recognize the substantial concentration risk in trading copper with a few counterparties, especially concentrated in copper instruments; to recognize the positions in the accounting system; and to supervise employees, given the lack of dual control. Most of the contributing factors are operational risk factors. It is interesting that market participants knew about the substantial positions and the behavior of Yasuo Hamanaka, but Sumitomo’s management was not aware of these facts. As a consequence, apart from management actions, the capital requirements would have been substantially higher.
6.5
LTCM 6.5.1 Background
Founded in early 1994, Long Term Capital Management, L.P. (LTCM) is a limited partnership based in Connecticut that operates Long Term Capital Portfolio, L.P., a partnership based in the Cayman Islands. LTCM operates a hedge fund that uses a variety of trading strategies to generate profit, but it initially focused on convergence or relative-value trading. Convergence trading is done by taking offsetting positions in two related securities in hopes of a favorable move in the direction of the price gap. A hedge fund is not defined by statutes, but rather is considered a pooled investment vehicle that is privately organized, administered by professional investment managers, and not widely available to the public. Investors in a hedge fund typically number fewer than 100 institutions and wealthy individuals. Since money is not raised via public offerings, hedge funds avoid the registration and reporting requirements of the federal securities laws. However, hedge funds that trade on organized futures exchanges and that have U.S. investors are required to register with the CFTC as CPOs.40 Hedge funds usually focus on one of three general types of investment strategies: (1) taking advantage of global macroeconomic developments; (2) capitalizing on event-driven opportunities including bankruptcies, reorganizations, and mergers; and (3) relative-value trading. LTCM’s investment strategy was focused mainly on relative-value trading of fixed-income securities. Here LTCM used sophisticated mathematical models to locate bonds that were closely related to one another but that had a price difference. By taking both a short and a long position in overpriced and under-
2/27/03with 9:14 AM Page 467 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
467
priced securities, respectively, LTCM would earn a profit as market forces moved to eliminate the arbitrage opportunity. For example, a difference in yields between two U.S. Treasuries with the same maturity and coupon rate but different issuance dates represents an opportunity to profit since market forces should drive the yields to converge. The relative value strategy worked well for LTCM in 1995 and 1996, with a return on equity of 43 percent and 41 percent, respectively. By 1997, other firms had started copying LTCM’s strategy, resulting in fewer opportunities for LTCM to profit from arbitrage in top-quality securities. In an effort to continue generating spectacular returns, LTCM began taking speculative positions in equities and trading extensively in emerging market debt. At one point, Russian debt may have accounted for as much as 8 percent of the total fund value. At the end of 1998, there were approximately 3000 hedge funds in existence.41 However, LTCM was unique because of its degree of leverage and scale of activities. Leverage has two different components: 1. Balance sheet leverage. Ratio of assets to net worth. 2. Economic leverage. Due to its use of repurchase agreements, short sells, and derivative contracts, LTCM saw its capital account mushroom to $7 billion (almost equal to that of Merrill Lynch) by the summer of 1996. The fund struggled throughout 1997, managing to record a gain of only 17 percent. At the end of 1997, the partners decided to return $2.7 billion to the original investors. The original investors got back $1.82 for every $1 invested in the fund, while still retaining their original $1 investment in the fund. In the beginning of 1998, the fund had capital of about $4.7 billion and LTCM’s leverage reached 28 to 1, or roughly $125 billion. The fund had derivative positions in excess of $1250 billion of notional value. By July, LTCM had mostly uncorrelated (under normal conditions) positions in a wide variety of markets: Danish mortgages, U.S. Treasury bonds, Russian bonds, U.S. stocks, mortgage bonds, Latin American bonds, U.K. bonds, and U.S. swaps. LTCM wanted the volatility of the fund to be roughly 20 percent on an annualized basis. Before April 1998, the fund’s volatility consistently measured 11.5 percent, which was below average. Even after the fund returned its original capital in 1997, its volatility still fell well below 20 percent. With capital of $4.7 billion, a monthly value at risk (VaR) of 5 percent, corresponding to a volatility of 20 percent, is $448 million. In other words, the fund was expected to lose in excess of $448 million in 1 month out of 20 at its target volatility. On August 17, Russia defaulted on debt and Russian interest rates surged to 200 percent. On August 21, 1998, the Dow fell 280 points by noon and U.S. swap spreads oscillated wildly over a range of 20 points.
2/27/03with 9:14 AM Page 468 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
468
(Volatility is around 1 point on a normal day.) They ended 9 points higher, at 76, up from 48 in April. Mortgage spreads and high-yield bonds climbed. LTCM’s models considered it a once-in-a-lifetime occurrence and a practical impossibility. On that day, LTCM lost $553 million (15 percent of its capital) when it wasn’t supposed to lose more than $35 million on any single day, per the models. This loss was more than 10 times the target daily fund volatility. LTCM had started the year with $4.67 billion; suddenly, it was down to $2.9 billion. LTCM’s leverage stood at an untenable 55 times its now shrunken equity (in addition to the massive leverage in derivative bets, such as “equity vol” and swap spreads). Yet the leverage could not be reduced. One dollar invested in the partnership in March 1994 grew to more than $4 by the end of 1997, but within the first six months of 1998 it dwindled to only 50 cents. More important, the fund was running out of capital. Meeting under the auspices of the Federal Reserve Bank of New York on September 23, the heads of 14 leading banks and investment houses decided to invest $3.65 billion in the fund and obtain a 90 percent stake in LTCM. This was the equivalent of prepackaged bankruptcy. 6.5.2 Cause The event trigger for the LTCM crisis was model risk. The contributing factors included taking on excessive risks and a general flaw in strategy. The following assumptions and conditions about instruments and models were applied: •
•
•
Risk models relying on portfolio return distribution forecasting. This is based on the assumption that the past repeats itself in the future. Crisis periods are exceptions where the past is meaningless because volatility increases dramatically and instruments become highly correlated. This is what happened in August 1998. Leverage application. In theory, market risk does not increase with increase in volume, provided the liquidity of the traded securities is known and the trader does not become the market maker. Relative-value trading. LTCM spotted arbitrage situations, bet that spreads would narrow and converge (securities that diverged from their historic relationships would eventually converge to the original relationship), and hedged risks. In other words, LTCM would buy huge amounts of six-month-old, 30-year Treasury bonds, and sell equally huge amounts of the just issued but more expensive 30-year Treasury bonds, aiming to profit from the expected convergence in the yields of the two bonds.
The work of Merton and Scholes is grounded in the assumption that there is enough competition in markets that investors can take prices as
2/27/03with 9:14 AM Page 469 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
469
given and simply react to them. Yet, in 1998, the prices at which LTCM could trade depended on what the market thought LTCM would or could do. Traditional risk measures, which assume that one can trade out of positions without affecting prices, thus become much less useful. LTCM’s short-term risk measures took some of these effects into account, but the extent to which prices depended on its positions and actions took the fund’s managers by surprise. The problem became critical after the impact of the market events of August 1998: •
•
LTCM’s risk management models relied too heavily on the bellshaped normal distribution curve, assuming that bad draws occur randomly. A large loss today does not foretell a large loss tomorrow. Unfortunately, in August 1998, risk models indicated that certain events had an infinitesimal probability of happening even though, in reality, they were occurring several times a week. LTCM’s signature trade, known as equity volatility, comes straight from the Black-Scholes model. It is based on the assumption that the volatility of stocks over time is consistent. Sometimes the market might be more volatile, but it always reverts to form. This theory was guided by the law of large numbers, assuring a normal distribution of quiet trading days and market crashes.
Assuming a swap spread divergence effect, LTCM was betting that the spread between swap rates and liquid treasury bonds would narrow. For each movement of 5 basis points (BPs), LTCM could make or lose $2.8 million. The expected volatility of the trade over a one-year period involves five such jumps, meaning that, according to its models, LTCM’s yearly exposure was no more than $14 million. The Commodity Futures Trading Commission (CFTC) estimates that 70 percent of all hedge funds have a balance sheet leverage ratio of less than 2 to 1, whereas LTCM, in its year-end 1997 financial statements submitted to the CFTC, showed it had approximately $130 billion in assets on equity capital of $4.8 billion or a ratio of 28 to 1. Approximately 80 percent of LTCM’s balance sheet assets were in G-7 nation government bonds. In addition, LTCM had over $1.4 trillion in economic, or off-balance-sheet, leverage, of which $500 billion was in futures exchange contracts and $750 billion was in OTC derivatives.42 Although very high compared to the industry average, LTCM’s leverage was comparable to the leverage of investment banks at the beginning of 1998. The difference was in LTCM’s exposure to certain market risks, which was much greater than for other typical trading portfolios (see Table 6-10), and a global diversification plan that used the same trading strategy in each market.
2/27/03with 9:14 AM Page 470 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
470
T A B L E 6-10
Leverage Comparison of LTCM Versus Other Large Investment Banks
Institution LTCM
Balance Sheet Leverage Ratio 28 to 1
Total Notional Value of OTC and ExchangeTraded Derivatives $1400 billion
Goldman Sachs Group, L.P.
34 to 1
$3410 billion
Lehman Brothers Holdings, Inc.
28 to 1
$2398 billion
Merrill Lynch & Co., Inc.
30 to 1
$3470 billion
Morgan Stanley Dean Witter & Co.
22 to 1
$2860 billion
SOURCE:
Commodity Futures Trading Commission (CFTC), “Hedge Funds, Leverage, and the Lessons of Long-Term Capital Management: Report of the President’s Working Group on Financial Markets, Washington, DC: Commodity Futures Trading Commission, April 1999, www.cftc.gov/tm/hedgefundreport.htm.
In addition to government bonds, LTCM also participated in following markets: •
•
•
Mortgage-backed securities, corporate bonds, emerging market bonds, and equity markets Futures positions, primarily concentrated in interest rate and equity indexes on major futures exchanges worldwide OTC derivatives contracts with over 75 counterparties that included swap, forward, and options contracts
By the end of August 1998, LTCM reportedly had more than 60,000 trades on its books.43 The circumstances that created the LTCM disaster resulted from the combination of internal and external factors. Government regulatory agencies have known for some time that the unregulated activities of hedge funds could significantly affect financial markets because of their capacity to leverage. However, research by the Federal Reserve Board indicated that banks had adequate procedures in place to manage the credit risk presented by hedge funds. In the case of LTCM, good national economic conditions and the reputation of the management team enticed banks to provide the company with favorable credit arrangements, including no initial margin requirements, that did not adhere to stated policies. This favorable credit treatment allowed LTCM to achieve a high leverage ratio. In addition, LTCM returned $2.7 billion in capital to its investors at the end of 1997 without significantly reducing its positions in the markets, thus pushing the leverage ratio even higher.
2/27/03with 9:14 AM Page 471 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
471
In July 1998, LTCM noticed a flaw in its relative-value trading model. Salomon had decided to lower its risk profile by disbanding its bond arbitrage unit. Salomon was selling some of the same positions held by LTCM, which caused a divergence of certain markets that were expected to converge. By the end of the month, LTCM had lost 15 percent of its capital. International markets were wary because of the turmoil in the economies of Asian countries that had begun in June 1997, causing yields on long-term government bonds in industrial countries to fall. However, most market participants also reasoned that the problems in Asia would lessen worldwide inflationary pressures because of expected weakening in the amount of exports to industrial countries. Thus, the industrial countries largely avoided the negative effects of the Asian crisis. The situation changed in August 1998, when Russia defaulted on government debt obligations and devalued the ruble. This resulted in sizable losses for some investors who had positions that were highly leveraged through collateralized financing. The drop in the value of the ruble in effect caused a global margin call. The Russian default may have also increased investor concern about the risks of investing in other credit-strapped emerging markets. In many emerging markets, both the currency and market value of international debt obligations declined sharply. Uncertainty about futures prices also broadly affected all financial instruments, causing investors to reduce their tolerance for risk. This created a shift toward the safe and liquid government debt of the major industrial countries, while the yields on both high- and low-quality corporate securities increased sharply. As a result, the spread between rates on corporate and government debt increased substantially around the world.44 For LTCM, the dramatic increase in credit spreads meant that its strategy of betting that spreads in all global markets would converge to historical levels was not working, because credit spreads were in fact diverging. Since LTCM had employed the same tactic in markets around the world, there was a lack of diversification that resulted in losing positions in numerous markets. Consequently, LTCM lost 44 percent of its capital in August alone and 52 percent for the year. Because of the high degree of leverage, LTCM would have been unable to make the margin call had it not been for the bail-out package orchestrated by the Federal Reserve Bank of New York. Problems began for LTCM in July 1998, when Salomon Smith Barney instituted a margin call to liquidate its dollar interest arbitrage opportunities. The interest rate spread arbitrage opportunity on U.S. government bonds and treasuries had blown up on LTCM. The firm had counted on the interest spread closing between the high-liquid and low-liquid treasuries. The crisis in Russia was leading investors to invest in the most liquid U.S. treasuries they could find. This caused the spread to widen instead of close, and convergence turned into divergence. The counterparties of
2/27/03with 9:14 AM Page 472 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
472
LTCM began to call for more collateral to cover this divergence. LTCM still believed in its strategy, but required more collateral to cover what it thought were temporary losses.
6.5.3
Effect
LTCM and its investors were impacted most by the following issues: •
The enormous profits LTCM made early on focused the attention of the financial sector on LTCM. This affected LTCM because: A large number of imitators appeared in the market. LTCM bought mispriced securities (high yields on a security) while hedging the risk. When imitators did the same, the price of the securities rose, eliminating the profit opportunity LTCM had first identified. This reduced the size of the LTCM trades, decreased the profits on those trades, and destroyed the diversification benefits of the strategy. Rather than acting in isolation, LTCM became the market mover, such that all imitators moved with LTCM. The unfortunate side effect was that seemingly unrelated instruments became linked by common ownership. LTCM partly recognized this in its risk measurement by using correlations that were greater than historical correlations. It also meant that the value of the fund’s positions was at the mercy of its imitators pulling out of their positions. In the summer of 1998, Salomon did just that—it closed its bond arbitrage department, resulting in losses for LTCM. It put pressure on LTCM to keep pursuing high profits in an environment where this was no longer possible, leading it to create positions in which outsiders would not think it had a competitive advantage. It made markets less liquid for LTCM.
•
Speculative positions in takeover stocks (e.g., Tellabs, whose share price fell more than 40 percent when it failed to take over Ciena) and investments in emerging markets (e.g., Russia, which represented 8 percent of LTCM’s books or $10 billion) caused losses for LTCM. There was fallout when spreads widened (as happened during the Russian debt default). LTCM was unregulated, which meant it was free to operate in any market without capital charges and with reports required only by the SEC. This enabled LTCM to pursue interest rate swaps with no initial margin (important to its strategy) and implied infinite leverage.
•
•
2/27/03with 9:14 AM Page 473 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
•
• •
•
473
Financial investors charge a premium to provide liquidity to investors when they want to get out of positions. So, in August 1998, financial intermediaries should have made profits. But federal regulations require banks to use risk management models to set capital. This capital requirement increased with volatility, as banks had to unwind positions themselves and shrink their trading portfolios. As a result, these financial institutions went from being stabilizing to destabilizing forces. Adverse price movement caused losses for LTCM. Lack of liquidity hampered LTCM’s ability to unwind its positions. Omitting derivatives, LTCM’s leverage was 100 to 1. LTCM routinely borrowed 30 times its equity capital. 6.5.4 Risk Areas Affected
6.5.4.1 Market Risk Correlation changes or a breakdown of historical relationship is, by definition, a daily VaR that measures maximum loss (confidence level of 99 percent) as that which is exceeded 1 day out of 100 on average. The Russian devaluation and the capital outflows in Brazil started a cycle of losses that developed as positions could not be unwound without creating further losses, which themselves forced further unwinding of positions. This made one-day VaR measures irrelevant, because these measures assume liquidity of positions. As losses forced the unwinding of positions, the crisis spread to unrelated positions, making the returns of unrelated positions highly correlated.45 LTCM’s trading strategies also made it vulnerable to market shocks. While LTCM traded in a variety of financial markets in a number of different countries, its strategies proved to be poorly diversified. In fact, most of LTCM’s trading positions were based on the belief that prices for various risks were high. The company thought that the prices for these risks, such as liquidity, credit, and volatility, were high compared to historical standards. However, these judgments were wrong. In addition, markets proved to be more correlated than LTCM had anticipated, as markets around the world received simultaneous shocks. LTCM used value-at-risk models, which look backward and assume that as long as markets behave more or less as they have over some past period, a certain amount of losses will likely occur. LTCM studied the relationships between various markets all around the world, bond markets, equity markets, interest rates, and the rate at which those prices changed. When the relationships between these various markets diverged from their historical norms, LTCM would place bets that the norms would reassert themselves.46
2/27/03with 9:14 AM Page 474 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
474
LTCM’s model said the hedge fund was unlikely to lose more than $40 million or so on any given day. But come August 1998, it actually lost more than $500 million in one day, and it lost the same amount in September. Interestingly, even though LTCM lost hundreds of millions of dollars many days during that period, Wall Street has not dropped these models. LTCM made assumptions based on theoretical model results rather than stress testing. The company assumed that the market would basically behave similarly to how it had in the past, and that the divergence of the spreads it was betting on was limited. It also assumed that market risk would not increase with an increase in volume, provided two things happened: LTCM stuck to liquid instruments and did not get so large that it itself became the market.47 In sum, the results from stress testing were neglected, or the correlations and volatilities were not stressed enough. 6.5.4.2 Credit Risk In pursuing the trading strategies mentioned earlier, it appears that LTCM assumed the following: •
•
• •
That interest rates of liquid and illiquid assets would converge— for example, convergence between liquid treasuries and more complex instruments that command a credit or liquidity premium. That it was sufficiently diversified and that its bets were properly hedged. The company also assumed that its models and portfolios used enough stress tests and that risk levels were within manageable limits. In addition, the firm’s risk models and risk management procedures may have underestimated the possibility of significant losses. That it could be leveraged infinitely on the basis of its reputation. Above all, that markets would go up, particularly emerging markets, while credit spreads narrowed.
LTCM was exposed to model risk. LTCM’s models indicated that various instruments were mispriced. For example, since 1926, yield spreads between speculative debt-rated Baa bonds and Treasury bonds have ranged from roughly 50 basis points to almost 800 basis points. These large spreads either are due to mispricing (arbitrage profits) or are a market premium that compensates bondholders for the risk they take. It is possible to make large profits based on the mispricing theory, even if it is false. But eventually, if investors are being compensated for taking risks, their bets will result in losses (e.g., they will make profits by selling earthquake insurance only as long as there are no earthquakes). If the bets are highly leveraged, losses can be crippling. The situation changed dramatically with the Russian default. On August 17, Russia devalued the ruble and declared a moratorium on debt payments. Once again, this sparked a flight to quality as investors shunned
2/27/03with 9:14 AM Page 475 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
475
risk and sought out liquid assets. As a result, risk spreads widened and many markets around the world became less liquid and more volatile. LTCM was affected, even though the vast majority of its trading risks were related to markets in the major industrialized countries. Thus, LTCM, with 10 percent of its portfolio in Russian securities, found itself losing money on many of its trading positions and nearing insolvency because: •
•
•
Some counterparties saw the ongoing crisis as an opportunity to trade against LTCM’s known or imagined positions. LTCM’s counterparties completely ignored the discipline of charging nonbank counterparties initial margin on swap and repo transactions. Collectively, they were responsible for allowing LTCM to build up layer upon layer of swap and repo positions. Their loose practices allowed a nonbank counterparty such as LTCM to write swaps and pledge collateral. The results from stress testing were neglected or the credit spreads not stressed enough.
6.5.4.3 Operational Risk As a registered commodity pool operator (CPO), LTCM filed annual financial statements with the Commodity Futures Trading Commission (CFTC) for the year ending December 31, 1997. The financial statements were audited by Price Waterhouse LLP. LTCM also filed those statements with the National Futures Association (NFA) and provided copies to the fund’s investors and lenders. Nothing in the financial statements indicated reason for concern about the fund’s financial condition. The fund was well capitalized and very profitable. Its asset-to-capital ratio was similar to that of some other hedge funds as well as many major investment banks and commercial banks. While the CFTC and the U.S. futures exchanges had detailed daily information about LTCM’s reportable exchange-traded futures position through the CFTC’s required large trader position reports, no federal regulator received detailed and timely reports from LTCM on its funds’ OTC derivatives positions and exposures. Notably, no reporting requirements are imposed on most OTC derivatives market participants. Furthermore, there are no requirements that a CPO like LTCM provide disclosure documents to its funds’ investors or counterparties concerning its derivatives positions, exposures, and investment strategies. It appears that even LTCM’s major creditors did not have a complete picture. LTCM’s losses in the OTC market make the need for disclosure and transparency obvious. The Value of Disclosure and Transparency
This is an industrywide issue related to hedge funds. It is important to distinguish between hedging and speculation when using financial derivatives.
2/27/03with 9:14 AM Page 476 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
476
CHAPTER 6
Marking to Market
To minimize counterparty risk, LTCM chose derivatives contracts that were marked to market and settled daily, so that no counterparty would be indebted to LTCM for large amounts at any given time. In August 1998, as spreads widened, LTCM was making marked-to-market losses. In other words, long securities were losing value while short securities were gaining value. If LTCM was right about convergence, this was a temporary issue that would be resolved in the long term because the mispricing of the securities would disappear by maturity. Marking to market and the decreased market value of its positions caused LTCM to run out of cash. Although LTCM correctly wanted its investors to commit money for the long term to enable it to take advantage of convergence strategies, it put itself in a position where it could fail before convergence was reached. There was an obvious conflict between hedging strategies and cash requirements. Transaction Types
The hedge fund was involved in three types of equity trading: “pairs” trading, risk arbitrage (arbitrage positions in merger stocks), and bets on overall market volatility. A major Wall Street firm indicates that LTCM’s arbitrage reached $6.5 billion, and positions in individual takeover stocks were 5 to 10 times as large as this Wall Street firm’s own arbitrage positions. Some pairs trading positions were even larger. Relative value bets were similar but subtly different. These positions generated profits if LTCM correctly determined that securities were overpriced relative to each other. LTCM differed from the rest of Wall Street in that its investment strategy was backed by detailed and complex computerized analysis of historic patterns of behavior, which allowed it to make confident (but, as it turned out, fallible) predictions about future outcomes. Liquidity Squeeze
Following the Asian economic crisis, Brazil also devalued its currency. This move created hyperinflation, and interest rates skyrocketed, causing counterparties to lose confidence in themselves and LTCM. As a result of the flight to quality, the spread between liquid and illiquid assets diverged further. With the increased spread, the value of LTCM’s collateral assets declined dramatically. LTCM was forced to liquidate assets to meet the margin calls. Insufficient Risk Management
A significant point that was apparently missed by LTCM and its counterparties and creditors was that while LTCM was diversified across global markets, it did not have a well-diversified strategy. It was betting that, in general, liquidity, credit, and volatility spreads would narrow from historically high levels. When the spreads widened instead in markets across the world, LTCM found itself at the brink of insolvency. In retrospect, it
2/27/03with 9:14 AM Page 477 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
477
can be seen that LTCM and others underestimated the likelihood that liquidity, credit, and volatility spreads would move in a similar fashion simultaneously in markets across the world. Essentially, this summarizes the risk of a large loss that LTCM faced owing to its arbitrage strategy. As we have seen, LTCM was highly leveraged. Its on-balance-sheet assets totaled around $125 billion, on a capital base of $4 billion, translating into a leverage of about 30 times. But that leverage was increased 10-fold by LTCM’s off-balance-sheet business, where notational principal ran to around $1 trillion. This amount of leverage was reached by using the cash received from borrowing against initial collateral, purchasing securities, and then posting them as collateral for additional borrowing in a continuous cycle. LTCM was leveraged to infinity. Furthermore, as convergence turned to divergence, LTCM sought more borrowed money as capital, convinced that everything would turn out fine. Its leverage was risky due to its magnitude and also to the circumstances for which it relied on a return on investments due to the uncertain global markets. It traded in emerging markets, such as in Russia. The market risk could not be managed or predicted with its models. The risk that the loss would force liquidation turned into reality as LTCM struggled to raise $500 million in collateral. The more of an asset a company needs to sell, the more capital needs to be available in a very short time period. The number of investors that are ready to buy quickly and at such large amounts is limited. Another risk was that a forced liquidation would adversely affect market prices. LTCM sold short up to 30 percent of the volatility of the entire underlying French market such that a rapid close-out by LTCM would severely hit the French equity market. The company risked affecting market prices not only due to its own trades, but also as a result of the imitation that occurred in the marketplace. Some of the market players had convergence positions similar or identical to LTCM’s, such that if LTCM closed out, there would be a mad panic for everyone to close out. 6.5.4.4 Systemic Risk Systemic risk is the risk that problems at one financial institution could be transmitted to the entire financial market and possibly to the economy as a whole. Although individual counterparties imposed bilateral trading limits on their own activities with LTCM, none of its investors, creditors, or counterparties provided an effective check on its overall activities. Thus, the only limitations on the LTCM fund’s overall scale and leverage were ones provided by its managers and principals. In this setting, the principals, making use of internal risk models, determined the frontier for safe operations of the fund. Moreover, LTCM was unregulated, free to operate in any market without capital charges and with only minimal reporting requirements by the SEC.
2/27/03with 9:14 AM Page 478 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
478
What subsequent risks did LTCM face? By mid-September 1998, its capital had shrunk to less than $1 billion, from $4.7 billion at the beginning of the year. LTCM faced severe problems as it tried to unwind some of its positions in illiquid markets. The large size of its positions in many markets contributed to its inability to unwind these positions. As a result, market participants became concerned about the possibility that LTCM could collapse and about the consequences this could have on already turbulent world markets. With regard to leverage, the LTCM fund’s balance sheet on August 31, 1998, included more than $125 billion in assets (see Figure 6-3). Even using the January 1, 1998, equity capital figure of $4.7 billion, this level of assets still implies a balance sheet leverage ratio of more than 25 to 1. The extent of this leverage implies a great deal of risk. Although exact comparisons are difficult, it is likely that the LTCM fund’s exposure to certain market risks was several times greater than that of the trading portfolios typically held by major dealer firms. Excessive leverage greatly amplified LTCM’s vulnerability to market shocks and increased the possibility of systemic risk. If the LTCM fund had defaulted, the losses, market disruptions, and pronounced lack of liquidity could have
F I G U R E 6-3
LTCM’s Leverage. (Source: Commodity Futures Trading Commission (CFTC): Testimony of Brooksley Born, Chairperson, on Behalf of the Commodity Futures Trading Commission before the United States House of Representatives, Subcommittee on Capital Market, Securities and Government Sponsored Enterprises of the Committee on Banking and Financial Services, Washington, DC: Commodity Futures Trading Commission, March 13, 1999.)
1000 900 800 700 600 500 400 300 200 100 -
Capital base LTCM's leverage ($ billion)
4.5
Balance sheet assets 125
Off-balance-sheet assets 1000
2/27/03with 9:14 AM Page 479 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
479
been more severe if not for the use of close-out, netting, and collateral provisions. 6.5.4.5 Additivity of Risk Management Framework The circumstances leading to the disaster are rooted in the infancy of LTCM. The experience and reputation of its members were renowned throughout the industry. The company was given preferential treatment by investors as well as lending institutions. LTCM was allowed to execute interest rate swaps with no requirement for initial margin, and was also able to use securities purchased with borrowed money to borrow additional money to purchase further securities. In effect, it was able to leverage itself to infinity. This circumstance, coupled with the fact that LTCM kept most of its notational principal off the books, where investors (and the SEC, for that matter) could not monitor it, would prove to be a critical factor in the downfall of the company.48
6.6
BARINGS 6.6.1 Background
Barings PLC went bankrupt because it could not meet the trading obligations incurred by Nick Leeson, a British trader at Barings Futures (Singapore). The unauthorized trading positions were made in a fraudulent account from 1992 to 1995. The credit crisis caused by Leeson led to more than $1.39 billion in losses on futures contracts in the Nikkei 225, Japanese Government Bonds (JGB), and euroyen, and options in the Nikkei 225. The value of the venerable 200-year-old Baring Brothers & Co Bank was reduced from roughly $615 million to $1.60, the price it brought from ING, a Dutch financial institution.49 Leeson started engaging in unauthorized trading in 1992, and he lost money from day one. In 1994 alone he lost $296 million; however, through creative deception, he showed a gain of $46 million in that year. The primary locus of blame for all the activities that eventually brought down Barings was the lack of an adequate control system to monitor and manage traders’ activities. Without such a system in place, unscrupulous traders like Leeson were able to take advantage of the firm and engage in unauthorized activities. Moreover, the environment that allowed the hiding and manipulation of trades, which went virtually undetected, was again directly attributable to Barings’ lack of adequate controls. Between 1992 and 1995, the management of Barings had no real concept of Leeson’s true profit and loss positions. This is because the details of account 88888 were never transmitted to treasury officials in London. Account 88888 was used by Leeson to cross trades with other Barings accounts and to show false gains on these accounts (while the actual losses were accumulating in the 88888 account). Due to this, Leeson was able to show a flat book expo-
2/27/03with 9:14 AM Page 480 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
480
sure while in reality he had huge long and short positions. Leeson probably could have gotten away with his scheme free and clear if it were not for the Kobe earthquake that shattered the Japanese equity markets. Leeson was authorized to trade Nikkei 225 futures contracts and options contracts on behalf of clients on the Singapore International Monetary Exchange (SIMEX). A Nikkei 225 futures contract is a bundle of stocks that are equal in proportion to the stocks that make up the Tokyo Stock Exchange Nikkei 225 Stock Average. The value of the futures contract is derived from the value of the Nikkei 225 average. A long Nikkei 225 futures position is in the money if the Nikkei 225 average increases, because the futures price will be lower than the actual value of the underlying asset. Leeson was allowed to take advantage of the arbitrage opportunities that existed between the price of Nikkei 225 futures contracts listed on the Osaka Securities Exchange vs. the Tokyo Stock Exchange and the SIMEX. Barings referred to this arbitrage activity as switching. It was imperative to hedge all major proprietary trading positions undertaken on behalf of Barings Securities so that the firm would not be exposed to a large risk. For example, a short futures position is hedged by a long futures position. The gain in the long position will exactly counteract the losses if the short futures position loses value. Leeson was only allowed to make unhedged trades on up to 200 Nikkei 225 futures, 100 Japanese Government Bonds, and 500 euroyen futures contracts. However, Leeson greatly exceeded these allowable limits in unauthorized and unhedged futures trades and exposed Barings to a large amount of risk. His positions were unhedged to maximize the gains if the market moved in a direction favorable to his position. The hedged portion of his position would have to meet margin requirements due to unfavorable market movements. Leeson also engaged in the unauthorized sale of Nikkei 225 put and call options, because doing so meant he could generate premiums without having to meet margin calls. His positions in the options markets were also unhedged in order to maximize his potential gains. 6.6.2 Cause Leeson was hired as general manager of the newly established Barings Futures (Singapore) office in the spring of 1992. The most notable aspect of his position was that he was in charge of settlement operations and was the Barings Futures floor manager on the SIMEX trading floor. Barings Futures was a subsidiary of Barings Securities. Nick Leeson was the general manager of the Barings Futures (Singapore) office, and he was to report to both the London and Singapore offices. The Singapore office would oversee Leeson’s trading activities on the SIMEX, and the London office would oversee his futures and options settlements. However, Barings Securities was a very political company. Individual managers at the field offices, such as Singa-
2/27/03with 9:14 AM Page 481 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
481
pore, were fiercely protective of their control over their specific offices. It was difficult for the London headquarters to exercise control over the field offices. Either the managers had excellent past performance, meaning that central control was unnecessary, or they had strong personalities and could successfully thwart attempts from headquarters to increase oversight. Gordon Bowser, risk manager at Barings Securities (London), was to be responsible for Leeson’s futures and options settlements. The senior management of the Singapore office included James Bax, the managing director of the Singapore office and a master of Barings office politics, and Simon Jones, the finance director of the Singapore office and an expert at settling stock trades, but also the possessor of a legendary temper. The pair was known as “Fortress Singapore.” Jones took offense at sharing Leeson’s oversight responsibilities with Bowser. He felt that if the Singapore office was to oversee Leeson’s trading activities on the SIMEX, then it should also oversee his settlements activities. Bax communicated this disagreement to London, but it was never resolved because the London office did not want to usurp the authority of the Singapore office. The key people in the Singapore office did not fully understand Leeson’s role in the organization or were not interested in monitoring his activities. Bax thought Leeson was only running settlements. Jones took little interest in supervising Leeson because he was sharing this responsibility with London. Mike Killian, head of Global Equity Futures and Options Sales at Barings Investment Bank, on whose behalf Leeson executed trades on the SIMEX, was also responsible for Leeson’s activities. However, Killian did not like to take oversight responsibilities and preferred to take credit for a profitable operation. As a result, it was unclear to whom Leeson reported, and his activities were not scrutinized. On July 3, 1992, Barings Futures (Singapore) established error account 88888 as required by the SIMEX. A few days later, Leeson asked his computer consultant to modify the CONTAC software program so that the trading activity, prices of trades, and positions associated with error account 88888 would not be reported to the London office. A fourth item, margin balances, remained on the report. Leeson knew that trading activity, prices of trades, and positions were processed by the London office and downloaded into First Futures (Barings’ internal reporting system) and that margin balances were ignored. Leeson stated that Gordon Bowser had ordered the action because the volume of trades made by Barings Futures (Singapore) on the SIMEX was difficult to settle. In September 1992, Bowser provided the Barings Futures (Singapore) office with error account 99002, which was to be used as the Barings Futures SIMEX error account. Account 99002 was to be reported to London. However, Leeson kept error account 88888 active to deliberately hide trading losses and unauthorized trades.
2/27/03with 9:14 AM Page 482 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
482
Leeson needed funds to meet margin calls and support accumulating losses on his unhedged futures trades. In August 1992, Bowser surprisingly granted Leeson permission to receive funds from London without providing specific information on how these funds would be used. Leeson argued that the difficulty of raising funds from Japanese banks and the peculiarities of SIMEX margin calls required him to have easy access to funds. From 1992 until the collapse, Leeson was able to request and receive funds to meet the margins calls on his unauthorized trades without scrutiny. Leeson used his position running the back office to further conceal his trading activities. At the end of September 1992, he asked the settlements staff to temporarily debit a Barings receivable account at Citibank Singapore and credit the funds to error account 88888. The transfer was performed in order to hide Leeson’s trading losses from Barings Securities (London) monthly reports, which were printed at the end of the month. This first such transaction coincided with the end of Barings Securities’ financial year and the start of Deloitte and Touche’s 1992 accounting audit. At this time, Leeson also forged a fax from Gordon Bowser stating that error account 88888 had an insignificant balance. The fax kept the accounting firm from discovering his activities. The specific method Leeson used to cover up his losses and inflate Barings Futures profits was the cross-trade. In a cross-trade, buy and sell orders for the same firm occur on an exchange. Certain rules apply; for example, the transaction must occur at the market price and the bid or offer prices must be declared in the pit at least three times. Leeson would crosstrade between error account 88888 and the following accounts: •
• •
92000 [Barings Securities (Japan), Nikkei and Japanese Government Bond Arbitrage] 98007 [Barings (London), JGB Arbitrage] 98008 (Euroyen arbitrage)
This was done to make the trades appear legal per SIMEX rules. Back office staff at Barings Securities (Singapore) would then be ordered to break the trades down into many lots and record them in the Barings accounts at prices differing from the purchase price. In general, the cross-trades were made at prices higher than what Leeson had paid on the SIMEX. In performing cross-trades, Leeson could show a profit for his trading activities on various Barings accounts. However, the gains in accounts 92000, 98007, and 98009 also generated a corresponding loss, which Leeson buried in error account 88888. This activity required the complicity of the Barings Securities (Singapore) clerical staff, which would have been easy to secure by the person in charge of the back office—Nick Leeson. Leeson was selling straddles on the Nikkei 225. His strategic underlying assumption was that the Nikkei index would be trading in the range
2/27/03with 9:14 AM Page 483 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
483
of 19,000 to 19,500. In this range he would rake in the money on the premiums of the sold options, while the calls and puts he sold would expire worthless. However, after the Kobe earthquake on January 17, 1995, the Nikkei dropped to 18,950. At that point the straddle strategy was shaky. Leeson started to lose money on the puts, because the (short) value of the put options he sold was starting to overtake the (long) value of the premiums received from selling the puts and calls. Then he made a dangerous gamble; he believed that the market was overreacting and on January 20, three days after the earthquake, he bought 10,814 March 1995 futures contracts. On January 23, the Nikkei dropped 1,000 points to 17,950, and at that point Leeson realized his gamble was a huge mistake. He was facing enormous losses from the long positions that he had just bought, along with unlimited losses on the puts. In addition to selling straddles, Leeson’s reported arbitrage strategy was to go long or short the Nikkei 225 futures on the Osaka exchange, while simultaneously going the other direction on those same Nikkei 225 futures on the SIMEX. This strategy would theoretically take advantage of temporary mispricing differences of the same futures contract on two different exchanges. Since these products were essentially identical (they derived all of their intrinsic value from the same underlying security), any large price differences between the Osaka and SIMEX Nikkei 225 March 1995 futures contracts would be short-lived (or nonexistent) in an efficient market. This trading strategy is what Barings referred to as switching. In reality, however, Leeson ignored the switching and was long the March 1995 contract on both exchanges. Therefore, he was doubly exposed to the Nikkei 225 instead of being hedged. On January 20, the Osaka exchange lost 220 points and the SIMEX lost 195. If Leeson were short on the SIMEX, the net effect would have been (−220 + 195) = −25. However, he was long on both exchanges; therefore, on January 20 he had a loss of (−220 − 195) = −415. During January and February of 1995, Leeson suffered the huge losses that broke Barings. 6.6.2.1 How Leeson Hid the Trades It is legal for an institution to separate a trade made on an exchange, assuming that the trade is large and that its size might affect the market price of the position. This is done through “block transaction,” which effectively splits the transaction into smaller transactions with different counterparts. Leeson traded this way within the Barings accounts (also known as cross-trading). After the transactions, however, when he was splitting the trades into the different accounts, he decided the price at which each trade should be recorded, and did not use the actual price of the trade. This is illegal. Although the sum of the small transaction matches the overall trade, and the books were flat, Leeson was crediting gains to the Barings accounts and was offsetting them by recording losses
2/27/03with 9:14 AM Page 484 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
484
CHAPTER 6
in the 88888 account. Since he was always losing money, he kept recording losses in this account, and was showing gains in the official books. This way Leeson fooled everybody at Barings and was able to show a profitable net position. Barings’ treasury never audited account 88888, which more accurately depicted Leeson’s true profits and losses. Account 88888 was a ticking bomb that exploded in February 1995 and broke Barings.50 6.6.2.2 Leeson’s Assumptions The facts just discussed show the reasons behind Barings’ collapse. When reading them, one openly wonders what made Leeson so aggressive in the derivatives markets, why he thought he could profit from such aggressive tactics, and why he thought he could cover up his activities from his employer. In every case involving huge derivative position losses, one usually sees the “double-down” mentality take effect. In this case, Leeson sealed his fate the first day he decided to eschew the official Barings derivatives trading strategy. He was destined to eventually put himself in a net loss position due to the risky nature of the products he was trading. Once he did this, he had no other option but to keep doubling down in the hope that he could extricate himself from the situation. He could not merely cap his losses and walk away, as that would mean he would have to inform Barings management of his improper trading, and he surely would have been fired by the firm at that point. That is why he did not hedge his positions once he started losing money. To do so might have saved Barings from its eventual collapse, but it would not have been enough to save his job. So, instead, he covered up his illicit trading practices and kept raising the stakes. Leeson had been trading derivative products improperly for some time prior to the disaster in early 1995. Because of his experience, albeit limited, with the Japanese equity markets, he felt confident enough to take some rather large risk positions in early 1995. The Nikkei 225 index had been trading in a very tight range at the beginning of January 1995. Between January 4 and January 11, for example, the Nikkei stayed between 19,500 and 19,700. With his double-long futures position on the SIMEX and OSE and his straddle options, Leeson was betting that the Nikkei 225 index would increase or remain flat. If it stayed flat, he would collect the premiums from his sold put and call options and these options would expire worthless. If the index increased greatly in value, the premium from the sold put options would partially offset the losing call option positions he sold, and he would more than make up for this difference with the windfall profits from the double-long futures positions on the SIMEX and OSE. Aside from his confidence in the volatility and future direction of the Nikkei index, there is another reason Leeson took such a large market gamble. As the case details, Leeson was already £208 million in the hole as of the end of 1994.
2/27/03with 9:14 AM Page 485 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
485
6.6.3
Effect
When a terrible earthquake rocked Japan on January 17, 1995, the Nikkei plummeted. Many people explain Leeson’s last crazy behavior as evidence that he believed the Nikkei was still undervalued and had overreacted to the disaster, and so continued to add to his futures positions. Leeson had already built a large quantity of positions. Many people may ask why he did not hedge those positions by building other positions in his account. This is a good question, but Leeson’s dilemma was this: he still believed prices would rise and his position would eventually break even or be profitable. However, even if he wanted to hedge those loss positions, he could not do so. If he used the official accounts, which would be reported to Barings, he had to establish huge positions, and he didn’t believe the price would crash deeper. Therefore, this strategy seemed too risky. But he could not hedge in his internal 88888 account, either, because in financial trading, a first-in-first-out rule is followed. Leeson’s hedging position was to liquidate all his Nikkei long and JGB and euroyen short positions. Thus, the floating loss became realized loss, and Leeson could find no place to recoup these huge losses. What he had to do was to keep them and roll them over with floating loss (a nominal loss not booked yet). In this light, it is very easy to understand the later actions of Leeson. Holding onto the belief that prices would rise, in order to protect his long Nikkei futures, short JGB, and euroyen futures positions and in order to stop the crash of his short put options positions, Leeson executed his final strategy by placing huge amounts of orders to prop up the market. Barings was on its way to collapse without realizing it due to a continuation of the deceptive practices that Leeson had engaged in since mid1992. Between January 23 and January 27, 1996, he lost approximately $47,000,000 but was able to present a $55,000,000 profit to London by crosstrading between error account 88888 and Barings account 92000. The London office heard rumors that Barings was not able to meet its margin calls in Asia, but was not concerned because it felt this rumor was based on its long Nikkei futures positions on the Osaka exchange, which were supposedly hedged by corresponding short Nikkei futures position on the SIMEX. After all, Leeson’s official trading policy was to short Nikkei 225 futures on SIMEX to hedge Barings’ long positions on the Osaka exchange. However, he went long on Nikkei 225 futures, did not hedge these positions, and exposed Barings to significant risk. During January and February 1995, Leeson was still able to receive funds from London to meet margin calls without being questioned. The payments forwarded to Singapore equaled $835 million, whereas Barings only had $615 million in capital. By late February the exposure in the Nikkei futures and options markets that Leeson created was larger than Barings could handle. The enormity of the Nikkei 225 futures margin calls and the losses on the put options bankrupted Barings.
2/27/03with 9:14 AM Page 486 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
CHAPTER 6
486
6.6.4 Risk Areas Affected The collapse of Barings could have been avoided by: •
•
•
Making all Barings traders meet London International Financial Futures Exchange (LIFFE) standards Managing account settlement and trading functions separately using management information systems Exercising rigorous management oversight
6.6.4.1 Market Risk The risks of Leeson’s strategy should be clear. If the market suffered a sharp decline, Leeson would be exposed to tremendous potential losses. The premiums from the call options he sold would have been locked-in profits, since these options would expire worthless in a sinking market. However, the put options he sold were increasing greatly in value as the market declined. With strike prices between 18,500 and 20,000 on the Nikkei 225 index, Leeson faced massive risk on these short put options if they became deep in the money. As the Nikkei plunged down under 18,000 in mid-February 1995, that is exactly what happened. The losses on these short options greatly exceeded the premiums gained on the expired sold call options. Of course, Leeson’s double exposure to the March 1995 Nikkei futures contract also left him open to the risks associated with the declining Japanese equity market. When he bought the additional 10,814 contracts on January 20, he further increased this risk. Between January 20 and February 15, the Nikkei dropped an additional 850 points. A declining Nikkei index was a large and obvious market risk that Leeson faced with his derivatives book in early 1995. In addition to market risk, Leeson was also leaving himself exposed to event risk—the risk that something unexpected and not directly related to the market could affect the market. A great example of event risk is the Kobe earthquake of January 17, 1995, which negatively impacted Leeson’s prospects for two reasons. First, it helped send the Nikkei index into a tailspin. Second, the earthquake caused increased volatility in these equity markets. Increased volatility adds value to options, both calls and puts. As Leeson was short options at this time, this increase in volatility further helped to destroy him. The short put options exploded in value as they became deeper in the money and as volatility increased. 6.6.4.2 Credit Risk By late February, Barings’ exposure in the Nikkei futures and options markets was larger than the bank could handle. The enormity of the Nikkei 225 futures margin calls and the losses on the put options bankrupted Barings. Leeson created counterparty exposure for other institutions, which finally collapsed the bank.
2/27/03with 9:14 AM Page 487 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
487
An appropriate management of counterparty risk and reporting of specific instrument exposures to counterparties would have been an additional signal for management that some exposures were intolerable. 6.6.4.3 Operational Risk As a result of Barings’ derivatives disaster, the market has attempted to head off potential government regulation by improving industry selfregulation. New standards have been developed in accordance with the regulations created by the SEC, FSA, and other national regulators of derivatives sales practices, capital standards, and reporting requirements. Most, if not all, financial firms participating in derivatives have taken a hard second look at their control systems as a result of the Barings collapse. Indeed, some have wondered why a disaster such as this hadn’t happened earlier. Valerie Thompson, an experienced trader at Salomon Brothers in London, claims that the deregulation of the British financial sector in the 1980s created a vacuum that was filled by inexperienced traders in the 1990s. Thompson observed that traders were created overnight without the benefit of proper training because firms such as Barings were chasing markets previously dominated by the Americans and Japanese. This inexperience contributed to Leeson’s undoing; he didn’t have the knowledge or experience to admit his mistakes to upper management.51 Perhaps the collapse of Barings was an unfortunate, yet necessary, lesson that the market needed to learn. Graham Newall of BZW Futures notes that upper management now regularly inquires about activity in the omnibus account. Merrill Lynch Futures’ Tom Dugan notes that firms are far less tolerant of individual stars these days and that everyone is held accountable for his or her actions. At the Futures Industry Association Exposition in Chicago in October 1996, most industry experts agreed that technology is a key ingredient in preventing scams such as Leeson’s in the future. Risk management computer systems have been developed and improved as a result of Barings’ demise.52 Nick Leeson was obviously a man of questionable character, and this was evident before he was transferred to Barings Securities (Singapore). He was scheduled to appear in court due to the accumulation of unpaid debt and had already been taken to court and ruled against on another unpaid debt charge. Leeson would not have been allowed to trade on the LIFFE due to these problems, and therefore Barings should not have allowed him to trade on the SIMEX. Making one person responsible for managing settlements and the trading floor created a conflict of interest. Leeson was able to use his influence in the back office to hide his actions on the trading floor. Assigning one of these responsibilities to a different manager would have kept Leeson from developing the ability to deceive the London office. Better management information systems were needed to ensure that all account information was available at a central location and
2/27/03with 9:14 AM Page 488 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
488
CHAPTER 6
that the complete status of all open accounts was known. Finally, Barings management should have monitored Leeson’s activities more proactively. Audits should have been performed more frequently and audit recommendations should have been immediately implemented or followed up on. Clearer lines of reporting should have been established, and office politics should not have stood in the way of proper supervision.53 After analyzing Leeson’s trading and operations activities, the question arises as to what role and responsibility risk management had or could have had. In general, three levels of risk management and valuation processes should be implemented by financial institutions: information and risk reporting, risk control, and risk management. Information and Risk Reporting
This is a basic process in measuring risk. The senior managers receive the information and reports showing risk created by trades and investments. The reporting side should provide complete, accurate, audited, and precise professionally standard information. Risk reporting is essential in valuing and managing risk. Leeson violated the principles of risk reporting. He secretly opened account 88888 and sent false information to Barings from the time he arrived in Singapore. He controlled both the front and back offices at Barings Futures (Singapore), which meant he was both chief trader and head of settlements. Taking advantage of his excessive power, he suppressed the information in account 88888, made unauthorized trades, and manipulated profits. The Barings risk reporting system was flawed. First, there was no one to supervise and assist Leeson in completing the reports and delivering reliable information to his managers. Second, the managers never investigated or doubted the credibility of Leeson’s trading activities as detailed in his reports. If the managers understood the nature of Leeson’s job, including arbitrage by taking advantage of the price differences between the SIMEX and the Tokyo Stock Exchange or the Osaka Securities Exchange, they would have been suspicious of the unusual level of profits. Arbitraging the price differences of futures contracts on separate exchanges entails very low risk. The fact that Leeson could make such a huge profit from almost riskless trading is counter to fundamental modern financial theory, which states that low risk equals low return and high risk equals high return. One question should have arisen: if such a low-risk and simple arbitrage could yield such high returns, why did rival banks not execute the same arbitraging strategy? In addition, as the volume of arbitraging trading increases, the price differences tend to decrease, and therefore the potential profit from arbitrage also likely shrinks. Why could Leeson continue arbitraging? Unfortunately no Barings executive recognized the obvious. Even when Leeson’s performance accounted for 20 percent of the
2/27/03with 9:14 AM Page 489 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
489
entire firm’s 1993 profits and about half of its 1994 profits, no one tried to determine where the enormous profits were coming from. Risk Control
Risk control is used to set position limits for traders and business units to prevent individuals from having too much power. It can be used to measure the risk in a variety of risky activities in diverse markets. Leeson continued his unauthorized trading by taking advantage of his positions. He never controlled the risk in his trading in Nikkei, JGB, and euroyen futures as well as straddles in Nikkei options. He took extreme positions without hedging the risk and continued to execute a faulty strategy. The market exposure of his positions exceeded Barings’ total capital. In 1994, Barings transferred $354 million to Barings Futures (Singapore) for the margin call from the trading Leeson explained as risk-free arbitrage. It is astonishing that no one even asked Leeson to justify his requests. Risk Management
Risk management includes the analysis and measurement of positions and strategies. It requires investment experience to supervise the exposures and the persons taking the exposures. Barings had neither the risk controls nor the risk measurement in place to analyze the exposure taken by Nick Leeson, nor the analytical framework to monitor where the huge profits came from and what kinds of risks were being taken to generate the profits. 6.6.4.4 Systemic Risk The systemic risks in the Barings case were substantial. However, all of the appropriate organizations moved to mitigate the problems created by the debacle. The Singapore stock exchange reacted quickly on the same day Barings was not able to cover the margin calls. The national banks provided additional liquidity to ensure that the markets in London and Singapore did not fall into a liquidity gap. The systemic risk was limited as the loss for counterparty risk was limited to a one-day uncovered margin call, which was settled by Barings and later through ING Groep, which acquired the bankrupt Barings. The systemic risk was further contained by the fact that Leeson’s speculation was not supported by an unheated market environment (such as in the months before the October 1987 crash) or the turmoils around the ruble and the Russian bond crisis in August and September 1998. 6.6.4.5 Additivity of Risk Management Framework The regulatory, supervisory, and corporate governance framework failed completely in the Barings case. The key failures were by weak managers who did not take responsibility for establishing systems and processes that would have prevented the bankruptcy of Barings.
2/27/03with 9:14 AM Page 490 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
490
CHAPTER 6
The capital adequacy framework should have required higher capital to support the risk of Leeson’s trading strategy, as the strategy did not allow matching and offsetting of the transactions. The internal and external bank auditors should have realized the speculative background and informed the appropriate supervisory authority.
6.7 NOTES 1. BBC News, “Business: The Economy Derivatives Firms Shut Down,” London: BBC News, Thursday, December 31, 1998. 2. Denise Lavoie, “Organized Criminal,” Associated Press and ABPnews.com, June 22, 1999; “Cendant to Pay $2.8 Billion Fraud Settlement,” APBnews.com, December 8, 1999, www.apbnews.com/safetycenter/ business/1999/12/08/fraud1208_01.html; SEC press release, “Financial Reporting Case Filed Against Cendant,” Washington, DC: SEC, June 14, 2000, www.sec.gov/news/press/2000-80-.txt. 3. “Three Bankers Brought Scandal to the Vatican,” Irish Times (August 29, 1998); “The Old Man Who Hid Gold Under His Geraniums,” Irish Times (September 16, 1998). 4. For a discussion of knowledge of the market and the bank’s capacity, see David Meerschwarn, Bankers Trust New York Corporation, Case Study 9-286005, Cambridge, MA: Harvard Business School Press, 1985. For the legal case between Procter & Gamble and Bankers Trust, see Procter & Gamble Co. v. Bankers Trust Co., 78 F. 3d 219 (6th Cir. 1996). 5. Senators John Kerry and Hand Brown, The BCCI Affair: A Report to the Committee on Foreign Relations, 102d Congress, 2d Session, Senate Print 102140, Washington, DC: Senate Printing Office, December 1992, www.fas.org/irp/congress/1992/1992_rpt/bcci/index.html; David McKean, Why the News Media Took So Long to Focus on the Savings and Loan and BCCI Crisis, Evanston, IL: Northwestern University, Annenberg Washington Program in Communications Policy Studies, 1993. 6. Deloitte & Touche: BRE-X Corporate Dissemination Services Inc.: The Deloitte & Touche Inc.’s Forensic Investigative Associate Inc. (FIA) Report to BRE-X Minderals, Deloitte & Touche, 1997. 7. Joseph Fitchett, “The Credit Lyonnais Debacle,” International Herald Tribune (London; October 3, 1996), p. 13; Ibrahim Warde, “Financiers flamboyants, contribuables brûlés,” Le Monde Diplomatique (July 1994), 18–19. 8. Alan Greenspan, “Statement to Congress, U.S. Operations of Daiwa Bank, November 27, 1995,” Federal Reserve Bulletin (January 1996), 31–35; Alan Greenspan, “Statement to Congress: Issues Relating to the U.S. Operations of Daiwa Bank, December 5, 1995,” Federal Reserve Bulletin (January 1996), 133–138; Eugene A. Ludwig, Remarks by Eugene A. Ludwig, Comptroller of the Currency, Before the Bank Administration Institute’s Asset/Liability and Treasury Management Conference, Release N6-119, Washington, DC: Office of the
2/27/03with 9:14 AM Page 491 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
491
Comptroller of the Currency, October 22, 1996; Mari Yamaguchi, “Convicted Japanese Trader Releases Memoir Accusing Daiwa of Cover-Up,” News Times (January 7, 1997). 9. Matthew Fletcher, “Whom to Trust? Investors are Spooked by Scandal in Asia’s No. 1 Fund Manager,” Asiaweek (September 27, 1996), www.pathfinder.com/asiaweek/96/0927/bizl.html. 10. Tim Spofford, Lynch Street, Kent, OH: Kent State University Press, 1988. 11. IMRO, “IMRO Announces Morgan Grenfell Compensation,” Press Release 37/96 (April 16, 1997), London; and IMRO, “IMRO Fines Morgan Grenfell £2,000,000 for Mismanagement of European Funds,” Press Release 05/97 (April 16, 1997), London. 13. SFA, “SFA Disciplines NatWest and 2 Individuals,” press release, May 18, 2000, www.fsa.gov.uk/sfa/press_releases/2000/sfa8-2000.html; comments in “NatWest Fined for ‘Rogue Trader’ Loss,” This Is Money, May 18, 2000, www.thisismoney.com/20000518/nm15300.html; “SFO May Examine NatWest,” Irish Times (July 31, 2001). 12. “The Big Noise from Columbus: The Journal of Finance Breaks the NASDAQ Scandal,” Investment Dealers Digest (May 22, 1995); Karen Donovan, “Third Circuit Reinstates Nasdaq Suit, Three Brokerage Firms Now Face Securities Class Action,” National Law Journal (February 16, 1998), B01; In RE: Nasdaq Market-Makers Antitrust Litigation to: Consolidated Amended Complaint, M2168(RWS), Civ. 3996 (RWS), M.D.L. No. 1023. 14. Sarkis Joseph Khoury, “It’s the Fundamentals: Stupid! The Orange County Bankruptcy in Perspective,” working paper prepared for the Bürgenstock Conference, University of California Riverside, September 1995; Philippe Jorion, Value-At-Risk: The New Benchmark for Controlling Market Risk, New York: McGraw-Hill, 1997, p. 32; Philippe Jorion, “Philippe Jorion’s Orange County Case: Using Value at Risk to Control Financial Risk,” www.gsm.uci.edu. 15. Anatoli Kuprianov, “Derivatives Debacles,” Economic Quarterly (Federal Reserve Bank of Richmond) 81/4 (Fall 1995), 1. 16. Ibid. 17. Ibid. 18. Reto R. Gallati, Futures, Options, and Financial Risk Management, Case: Metallgesellschaft, Reading Package FE829, Boston, MA: Boston University, Fall 2000. 19. Allen B. Frankel and David E. Palmer, “The Management of Financial Risks at German Non-Financial Firms: The Case of Metallgesellschaft,” publication no. 560, New York: Board of Governors of the Federal Reserve System; August 1996. 20. Arthur Benson v. Metallgesellschaft Corp. et al., Civ. Act. No. JFM-94-484, U.S. District Court for the District of Maryland, 1994. 21. Anatoli Kuprianov, “Derivatives Debacles,” Economic Quarterly (Federal Reserve Bank of Richmond) 81/4 (Fall 1995), 1.
2/27/03with 9:14 AM Page 492 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
492
CHAPTER 6
22. “Metallgesellschaft: Germany’s Corporate Whodunit,” The Economist (London) 334/7900 (February 4, 1995), 71ff. 23. John Digenan, Dan Felson, Robert Kell, and Ann Wiemert: “Metallgesellschaft: A Case Study,” working paper, Illinois Institute of Technology, Stuart School of Business, Financial Markets and Trading Program, undated. 24. Chicago Mercantile Exchange, Matching CME Quarterly Bankruptcy Index Futures to Different Trading Horizons: A Primer, Chicago Mercantile Exchange, www.cme.com/qbi/qbiprimer.html. 25. “Metallgesellschaft: Germany’s Corporate Whodunit,” The Economist (London) 334/7900 (February 4, 1995), 71ff. 26. Charles Cathcart, “The Lessons of Metallgesellschaft,” Global Investor (London) 78 (December 1994–January 1995), 64. 27. Reto R. Gallati, Futures, Options, and Financial Risk Management, Case: Metallgesellschaft, Reading Package FE829, Boston, MA: Boston University, Fall 2000. 28. Allen B. Frankel and David E. Palmer, “The Management of Financial Risks at German Non-Financial Firms: The Case of Metallgesellschaft,” publication no. 560, New York: Board of Governors of the Federal Reserve System; August 1996. 29. Reto R. Gallati, Futures, Options, and Financial Risk Management, Case: Metallgesellschaft, Reading Package FE829, Boston, MA: Boston University, Fall 2000. 30. Jim Kharouf, “The Copper Trader Who Fell from Grace,” Futures (August 1996). 31. Commodity Exchange Act, 7 U.S.C. §§ 6(a), 6(d), 9(a)(2). 32. Order Instituting Proceedings Pursuant to Sections 6(c) and 6(d) of the Commodity Exchange Act and Findings and Order Imposing Remedial Sanctions, Docket 98Civ. 4584(MP). Sumitomo was ordered to pay $125 million in civil punitive sanctions and $25 million in restitution to market participants harmed by the scheme. 33. Benjamin E. Kozinn, “The Great Copper Caper: Is Market Manipulation Really a Problem in the Wake of the Sumitomo Debacle?” Fordham Law Review (October 2000), 247. 34. Cargill v. Hardin, 452 F.2d 1154 (8th Cir., 1971). 35. Ibid., p. 1163. 36. Ibid. 37. Benjamin E. Kozinn, “The Great Copper Caper: Is Market Manipulation Really a Problem in the Wake of the Sumitomo Debacle?” Fordham Law Review (October 2000), 247. 38. Order Instituting Proceedings Pursuant to Sections 6(c) and 6(d) of the Commodity Exchange Act and Findings and Order Imposing Remedial Sanctions, Docket 98Civ. 4584(MP).
2/27/03with 9:14 AM Page 493 ThisGallati_06_1p_j.qxd chapter been reproduced permission from Risk and CapitalbyAdequacy, by Reto©Gallati, Reproduced withhas permission from Risk Management andManagement Capital Adequacy, Reto Gallati. 2003 The published by McGraw-Hill , New York 2003 (© McGraw-Hill, all rights reserved). McGraw-Hill Companies, Inc.
Case Studies
493
39. Ibid. 40. Commodity Futures Trading Commission, Testimony of Brooksley Born, Chairperson, on Behalf of the Commodity Futures Trading Commission before the United States House of Representatives, Subcommittee on Capital Market, Securities and Government Sponsored Enterprises of the Committee on Banking and Financial Services, Washington, DC: Commodity Futures Trading Commission, March 13, 1999. 41. U.S. Government, Hedge Funds, Leverage, and the Lessons of Long-Term Capital Management: Report of the President’s Working Group on Financial Markets, April, 1999, www.cftc.gov/tm/hedgefundreport.htm. 42. U.S. General Accounting Office, Long-Term Capital Management, Regulators Need to Focus Greater Attention on Systemic Risk, October 1999. 43. “Long-Term Capital Management: Technical Note on a Global Hedge Fund,” Thunderbird, American Graduate School of International Management, 1999. 44. Committee on the Global Financial System, A Review of Financial Market Events in Autumn 1998, October 1999. 45. Ibrahim Warde, “LTCM, a Hedge Fund Above Suspicion,” Le Monde Diplomatique (November 1998), English Internet edition, www.mondediplomatique.fr/en/1998/11/05warde2.html, accessed August 24, 2000. 46. Philippe Jorion, “Risk Management Lessons from Long-Term Capital Management,” Working Paper Series (draft), University of California at Irvine, June 1999. 47. “How LTCM Came to the Edge of the Abyss,” Wall Street Journal (September 11, 2000), pp. C1, C20. 48. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Highly Leveraged Institutions—Sound Practices, Basel, Switzerland: Bank for International Settlement, January 2000; Banks’ Interaction with Highly Leveraged Institutions, Basel, Switzerland: Bank for International Settlement, January 1999. 49. Barry Hillenbrand, “The Barings Collapse: Spreading the Blame,” Time (London) 146/18 (October 30, 1995), www.time.com/time/magazine/ archive/1995/951030/banking.box.html; Bank of England, The Bank of England Report into the Collapse of Barings Bank, London: HMSO Publications Center, 1995, www.numa.com/ref/barings/bar00.html. 50. Howard G. Chuan-Eoan, “Going For Broke,” Time 145/10 (March 13, 1995), 18–25. 51. Ibid. 52. Jim Kharouf, Carla Cavaletti, and James T. Holder, “Top 40 Brokers, Technology Key to Stay Alive,” Futures (December 1996). 53. “Simex Criticizes Barings for Role in Leeson Debacle,” Herald Tribune (March 16, 1995), p. 1; “Barings Abyss,” Futures 26/5 (May 1995), 68–74; “BoE Report Details Barings’ Guiles, Goofs,” Futures 26/10 (September 1995), 68–74.
03_jwHoffman_38246 11/20/01 6:47 AM Page 29
Reproduced from Managing Operational Risk: 20 Firmwide Best Practice Strategies, by Douglas G. Hoffman, Copyright © 2002 Hoffman. Reproduced with permission of John Wiley and Sons, Inc.
CHAPTER
3
What Is Operational Risk?
Operational risk is “the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events”* Basel Committee on Banking Supervision 20011
ne can scarcely pick up a newspaper without reading a story about an accounting embarrassment, fraud, legal action, or some other operational disaster. Operational risk seems so prevalent that one might wonder if it is too broadly defined to be useful to those in the field. How should we narrow our definition? Where should we set boundaries on operational risk? It is with these questions in mind that we begin our search for a proper and useful definition. No discussion of operational risk would be complete without some commentary on definitions. So many have approached the subject from different perspectives that finding common ground at the outset is not just important, it is essential. For instance, the subject has been approached from operations and processing managers, corporate risk managers, insurance risk managers, market and credit risk managers, auditors, regulators, and consultants. Each has brought a different but important perspective.2 Despite the definition of operational risk in the opening quote, complete consensus has not been reached, for reasons that we will explore more fully in this chapter. For one, although the Basel Committee notes in its January, 2001 release that the definition includes legal risk, it excludes reputation risk. Presumably the reason is that reputation risk is too difficult to measure, and
O
*
We might like to imply by this quote from an influential and standard-setting global regulatory body that there is full consensus on the definition of operational risk. But in reality, there is not, at least not full consensus just yet as evident by the references to definitions and risk classes throughout this book.
29
03_jwHoffman_38246 11/20/01 6:47 AM Page 30
30
WHAT IS OPERATIONAL RISK?
BP STRATEGY #1—DEFINE OPERATIONAL RISK FOR YOUR OWN ORGANIZATION Operational risk must be defined and that definition communicated in any given organization before it can be measured or managed. It is nearly impossible for a staff at large to be focused on, and committed to, a topic if the topic is not well understood.
measurement is a key part of the Basel Committee’s focus. But the danger in excluding reputation risk is that this might cause some to take their eye off the ball relative to the importance of reputation risk. It, therefore, remains critical that firms work to refine their own definitions and understanding of operational risk both individually and as an industry. Organizing a firmwide effort to manage operational risk before defining it is like going to war against an unknown adversary. The battle would be futile. Even though there is still no “generally accepted” definition, some basic components have begun to emerge, as the Basel Committee’s definition implies. This chapter will explore various considerations relative to operational risk definitions. It will address the what and why in the evolution of early definitions used by practitioners, produced by industry surveys, and adopted by regulators. It will draw a distinction between operational risk and the more narrow areas of operations risk. We will draw from research and case examples in Zurich IC Squared’s First Database3 to illustrate the significant impact of operational risk events.
BACKGROUND: OPERATIONAL RISK TRENDS AND DRIVING FORCES We all know that operational risk itself is not a new subject. In some sense, neither is operational risk management. Various functional groups within organizations have been managing these risks for years. Recent developments and trends, however, have brought new attention to the discipline. In describing the growth of operational risk, the word geometric may not be too strong. What is it about operational risk that has altered the risk landscape in recent years? There are a number of key factors that warrant study before we analyze definitions. For one thing, financial products and transactions are all more complex than ever before. Second, technological advances in the 1980s and early 1990s have given rise to financial engineering, affording firms the ability to dissect and analyze multiple dimensions of financial risks, applying hedges where advantageous. This evolution has been key in transforming
03_jwHoffman_38246 11/20/01 6:47 AM Page 31
Background: Operational Risk Trends and Driving Forces
31
corporate risk profiles and enabling reduction of the financial (i.e., market and credit) risk profiles for corporations and financial service firms alike. At the same time, however, this evolution has given rise to an entirely new phenomenon: greater complexity.4 Many of these financial structures cross many markets and product types. The underlying technology has also facilitated greater transaction velocity. In turn, however, the management of the complexity of those structures themselves has caused an even greater reliance on key systems—both central and distributed on desktops—along with key people who understand them. Thus, there are greater challenges in controlling and monitoring them, and less ability to operate manually should the technology itself fail. And so the cycle continues. The advances themselves have contributed to the expansion of operational risk. Today the advent of electronic commerce has ushered in yet another phase of change in the business and risk landscape, along with risk issues of confidentiality, identity, compromise, and repudiation.5 Several other factors are contributing to the growth of areas of operational risk. They include the continued global societal trend toward litigation as the method of choice for settling disputes, an increased frequency of large-scale natural disasters in recent years, constant change and evolution in the regulatory landscape, and problematical issues in operational risk transfer. The latter being the ability of insurance and other risk transfer products to align effectively to operational risk classes.6 More specifically, following are the factors that have prompted the acceleration of change underlying operational risks and industry emphasis on an operational risk management. 1. Headline Financial Services Losses/Recognition of Risk Costs: We have already discussed the loss figures in the introduction. Whether one focuses solely on the public figures of $15 billion annually over the past 20 years, or chooses a multiple of that amount industry-wide, the numbers cannot be ignored. As noted, some believe that the figure may be ten times the public figures. At that aggressive multiple, the figure may be closer to $150 billion. Even at a conservative multiple, however, we may be looking at $45 to $60 billion annually. 2. Other Life Threatening Corporate Events: In addition to the losses, numerous firms have been brought to their knees over operational risks and losses. The demise of Barings and Kidder Peabody are commonly given as examples. On a smaller scale, operational risk and loss have factored in firms’ decisions to exit certain businesses, or be forced into mergers because of mounting operational risk losses.7 In addition, there are scores of instances in which firms’ reputations have been damaged severely, and which now face a long slow recovery. 3. Advances in Technology: The advances in technology, processing speed, and increases in capacity have been evident throughout organizations.
03_jwHoffman_38246 11/20/01 6:47 AM Page 32
32
WHAT IS OPERATIONAL RISK?
Whether we are looking at trading operations in a financial institution front office, or origination and execution of transactions, more generally, in any organization the impact has been clear. The ability to conduct business, including necessary recordkeeping, at a far more rapid rate than ever before has been enabled by technology. Nothing underscored the pervasiveness of technological advances in the 1990s better than Moore’s Law, which states that, every 18 months, processing power doubles while cost holds constant. In other words, every 18 months you are able to buy twice the processing power at a constant price. Stated another way, every 18 months, the cost of your processing power is cut in half!8 Obviously, these technological advances have enhanced competitiveness, but they bring with them some cost, if only in terms of a variety of operational risk challenges such as the ability to process, structure, and execute increasingly complex transactions at greater than ever speeds! In the 1970s and 1980s, the greatest operational risk challenge, or one of them, was to protect an organization’s centralized data processing facilities. As time went on, technological advances gave rise to desktop computing, client-server and networked computing, and then with the advent of the Internet, open environments. Thus, whereas once the greatest challenge was in protecting the centralized data processing facility, along with software and data storage, today that challenge has been compounded many times over. Applications and data reside both in central data facilities and can reside in “miniature data centers” on virtually every desktop throughout the organization. In the perfect world, the loss of individual desktops would not present a threat to the organization. But as we all know, all employees maintain some degree of critical data on their desktop computer hard drives despite their employers’ efforts to stop them from doing so. 4. Societal Shifts/Complexity of Business: Global competition is probably the single most dominant factor driving the complexity of business today. But there are a variety of other factors as well, including changes in society, the workforce, and the needs of people. Increases in the number of two-income families, single-parent families, the dispersion of the workforce, including the advent of telecommuting, and the need to support remote workers—again supported by advances in technology, including the advent and dominance of the Internet—all contribute to additional business complexities and operational risks. 5. Societal Shifts/Global Litigiousness: Several current trends have also contributed to the rise of operational risk. One of these is the global propensity toward litigation. Not so long ago litigation was largely a phenomenon of the United States and, to a lesser extent, European and Australian society. Today we are seeing much more pervasive litigation trends around the world. Litigation has become more common in recent years even in global regions such as Asia, where it previously had been shunned. The apparent
03_jwHoffman_38246 11/20/01 6:47 AM Page 33
Background: Operational Risk Trends and Driving Forces
33
notion that there must always be a guilty party and that someone else must pay when there is a loss raises the standard of care, or at least the level of caution, and certainly reduces the margin for error in all business dealings today. Another phenomenon, particularly in financial service dealings, is the spectrum of fear and greed. Although discussions of the spectrum of fear and greed have always been present in psychological discussions among and about traders, they have only recently become part of the discussion about operational risk. 6. Increased Competition/Squeezed Margins: Increased competitiveness has also driven increased attention to operational risk and operational risk management. Simply stated, there is far less profit margin and thus far less room for error in business dealings today. In banking, for instance, whereas institutions once enjoyed generous margins on virtually all their products and services, today margins have been squeezed on all product lines to the point that some commodity-type products and services are barely profitable even before considering the cost that risk is applied to in those products and services. A risk-adjusted return might yield little or no profitability for those same businesses. Thus, operational losses, whether a function of customer dissatisfaction, booking error, or any other type—even the smallest—will be noticed. And given the increased volumes and velocities enabled by technology as discussed previously, the operational losses may be larger than what was once the case. 7. Regulatory Developments: In response to the speed of change in business, including new products, services, and processes, the global regulatory community has been scrambling to keep pace. Thus, regulations have emerged as a subsidiary factor to some of the societal and business changes. In turn, organizations must work to navigate product and service regulatory requirements and changes enacted. The patchwork of these regulations in individual countries, as a function of product and service changes, such as the proliferation of derivative markets and/or the need to navigate changes across borders, all present additional operational compliance and risk challenges. More recently, the Basel Committee’s Risk Management Group has issued a series of releases that have jolted the banking industry into action on operational risk management. 8. Problematical Insurance Environment: The presence or absence of viable insurance and risk financing solutions for operational risk has little relationship to the underlying risk trends themselves. Without a doubt, however, when left uninsured, operational losses are all the more evident. Studies have shown that the typical financial institution insurance program covers only 20–30% of the broadly defined universe of operational risks.9 Recognition of this statistic in recent years has underscored the importance of exploring areas of mismatch between operational risks and areas of insurability.
03_jwHoffman_38246 11/20/01 6:47 AM Page 34
34
WHAT IS OPERATIONAL RISK?
9. E-Commerce Activity: For the most part, Internet commerce has brought little in the way of new risks to the operational risk discussion. It has, however, accentuated some existing ones. Internet commerce has shed additional light on a variety of operational risk issues, such as security of the transaction for both buyers and sellers, legal risks relative to representation on the Internet, and vulnerability to acts of sabotage and website vandalism. All of these risks are already present in the marketplace. They are just now accentuated with a different emphasis. It is precisely this heightened emphasis, coupled with the proliferation of the Internet in society today, that has presented greater focus on operational risk and operational risk management. In fact, it can be argued that operational risk management will become an enormous part of e-commerce and e-business strategies as the Internet and use of the Internet mature. As the e-business marketplace matures in the very near future, there will be far less forgiveness for interruptions of service, less than optimal performance or service, and anything less than continuous and high-speed processing. Whereas once chief executives were primarily facing a strategic risk of not being represented on the Internet, by 2000 the issue became one of optimal performance and operational risk management of online services. Incidentally, the only new risk presented by e-commerce is probably repudiation risk, which is the risk that a party denies that they were present and a party to a transaction at all. (Chapter 18 provides a case study on risk management involving the implementation of an e-commerce business strategy.) 10. Frequency of Natural Disasters: Physical losses in the form of fire, windstorm, flood, and earthquake are the oldest form of operational risk. Many firms have been reminded of this since the 1990s as sizable windstorms have threatened the East Coast of the United States, the United Kingdom, and Europe, and earthquakes were felt in Japan, Latin America, and on the West Coast of the United States. 11. Interest in Enterprise-wide Risk Management: Last, but certainly not least, more holistic perspectives on risk in recent years, and the advent of enterprise-wide risk management programs, have placed a significantly new focus on operational risks. These developments have uncovered risks that have, heretofore, not been addressed in most financial service firms’ risk capital recognition systems.
AN EVOLUTION OF DEFINITIONS Definitions of operational risk have progressed through several iterations since widespread discussion began on the topic in the mid-to-late-1990s. In this section we will explore the thought process. As part of our operational risk management strategy at Bankers Trust, we began in about 1990 with a serious study of operational risk by asking a
03_jwHoffman_38246 11/20/01 6:47 AM Page 35
Sample Definitions and Risk Classes
35
very simple question: What risks were our market and credit risk management models and functions not addressing? Answering this question led us to identify the risks associated with key resources of the firm, such as its relationships, people, technology/processing, physical assets, and other external sources.10 The journey was instructive. Because having a full understanding of the thought process is important for any organization developing its own definition and risk classes, we will take a quick tour of our own thinking and experience before moving into the details of definitions.
A PLACE TO START Anything That Is Not Credit- or Market-Related Despite the fact that consensus on definitions of operational risk is just beginning to emerge, agreement has come a long way in a very short period time. When we began our initial study of operational risks in 1990, it was not at all clear what the area should and should not cover. By now, there has been much said about our initial parameter: “. . . anything that does not fall in the market risk or credit risk categories.” This description has been soundly criticized industry-wide, as is appropriate. For our purposes, at the time, it served as a very practical beginning point. That is, since we did not know what we were dealing with, we decided to begin looking at actual cases to help us formulate a definition. This was the origin of our initial construction of an operational loss database. The process was quite simple. We began gathering information on any loss that was not market-related (i.e., caused by asset price movements) or credit-related (i.e., caused by an inability to meet payment obligations). As such, we captured a variety of both industry and proprietary losses and began to categorize them. Once we had several hundred of them in an Excel™ spreadsheet, we began to draw some conclusions about categories, causation, and the like. This then took us in the direction of an inclusive definition. And, after awhile, we noticed some patterns beginning to form in our collection of losses.
SAMPLE DEFINITIONS AND RISK CLASSES Following some trial and error we arrived at a definition that spanned several risk classes. We liked this approach in particular because it served as a means to categorize the various loss scenarios that we were observing in the marketplace and at our own firm. The risk classes were helpful for risk modeling purposes as well. That is, we were in a position to capture losses by risk class and began to analyze them accordingly. These ranged from simple
03_jwHoffman_38246 11/20/01 6:47 AM Page 36
36
WHAT IS OPERATIONAL RISK?
mathematical totals and averages to actuarial simulations of expected and possible loss outcomes by risk class. Following is the definition we developed. It established a framework for us that was key for risk identification, measurement, management, and mitigation. The risk of loss from business disruption, control failures, errors, misdeeds, or external events We then specified that operational risk will manifest itself in five key risk classes. We settled on five because they represent responsibility and accountability, either on a firmwide basis or within individual business lines or profit centers.11 We also found it essential to apply the MECE Principle. That is, we wanted to be certain that our categories were Mutually Exclusive and Collectively Exhaustive. The five primary operational risk/exposure classes were people/human capital, relationships, systems and technology, physical assets, and other external sources.12 Brief definitions follow: 1. People Risks: The risk of loss caused intentionally or unintentionally by an employee (e.g., employee error, employee misdeed) or involving employees, such as in the area of employment disputes. 2. Relationship Risks: Non-proprietary losses to a firm and generated through the relationship or contact that a firm has with its clients, shareholders, third parties, or regulators (e.g., reimbursements to clients, penalties paid). 3. Technology and Processing Risks: The risk of loss by failure, breakdown, or other disruption in technology and/or processing. It also includes loss from the piracy or theft of data or information, and loss from technology that fails to meet its intended business needs. 4. Physical Risks: The risk of loss through damage to the firm’s properties or loss to physical property or assets for which the firm is responsible. 5. Other External Risks: The risk of loss caused by the actions of external parties, such as in the perpetration of fraud on the firm or, in the case of regulators, the promulgation of change that would alter the firm’s ability to continue operating in certain markets. All five exposure classes included several dimensions of risk, including direct economic loss, the economic impact of indirect loss or business disruption, and/or legal liability.13 The first four risk classes were logical and convenient given our objective—proactive risk management—because they relate back to functions and managerial responsibility, such as sales and marketing relationship man-
03_jwHoffman_38246 11/20/01 6:47 AM Page 37
Key Observations
37
agers, senior business management, human resource management, operations management, and senior technologists. Others, such as the compliance, legal, and security functions, can also take on matrixed responsibilities for managing risk.14 The fifth category captured certain external areas such as regulatory risk and fraud risk. Note that recent regulatory discussions have combined the scope of these risk classes. I have chosen not to do so here partially because at the time of this writing, the regulatory developments are still fluid, and they are not universally accepted yet, as shown by some of the case studies included herein. In addition, rather than re-write history, I prefer to share the evolution of our thought process here and in other parts of the Bankers Trust case throughout the book.
KEY OBSERVATIONS Along the way, we came to several observations and conclusions: ■
■
■
■
Recognize the Dimensions of Loss: As noted, we looked at multiple dimension loss scenarios involving each of the five risk classes, including their direct impact and cost, their indirect business disruption and interruption, and legal considerations.15 Broaden Perspective to Operational Not Just Operations Risk: For the most part, there is consensus today that the universe of operational risk includes, but is broader than, operations or processing risk alone. It transcends all business lines, not just information and transaction processing businesses (i.e., operations risk). Operational risk spans front, middle, and back office business operations. It is broader than just conventionally insured risk. And it is broader than studies of control failures alone.16 Represent the Business Process: Operational risks relate to all phases of the business process, from origination to execution and delivery. Exhibit 3.1 illustrates this intersection. Can these risks and their associated loss costs be sorted so that each risk and loss fits neatly into one category without overlapping one another? Is it possible to identify categories that would both be logical to senior managers and imply risk management responsibility? It was critical to the development of Operational RAROC that the answer to these questions be a resounding “yes.”17 Focus on Cause, Not Just Effect: First and foremost, being that our ultimate objective was to manage risk, we recognized early on that we were most interested in loss causes. Where were the losses coming from? For example, we were more interested in knowing that people’s errors or lack of training of people were causing losses than in knowing that we had an operational trading loss on our hands. We would be interested in where the loss had manifested itself too, of course, but that was not our first classification concern.18 In doing so, we found that we could get closer to the
03_jwHoffman_38246 11/20/01 6:47 AM Page 38
38
WHAT IS OPERATIONAL RISK?
Physical Assets
Technology
Transaction Process
EXHIBIT 3.1
■
People
Relationship
Business Management
Other External
Reputation
Risk Class vs. Business Process Intersect
underlying source, circumstances, and causative factors for each loss event. For instance, by focusing on people risk one may be more inclined to analyze the human behavior that might cause negative outcomes, whether they are simple carelessness, inadequate control, cultural, peer pressure, or dishonest tendencies. In contrast, conventional approaches to risk definition, whether borrowed from auditing, regulatory, or insurance communities, for instance, often tend to focus on the outcome or symptom (e.g., “it was a compliance, reporting, or legal risk”), rather than the underlying behavior. Although the latter terms might be useful for classification purposes and in reengineering control functions, they have limited value in analyzing causation. After all, the objective should be to facilitate and promote effective risk managed behavior, not to only measure compliance with controls alone. So whatever categories one chooses for analyzing operational risk, they should have a solid foundation for practical risk management and behavioral modification.19 Target Functional Responsibility for Risk Management: In addition, and perhaps more importantly, these five risk classes served a useful purpose for risk response. As of this writing, we have used them for many years now in risk systems because they focus on responsibility and accountability; they are not simply a convenient way to measure operational risk. Each class is multidimensional. In each class, where a loss occurs, there is direct economic impact, but there is also indirect impact. Operational loss is measured by direct economic loss, indirect expenses associated with business interruption and legal risk, and sometimes can include immeasurables, such as the negative impact operational loss has on a company’s reputation or brand.
03_jwHoffman_38246 11/20/01 6:47 AM Page 39
39
Key Observations
Functional Responsibilities
Risk Categories
Examples
People
Human error; internal dishonesty; staff unavailability (i.e., physical injury or competitive loss)
Business line human resources; Security
Relationship
Legal and/or contractual disputes
Sales and marketing; Business management; Legal; Compliance
Technology and Processing
Failure of technology; damage caused by virus/cost of eradication; loss costs due to antiquated system.
Business line technologists; Central infrastructure; Data center; Operations
Physical Assets
Loss of physical environment/business interruption; loss of negotiable assets
Operations Management
Other External
Changes in regulations; external fraud
Business line compliance; Regulatory; Security Services
EXHIBIT 3.2 Mapping Operational Risk Categories to Functional Responsibilities20 Exhibit 3.2 is a matrix that we developed to begin aligning the risk classes with various functional areas of primary responsibility. That is, we envisioned that both on a firmwide basis and a business unit basis that people risks will be presented to business managers and human resource managers for their attention. Similarly, relationship risks will be aligned to business management and sales and marketing managers for attention. Line managers, chief information officers, and operations managers will address technology and processing risks, and chief administrative officers and corporate real estate managers will manage physical risks. Last, we wanted to quantify operational risks so that severity and frequency distributions could be developed and analyzed. We were interested in events that had been experienced by our own firm, of course, but our risk exposure is broader than just our experience. We wanted a database of events that reflected relevant parts of the financial service sector’s direct and indirect exposure. An example of indirect exposure was first witnessed during the 1980s litigation
03_jwHoffman_38246 11/20/01 6:47 AM Page 40
40
WHAT IS OPERATIONAL RISK?
over lender liability, when lenders were sometimes held liable for the operational risk exposure involving tort litigation over tobacco, silicon, and asbestos. The legal theories, outcomes, and size of exposures in these cases can be analyzed and used in the development of risk management tools and predictors.21 And if all this didn't present enough challenge, although they have backed away from the notion more recently, when we began, regulators had been anxious to see reputation risk considered alongside of operational risks. In any case, it is a key consideration and factor in many operational events, particularly for banks and where human behavior is concerned. Admittedly, however, it is probably the most difficult area to quantify.22
DISSECTING RISK CLASSES AND SUBCLASSES Regardless of the high-level definition and whether there are four classes (i.e., people, process, systems, and external), five classes (i.e., people, relationship, technology, physical assets, and external), or just one aggregate risk class, a firm must have a series of meaningful subclasses. They play an important role and basis for analysis. This is also the place and point at which the definition begins to hold meaning for day-to-day business managers. It is a bit difficult for a manager to manage against a forecast number for “people risks,” for instance. On the other hand, if an analyst can provide greater detail, for instance, with numbers for people risk or losses due to employee turnover, or due to employee errors, or because of employment disputes, then the numbers have more relevance and can be addressed by management and staff alike. Regardless of your choice (or the industry’s choice) of overall definitions, therefore, it is key that the operational risk practitioner be clear about the contents of that definition. The development of the risk categories was the turning point in our early work on operational risk. We found that the operational risks had been defined so broadly that any one risk might fit into a number of classifications. In order to develop a rigorous model, we needed to be able to place each risk in one, and only one, class. We have had to continue to evolve the definitions and risk categories, but the changes have been relatively minor.23 The following examples are illustrative only for our original five risk classes. They are not meant to represent industry consensus on definitions or examples. In fact, as noted, that consensus has not yet been finalized. Thus, I present our original definitions for purposes of discussion here. In any event, it is also quite possible to combine these five classes in different ways. For example, although we always found it useful to keep them separate, some might choose to combine the People Risk class below with the Relationship class. Such combinations at a risk class level would serve to produce the evolving industry consensus classes, if desired.
03_jwHoffman_38246 11/20/01 6:47 AM Page 41
Dissecting Risk Classes and Subclasses
41
People Risk The risks associated with the employment of people (e.g., that an employee intentionally or unintentionally causes loss to the firm; losses involving employment liabilities) is the first risk category. Exhibit 3.3 is an illustration. Some examples of specific loss scenarios are employee errors, employee misdeeds, employee unavailability, and employment practices. Employee errors cause a disruption in the business processes due to an employee’s mistakes: ■ ■ ■
Documentation and keying-in errors Programming errors Modeling or pricing errors
Employee misdeeds cause a disruption in the business processes resulting from an employee’s dishonest, fraudulent, or malicious activities against a firm. It does not include employee theft of a physical asset, which is included under the main risk category of physical asset risks. ■ ■
Insider trading/rogue trading Theft from a client’s money into employee’s own account
Employee unavailability results in a disruption in the business processes due to personnel not being available at vital times or the risk of key people leaving the firm. ■ ■ ■
Loss of intellectual capital when key employees leave the firm Loss of key employees due to death, illness, or injury A strike by employees
Employment practices cause losses to a firm due to discrimination within the firm, harassment of employees or other civil rights abuses, wrongful termination of employees, and employee health and safety issues. It includes former employees, current employees, and job applicants but does not include discrimination of clients/customers. Examples include allegations of: ■ ■ ■
Improper terminations Sex, race, age discrimination toward employees with regard to promotions Discrimination with regard to hiring
Typically, the head of human resources or personnel is responsible for hiring “the best and brightest.” Good operational risk practices here can enable a firm to control the flip side of the human equation: human error, employment-related liability, fraud, or misdeeds.
03_jwHoffman_38246 11/20/01 6:47 AM Page 42
42
WHAT IS OPERATIONAL RISK?
The Orange County case is one of the largest people risk class cases in financial history. In December 1994, Orange County in Southern California publicly announced that its investment pool had suffered a $1.6 billion loss. This was the largest investment loss ever registered by a municipality and led to bankruptcy, and a mass layoff of municipal employees. The loss has been blamed on the unsupervised investment activity of Robert Citron, the county treasurer. In 1998, the Los Angeles District court upheld Citron’s authority to invest in derivative securities, despite the fact that he made “grave errors” and “imprudent decisions.” It was difficult for Citron to represent himself as an “inexperienced investor” and “lay person” after he testified that he had more than 20 years experience in the investment industry . . . . Citron had delivered returns that were 2% higher than other municipal pools in the state of California, and was viewed as a “wizard” who obtained better than average returns in difficult market conditions. Citron placed a bet through the purchase of reverse repurchase agreements (reverse repos) that interest rates would fall or stay low, and reinvested his earnings in new securities, mostly 5-year notes issued by government agencies. The strategy worked until February 1994 when the Federal Reserve undertook a series of six interest-rate hikes that generated huge losses for the fund. The county was forced to liquidate Citron’s managed investment fund in December 1994, and realized a loss of $1.6 billion. It is worth noting that, according to Philippe Jorion in his case study on Orange County, a huge opportunity was lost when interest rates started falling shortly after the liquidation of the fund, and a potential gain of $1.4 billion based on Citron’s interest-rate strategy was never realized. He found the county most guilty of “bad timing.” The lessons learned from this debacle include the lack of employment of classic risk management techniques by Citron, and his investors, including the use of Value-at-Risk (VAR), and the lack of intelligent analysis of how the county was managing to realize above-market returns.
EXHIBIT 3.3 Illustrative People Risk Case: Orange County, California Reprinted with permission from Zurich IC Squared First Database.
Here, too, human resources and business management can monitor risk and even encourage positive behavior by looking at the correlation between turnover rates, training levels, and customer complaints, and the overall quality of the people a firm is hiring: their education, experience, and the number of years of relevant expertise they bring to a company (see Exhibit 3.3).
Relationship Risks Nonproprietary losses caused to a firm and generated through the relationship or contact that a firm has with its clients, shareholders, third parties, or regulators is the second risk category. Exhibit 3.4 is an illustration.
03_jwHoffman_38246 11/20/01 6:47 AM Page 43
Dissecting Risk Classes and Subclasses
43
In February 2000, Bear Stearns & Company agreed to pay $39 million to settle a relationship risk suit brought by Granite Partners L.P., Granite Corp., and the Quartz Hedge Fund. These three hedge funds were driven into bankruptcy when the value of their collateralized mortgage obligations (CMOs) sharply fell. The hedge funds charged the New York brokerage firm with misconduct in its sales of risky CMOs. The suit alleged that Bear Stearns and two other brokerages committed fraud by selling the hedge funds’ manager, David J. Askin, esoteric mortgage-backed securities with derivative factors such as floaters and inverse floaters that peg the security’s coupon and value to an independent financial benchmark. In addition, it alleged that Askin, Bear Stearns, and two other brokerages colluded on the sales of these instruments for the fees and commission they generated. It also claimed that the brokerages loaned the hedge funds money through repurchase agreements (REPOS) in order to allow Askin to leverage the funds’ holdings. In a REPO transaction, the borrower gives securities to the lender in exchange for cash. The REPO is similar to a forward contract in that the borrower is obligated to repurchase the same securities at a specified price and date in the future. When the Federal Reserve Board unexpectedly raised interest rates several times in 1994, the value of the collateralized mortgage obligations decreased by $225 million, leaving the funds unable to meet their repurchase commitments. The brokerages then liquidated the funds’ REPO collateral, forcing Askin into bankruptcy.
EXHIBIT 3.4 Illustrative Relationship Risk Case: Bear Stearns Reprinted with permission from Zurich IC Squared First Database.
The submodule is determined by the parties affected or by the source of dispute or complaint. Some examples of specific loss scenarios are client-originated, shareholderoriginated, third-party-originated, and regulator-originated. Client-originated are losses to a firm resulting from negligence or professional errors or during the business process. Examples include: ■ ■
Faulty or inappropriate products/services causing a suit by a customer Tort or professional negligence causing a suit by a client
Shareholder-originated are losses to a firm resulting from shareholder lawsuits. Examples include: ■ ■
Unrealistic profit projections, misleading financial statements Improper business ventures or investments
03_jwHoffman_38246 11/20/01 6:47 AM Page 44
44
WHAT IS OPERATIONAL RISK?
Third-party-originated are losses to a firm stemming from interactions with third parties or suits taken by regulatory bodies. Examples include: ■ ■
The holder of a patent sues over infringement Contractual disputes with third parties
Regulator-originated are losses to a firm stemming from fines and charges extracted by regulatory bodies. Examples include: ■ ■
Enforcement of securities laws and issuing fines for breach of same Enforcement of environmental regulations and charging cleanup costs
Well-managed relationships are key to a company’s success and encompass everything from relationships with customers, regulators, and other companies to relationships with stakeholders, colleagues, media, and the public. For example, an individual or group is charged with maintaining those relationships. If any of those relationships is handled poorly or neglected, the direct operational loss includes lost sales, customers, revenue, and opportunity and higher expenses; the indirect operational loss may result in additional legal expenses, impact on reputation, and—potentially—a lower stock price.
Systems, Technology, and Processing Risks The risk that a firm’s business is interrupted by technology-related problems is the third risk category. Exhibit 3.5 is an illustration. Some examples of specific loss scenarios are external disruption and systems maintenance. External disruption is a disruption in the business processes due to systems failures outside of the firm. Examples include: ■ ■
Failure of exchanges (equities, futures, commodities, etc.) Third-party systems failure
Systems maintenance is a disruption of the business processes due to the firm’s technological (hardware and software) failures. Examples include: ■ ■ ■ ■ ■
Software problems Systems outdated and unable to handle firm’s needs Computer viruses Systems integration risks Systems developments being delayed and over budget
Most firms today have a chief information officer or chief technologist who is accountable for the firm’s technology and processing resources.
03_jwHoffman_38246 11/20/01 6:47 AM Page 45
Dissecting Risk Classes and Subclasses
On November 26, 1999, a technology problem caused reputational losses, as well as unreported monetary losses, for Halifax Bank. Sharexpress, its online share trading system, experienced a security breach, which Halifax attributed to a technology glitch during a software upgrade. In analyzing this situation, Simon Goodley and Steve Ranger wrote that “Inadequate software testing seemed to be at fault for . . . (the) . . . security breach at Halifax’s online share dealing service.” The computer glitch occurred after system modifications and testing by Halifax’s software supplier TCA Synergo. Trading began at 8 AM but was suspended at 10:30 AM on Friday morning. . . . The security breach allowed Sharexpress customers to access other customers’ personal details online. Even worse, customers were able to buy and sell shares through other Halifax customers’ accounts. In dealing with this security issue, Halifax contacted its customers to verify that accounts were in order before restoring the service. Halifax said customers’ accounts were not affected by the breach. A statement issued by the firm said that after conducting a comprehensive audit, it was found that “all trades carried out on Friday were legitimate and that customers accounts are in order.” According to a statement by Halifax, “The fault, which was identified on Friday [the day of the security breach] has now been eliminated.” Sue Concannon, Halifax’s share dealing managing director, said “the error was due to a combination of factors that the system hadn’t seen before.” Ms. Concannon agreed that similar situations could be avoided as companies gain more experience in e-commerce. A spokesman for TCA said Halifax had implemented additional controls following this problem. Halifax said that the incident affected 10 customers, but that no erroneous trades were carried out. After a weekend shutdown, Halifax’s Sharexpress resumed trading at 8 AM on Monday, November 29, 1999. This problem was a severe embarrassment to Halifax because the firm was working to turn itself into a leading e-commerce player by spending GBP 100 million to set up its Internet bank. Other e-businesses were annoyed because security breaches like Halifax’s tend to erode consumer confidence in e-commerce security across the board. As a result of this technology issue, one customer was quoted in the press as stating that he planned to change his account, move his portfolio, and cancel all standing orders and direct debits. Reportedly, Sharexpress customers had complained of technical difficulties from the time of its launch in September until this event in November 1999.
EXHIBIT 3.5 Illustrative Systems and Technology Risk Case: Halifax Bank Reprinted with permission from Zurich IC Squared First Database.
45
03_jwHoffman_38246 11/20/01 6:47 AM Page 46
46
WHAT IS OPERATIONAL RISK?
A fire ravaged the Paris headquarters of Credit Lyonnais in May 1996 in an incident that initially appeared to fit squarely in the area of physical asset risk. . . . There were, however, press murmurs from the beginning that the fire might have been an act of sabotage. A government report was released in 1998, two years after the fire, stating that it was started in two separate places before spreading rapidly through the bank’s trading floor and eventually destroying a large portion of the historic headquarters building (and a highly prized art collection). The report strongly suggested that the fire had been set deliberately and was linked to an incident that broke out in August 1997 in a bank warehouse just a few days after records were requested by the government. The earlier fire also destroyed substantial documents and files that are alleged to have shed light on the fraud case. (As of the time of this writing) an ongoing investigation into allegations of gross mismanagement of the French bank continues (as of 2001) five years after the 1996 fire and touches the bank’s operations in several European countries and the United States. In spite of the separate investigation, the case underscored the significance of concentration-of-risk concerns relative to trading floor operations from the standpoint of key people (top traders) and concentration of systems, and the need for reliable business continuity plans.
EXHIBIT 3.6 Illustrative Physical Asset Risk Case: Credit Lyonnais Reprinted with permission from Zurich IC Squared First Database.
Physical Asset Risks The risk to a firm’s business processes and key facilities due to the unavailability or improper maintenance of physical assets is the fourth risk category. Losses also include the cost of replacing items. Exhibit 3.6 is an illustration. Some examples of specific loss scenarios are crime, disasters, and product/facility damage. Disasters: ■ ■
Natural disasters include earthquakes, tornadoes, and hurricanes Unnatural disasters are bombs, fires, and explosions
Product/facility damage is damage to physical plant, facility, or product leading to losses. Examples include contamination (i.e., air, water, raw materials) and product recalls. Usually, the chief administrative officer, chief of staff, or the chief operating officer has responsibility on a corporate or business line/profit-center level for a firm’s physical assets.
03_jwHoffman_38246 11/20/01 6:47 AM Page 47
Dissecting Risk Classes and Subclasses
47
This 1999 case involves a number of insurance companies, Liberty National Securities and Martin Frankel, a money manager who is being investigated in connection with the disappearance of funds entrusted to him by the insurers. Frankel used his home as an office for his investment firm, Liberty National Securities. He was not a registered broker as his license to trade securities had reportedly been revoked by the Securities and Exchange Commission in 1992 due to investor complaints. According to the FBI (U.S. Federal Bureau of Investigation), Frankel had been defrauding insurance companies since at least 1991. Reports indicated that a dozen Southern U.S. insurance companies were missing at least $218 million that they entrusted to Frankel. Several of the companies have filed a joint lawsuit in which they represented they were missing $915 million. Frankel is alleged to have set up several corporate entities under different aliases in order to gain control of insurers’ assets. He allegedly defrauded investors by falsely promising to invest their cash and profits in his brokerage firm. In reality, Frankel “systematically drained” the insurers’ assets by laundering their funds through bank accounts he controlled in the United States and abroad and by purchasing untraceable assets. The insurance companies were headed by John Hackney and were related to a holding company, Franklin American Corp. They are reportedly controlled by Thurnor Trust, which is headed by Mr. Hackney. Hackney alleged that Thurnor Trust was owned by Frankel’s charity, the St. Francis of Assisi Foundation. Frankel was charged with wire fraud and money laundering, but the insurance companies suffered huge losses in this case of alleged external fraud.
EXHIBIT 3.7 External Loss—Liberty National Securities and Various Insurers Case excerpted from IC Squared First Database.
Note that some risk class categorizations have included physical asset risk in the external category.
External Fraud/Regulatory Change Risks Risk to business processes stemming from people or entities outside of the firm is the fifth risk category. Exhibit 3.7 is an illustration. Some examples of specific loss scenarios are external fraud and regulatory changes. External fraud are losses to a firm due to the fraudulent activities of nonemployee third parties (including clients). Regulatory changes are losses to a firm due to changes in regulations, such as the cost of implementing new procedures to comply with the regulatory change (e.g., SEC reporting modifications). They do not include fines for noncompliance of regulations.
03_jwHoffman_38246 11/20/01 6:47 AM Page 48
48
WHAT IS OPERATIONAL RISK?
Chief legal counsel and/or the compliance officer and head of security would be responsible for this category of operational risk, which includes regulatory change from a business and strategic-planning standpoint, external fraud, or other environmental change.
BUSINESS PROCESS RISK In addition to classing risks by the five “asset- or resource-related dimensions” previously outlined, we believed that there is a business process dimension of each. In other words, each of these risks classes impacts business processes throughout a firm, and vice versa. The business process is divided into four categories: (1) origination, (2) execution, (3) business line management, and (4) corporate.
Origination This includes all aspects of structuring a customer deal involving high-level customer contact. Examples of activities include, among others: ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
Advising/educating the customer about a product/service Consulting with customers about their needs Defining product and service procedures Defrauding customers/clients Designing contracts Front office activity Full and timely disclosure of information to stakeholders Insider trading Market manipulations Misleading shareholders/clients Misrepresentations in an IPO prospectus Negotiations Nondisclosure of company relationships (e.g., conflicts of interest) Overbilling Price fixing/antitrust/monopolies Pricing risk Bribes to obtain sales contracts Selling and marketing Stock price inflation due to release of misleading information by the company Structuring and customizing a contract
Execution This includes all aspects of implementing the deal and associated maintenance. Examples of activities include, among others:
03_jwHoffman_38246 11/20/01 6:47 AM Page 49
Business Process Risk
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
49
Breach of contract not related to a product Development of systems to complete contract Breach of fiduciary duties Environmental damage Execution and processing trades or transactions Health and safety of customers/nonemployees Customer service and relationship management errors or omissions Documentation issues Product liability Professional malpractice Securities violations/industry regulatory violations
Business Line Management This category includes aspects of running a business not directly linked with the creation and sale of a particular product or service, but related to the management oversight. This will include the following examples of activities, among others: ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
Business and technology strategy Fraudulently obtaining loans to support one’s business Health and safety of employees Employment practices (e.g., discrimination with regard to employees) Labor dispute/strike Excessive management control (e.g., liabilities) Money laundering Obstructions of justice Patent infringement Product strategy Tax fraud
Corporate This fourth category includes events over which an individual business line has little or no control. Corporate management, on the other hand, may have control. This will include events such as: ■ ■ ■
Physical damage due to natural disasters (i.e., earthquakes, storms, floods, etc.) Physical damage due to a major incident or nonnatural disaster (i.e., fire, terrorism, explosion) Segregation of businesses (to avoid conflicts of interest)
03_jwHoffman_38246 11/20/01 6:47 AM Page 50
50
WHAT IS OPERATIONAL RISK?
Origination
Execution
Risk and Controls
People
Relationship Technology and Processing Physical Asset Other External
EXHIBIT 3.8 Operational Risk Class Worksheet Once combined with the risk classes, the introduction of business process provides a much more complete understanding of the risks. Exhibit 3.8 is an example of an operational risk class worksheet.
AN INDUSTRY DEFINITION EMERGES In 1998 and 1999 the British Bankers’ Association (BBA), International Securities Dealers Association (ISDA), and the Risk Management Associates (RMA), and their members, sponsored a study on operational risk management. The associations retained the services of Pricewaterhouse Coopers (PWC) to conduct the project. That effort consisted of yet another, far more detailed survey of operational risk management at banking firms than those of the past. The sponsors and consultants (PWC) coordinating the BBA, ISDA, and RMA survey attempted to conclude consensus on a definition of operational risk in its 1999 final report. They noted that “while the definitions in each specific firm are different, the underlying message is the same: Operational risk is the risk of direct or indirect losses resulting from inadequate or failed processes, people, and systems or from external events.” Several key factors went into their decision to conclude this definition. They noted that it is a positive statement, rather than a negative definition, such as “everything other than credit and market risk”; they agreed that individual firms should elaborate on the stated definition with some classes of risk; and they recommended a firm’s chosen definition be included in operational risk policies in order to support and promote a common language for operational risk management.24
03_jwHoffman_38246 11/20/01 6:47 AM Page 51
An Industry Definition Emerges
51
Loss Databases and Consortia In Chapter 10 we will discuss loss databases and consortia in detail. Clear definitions are essential for maintaining consistency in the construction and maintenance of a loss database. In another attempt at achieving an industry standard on definitions, and consistency in the databases, each of the loss consortia initiated their efforts with a definition of operational risk. In another attempt at reaching consensus on an industry definition, while promoting its consortium effort, during February 2000, NetRisk, the promoter of the MORE Exchange loss consortium, released its proprietary methodology for classification of operational losses and risks available to the public.25
The Institute for International Finance (IIF) and The Industry Technical Working Group on Operational Risk (TWGOR) Definition The Institute of International Finance (IIF) is a private research and advocacy group that serves large international banks. In 1999–2000 its Working Group on Operational Risk (WGOR) and a subset of it, the Industry Technical Working Group on Operational Risk (ITWGOR) were formed consisting of representatives from a number of large international banks. A key objective was to respond to the Basel Committee’s June 1999 consultative paper on the revision to the 1988 Basel Accord. The ITWGOR is an independent body, but sometimes serves as a subcommittee of the WGOR and the IIF. The WGOR/IIF and ITWGOR have each released the papers on operational risk. In an October 2000 document,26 among its discussion of measurement approaches (specifically the Internal Measurement Approach), they advanced the following commentary on definitions: Definition of Operational Risk The ITWGOR adopted and advanced the following definition of operational risk used by the Institute of International Finance: The risk of loss resulting from inadequate or failed internal processes, people, and systems or from external events that are not already covered by other regulatory capital charges (i.e., credit, market, and interest rate risks). Business, strategic, liquidity, and reputation risks are expressly excluded. Definition of Operational Risk Losses The WGOR continues by noting that, “In any attempt to quantify operational risk, it is necessary to define what types of losses or costs are to be included in the measurement. We are using the following definition: The direct loss, including external direct cost or write-down involved in the resolution of the operational loss event, net of recoveries.
03_jwHoffman_38246 11/20/01 6:47 AM Page 52
52
WHAT IS OPERATIONAL RISK?
The definition of operational risk losses specifically excludes timing mismatches, opportunity costs, indirect losses, and near misses.”27,28 Last, the ITWGOR proposed the following list of the loss types with definitions, as part of its discussion of measurement approaches:
■ ■ ■
■
■ ■
Legal Liability: Consists of judgments, settlements, and other legal costs Regulatory, Compliance, and Taxation Penalties: Consists of fines, or the direct cost of any other penalties, such as license revocations Loss of or Damage to Assets: Consists of the direct reduction in value of physical assets, including certificates, due to some kind of accident (e.g., neglect, accident, fire, earthquake) Restitution: Consists of payments to clients of principal and/or interest by way of restitution, or the cost of any other form of compensation paid to clients. Loss of Recourse: Consists of payments or disbursements made to incorrect parties and not recovered Write-downs: Consists of the direct reduction in value of assets due to theft, fraud, unauthorized activity, or market and credit losses arising as a result of operational events29,30
THE BASEL COMMITTEE DEFINITION The most important developments toward consensus, however, involved in the actions of the Basel Committee’s Risk Management Group. The Basel Committee issued its first paper in September 1998. That document was the result of a survey of 30 major banks. It was the first of several regulatory working papers intended to define the state of operational risk management at major institutions, and advance the discipline. As a subsidiary objective, the Committee has been seeking to finalize a definition of operational risk. The most recent release from the risk management committee as of the time of this writing was the Consultative Document dated January 2001. This paper proposed the definition that appears at the opening of this chapter. Clearly, in writing this document, the Committee picked up on the definitions from the IIF, the ITWGOR, and the RMA/BBA/ISDA/PWC study as a reference to the definition it would be using. The paper states that, “In framing the current proposals, the committee has adopted a common industry definition of operational risk, namely: ‘the risk of direct or indirect loss resulting from inadequate or failed internal processes, people and systems or from external events.’ ” They continue, in a footnote, to clarify that the definition includes legal risk.31
03_jwHoffman_38246 11/20/01 6:47 AM Page 53
Conclusion
53
SOME OTHER PERSPECTIVES The industry seemed to breathe a collective sigh of relief when consensus began to emerge on an overall definition. After all, definitions had been debated at industry conferences and industry association meetings for several years. To many, the debate has seemed endless. Individual firms would do well, however, to continue working on their own definitions. Most recognize that even this most recent development from Basel requires far more refinement in the development of risk classes and subclasses, and further work on the definition itself. In addition, most firms recognize that although some consistency will be required relative to regulation and data sharing, it is most important to maintain a definition that is meaningful, generally understood, and effective within one’s own organization. In addition, some make the distinction that in the toil to arrive at a positive or inclusive definition certain risks have been left on the table. The simple phrase “people, process, systems, and external events” is not all-inclusive. Although it is convenient and provides some clarity for risk measurement purposes, it is lacking for risk management purposes. As a result, some suggest that in managing risk, firms should continue to focus on the more inclusive negative definition (“everything other than credit and market risk”). As one example, the Committee has been clear to omit reputation risk from their definition because it is so difficult to measure (understandably so). In doing so, however, they have omitted a major dimension of operational risk concern. The best firms will not lower their standards in managing risk simply because it cannot be measured conveniently.
CONCLUSION Numerous business, societal, and technological changes have sparked a dramatic growth in operational risks on a global scale. Perhaps because of its far-reaching nature and many dimensions, the debate over a definition of operational risk has been one of the most painstaking aspects of the disciplines evolution, with the single possible exception of more recent discussions about measurement and modeling. In hindsight, however, the discussion and debate have been appropriate, because it is critically important to have a definition in place before beginning the process of managing risk. The evolution began with a simple catchall phrase: “anything that is not market- or credit-related.” It has evolved through several studies sponsored by the British Bankers Association, and more recently together with RMA and ISDA, with the help of Pricewaterhouse Coopers. Most recently, the Basel Committee has picked up on the discussion and based its recent releases on the generalized definition that operational risk is
03_jwHoffman_38246 11/20/01 6:47 AM Page 54
54
WHAT IS OPERATIONAL RISK?
“ the risk of direct or indirect loss resulting from inadequate or failed internal processes, people and systems or for external events.” As this book goes to print, additional thoughtful treatment of definitions was released by the Institute of International Finance.32 There was not time to include commentary on it here. Clearly the discussion will continue for some time yet. From an individual firm’s perspective, however, it is most important to adopt and communicate a consistent definition internally, such that there is a basis for discussions about the topic of operational risk management. At the same time, there should be flexibility to allow for some consistency with the ultimate regulatory definition.
LESSONS LEARNED AND KEY RECOMMENDATIONS ■
■
■
■
■
■
Define operational risk for your organization. Operational risk must be defined and that definition communicated before it can be measured or managed. It is nearly impossible for any staff at large to be focused on, or committed to, a topic if the topic is not well understood (BP Strategy #1). Operational risk has come to be defined by some in the industry and by regulators as “the risk of direct or indirect loss resulting from inadequate or failed internal processes, people, and systems or for external events.” Although this development represents progress, and is helpful in risk measurement, it does not include strategic or reputation risk. Beware of the “out of sight, out of mind” syndrome. Definitions should include subclasses for greater specificity and focus on causative factors, as opposed to those that focus only on the effect or symptoms of operational risk and losses. The underlying risk trends and factors shed light on the real drivers of operational risk and the need for operational risk management. Studying and understanding these trends sheds additional light on where resources should be committed for mitigating causative factors. Although it is important to remain in sync with regulatory developments, it is more important to use a definition that works for your organization rather than one that conforms precisely to an industry definition. That is, you can align to regulatory definitions as a subset of your internal definition. You should also consider whether you intend to make extensive use of industry benchmark data by risk class or intend to participate in an operational loss consortium. In managing their own risks, the best individual firms will be mindful of, but not limited to, regulatory definitions. Keep the definition simple and comprehensible. It is more important to communicate the scope of your operational risk program to staff at large simply and concisely rather than to communicate a definition that is completely comprehensive and all-encompassing. Save your all-encompassing
03_jwHoffman_38246 11/20/01 6:47 AM Page 55
Lessons Learned and Key Recommendations
■
■
55
definitions for your data standards and for those who will be most involved in the data gathering process. Operations or processing risk is a key component of operational risk but should be recognized as a subset. The risk characteristics of operations risk generally fall in the high-frequency low-severity category, whereas other risks in the universe represent more catastrophe loss potential (i.e., low-frequency/high-potential severity). Although the earlier “exception” definition of, “anything that is not market- or credit-related” is not specific enough for risk measurement purposes, it remains an all-inclusive definition and is useful for maintaining a broad management perspective.
09_jwHoffman_38246 11/20/01 7:10 AM Page 181
Reproduced from Managing Operational Risk: 20 Firmwide Best Practice Strategies, by Douglas G. Hoffman, Copyright © 2002 Hoffman. Reproduced with permission of John Wiley and Sons, Inc.
CHAPTER
9
Risk Assessment Strategies
risk 1: possibility of loss or injury: PERIL 2; a dangerous element or factor; 3 a : the chance or loss of the perils to the subject matter of an insurance contract; also, the degree of probability of such loss . . . Webster’s Ninth New Collegiate Dictionary
INTRODUCTION sn’t it interesting that Webster’s still has no reference to an upside in its definition of risk? Our endgame is balancing risk and rewards. Risk response and risk mitigation are the top priorities in risk management. We covered those strategies before risk assessment and measurement to underscore that very point and to set the stage for activities required to achieve them. Practically speaking, before we can deal with risk we need to identify the sources and types of it, define them, and understand the underlying characteristics and behavioral issues as well as the external forces involved. Then, we must quantify the risk: What are the probabilities of a low-level loss versus a catastrophic loss, and how severe is it likely to be? We will include in our broad category of risk assessment the component processes of risk identification, analysis and evaluation. Risk assessment is another critical step in the risk management process. Suggesting that one should assess risk before deciding on the appropriate risk treatment measure is like saying that it would be wise to learn how to fly before getting in the cockpit. The tricky part comes in when we begin to discuss what risk assessment method is most appropriate for your organization. In this chapter we will explore the two key dimension of risk assessment: bottom up versus top down and qualitative versus quantitative. Then we will explore various qualitative approaches here. We limit our exploration of quantitative approaches for now to the last section of this chapter, “Introduction to
I
181
09_jwHoffman_38246 11/20/01 7:10 AM Page 182
182
RISK ASSESSMENT STRATEGIES
the Data Universe.” It serves as a preface to the next several chapters on loss databases and consortia, risk indicators, risk measurement and analytics, and risk capital modeling.
OBJECTIVES AND GOALS FOR RISK ASSESSMENT There are at least three key objectives here. First, determine the types of loss scenarios that we face. What risks do existing business activities, or new ones, such as e-commerce or e-business, bring in terms of operational risk? One way to do that is to determine what characteristics new businesses and older established businesses have in common and to use those as a starting point. Second, recognize the causes and how large the potential losses are. Identify the relative probabilities and loss potential. We want to fully understand what is causing the losses: Is it a quality-of-people issue, a know-your-customer issue, or a quality-of-systems issue? What are the common threads? Is it a lack of adequate supervision? Are the potential losses frequent and modest or uncommon and potentially catastrophic? How can we measure the possibilities? Third, complete the cycle by applying the results to risk mitigation. Determining capital at risk is important, but alone it is insufficient. People or organizations that are concentrating solely on capital adequacy are targeting only one of the objectives and may be missing other potential weapons in the operational risk arsenal.1
DIMENSIONS OF RISK ASSESSMENT There are two key dimensions of risk assessment. The first is the continuum from top down, high level portfolio-based views to specific bottom up processes. The second is the continuum from subjective to quantitative assessments.
The First Dimension: Top Down versus Bottom Up In the process of risk assessment, the focus should be on those exposures that can significantly impact the ability of the firm to continue operations. This is relevant at all levels in the organization, although the specificity will differ depending upon the objective of the risk assessment being undertaken. For instance, a business manager will need specific insight on individual exposures in risks in order to make prudent decisions about running the business. In contrast, operational risk practitioners who are charged with developing operational risk capital models may only need portfolio views of individual profit centers and business line operations. Similarly, insurance risk
09_jwHoffman_38246 11/20/01 7:10 AM Page 183
Dimensions of Risk Assessment
183
managers may only need exposure information by risk class in order to make decisions about constructing and fine tuning risk finance and insurance programs to hedge the risks in question. The best firmwide risk assessment programs, however, will be designed to meet these information needs at multiple levels. Hence, there is a need for both specific or granular level risk assessment processes on one hand, and more generalized, higher or aggregated portfolio-level risk assessments on the other. These have come to be known as bottom up and top down risk assessment strategies, respectively. Bottom-Up Strategies Three types of bottom up strategies all involve business level scenario analysis, often in the form of control self-assessment, independent audit reviews, and collaborative risk assessments. In concept, bottom up self-assessment processes represent an excellent way for business management to get a handle on control process gaps. If well structured, they can identify key risks in both origination and execution of transactions. But by definition, many of these analyses become extremely detailed in nature. The fact is that most bottom up self-assessment processes become so granular and time-consuming that some lose sight of the bigger picture. What is worse, they are often delegated away from busy line managers for completion—often to consultants, interns, or new junior hires— because line management simply does not have the time required to conduct the analyses. Thus, in the process, the exercise oftentimes becomes divorced from business managers themselves, thereby defeating the entire purpose! Another drawback is that too few self-assessments are conducted continuously and in “real time.” The trick is to strike a careful balance between detail, relevance, and priorities.2 Top-Down or Portfolio-Level Strategies Top down risk assessment is defined as a determination of risk potential for the entire firm—the entire business, organization, or portfolio of business. By its very nature, it is a high-level representation. It cannot get involved in a transaction-by-transaction risk analysis. A criticism often leveled against top down methods, however, is the direct opposite of its cited benefits. That is, although useful for a manager at the corporate center, it is relatively useless for managers (or risk managers) in line positions. These portfolio-level strategies seek to arrive at an aggregate representation of the risk in a business unit, an overall business line, or for the firm as a whole. Alternatively, they might seek to take a firmwide representation of riskby-risk class (e.g., by the broad classes of people, processes, and systems across the entire firm on a global basis). Portfolio-level strategies range from various types of scenario analysis to risk mapping strategies, or actuarial analysis.
09_jwHoffman_38246 11/20/01 7:10 AM Page 184
184
RISK ASSESSMENT STRATEGIES
The reality is that once one considers a full spectrum of enterprise-wide ORM objectives, a debate over top down versus bottom up is pointless. The two analyses have different uses. It all comes down to the objectives of the specific audience. The important first step is to determine one’s objectives in both risk measurement and in risk management. How broad or granular is your focus? Are we only attempting to determine the firm’s total exposure to operational risk, or are we attempting to go deeper? Do we want to understand loss potential and risk control quality by risk class (e.g., subrisk class), by business, by profit center, or even by product? From an economic capital objective, it is probably more a question of measuring the former aggregate perspectives, but from a business management view it is clearly much closer to the latter detailed views. To a line manager it is far more important to understand the loss potential in his or her processing system, or in e-commerce, than to a broader risk class like technology generally.3 Both top down and bottom up views add value in risk measurement and management, but here again neither should be used in isolation. Top down analyses are often useful for senior management (i.e., across business lines) in identifying large-scale risk management priorities (i.e., need for enterprise-wide technology initiatives, talent upgrades, etc.), or for firmwide capital-at-risk analyses. At the same time the top down analyses will have relatively less value to line managers, confronting day-to-day risks embedded in business transactions and processes. A carefully designed bottom up (i.e., self-assessment or risk assessment) approach, on the other hand, can be useful for line management in identifying control gaps, flaws in front-to-back trade processing, or staff management issues, for instance. Exhibit 9.1 is an overview of the scope of bottom up versus top down techniques. Let’s begin with bottom up best practices. When pressed, many admit that they are striving for a bottom up approach in the end because it is seen as bringing immediate tactical value to the business. By definition it is more specific as to individual business processes and yields a more detailed and complete picture of the risks embedded there.
BP STRATEGY #12—IMPLEMENT A BOTTOM-UP PROCESS TO IDENTIFY, EVALUATE, AND MANAGE OPERATIONAL RISKS Effective operational risk management implies having a clear understanding of the risks that can cause serious harm to the organization. This requires a process for identifying and evaluating new risks on a continuous basis (e.g., independent risk assessment, control selfassessment, process analysis).
09_jwHoffman_38246 11/20/01 7:10 AM Page 185
185
Dimensions of Risk Assessment
Bottom Up Strategy
Top Down Strategy
Objectives
To identify, evaluate, and quantify the risk potential at a transaction or business unit level.
To identify, evaluate, and quantify the risk potential at an enterprise-wide and/or top line business level.
Uses
• To assist in day-to-day risk–reward business decision making. • For the allocation of risk control resources, control technology expenditures.
• To support firmwide risk quantification and/or risk capital calculations. • For the allocation of enterprise-wide Internal Audit resources. • To assist in making risk finance and insurance decisions.
Tactics and • Control self-assessment Techniques • New product reviews • Business unit level scenario analysis • Process analysis VAR calculations. • Unit level interviews.
• Risk inventories. • Risk maps. • Businesswide or enterprise-wide scenario analysis. • Risk class or enterprisewide level VAR analysis. • Mid-to-top level interviews.
EXHIBIT 9.1 Risk Assessment Strategies: Bottom Up versus Top Down
The Second Dimension: Qualitative versus Quantitative Risk Assessment In another dimension, there are the extremes of qualitative or subjective risk assessments on one hand versus numeric or quantitative analyses on the other. Both extremes bring value to the process. For their part subjective risk analysis accommodates for the complexities of operational risk. In contrast, there’s enormous value in getting to a number. Most of us are now familiar with the adage “You can’t manage what has not been measured.” This is probably a bit extreme, but it certainly drives home the idea that having numeric points of reference is extremely valuable when attempting to convince a reluctant manager that he or she must invest scarce resources to address a risk. How many times have you attempted to convince a reluctant audience that they must do something and your only ammunition is a statement like “because it is important, critical, or we could have a loss if we don’t do this?”
09_jwHoffman_38246 11/20/01 7:10 AM Page 186
186
RISK ASSESSMENT STRATEGIES
Bottom Up
Top Down
Qualitative
Business Unit Level: • Control SelfAssessment (CSA) • Risk Assessment Interviews
Firmwide Level: • Interviews • Delphi Scenarios
Quantitative
Business Unit Level: • Unit level trends, regressions • Loss Distribution Analysis • Causal/Baysean Belief Network Analysis • System Dynamics Approach
Firmwide Level: • Trends/Regressions • Loss Distribution/ Actuarial Analysis • Score cards
EXHIBIT 9.2 The Quadrants and Tools of Risk Assessment
It is far more convincing to say, “We measured the loss potential to a 95% confidence level. In other words, it is highly probable that we could face a loss upwards of $100 million if we don’t address this risk.” Of the two dimensions (or four quadrants) of risk assessment illustrated in Exhibit 9.2, there is no single correct approach for all organizations. One can make a strong argument for saying that an organization should use a blend of these methodologies to reach a reasonable representation of their loss and risk profile. Finding the right “blend” all depends on your own firm’s organization, culture, risk management experience, and related objectives.
THE QUANTITATIVE VERSUS QUALITATIVE TUG-OF-WAR One danger created by the evolution of operational risk management from existing disciplines is that some practitioners will have difficulty letting go of their prior perspectives in isolation. For instance, some will continue to argue that modeling is the extent of operational risk management. Others might argue that control self-assessment defines it. Others still may argue that their business line risk control work is operational risk management. In fact they are all parts of a larger whole. One perspective and practice is simply not complete without the others. In the short time since the discipline has been developing, it has already become apparent that there are two very distinct camps forming on how best to manage these risks. On one side is a group that formed quickly and rallied around the belief that quantification is by far the most important activity for advancement.
09_jwHoffman_38246 11/20/01 7:10 AM Page 187
Bottom-Up Risk Assessment Methods—Scenario Analysis
187
Elsewhere, there are risk practitioners that are convinced that softer qualitative risk management methods, such as self-assessment, risk mapping, and scenario analysis, are the superior techniques. Some members of this group believe that quantification of operational risk is a waste of time and far better results would be obtained in focusing on these softer techniques together with behavior modification. My own experiences suggest that the best results have been obtained in applying a balance of both qualitative and quantitative techniques. It is simple enough to find illustrations of the fallacy of embracing one technique exclusively over the other.
IN RISK MANAGEMENT, BALANCE HAS BECOME EVERYTHING Long live qualitative reviews and stress testing! In case there was any doubt about the future of qualitative reviews, the Long Term Capital Management (LTCM) debacle in 1998 settled the debate. The case serves as a great illustration of embracing quantitative techniques while completely ignoring the softer qualitative approaches, including scenario analysis. LTCM may cast a long shadow on the sophisticated quantification techniques practiced by financial risk managers. Regardless of whether the case is classified as market or operational risk, the principles and the fallout are the same. After all, the management team at LTCM included some of the most sophisticated financial engineers in the industry. Their highly sophisticated models failed them in considering extreme loss scenarios, which may have also left the population-at-large questioning the wisdom and value of quantitative modeling, but certainly questioning the wisdom of quantitative modeling in isolation. Conversely, organizations such as Barings occurred while qualitative techniques such as internal auditing were already in place. In short, employing both approaches can tighten the weave in the net to catch weaknesses in the firm’s risk profile and risk management defenses. Last, because operational risk management has evolved from both qualitative and quantitative disciplines, it has the potential of making a far greater impact on the evolution and transformation of enterprise-wide risk management through balance and the inclusion of an organization’s mainstream population in the discipline.
BOTTOM-UP RISK ASSESSMENT METHODS — SCENARIO ANALYSIS There are a variety of qualitative methods in use. The remainder of this chapter will be devoted primarily to qualitative assessment techniques. They include interviews, Delphi-type scenario analysis, such as using the business vulnerability analysis part of business continuity planning as control self-assessment,
09_jwHoffman_38246 11/20/01 7:10 AM Page 188
188
RISK ASSESSMENT STRATEGIES
collaborative risk assessments, internal audit reviews, and new product reviews. Chapters 10–12 will examine a variety of aspects of quantitative techniques — that is, risk measurement.
The Risk Assessment Interview Risk assessment scenario analysis strategies can range from simply asking a few easy questions to get people thinking about the risks, the business, the processes, and the vulnerabilities, to the completion of a few grids, to very detailed process reviews. Everyone should be involved in risk assessment at one level or another. Senior managers generally think of risk intuitively. But it doesn’t hurt to ask a few high-level risk questions to get a manager’s creative juices flowing. For instance, ask key questions like: What keeps you awake at night? What is the worst thing that can happen in your business? When is the worst time it can happen? Questions such as these can bring to mind the following nightmare loss scenarios: ■ ■ ■ ■ ■ ■ ■
Loss of market share, major customer or market segment Market crash or rate spike, extreme volatility, or significant losses to market positions Technology failure, large-scale systems fault, or business interruption Control failures, errors, or unauthorized activities Large credit loss Class action legal risk Combination of events
Operational risks make the list in several places.
Delphi-type Scenario Analysis Delphi-type scenario analysis involves a number of people in the process of devising loss scenarios through collective judgment. A good example of the exercise is the typical business continuity planning risk assessment exercise.
The Business Continuity Risk Assessment Analogue Once again, there is a useful analogy to business interruption risk assessment processes that should already exist in most firms (See Exhibit 9.3). There is much to be said for leveraging these existing processes. Businesses that focus their business interruption risk management efforts toward determining where they are most vulnerable or most at risk will be better able to recover. Plan development should prioritize the urgency
09_jwHoffman_38246 11/20/01 7:10 AM Page 189
189
Bottom-Up Risk Assessment Methods—Scenario Analysis
A Strategic Perspective — Four Risk Dimensions Risk Dimensions
Definitions
Examples
Revenue and Expenses
The impact on both short term and longer term revenue streams if the business is not able to resume normal operations in a timely manner. This might include an expense associated with being unable to perform a business function.
Destruction of dealing room(s) means that traders cannot generate income and that expenses are incurred in business recovery.
Reputation and Franchise Value
The impact on current and long-term ability to attract and maintain customers. Consider the firm’s position in the market where it is a significant player and/or where its absence might have a significant impact on the market. Also consider the impact on customers/counterparties.
If the outage lasts more than a day then the firm may struggle to regain its former position or maintain its client base. For some business lines, appearing “open for business” is critical in order to retain customers/ counterparties.
Risk of Loss
The cost of significant one-time losses due to an inability to operate. Crisis management expenses, commitments made in contracts (both to customers and internal units), and guarantees should be considered.
Because a trade could not be confirmed, a payment was sent to a counterparty in error who is reluctant to return the funds.
Regulatory and Legal
Central compliance/ regulatory requirements and the cost of noncompliance.
Failure to comply with regulations could lead to fines or more serious regulatory interruptions of business
EXHIBIT 9.3 Business Disruption Risk
09_jwHoffman_38246 11/20/01 7:10 AM Page 190
190
RISK ASSESSMENT STRATEGIES
of each business function. Businesses will identify their interdependencies, both internal and external, and have an understanding of how a group providing a key service would manage its own interruption. The business continuity risk assessment process is meant to help each business line evaluate their vulnerability to business interruption risk. A risk assessment enables the business to prioritize its functions and highlight creative alternatives if a major supplier of information or service (either another internal unit or an outside vendor) is not available. By measuring and assessing the risks over time the business can determine its need for an alternate site and outline required alternate operating procedures. Business lines that must resume key functions within hours will require a site that is fully wired and can be operational quickly. Those whose operations are not as time sensitive will not require the same level of readiness. Identification of critical resources is a natural outcome of the prioritization process. All business units will review and update their risk assessment as appropriate, but at least every 12 months. Business continuity risk assessment can be organized into a three-part process. The phases include analysis of the impact of individual loss scenarios on the business unit’s functions over time, identification of critical resources, and assignment of a downtime tolerance threshold to use for classifying the criticality of the business. The outcome of each plays a key part in the development of a business continuity plan. 1. Analysis of Interruption Scenarios’ Impact on Business Functions. The objective here is to identify and analyze various interruption scenarios against four risk dimensions: revenue, reputation, risk of loss, and regulatory/legal requirements from the time of an event onward, as outlined in Exhibit 9.3. The result is a prioritization of business functions for the various interruption scenarios against the four dimensions over time. Here the goal is to define the critical objectives of the business. We prioritize key business processes and identify the dimensions of interruption risks given a range of scenarios. The business continuity risk assessment process begins with an analysis of the ways in which the scenarios impact a business unit’s product and service offerings. The nature of the business, including the complexity of transactions, will be taken into consideration, of course, when determining the scope of the risk assessment. The following steps assist in the analysis and prioritization of business functions. (a) Exposure Identification: Identify key exposures, or the business processes that may be vulnerable to interruption. This can consist of a brief description or flow chart of the operating/business environment.
09_jwHoffman_38246 11/20/01 7:10 AM Page 191
Bottom-Up Risk Assessment Methods—Scenario Analysis
191
(b) Scenario Identification: Identify the possible scenarios that could interrupt the business. These will cover situations involving building access and application availability. A thorough risk assessment will cover the complete range of possible scenarios from short-term outages to more severe longer-term interruptions. (c) Loss Potential: Evaluate the potential severity of an event on each dimension of business interruption risk (revenue, reputation, risk of loss, and regulatory. Based on a full range of interruption scenarios, business lines will study their priorities and the degree of risk attached to each. The decentralized functions in a business line and their rate of change require a periodic and continual review of priorities by all functional groups to ensure all critical functions are represented. This review will include the recovery procedures of interdependencies and key resources, as these may impact the level at which the business can develop an effective plan and recover following a disruption. The risk dimensions are designed to prioritize those business functions that need to be completed in order to protect the business. It is important to remember that while all business functions have a purpose, they do not all have the same priority, nor do they require the same level of resources. For some of the risk dimensions (especially reputation) it may be difficult to apportion an accurate dollar impact. The aim is not to have an exceptionally detailed analysis of the dollar impact of a business interruption but rather to identify the speed and severity with which the business line will be affected and necessary time frames for recovery. To develop the analysis it may be useful to plot a rough graph of dollar impact versus time. For example, a business that processes a heavy volume of high-value transactions may be vulnerable very quickly; such a business should consider having a dedicated “hot site,” with data being replicated on a real-time basis, etc. On the other hand, a relatively new or developing business may not have the same degree of vulnerability and might not require such extensive recovery capabilities. Risk assessment will be performed at all levels of the organization. For instance, exercises at the individual profit center level will complement and be consistent with more comprehensive analyses performed at the business division level. 2. Identification of Critical Resources and Interdependencies: Once a business’ priority functions have been established, the critical internal and external resources required for recovery will be identified. The objective here is to identify the key staff, equipment, and connectivity to applications.
09_jwHoffman_38246 11/20/01 7:10 AM Page 192
192
RISK ASSESSMENT STRATEGIES
The result should be a list of resources needed to recover high-priority business functions. For instance: ■
■ ■ ■
Key Staff: Identification of staff to perform key functions. This includes identifying where there are only one or two people who can fulfill a function. Applications: Both proprietary and nonproprietary applications that operate on internal equipment or at a third-party site. Types of Equipment: Personal computers, market data services, palmtops, printers, phones, faxes, photo copy machines. Types of Connectivity: Internal and external voice and data connections.
3. Downtime Tolerance: The objective here is to determine a business’ overall downtime tolerance to an interruption of operations. The resultant downtime tolerance threshold is a criticality rating that equates to the speed of recovery needed by each core business. In this phase, the planning team determines the threshold for the unit’s core business activities. This rating identifies a time frame in which its core business functions must recover. If the time frame varies based on the time of the day, week, month, or year, then businesses will err on the side of greater urgency (i.e., base the business’ risk classification rating on the most vulnerable time a business interruption event may occur). Downtime tolerance thresholds are self-assigned because the business itself is the most qualified to ascertain the margin of time between an interruption and when significant losses or exposures are incurred. A business unit’s self-assigned downtime tolerance threshold (i.e., for its core functions) will drive many other business continuity risk management considerations. Examples of these are the need for a fully readied alternate site, the frequency and thoroughness of testing requirements, and crisis management resource allocation. The classifications, might range from as little as 1 or 2 hours, to a maximum of 3 to 5 days.
Management Considerations A business’ downtime tolerance assessment might be linked to its key technology applications’ downtime tolerance, but the two are not necessarily the same. In some cases, alternate-operating procedures may enable the business to manage its risk sufficiently until the applications are available. Conversely, applications can have downtime tolerances less than the business if transactions can be processed without the business being fully operational. Depending on when applications can be recovered (i.e. “start of day” versus “point of failure”), plans will have operating procedures that adequately mitigate the interruption exposure.
09_jwHoffman_38246 11/20/01 7:10 AM Page 193
Bottom-Up Risk Assessment Methods—Scenario Analysis
193
In summary, it is clear from this overview that the business continuity risk assessment process has numerous parallels to a separate operational risk assessment exercise. The better firms will coordinate business continuity risk assessment and operational risk assessment efforts for greater efficiency overall.
Control Self-Assessment Control self-assessment (CSA) is the process by which individual business units analyze their own business processes step by step to identify the strength and weaknesses of their risk control programs. In so doing, they identify control gaps and risks. In certain respects, CSA applies scenario analysis. That is, the development of a sequence of events, when projected into a variety of outcomes, will employ various counterbalancing risk mitigation measures. CSA programs have come into vogue in recent years with the recognition that business units can be empowered to control their own business architectures on a local level, including but not limited to management of local control infrastructures. CSA programs have been developed and installed to supplement internal audit reviews, not replace them. When designed properly, a portion of the control infrastructure can be moved from internal audit to the local business line in keeping with the notion of local empowerment. This alignment does not relieve internal audit of its role for conducting independent reviews. Many risk practitioners see CSA as the cornerstone of an operational risk management program. In many respects, use of control self-assessment also fits very neatly with our BP Strategy #5 — Empower Business units with responsibility for risk management.
CASE ILLUSTRATION Control Self-Assessment The Bank of Tokyo Mitsubishi The Bank of Tokyo Mitsubishi (BTM) has used control self-assessment as an important foundation for its operational risk management program in New York. Mark Balfan, SVP, who heads market risk and operational risk management there, outlines their approach in this section. Background The concept of self-assessment has been around for many years, as has operational risk. How we manage and think about operational risk has undergone, and will continue to undergo, major changes. However, self-assessment continues to be performed in much
09_jwHoffman_38246 11/20/01 7:10 AM Page 194
194
RISK ASSESSMENT STRATEGIES
Operational Risks
People • Human resource • Sales practices • Unauthorized activities
Process • Management • Transaction
Technology • Hardware • Software
External • Criminal activities • Business environment • Disasters • Vendors /suppliers
EXHIBIT 9.4 The Bank of Tokyo Mitsubishi Risk Class Hierarchy
the same manner as it always has. Either through flowcharting or process analysis, someone determines a set of controls that should exist or do exist and assembles a set of questionnaires for each business based on those controls. The questionnaires are usually yes/no-based and tend to get stale as processes and technology change. Further, since every business is different, the set of questions in each questionnaire is different, which makes aggregation and analysis at a higher level almost impossible. Goals and Objectives The primary goal for self-assessment at BTM was to use it as a tool in identifying and measuring operational risk. In order to achieve that goal, it was essential that self-assessment be integrated with every other aspect of operational risk assessment. In order to achieve that integration, a common hierarchy of risks was established across all tools. Exhibit 9.4 is the risk class hierarchy for BTM. The hierarchy was divided into 103 subrisks. These risks formed the basis of the self-assessment. Every business was asked by operational risk management to evaluate their risks and controls for the same exact set of 103 risks. This allowed for easy aggregation and analysis. A second goal for self-assessment was that it should be riskfocused. By risk-focused we mean that rather than evaluating a long list of controls, the focus was on evaluating the risks. We continued to evaluate the controls separately as a means to manage the risks, but risk was paramount. While this distinction may sound academic, we believe it is an important one. Our experience shows that most businesses would prefer not to sound any alarm bells. As a result they tend to understate the net risk in the business. However, by focusing on risk separately from controls, we have been able to achieve more honesty
09_jwHoffman_38246 11/20/01 7:10 AM Page 195
Bottom-Up Risk Assessment Methods—Scenario Analysis
195
and consistency in the responses received from the departments. For example, most managers are quite willing to acknowledge the existence of a major risk but will most likely say that that risk is well managed. By focusing on risks separately from controls we can at least identify the high-risk areas. While these were our two main objectives, others include quantification of risk and satisfaction of regulatory purposes such as compliance with FDICIA. To achieve these additional objectives one must design the self-assessment differently to elicit the necessary information from the businesses. Design Exhibit 9.5 is a sample screen from our self-assessment program. Notice several items. (1) The business is initially prompted with a definition of the risk to be evaluated. These are from the 103 risks that we discussed before. Exhibit 9.5 is an example of question 61 which deals with data entry. (2) The business is then asked to evaluate the amount of the inherent risk to their business for that question. Inherent risk is divided into the maximum potential loss (i.e., severity) and the potential frequency. Severity and frequency combine to arrive at total inherent risk. We deliberately separated the inherent risk assessment into severity and frequency to allow for better management and control of the risk. For example, higher frequency/lower severity risks may be managed through increased controls whereas higher severity/lower frequency risks may be better managed through insurance or simple assumed by the business. (3) The controls are assessed through a very simple control effectiveness percentage (between 0 and 100%). Percentages were preferred over the standard high, medium, and low to allow for more consistent responses across businesses and to allow for easier aggregation and analysis later on. (4) We then asked business units to provide us with a list of risk indicators they use to manage that risk themselves. It’s easy for a business to say they have an effective control, but to monitor the effectiveness through indicators confirms that effectiveness. Further, providing us with indicators facilitates one of our group’s missions, which is to collect and analyze risk indicators. (5) Finally, we asked if the business has ever sustained a loss from that risk. A yes response to that question is followed up with a phone call to understand the nature of the loss and where in the organization that loss was recorded. This facilitates our loss collection efforts. Thus, it is critical to design the self-assessment in such a way so as to ensure consistent responses and to allow you to leverage off the responses for some of your other risk management initiatives such as collection of risk indicators or losses.
EXHIBIT 9.5 The Bank of Tokyo Mitsubishi Self-Assessment Data Entry Screen
09_jwHoffman_38246 11/20/01 7:10 AM Page 196
196
09_jwHoffman_38246 11/20/01 7:10 AM Page 197
Bottom-Up Risk Assessment Methods—Scenario Analysis
197
Implementation Once you have designed the self-assessment, getting the forms out to the businesses and back from them can be a monumental task. Technology has certainly assisted us in that effort. A bank’s intranet can be perfect for such a task. We distributed the forms to businesses and collected them back on the net. Receiving information electronically also allows for easier aggregation at the end. There are also various software packages out there to accomplish the tasks. However, it is impossible to judge them against each other especially if you are not very familiar with self-assessment. They all have unique strengths and weaknesses. We initially looked at them and decided to go it alone. Now that we’ve been through the process once, we are in a much better position to judge each of them. Validation Self-assessments cannot be used unless there is an in-depth validation process in place. We have three levels of validation. The first and most detailed is done by internal auditors during their annual audit cycle for each business. Each response is assessed and the control effectiveness verified. Other institutions may find it easier to conduct a special audit during the self-assessment to ensure that the responses don’t become stale by the time the audit is conducted. Our risk specialists do the second validation. Each specialist receives the results for the risks assigned to them. We ask the specialists to opine on the risk in total and not on each department’s assessment. Thus they look at the severity and frequency distribution along with the economic risk calculations and determine their appropriateness in total. Finally, our Operational Risk Management Committee reviews all of the summary analyses and raises any issues that need to be investigated further. Follow-up The whole point of self-assessment is to improve the control environment. Without a formal issue tracking process, the self-assessment just winds up as some pretty graphs. Any issues that arise from this process should be tracked and followed up on just like all other institutional issues. The Bank of Tokyo Mitsubishi case is continued in Chapter 13 Risk Profiling and Monitoring. ■ ■ ■
Collaborative Risk Assessment Approach Some firms prefer to take a different approach. Rather than leave the assessments completely in the hands of the business units, or leave them entirely in
09_jwHoffman_38246 11/20/01 7:10 AM Page 198
198
RISK ASSESSMENT STRATEGIES
the hands of Internal Audit as an independent group, they take a collaborative approach. The assessments in the following Case Illustration below are conducted by the independent operational risk management team in combination with the business units themselves. This approach can benefit from greater consistency in the results, along with the added advantage of an independent review, but requires adequate resources to get the job done. Marie Gaudioso, Vice President of The Bank of New York describes their program below.
CASE ILLUSTRATION The Bank of New York Case Organization Structure The Operational Risk Management division of the Bank of New York was established by senior management in 1999, as an independent function, to develop a framework for assessing, monitoring, measuring, and reporting on operational risk throughout the organization. Operational Risk Management, while independent, works with the business units to define the key risks in each business and assess those risks in terms of severity and probability or likelihood of occurrence. The bank’s definition of operational risk is: Operational risk is the potential for unexpected financial losses, damage to reputation, and/or loss in shareholder value due to a breakdown in internal controls, information system failures, human error, or vulnerability to external events. The Operational Risk Management unit is an independent function reporting to the Chief Risk Officer of the bank, who reports to the Chairman. The department consists of the Department Head and staff, called Business Risk Monitors, who physically reside in and are responsible for assessing the risks in specified business units. The Business Risk Monitors are responsible for identifying, assessing, monitoring, and reporting on the operational risks in those businesses. The initial stage of their job responsibilities includes mapping business processes and conducting risk assessments. Exhibit 9.6 is a sample risk assessment profile, which is created for each business and identifies risks and contains recommendations to mitigate those risks. In addition, the Business Risk Monitor is the coordinator of the Business Infrastructure Group, a multidisciplined group that meets regularly to review all current and outstanding risk issues and initiatives within each business unit and reports on the status of all risk management efforts. The second stage builds upon the risk assessments and establishes a risk monitoring process. Operational Risk Management has developed a methodology for the identification and tracking of key risk indicators
09_jwHoffman_38246 11/20/01 7:10 AM Page 199
Bottom-Up Risk Assessment Methods—Scenario Analysis
199
(KRIs). The process identifies both the drivers of risk and related metrics to enable the organization to highlight potential high risks and monitor, track, and report on the level of risk in each business unit. The third stage involves measuring losses arising from operational risk events to determine the level of regulatory capital needed to support each business and to further refine our capital allocation methodology. Operational Risk Management Objectives The Bank of New York’s Operational Risk Management unit has several objectives, namely to: ■ ■ ■ ■ ■ ■ ■
Develop a uniform and comprehensive operational risk management framework and risk assessment methodology for the organization. Develop risk profiles and monitor the status of risk mitigating action plans and other risk management initiatives in the business units. Align controls with the business objectives. Ensure that all material risks are identified and managed in accordance with management’s expectations. Provide senior management with risk-related information and the status of implementation plans. Develop and track key risk indicators. Promote control awareness among staff and throughout the business lines by sharing best practices and recommendations for improvement.
Strategy and Approach This initial stage involves the use of a qualitative risk assessment model that determines an Operational Risk Score, which incorporates an inherent risk score and a business risk assessment score. The central objectives of the evaluation process are (1) a meaningful assessment of operational risk, and (2) a balance between risks and controls that best suit the organization, provides appropriate incentives, and results in continuous improvement and resolution of operational problems. The Business Risk Monitor facilitates the risk assessment with the business unit managers and provides a level of independence. ■
■
Inherent Risk Score: The inherent risk score measures the degree to which the business unit being assessed is exposed to a set of inherent risk criteria, such as average transaction values (e.g., transaction volumes, settlement risk, transaction complexity, regulatory complexity, technology fail exposure, etc.), adjusted by a scaling factor. Business Risk Score: The business risk score is derived from a binomial model in which the risk impact of an event and its probability are rated. The risk impact denotes the degree of severity should the event occur (using a scale of 1 to 5), in terms of economic loss, damage to reputation, or loss in shareholder value. The probability is rated on a similar scale based upon the quality and effectiveness of the control environment, processes, people,
09_jwHoffman_38246 11/20/01 7:10 AM Page 200
Dept Objective Objective 1: Sufficient counterparty margin/ collateral or underlying collateral that is properly controlled or valued. The corporation’s interest in underlying collateral is perfected on a timely basis.
Significant Risks
Impact on Objective
1. Margin/collateral that is due is not tracked for timely receipt.
Bank could be exposed if customer defaults with insufficient margin.
3
1) System calculations to measure exposure periodically. 2) Notification of limit excesses.
2. Margin/collateral is not periodically marked to market.
Bank could be exposed if customer defaults with insufficient collateral value.
4
1) Vendor feeds of asset pricing. 2) Multiple feeds daily. 3) Multiple vendors. 4) Conservative valuation techniques.
3. Margin/collateral is not adequately safeguarded against inappropriate access.
Bank could suffer financial loss, reputation risk, or fraud if a customer defaults with insufficient margin.
4
1) Dual system controls. 2) System password/security methods. 3) Strong procedures and collateral confirmation methods.
4. Records of margin/collateral are not adequate.
Bank suffer financial losses if customer defaults with insufficient margin.
3
1) System specifications ensure proper records exist for audit trail. 2) System overrides are subject to dual controls and senior approval.
5. BNY’s interest in the Bank suffer financial underlying collateral is losses if the lien is not perfected. not perfected.
4
1) Periodic review of appropriate law with Legal Department and external counsel conducted. 2) Client agreements in place to document contract. 3) Legal Department and External counsel are engaged for client contract.
RI
Key Controls
EXHIBIT 9.6 Bank of New York Operational Risk Management Risk Assessment of Division ABC
200
09_jwHoffman_38246 11/20/01 7:10 AM Page 201
Risk Drivers/ Issues
Prob
Risk Score
TRS
Action Plan
P/I
RC
Priority Due Date/ H/M/L Responsibility
1) TechnologyBatch processing creates timely delays. 2) ExternalPrices are often not updated, so stale prices are used. 3) People. Insufficient number of staff to process and monitor this function.
3
9
3
1) Develop real time processing. 2) Review staffing levels. 3) Institute review of stale prices.
6
O
M
1) Thomas 2Q2001. 2) Thomas/ Smith 3Q2001. 3) Smith 4Q2001.
1) External-Prices are often not current so prices may be stale for certain assets. 2) Diverse collateral types complicate the valuation process. 3) Asset price volatility. 4) Hard to price assets.
3
12
8
1) Create reports that age the length of stale pricing. 2) Analyze stale pricing to determine trends/categories. 3) Develop a strategy to decrease stale pricing from 2 above.
4
O,M,C
M
1) Thomas 2Q2001. 2) Thomas/ Smith 3Q2001. 3) Smith 4Q2001.
Lack of supervision for segregation.
1
4
4
Current environment requires no action plan.
O
O
Not Applicable
Not Applicable.
1) External-Potential litigation and disputes from clients and counterparties. 2) ExternalComplexity of client requirements. 3) Process-Manual error.
2
6
6
Current environment requires no action plan.
O
O
Not Applicable
Not Applicable.
1) People-Lack of knowledge by staff of current law. 2) External-Changes of existing law. 3) Process-Lack of execution of periodic filings.
2
8
4
Expand Tickler system functionality to periodically review security instrument filings with appropriate jurisdictions.
4
O,L
M
Jones 3Q2001.
201
09_jwHoffman_38246 11/20/01 7:10 AM Page 202
202
RISK ASSESSMENT STRATEGIES
Potential financial impact or reputational damage would be described as follows for the various operations risks: Risk Impact Rating (RI) 1. Minor expense, industry acceptable risks type; no damage to reputation
1
2. Moderate expense and/or damage to reputation; acceptable industry risk type
2
3. Significant expense and/or damage to reputation; unusual financial risk type
3
4. Substantial economic loss including loss of shareholder value and damage to reputation; unacceptable or unusual nature or extent of risk
4
5. Major economic loss including loss of shareholder value and damage to reputation
5
Risk Probability (Prob)
Probability Weight
Very High High Mod High Medium Low
5 4 3 2 1
Definitions: Risk Score: The Risk Score represents a numeric factor based on potential risk impact and the probability based upon the existing key controls of the Impact occurring for each risk. The Risk Score is computed by multiplying the Risk Impact Probability Weight. Target Risk Score (TRS): This is the adjusted Risk Score assigned to the particular risk should the action plan be fully implemented. It is computed by taking the Risk Impact Rating (RI) and multiplying by the new Probability Weight resulting from the Risk Mitigation Plan. Potential Improvement (PI): This is the potential gain to be derived from the full implementation of the Action Plan. It is the difference between the Risk Score and the Target Score. Risk Category (RC): Operations (O), Credit (C), Legal (L), Market (M), Liquidity (Q). Overall Risk Score: It is computed by taking the total aggregate Risk Scores and divided by the aggregate number of risks.
EXHIBIT 9.6 The Bank of New York Operational Risk Assessment Legend
09_jwHoffman_38246 11/20/01 7:10 AM Page 203
Bottom-Up Risk Assessment Methods—Scenario Analysis
■
203
adequacy of systems, and management oversight. The product of the risk impact rating times the probability rating is the overall business risk score (the higher the score the higher the overall perceived operational risk). Operational Risk Score: The overall Operational Risk Score is calculated by multiplying the Inherent Risk Score by the Business Risk Score. This score can be improved once the business unit implements the recommended action plans and controls.
This model provides a “risk assessment profile” of the business overall and creates a platform to develop action plans for risk mitigation, which is monitored and updated periodically as action plans are implemented. Link to Economic Capital Allocation The risk assessment methodology is also used in the allocation of economic capital to the business lines. The allocation of economic capital is based upon a composite rating derived from the ratings from the operational risk assessments and other related factors. The Benefits for the Bank of New York are that the process: ■ ■ ■ ■ ■ ■
Assigns accountability at the business line level Provides incentives and motivates behavior to drive continuous improvement of internal processes Allocates capital based upon the risk profile and quality of the risk management and control processes in the business line Allows for proactive monitoring of risks over time and alerts management to rising levels of risk Provides flexibility in determining internal measures appropriate to the organization Provides a platform for decision making and risk mitigation strategies ■ ■ ■
Leveraging Internal Audit Reviews The assessment of operational risk has always been included in internal audit departments’ charters, whether expressly or implied. The role and reporting relationship of auditors is such that their focus is a bit different, by definition, however, than that of operational risk management. Internal auditors have responsibility and reporting relationships to the board of directors, thereby underscoring their independence from the business operation itself. An operational risk management function has a bit more flexibility in this regard. For the purposes of operational risk management, however, the work of internal auditors is entirely relevant and integral to firmwide operational risk assessment. As evidence of this, at Bankers Trust, for instance,
09_jwHoffman_38246 11/20/01 7:10 AM Page 204
204
RISK ASSESSMENT STRATEGIES
our operational risk management department was born out of collaboration from Internal Audit, Corporate Risk and Insurance Management and Strategic planning. The firm’s General Auditor played a key role in driving the development forward. Over time, however, as a bank it became advisable to separate internal audit from operational risk management. A productive working relationship remained, however. At Bankers Trust, we used internal audit reports as part of the qualitative side of our risk-based capital models. A review of the audit reports, their ratings, and the status of business management’s response formed the basis for additional risk-based modification to our statistically derived risk capital. Other firms have also used audit reports as part of their operational risk management programs. Along with their many other tools and techniques, Hansruedi Schuetter, Group Operational Risk Manager for Credit Suisse Group, has found these reports to be extremely helpful as an independent source of documented risk information. He offers his advice on the use of them in the following section, which he authored.
CASE ILLUSTRATION Leveraging Internal Audit Reviews Credit Suisse Group Internal Audit is the Chairman’s personal team of experts who perform regular independent health checks on the business. It may be safe to assume that internal auditors generally satisfy the highest integrity standards and are not driven by any profit and loss or bonus considerations in their assessments. Given the pole position that Audit enjoys, management must strive to use Audit as a powerful ally and rich source of insight and information that may otherwise be hard to obtain. This must appear as a trivial statement, however, the reality is that in many institutions, Internal Audit’s existence is considered as some sort of a necessary evil. There is probably nothing more frustrating for an auditor than knowing that nobody really cares about most of his output. Barings’ auditors pointing to Nick Leeson’s concentration of power in Singapore bears grim witness of this. At Credit Suisse Group, we pay great attention to every single audit report. Due to its early establishment and top down implementation, Internal Audit applies consistent methodologies and uniform standards. For the Operational Risk Manager, a detailed analysis of audit reports is of particular value because it provides: ■ ■ ■ ■
Firmwide coverage at all areas, all departments, all levels Examiner commands broad company knowledge and overview Uncompromising, but fair, scrutiny Findings based on documented facts
09_jwHoffman_38246 11/20/01 7:10 AM Page 205
Bottom-Up Risk Assessment Methods—Scenario Analysis
■ ■ ■ ■
205
Tailor-made recommendations Business response to findings Commitment of deadlines for remediation Early warning signals of potential danger
Shortcomings consist of: ■ ■ ■
Freeze frame type inspection Irregular inspection intervals Valuable, but potentially time-consuming, routine checks
The first two shortcomings are probably in the nature of Audit’s mandate and resources, whereas the last one is different from firm to firm. Auditors at Credit Suisse Group endeavor to dig deeper into nonroutine aspects, without neglecting to produce the necessary statistical findings. This not only enriches the auditor’s job, but also requires a much more detailed knowledge of the nature of the business inspected. How does Operational Risk Management use Audit Reports? At the Corporate level, we track audit points routinely across all business units as well as per individual unit. These high-level statistics are presented quarterly to the Executive Board and the Group Risk Coordination Committee as indicators of where management attention should be directed. As Operational Risk Manager, I sometimes have my own opinion of what is a good or a bad report. Mostly, my opinion will coincide with Audit, but often I tend to be more demanding and critical. Completely opposing overall judgments are seldom, but it has happened, mostly due to differing judgment criteria. A report calling for a few dozen laborintensive improvements is undoubtedly one that would carry a “major action required” tag, however they may represent a limited indicator only of the overall risk posed. Things I would personally consider in my own judgment would include: ■ ■ ■
Management attitude to the audit points Deadlines proposed Number of issues resolved by the time the report is delivered to senior management
Occasionally, cultural differences in the business environment may be applied when deciding on a subjective management rating. The CRO, the CFO, or the Chairman will follow up on unsatisfactory audit reports if they contain points that have not been resolved since the previous inspection or point to a substantial risk of any sort for the bank. These follow-ups are intended as a clear message to the business lines that senior management all the way at the top cares. As a consequence, it is
09_jwHoffman_38246 11/20/01 7:10 AM Page 206
206
RISK ASSESSMENT STRATEGIES
encouraging to observe the percentage of bad reports decreasing steadily, whereas the very good reports remain at a stable 20% across the group. In summary, the use of internal audit reports as a prime management tool results in: ■ ■ ■ ■ ■ ■ ■
Greater recognition, importance, and impact of Internal Audit Closer integration of Audit with the business Comprehensive management overview Judgmental health certificate (versus, e.g., VAR or similar numbers) Early warning signals of potential danger Senior management follow-up as clear message Additional bonus relevant factor
Audit reports are a powerful, value-adding tool only if senior management is prepared to fully support Internal Audit and insist on remediation of all audit points raised, something that Credit Suisse Group’s top management has committed to. ■ ■ ■
New Product Review Processes Corporations have struggled with new product and new process review processes for many years. The concept is simple: Put in place a system of review such that new products and/or processes are evaluated by risk management and control groups prior to roll-out. New product and process reviews usually involve a team of diverse corporate staff functions such as operational risk management, market and credit risk, legal, compliance, audit, technology, insurance risk management, and others, as appropriate. The challenges are also easy to understand: Business units are anxious to roll out their new products and processes. Speed to market is key and any roadblock that appears to slow things down unnecessarily is resented and often skirted, if at all possible.
TOP-DOWN (PORTFOLIO-LEVEL) RISK ASSESSMENT STRATEGIES In this section we will examine a qualitative portfolio-level method— namely, the process of building risk inventories.
CASE ILLUSTRATION Early Operational Risk Management Work Bankers Trust
At Bankers Trust,4 we began looking strategically at operational risk management as a part of an early attempt at strategic firmwide risk
09_jwHoffman_38246 11/20/01 7:10 AM Page 207
Top-Down (Portfolio-Level) Risk Assessment Strategies
207
BP STRATEGY #13—USE A PORTFOLIO-BASED ANALYSIS TO EVALUATE AND MANAGE FIRMWIDE LOSS POTENTIAL Bottom up process reviews are important for individual business unit and line managers. At a firmwide level, however, senior management must have an aggregate view of operational risk for strategic planning and decision-making. This is where the portfolio-level analysis comes in.
management. We had already developed models for market and credit risk, and now the question was: What’s missing? Thus, in 1990 we began capturing risks outside of our market and credit risk measurement criteria (i.e., beyond 99% confidence level) and calling them long-tail event risks. We also began capturing risks of a nonmarket and credit variety. The trick was not only identification of them, but at a later stage, measurement of them. Our first pass involved simple scenario analysis from the corporate level; asking questions of key managers about the loss scenarios most likely to “keep them awake at night.” Admittedly many involved credit and market risks, but oftentimes there was also an operational risk dimension (e.g., large-scale failure of key systems, overarching regulatory change, class action legal concerns, loss of key people). The exercise involved a systematic pass through risk identification, identification of past losses, assessment of projected probabilities, frequencies and severities, risk finance and/or insurance in place, and most important of all, effective risk response measures. At the time, the cornerstone of Bankers Trust’s work on operational risk was a long-tail event risk assessment project initiated in 1990 by our team, Operational Risk and Insurance Management, together with the strategic planning group. The study was intended to identify and assess all major “long-tail” event (LTE) risk classifications (i.e., event risks under the tail of the firm’s RAROC probability distribution curve, but not captured by those models at the time). This assessment led to a continuous process of work with others enterprise-wide toward enhanced management controls for each risk. Risk identification and assessment efforts in this area resulted in an extensive inventory of risk classes. Early on in the process we began to differentiate between two general areas of event risks. They were business-specific risks and universal-corporate risks. One of the first efforts that developed from this study was work based on the need to integrate defensive actions into the fabric of the firm and its day-to-day operations. Specific results of this effort were (1) the
208 • Conflicts of interest allegations involving client relationships with two or more business lines, where there is the potential for inappropriate sharing of confidential information. • Improper management of credits, particularly where the firm has responsibility as adviser or agent for a loan facility or participation. • Breach of fiduciary duties, where errors may be alleged in the handling of customer assets. • Failure to perform or execute trading commitments that result in a client’s or counterparty’s inability to meet obligations. • Investment performance involving real or perceived guarantees of investment returns. • Special loans/workouts situations in which it is alleged that the firm has become involved in the wrongful management of the customer’s business. • Improper or inadequate advice in structuring complex financial transactions. • Fraudulent misrepresentation in allegations of breached transaction warranties. • Valuation errors or omissions in investment banking transactions.
Specific areas of concern firmwide include:
EXHIBIT 9.7 Portfolio-Level Risk Inventory
There is no limitation to the reach of this risk; it is present in virtually every business unit of the firm.
It was identified that the firm’s Structured Products Group has a very effective risk response program in place, which should be promoted as a best practice for improving other divisional programs firmwide.
• Special sales and marketing product and compliance training • Product disclosures • Indemnification agreements • CSA reviews to identify and address specific vulnerabilities • Active review of customer satisfaction and/or complaints
The business divisions have the responsibility to manage the individual risks represented by these scenarios. Some of the measures being taken to respond include:
Financial services’ professional liability is becoming a major problem for financial service firms worldwide, as have liabilities for other professional disciplines, such as medical, accounting, legal, engineering, and architectural firms. The expected annual loss exposure to this risk on a firmwide basis is estimated at less than $5 million. This estimate is comprised primarily of legal defense costs. Firmwide interviews, scenario analysis discussions, and a review of external industry loss data have implied that the firm’s exposure to this risk can range, however, from $5 to $500 million!
Professional Liability Risks Legal liabilities for errors, omissions, or “wrongful acts” with respect to feebased financial services or other activities of the firm.
Risk Response Activities
Risk Assessment
Risk Description
Hypothetical Entry for Professional Liability Risks
09_jwHoffman_38246 11/20/01 7:10 AM Page 208
09_jwHoffman_38246 11/20/01 7:10 AM Page 209
209
Introduction to the Data Universe
firmwide standards for long-tail event risk and business continuity risk, (2) introduction of broader-based operational risk management research and development, and (3) the operational risk group’s coordination of round table discussions with business lines where risks were identified and management controls discussed. Exhibit 9.7 presents a fictitious illustrative risk inventory entry from this type of scenario analysis exercise. We continued this approach over several years as our early attempt at tracing large-scale firmwide long-tail event risks, as we were calling them. A key benefit of the process was the identification of low frequency/high severity risks that had not previously been in focus. In 1992 and 1993, we set out to identify a methodology that might actually align to our market and credit risk functions. Our objectives were simple enough. They spanned (1) risk measurement, in supporting capital adequacy and attribution; (2) risk management, in support of strategic decision making (i.e., invest, disinvest, or divest), and to provide support of the risk control environment; and (3) risk finance, in providing tools to support decision making relative to risk finance designs and insurance/reinsurance purchases. This time we initiated our scenario analysis approach by business. After several detailed reviews, however, we realized that while the analysis served as an informative exercise, from a loss potential perspective its results were too subjective to be completely convincing and comparative in the absence of other approaches. This observation caused us to work toward supplementing these analyses with quantitative analysis for more consistent risk-based capital measurement and allocation purposes, particularly for uses that might involve strategy decisions. Thus we move on to the universe of operational risk data. ■ ■ ■
INTRODUCTION TO THE DATA UNIVERSE Risk practitioners are thirsting for operational risk data, whether it is for modeling or simply for benchmarking purposes.5 The need for operational risk management data sets is fundamental to understanding the potential for operational risk. By way of historical perspective, operational risk and losses have always existed in financial services firms. Operational risk management has come alive in recent years because of a string of large-scale and colorful losses. So when it comes to arguing the importance of loss data, you don’t have to take anyone’s word for it. The losses speak for themselves.
09_jwHoffman_38246 11/20/01 7:10 AM Page 210
210
RISK ASSESSMENT STRATEGIES
BP STRATEGY #14 — COORDINATE EVENT AND RISK INDICATOR INFORMATION FIRMWIDE Coordinate data and information about operational risk issues, incidents, and losses by developing a process to capture and track them, including their cost and causative factors, at both business and corporate levels firmwide. Identify and track predictive indicators and drivers of operational risks. Capture both quantitative and qualitative driver data. Provide indicator reports and scores to management levels appropriate for action. A first critical step is to begin to quantify risk and losses so that we can get our arms around the depth and breadth of the problem. Once we quantify risk, it becomes both a cost and an opportunity. Operational risk data are key to understanding, measuring, and evaluating the myriad mounting risk losses cutting into the bottom line. In operational risk management, regardless of data type, the most valuable data for risk profiling will be your firm’s own. It would be ideal if operational risk data were as available as other sets such as market and economic indicator data. Unfortunately, it is not. There are several constraints that make it difficult to gather historical loss information. As a partial solution, risk management practitioners have come to realize the value of using historical industry data to supplement their own firms’ loss histories and distributions for analysis and corporate learning. What will this universe of internal and external consist of? How do we go about tracking, gathering, and organizing our data universe? Where will the information come from? Developing an operational risk data framework is the first step. When we begin to construct a framework and risk profile, we do so with the universe of information known about the organization’s experience. Then we move on to look at predictors of risk. These include broad categories of risk indicators: inherent risk variables, management controllable risk indicators, composite indicators, and model factors. Thus, the two major categories are: 1. Experience/Event Data: The capture of operational loss data has for quite some time now been a fundamental feature in support of risk management processes, in particular insurance risk management. Along with issues and incidents it represents a whole dimension of operational profiling. 2. Risk Indicators/Predictors of Risk: These enable risk managers to monitor and track several different types of data sets. Broadly defined, they include inherent risk variables or exposure bases, management control risk indicators, composite indicators, and model risk factors.
09_jwHoffman_38246 11/20/01 7:10 AM Page 211
Lessons Learned and Key Recommendations
211
The use of risk indicators and analysis is still relatively new. Before we begin, it is important to understand the subtle difference between inherent risk variables and control-oriented risk indicators. Inherent risk variables are those exposure bases or factors that describe characteristics of a business: numbers or values of transactions, assets, and fixed costs. Control-oriented risk indicators are things a manager can control, such as investments in training or systems maintenance.6 Most important of all, each variable or risk indicator must be evaluated on the basis of its significance, or predictive capabilities, to ensure accuracy and relevance throughout the various levels of the organization. The next two chapters expand the discussion of event data and risk indicators, respectively, in detail, both in preparation for the subsequent chapters on risk measurement and modeling, capital models, and risk profiling and monitoring.
CONCLUSION One of the most important steps in the risk management process is risk assessment analysis of the uncertainty of all outcomes. Understanding not only the range of possible economic impacts, but understanding the circumstances that might contribute to a loss, the scenarios that have occurred at your own firm or at other firms before, contributing factors, and the likelihood of the event are all important to analyze and understand. Every competitive organization must have a perspective on threats to its forward progress, its strategies, and certainly its survival. This is what risk assessment is all about. Viewed in this way, operational risk assessment becomes a critical part of the business, its strategy, evolution, and execution of key business plans, certainly not just a necessary evil mandated by the corporate center and industry regulators. So, regardless of the simplicity or complexity of risk assessment, the process itself is an essential part of business success.
LESSONS LEARNED AND KEY RECOMMENDATIONS ■
■
There are two key dimensions of risk assessment. The first is the continuum from top down portfolio-based views to specific bottom up processes. The second is the continuum from subjective to quantitative assessments and risk measurement. Each of the four quandrants of risk assessment adds value to the firm. Once again, balance is key. Bottom up analyses (i.e., process-level scenario analyses, such as control self-assessment) are very useful for (1) identifying specific control weaknesses in discrete processes, and (2) providing the basis for the most tangible remedial or mitigation action steps.
09_jwHoffman_38246 11/20/01 7:10 AM Page 212
212 ■
■
■
■
■
■
■
RISK ASSESSMENT STRATEGIES
Implement a bottom up process to identify, evaluate, and manage operational risks. Effective operational risk management implies having a clear understanding of embedded risks that can cause serious harm to the organization. This requires a process for identifying and evaluating new or existing risks on a continuous basis (e.g., independent risk assessment, control self-assessment, process analysis) (BP Strategy #12). Bottom up risk assessment can be very effective for analyzing specific business processes. One should be careful, however, since one size does not fit all. That is, the strategy will have to be tailored for different types of businesses. For instance, some CSA programs often result in resistance if an organization attempts to apply without modification across the entire firm. For instance, the detailed nature of these programs often work best in analyzing certain routine processes, such as money transfer or settlement businesses. Without modification, they may be rejected by non-routine functions, such as investment banking and capital markets businesses. Use a firmwide portfolio-based approach to monitor operational risks. Although bottom up process reviews are helpful for individual business unit and line managers, senior management at a firmwide level must have an aggregate view of operational risk. This is where the portfolio level analysis comes in (BP Strategy #13). Firmwide or top down analyses (i.e., class loss analyses, actuarial analyses, risk inventories, risk maps) are most useful for (1) Strategic planning and portfolio-level decisions about allocations of capital and (2) risk class-based decisions about enterprise-wide risk financing and insurance programs. Use of internal audit reports by operational risk management can leverage the audit function for even greater impact and, on occasion, provide a second opinion on audit findings (useful to avoid the Barings’ syndrome). One key feature that differentiates modern-day operational risk management programs from its predecessor programs of the past is the concept of identifying risk classes, gathering data, and beginning to prove causation. All of this plays to a need for a universe of data to profile, understand, and track various characteristics of the risks. Coordinate event and risk indicator data firmwide. Track operational risk issues, incidents, and losses by developing a system to capture and track them, including their cost and causative factors, at both business and corporate levels firmwide. Identify and track predictive indicators and drivers of operational risks. Capture both quantitative and qualitative driver data. Provide indicator reports and scores to management levels appropriate for action (BP Strategy #14).
12_jwHoffman_38246 11/20/01 7:25 AM Page 257
Reproduced from Managing Operational Risk: 20 Firmwide Best Practice Strategies, by Douglas G. Hoffman, Copyright © 2002 Hoffman. Reproduced with permission of John Wiley and Sons, Inc.
CHAPTER
12
Operational Risk Analysis and Measurement Practical Building Blocks
INTRODUCTION ne of the more significant advancements in recent years that has served to define operational risk management is the introduction of greater sophistication in risk measurement techniques. This has included the use of quantitative techniques for measurement and modeling future loss scenarios. In and of itself, this change ranks high among Best Practice advancements. Any technique that increases the confidence of forecasting potential risk and loss outcomes must be viewed as a step forward. The bottom line objective, of course, is to get ahead of loss scenarios before they develop and take action to eliminate or minimize ultimate losses. For some, the shift away from using only subjective risk assessment techniques has been a natural progression; for others, it has simply added more confusion to an already complex topic. I am certainly an advocate of using analytics to advance the state of operational risk management, including but not limited to actuarially based risk capital models. However, I would certainly not suggest that the most sophisticated of these techniques are practical for firms of all sizes, cultures, and business compositions. In addition, as we learned from cases like Long Term Capital Management, they should not be the sole method of operational risk assessment at any firm. Recognizing that one size does not fit all, this chapter presents a series of building blocks—a progression of metrics and analysis topics, and lays the groundwork for economic capital models and regulatory capital discussions. At the outset, we cover our objective for analysis. Then, we cover some background and introduction to data interpretation, analytics, and metrics. Next, we look at simple calculations, such as indices, cost-of-operationalrisk (COOR) calculations, trend line, and expected loss calculations. We
O
257
12_jwHoffman_38246 11/20/01 7:25 AM Page 258
258
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
then introduce some emerging application of more sophisticated analysis in operational risk. The latter include correlations between risk indicators, actuarial analysis, and causal analysis, all with a view toward management reporting topics such as the need for an operational risk management dashboard, and the like. Perhaps most timely, given the industry focus on the prospect of regulatory capital and the still early stage of the operational risk management discipline, this chapter also provides an important foundation for later treatment of economic capital models (Chapter 16) and regulatory developments (Chapter 17). It is not the intent to cover a detailed technical discussion of each modeling approach in this book. The reader who wants to take the topic further should look to several excellent texts that have recently emerged on the subject (see Additional Readings at the end of the book. In addition, the reader can find several sources of good information about quantitative analysis and economic capital modeling in the bibliography to this book.)
MANAGEMENT REPORTING AND IMPLIED ANALYTICS Experience has taught us that one of the places to begin planning for management reporting and the need for analytics is with the audience. If our goals are to influence decision making in a productive way, and spur management to act to avoid or minimize losses, then the key is to determine what information is needed to achieve that goal. What data, information, and reporting would be most useful to answering the relevant questions at a line management level, at a senior management level, or at a Board level? Knowing this will help to identify what data and analytics would be most useful. With that in mind, one of the first aspects we look at in this chapter is the relationship of analytics and management reporting. The overall objective for ORM is to create an integrated program and arsenal of information. A logical place to begin our discussion of analytics and metrics is by revisiting our Management Reporting and Decision Tools Matrix from Chapter 8 here. Exhibit 12.1 illustrates the component parts required to support an integrated program and the management reporting that we discussed in Chapter 8. Here we add the dimension of implied data needs and analytic implications for the management reports and decision tools needed. Later, in Chapter 13, we look at the implications of the reports and system screens needed for risk monitoring. Exhibit 12.1 shows that much can be accomplished with the basic data and some simple mathematics alone. Many of the individual reports, data needs, and implied analytics shown should be self-explanatory from the exhibit.
12_jwHoffman_38246 11/20/01 7:25 AM Page 259
259
Management Reporting and Implied Analytics
Management Need and Implied Reporting 1. Consolidated Risk Profile Dashboard
2. Risk Assessment Tracking
3. Individual Risk Indicator Report and Monitoring
Implied Data Needs Extensive use of: • Risk indicators • Issues • Incidents • Losses
Implied Analytics and Report Format • Range from simple math to more complex analytics including regressions and simulations • Normalize to an index, benchmark • Integrate many of the other analyses outlined below
Numbers of assessments • Percentages of totals, or against goals, completed benchmarks, etc. • Produce pie charts, bar graphs • Risk and performance • Bar charts, line graphs indicators by business • Dials and gauges unit or by risk class. • Data capture from internal and external systems
4. Risk Indicator Risk indicators by Composite Reviews business unit or by risk class.
5. Customized Risk Index (indicator index) creation
Risk indicators scoring system (e.g., min-max)
6. “Issue Display” and Management Report
Display of issues identified
Interest in: • Testing correlations between risk indicators • Testing certain indicators as predictors of losses, thus narrowing the need to track a long list
Simple math (addition, percentage completed, addressed) Continued
EXHIBIT 12.1 Sample Management Reporting Needs: Implied Data and Analytics
12_jwHoffman_38246 11/20/01 7:25 AM Page 260
Management Need and Implied Reporting 7. Risk Management Initiative (Project) Tracking
Implied Data Needs Listing of projects
Implied Analytics and Report Format None—data display only from issues listing
8. Causal Analysis Pre- Need to populate a fault Might imply the creation of a fault tree (e.g., tree with assumed dictor Report if x, then y), use of a probabilities and tree Baysean Belief branches with outNetwork comes from risk indicator pick list and from firm’s own incident categories 9. Incident Displays
Listing of incidents, along with data dimensions about individual incidents (e.g., numbers of incidents by type, dates, descriptions, cause [see Chapter 10 for detailed descriptions])
10. Incident Trends and • Incident capture firmwide Forecast Needs • Key risk and performance indicators for use as exposure bases
Nothing unique—might imply a simple tabular display of all incident types
• Might imply a graphical trendline of incident types • Might imply need for regression capabilities Might entail: • Regression, simulation, and other capabilities • Need to produce frequency, severity, and combined loss distributions Use of Extreme Value Theory
11. Loss Forecasting
• Access firm’s own loss data along with industry loss data for combined analysis • Need to access select risk indicators to serve as exposure bases for forecasting
12. Monitoring Risk During Threshold Events
Manager wants to proData on new and old duce a Threshold Event organization scenarios or Accelerator Effect Losses suffered by Report. There is ample others in industry evidence to show that involved in similar certain threshold events situations can accelerate the probability of losses
EXHIBIT 12.1 Sample Management Reporting Needs: Implied Data and Analytics
260
12_jwHoffman_38246 11/20/01 7:25 AM Page 261
261
Operational Risk Analysis and Decision Tools in Practice
Management Need and Implied Reporting
Implied Data Needs
Implied Analytics and Report Format
Depends on the apLoss data proach taken—might Exposure data imply anything from Risk factors simple mathematics Business line financial to regression analysis information and Monte Carlo simulations: • Loss data-based/ actuarial analysis • Issue-based • Causal factor-based • Economic pricing • Expense-based
13. Economic Risk Capital Analyses and Reports
• • • •
14. Regulatory Risk Capital Analysis and Reports
Prescribed by regulators: Simple math only in most scenarios. Might imply • exposure bases the need for Monte • internal loss data Carlo simulations • industry data
15. Cost of Operational • Loss data by class, by In most cases requires only simple math business Risk Reports • Insurance/risk finance premiums, recoveries • Risk control/response costs 16. Risk Finance/ Insurance Decision Reports
• Proprietary loss data Analysis may be too labor intensive to be by exposure/risk class automated. Artificial • Industry loss data intelligence application needed ?
17. Risk Response Reports
Example: Business Continuity Planning Status Report
EXHIBIT 12.1 Sample Management Reporting Needs: Implied Data and Analytics
OPERATIONAL RISK ANALYSIS AND DECISION TOOLS IN PRACTICE Marcelo Cruz, formally of UBS Warburg, and a recognized leader in operational risk measurement analytics, uses the compelling example of the models underlying sophisticated weather systems, run on supercomputers, to
12_jwHoffman_38246 11/20/01 7:25 AM Page 262
262
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
predict hurricane paths. He has cited the example of Hurricane Lenny in 1999 in which sophisticated measurement was used to forecast its path with 90% accuracy. By predicting the path of the hurricane with high accuracy, farmers and others in the hurricane track were provided reasonable warning of the storm. The systems saved an indeterminable number of human lives. In addition, businesses were in a better position to take reasonable precautions and property losses were mitigated. He uses this as an example of the benefits of investment to supplement judgment with sophisticated measurement techniques, rather than continue to rely solely on managers’ and operational risk professionals’ experience and judgment alone.1 Our own operational risk management team at Bankers Trust has been credited with advancing operational risk management through the use of data capture and risk measurement techniques in the modeling of operational risks. In the process our work supported operational risk-based strategic decisions (i.e., business strategy investments) and helped to target areas warranting control and risk finance investments. Retracing the evolution of our own work will be helpful and instructive to others just getting started in operational risk analytics and measurement. Our first risk measurement effort began in 1990 with scenario and single risk class modeling, expanding to operational risk actuarial and capital allocation techniques, and then to firmwide production models beginning in 1995. In production we modeled individual operational risk classes and the firm’s operational risk exposure across all business lines and on a global basis. After developing a methodology to measure operational risk, we moved on to design an allocation methodology for aligning the model results with risk profiles of the individual business lines within the bank’s overall portfolio. We dubbed this overall program “Operational RAROC (Risk-Adjusted Return on Capital)” because it fit under the firm’s existing risk capital architecture. Internally at Bankers Trust this development work was seen as a great leap forward in operational risk management because, among other things,
BP STRATEGY #15—APPLY ANALYTICS TO IMPROVE ORM DECISION MAKING One of the most significant advancements in modern operational risk management is the introduction of quantitative techniques for risk assessment and modeling of future loss scenarios. Apply analytics to support operational risk management decision making on a day-to-day business level, as well as in strategic risk–reward decision making on a portfolio level. Apply levels of analytic sophistication appropriate for your individual firm’s size, culture, and business mix.
12_jwHoffman_38246 11/20/01 7:25 AM Page 263
263
Modeling: What Is a Model?
PAST
PRESENT
FUTURE
• Incidents • Losses • Risk indicators
• Risk assessment / Selfassessment • Risk indicators • Issue tracking • Fuzzy logic
• • • •
Scenario analysis Risk mapping Trending risk / data set Monte Carlo simulation
EXHIBIT 12.2 Operational Risk Measurement: Getting a Handle on the Past, Present, and Future
it introduced far greater credibility to the firm’s measurement of potential losses from the scenario analyses. Many firms have since joined the effort and continue to move operational risk management Best Practices forward. To be successful in operational risk management, one must understand the differences between leading and trailing indicators, analytic tools, and risk measurement overall. We list the different approaches in Exhibit 12.2. For instance, tracking incidents, losses, and risk indicators are all examples of getting a handle on the picture of operational risk in the past. On the other hand, risk assessment, self-assessment, current risk indicators, and issue tracking are all examples of profiling operational risk in the present. Last, scenario analyses, risk maps, trending risk and data sets, and Monte Carlo simulation are all examples of profiling future risk. All of the tools that are presented here have their use and place, but each should be evaluated for its relative strengths and weaknesses in terms of how accurately they present the past, present, and future, and how effective they are in accomplishing our risk management goals. Exhibit 12.2 lists some of the data and tools available to us today in undertaking operational risk measurement.
MODELING: WHAT IS A MODEL? This isn’t a trick question. It is actually very useful to step back for a moment and look at a few definitions. Among the definitions of models found in Webster’s dictionary is: (1) “a description or analogy used to help visualize something that can be directly observed” and (2) “a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs.” We will apply both of these definitions in this chapter. That is, we will take a very broad, and perhaps liberal, definition of modeling. For our purposes, we will define an operational risk model as any methodology or routine that provides information and helps us to make decisions regarding the management of operational risk.
12_jwHoffman_38246 11/20/01 7:25 AM Page 264
264
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
Analysts often become passionate about their models. Some observers have suggested that the word might be “obsessive.” As evidence, operational risk conferences are often divided into two or more streams of sessions. At one such recent conference, there was a stream dedicated to quantification and measurement sessions. In the other stream were sessions on softer operational risk management techniques. It was interesting to observe the very distinct camps that were forming between the two, but somewhat troublesome to observe the lack of patience and, dare I say, respect that some of the “modelers” shared for the “managers,” and vice versa. I will take this opportunity to remind the reader that balance between the two camps will be key to the most effective operational risk management programs.
SOME MODELING ISSUES FOR RESOLUTION Before we begin a discussion of alternative modeling approaches, there are some additional issues that must be considered by the modeling team. They range from definitions, to scope, credibility, balancing causes and symptoms, and balancing predictive and reactive modeling features. ■
■
Definitions, Again: First and foremost, there should be a universal definition of operational risk used in all of your models. If you have not yet settled on a definition of operational risk by the time you get to modeling, you should return to square one. Definitions are generally important enough in operational risk management, of course. When it comes to the subject of models, however, it is critical that all business units and staff are speaking the same language with regard to the model application. Imagine the confusion that would arise in an organization if business “A” had not defined “people risk” to include the same subclasses as business “B.” Representing the Organization / Granularity: A second challenge when it comes to modeling is how best to represent the organization. Does it make more sense to construct a model and derive numbers at a firmwide, business line, profit center, portfolio, or desk level?
Initially, much of the answer to this question lies in the risk management and modeling objectives of the firm, coupled with the availability of data at the levels desired. Is the purpose of the model to derive a representative risk number at the highest levels of the firm (i.e., for the firmwide portfolio of businesses) such that only a comparative analysis is needed on a risk–reward basis between business lines and business line managers? Or, are you seeking to create incentives for the entire employee base and staff within a unit level by function? If the motivation is more toward the former, then it will
12_jwHoffman_38246 11/20/01 7:25 AM Page 265
Some Modeling Issues for Resolution
265
be key to apply uniform model variables across the entire firm, and a top down modeling approach may suffice. If the objective is more toward a granular assessment and calculation, then the model may require a blend of variables that apply both firmwide on the one hand, and some that are unique to the individual business on the other. In this case, the model may require both a top-down and bottomup orientation, or be entirely driven from the bottom of the organization to the very top. As will be evident from the following sections of this chapter, a detailed bottom-up approach will require far more time and effort than a portfolio-based top-down model. ■
■
■
■
Risk Assessment—Depth versus Breadth: When designing models, we will balance what is realistic as to depth and breadth of data capture and modeling. When we began our process at Bankers Trust, we had great plans to develop detailed risk assessment questionnaires and link them to scoring at multiple levels from the bottom up. The problem was that our risk assessment rigor was vastly out of sync with our resources and timetable. This became painfully apparent after having spent nearly four months in a single business line. If we were to complete a first cut at our model and capital attribution within the initial 12–18-month timeframe that we had set for ourselves, we would have to step back and be a bit more superficial at each business (i.e., top or at least mid-tier-down). Each firm will naturally establish its own such targets and balance. Credibility in Sizing Operational Risk: Whichever technique is chosen, it goes without saying that the process must be credible to the audience. If the model uses a simplistic calculation with only two variables, such as income and error rates, the conscientious business manager knows that there are dozens, if not hundreds, of indictors that drive his business and risk profile and will undoubtedly question it. Balancing Causes and Symptoms: In looking at loss outcomes and values, one may develop an estimate of the costs of operational risk, but not understand the underlying causes. To understand the drivers and recommend appropriate loss mitigation efforts, a more detailed insight is desired, but requires more detailed data. This tradeoff must be considered early on in the data collection phase, as was noted in Chapter 10 on loss databases. Balancing Predictive and Retrospective Features: We are seeking to promote proactive, not just reactive, behavior. Be careful, when developing models, that they are not based entirely on historical data, as it is difficult to predict the future using only historical data. As noted, the business environment and associated operational risks are continually changing. Models that represent only a historical environment do not represent
12_jwHoffman_38246 11/20/01 7:25 AM Page 266
266
■
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
recent developments like e-commerce, wireless trading, and others, and therefore could miss part of the operational risk picture. Data Availability/Capture: Suffice it to say that at this stage in operational risk management, our imaginations in developing and using models probably far outstrip the availability of necessary types and amounts of data to support them. To the degree that data necessary for certain analytics are not available, adjustments in the models will need to be made until this is remedied.
Now, we are ready to begin.
DATA INTERPRETATION 101: THE RETROSPECTIVE VIEW You can observe a lot by watching. —Yogi Berra Before we launch into a discussion of analytic methods, we should heed some of Yogi Berra’s advice and spend a moment on the basics of simple observation and data interpretations. Clearly there is no reason to repeat the past ourselves if we can learn from the errors and misfortunes of others. However, this is certainly easier said than done. A simple compilation of events creates a powerful risk database of real events, situations, and outcomes that we can use for direct observation. We have already discussed the value of simple observations about loss data and many of the descriptive and interpretive questions that you should ask about losses in Chapter 10. We will not repeat that material here. Suffice it to say that there is much to be gained by making simple observations and interpretations even in the absence of quantitative analysis. Loss data containing thorough descriptions about losses, their causes, outcomes, persons involved, and loss severity (dollar amounts) can be helpful in making business decisions and are effective in presenting and winning an argument for higher risk standards and company investments. The more detail the database contains, the better. For instance, at one time or another most risk managers have encountered the difficulty of convincing management to set up certain precautionary risk controls. The challenge can be even greater when seeking to avoid possible losses of catastrophic events that occur only infrequently, or more difficult still, perhaps have never happened. It is always best to make an argument for risk mitigation armed with as many facts as possible both in statistically probable events and in raw data. Simple observations about the data can be helpful in this regard, but oftentimes more sophisticated analysis can be even more convincing.
12_jwHoffman_38246 11/20/01 7:25 AM Page 267
Cost of Operational Risk: Simple Addition and Subtraction
267
COST OF OPERATIONAL RISK: SIMPLE ADDITION AND SUBTRACTION The first measurement tool, cost of operational risk (COOR), may be both the simpliest, yet most useful measurement tool of all at the firmwide level. It is used for recording and reporting costs associated with operational risk.
Risk and Insurance Management Society and Cost of Risk Calculation This calculation has been borrowed and adapted from the calculation developed by Douglas Barlow, then risk manager of Massey-Ferguson, Ltd., and endorsed by the Risk and Insurance Management Society’s (RIMS). The RIMS version has traditionally defined COR to include the sum of four basic elements: 1. 2. 3. 4.
Insurance and Risk Finance Costs Self-Insured Loss Costs Risk Control Costs Risk Administration Costs
Because of changes in insurance policy limits and risk retention, this concept is more practical than monitoring trends of insurance premium costs alone over time. Specifically, the calculation includes the sum of (1) premiums paid to insurers and reinsurers; (2) self-insured losses including losses that fall within deductibles or retention arrangements, losses above coverage limits, changes in reserves associated with outstanding or “incurred but not reported” (IBNR) losses, and losses that were insurable events, such as settlements of legal disputes, that fall outside insurable operational categories; plus (3) expenses associated with administration of the operational risk management function; minus (4) captive subsidiary earnings (e.g., investment gains).
The New Cost of Operational Risk Calculation For application in operational risk management, we take the emphasis off insurance and risk finance a bit. Thus, we turn the calculation around to put the primary focus on operational losses, and use them as a point of reference for stress-testing a firm’s risk finance and insurance programs. We then modify this concept and calculation further to include recognition of insurance proceeds as a direct offset to operational loss costs. Our objective in doing
12_jwHoffman_38246 11/20/01 7:25 AM Page 268
268
COOR 1997–2000 (Millions) Total Operational Losses Operational Risk Management Administrative Costs Self-Insurance Reserve Contributions Insurance and Risk Finance Premiums Total Cost of Operational Risk Before Recoveries Recoveries Total Net Cost of Operational Risk (After Recoveries)
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
4-Year Total
1997
1998
1999
2000
$135
$426
$218
$72
$851
1
2
3
3
9
5
6
10
16
37
19
20
21
22
82
$160 ($49)
$454 ($20)
$252 ($46)
$113 ($88)
$979 ($203)
$111
$434
$206
$25
$776
EXHIBIT 12.3 Cost of Operational Risk (COOR) so is to better align the concept with financial reporting and a firm’s operational loss data. Thus, the new components are as follows: 1. Operational Loss Costs ■ by business line ■ by risk class 2. Plus: Operational Risk Management Administrative Costs ■ Operational risk management department ■ Other departments and expenses (e.g., Risk-assessment group, Internal Audit) 3. Plus: Insurance and Risk Finance Costs ■ Annual self-insurance reserve contributions ■ Insurance / reinsurance premiums 4. Minus: Insurance and Risk Finance Recoveries ■ Investment income on self-insurance reserves ■ Incremental residual self-insurance reserves Exhibit 12.3 is a sample of a firmwide cost-of-operational-risk (COOR) summary calculation. It is particularly important to look at the cost of operational risk over a long enough period of time. This probably translates to a 5–10-year calculation. There are several reasons for this: (1) There is the reality of timing
12_jwHoffman_38246 11/20/01 7:25 AM Page 269
Cost of Operational Risk: Simple Addition and Subtraction
269
mismatches that generally take place between a loss occurrence, the settlement of legal disputes or the filing of a claim, and ultimate recovery of losses under risk finance and insurance programs. (2) Because of the very nature of large infrequent events, in order to obtain a reasonably accurate picture of cost of operational risk you must capture a long enough period of time. Longer time periods will likely capture periods of both expected and unexpected loss levels. As such, they should be compared against a commensurate period of risk finance and insurance costs.
COOR Calculation Key Advantages Use of the COOR calculation has a number of advantages. Two key ones are: 1. Once a data capture program for operational losses is functional, and assuming that the firm already tracks its current and past insurance and risk finance costs, COOR is relatively simple to calculate, and simple enough to explain to a broad audience of management and the Board. 2. The calculation can be used to track the long-term responsiveness of risk response efforts, including controls, risk mitigation investments, and risk finance and insurance programs against the firm’s loss history. Long term is emphasized here to reflect the inherent nature and objective of risk finance and insurance programs as a tool to smooth costs over time.
COOR as a Benchmarking Tool Numerous attempts have been made over time to conduct surveys of cost of risk and compare the results between firms. The difficulty of these surveys and comparisons is to establish common ground between the firms being compared. Like many benchmarks and comparisons, it is difficult to make generalizations between different-sized firms, and firms with different risk control and risk management programs and infrastructures. In addition, you often have basic differences in data collection and decisions about the level of detail to track components like losses, loss categories, risk control, and administrative categories. For these reasons, COOR is more useful as a tool to benchmark a company’s own performance over time. At the risk of stating the obvious, losses and cost of operational risk reports are important and useful for tracking the historic costs of operational risk and losses. The problem is that we also want to be in a position to take the analysis one step further—to project future loss and risk costs. And for that, we must apply some assumptions about the future and, in most cases, some more advanced mathematics (and analytics). These analytics range from simple trend lines to regressions, expected loss analysis, and actuarial analysis. Later in this chapter we also look at
12_jwHoffman_38246 11/20/01 7:25 AM Page 270
270
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
financial statement-based analysis; factor analyses, such as causal models; a System Dynamics model; and neural networks. But before we move into modeling, let’s look at some important background issues.
ALTERNATIVE MEASUREMENT METHODS: INDUSTRY PROGRESS TO DATE The term measurement in the operational risk context encompases a wide variety of concepts, tools, and information bases. For instance, we know that although two firms say they use an operational VAR or RAROC methodology, it is virtually certain that, when compared, the approaches will differ. This will be a factor in progressing industry standards and regulatory guidelines for some time yet—the interpretation and application may give rise to many variations on the same theme. In this section we review some of the methodologies currently in use or in experimentation by operational risk teams. The broad categories include (1) Financial Statement-based models; (2) Loss Scenario Models (LSMs), including Risk Mapping methods; (3) Trend Analysis for Projecting Aggregate Losses; (4) Expected Loss Calculations; (5) Loss Distribution and Statistical/ Actuarial Models; and (6) Risk Indicator and Factor-based Models, including causal analysis such as Bayseam Belief Networks System Dynamics, and behavioral analysis, such as Neural Networks.2
Financial Statement Models Economic pricing models use forecasting based on financial data and application of modeling. Probably the best known in operational risk circles is the use of the Capital Asset Pricing Model (CAPM). It is based on the assumption that operational risk has an influence on an institution’s stock price moves and market value overall. The pricing model suggests that operational risk is the differential between credit and market risk, and a security’s market value (see Exhibit 12.4). Some firms have applied the CAPM to their financials and have derived an economic formula for operational risk. They have used CAPM’s systematic risk component as a start toward dissecting components that contribute to their risk profile. Some have found the approach useful in dimensioning a figure for the aggregate operational risk to the firm’s capital. Without other information, however, the approach would only be useful in considering aggregate capital adequacy. Also, in and of itself, it would lack information about specific operational risks. For instance, what loss scenarios are producing the worst possible aggregated outcome for a one-year horizon? What scenarios would represent more moderate outcomes? For this underlying information, one must look further to other models and analyses.
12_jwHoffman_38246 11/20/01 7:25 AM Page 271
Alternative Measurement Methods: Industry Progress to Date
271
Firmwide Capital for Operational Risk Required Earnings (operational risk) / r (firm) where r rate of return and Required Earnings (operational risk) r (operational risk) * book value (firm) where r (operational risk) r (firm) r (investment risk) where r (firm) using CAPM r (risk free) beta (firm) * [r (market) r (risk free)] and r (investment risk) r (risk free) beta (financially leveraged) * [r (market) r (risk free)] where Beta (financially leveraged) beta (firm) / Operating Leverage
EXHIBIT 12.4 Modeling Operational Risk Using CAPM Thus, the advantages of this approach are: ■ ■
Readily available information sources Relative simplicity to implement The disadvantages are:
■ ■ ■ ■
Taken alone it only looks at the ‘big picture’ (entire firm view) in terms of a capital number. Inability to drill down to analyze specific type of operational risk responsible for the volatility (e.g., scenario or loss). For the above reason, it may be difficult to sell to business lines. No apparent positive motivational element.
Another example of financial statement-based models involves the use of expenses as a proxy for operational risk. The idea was that “operating risk” could be expressed as a function of operating expense. These models were abandoned by many, however, as being too random. For instance, does an expense-cutting move increase risk or reduce it? The answer depends, of course, on what the move was and the care with which it was implemented.
12_jwHoffman_38246 11/20/01 7:25 AM Page 272
272
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
Loss Scenario Models (LSMs) Loss scenario models are used to attempt to convert one or more descriptive loss possibilities into a measurement outcome. There are many types of loss scenario models. For example: ■
■
Issue-based models will generally be based on some formal source of issue generation, such as Internal Audit, but could also be based on the output of a control self-assessment (CSA) process. The challenge is to derive a consistent methodology for ranking and scoring the results. These can then be used as the basis for capital allocation. Risk maps are the results of a scenario analysis and are mapped onto a grid that portrays frequency and severity loss potential. These are described in further detail below.
LSMS have been applied for years and can be useful in many ways. Exhibits 12.5 through 12.7 illustrate a very simple loss scenario model from end to end. Exhibit 12.5 illustrates an excerpt of a risk identification and assessment matrix. Individual loss scenarios like this system disruption example are then represented by probability and severity dimensions and summarized in a single exhibit like this one or series of risk inventory exhibits. The collection of exhibits is useful in representing the qualitative or descriptive nature of operational risk. By definition they are descriptive and not quantitative, but their very nature makes them useful for representing the circumstances for which data are lacking. They can also represent operational risks that are still emerging and for which only limited data are available, such as electronic commerce-related risks or risks involving intellectual capital. Another
Risk / Scenarios
Description
Loss Potential
System Disruption: Outage
Short-term service interruptions of critical systems: 1–3 hours
US $50,000– $100,000 range
System Disruption: Total Failure
Moderate to long-term disruption; three hours to several days: risk of errors during period of manual processing, if that is even feasible.
US $5 million– $40 million range
EXHIBIT 12.5 Risk Assessment Matrix
12_jwHoffman_38246 11/20/01 7:25 AM Page 273
Alternative Measurement Methods: Industry Progress to Date
273
advantage is that they can capture the precise details of loss scenarios on the minds of managers surveyed. In contrast, however, their subjectivity can be their weakness, particularly when there is a need to convince the audience of the urgency of a possible outcome.
Scenario-based Model Recap—Advantages and Disadvantages This scenario-based model attempts to summarize possible operational risk/loss outcomes for a variety of scenarios. It is often mapped into a matrix of probabilities: frequency and severity outcomes. Scenario models are reliant on the vision and breadth of knowledge and experience of the person(s) conducting the modeling. Advantages include: ■ ■ ■ ■
Involves/builds business line managers’ experience into profiling—enhances buy-in. Intuitive and easy to understand in concept. Sometimes effective in accentuating weak areas in a business strategy Can be used to highlight the need for a robust firmwide disaster recovery plan; may lead management to a structured crisis management strategy. Disadvantages are:
■ ■
Often subjective, based on personal experience / expertise Can be difficult to build an entire portfolio of scenarios that are totally representative of the institution’s operational risk profile
Risk Mapping Method The second phase of a scenario-based model sometimes involves the creation of one or more risk maps. Risk mapping is one of the oldest forms of analysis for operational risks, probably because it is also simple and straightforward. Yet it can introduce a degree of sophistication over more rudimentary data observations, such as benchmarking, use of simple indicators, and the like. Most risk maps will analyze frequency and severity separately, as each tell a different part of the story. Let’s be clear about the terms first. Frequency is a measure of the number of losses, independent of the size of loss. This measure is often indexed to an exposure base, such as revenue, income, or transaction volume to reflect correlation to the extent that it exists (i.e., the greater number of losses as activity increases). Severity is a measure of average loss size, usually in monetary terms, although it could be expressed in other terms, such as length of time, as in the case of a business
12_jwHoffman_38246 11/20/01 7:25 AM Page 274
274
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
disruption. For context, the following are some observations on frequency and severity: ■
■
Loss Frequency: When examining high-frequency/low-severity (HF/LS) losses, the analyst will find, by definition, that data are generally plentiful, which provide a larger sample size to work with, versus the inherently smaller datasets available for low-frequency/high-severity events. Frequency is also a particularly good indicator of risk because as frequency increases, so does the expected number of random (LF/HS) large losses. In other words, examining high-frequency events can help managers understand risks that may seem to be relatively small (because of relatively low average severity values) but contribute to a large part of the losses and harbor the potential to produce an occasional large random event. Given this, the accumulation effect of small steps in risk mitigation may have a large impact on the firm by minimizing the chance of a snowballing effect. The probability of a firm suffering from a catastrophic loss is therefore minimized. Loss Severity: Loss severity, or the average monetary value of loss events, on the other hand, is far more random. Tail (low-frequency/high-severity or LF/HS) events receive worldwide attention and tend to carry huge consequences. One-off catastrophic losses (e.g., Barings) are often caused by a combination of factors (i.e., inadequate staff and resources, concentration of power, lack of dual controls, and failure to heed audit findings). When allowed to accumulate, these factors, or others, can result in a loss that may lead to severe consequences. These events are fascinating anecdotally, and are useful for analysis of contributing risk factors, but usually statistical analysis of such individual large losses alone does not tell us anything about patterns of those factors and behavior over time—if for no other reason than we simply do not have enough observations of them! LF/HS losses are highly random in nature, difficult to predict (like earthquakes), and sometimes impossible to prevent completely. In essence, this is why many firms seek out insurance or catastrophic risk financing for large loss events, and why regulators are seeking to require capital for them. On a quantitative level, however, industry tail events can help managers assess the upper range of losses when compiling risk profiles.
The risk mapping process requires a user to establish a series of categories for its two map dimensions. Exhibit 12.6 illustrates these dimensions, along with a sampling of selected categories. The first step is the creation of a relationship between frequency and probability (or likelihood) categories.
12_jwHoffman_38246 11/20/01 7:25 AM Page 275
275
Alternative Measurement Methods: Industry Progress to Date
Probability (or Likelihood) Categories Category
Probability of Event
Chance of Occurrence
Expected—Routine Unexpected Rare Extremely Rare
100.0% 10.0% 1.0% 0.1%
At least annually 1 in 10 years 1 in 100 years 1 in 1000 years
Severity Categories Category
Annual Monetary Loss
Normal Moderate High Extreme Catastrophe
Less than $1 million $1–9 million $10–99 million $100–999 million $1 billion
EXHIBIT 12.6 Risk Map Dimensions That is, as the upper portion shows, frequencies are expressed in categories that range from expected levels to extremely rare events. For instance, the extremely rare case will be expressed as a probability of 0.1% or that of a 1in-1000 year event. These categories are relatively standard in many risk map exercises. Choice of the severity categories, on the other hand, is left to the discretion of the user. The dimensions shown in this particular illustration start with a normal or expected loss level range of $1 million or less and are characteristic of a larger firm. In all probability, a smaller firm would have a lower normal or expected severity category. The results of the scenario analysis will be mapped on a grid similar to the one shown in Exhibit 12.7. Each letter in the alphabet represents a different risk subclass or loss scenario. The scenarios can be represented on the grid as datapoints, similar to that of an expected loss calculation. Alternatively, the analyst can show a range of severity possibilities depicted vertically as a representation of variance around an expected loss amount for each one of the scenarios depicted on the grid. The risk map process often fits well together with a qualitative risk assessment process that entails interviews, a team-based Delphi risk assessment process, or some other scenario-based approach. Conceivably, it could also be linked with a control self-assessment program. Some of the obvious advantages of the approach are its simplicity and the speed with which the analysis can be completed. In addition, it does not require
12_jwHoffman_38246 11/20/01 7:25 AM Page 276
276
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
Probability or Relative Likelihood C A
Expected
D E B
G F
Unexpected
J H K I L
P
M N
R O
T S
Q
U
Rare
W V
Extremely Rare
X
Y
M 00
llio bi
$1
$1
99 –9
99 0– $1
–9 $1
M
M M
M M
M M $1 an th ss Le
n+
Z
Severity
EXHIBIT 12.7 Risk Map: Firmwide Representation
a database to complete it. Conversely, as disadvantages, it suffers from some of the same criticisms leveled against other types of scenario analysis approaches; namely, the process is subjective. However, the analyst is certainly free to supplement the subject of scenario analyses with empirical data on losses and loss experience, where available. Thus, the process presents itself nicely as a tool for hybrid qualitative–quantitative approaches.
Using Trend Analysis to Project Aggregate Losses Aggregate loss projections attempt to calculate expected loss levels based on historical aggregate loss data by periods of time—which may be on an annual, monthly, or weekly basis. The loss data may represent the entire firm, an individual business unit, or new individual risk class. In any event, in the case of aggregate of loss analysis, there has been no attempt to separate frequency of losses from severity of those losses. For example, the analyst may have collected loss data for a business unit over the course of two years, and now wants to determine the future potential of losses for that business.
12_jwHoffman_38246 11/20/01 7:25 AM Page 277
Alternative Measurement Methods: Industry Progress to Date
277
Simple forecasts of aggregate loss are developed using two variables and can be plotted on a simple x- and y-axis graphical representation. In this case, we use time as our x-axis representation and independent variable. The loss costs will be the dependent variable and plotted on the y-axis. There are several different techniques that can be applied to project aggregate loss potential: ■
■
Simple Trend Line: A line projection will generally represent a visual application of a line to historical data points available. Think of it as simply a “connecting line” spanning a few data points. This is a simple trend line. Your projection of future losses can be observed as the next point of intersection between the trend line and the future period in question. Simple trend lines can be useful where the analyst has only a few data points at his or her disposal. When more data are available, more sophisticated analysis is warranted, beginning with linear regressions. Regression Analysis: A trend line that represents the calculation of the “best fit” of a trend line to the data points available is a linear regression. Regressions are useful when we have a greater number of data points at our disposal, and where inflation has been fairly consistent over time and is expected to continue as such. In addition, the mathematical calculations involved allow us to begin to examine confidence intervals around our estimates. Exhibit 12.8 illustrates these two very simple trend analyses.
Aggregate Monthly Loss Results
Time
EXHIBIT 12.8 Simple Trend Line and Regression Forecasts
12_jwHoffman_38246 11/20/01 7:25 AM Page 278
278
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
Insurance risk management professionals have used these techniques for as long as anyone can remember to project loss potential as a basis for making decisions about risk retentions and the need for insurance capacity (e.g., limits of coverage). In or about the 1970s, however, they recognized that these projections had limitations and that alternatives were available. So, leaning on work undertaken for a much longer time by insurance actuaries, they began to examine loss frequencies and severities in isolation. Analysts found that each of these dimensions provided useful insight into loss potential.
Expected Loss Calculations A limitation to projecting aggregate losses is that the results provide limited insight about the causes of trends. As the name implies, in expected loss analysis one can use the trends observed in loss frequency and severity to project future expected frequency and severity. The concept here is straightforward enough. Simply by multiplying projected expected frequency by projected expected severity, the analyst can derive an expected loss value. For example, if it is estimated that a trading firm will suffer an average of 10 booking errors per year on a given desk, at an average value of $25,000 each, its projected average trade entry losses would be $250,000 annually for that desk. This approach is an improvement over the others described in developing expected loss estimates. However, it doesn’t provide insight into the potential for deviations from the expected values. This is why we look to more sophisticated statistical and actuarial analysis for guidance on managing expected, unexpected, and even worst case events. We find ourselves asking for more information from the analysis. Beyond insight about the expected case results, we want to know what is the loss potential for one or more scenarios. We want to know what the worst case occurrence would be. We want to know what degree of confidence we have in the result of our analysis. All of this cries out for moving up another rung on our analytic sophistication ladder.
Loss Distribution and Statistical/Actuarial Models Loss distributions and actuarial methods, of course, have been used by insurers and insurance risk managers for many years in projecting the potential outcomes of singular risk classes (e.g., general liability, workers’ compensation, medical malpractice). Simply stated, they are derived from loss and exposure data. By capturing representative historical data the actuary can construct representative distributions of loss frequency and loss severity
12_jwHoffman_38246 11/20/01 7:25 AM Page 279
Alternative Measurement Methods: Industry Progress to Date
279
data, and has a basis for further analyses. For instance, standard statistical approaches can be used to develop a probability density function for each risk class and/or the firm as a whole. These models are among the most commonly discussed for operational risk today, although approaches differ. At the time of this writing, however, only a handful of firms are using them for risk capital models. Commonly the source information will be operational risk event and loss data, which can in some cases be a mix of that internal and external data. Frequency and severity distributions are assembled based on the data, then simulated via a technique such as Monte Carlo to arrive at a range of possible loss outcomes; figures are produced for a stipulated time horizon and range of confidence levels. As we continue to progress in the sophistication of our analyses, there are several other concepts and variables to consider: ■
■
■
Exposure Bases and Scaling: Let’s return to our discussion of inherent risk indicators and exposure bases in Chapter 11. The use of exposure bases implies that there is some degree of scaling that should be recognized in looking at the potential loss experience of different size organizations. Insurance actuaries examine exposure bases routinely when analyzing insurance loss experience. Traditionally, financial institution bonds have been scaled and rated on the basis of employee head count, workers compensation insurance has been scaled on the basis of payroll, and product liability insurance has been scaled on the basis of revenue. The use of exposure bases also implies that we can determine a key driver for the loss type. In the end, the use of exposure bases and scaling is a function of a correlation that exists between the relative size of the exposure base and loss potential. Loss Development: This concept represents the reality that some loss types (risk classes) take longer than others to develop to their ultimate loss costs. For instance, at one extreme, a physical damage loss, such as a fire or flood in an individual location, can be assessed and quantified within a relatively short period of time. Short in this sense is perhaps 3 to 6 months for the fire damage itself, and 6 to 18 months when considering all dimensions of the damage and indirect impact to business disruption, loss of earnings, cleanup, and reconstruction costs. In contrast, a major legal action could easily take much longer (several years) to develop to the point that the final cost of the lawsuit, its judgment, defense costs, investigation, and other associated costs are known. Variance and Tail Risk:3 Another fundamental concept in more sophisticated risk analysis is to consider variance, or the potential variability of loss from an expected outcome. Questions regarding volatility of results, and therefore variance, require us to consider more sophisticated analysis techniques than the use of expected frequencies and severities alone.
12_jwHoffman_38246 11/20/01 7:25 AM Page 280
280
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
The story of the line manager back in Chapter 10 who had no losses but was shocked that, despite this, he was still receiving a capital charge is a classic case of denial about variance and tail risk. This is the risk of loss involving those potential low-frequency/high-severity loss events that are so dangerous. Operational tail risk is perhaps the dimension of operational risk most often misunderstood, and therefore also overlooked by line management. Simply stated, it is the representation of the extreme low-probability/highseverity loss events. When operational losses are plotted as a probability distribution, by definition, the vast majority of outcomes are expected to fall in the body of the distribution. Thus, people who have not ventured into statistical measures of operational risk, including variance, are by definition assessing risk at only expected levels. In other words, they are only considering losses that are known and have usually occurred. It is not until one ventures into statistical measures for extreme probabilities (i.e., 95th or 99th percentile) or at least, considers the less probable or less likely outcomes intuitively, that one is truly considering tail risk. Let’s consider the example of systems risk. In the body of the distribution, one would consider routine outages of relatively minor duration, say from ten minutes to several hours. This might be an expected and acceptable occurrence for a noncritical system. When considering a more critical system, such as money transfer, market data feed systems for trading operations, or customer service systems for funds management operations, the downtime tolerance must be lower. In the latter, more critical case, the occurrence would be unacceptable and hopefully less likely as well. For them, outages in the body of the distribution might fall in the range of seconds, if tolerated at all. So one can identify the types of events that would naturally fall in the body of a probability distribution. We have also begun to identify those deemed less acceptable and, hopefully, less probable. Assuming then that they are either inherently less probable or have been engineered to be so, they would logically fall further out on the probability distribution—in the tail. When combined with a risk management process, one can either map loss scenarios against probabilities and create a distribution, or actually work with empirical data. A number of firms do both. Early in our work on operational risk, we found a need to build subjective scenarios and subjective mappings against probabilities. With time, we invested in the extensive collection and collation of empirical data not only to reflect our own experience, but to track that of other firms as well. The data helped to confirm our expectations of scenarios and outcomes. The real message here, however, is that one must consider tail risk. This can be done either by analyzing the experience of other unfortunate firms who have suffered large losses in areas that you have not, or by dreaming up some of your own worst case nightmares. The confidence of your result can
12_jwHoffman_38246 11/20/01 7:25 AM Page 281
Alternative Measurement Methods: Industry Progress to Date
281
be boosted, of course, by analyzing numerous events and then producing simulation results from Monte Carlo or other models. In our work at Bankers Trust, we used our database, supplemented by some hypothetical scenarios and our analytics, to produce results not only at expected levels, but also at a 99% confidence level. With the data and analytics in hand, a risk manager is then in a far better position to discuss the prospect of a tail (low-probability/high-severity) event, and perhaps more importantly, the control investment options available to reengineer its outcome. That is, through investment in control measures, a firm might reduce its probability further (although the change might be academic), or it might minimize the possible size of the outcome should the event occur. The Data Challenge, Part II One of the interesting problems that we did not address in Chapter 10, or have not yet addressed here, for that matter, is the practical reality of massaging loss data, working with expected losses and tail losses, and avoiding double counting for analytical purposes. From the perspective of analytic needs, it is important to have information not only on the individual risk class, but on loss amount, current state, and a broad description of the event. Once collected, loss amounts must be adjusted for inflation to current cost levels, and to the extent possible for changes in procedures and controls. This is also the point at which you would apply scaling factors. Because we are looking to simulate the impact of losses as they occur, the loss data used in supporting the model must be analyzed on the date the event was reported, not settled, as is normally the case with insurance actuarial models. The next problem for many is that you still may not have enough data to be able to formulate any conclusions about the risk of loss in a given business line or attain statistical significance. Or you may not have enough to make adequate statistical calculations, or have “statistical significance.” There are two component parts to this type of statistical significance. The first is one of having enough data to completely represent the body of the distribution. The other is having enough data in the tail of the distribution. Let’s start first with a key conceptual issue and look at the component data challenges and possible solutions for expected loss levels (“body-of-thedistribution” risks) and tail risk, individually: ■
Unexpected Loss and Tail Risk: The latter can be addressed by using a large loss external database. As noted, fortunately most firms do not have many large losses of their own. If they did, chances are that they would not be around for very long to talk about them. Thus, many firms will look to central repositories of industry operational losses, whether
12_jwHoffman_38246 11/20/01 7:25 AM Page 282
282
■
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
in the form of external databases or loss consortia, in order to represent more fully the possible outcomes that might befall them, particularly when it comes to loss severities. There are several around today to choose from (see Chapter 10). Expected Losses and the Body of the Distribution: Being confronted with insufficient data in the body of the distribution presents a slightly different problem. In attempting to represent the large loss potential, one is seeking to “borrow” the severity or size of the losses from others for analytical purposes. On the other hand, in seeking to portray the more routine or expected losses (i.e., the body of the distribution), some issues of using external data become even more pronounced. These include issues such as relevance of the loss data, like products, business lines, operations, and control environments, etc.
The emerging operational risk data consortia are, or should be, exploring either one or both of these data needs. Internal Measurement Approach As this book is being finalized there is much discussion about a regulatory capital proposal called the Internal Measurement Approach (IMA). The final version of this measurement option is yet undetermined, but most recently its composition consists of calculations by business type that include exposure indicators, an event probability parameter using a bank’s own loss data, a parameter representing the loss given the type of event in question, and a sealing factor that regulators intend to develop in conjunction with the industry using industry data. Chapter 17 contains a more complete discussion of the IMA and other regulatory developments. Suffice to say that IMA is a developing approach that draws on both exposure bases, loss data, probabilities, and loss distributions. The intent is to reflect the value of sealed loss histories for measuring risk. It is a reasonable approach, in context. Like most methods, however, its relative success will depend on its final implementation details. At this stage, among their criticisms, opponents argue that it does not capture qualitative information about risk that is not reflected in available loss data.
CASE ILLUSTRATION Actuarial Methods, Monte Carlo Simulation, and Loss Distributions Bankers Trust In the early 1990s senior management at Bankers Trust decided that the time had come to graduate from using “plug number” estimates in our
12_jwHoffman_38246 11/20/01 7:25 AM Page 283
Alternative Measurement Methods: Industry Progress to Date
283
economic capital models for operational risk. Following some experiments in risk assessment, we began exploring actuarial analysis and loss distribution approaches to estimate our annual exposure to operational loss. Prior to this, the plug number had come from an expense-based estimate (see “Financial Statement Models” section) relative to a select number of the firm’s fee-based businesses. In essence, we knew we could do better. In thinking about the problem, we noted some interesting parallels between insurance-related analysis and our own objective of determining exposure, or value at risk, over a one-year time horizon at a high level of confidence. It occurred to us that there is a striking similarity to the various funding studies we have done in the insurance and risk financing industries over the years. There, an organization is seeking to answer the same questions: What is my potential loss from a particular source of risk, at both an expected level and at some higher level of confidence (such as 95% or 99%)? And how do we price this on both a singleyear and multiyear basis? Thus, it was an insurance-like funding study that actually formed the basis of our first actuarial risk measurement model for operational RAROC. However, we recognized that traditional high-frequency/low-severity actuarial techniques would be only partially relevant. Because of the large loss nature of headline operational events at the time (e.g., Barings), we sensed that we would need to look at additional loss distributions more relevant to extreme events (low-frequency/high-severity).4 This was especially true given our particular concern—protecting our capital in the face of one-in-100–year events. The parallel was also very fresh in our minds because in 1991 we had just applied similar actuarial techniques in assessing the feasibility and forming a captive insurance company to protect the bank from large loss exposures, where conventional insurance solutions were lacking. Thus, we formed a Bermuda captive to underwrite our risk directly, and accessed the reinsurance market for risk-sharing purposes. We will reveal more on this type of undertaking in Chapter 15 on Alternative Risk Finance. Key Considerations / Objectives for Analysis Some of the considerations that must be addressed at the outset by a firm considering this type of approach include: ■ ■
Decide whether we are attempting to calculate an aggregate value for risk capital, or by business line. Confirm the time horizon (single-year or multiyear).
12_jwHoffman_38246 11/20/01 7:25 AM Page 284
284
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
■ ■ ■
Select the mathematical models. Select frequency/severity parameters. Choose a confidence level (e.g., 95%, 99%).
In terms of our own confidence levels, we recognized that in order to be consistent with our credit- and market-risk models, we needed to select a model that would help us to define the capital required to support losses incurred in a single year 99% of the time. We concluded that this capital definition required a probability distribution of aggregate losses. We also concluded that a behavioral simulation model was required, because a scenario-based model could not assign probabilities.5 The Monte Carlo Simulation What is Monte Carlo Simulation? It is the process of simulating or representing an event or scenario using a series of random pairings of variables, generally referred to as iterations or trials. This situation generally involves hundreds or thousands of these iterations. We chose the latter. The samplings from Monte Carlo are such that they reproduce the aggregate distribution shape. Thus, the results of the calculation reflect the probabilities of the loss values that can occur. Some key advantages of Monte Carlo simulations are that correlations and other interdependence can be modeled, accuracy can be improved by increasing the number of iterations, mathematical complexity can be varied (e.g., power functions, logs), and the model can be analyzed relatively easily. Much of this has been made possible, not to mention easier, in recent years with the increased availability of software for performing the calculations.6 In modeling event frequency and event severity separately, we chose to use the Poisson distribution for frequency and a Pareto distribution for severity because they are commonly used in analyzing insurance loss data. They also seemed appropriate based on an assessment of the key characteristics of our own operational loss data. ■
Frequency:7 In modeling loss frequency, we first had to determine an exposure base. As previously discussed, this is a piece of information that acts as a proxy for exposure to loss (e.g., number of transactions, square footage of office space). Recall that these would be selected from our universe of inherent risk or exposure indicators. We then model annual event frequency, considering changes in exposure and claims that have not yet been reported. The model considers some perspective on exposure growth. One objective might be to link operational risk estimates to economic phenomena. In that
12_jwHoffman_38246 11/20/01 7:25 AM Page 285
Alternative Measurement Methods: Industry Progress to Date
■
■
285
scenario we will compare the frequency trends to economic timeseries data and incorporate the relationship, if any, into our model. Severity:8 Event severity is modeled after considering how to blend supplementary data (i.e., in our case this was the external loss data in our industry loss database, or in the future this will include consortium data). The approach will differ depending on the type and quality of supplementary data. “Synthetic Data Points” for New Risks: There is a unique data problem relative to newly emerging exposures where losses are not plentiful. What about scenarios that have never been experienced or logged before, but can be imagined? Here, there is a unique concern about the lack of data to represent certain tail risk scenarios. For these, you can apply a concept that we have sometimes used in loss scenario analysis. We dubbed it the creation and use of “synthetic data points.” For these cases, such as large-scale outages involving critical systems, we still want to have an option of mapping an assumed probability into our collection of empirical frequencies and severities for specified events. So, we interview experts for their insight on loss potential, then use resultant consensus estimates to represent a loss in the database. This approach is applied in only a handful of cases, but when used, we view it as important to represent the total exposure. The combination of empirical data and synthetic data provides a far more robust database than one would have in using either empirical data or hypothetical scenarios alone.
Correlation Correlation affects the spread of results. Negatively correlated categories reduce the spread while positively correlated categories increase it. The measurement of correlation is difficult as statistical measures of correlation are highly volatile and often need relatively large values ( 30%) to be considered significant. In examining data for correlation, it is also important to adjust for the effects that you are already considering in the model, such as exposure growth and inflation. In general, results from any type of correlation study will be tempered with judgment. The application of correlation in the simulation process depends on whether the correlation is frequency- or severity-based. Severity correlation will be implemented during the course of generating events, while frequency-based correlation will be implemented during aggregation. As noted, because of the relative paucity of loss data available in our initial models, we were unable to conduct our analyses by business line.
12_jwHoffman_38246 11/20/01 7:25 AM Page 286
286
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
Thus, our calculations were limited to simulating risk classes only. In this particular exercise, we found no strong signs of correlation between risk classes. This was confirmed during the testing process.9 Model Testing We tested each of the risk classes to see how the simulations replicated the data. Ideally, the middle of the distribution should be similar to the data, but the spread of results should be wider. In addition, the joint simulation will be compared to the historical aggregate results. Satisfactory group models with inappropriate aggregate results could point to a shortcoming in the correlation process. Based on the results of our testing, we were able to make adjustments to the model parameters, which led to improved calibration of the model.10 Application of Model Results After simulating dozens of events for each of the thousands of trials (years in this case), with the appropriate considerations for correlation, exposure group, and the like, the model produced an aggregate operational loss distribution. In addition to the aggregate results, and the ability to represent aggregate exposure for the firm, we were able to produce other useful information from our analysis. For one, we were in a position to see which risk category drove the capital constraint and drill down to see if it is frequency or severity driven. This led to better-focused risk management efforts. The net result is that the model was useful in producing aggregate firmwide capital measures at selected confidence levels.11 ■ ■ ■
Exhibit 12.9 is a tabular presentation of some hypothetical business-bybusiness and firmwide value-at-risk results from a loss distribution model. Exhibit 12.10 is a graphical presentation of hypothetical results by risk class over time. Note that diversification is assumed in both exhibits relative to the five business lines and risk classes, respectively. Thus, in both cases the diversified total is smaller than the sum of the individual parts. The time series graph is the type of trend analysis produced when an external database is combined with a firm’s own internal data. The database was comprised of operational risk events that had occurred at other firms but were relevant to the user’s business operations. In the time series version the analyst is in a position to analyze the reasons for the trends and pass the results over to management for appropriate action. There has been much discussion in operational risk circles about the use of loss data in predicting future operational losses. To a large extent, past
12_jwHoffman_38246 11/20/01 7:25 AM Page 287
287
Alternative Measurement Methods: Industry Progress to Date
50% Business Line 1 Business Line 2 Business Line 3 Business Line 4 Business Line 5 TOTAL Diversified
(Per Confidence Interval) 75% 80% 90% 95% 99% #30 #182
99.5%
99.9%
#437
#504
#1
#5
#7
#14
1
1
2
4
9
43
74
311
1
3
4
9
19
75
121
258
37
73
80
161
298
554
609
843
2
6
6
18
39
207
370
502
#58
#108
#129 #243 #429 #604
#700
#1080
EXHIBIT 12.9 Operational Risk Capital Results* *Capital reported in millions of dollars (USD).
$1,400 $1,200
Diversified Total
$1,000
Technology* People*
$800
X
X
X
X
X
X
External*
*
Relationship* Physical Assets*
X
Dec-01
X
Jun-01
$0
X
Dec-00
$200
Jun-00
$400
* ***** *** Dec-99
$600
X
This is an hypothetical illustration of trend lines of both diversified and undiversified simulated exposure by risk class at a selected confidence level (e.g., 99%). In this scenario, the results highlight a longer term increase in the probable loss exposure, particularly in the technology and people/human capital areas. It also shows a slight upturn in external, physical asset, and relationship risk classes in the 4th quarter of 2001.
EXHIBIT 12.10 Capital by Risk Class
12_jwHoffman_38246 11/20/01 7:25 AM Page 288
288
OPERATIONAL RISK ANALYSIS AND MEASUREMENTS
loss trends have provided a reasonably good indication of the future, but we must take into account a variety of factors in using them. As we all know, there is a fundamental shortcoming in looking solely at operational loss experience—it is a retrospective view! Thus, for one, in using past loss data we are making a huge assumption that the future will resemble the past. All things being equal, that may not be too much of a stretch. We have already discussed supplementing past loss data with scenario analyses, “synthetic data points,” and the like. Even with all of that in our arsenal, all is not equal. We must consider the rate of change in our environment. These include the speed of change in the environment; changes in management teams, control structures, business mix, and product offerings; changes in the technological environment, in society, and so on. There is much to be said about using past loss data, but we must be comfortable with these assumptions before using them. Advantages of the loss database and statistical/actuarial approach: ■ ■
Attempts to be predictive—ensure users are aware of its limitations. By definition, it is based on empirical data. It is more defensible than subjective scenarios. Disadvantages:
■ ■ ■ ■
Difficult to source the depth of data required to accurately calculate a firm’s operational risk capital Time intensive operation to gather the data; even then they may not be complete In its pure form, quantitative based—no qualitative assessment Have to ensure a risk management motivational element is built into the methodology
Extreme Value Theory As noted, most firms (thankfully) do not have many large losses of their own to include in a proprietary loss database, or, in turn, to include in their loss distributions for analytic purposes. Because of this data problem, more recently some have been exploring the use of extreme value theory (EVT). EVT is relatively new to risk managers in financial services, but has been applied to market risks in estimating value at risk for extreme positions, such as those represented by the stock market crash of 1987 or the Bond market backup of 1994.12 Interestingly enough, apparently it has been used even longer in operational risk situations in other industries, although perhaps its application have not been recognized as such. Dowd notes that EVT has been applied by statisticians and engineers in areas like hydroponics for estimating the
12_jwHoffman_38246 11/20/01 7:25 AM Page 289
Alternative Measurement Methods: Industry Progress to Date
289
height of sea walls when considering the extreme severity problem of flood risk. In many cases they have had even less data to work with than the financial services operational risk managers do!13 EVT is focused on the extreme observations of a distribution rather than on all observations in the distribution, or in other words, the entire distribution. It applies a parametric method to compute the extreme values for the problem in question. It can be applied for a specific asset position (i.e., market risk) or risk scenario, such as flood (i.e., operational risk). The EVT explicitly takes into account the correlation between risk factors during extreme conditions.14 It is applied when the analyst has a small number of large loss observations and is seeking to determine how the asymptotic distribution of extreme values should look.15 Sound familiar? This is precisely why it has sparked the interest of analysts looking at extreme operational risk scenarios.
Risk Indicator and Factor-based Models Let’s return to our discussion in Chapter 11 on risk indicators and their use as factors for modeling. These methodologies originate from risk indicator information in isolation or in combination with loss information. Risk indicator or factor models are derived from various types of data input that serve to dimension the evolution of a risk profile. There are exceptions, of course, but these often give rise to bottom-up approaches due to the granularity and nature of the information used as the source. As a simple illustration, the combination of technological operability, application viability, and technology staff competency versus system downtime suggest an interesting, albeit partial picture of the operational risk profile of a business. Exhibit 12.11 shows that when trended over time the picture can be even more informative and useful. In and of themselves, these trends only project the evolution of a risk profile. Is it evolving toward higher or lower risk? While they might be trended forward through regression analysis, they will only produce a relative future value of the individual or aggregated factors, but not necessarily a loss outcome. Thus, initially these representations are indicative of cause or causation, not effect, or loss outcome, as a loss scenario or actuarial model might. When these factor or causation profiles are combined with representations of outcome they begin to reach their full potential. Let’s look at some examples. One example of a model that endeavors to bridge this gap in representing firmwide risk measurement is Delta-EVT™. The method is an interesting combination of risk factor calculations that are used to produce an operating loss distribution and extreme value theory (EVT), which is used to produce an excess loss distribution. Jack King
12_jwHoffman_38246 11/20/01 7:25 AM Page 290
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
100
10 9 8 7 6 5 4 3 2 1 0
90 85 80
Percent
95
75 70
Ja n1 99 9 Fe b1 99 9 M ar 19 99 Ap r1 99 9 M ay 19 99 Ju n1 99 9 Ju l1 99 9 Au g1 99 9 Se p1 99 9 O ct 19 99
Rating
290
Technological operability rating
System downtime
Application viability rating
Technology staff competency %
EXHIBIT 12.11 Risk Factor Trends Over Time describes the methodology in detail in his book, Operational Risk: Measurement and Modeling (2001). In brief, his steps for implementation are: 1. “Establish the business model with value-adding processes and activities, and any available (historical) large losses.” 2. “Determine the risk factors for the major activities in the value-adding processes and their relation to earnings (the earnings function).” 3. “Estimate operational losses using uncertainty of the risk factors propagated to the risk in earnings (Delta method).” 4. “Set the threshold of operating losses from the processes using the risk factor uncertainties and operating losses from the Delta method, and filter the large losses using the threshold.” 5. “Create a set of excess losses greater than the threshold using plausible scenarios based on actual historical losses, external events, and near misses and model them using extreme value theory (EVT).”16 The method benefits from the qualitative use of risk factors. With careful selection, these factors can provide a more tailored and useful representation of risk than loss data alone. The method also benefits from use of loss data, to the extent available, and EVT to help develop a large loss representation, which also serve to buffet the model against criticism about subjectivity. Skeptics have expressed concern about the selection of factors, judgment applied in developing the large loss representations, and instability of the EVT tail when data are sparse. For its balance as a risk management tool, the method deserves consideration and experimentation.
12_jwHoffman_38246 11/20/01 7:25 AM Page 291
Alternative Measurement Methods: Industry Progress to Date
291
Other indicator or factor-based models in development or use for operational risk management include process maps, causal analyses, such as those using Bayesian Belief Networks or System Dynamics, and behavioral models such as Neural Networks. On the following pages we will examine several illustrations of factor-based models, including a case applying Baysean Belief Networks for casual analysis in the settlement process from West LB, a discussion of the System Dynamics approach from Tillinghast/ Towers Perrin, and a discussion of Neural Networks from NASA. For the most part, these methods bring value to the table as measurement and management tools for specific risks or business functions in a firm as opposed to firmwide risk measurement for VAR and risk capital applications.
CASE ILLUSTRATION Causal Models—Bayesian Belief Networks OpVAR Project West Landesbank (This case was written and contributed by Karolina Kalkantara and Riaz Karim of West LB, and David Syer of Algorithmics.) In October 2000, the London branch of WestLandesbank (WestLB) embarked upon a three-month pilot project to model the operational risk associated with the Euroclear bond settlement process. The Euroclear bond cash settlement was chosen as the initial vertical process within WestLB’s Global Financial Markets division due to the transparency of determining tangible and quantifiable operational risk factors relative to other operational processes within a large investment banking environment. The working party consisted of various departments within the bank (Trade Control Market Analysis, Bond Settlement, Project Management, IT, Business Process Reengineering) as well as Algorithmics UK and Droege & Co. Management Consultancy. The aim of the project was to provide two things: a predictive look at new transactions and a retrospective picture of the historical patterns of risk in the process. The predictive element was to rank new transactions in order of decreasing likelihood of failure, or alternatively expected cost, in a risk-adjusted sense. The retrospective element was twofold: to provide a cash-based measure of risk in the process through a daily (or monthly) operational risk VAR at various confidence levels and to report quantitatively on the historic settlement efficiency based on the data that were at hand. The models were predictive and estimate the number and cost of failed trades (there were seven types of fails) that are likely to occur on a given day. The models constructed a predictive history of the most likely future events using Bayesian probabilities. The insight for this is
12_jwHoffman_38246 11/20/01 7:25 AM Page 292
292
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
derived from a model of the Bond Settlement Process. The model is said to be causal (cause versus effect); that is to say it looks for the likely cause of failure and predicts the likely effect. It achieves this by mapping out the steps in the process and says “What happens if the process fails at such and such a point (or node)?” and then “What happens if there is a system failure at the next node?” and so on, until it has “stepped through” the entire process. Based upon historic data (we used trade files and trade fail data for a period of three months obtained from WestLB’s MIS Bond system), the model attributed probabilities of failure to each trade. For the purpose of modeling, the data were split into two parts: Settled (containing 67% of the data) and Open (containing 33% of the data). The models were trained with the Settled data and their performance measured when the Open trades were entered. By supplying current market price data, related volatility, and central treasury costs of funding and inputting this information to the model, it was possible to calculate both the probability of failure and its expected monetary cost to the firm. This is the measure of operational risk inherent in the process. The data source was obtained via the export facility of the existing MIS in the bank, which provided us with a list of all the attributes of the trades in a three-month period. Information about which of these trades had failed, and for what reason (classified into seven categories), was collected by the Settlement team itself through their internal processes and made available to us in a database. These data had been collected for some time by the Settlement team, but not analyzed in any depth, and detailed information about settlement failures was not systematically or centrally collated. We assigned a different probability of failure to each individual transaction using the Algo WatchDog software and stored the results back into the same database that had been used to collect the transaction and fails data. The total potential cost of a failure, based on the nominal value of the transaction and the length of time that it took to resolve, were also stored in the database. In a credit risk analogy, we now had a list of all our counterparts (transactions), each with default (failure) probability and exposure (failure cost), and this enabled us to estimate a cash-based measure of risk in the Settlement process. Reports were generated showing daily VAR at 99% confidence over a period of three months (see Exhibit 12.12), to be used by operations management in their budgeting and cost setting (the firm has an internal service provider model for operations). Exhibit 12.12 illustrates a daily VAR figure for Open trades from March 1, 2000 to May 31, 2000. The daily VAR figure was also used as a risk indicator, showing its development over time when the bank was developing new and riskier
12_jwHoffman_38246 11/20/01 7:25 AM Page 293
293
Alternative Measurement Methods: Industry Progress to Date
Daily VAR 40,000 30,000 20,000 10,000
01 /0 3 08 /00 /0 3 15 /00 /0 3 22 /00 /0 3 29 /00 /0 3 05 /00 /0 4 12 /00 /0 4 19 /00 /0 4 26 /00 /0 4 03 /00 /0 5 10 /00 /0 5 17 /00 /0 5 24 /00 /0 5 31 /00 /0 5/ 00
0
EXHIBIT 12.12 WestLB Project—Daily VAR Source: WestLandesbank, London Branch.
Failure Code
Failure Probability
Predicted Cost (EUR)
VAR (EUR)
Code_1 Code_2 Code_3 Code_4 Code_5 Code_6 Code_7 Total
20.7573% 0.3422% 4.3863% 0.0495% 18.4237% 1.8922% 0.1906% 46.0419%
857.96 11.32 126.80 1.21 254.31 104.19 0.00 1122.35
50.99 8.40 6.60 1.02 25.21 2.83 0.00 57.96
EXHIBIT 12.13 VAR Figure for April 1, 2000 Source: WestLandesbank, London Branch.
(or less risky) practices in fixed income trading and settlement. Exhibit 12.13 illustrates the VAR figure (57.96M Euro) for a particular day (April 1, 2000), the failure probability for each fail code, and the predicted cost of failure. In addition, we looked retrospectively at “hotspots” or “stress scenarios” by reporting on particular trade attributes, or particular historic transactions, whose attributes combined to signify a high probability of failure. These reports could be used by settlement personnel to focus their
12_jwHoffman_38246 11/20/01 7:25 AM Page 294
294
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
Index
Trade Attribute
Variance Reduction
Variance Reduction Percent (%)
0 1 2 3 4 5
DaysLate Nat_of_Cpty Book_ Ccy_Dealt Dealer Industry
0.26 0.03 0.03 0.02 0.02 0.02
100.00 11.56 10.31 8.90 7.94 7.50
EXHIBIT 12.14 Trade Attributes Source: WestLandesbank, London Branch.
Rank
Nat_of_Cpty
Number of Trades
Number of Fails
Prob (Late True I Nationality)
1 2 3 4
Country_1 Country_2 Country_3 Country_4
34 108 193 29
10 21 34 5
29.41% 19.44% 17.62% 17.24%
EXHIBIT 12.15 Influence of Attribute Levels Source: WestLandesbank, London Branch.
efforts on improved processes or controls and are displayed in Exhibits 12.14 and 12.15. Exhibit 12.14 displays the trade attributes that are most important in determining trades that settled late. For example, Nationality of Counterparty is the most influential in determining failed trades (11.56%), whereas Book and Currency dealt are less influential (10.31% and 8.9%, respectively). Exhibit 12.15 displays the influence of each attribute level of the variable Nationality of Counterparty in determining failed trades. As can be seen from the exhibit, counterparties from Country_1 were associated with 34 trades of which 29.41% (10 trades) failed. On the predictive side, we produced the same kind of reports, focusing on a “hot list” of transactions likely to fail and an assessment of the predictive power of the model. Exhibit 12.16 shows the five most likely trades to fail on a given date (April 25, 2000) and the most likely reason for failure. Hence, the security SAFFRN05 is likely to fail be-
12_jwHoffman_38246 11/20/01 7:25 AM Page 295
295
Alternative Measurement Methods: Industry Progress to Date
Buy/ Book Sell Amount MBAV TLC1 EDLQ EDLQ EDLQ
B B B S S
Sec_Code
FailCode 1
FailCode 2
FailCode 3
FailCode 4
0.7510 0.1818 0.0000 0.0000
0.0000 0.0000 0.0000 0.1623 0.3419
0.0013 0.0000 0.5478 0.6410 0.5296
0.0142 00157 0.0178 0.0196 0.0352
Ccy
2E 08 ITAFRN02A EUR 807654.6 SAFFRN05 USD 214504.8 AUS06706 AUD 214550.7 AUS06706 AUD 478795.1 SGB06005 SEK
EXHIBIT 12.16 Daily Hot List Report: Five Most Likely Trades to Fail Source: WestLandesbank, London Branch.
Predictivity
Open Settled
Accuracy
Success
Blind Luck
Ratio
47.37% 65.71%
18.00% 30.80%
6.81% 10.41%
2.6 3.0
EXHIBIT 12.17 WestLB Project—Predictivity Results Source: WestLandesbank, London Branch.
cause of insufficient bonds to deliver (probability 75.1%) whereas the security SGB06005 is likely to fail because of unmatched instructions (probability 52.96%). The latter security (SGO009001) is expressed in Exhibit 12.17 as the Predictivity results for Open and Settled trades. Accuracy is defined as the quotient of the number of predicted fails and total predicted fails. Success is defined as the quotient of successful predictions (predicted fails that actually failed) and total predictions. Blind luck is the average fail rate. Predictive power is the ratio of success to blind luck. From Exhibit 12.17 it follows that for the parameters chosen, the model is 2.6 times better at failure prediction than pure chance! The model’s predictive power can be boosted to six times better than pure chance, by focusing on the most common kinds of transactions. A suite of associated online reports are available to support the data analyses. The firm’s intention, ultimately, is to identify and calibrate all operational risk in the London Operations group through a stepwise review of each area, process by process. ■ ■ ■
12_jwHoffman_38246 11/20/01 7:25 AM Page 296
296
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
CASE ILLUSTRATION System Dynamics Approach Another method showing promise in the developmental stage is the System Dynamics Approach. System Dynamics is a robust simulation modeling approach developed by Jay Forrester of the Massachusetts Institute of Technology. The approach involves developing a computer model that simulates the cause–effect interactions among all the key variables underlying a specific system. The following summary was written and contributed by Jerry Miccolis and Samir Shah of Towers Perrin. There are some important distinctions between operational risks and financial risks that require a different approach to modeling operational risks than those traditionally used to quantify financial risks: ■
■
■
■
The source of financial risks (such as volatility in interest rates, foreign exchange rates, and equity returns) are beyond a company’s direct control; whereas, operational risks (such as employee fraud, technology failure, and agent misselling) are a direct consequence of a company’s organization and operation. Operational risks and their magnitude vary significantly from one company to another depending on the unique combination of business processes, people, technology, organization, and culture. Some operational risks only impact earnings volatility, whereas other operational risks impact capital. The ones that impact capital are typically those that are characterized by low frequency and high severity. These risks have a skewed probability distribution, whereas financial risks typically have symmetric distributions. If the purpose of operational risk management is capital determination, then it will be necessary to use modeling methods suited to skewed probability distributions with fat tails. Whereas financial risks can be hedged, operational risks are typically managed through changes in operations such as changes in business processes, organization, technology, and training, for example. Finally, operational risk modeling is a relatively new endeavor for most companies. There is much less reliable historical data for risk modeling than there is for financial risk. However, in the financial services industry, initiatives to gather industry-wide data as well as efforts by individual companies to gather internal data offer promise.
For these reasons, simply applying the same methods that are now used to model financial risks is not reliable or even possible in some
12_jwHoffman_38246 11/20/01 7:25 AM Page 297
Alternative Measurement Methods: Industry Progress to Date
297
cases. Furthermore, it’s unlikely that just one method will be appropriate for quantifying all operational risks. In addition, representative historical operational loss data are not always available. For reasons described above, industry-wide data must be adjusted to reflect company-specific information. Even if it was possible to gather enough representative data, it’s virtually impossible to determine how the operational risk will change prospectively with changes in operations. The ultimate objective, after all, is not to quantify operational risks but to reduce operational risks and its impact on capital and earnings volatility. The predominant approach to reduce these risks is through changes in how the business is managed—as opposed to hedging in the financial markets for financial risks. For these reasons, it’s necessary to supplement parametric approaches based on historical data by other methods. The System Dynamics approach offers potential to address the difficulties of modeling operational risks described above. The first step is to prepare a graphical representation (system map) of the interconnected causal relationships for the operational risk. The second step involves quantifying the cause–effect relationships between variables based on a combination of historical data and expert input. Since the data needed to model operational risks are generally sparse, this step leverages the knowledge and experience of senior managers who best understand the dynamics underlying their business. Expert input is represented as stochastic cause–effect relationships to explicitly reflect the uncertainty of the input. Finally, the results of the first two steps are combined into a computer simulation model that is used to generate scenarios for the output variables of the system being modeled. The outputs of the simulations are probability distributions for financial and operational metrics, such as profit, premium, market share, and number of policies. An example of a system dynamics map representing the risk from a computer virus is illustrated in Exhibit 12.18. The map explicitly represents the cause–effect relationships among key variables for both the sources and consequences of a computer virus. Each relationship is quantified using a combination of industry data, internal company data, and expert input. The resulting simulation model can be used to develop a distribution of outcomes for variables such as penalties, lost business, and lost productivity. The approach is equally applicable for modeling the risk associated with the decision to use the Internet as a distribution channel. The system dynamics simulation model will capture the interaction of variables such as brand name, marketing and advertising expenditure, complexity of product features, hit rates to website, availability of online support, and performance of competing distribution channels.
12_jwHoffman_38246 11/20/01 7:25 AM Page 298
298
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
Consequences
Causes
Virus protection software
E policies
Risk Lost time Time to recover systems
Infected disk
Employees following policies?
Shutdown
Computer virus infection Desktops and servers down Web download
Information backed up?
Failed client commitments
Email
Firewall
Lost productivity Time to recover info
Lost information
Financial penalties
Propogation to other computers Public Reputation
Lost Business
EXHIBIT 12.18 Operational Risk Modeling System Dynamics Approach Source: Tillinghast/Towers Perrin.
In addition to addressing the unique challenges of modeling operational risks, use of system dynamics simulation models provides some additional advantages: ■
■
■
It helps focus further data-gathering efforts. A simulation model can be built quickly using expert input to supplement existing data. Sensitivity analysis can identify the specific assumptions that have the greatest impact on the results. This helps an organization deploy resources to gather specific data to tighten key assumptions. It provides a better understanding of the dynamics of operational risks. A graphical depiction of the cause–effect relationships helps to identify interventions to manage the sources and consequences of operational risks clearly. It provides a means for reflecting the interactions of operational risks across the enterprise. As businesses become larger and more complex, knowledge of their underlying dynamics becomes fragmented and localized. Although many managers have a good understanding of their own functional areas, few have a solid grasp of the interactions across the enterprise. Development of a system map provides a way to combine the knowledge and experience of managers across the enterprise.
There are several disadvantages, however, in applying the system dynamics approach to model operational risks. First of all, it takes time and
12_jwHoffman_38246 11/20/01 7:25 AM Page 299
Alternative Measurement Methods: Industry Progress to Date
299
effort to build a simulation model. Therefore, the approach is not the ideal method for analyzing a large number of operational risks. It should be reserved for modeling the most important and complex operational risks. Also, it is not a robust method for modeling the tail of a probability distribution. For low-frequency/high-severity risks that affect capital requirements other specialized approaches are better. Thus, like Bayesian Belief Networks the System Dynamics approach is another important tool for management and monitoring of specific risks and/or parts of the enterprise. ■ ■ ■
CASE ILLUSTRATION Applying Neural Networks to Operational Risks NASA Jeevan Perera of the National Aeronautic and Space Administration (NASA) in the United States has initiated experimental work on the application of neural networks to operational risk management and provided material for this section as an illustration of how a neural network model might extrapolate an operational risk conclusion from present and past data and information. Neural networks involve modeling the brain and behavioral processes for subsequent use in computer applications. These models make use of significant amounts of complex input and data relationships, and a data mining process to arrive at a “reasoned” conclusion. They have been applied in a variety of fields including psychology, neural biology, mathematics, physics, computer science, and engineering. They represent yet another exciting opportunity for the management of operational risks. Although it might come as a surprise, neural networks have been applied toward engineering applications at NASA. To date, they have been an effective reliability tool for concept design and planning of microelectromechanical systems (MEMS), which are small mechanical electrical devices and systems used in microspacecraft technology. He describes the data mining process for neural networks and its four steps, as follows: 1. Identification Step: Here we select the data and information to be used for both training and testing of the model. It is at this stage that the analyst will specify the input data and expected output. In addition, the organization will be segmented by unit (e.g., by design or fabrication teams, or by business unit). 2. Transformation Step: Somewhat akin to operational risk scoring, here we convert the raw input data into usable data and convert nonnumeric data into a numeric format using various techniques (e.g., mapping, sampling, feature extraction); the analyst will also compensate for outliners and sparse regions.
12_jwHoffman_38246 11/20/01 7:25 AM Page 300
300
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
3. Modeling Step: In this step we apply one of several algorithmic schemes to learn the mathematical relationships between the inputs and outputs. These schemes might entail statistical networks, the knearest neighbor, logistic regression, or decision tree approaches. 4. Analysis Step: Last, we define performance expectations and judge the model’s results against them. As a next phase in experimentation with neural networks the challenge will be to determine whether diverse types of operational risk data will fit the mold of other uses of these models to date. The ultimate success of using neural networks will depend on the availability of data, which of course is similar to the challenge that we have with most models, but it may, in fact, be even more important here. Because of the nature of the analytics and need to train the model, an abundance of data, along with the ability to manipulate it, is perhaps even more critical. Insufficient data or the wrong types of input will cause problems in deriving reliable correlations. Data issues probably will require application of neural networks to isolate risks or business operations for the foreseeable future. Jeevan is optimistic that he will be able to apply neural networks to his operational risk management program at NASA. He is also confident that software is already available in the marketplace that will fit operational risk data to the various types of modeling schemes, allowing the user to select the best one. As he continues his experimentation, he cautions others to avoid work in a vacuum. As in other model development, he advises that analysts will be more successful if they include others in the process for validation of the results. He also advises practitioners to undertake a careful segmentation of the organization being modeled. This will be an interesting space to watch (no pun intended) in the development of operational risk analysis.17 ■ ■ ■
MODELING OPERATIONAL RISK: ADDITIONAL UNIQUE COMPLEXITIES By definition, some of the analytical challenges of dealing with operational risk include the difficulty in modeling complexity. In addition to settling on the most appropriate means of modeling complex, multifactor risks, it is also important to recognize the need to model interdependencies. For instance, this involves the risk of loss involving transaction handoffs from one business to another (e.g., risk involving gaps in responsibility from one business to the next). Thus a model should attempt to represent these interdependencies by first identifying business lines that rely on one another (i.e., those that rely on the business in question or on which it depends), then consider the downside risk of a failed handoff.
12_jwHoffman_38246 11/20/01 7:25 AM Page 301
Analytics: Some Measured Words of Caution
301
Another area of complexity is integration risk (i.e., the risk of gaps in responsibility that result from acquisition, restructuring, or reorganization). Here too a place to start is in illustrating transaction flow. Third, there is concentration risk. All risk maps and process models can be rendered useless if they don’t consider the tail event of a single event disrupting the firm’s entire operation. Thus, any firmwide representation of operational risk must look at singular concentrations such as the risk to a home office location, primary trading floor, processing center, and data centers. These variables present unique challenges for operational risk modeling. Some tools are already available to deal more effectively with complex operational risks. For instance, stress testing (e.g., combining tail risk scenario analysis with quantification models) can and should be applied to all models as a reality check. But there is evidence that tools might already be developing to deal more effectively with complex operational risks. These might include application of fuzzy logic, as just discussed, the use of nontraditional mathematical thinking, enterprise-wide dynamic operational risk monitoring (see Chapter 13), and modeling along the line of complexity theory. W. Michael Waldrop referenced this phenomenon in his book Complexity in 1993,18 and it may simply be a matter of time until the nontraditional thinking that he highlights makes its way into corporate risk management and control functions.19
ANALYTICS: SOME MEASURED WORDS OF CAUTION Myth: Sophisticated analyses will save the day. With all due respect to the editors, the February 2000 issue of Operational Risk might have left some readers to conclude that once they have complete risk class definitions and a good industry loss data set in hand, all they need is to acquire some actuarial models, implement a reasonable level of curve fitting, and they’ll have the subject of operational risk management nailed. Recent financial services history is replete with instances of disasters in spite of (and perhaps with contribution from) risk analysts’ love for quantitative analysis. Hopefully the operational risk management discipline will not fall into the trap that some shortsighted market risk managers have. As recently as 1998, investors in Long Term Capital Management were lulled into believing that models could represent all risk. And in the wake of that debacle, and others, we were once again reminded that a mix of quantitative analysis and qualitative insight is the most effective way to understand risk. Just as some of the more successful insurance companies benefit from applying a healthy dose of stress loss and futurist judgment to the results from their actuaries, many in operational risk management would profit from combining both quantitative and qualitative analysis. To be effective, quantitative methods must be based on a robust and relevant data set, credible
12_jwHoffman_38246 11/20/01 7:25 AM Page 302
302
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
methods (e.g., curves, simulations, trials, confidence levels), and tested/ used successfully in business environments. Quantitative tools can add much credibility to operational risk management by projecting a series of loss outcomes but should be kept in perspective relative to a broad-based operational risk management function. The best firms conduct analysis by risk class, by business activity or product line, then relate them to the strength of controls, quality of staff, management, and organization.
Balance, Revisited From an industry perspective, much time and attention is placed today on increasingly sophisticated quantitative analysis and modeling in anticipation of regulatory operational risk capital charges. Generally speaking this has been a very positive and productive development. Although I certainly advocate further advancements in quantitative techniques, the industry and individual firms must keep these efforts in perspective. If we are not careful, these tools run a significant risk of missing the mark with respect to basic risk management needs. That is to say, the process of gathering the data and conducting the analysis and meeting reporting deadlines can become a selffulfilling process in and of itself, and a distraction from behavioral modification and productive risk management investment, if one is not careful. Second, although the more sophisticated modeling that we have discussed will always have a place at major financial institutions and corporations alike, use of them may not be right for every firm. In fact, for medium-sized and smaller firms, with fewer resources available for their entire risk management effort, and even for some larger organizations, sometimes simple versions of them may be more effective. That is to say that for day-to-day management decision making, some simple analysis, reporting, and communication may in fact be more important in view of the ultimate goal of mitigating risk. And there is some truth there for larger firms as well. Too often analysts can fall in love with their models and lose focus on their interpretation, application, and practical use in day-to-day business decision making. The case of Long Term Capital Management is the poster child for this gaffe, but there are hundreds of less visible instances of this that go on in companies on a daily basis but never make it to the media.
CONCLUSION Operational risk analysis exists to support management decision making. Generally this support comes through answering two key questions. First, how much risk is our enterprise exposed to? Second, what are the sources of these risks and how can we mitigate them? The development of more sophisticated tools has led to more insight into the answers to these questions.
12_jwHoffman_38246 11/20/01 7:25 AM Page 303
Lessons Learned and Key Recommendations
303
The enigma about risk is that until we attempt to apply some measures to it, we have no idea where its uncertainty begins and ends. That is, what are the extremes of risk potential? It is useful to understand what expected loss potential might be, but it is probably more important to understand where the worst case loss potential lies. The recent recognition that sophisticated analytic and risk measurement techniques can bring value to operational risk is helping to define operational risk management as a new discipline. Managers and risk practitioners are finding themselves in a position to make far better business decisions in view of better data, analytic methods, and findings. The prospect of elevating the sophistication, reliability, and confidence in loss forecasts is already contributing to the further evolution of enterprise-wide risk management. Now firms will be in a position to factor most all dimensions—credit, market, and operational risk—into their strategic and day-to-day business decisions.
LESSONS LEARNED AND KEY RECOMMENDATIONS ■
■
■
■
■
Apply analytics to support operational risk management decision making on a day-to-day business level, as well as in strategic risk–reward decision making on a portfolio level. Apply levels of analytic sophistication appropriate for your individual firm’s size, culture, and business mix (BP Strategy #15). Loss capture by business units can be combined with simple mathematics to develop loss stratifications, loss class analyses, or simple or weighted averages of past losses by business line. The results can be useful for simple observations about trends and loss causation. Cost of operational risk analysis, which requires extensive data input, but only simple mathematics, can be a very valuable tool for tracking the long-term cost impact of operational risk on the organization. The input components include aggregate operational losses (preferably by risk class and business unit), annual costs for risk finance and insurance, annual recoveries, risk control, and administrative costs for management of the operational risk and related control functions. Economic pricing models are either financial statement-based or simply expense-based. The advantage is that they involve readily available information relatively simple to implement. The disadvantages include the fact that too often they only provide a big picture results in terms of the capital number and do not provide insight as to loss types or causation. Examples of loss scenario models include issue-based scenarios and risk maps. These models are generally useful for providing a predictive nature, involving business managers and staff, enhancing buy-in; disadvantages include their subjectivity and ability to attain consensus in the
12_jwHoffman_38246 11/20/01 7:25 AM Page 304
304
■
■
■
OPERATIONAL RISK ANALYSIS AND MEASUREMENT
results overall. They also sometimes lack the credibility that comes with using hard data. Use of loss databases, loss distributions, and Monte Carlo simulation in actuarial analysis has become widely adopted as an industry best practice in estimating expected and extreme loss potential. Firms will have to track their own data in databases and, in many cases, supplement the data with external industry data in order to conduct the analysis. Variations on this theme have included the Internal Measurement Approach, which has been proposed among emerging measurement options for regulatory capital. Statistical/actuarial models use a combination of frequency and severity loss distributions and Monte Carlo simulation or extreme value theory for modeling to develop a representation of possible outcomes. They can be useful for their predictive abilities if sufficient data are available and relevant. Data remain a challenge, however. Another disadvantage is that when developed using only empirical data, the models can be retrospective in nature and must be modified to enhance predictive abilities and risk matter motivational dimensions. Hybrid models, using risk factors and in some cases, extreme value theory, along with loss data, present an interesting alternative to pure statistical/actuarial models on this theme. Indicator or factor-based models include process maps, causal models such as Bayesian Belief Networks and System Dynamics, and behavioral models such as neural networks. They are particularly useful when full data are available and for high-frequency/low-severity events. Analysis candidates include processing groups and typical back office operation functions. In all probability they will not be as useful for developing overall enterprise-wide risk and loss potential and aggregating results from all risk and loss classes.
16_jwHoffman_38246 11/20/01 7:33 AM Page 375
Reproduced from Managing Operational Risk: 20 Firmwide Best Practice Strategies, by Douglas G. Hoffman, Copyright © 2002 Hoffman. Reproduced with permission of John Wiley and Sons, Inc.
CHAPTER
16
Economic Risk Capital Modeling Allocation and Attribution
INTRODUCTION e covered the various approaches to Risk Assessment (mostly qualitative) in Chapter 9, the data considerations (the operational risk data universe, databases, consortia, risk indicators) in Chapters 10 and 11, and then Risk Measurement and Analytic Building Blocks in Chapter 12. All of that background is important to factor into the development of an operational risk capital model, along with critical Risk-Adjusted Performance Measures (RAPM). For clarity, of course, each of the topics have been presented incrementally. At this stage in the process, we are assuming that we have the results of those risk assessment and measurement exercises in hand and have been charged with seeking ways to develop operational risk capital models and performance enhancement systems from them. Thus, the endgame here is to cover a discussion of economic capital, along with attribution or allocation methodologies. Suffice it to say that most economic capital systems are focused on answering the key question of whether the firm’s capital is sufficient to support its risk profile and possible losses. Economic capital systems are most effective when used in conjunction with a performance measurement approach such as RAROC (risk-adjusted return on capital). The basic principle here is that high-risk activities will require more capital than lower risk activities in order to maintain a consistent level of balance sheet strength. The best-managed companies already use some form of performance metrics to monitor and manage their business. Only a handful of these firms have moved on from that point, however, to weave in the allocation of the firm’s capital to businesses based on their operational risk characteristics. Thus, the first key component of the current state of best practice is to link economic capital models to performance measurement and management
W
375
16_jwHoffman_38246 11/20/01 7:33 AM Page 376
376
ECONOMIC RISK CAPITAL MODELING
BP STRATEGY #18—APPLY ECONOMIC CAPITAL MODELS AND OPERATIONAL RISK-ADJUSTED PERFORMANCE MEASURES Use economic risk capital models and risk-adjusted performance measures (RAPM) to calculate, monitor, and manage the effect of operational losses on firmwide and business unit levels. Monitor capital structures on top-down and bottom-up bases. Embed the models and processes to drive strategic and tactical risk-based decisions firmwide. Work toward application of the models in product pricing.
systems such that there is a productive incentive applied for risk management. The second dimension of best practice is to integrate the analysis and calculation of capital for operational risks together with those for financial risks. So the ultimate goal here goes beyond simply the measurement of operational risk. Most risk-based capital systems are intended to position their users to make strategic and tactical business decisions based on a complete view of risk (market, credit, and now operational risk measurement as well). The last segment of this chapter is a detailed discussion of Bankers Trust’s groundbreaking operational RAROC approach, including its evolution, details of implementation, and lessons learned. It is included because of the industry’s ongoing interest in our early work, and its continued relevance to recent industry developments.
ECONOMIC VERSUS REGULATORY CAPITAL MODELS At the outset, it is important to differentiate between our discussion of economic capital and the regulatory capital discussions under way relative to the Basel Risk Management Committee. Although there is much to be said for a consistent approach to both economic and regulatory operational risk capital models, this has not always been practical with other risk classes and risk management models. For one thing, regulators must apply consistency to their modeling components across a wide range of regions and firms, both from the perspective of size and business line composition. Unfortunately, too often the result of developing one standard is that this process forces modeling rigor to the lowest common denominator. In contrast, the development of economic capital models is completely discretionary. These are management tools. They can be developed with as much or as little sophistication as the firm desires, depending upon its risk management needs. Thus, if the firm is seeking to drive the models from bottom up or top down, at a profit center or even a desk level, management has
16_jwHoffman_38246 11/20/01 7:33 AM Page 377
Benefits of Economic Capital Models and Performance Measurement
377
all of those options. One would certainly not expect this level of specificity to appear in regulatory models and regulatory capital requirements.
BENEFITS OF ECONOMIC CAPITAL MODELS AND PERFORMANCE MEASUREMENT The most important benefit of economic capital models, when used in conjunction with performance measurement tools, is the leverage they provide in creating and supporting risk awareness and a risk aware culture over the longer term. One of the unique aspects of operational risk is that there are literally hundreds, if not thousands, of loss scenarios that can be developed, all with different causative and contributory factors. Because of this vast spectrum, a risk practitioner is faced with the dilemma of how best to promote operational risk management throughout the firm. Do you simply choose a half dozen scenarios as your sound bites to get people’s attention and hope that they catch on to all of the other scenarios that might take place? The answer is that you probably do, but the second question is how do you keep your audience’s attention focused on the risk scenarios that you have chosen? One way is by benchmarking your scenarios against other firms’ losses from an external operational loss database. This approach is useful, but be forewarned that it is vulnerable to criticism. Skeptics in your audience will argue that you are describing someone else’s losses, control environment, and management team, and it simply does not apply to your own. These are valid points, of course, but I would argue that the knowledge gained from that benchmarking exercise far outweighs its shortcomings, particularly if your organization does not have enough of its own large loss experiences to achieve statistical significance (thankfully). Modeling can help us to get closer to a representative situation by focusing on a number, or series of numbers, that gets people’s attention. This assumes, of course, that we are using representative data as input. For instance, these may include predictive variables from the business itself, loss experience or other observations from the firm itself, and characteristics of the management team itself. In the end, we are working our way toward a series of numbers. The fact is that it is those numbers that are what gets people’s attention. Clearly, risk-adjusted performance measures such as RAROC provide a number of strategic advantages. As noted, they help to determine whether the firm’s capital is sufficient to support all of its risks. With the advent of operational risk models, firms will be in a better position than ever to answer this question when those models are used in conjunction with credit and market models. In addition, the process helps us to determine whether the firm can increase its returns without increasing its risks, or conversely
16_jwHoffman_38246 11/20/01 7:33 AM Page 378
378
ECONOMIC RISK CAPITAL MODELING
reduce its risks without reducing its returns. From a performance assessment standpoint, they help to determine whether a specific activity or business is producing a reasonable return relative to its risk profile. From a risk mitigation perspective, the risks measured by the underpinnings of the RAROC approach helped to pinpoint areas requiring specific attention. Following are the specific benefits that have come from economic capital and performance measurement models for operational risk:1 ■ ■ ■
■
■
■ ■
They create and support a risk aware culture. They improve measurement of risk and risk costs (i.e., improved expense management). Along with enhancement of business line awareness toward operational loss potential and causative factors, they contribute observed actions toward refocusing control initiatives. They focus the business line’s attention on open risk issues witnessed by the significant reduction in frequency and the duration over which the issues remain open (e.g., internal audit or regulatory issues). They position the firm to achieve enterprise-wide risk management (i.e., integration of market, credit, and operational risk management) by: ■ Expanding evaluation of new initiatives to include operational RAROC, a more wholesome analysis of the potential risk exposure representing a more efficient allocation of capital to the business lines. ■ Supporting ongoing integration of market, credit, and operational risk groups by developing a common language. ■ Supporting ongoing exploration of integrated risk finance, using insurance and capital markets tools, for integrated risks that transcend operational, market, and credit exposures. They improve risk recognition by business line managers and place greater focus on risk control. They result in risk finance cost savings (i.e., operational cost-of-risk has been reduced over time).
TOP DOWN VERSUS BOTTOM UP, AGAIN We should pause a moment to visit the distinction between allocation and attribution in the capital sense. In order to do so, we should reference back to our discussion in Chapter 9, Risk Assessment, about top-down and bottomup analysis. In essence, capital allocation is derived from a top-down capital calculation. In other words, under a capital allocation regime we will develop an overall estimation or calculation of capital for the entire firm on a broad level, then apply the best means for allocating that capital downward throughout the firm based on an appropriate risk profile.
16_jwHoffman_38246 11/20/01 7:33 AM Page 379
Top Down versus Bottom Up, Again
379
In contrast, a capital attribution process is simply an extension of a bottomup risk assessment or measurement approach. That is, we calculate risk values (i.e., the value at risk) on a product-by-product or unit-by-unit basis and aggregate risk values in a logical way to represent a firmwide view of risk. The result is that we will have completed a capital development process including capital attribution. Undoubtedly, over the longer term, the best program will be a bottomup, capital attribution approach. It will involve several key advantages over capital allocation. Some of those include greater accuracy at the profit center or business unit level and therefore greater relevance of the risk factors and variables to the line manager. Thus, the process will support both risk measurement and risk management. The advantages of capital allocation, on the other hand, include the relative ease with which the program and calculation can be developed. That is, the analyst can work with aggregate values for the entire firm, whether they are aggregate representations of risk classes, loss scenarios, or simply a pooling of expected and possible losses for the entire firm. The process is simplified and streamlined. The disadvantage, however, is that its high level of simplicity keeps it somewhat removed from the line manager in terms of relevance of the individual variables and risk factors, and thus less useful to him or her on a day-to-day basis than a bottom-up line management tool.
CASE ILLUSTRATION Operational Risk Capital Allocation—An Overview of Early Work at Bankers Trust Bankers Trust has generally been credited with development of the first and most extensive attempt at integrating portfolio-level risk assessment, an operational loss database, use of risk factors, and statistical and actuarial modeling for operational risk. Many of the foundation concepts in Bankers Trust’s Operational RAROC model have since been adopted by several other banks and promoted by consulting firms. Some have even attempted to lay claim to development of its operational value-at-risk measurement foundation (i.e., the statistical/actuarial/loss distribution risk measurement model described in Chapter 12). In addition, the Loss Distribution Approach to risk capital in discussion with the Basel Committee on Banking Supervision bears some striking similarities to its measurement foundation.
Operational RAROC Development Development of the operational risk models at Bankers Trust (BT) was an evolutionary process. BT developed its first-generation operational
16_jwHoffman_38246 11/20/01 7:33 AM Page 380
380
ECONOMIC RISK CAPITAL MODELING
risk measure as early as 1979 in the form of a percentage of expense approach. Reevaluation of that measure began in 1990. In early 1996, we introduced our first phase of a new generation of models that served to measure and allocate operational risk capital to BT business lines. They included two types of models for use in advancing operational risk management in the firm:2 ■
■
Risk Measurement Model: As described in Chapter 12, using the loss data gathered, we applied the Monte Carlo simulation to develop loss expectancies by our five risk classes and the firm as a whole. Capital Allocation Model: Using a broad array of risk factors (approximately 70), we allocated the firmwide risk capital to each of the firm’s business lines and profit centers.
For our capital allocation model we engaged in additional work on new factor models using data specific to individual business lines in order to supplement our firmwide risk measurement model.3 The combination of these models brought to the table the value of a top-down portfolio approach toward firmwide and risk class-wide risk measurement at various levels of confidence (i.e., expected loss and outward to a 99% confidence level). In total, we had the benefit of a well-populated and information-packed loss distribution, combined with a representation of long-tail risk representation. When our allocation model was applied, we had the added benefit of a bottom-up factor-based model and representation of risk predictors that could also be quantified, traced, and trended.4 All of these dimensions were captured in our early stage data capture and management system for ease of data compilation, sorting, and analysis.5 Background Because of all of the more recent interest in approaches that bear similarities to our early work and approach, I have dusted off and elaborated on the following case overview of our early work on Operational RAROC. This section is based on an overview of our models. It was developed by Marta Johnson and me while at Bankers Trust for Treasury and Risk Management Magazine in 1997. It is provided courtesy of Deutsche Bank, which acquired Bankers Trust in 1999. As an independent firm, the measurement and monitoring of risk were cornerstones of Bankers Trust’s competitive strengths. With the development of a RAROC methodology for market and later credit risk during the 1970s and 1980s, Bankers Trust business lines used these risk management tools, including allocation of capital required, to make key strategic decisions about funding its businesses. For over a decade, since RAROC models were first implemented at BT, operational risk had been acknowledged as the third major component of the
16_jwHoffman_38246 11/20/01 7:33 AM Page 381
Top Down versus Bottom Up, Again
381
firm’s risk portfolio. There never existed a rigorous framework with which to define, quantify, or allocate operational risk at Bankers Trust and at virtually all other financial service firms, however, until the development of our more sophisticated operational risk models. In 1990, Bankers Trust’s Chairman and CEO Charlie Sanford challenged the firm’s risk specialists to answer the question, “What [was then] missing from BT’s RAROC (risk-adjusted return on capital) models?” That question lead us to pioneer a series of projects that first created an inventory of long tail event risks (described briefly in Chapter 9, Risk Assessment Strategies). Then later in 1992 we initiated development of an elaborate model for analyzing operational risks under the name Operational RAROC. As such, the impetus for investing in operational risk management systems was part evolutionary and part event-driven. It was evolutionary in response to underlying risk trends (e.g., exponential reliance on technology in the past two decades, greater product complexity, and dramatic increases in litigiousness globally) that have elevated operational risks significantly in the eyes of senior managers. On a broader level, the field of risk management has been evolving in response to the need to measure and manage operational risks more thoughtfully, thoroughly, and in a way that is consistent with other major risk classes, such as market and credit risks. Part way into the process, development became event-driven. Early in 1994 Bankers Trust faced dissatisfaction and legal action from several customers regarding Leveraged Derivative products and services (i.e., customer disputes involving the structure and sale of derivatives by Bankers Trust and other financial services firms). All of this came to light shortly after work on the long tail event risks was expanded to include the analysis of operational risk. Clearly it raised the visibility of operational risk among all of the firm’s senior managers and staff. The firm became much more intent on working to improve management information on operational risk in the wake of these high-profile events. Elsewhere in the industry the experiences of other large, highly publicized losses elsewhere in the global financial services community (e.g., unauthorized trading, errors in hedging, pricing), as well as those of nonfinancial firms in the global market had already highlighted the potentially devastating impact of operational risk. The experiences showed that the result of an operational breakdown, at the extreme, could include the demise of a firm (e.g., Drexel Burnham Lambert and Kidder Peabody). In addition, senior management’s memories of other banks’ experiences with lender liability patterns in the late 1980s were still fresh and provided a viable backdrop against which to quantify, understand, and manage our own operational risks. There was concern that despite control systems and processes in place at the time, operational risk was
16_jwHoffman_38246 11/20/01 7:33 AM Page 382
382
ECONOMIC RISK CAPITAL MODELING
not being recognized, measured, and managed as well as it could be due to the lack of a consistent and robust risk management framework. It was thought that as in the case of market and credit risk, such a framework could be designed to provide an incentive for managers to invest in the management of operational risk, with the objective of reducing the chance of the risk resulting in a loss, or particularly a sizable loss. This combination of events and perspectives was powerful enough to build momentum for quantifying the firm’s total global exposure to operational risk and, at the same time, develop a framework for reinforcing business line’s responsibility and accounting by attributing capital based upon their operational risk profile. Thus, this elevated the requirement to quantify, allocate, and manage operational risk into one of the firm’s top priorities. As with most projects, there were times when the development could have slowed or even stopped. The opposite happened: The pace of the project continued to accelerate, with its scope and depth expanding well beyond initial expectations. Senior management was instrumental in supporting the allocation of resources required to develop Operational RAROC as an informational tool, and ultimately as a risk management tool. More importantly, they also supported the advancement of all of the RAROC capital allocations toward becoming part of the cost of capital charge for each business line, providing an expense to the profit and loss (P&L) of each based on the level of operational risk contributed to the firm. Charlie Sanford had already requested that BT’s risk management scenario analyses be expanded to the concept of “shocks” to include operational risk shock loss scenarios, thereby providing a more holistic analysis of the risks being faced. Thus, a key consideration for the project was to include operational risk in analyses used to determine the sensitivity of the firm’s risk profile to an unexpected “shock” (e.g., an earthquake in Tokyo, the operational failure of a counterparty, a technology failure). Initially, the firm’s operational risks were evaluated within the context of an analysis of long tail event risks (i.e., referring to the long tail of a probability distribution). We conducted interviews of senior management members and developed risk identification/mitigation techniques accordingly. This work provided the foundation for building a more robust infrastructure to perform operational risk management. A recognition along the way was that the evolution involved a nagging concern that even expected or “normal loss” risks (i.e., the body of the probability distribution) were not being measured appropriately.6 Operational RAROC Objectives As with any project, the development of objectives is critical. Because there was already a risk measurement culture in place in the firm, along with existing RAROC objectives, we were able
16_jwHoffman_38246 11/20/01 7:33 AM Page 383
Top Down versus Bottom Up, Again
383
to leverage off of this foundation when developing the new operational RAROC component. The development of our Operational RAROC models took us through the exploration and development of a variety of other program features that have become important components of an operational risk management program. We set out to develop, and place in active use, a firmwide risk management system for defining, quantifying, and attributing risk-based capital, and for providing directional underlying risk information on operational risk in its broadest possible sense, extending well beyond traditional insurable risk. So, in the end, our Operational RAROC effort became an important focal point of our operational risk management effort and supported features that served as an important foundation for our operational risk management program. It was far more than just a model. Following is a summary of our key objectives: ■
■
■
Promote Active (Not Just Reactive) Risk Management: Our models were to be developed with a view toward active risk management using both directional risk predictors (trends in underlying causative factors or indicators) and observed risk (loss experiences and known risk issues). Enhance Risk-based Strategic Decision Making: To develop a tool for understanding business operational risks on a business-specific basis and for making strategic risk-based decisions. To support strategic risk-based decision making by adding operational risk information to that of other (credit, market) risk classes. Develop a Foundation for Better Informed Risk Finance and Insurance Decision Making: To create linkages to risk finance that support more selective purchase of monoline insurance for cost savings (e.g., more intelligent self-funding applications) and the creation of blended programs that better reflect the risks being faced by the firm.
Strategies and Tactics In response, the key strategies used in developing Operational RAROC included: ■
■
Capital Adequacy and Allocation: In response, we decided to model operational risk capital adequacy needs for Bankers Trust and develop an allocation system. We worked to develop a methodology for recognizing and measuring business operational loss potential and attributing risk capital, applying parameters similar to those used for market and credit risk capital (i.e., a one year time horizon; a 99% confidence level for risk analysis). Support and Coverage for Control Environment: We also decided to provide incentives for reducing operational risks and losses through
16_jwHoffman_38246 11/20/01 7:33 AM Page 384
384
ECONOMIC RISK CAPITAL MODELING
linkages with other control group issues/initiatives, including data capture from those groups and risk information reporting to business lines and control groups. Some of the tactics applied involved the: ■
■
■
■
Construction of a Unique and Extensive Database of Operational Events From Numerous Organizations Globally: Extensive global empirical loss data serves as a foundation for analytical modeling of the firm’s loss potential at the 99% confidence level. Directional Risk Information: We gathered, analyzed, and disseminated consistent directional risk data for enhancement of the firm’s control environment. With a focus on sources, rather than on symptoms of risk, we “mined” a vast array of operational risk data for use as factors, or risk “predictors.” These included behavioral issues such as staff turnover, tenure, and training, as well as systems characteristics such as age, complexity, and support with which to allocate risk-based capital to each Bankers Trust business. Risk Capital for Operational Risk Issues Outstanding: We elected to allocate capital for outstanding risk issues, including but not limited to control and audit issues, and regulators’ comments. Senior Management Risk Reporting: We introduced enhancements to existing business line performance measurement by setting the bar at different levels for businesses depending upon their allocated level of operational risk capital.
One of our key goals was to place operational risk management on a similar footing with market and credit risk management systems (in terms of risk quantification, risk profile analysis, capital allocation), and interface with all Bankers Trust business lines. We believed that it is equally important to promote proactive risk management tools for decision making at both corporate and business line levels. For instance, we believed that consistent and complete loss exposure information would add significant value when factored into priorities for investments set by line managers. Hybrid Model Design and Implementation As outlined in the discussion of models in Chapter 12, a truly optimal approach has not yet been identified for the industry. Each has its advantages and disadvantages. Depending on a firm’s management objectives, a combination of model types may yield the best results. This was also our early conclusion at Bankers Trust given our aggressive goals. Thus in the end, we developed our operational RAROC framework and modeling process from a combination, or hybrid, of several of the approaches outlined above, attempting to represent the best features of each.
16_jwHoffman_38246 11/20/01 7:33 AM Page 385
Top Down versus Bottom Up, Again
385
In getting started, we attempted to leverage off work that had already been completed in the market, or in the academic world. We were shocked to realize how little work was available that we could integrate into the Bankers Trust definition of operational risk. Frequently, the definitions of operational risk were viewed as too narrow, or focused on an aspect of operational risk that did not support our objectives. For example, some firms had been experimenting with valuing business operational risk using an expense-based system. But there are flaws in this approach: for example, what relation does expense have to the dimensions of risk, and does cutting costs reduce risk or increase it? Flow charts and time studies can be developed to determine how many “hands” or systems are required to complete a transaction from start to finish. These approaches provide road maps for the controls that need to be reviewed or reconsidered. However, they do little to assist in quantifying the risks being faced by the business line. We soon realized that we were onto something entirely new. We also realized that in order to satisfy our deliverables, we would have to start with a blank piece of paper and design the whole process, borrowing little from existing work. The advantage to this approach was that we were able to take a more strategic view of how we wanted to use the Operational RAROC components for other aspects of risk management, and we were not constrained by the assumptions of previous work. Plan of Attack With our key objectives in hand, along with key strategies, tactics, and the deliverables agreed upon, we put a plan in place for prioritizing resources to meet them within our set time frame. This resulted in the development of three major phases, each with major deliverables that enabled us to work concurrently on multiple objectives. These included: 1. Development of a loss database 2. Development of a risk measurement model 3. Development of an allocation model, with three subparts: a. Core Statistically-derived capital, and scorecard allocation model b. Development of risk issue tracking, and allocations c. Risk finance and insurance hedge allocation Exhibit 16.1 summarizes our project worksteps. The following sections provide more detailed descriptions of our development and application of Operational RAROC.
Phase I—Development of the Loss Databases Our internal and external databases were a key part of the foundation for risk measurement. We have already discussed database development
16_jwHoffman_38246 11/20/01 7:33 AM Page 386
386
ECONOMIC RISK CAPITAL MODELING
Our major project worksteps included actions to: 1. Define operational risks. 2. Conduct initial business line risk assessments. 3. Gather relevant internal and external operational loss data. 4. Refine the definition of operational risks. 5. Apply Monte Carlo simulation to develop loss expectancies. 6. Develop loss cause analyses/identify risk factors. 7. Gather risk assessment and risk factor or risk “predictors” data for all business lines. 8. Combine loss expectancies and risk factor or risk “predictor” analysis. 9. Complete risk-based capital allocation by business. 10. Update and repeat all data gathering and analysis on a regularly scheduled basis.
EXHIBIT 16.1 Operational RAROC Development: Primary Project Worksteps extensively in Chapter 10, so we will not dwell on the topic any further here, with the exception of a few additional observations relative to our specific use for Operational RAROC. Combining Proprietary (Internal) Losses and Expert Opinion Some risks are difficult to quantify because the data are not publicly available, but to ignore them would significantly bias the overall estimate of business operational risk. One example is the cost of a technology failure. Today, a financial firm’s exposure to operational risks through technology is huge, yet rarely do all the parties involved think of calculating the business impact (e.g., management and staff time spent analyzing the problem, the cost of developing “work arounds,” and the cost of projects being delayed to solve the problem). For these types of risks, we chose to supplement the loss data with expert opinion on the potential exposure (i.e., the synthetic datapoints described in Chapter 12). Together, the combination was quite powerful. It enabled us to characterize the risk events with the frequency and severity distributions that both managers within the firm and industry experts had agreed upon, providing for a more wholesome array of risks being represented in the database. There may be critics who voice their objections over the use of “soft” datapoints. However, in recent years, operational risk managers have found this type of Delphi technique useful in sizing exposure to loss, particularly where datapoints are not readily available elsewhere. External Losses and Relevance Rankings We realized early on that not all losses would be relevant to our analysis and model and, for those that
16_jwHoffman_38246 11/20/01 7:33 AM Page 387
Top Down versus Bottom Up, Again
387
are relevant, not all would be equal in their importance to the analysis. To reflect this view, we developed a three-point scoring system in ranking the relevance of losses to be included. Those losses carrying a one ranking would be viewed as the most important or relevant to our business. We asked ourselves the questions: Did the loss occur in a financial institution? Did it occur in one of our business sectors? If the answer to these questions was yes, more than likely we included these losses in our top ranked category and included them in the analysis at full value. To the extent that the answer was no to either or both of these questions, we applied additional tests and ranked the losses in category two or category three. In any event, the losses in the second and third categories were included in our analysis database at discounted values, thereby diminishing their impact on the outcome of the analysis itself.
Phase II—Risk Measurement Model In brief, we used severity and frequency distributions, along with sophisticated actuarial tools (including Monte Carlo simulations) to develop an aggregate distribution both on a portfolio basis and for each of the five risk categories. The resulting figures showed the amount of potential loss that could be expected for the firm overall (diversified) and in each of the five risk categories (undiversified). The distribution allowed for observation at a range of confidence levels, depending on the uses for the data. We used a 99% confidence level to be consistent with the theoretical framework used by market and credit RAROC and called the resulting number our “core” capital figure. The total capital exposure was first derived in December 1995. In time, expansion of the database enabled us to refine the distributions for each risk class and for the total diversified capital. Trend analysis is conducted on the portfolio level representing a diversified view of the risk. Undiversified potential loss exposure was also trended and similarly used to highlight risk categories and specific types of risk whose exposure increases or decreases. For instance, the business lines required more specific trend analysis when they consider specific initiatives. (See the Actuarial and Loss Distribution method in Chapter 12 for a more detailed description of our risk measurement approach.) In the early years of development, it became apparent that even though our loss database was growing on a weekly basis, we would not have enough data to support a bottom-up analysis and Monte Carlo simulation. It was clear that for the foreseeable period of time we would be constrained by the depth of our database. Thus, as described in Chapter 12, we were limited to producing a firmwide simulation by our five risk classes. It had been our intent from the outset to get to a point
16_jwHoffman_38246 11/20/01 7:33 AM Page 388
388
ECONOMIC RISK CAPITAL MODELING
Internal Loss Data
Core Capital
External Loss Data
Actuarial estimate of capital at risk due to operational exposure (1 Year/99% C.I.) Attribution based on Risk Factors (i.e., Control, Inherent, and Loss dimensions)
PLUS Capital Surcharge Source: Operational Risk Issues
LESS Hedge Value Credit or offset as a proxy for risk finance and insurance coverage.
EQUALS
Total Period Capital Attribution
EXHIBIT 16.2 Component Parts of the Operational RAROC Attribution Model of statistical significance in the data to be able to support a business line specific risk measurement model analysis and Monte Carlo simulation. Our own experience certainly supports the current focus and need for the industry-wide efforts to build industry databases and loss consortia. Sufficient business-specific data will be essential to be able to support business line-by-line risk analysis.
Phase III—Scorecard Capital Allocation Model Once again, because our limited data were unable to support bottom-up calculations by business, we were left to produce a top-down measurement model, together with a separate allocation model. In essence, this model was a scorecard system. There were three components to the allocation
16_jwHoffman_38246 11/20/01 7:33 AM Page 389
Top Down versus Bottom Up, Again
389
model: (1) statistically derived core capital, (2) risk management overlay, and (3) risk finance hedge. Following is a discussion of development and refinement of the allocation methodology. Exhibit 16.2 is a graphic depiction of the component parts. Allocation of Statistically Derived Core Capital How can businesses with dramatically different characteristics (e.g., check processing versus highyield corporate finance) be compared with each other? This is a reasonable question, but one to which a reasonable answer had to be developed. Our methodology provided for relative ranking of the business lines against each other based upon the risk profiles of each. In early 1996, 20 risk factors or “predictors” were developed and applied in the model. Within two years there were nearly three times that number representing a more wholesome capture of the operational risks being faced by the business lines. Also, over time the focus of the model was refined further to be more prospective than retrospective. A richer analysis process of the internal and external loss database and a closer alignment with the project’s objectives resulted in a rebalancing of the model. This shift in focus enabled us to feel more confident that the model took history into account, but also incorporated that facet of risk that is represented by the realization that “just because it hasn’t happened here doesn’t mean it couldn’t.” Starting Point. The loss events in the internal and external databases served as the starting point for determining the information to be used from the centralized data sources. Then two questions were asked: What types of information are predictors of control risk failures? In which risk category do the risks fall? If the centralized data sources gave us information for only one of the risk categories, say people risk, we knew this approach was not going to work. The information in the centralized data sources was analyzed against the risks that had appeared in the internal and external loss database. The risks were separated into each of the risk categories and “tested” against the loss events in the database to ensure a match between the reasons for the losses occurring and the information available from the centralized data sources. The Components. The methodology for developing the allocation of capital to the business lines, based on the level of operational risk they were contributing to the firm, was determined by the objectives of the project as outlined above. There are three main components of the allocation methodology, all of which stem from in-depth analysis of the events in the loss databases. To allocate the estimated capital number, a framework was developed within which we could categorize and rank the operational
16_jwHoffman_38246 11/20/01 7:33 AM Page 390
390
ECONOMIC RISK CAPITAL MODELING
Inherent Risk Factors
Control Risk Factors
Loss Experience Factors
Assess operational risks intrinsic to the business Inherent factors define the business; serve as exposure basis Primarily used for modeling
Define operational risk dimensions over which management can exert influence Valuable for both active risk management MIS and for modeling
Loss frequency and severity histories by business Incident tracking
Examples: Average transaction value Number of employees Number of system applications
Examples: Turnover rates Training investments Systems maintenance Business continuity status
Examples: Businesses’ own loss experience by overall risk class Errors Legal liabilities
EXHIBIT 16.3 Risk and Loss Indicators Application as Model Factors
risks that the business lines were taking. Our initiative resulted from a joint effort by the global risk management and internal audit teams, so that it benefited by borrowing risk analysis concepts from the audit function, such as inherent risk and control risk. These concepts were combined with risk assessment methods and other concepts applied in risk and insurance management in the allocation of risk finance costs. The result was that the “core” capital figure was allocated using the three components—inherent risk, control risk, and loss factor—to rate the operational risks each division was taking (Exhibit 16.3 presents an illustration of the three categories). The first two categories have already been discussed in a general sense in Chapter 11, Risk Indicators. 1. Inherent risk factors: Those created by the nature of the business itself. They can be understood as the baseline risks associated with the choice of being in a particular industry or sector. The only way to change them is to leave the business, or change it dramatically by selling or buying a major component. Examples of inherent risks would be product complexity, product life cycle, level of automation, and the level of regulation, litigation, and compliance. The information gleaned on each division’s risk factors was compared with that of each of the other business lines, and force-ranked on a relative scale.
16_jwHoffman_38246 11/20/01 7:33 AM Page 391
Top Down versus Bottom Up, Again
391
2. Control risk factors: Those meant to highlight existing and potential areas of controlled weaknesses. These factors are controllable by management. Examples include staff turnover, level of product compliance training, age of technology systems, and the level of straightthrough processing. Again, in our model the information gleaned on each division’s risk factors was compared with that of each of the other business lines, and force-ranked on a relative scale. 3. The third component was our loss factor. It was a combination of the losses incurred by the business line and those losses in the external database that are relevant to the business. The internal and external losses were weighted at 80/20 providing for the bulk of the loss factor to reflect the business line’s own loss experience. However, the external component provides a prospective view into the loss profile experienced by other firms in a similar business. This combination of prospective and retrospective losses enables both aspects to be taken into account in determining the allocation of capital to the business lines. Management can control the largest contributor to the factor since operational loss events can be monitored and steps implemented to minimize them. The component scores for each division were weighted. The weighting reflects the project’s objectives and was used in an attempt to achieve a balance between them. The core capital figure was allocated proportionally across the divisions, based on their total weighted score for overall operational risk. Broader Application. Overall, this statistically-derived core capital part of the allocation methodology met our objective of risk ranking business lines against each other, even though the businesses were different. It served as a management tool to control the risk factors and internal losses: managers could reduce their overall capital charge by reducing their score on specific risk factors. We also used it to look more closely at the business lines and risk-rank them at a lower level. In addition, the approach is representative of broader scoring methodologies that can be aligned with any top-down allocation model, whether it is quantitatively or qualitatively based. Risk Management Overlay—Allocation of Risk Issues and Credits. A second feature of the allocation model was a ranking and scoring of outstanding risk issues and credits. Initially, we called this entire second component of the model our Operational Risk Issues Surcharge (ORIS) because it only included capital charges (i.e., disincentives). Over time, we expanded this part to include credits (i.e., incentives) and other features as well, and renamed it our Risk Management Overlay.
16_jwHoffman_38246 11/20/01 7:33 AM Page 392
392
ECONOMIC RISK CAPITAL MODELING
Operational Risk Issues Surcharge (ORIS). The surcharge issues themselves were representative of outstanding audit and regulatory issues. We developed an elaborate scheme of scoring the issues for relative severity, along with a menu of capital charges for the different characteristics of issues. We did not attempt to place a precise value on the individual risks embedded in the audit or regulatory finding, but we did attempt to track our relative scoring and capital charges to the classifications assigned by the auditors. That is, issues identified in a failed audit received a higher risk rating than those in a marginal audit, which in turn would receive a higher ranking than issues from an audit that received a “well-controlled audit” rating. In fact, we did not include any of the latter for the purposes of assigning capital charges. Other features of the issue scoring process included additional charges for issues that were past due. It was essential to have a link between the record of the status of audit issues in the internal audit department and our operational risk group. This way, the most current status of an issue could be reflected in our operational RAROC model. Internal Audit maintained the official record on status. That is, if a business unit had questions about the status of an issue and its associated capital charge in the model, their question could only be resolved by the audit liaison responsible for their business. Without question, this part of the model was not statistically based at all. On the other hand, it was one of the most important risk-sensitive features of the model. And it created enormous incentive for business units to clear outstanding issues. Some of our regulatory representatives noted on more than one occasion that they were particularly pleased with the incentives that this feature generated toward clearing outstanding audit concerns. Expanding the Scope of Issues. As time went on, we worked to expand the scope of the operational risk issues surcharge. Our plan was to include other types of issues, such as technology, compliance, and legal aspects. A key determinant for inclusion was the need for a formal process and source for the information elsewhere in the firm. That is, we felt it important that operational risk be an independent unit that would track the ORIS issues identified, ranked, and scored from other sources and departments. Certainly, for instance, a firm could use issues identified and sourced in existing risk assessment programs as a feeder to this type of capital surcharge program. Self-identified Issues. We also worked to develop incentives in this second major component of the model for issues that were identified by the business unit itself, rather than internal or external auditors. The feature involved a discount on issues that were self-identified, versus the charge
16_jwHoffman_38246 11/20/01 7:33 AM Page 393
Top Down versus Bottom Up, Again
393
that would be imposed if an auditor identified the issue. This way, a business had an incentive not only to address and clear issues than were known, but also to self-identify others at much lower capital charges that would have been ordinarily imposed if they were to later be identified by Internal Audit. Risk Management Credits. In time, we introduced the concept of granting capital credits for bona fide risk management investments by business units. These credits took the form of capital relief for businesses that were making measurable progress and investment. Examples of actions that qualified included upgrading their control infrastructures and their own decentralized operational risk management programs and holding productive risk management committee and team meetings that discussed, addressed, and took tangible action toward advancing the discipline of risk management in the business itself. Here too, we developed a menu of risk management credits that were available to the individual business lines. The menu was made public such that the business units could work to attain these “extra credits.” Introduction of this feature helped to balance the incentives and disincentives in the program overall. As all of these features—expanded scope of types of issues, self-identified issues, and risk management credits—came together, we began to refer to this second part of the model as our Risk Management Overlay. This name reflected the fact that it was representing a broad range of risk and risk management issues, incentives, and disincentives, albeit not necessarily statistically based. Certainly, a statistician would take issue with this second component of our model. One could argue that we were being redundant in this section relative to the statistical representation of the first model component. Certainly we saw the component as adding extra conservatism to the model. We did not see this as a problem in an economic capital model, since the entire program was designed as an internal management tool, and the feature was applied consistently to all of our business units. Certainly, this redundancy would be more of a concern if the component were to be built into a regulatory capital model, thereby placing a redundant burden of capital on industry.
Risk Finance Hedge Component The third major component of our operational RAROC model was the inclusion of a risk finance and insurance hedge. This component was developed in recognition of the economic benefit of our risk finance and insurance programs. There should be no question these programs provide an economic benefit. Otherwise there would be little point in maintaining them, other than to meet regulatory insurance requirements.
16_jwHoffman_38246 11/20/01 7:33 AM Page 394
394
ECONOMIC RISK CAPITAL MODELING
In fact, as we discussed in Chapters 12 and 14, with some investment of time and effort on a routine basis, the firm can track the precise benefit of these programs over time using a calculation called cost of operational risk (COOR). At Bankers Trust, we calculated our COOR over a rolling ten-year period. We then determined the percentage of recovery that our risk finance and insurance programs produced against our own universe of operational losses over ten years and applied this percentage as an offset to our quarterly capital calculations. For argument sake, let’s say that, consistent with the industry analysis in the risk finance and insurance chapter, the offset amounted to 25% of historical operational losses. In this scenario, the 25% figure will be applied as an offset to operational capital as well. In our model, we would apply a percentage to the entire firmwide calculation of capital and distribute the benefit proportionally to each business unit, consistent with its individual allocation of capital. As one can see, this portion of the model was not particularly risk sensitive in and of itself for an individual business unit, other than the fact that it tracked proportionally to the unit’s core capital allocation. We believed, however, that it was a reasonable representation of the reduction that should be shown for the value of these programs.
Interaction with Business Units and Other Corporate Groups We tried to develop a framework to analyze operational risks within Bankers Trust and influence, in a productive risk management way through incentives, the behavior of our business line management teams. Beginning with the early development phase in 1990–1992, there had been a considerable amount of ongoing interaction and cooperation forged with a wide variety of groups within Bankers Trust. The groups we interacted with most closely included the business lines themselves, business line controllers, business line self-assessment groups, Internal Audit, Regulatory Compliance, Legal, Credit, property management, technology risk management, risk finance, business continuity planning, human resources, and corporate controllers. Risk measurement and modeling discussions often fall short when it comes to interaction outside of the risk management department. In our case, we worked hard to promote extensive interaction with others. In particular, all Internal Business Lines were involved with us in the gathering of uniform risk factor or “predictor” and loss data, and all corporate center internal control groups were polled to help identify risk factors and issues pertaining to all business lines or specific to a particular business. Each group was responsible for specific aspects of risk, with some groups having a broader scope than others (Internal Audit versus business line self-assessment). There was not a significant amount of over-
16_jwHoffman_38246 11/20/01 7:33 AM Page 395
Top Down versus Bottom Up, Again
395
lap (if any) among the groups, as their charters were sufficiently varied to prevent duplication. Each group approached operational risk from a slightly different standpoint resulting in a multifaceted profile for each risk being evaluated. Numerous important behavioral lessons were learned from the interaction and are worthy of note for constructing effective operational risk modeling and capital adequacy systems. Among them, from design through implementation we found ourselves having to battle the tendency of business line representatives to reduce their capital allocations as a prime objective, in contrast to, and at the expense of, more primary risk mitigation objectives. In other words, there was a tendency to practice cost management over risk management. But through a combination of model approaches—a statistical/actuarial and scenario-based measurement approach blended with risk factor and issues-based methods—we were able to make good headway toward satisfying both objectives of risk measurement with those of providing incentive for productive risk management behavior.
Management Reporting One of our program goals included development and implementation of operational risk management information for use by the business lines. The success of the project hinged on the use of the operational risk management information by senior management and the business lines in their measurement of performance, business decisions, and proactive risk management. From the beginning of its rollout in the first quarter of 1996, the business line allocation of Operational RAROC was reported in the management books and records of the firm. Our capital allocations were used to measure the performance of the business lines on a risk-adjusted basis and to determine where they were running compared with the hurdle rate set by the Chairman and CEO. Operational RAROC was a component in the budgeting process, and this required business lines to discuss with us their goals and strategic objective for the following year and beyond. The process produced both business line and high-level management reporting for our management committees, the Board of Directors, and specific reports for the business lines themselves. To be proactive, management must be able to ascertain what their risk “levers” are so they can take steps to improve them. Our reports were designed accordingly. The array of reports and graphs was too extensive to include samples of all of them here. Following is an outline of some of the reports produced: ■ ■
A risk indicator and factor scorecard by business and profit center Trend lines and graphs of key factors over time
16_jwHoffman_38246 11/20/01 7:33 AM Page 396
396
ECONOMIC RISK CAPITAL MODELING
Average Operational RAROC by Business Line
Time 1 Dollars
Time 2
BL 1 BL 2 BL 3 BL 4 BL 5 BL 6 BL 7 BL 8 BL 9 BL 10
EXHIBIT 16.4 Operational RAROC Capital Allocated by Business ■ ■ ■ ■ ■ ■ ■ ■ ■
A summary of risk issues and investments included in the Risk Management Overlay along with surcharges and credits A listing of important business line losses included in the loss factor Loss factor graphs Tables and graphs of firmwide capital over time Business line and profit center-specific capital allocations over time Complete descriptions and rationale for all factors used A summary of the key losses, factors, or issues having a major influence in the current period Interpretative observations and risk management recommendations based on trends and current period results An outline of current period refinements to the model
For instance, Exhibit 16.4 is a high-level relative ranking of business lines provided to management with a view of how the businesses were performing on a risk-adjusted basis relative to one another over time. These types of charts would frequently prompt questions regarding the risks being run by one business relative to another.
Challenges and Solutions As noted, our pre-rollout development phase spanned nearly five full years (1990–1995) during which time we were experimenting with internal risk
16_jwHoffman_38246 11/20/01 7:33 AM Page 397
Top Down versus Bottom Up, Again
397
assessment and risk ranking approaches, gathering loss data from internal and external sources, gathering internal exposure data for causative factor analysis and risk factors/predictors, and pilot testing various risk capital methodologies. We continued to develop and refine the project throughout the rollout phase, beginning in the first quarter of 1996. Once the firmwide total risk capital figure was calculated using the agreed-upon methodology, rollout to the business lines began with the risk-based capital being allocated to the broadest divisional or business line level. We implemented an ongoing refinement of the allocation methodology as our rollout continued and additional data became available. In essence, then, we were in a position to provide more meaningful risk management tools to the business lines. Some of the major challenges encountered in the initial implementation of Operational RAROC included: ■ ■
■
■ ■
■ ■
Initial project funding (always a challenge on projects, of course) Lack of initial focus and attention by business line managers, which is a common risk management challenge due to the inherent infrequency of large operational losses (i.e., how to gain attention to loss potential where losses have not yet occurred) Extremely limited number and scope of loss information impeding the ability to achieve statistical significance for analysis and forecasting Inconsistent risk data for relative risk ranking of business lines Qualified permanent staff (versus staff that was on short-term assignment) since the quantification and allocation of operational risk capital to business lines was relatively new Preconceived notions about definitions and data availability The type of statistical analysis that should be conducted (e.g., the potential for extensive correlation and regression analysis for each risk category)
Probably the most significant single hurdle for the effort was determining the most credible way to quantify the firm’s global exposure to operational risk, while also supporting an active risk management agenda. Since a core competency of the Bankers Trust staff was its quantification skills, the firm’s culture required a sophisticated, rigorous approach to the quantification of risk. There were multiple levels of risk that needed to be quantified in order to capture the attention of management. They included: ■ ■
Total firmwide exposure on a portfolio basis Total exposure for each business line
16_jwHoffman_38246 11/20/01 7:33 AM Page 398
398
ECONOMIC RISK CAPITAL MODELING
■ ■
Contribution of each risk predictor to the total and business line exposure Use of analytical skills consistent with those used in the existing market and credit risk models
When we began, the expectation was that the nature of operational risk did not lend itself to the type of rigorous analysis that can be performed on market, or even credit, risk data. The challenge was to find an approach that would lead to the quantification of each aspect of operational risk listed above and provide information for proactive management of the risks by business line managers. The approach we took was to: ■
■
■
■ ■
Define operational risks so they encompass all phases of the business process—from origination to execution and delivery—spanning the front, back, and middle office. Define risk categories that correspond to responsibility for managing and mitigating risks by aligning them to resources (e.g., sales and marketing technology, human resources staff, etc.). Combine the risk categories and business process to create a twodimensional system for categorizing risk with no overlap of risk categories or business processes. Develop a database of loss events that have been experienced by our own firm, as well as other firms. Develop frequency and severity distribution for the losses as a whole (diversified) and for each risk category (undiversified).
Gauging Relative Success The benchmarks we applied to gauge our success included: (a) the construction of a credible and defensible model to calculate operational risk capital, (b) a defensible allocation process, (c) benchmarking against other financial service firms, and (d) acceptance by regulatory examiners. Following is a discussion of how we performed against these benchmarks: ■
■
Initial capital calculation was completed following an intensive period of data gathering, model development, and vetting. Senior managers and management committees accepted results firmwide during the first quarter of 1996. Initial capital allocations were completed during the first and second quarters of 1996 and were under discussion with business line managers at least quarterly thereafter. Even though there had been many lively debates with individual internal business lines over relative details, there was agreement on the benefits and objectives of
16_jwHoffman_38246 11/20/01 7:33 AM Page 399
399
Reconciling Top-Down Models
■
the initiative, and on the framework for the allocation methodology. There was concurrence among senior business line managers that the process and methodology represented an important component in enterprise-wide risk management. Operational RAROC was a tool used by senior business line management to evaluate the performance of a particular business and when considering a shift in business strategy.
Not only did Operational RAROC aid BT in quantifying its total exposure to operational risk and develop a framework within which to allocate related capital, but at the time implementation of the program brought the firm closer than any other financial service firm to practicing enterprise-wide risk management (integration of market, credit, and operational risks). It put the firm’s managers in the unique and advantageous position of being able to make strategic decisions based on their “total risk” profile and risk-adjusted returns. Risk mitigation efforts became more focused and resources were redirected as needed. In addition, at a corporate level, by considering “total risk” exposure, more intelligent decisions could be made about risk finance alternatives, including, but not limited to, the purchase of insurance for operational risks. ■ ■ ■
RECONCILING TOP-DOWN MODELS As noted at the outset of this chapter, top-down and capital allocation models harbor a number of challenges. Both types of models are complex, of course, but allocation models are easier to implement on a relative basis. In exchange for that convenience, however, a number of challenges emerge in implementation. These include the challenge of maintaining relevance to the business lines, recognizing tail risk at a line management level, and the “zero sum game”. Following are some observations about how to deal with the issues at hand.
Relevance to the Business Units Many firms will attempt to apply one or two factors to allocate capital for a given business line. Unfortunately, all of the complexities of operational risk cannot logically be boiled down to one or two factors. As a result, models striving for this level of simplicity will suffer from a lack of relevance to line managers and their staff. An alternative is to use more factors and variables, thereby making the model more complex, or to strive for a reconciliation between the top-down calculations and bottom-up risk assessment.
16_jwHoffman_38246 11/20/01 7:33 AM Page 400
400
ECONOMIC RISK CAPITAL MODELING
Recognizing Tail Risk at a Line Management Level One advantage of top-down models is that there is a built-in diversification effect when capital is calculated for the entire firm versus business lines individually. Simply stated, independence of events is assumed, so the calculation for the whole is less than the sum of calculations for the individual parts. Therefore, top-down economic capital models cannot be applied in a vacuum. One way to communicate the results is to show risk-based capital calculations against a backdrop of considered business line–specific operational risk assessment. One way to do this is to contrast MFLs (maximum foreseeable losses) to economic capital allocations as part of their broader risk management efforts, with the better line managers implementing self-assessment or independent risk assessment programs by asking themselves “What is the worst operational loss scenario for our business?” Resultant loss scenarios will be translated into both risk mitigation strategies and economic MFL estimates. Traditionally, MFLs have been used by engineers to describe the extreme loss potential for a structural failure or extreme case of fire or natural disaster. When applied by the individual business units and for operational loss exposure classes, MFL examples might involve a large-scale failure of controls, unauthorized activities that result in a market or credit loss scenario, large-scale legal liability allegations, technology failure, large-scale external natural disasters, and related or unrelated business disruptions. Large-scale operational losses have been tracked industry-wide for all business sectors in recent years and suggest that when viewed independently any single business unit could conceivably face a loss potential well in excess of $100 million or $200 million. In some cases the number could approach $1 billion. When viewed at a 99% confidence level equivalent, these scenarios represent an undiversified view of operational risk by business. In contrast, when analyzed as part of a total diversified firm, the individual business will benefit in the form of a lower diversified capital allocation.
The Zero Sum Game Related to these differences between capital attribution and capital allocation, it is important to consider the “zero sum game” problem. To recap, the distinction we make is that capital attribution is deemed to be a bottoms-up type of capital calculation. That is to say, capital is derived for each trade, transaction, or portfolio individually, and then aggregated in order to arrive at a total capital figure for the subject at hand (item or items being measured). Conversely, the capital allocation process implies that capital is derived for a portfolio, and then distributed among all the units in a portfolio or in an entire firm. The challenges that a capital allocation process presents are many. One of the most frustrating ones for a business line manager is the notion of a zero sum game. That is, as long as we are dealing with a fixed sum of capi-
16_jwHoffman_38246 11/20/01 7:33 AM Page 401
Bottom-Up Models
401
tal, we force individual business lines into a collection of capital winners and losers. For one portfolio or business to improve upon its risk profile, or “win,” thereby reducing its allocation of capital, other businesses are forced to “loss,” or pick up the slack for their colleagues’ reduction in capital, with increases of their own. Thus, the latter groups “lose.” The system works as long as there is a clear distinction between the relative high-risk and low-risk units or businesses being measured. And even then, it works best when we are measuring relative rankings for a specific point in time. Problems begin to show up, however, as soon as we begin to look at how the units are performing on a relative basis over time. Imagine yourself as the business manager, or member of a team, who has been working hard to hold the line on your risk profile, as described by their collection of risk indicators. You feel a justified sense of accomplishment by maintaining your aggregate risk indices at a low level, and in actuality, at levels lower than most other businesses in the firm. Now, imagine your frustration, at best, upon learning that one of the other businesses in the firm has made only marginal improvement in its already high level of risk indices, but that their improvement causes your business’s capital to rise. On the one hand an advocate of competition might argue that the situation would press both businesses to strive for better results. The reality, however, is that the zero sum turns out to be the capital allocation system’s undoing. That is, the fixed sum of capital eventually causes both business managers to become critical of the system. The zero sum game problem, therefore, presents one of the strongest arguments for bottom-up models, and capital attribution over top-down, capital allocation models.
BOTTOM-UP MODELS Because of these challenges, the next wave of economic capital models will focus on attempting to find a solution to the bottom-up modeling challenge. For instance, the West LB case in Chapter 12 serves as an illustration of calculating the value at risk at a very detailed, individual business process level. A true bottom-up model would take values such as these and, developing respective VAR figures for all corners of the organization, ultimately drive a comprehensive value at risk for the entire firm. In our own experience with early models we found the data problem to be one of the major challenges in using statistical and actuarial models. That is, it would have been our first choice to get one step closer to bottom-up model development than we did by developing calculations at the “middle tier.” That is, to the extent that we would have had sufficient data to complete our calculations business by business, we would have been developing much more relevant figures for individual line managers. The financial services industry may well be close to realizing this development with the advent of loss
16_jwHoffman_38246 11/20/01 7:33 AM Page 402
402
ECONOMIC RISK CAPITAL MODELING
data consortia. If those efforts are successful, there will be a far greater chance of having sufficient data to at least support middle tier model development. At the time of this writing, in mid-2001, some firms, in consultation with the Basel risk management committee, seek to advance the development of “middle tier” models. We explore early model proposals in Chapter 17 on regulatory developments. Early proposals are struggling with the issue of relatively blunt calculations at the middle tier. They too will require sufficient data by the business line in order to support advancement in sophistication.
CONCLUSION Many of the risk measurements in modeling advances discussed in Chapter 12 will have limited use unless they are integrated into a RAPM program. The combination of more sophisticated measurement, coupled with incentives and disincentives built into the performance management program, can yield very powerful results. One of the tricks, of course, is to build the RAPM measures such that they motivate individuals to manage risk, not capital. Recent developments in operational risk management have raised the standard for all firms. Unfortunately, in today’s society one cannot lose sight of the potential for criticism and liability of senior officers and directors if they do not sponsor the exploration of these more advanced techniques. We saw our Operational RAROC methodology as representing a major breakthrough in the evolution and advancement of the risk management discipline. When coupled with our tested and proven risk measurement and monitoring methodologies for market and credit risk, we were in the best position ever to advance the measurement, management, and finance of business risks on an enterprise-wide, total, or “holistic” risk basis. Each business line’s performance was measured on an adjusted integrated risk basis, supporting the firm’s objective of efficiently allocating capital.
LESSONS LEARNED AND KEY RECOMMENDATIONS Economic Capital Models: ■ Use economic risk capital models and risk-adjusted performance measures (RAPM) to calculate, monitor, and manage the effect of operational losses on firmwide and business unit levels. Monitor capital structures on top-down and bottom-up bases. Embed the models and processes to drive strategic and tactical risk-based decisions firmwide. Work toward application of the models in product pricing (BP Strategy #18). ■ Operational RAPM holds infinite promise. Breakthroughs in risk analytics and performance measurement are just beginning to emerge, with some anecdotal success stories and pockets of uses. Unfortunately, one cannot ignore the downside either. Keep in mind the potential for creat-
16_jwHoffman_38246 11/20/01 7:33 AM Page 403
Lessons Learned and Key Recommendations
■
■
■
■
■ ■
■
■
403
ing the wrong incentives. Also, don’t lose sight of the risk of creating “analysis paralysis.” Effective risk management is difficult. Creating incentives and changing behavior in a productive way is difficult. Be mindful of the tendency to take the easy path toward analysis and measurement in the absence of using those measures and results to enhance management. That last mile is often the most difficult, but the most important. A model (in the economic capital management sense versus regulatory capital) can be any design or construct that assists in decision making about the management of operational risk. Because operational risk is so difficult to quantify, even a very basic model can help to add value to the topic. This can be invaluable for maintaining attention to the subject firmwide and maintaining an operational risk-aware culture. Getting to a capital number is of considerable value for estimating and communicating the potential downside of operational risk as a whole, or by an individual risk class as a whole. Capital calculations should be developed by risk class and business type. Hybrid economic risk capital models can be developed using a combination of the modeling and analytic techniques. By combining the positive features of the various models, one can develop a more responsive hybrid overall that meets the needs of the firm for providing both a view of potential risk and loss, as well as the basis for risk management incentives. Risk-based capital allocation programs must be responsive to changes in risk profile, control structures, and risk management investment. Managers and teams want to see results from their efforts and investments. A model that is responsive will reinforce productive risk management behavior. Nothing will create nearly as much disillusionment with a risk capital program as one that is unresponsive or counter-intuitive to bona fide efforts and investment in risk reduction and mitigation. Beware of model behavior that creates incentives for capital and cost management versus risk management. Beware of the zero sum problem in capital allocation systems. All things being equal, improvement in the risk profile of one unit should not cause an increase in capital allocation to other units. This phenomenon can wreak havoc with your capital allocation program. Let business line numbers float independently or use a corporate “plug” number to fill the gap. Bottom-up capital attribution programs can be useful but require commitment and data. The amount of benefit gleaned from these programs may not always be in direct proportion to the amount of commitment, effort, and analysis committed to making them work. Beware of reaching the point of diminishing marginal returns. The risk measurement and economic capital model should be managed by a function independent of the business units and Internal Audit.
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 529
CHAPTER
14
Capital Allocation and Performance Measurement
1. INTRODUCTION
I
n recent years, banks and consulting firms have sought to develop methodologies that will help financial institutions relate the return on capital provided by a transaction, or business, to the riskiness of the investment. The risk-adjusted return on capital (RAROC) methodology is one approach to this problem, and it is likely to prove a critical component of any integrated risk management framework. Indeed, one can think of RAROC analysis as the glue that binds a firm’s risk management and business activities together. As illustrated in Figure 14.1, RAROC analysis reveals how much economic capital is required by each business line, or product, or customer—and how these requirements create the total return on capital produced by the firm. Further, RAROC provides an economic basis from which to measure all the relevant risk types and risk positions consistently (including the authority to incur risk). Finally, because RAROC promotes consistent, fair, and reasonable risk-adjusted performance measures, it provides managers with the information that they need to make the trade-off between risk and reward more efficient. RAROC thus generates appropriate risk/reward signals at all levels of business activity, and should form a critical part of the 529
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 530
CHAPTER 14
530
FIGURE
14.1
RAROC Analysis
Total Firm-Wide Level RAROC
Business Unit Level RAROC
Customer Level RAROC
Product Level RAROC
Transaction Level RAROC
business “mindset.” (Banks also need to take into account their regulator’s capital adequacy requirements.) Figure 14.2 shows how today’s approach to measuring riskadjusted returns has evolved out of relatively unsophisticated measures of appraisal, which used revenue as the primary criteria for judging business success.1 During the late 1990s, the RAROC approach began to be accepted as a best-practice standard by the financial industry and its regulators. This was made possible by the development of sophisticated risk measurement tools of the kind discussed in other chapFIGURE
14.2
Evolution of Performance Measurement
Revenues
Return on Assets (ROA)
Return on Equity (ROE)
RAROC
LeadingEdge Methodology
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 531
Capital Allocation and Performance Measurement
531
ters of this book. These tools offered banks the practical capability to assign economic capital and measure performance on a riskadjusted basis. These risk measurement tools also encouraged banks to manage their capital on an integrated, portfolio management basis. In particular, banks increasingly recognized that market risk and credit risk were interconnected and needed to be measured simultaneously. The implementation of RAROC requires a well-judged blend of art and science. In Figure 14.3, we offer a rule-of-thumb guide to the current state of art in terms of how “scientific” each risk area in a bank really is. Methodologies tend to become more useful as they become more scientific. However, waiting for the science to be perfected before implementing a methodology can lead to damaging delays in implementation. 1.1 Definition of Capital In a financial institution, economic capital is the cushion that provides protection against the various risks inherent in the institution’s businesses—risks that would otherwise affect the security of funds that are deposited with, or loaned to, the institution. The purpose of economic capital is to provide confidence to claim holders such as depositors, creditors, and other stakeholders. Economic capital is designed to absorb unexpected losses, up to a certain level of confidence. (By contrast, “reserves” are set aside to absorb any expected losses on a transaction, during the life of FIGURE
14.3
Science and Art in Risk Management
Total Firm Art - 35% Science - 65%
Market Risk
Credit Risk
Operational Risk
Art - 10% Science - 90%
Art - 30% Science - 70%
Art - 80% Science - 20%
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 532
CHAPTER 14
532
the transaction.) It would be too costly for a financial institution to operate at a 100 percent confidence level, i.e., the level that would ensure the institution would never default, whatever its future loss experience. Instead, economic capital is set at a confidence level that is less than 100 percent, say, 99 percent; this means that there remains a probability of, say, 1 percent, that actual losses will exceed the amount of economic capital. Regulatory capital, on the other hand, is derived from a set of rules, such as the Bank for International Settlements (BIS) capital accords—BIS 88 and BIS 98. These are designed to ensure that there is enough capital in the banking system. In fact, most financial institutions hold more capital than the regulators require (see Chapter 1). Economic capital is what really matters for financial institutions and their stakeholders. Economic capital may be derived from sophisticated internal models, but the choice of the confidence level and the risk horizon are key policy parameters that should be set by the senior management of the bank and endorsed by the board. The determination of economic capital, and its allocation to the various business units, is a strategic decision process that affects the risk/return performance of the business units and the bank as a whole. It influences dramatically the way that capital is allocated and reallocated among the various activities and projects. Figure 14.4 offers an example that illustrates the RAROC calculation. On the loss distribution derived over a given horizon, say, one year, we show both the expected loss (EL), 15 bp, and the worst case loss (WCL), 165 bp, at the desired confidence level (set in this example to 99 percent). FIGURE
14.4
The RAROC Equation Revenues
Risk-Adjusted Return
RAROC =
= Risk-Adjusted Capital
Loss (outside of the confidence level)
- Expenses + Return on Economic Capital +/- Transfer Prices - Expected Losses
0%
Capital • Credit Risk • Market Risk • Operational Risk
15 bp Expected Loss (EL)
Capital = WCL – EL = 150 bp
100% WCL = 165 bp Probability of losses being less than this amount is equal to our desired confidence level, say 99%
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 533
Capital Allocation and Performance Measurement
533
The unexpected loss is, therefore, the difference between the total loss and the expected loss, i.e., 150 bp at the 99 percent confidence level, over a one-year horizon. In Sections 3 and 4 we present the standard approach for determining economic capital. The numerator of the RAROC calculation, as illustrated in Figure 14.4, is composed of revenues plus return on economic capital minus expenses for the given business activity, minus expected losses. A typical RAROC process also calls for specific business functions to be credited with revenue, or debited with relevant expenses, through a transfer-pricing mechanism. The denominator of the RAROC equation measures the capital required to absorb the unexpected loss. In Section 5 the procedure for extending expected loss is described. To illustrate the RAROC calculation, let us assume the following: A loan portfolio with a principal of $1 billion is considered, paying an annual rate of 9 percent. The economic capital against such a loan is estimated to be $75 million (i.e., 7.5 percent of the loan) which is invested in Government securities returning 6.5 percent per annum. Therefore, $925 million should be raised by deposits with an interest charge of 6 percent. The bank in our example has an operating cost of $15 million per annum, and the expected loss on this portfolio is assumed to be 1 percent per annum (i.e., $10 million). The RAROC for this loan is thus: 90 4.9 55.5 15 10 RAROC 19.2% 75 where 90 is the expected revenue, 4.9 is the annual return on the invested economic capital, 55.5 is the interest expense, 15 is the operating cost, and 10 is the expected loss. The RAROC for this loan portfolio is 19.2 percent. This number can be interpreted in terms of the annual expected rate of return on the equity that is required to support this loan portfolio. We should emphasize at this point that RAROC was first suggested as a tool for capital allocation, on an ex ante basis. Hence, expected losses should be determined in the numerator of the RAROC equation. RAROC is sometimes also used for performance evaluation. In this case, it is calculated on an ex post basis, with realized losses rather than expected losses.
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
534
2:08 PM
Page 534
CHAPTER 14
1.2 Three Broad Classes of Risk Capital: Market Risk, Credit Risk, and Operational Risk Above, we talked about risk in a generic sense. In practice, banks manage risks according to three broad classifications: credit, market, and operational risk. Market risk, as described in Chapter 5, is the risk of losses arising from changes in market risk factors. Market risk can arise from changes in interest rates, foreign exchange, equity, and commodity price factors. Credit risk, as described in Chapters 7 to 11, is the risk of loss following a change in the factors that drive the credit quality of an asset. These include adverse effects arising from credit grade migration (or credit default), and the dynamics of recovery rates. Credit risk includes potential losses arising from the trading book (e.g., contingent credit risk such as derivatives) as well as potential losses from the banking book. The possible impact of any credit concentration, or lack of liquidity in a portfolio, also needs to be incorporated into the level of credit risk capital attributed to the portfolio. Operational risk, as described in Chapter 13, refers to financial loss due to a host of operational breakdowns (e.g., inadequate computer systems, a failure in controls, a mistake in operations, a guideline that has been circumvented, a natural disaster). The measurement of operational risk also needs to cover the risk of loss due to regulatory, legal, and fiduciary risks. 1.3 Integrated Goal-Congruent RAROC Process The fact that banks classify, measure, and manage their risk in (at least) the three main categories just described poses a considerable challenge to risk-adjusted measurement and management. The huge number of business lines that need to be managed in any sizeable concern represent another major obstacle. To be successful and consistent, an RAROC process must be integrated into the overall risk management process (Figure 14.5), as we discussed in more general terms in Chapter 3. An “integrated” RAROC approach is one that implements a set of RAROC risk management policies that flow directly from business strategies. A consistent RAROC process is one in which the policies and methodologies applied to various kinds of risk are consistent with one another.
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9/27/00
2:08 PM
Page 535
Capital Allocation and Performance Measurement
FIGURE
535
14.5
Integrated Goal-Congruent Approach
C RO RA
Best-Practice RAROC Methodologies (Formulas) Valu ation
onal Operati Risk
Dis clo su re
Be e st tic c RA -Pr ra C e a P P ol RO cti st RO tur ic C ce Be RA truc ie s s fra In Independent First-Class Active Risk Management • Limits Management • Risk Analysis • Capital Attribution • Pricing Risk • Portfolio Mgmt
ties Authori
RAR Oper OC ation s
Busin Stra ess tegie s sk ce Ri ran le To
Ac Da cur RA ta ate RO for C
ware Hard Software n o cati Appli OC RAR logy o n h Tec
OC RAR lass t-C lls) s r i F ki ff (S Sta
9699.Ch.14
nd ta k ke Ris r a M edit Cr
To achieve both integration and consistency, an institution requires a well-developed set of RAROC methodologies that are supported by an RAROC infrastructure that can function across all risk types and businesses. RAROC methodologies rely on analytical models to measure market, credit, and operational risk. A proper RAROC infrastructure implies that the bank should have sufficient data, processing ability, and skilled staff to implement RAROC throughout the entire firm. One way of organizing this within a bank is to develop an RAROC policy and methodology unit, which has the task of synthesizing the bank’s various risk methodologies. A key problem here is to ensure that the RAROC policy and methodology unit is
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 536
CHAPTER 14
536
not so removed from the complexities of the various bank businesses that it fails to add value to the process. The goal is a “one firm—one view” approach that also recognizes the specific risk dynamics of each business. The output from an RAROC process affects a whole range of analyses and decisions in a bank. As Figure 14.6 illustrates, these include how the bank allocates limits, performs risk analyses, manages capital, adjusts pricing strategies, and performs portfolio management. RAROC analyses also feed back into capital management, financial planning, balance sheet management, and compensation practices. It should be emphasized that RAROC calculations may be adjusted for different applications. Again, all this implies that RAROC must be managed from an integrated firm-wide perspective (Figure 14.7). 1.4 Risk MIS: A Prerequisite for RAROC A risk management information system (MIS) is a key component of the RAROC infrastructure. The risk management information for each business unit and customer should be credible, regular (e.g., daily), and useful to business management. RAROC performance reporting platforms must integrate risk-based capital and loan losses and ensure integrity with other financial information at various levels of aggregation. When banks first attempt to build a risk MIS system, they often start with a prototype RAROC approach that tries to collect limited FIGURE
14.6
Impact of Output from RAROC Process
RAROC
Limit Setting
Risk Analysis
Capital Management
Pricing Strategy
Portfolio Management
Financial Planning
Balance Sheet Management
Compensation Paractice
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 537
Capital Allocation and Performance Measurement
FIGURE
537
14.7
Integrated Bank-Wide Perspective
Performance • Customer • Business • Product From Figure 14.6
Systematic Events
Limit Setting
From Figure 14.5 From Figure 14.4
Revenues
Policies
including return on economic capital minus Expenses including Transfer Prices minus Expected Losses
Methodology
Risk Analysis
Expected
RiskAdjusted Return
Infrastructure
=
Capital Compensation Philosophy
• • • •
Credit Risk Unexpected Market Risk Operational Risk New Risks
Tactical Planning
Strategic Planning
RiskAdjusted Capital
Market Risk Limits Firm-Wide Risk Management
Capital Management
• Portfolio VaR • Cumulative loss from peak • Stress testing • etc.
RAROC Pricing Strategy
Portfolio Management
Financial Planning
Credit Risk Limits • Counterparty • Product • Industry • Geography • Maturity • Risk Rating • etc. Operational Risk Limits • People • Process • Technology • Etc.
Balance Sheet Management
Compensation Practice
amounts of high-level data to help drive and develop the RAROC methodology. As a result of business pressure, the working prototype is often pressed into production prematurely. A short-term approach often also results in a system that is laborious and manually intensive. Typically, banks then embark on a more comprehensive and integrated risk MIS system that requires sophisticated, detailed
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 538
CHAPTER 14
538
data collection, a powerful computation engine, massive storage capability, and information distribution capability. Where this is successful, the RAROC effort can become a hub of the bank’s information infrastructure, fostering the integration of numerous risk control processes and strengthening alliances with and among many business units. One possible design for a sophisticated risk MIS architecture is provided in Figure 14.8. As the MIS is so crucial, RAROC projects often turn out to be either the victim or the beneficiary of a bank’s success or failure in building an integrated MIS approach.
2. GUIDING PRINCIPLES OF RAROC IMPLEMENTATION 2.1 Capital Management As a general rule, capital should be employed so as to earn the shareholders of a firm at least the minimum risk-adjusted required return above the risk-free rate of return on a sustainable basis. FIGURE
14.8
Risk Management Information Architecture
Risk Management Reporting
Market Risk Management Analytics Workstation
Credit Risk Management Analytics
Reports
GL
Workstation
Reports
RAROC Risk Data Warehouse
GL
Workstation
GL Multiple General Ledgers (GL)
Multiple Source Systems
Reports
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9/27/00
2:08 PM
Page 539
Capital Allocation and Performance Measurement
539
Otherwise the share price of a firm will underperform relative to top-performing competitors. In addition, within a firm capital is not an inexhaustible resource and should be used prudently. For example, if one accepts the standard practitioner application of RAROC, in Figure 14.9 businesses A through D can be said to add value to the firm: they surpass the prespecified hurdle rate (say, 15 percent). On the other hand, business units F through H destroy shareholder value. One should also examine the amount of risk-adjusted capital utilized by each line of business. For example, observe that business unit B has a higher adjusted return than business unit C, but business unit B utilizes more capital than business unit C. An RAROC model, as we pointed out earlier, is not meant to capture catastrophic risk since potential losses are calculated only FIGURE
14.9
Measure of Success—Building Shareholder Value
Capital Business Employed Unit ($MM)
($)
Risk-Adjusted Return on Capital (%)
Risk-Adjusted Capital
9699.Ch.14
0
10
Value Destruction
20
30
Value Creation
Hurdle Rate
40
Excess Economic Return Value Added (%) ($MM)
A
10
25
2.5
B
50
20
10.0
C
20
10
2.0
D
10
1
0.1
E
70
0
0
F
30
(5)
(1.5)
G
10
(8)
(0.8)
H
15
(10)
(1.5)
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 540
CHAPTER 14
540
up to a certain confidence level. (Instead, since capital will not protect a bank against catastrophic risks, banks may choose to insure themselves.) However, banks can use the RAROC model to assist their insurance purchase decisions. For example, a bank may decide to retain (and set capital aside to cover) a risk if the cost of the capital to support the risk is less than the cost of insuring it. 2.2 Ten Commandments of RAROC Generally Accepted Accounting Principles (GAAP) provide a level playing field in terms of providing a common set of rules to evaluate the health of a business entity. The banking industry has made significant advances in terms of the measurement of risk through what we will call here generally accepted risk principles (GARP). For example, a consensus has emerged on how to measure market risk in the trading book. The next evolution, beyond GARP (as shown in Figure 14.10), is toward a set of generally accepted capital principles (GACP). Box 14.1 attempts to specify 10 such principles to highlight the central importance of the RAROC methodology.
FIGURE
14.10
Generally Accepted Capital Principles (GACP)
GACP GARP GAAP Generally Accepted ACCOUNTING Principles Yesterday
Generally Accepted RISK Principles
Today
Increasing Sophistication
Generally Accepted CAPITAL Principles
Tomorrow
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 541
Capital Allocation and Performance Measurement
BOX
541
14.1
RAROC 10 COMMANDMENTS OF GENERALLY ACCEPTED CAPITAL PRINCIPLES
1. Include all business activities and the global operations of the bank. 2. Strive to implement an RAROC system impervious to arbitrage (including tax differentials). 3. Be explicit, consistent, and goal congruent with other policies (e.g., transfer pricing, price guidance, performance measurement, compensation, etc.). 4. Recognize different types of capital, but the primary emphasis will be on economic capital. 5. Use a single risk-adjusted hurdle rate charged as a cost of capital (which shall be broadly consistent with the bank’s longterm target return on capital). 6. Develop and implement an economic risk framework comprising credit risks, market risk (trading and banking book), and operational risks (funding liquidity risk is captured in the transfer pricing system). 7. Recognize funding and time-to-close liquidity. 8. Attribute capital as a function of risk and the authority to take risk (e.g., market risk limit). 9. Economic capital should be based on a confidence level deemed appropriate to achieve target rating. 10. Promote matching of revenues and risk charges where risks are incurred.
2.3 Management as a Critical Success Factor To implement RAROC on a bank-wide basis, the full cooperation of senior management is essential. This requires a clear understanding of the value of RAROC and a commitment to “stay on course.” Strategic programs, such as RAROC, are apt to come under review for cancellation in difficult business environments. RAROC must permeate the culture of an institution and be “second nature” to the business decision process. RAROC must be
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 542
CHAPTER 14
542
championed by the actions of senior management: risk-adjusted numbers should be used for performance measurement and compensation. Finally, successful implementation of a full RAROC program requires not only a sound conceptual framework but also careful planning and strong project management. 2.4 Implementation Stages Like the implementation of a risk MIS system, the ambitious nature of the RAROC process typically requires a bank to implement RAROC in stages. The first stage is an initial product phase where one prototypes “top of the house” indicative numbers (Figure 14.11). This is, essentially, an educational phase. The second stage involves producing reports that are used on a regular basis (say, monthly), through a repeated process across multiple business lines. The RAROC results in the second stage are used to add value to analyses as well as to provide input to the planning process.
FIGURE
14.11
RAROC Development Stages
Proactive Capital Management
nt me e ag an M sk Ri e tic Drill down: rac P • monthly reports t s • repeatable process Be • multiple business lines • value-added analysis • input to planning process Initial Production: • • • •
Prototype top of the house indicative numbers educational Time
Impact Behavior and Decisions • • • • • •
business goals risk strategy pricing and structuring competitive moves performance measurement compensation
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 543
Capital Allocation and Performance Measurement
543
In the third stage, RAROC begins to have an impact on business decision making, including business goals and the associated risk strategy. RAROC is used as a critical input for pricing and structuring deals, and is applied to the measurement of a business unit’s performance and the equitable compensation of staff.
3. RELATIONSHIP OF RAROC CAPITAL TO MARKET, CREDIT, AND OPERATIONAL RISKS In this section we discuss how economic capital, or “RAROC capital,” is set. We compare the approach to the procedure for setting regulatory capital (the subject of previous chapters). We divide the discussion into the problem of attributing capital to each risk element: market, credit, and operational risks. 3.1 Capital for Market Risk The approach to allocating RAROC capital for market risk has evolved to attributing RAROC capital as a function of the amount of risk expressed in the value-at-risk calculation. Further, practitioners often charge RAROC capital as a function of both unused market risk limits and penalties for exceeding limits. For example, let us assume that the formula for market risk capital is equal to F1 VaR (where VaR is set at, say, a 99 percent confidence interval) and F1 is a preset constant based on adjusting the VaR measure to account for exceptional shocks (say, F1 2). In other words, F1 multiplies the VaR to account for a day-to-day event risk not captured by the VaR model. (One may also adjust VaR as a function of the time it would take to liquidate risky positions.) The charge for the unused portion of a limit would equal F2 unused VaR, with F2 equal, say, to 0.15 (i.e., 15 percent of the unused limit). So, if we assume that the VaR, at the 99 percent level of confidence, is $200,000 and that the VaR limit equals $500,000, then the RAROC capital is equal to 2*$200,000 0.15*($500,000 $200,000) $445,000. The penalty charge for exceeding a limit is F3*excess VaR (where, say, F3 3). If, for example, the VaR had been $600,000, then the RAROC capital charge would have been: 2*$600,000 0.15*(0) 3*($600,000 $500,000) $1,500,000
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 544
CHAPTER 14
544
The interest rate risk in the “gap,” i.e., the mismatch between the interest rate sensitivities of the liabilities and the assets, constitutes the major source of market risk in banks. Banks are also exposed to foreign exchange risk. All these risks, and others such as the risks originating from embedded options in mortgages, should be taken into consideration when estimating the loss distribution over the RAROC time horizon set by the bank. This horizon usually differs from the regulatory horizon used to derive regulatory capital. The RAROC horizon depends on whether the positions are structural and are core positions for the bank’s franchise, the size of the positions, and how liquid they are. RAROC, or equivalently economic capital, is set to provide a cushion against unexpected losses at a desired confidence level. Regulatory capital for market risk is derived at the 99 percent confidence level (see Chapter 4). The confidence level for economic capital is set at the level that corresponds to the targeted credit rating for the bank. As we discussed in Chapters 8 and 9, an AA rating, for example, corresponds to a confidence level of 99.96 percent (or, equivalently, 4 bp) for the bank as a whole. Given that the various businesses in the bank are not perfectly correlated, this confidence level at the top of the bank translates into a lower confidence level at each business level, say 99.865 percent, which accounts for the portfolio effect of the various bank’s activities. In other words, attributing economic capital at, say, 99.865 percent confidence level for each business is such that the overall economic capital for the bank (i.e., the sum of the allocations to all the businesses) corresponds to an overall 99.96 percent confidence level at the top of the bank. 3.2 Capital for Credit Risk Practitioners attribute credit risk capital as a function of exposure, the probability of default, and recovery rates. The probability of default is often determined as a function of a risk rating or directly from a carefully structured algorithm, as we described in Chapters 7 through 10. Clearly, as illustrated in Figure 14.12, the poorer the quality of the credit, the larger both the expected loss and the attributed capital. A table of capital factors, such as those illustrated in Table 14.1, can be derived from a combination of sources. The capital factor is
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 545
Capital Allocation and Performance Measurement
FIGURE
545
14.12
The Poorer the Quality of the Credit, the Larger the Expected Loss and Attributed Capital
Risk Rating 3 Risk Rating 4 Remote loss (outside of the confidence level)
Risk Rating 5
100%
0% 15 bp Expected loss (EL)
WCL = 165 bp Probability of losses being less than this amount is equal to our desired confidence level
Capital = WCL – EL = 150 bp
T A B L E 14.1
General Capital Factors at a 99.865% Confidence Level (Assuming 60% Recovery Rate or 40% Loss Given Default)
Risk Rating (RR)
Tenor 1
2
3
1 2 3 4 5 6 7 8 9 10 11 12
Note: Only part of the table is shown.
4
5
6
1.74% 2.31% 8.03%
1.89% 2.47% 8.32%
2.03% 2.60% 8.50%
7
8
9
10
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
546
9/27/00
2:08 PM
Page 546
CHAPTER 14
typically expressed in terms of the percentage of the market value of the position. The capital factor expresses the amount of credit risk as a function of the risk rating and tenor. A risk rating can be mapped to each asset capital factor. For example, a five-year loan that is risk rated as 3 might have a capital factor of 1.89 percent. A five-year loan that is risk rated as 4 might be assigned a 2.47 percent capital factor, etc. The capital factor rises as a function of the tenor for the same risk rating. Similarly, the capital factor rises as a function of deteriorating credit quality for the same tenor. In other words, other things being equal, a five-year loan that is risk rated 4 has a greater capital factor (say, 2.47 percent), associated with a higher probability of loss, than does a four-year loan that is risk rated 4 (say, 2.31 percent). Similarly, a five-year loan that is risk rated 5 has a greater capital factor (say, 8.32 percent) than a five-year loan that is risk rated 4 (say, 2.47 percent). Accordingly, the capital charge is the product of the capital factor and the market value of the position. The capital factors are obtained through publicly available sources (e.g., Moody’s and S&P’s corporate bond default data, as explained in Chapter 7), proprietary external models (e.g., KMV, explained in Chapter 9), and publicly available models (e.g., CreditMetrics, CreditRisk, etc., explained in Chapters 8 and 10), as well as by means of proprietary internal models. A typical table of capital factors provides capital for a combination of risk rating and maturities. The derivations of credit risk factors for these tables typically follow a four-step process. First, one needs to select a representative time period to study a portfolio (e.g., ideally over a full business cycle). Second, one needs to map risk ratings to the portfolio. Third, expected and unexpected losses need to be estimated. Fourth, one needs to exercise appropriate management judgment in terms of assigning capital factors to adjust for imperfections in the data. RAROC factors should be examined to evaluate their ability to describe risk and to ascertain that a change in the inputs that drive these capital factors represents the appropriate sensitivity to risk. For example, we can evaluate the impact of risk rating and tenor on capital by comparing a risk rating of 4 with a maturity of five years (at 2.47 percent capital) to the capital required for a risk rating of 5 with
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 547
Capital Allocation and Performance Measurement
547
T A B L E 14.2
Standardized Capital Factors
Credit Rating
Tenor
Internal Rating
Moody’s Rating
4
5
6
3 4 5
A Baa Ba
1.74% 2.31% 8.03%
1.89% 2.47% 8.32%
2.03% 2.60% 8.50%
the same maturity (at 8.32 percent capital). If the quality of the fiveyear loan rises to risk rating 3, then the capital factor declines to 1.89 percent. One could calibrate the risk rating (say, 4) assigned to these entities internally, to the ratings provided by an external agency (say, Moody’s Baa rating), as shown on the left-hand side of Table 14.2. The process flow for calculating credit risk capital typically involves utilizing loan equivalents as shown in Figure 14.13.
FIGURE
14.13
Credit Risk Methodology—Process Flow Credit default history by risk rating and tenor • external data • internal data
RAROC Credit risk model
Loss given default • external data • internal data
Loan equivalent factors: • risk rating • tenor • product
Expected loss and capital factors by • risk rating • tenor
X
X
Transaction data: • amount • risk rating • tenor • product
Loan equivalent by transaction: • risk rating • tenor
Expected loss and capital by transaction
Aggregate expected losses and capital by summation
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
548
9/27/00
2:08 PM
Page 548
CHAPTER 14
3.3 RAROC Capital for Operational Risk Leading-edge banks have developed fairly good measurement methodologies for market and credit risk. However, as we reviewed in Chapter 13, operational risk is a comparatively difficult risk to quantify. Most banks admit to having poor measures of operational risk. An article in the December 1996 edition of Euromoney magazine pointed out that “Banks measure credit and market risk because they can, not because they are the biggest risks that they face. Operational risk is larger, more dangerous, and no one knows exactly what to do about it.” Operational risk measurement is very much a “work in progress.” One approach is to define an operational value-at-risk as the loss that is likely to arise from an operational failure over a certain time period, with a particular probability of occurrence. A primary difficulty with estimating operational risk in this way is that there are very few internal data points available to build the loss distribution. Nevertheless, one can look to external information. Some of the information to build a loss database may be gathered from court records (e.g., extensive information is available on retail and wholesale money transfer operational losses). A database is relatively easy to develop for those losses that are incurred regularly, such as credit-card fraud. One must be careful not to double-count operational failures. For example, operational risk may be reflected in loan losses (e.g., improperly assigned collateral), and may already be captured in the RAROC credit capital model. The measurement of operational risks is least reliable at the catastrophic end of the operational risk spectrum—those risks that occur very rarely even at an industry level but which might destroy the bank. Here, judgment is required. One can expect that advanced analytic tools, over time, will be developed to analyze catastrophic operational risk capital more satisfactorily. One simple approach to the allocation of operational risk capital is to assign a risk rating to each business (for example, on a scale of 1 to 5), based on operational risk factors defined in terms of a breakdown of people, processes, or technology. This rating is designed to reflect the probability of a risk occurring (inclusive of mitigating factors introduced by management). The capital is then
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 549
Capital Allocation and Performance Measurement
549
assigned based on the operational risk rating of the transaction or business line. The expected loss and risk-based capital charge are attributed to a position on a sliding scale that is nonlinear. The bank needs to develop capital factors based on a combination of internal loss history, losses at other banks, management judgment, etc. A central policy and procedure needs to be developed by banks to ensure the consistency and integrity of these ratings on a bankwide basis, as we described in Chapter 13. This will result in “relative” risk ratings for each business, which can then be attributed capital so that the desired “all-bank operational risk capital number” is achieved.
4. LOAN EQUIVALENT APPROACH Modern banks offer many financial products in addition to straightforward loans. Capital must be allocated to these products, and it is helpful, as a first generation approximation, to think of the risks generated by them in terms of their “loan equivalence.” 4.1 Loan Equivalence for Guarantees, Commitments, and Banker’s Acceptances Typically, the RAROC capital for each nonloan product is computed by multiplying the loan equivalent amount by a capital factor that is related to the risk rating and tenor. For example, if we examine typical RAROC factors for bankers acceptances, then we find that they typically have the same capital factors as for loans (Table 14.3). Loan equivalents for bank guarantees and standby letters of credit vary from a high of 100 percent for financial related products to 50 percent for nonfinancial related products, and to a low of 20 percent for documentary products such as the Note Issuance Facility (NIF), the Revolving Underwriting Facility (RUF), and the Guaranteed Underwriting Note (GUN). For NIFs, RUFs, and GUNs2 the loan equivalents are, say, 50 percent for risk rating 1 to risk rating 9, and, say, 100 percent from risk rating 10 to risk rating 12.
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 550
CHAPTER 14
550
T A B L E 14.3
Loan Equivalent Factors (Illustrative Only)
Loans and bankers’ acceptances Guarantees and standby L/C Financial Nonfinancial Documentary NIFs, RUFs, and GUNs Undrawn credit commitments 1 Year 1 Year General (demand) Uncommitted/unadvised lines
RR 1–9 (%)
RR 10–12 (%)
100
100
100 50 20 50
100 50 20 100
50 10 5 0
100 100 100 0
To illustrate the way in which RAROC is calculated, suppose that a bank has made a $100 million credit commitment of a fiveyear tenor to a customer that has a risk rating of 3. Assume also that $60 million has been drawn down. The capital required to support this position equals the sum of the drawn amount plus the undrawn amount, multiplied by the capital factor. Accordingly, the required capital equals ($60,000,000 ($100,000,000 $60,000,000) * 50%) * 1.89% $80,000,000 * 1.89% $1,512,000. In the case of bankers’ acceptances, guarantees, and financial letters of credit, there is little a bank can do to reduce the risk within the time frame of the instrument and, therefore, these instruments are best treated as loans. For credit commitments, however, a number of factors may reduce the likelihood of a drawdown. In some instances, the customer is only allowed to draw sums at the discretion of the bank. In these cases, the “loan equivalent” figure would be only a fraction of the total commitment. Term commitments are more likely to suffer a drawdown in the event of a customer default. For term commitments, the remaining term and credit quality of the customer both affect the likelihood of drawdown. However, there may be covenants that allow the bank to
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 551
Capital Allocation and Performance Measurement
551
withdraw these commitments if there is a deterioration in the credit quality of the customer. 4.2 Loan Equivalent for Derivatives The RAROC methodology typically calculates loan equivalents for derivative products (e.g., swaps, forwards, forward rate agreements (FRAs), etc.), at both the deal and the counterparty level. The loan equivalent is an estimate of the average positive exposure, over the life of a deal. Accordingly, the loan equivalent value is equal to the mark-to-market value of the derivative instrument plus the expected exposure (as explained in Section 5.2). The counterparty loan equivalent, counterparty risk rating, and tenor are used to calculate capital in a manner that is similar to risk-rated lending. For example, let us assume that a five-year, $100 million fixed/floating interest rate swap has a loan equivalent exposure of $2 million. If we assume that the swap has a counterparty risk rating of 4 (equivalent to Moody’s BBB rating), then the capital attributed, at the inception of the deal, would be derived by multiplying $2 million by 2.47 percent, which equals $49,400.
5. MEASURING EXPOSURES AND LOSSES FOR DERIVATIVES3 5.1 Measuring Exposures The crucial problem in developing an accurate loan equivalent measure of credit risk for derivatives for the purpose of an RAROC analysis is to quantify properly the future credit risk exposure. This is a complex problem because it is the outcome of multiple variables, including the structure of the financial instrument that is under scrutiny, and changes in the values of the underlying variables. The amount of money that one can reasonably expect to lose as a result of default over a given period is normally called the “expected credit risk exposure.” The expected credit exposure is an exposure at a particular point in time, while the “cumulative average expected credit exposure” is an average of the expected credit
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
552
9/27/00
2:08 PM
Page 552
CHAPTER 14
exposures over a given period of time. The average expected credit exposure is typically used as the loan equivalent exposure for the purpose of RAROC analysis. The maximum amount of money that could be lost as a result of default within a given confidence interval is called the “worst case credit risk exposure” (sometimes called the “maximum potential credit risk exposure”). The worst case credit risk exposure is an exposure at a particular point in time, while a related measure, the average worst case credit risk exposure, is an average of the worst case exposures over a given period of time. If one wishes to control the amount that could be at risk to a given counterparty, then the worst case exposure is particularly important in terms of allocating credit risk limits. One can use either the worst case or average worst case credit risk exposure as a measure when setting limits to credit risk exposure—one simply needs to be consistent. If one uses the worst case credit risk exposure to measure credit risk, then limits should obviously be set in terms of worst case credit risk exposures (in contrast to the average worst case credit risk exposures). The bank needs to estimate how much economic and regulatory capital should be set aside for a transaction or portfolio. The amount and the cost of the capital set aside for a portfolio, and for incremental transactions added to that portfolio, are vital factors in determining the profitability of lines of business and of individual transactions. The cost of the capital set aside for a single transaction is also a vital factor in calculating a fair price for that transaction. For a typical single cash flow product, for example an FRA, the worst case credit risk exposure at time t (Wt) grows as a function of time and peaks at the maturity of the transaction. Figure 14.14 illustrates the worst case credit risk exposure for such an instrument, and illustrates some typical relationships between this and the other measures mentioned above. Let us look at the relationship between the worst case credit risk exposure and the average worst case credit risk exposure in more detail. The worst case credit risk exposure is defined as the maximum credit risk exposure likely to arise from a given position within the bounds of a predefined confidence interval. For example, many dealers define the worst case credit risk exposure at a two-standard-deviation level, or a one-sided 97.5
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 553
Capital Allocation and Performance Measurement
FIGURE
553
14.14
Credit Exposure of an Instrument Expressed as Different Exposure Functions
750
500
“Worst Case” Terminal Exposure (e.g., 750)
Cumulative Average “Worst Case” Exposure (e.g., 500)
Exposure 150
100
Expected Terminal Exposure (e.g., 150)
Cumulative Average Expected Exposure (e.g., 100)
Time
percent confidence level. Let us assume, for illustrative purposes, that the worst case credit risk exposure at time t is equal to K t, where K is a function of the desired confidence interval, is the overnight volatility of the position’s percentage change in price, and t varies from 0 to T. Observe, for simplicity, that the standard deviation is assumed to come from a stable stochastic process where the risk grows as a function of the square root of time. For illustrative purposes, we will also assume that the probability of default is uniformly distributed over the time period. If we integrate the worst case function over the entire time period (and divide this result by the time period T), then we can see that the cumulative average worst case credit risk exposure is two-thirds of the worst case credit risk exposure, as indicated in Figure 14.14.4 Now let us look at how one can compute the expected terminal credit exposure—sometimes referred to as the expected terminal replacement cost. This computation, for time T (E[RCT]), can be approached using an option pricing framework. Assume that the distribution of returns is normal, with a zero mean and a standard
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 554
CHAPTER 14
554
deviation that grows as a function of the square root of time. Then, ignoring present-value considerations, one needs only to perform the necessary integration to show that E[RCT] FE/3.33, where FE is defined in this application as 2/3 WT. 5.2 From Exposure to Loss In a “nightmare” scenario, an institution might suddenly realize that it is virtually certain to lose the total amount exposed to loss. More typically, the probable loss on any transaction or portfolio of transactions depends on three variables: • Amount exposed to credit risk • Probability of the counterparty defaulting • Amount that is likely to be recovered (the recovery rate)
if the counterparty does indeed default The problem of measuring potential credit losses can thus be restated as finding the best way of estimating each of these variables, and an appropriate way of combining them so as to calculate the loss given default. With regard to default rates, an institution needs to develop techniques to calculate the default rate path and the distribution around the default rate path, estimated by examining those distributions at specific points in the future. The default rate distributions at specific points over the life of a transaction can be modeled through analyses of Standard & Poor’s or Moody’s data concerning the default rates of publicly rated institutions. Most institutions combine information gathered from rating agency data with their own proprietary default rate data (e.g., loan default data). They also analyze the credit spreads of securities, e.g., yields of specific securities over duration-equivalent risk-free securities, to generate a default rate distribution. These estimates of future default rate distributions are calculated for each credit grade. Just like the credit risk exposure measures described above, the distribution of future default rates can be usefully characterized in terms of an expected default rate (e.g., 1 percent) or a worst case default rate (e.g., 3 percent). The difference between the worst case default rate and the expected default rate is often termed the “unexpected default rate”
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9/27/00
2:08 PM
Page 555
Capital Allocation and Performance Measurement
555
(i.e., 2 percent 3 percent 1 percent). Typically, as illustrated in Figure 14.15, the distribution is highly asymmetric. A worst case default rate (e.g., the aforementioned 3 percent) may be structured so that one can say that there is a prespecified probability (e.g., 2.5 percent) of exceeding the worst case default rate. The probability density function describes how the probability of default varies over time; clearly, the longer the maturity of the financial instrument, the greater the default rate. The third factor needed to calculate counterparty credit loss is the recovery rate path. The distribution around the recovery rate path needs to be estimated at specific points in the future. Just like the other two variables, one can use the recovery rate distribution to determine an expected recovery rate, or a worst case recovery rate. The recovery rate distributions may be modeled by means of Standard and Poor’s or Moody’s recovery rate data. Surveys on the recovery rate of senior corporate bonds that have defaulted indicate that they vary as a function of the “pecking order” (i.e., lien position) of the debt. For example, senior debt has a higher recovery rate than junior (subordinated) debt. As with default data, institutions normally combine information gathered FIGURE
14.15
Distribution of Default Rates
Distribution of Future Default Rates
Expected Default Rate Path
PROBABILITY
9699.Ch.14
tN
0 D E
FA UL TR AT E
TIME
t
10 0%
“Worst Case” Default Rates
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 556
CHAPTER 14
556
from rating agency recovery rate data with their own recovery rate data—some institutions also obtain input from specialized legal counsel or insolvency practitioners—in order to provide a recovery rate distribution for each credit grade. These analyses, as illustrated in Figure 14.16, produce estimates of future recovery rate distributions that vary as a function of time. Just like default rate distributions, recovery rate distributions do not typically follow a normal probability density function. Having analyzed the distributions of the three credit risk variables—credit risk exposure, default, and recovery data—these can be combined, as illustrated in Figure 14.17, to produce future credit loss distributions. One would perform the necessary integration in order to generate the expected credit loss. Theoretically, these three distributions can be combined by integrating across the combined function.5 Observe that the graph in Figure 14.17 does not pass through the origin, as there is a positive probability of a nonzero loss. Again, observe that the summary credit loss distribution can be characterized as an average expected credit loss (LE) and an average worst case credit loss (LW). Ideally, one needs to construct a cumulative probability density loss function by integrating the multivariate
FIGURE
14.16
Distribution of Recovery Rates
PROBABILITY
Distributions of Future Recovery Rates
Expected Recovery Rate Path
0
RE
tN CO
VE
RY
RA
E TIM
TE 100%
t0
“Worst Case” Recovery Rates
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9/27/00
2:08 PM
Page 557
Capital Allocation and Performance Measurement
FIGURE
557
14.17
Creating a Credit Risk Loss Distribution Summary
DISTRIBUTIONS OF FUTURE CREDIT LOSSES
0
CR
SUMMARY CREDIT LOSS DISTRIBUTION
tN
ED
IT
LO
PROBABILITY
9699.Ch.14
TIME
SS
LE
t0
L E = Average Expected Credit Loss L W = Average “Worst Case” Credit Loss L C = LW - LE = Economic Capital
LW Lc
= Average Unexpected Credit Loss
probability density function, such that the worst case credit loss over the time period is set to the desired worst case probability of loss. The difference between LW and LE can be described as the average unexpected credit loss LC (i.e., LC LW LE). If a Monte Carlo simulation approach is adopted, then one first simulates an exposure value from a credit risk exposure distribution given default, at a particular point in time. Second, one simulates a default distribution, typically a binomial probability function with a single probability of default. Finally, assuming negligible recovery rates, one then summarizes the credit losses that occur across all points in time. Future credit loss distributions at various points over the life of the instrument may be combined as illustrated in Figure 14.18 to produce a single summary credit loss distribution. As pointed out earlier, combining credit risk exposure with the distribution of default rates, net of recovery, yields the distribution of credit risk losses. The distribution of credit loss needs to be translated into a provision (expected loss) and economic capital (unexpected loss). The loan equivalent approach estimates the loan equivalent as the average expected exposure. For example, as illustrated in Figure 14.19, assume that the average expected credit risk exposure for our derivative is 480 and
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 558
CHAPTER 14
558
FIGURE
14.18
Combining Variables to Produce Credit Loss Distributions
CREDIT RISK FACTORS MAY BE COMBINED . . .
TO PRODUCE COMBINED DISTRIBUTION OF FUTURE CREDIT LOSSES
PROBABILITY
EXPOSURE
DEFAULTS
0
CR ED IT
LO SS
TIME t0
RECOVERIES
that the expected probability of default is 1 percent. In our example, the expected loss is calculated by multiplying the expected probability of default by the average expected credit risk exposure, to arrive at an expected loss of 4.8. Further, since the worst case probability of default is 3 percent, then one can say that the worst case loss is 14.4 (480 .03); therefore, one would assign an unexpected loss (economic capital) of 9.6 derived from the difference between the worst case loss (14.4) and the expected loss (4.8). The loan equivalent approach utilizes the same default factors for contingent credit products as for loans. The potential unexpected loss is clearly a function of the confidence level set by policy. For example, a confidence level of 97.5 percent would call for less economic capital than a confidence level of 99 percent. This loan equivalent approach to calculating the average expected exposure is a proxy for more sophisticated approaches; it has the virtue of facilitating comparison to a more conventional loan product. Another approach would be to generate—using analytical, empirical, or simulation techniques—the full distribution
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 559
Capital Allocation and Performance Measurement
FIGURE
559
14.19
Calculating Risk-Adjusted Capital Requirements
Credit Exposure Worst Case Terminal Value (e.g., 3600)
Distribution of Default Rates (Net of Recoveries)
(e.g., 2400) Cumulative Average Worst Case
=
X
Credit Risk Capital
Expected Terminal (e.g., 720) (e.g., 480) Cumulative Average Expected Value
Time
Expected Probability of Default 1%
“Worst Case" Probability of Default 3%
2% (=3% – 1%)
“Worst Case" Expected Credit Loss Credit Loss $4.8 (=1% $480) $14.4 (=3% $400)
$9.6 (=$14.4 – $9.8)
Note: Assumes Capital = Unexpected Loss
of losses, and then to select the appropriate confidence interval percentile. A third approach would be to multiply a binary probability of default by the difference between the average worst case credit risk exposure and the average expected credit risk exposure to compute LC. This third approach may not provide the same answer as the earlier two approaches. In any event, the amount of risk capital should be based on a preset confidence level (e.g., 97.5 percent). The amount of unexpected credit loss (LC) should be used to establish the projected amount of risk capital. The dynamic economic capital assigned is typically the sum of the current replacement cost plus the projected LC.
6. MEASURING RISK-ADJUSTED PERFORMANCE: SECOND GENERATION OF RAROC MODEL6 Many modern banks attempt to maximize their risk-adjusted return on economic capital (subject to regulatory constraints). The typical RAROC approach consists of calculating the risk-adjusted return on economic capital, and comparing this RAROC ratio to a fixed hurdle rate. According to the accepted paradigm, only
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
560
9/27/00
2:08 PM
Page 560
CHAPTER 14
activities for which the RAROC ratio exceeds the hurdle rate contribute to shareholder value. Unfortunately, this commonly employed approach (firstgeneration RAROC), described earlier in this chapter, can result in decisions that adversely affect shareholder value. A secondgeneration methodology, “adjusted RAROC,” corrects the inherent limitations of the first-generation method. The key aim of this new RAROC measure is to adjust the risk of a business to that of the firm’s equity. For example, if a firm is considering investing in a business (or closing a business down), then it might compute the RAROC for the business (e.g., 16.18 percent) and compare this figure to the firm’s cost of equity capital (e.g., 16 percent). If the RAROC number is greater than the firm’s cost of equity capital, then the business will add value to the firm. To help clarify this, consider an all-equity firm undertaking a risky investment, with an economic capital reserve set up so that the probability of default remains constant at some prespecified level. It follows that risk-adjusted performance measures (such as RAROC) change as the risk of the business changes, even though the probability of default is kept constant. In other words, maintaining the probability of default constant is inconsistent with a constant expected rate of return on equity, and vice versa. The adjusted RAROC measure corrects this problem. Crouhy, Turnbull, and Wakeman (1999) (CTW) designed an “adjusted RAROC” measure at CIBC. They consider a firm that undertakes a project and adjusts its capital structure so that the probability of default (p) is set at some prespecified level (say, 1 percent). They compute the expected rate of return on equity capital for two cases. First, they alter the volatility of the firm’s risky assets ( A), adjust the firm’s capital structure (say, the debt-to-equity ratio) so that the probability of default is kept constant, and compute the exs). Using the simple Merton pected rate of return on equity capital (R model (see Chapter 9), they show that keeping the probability of default constant does not imply that the cost of equity capital is invariant to changes in the risk of the firm’s assets (Table 14.4). In Part A of Table 14.4, observe that in order to maintain the probability of default, p, constant (at 1 percent), the debt-to-equity ratio needs to be adjusted downward from 8.4 to 0.6, while the
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 561
Capital Allocation and Performance Measurement
561
expected rate of return on equity increases from 10.46 to 12.48 percent as the standard deviation of the assets increases from 5 to 40 percent. In Part B, the correlation coefficient is set at 0.50. Comparing Parts A and B, consider the case in which the standard deviation is 5 percent. Due to the higher correlation in Part B ( .50), relative to Part A ( .25), the expected rate of return on the risky asset is higher in Part B (i.e., 6.27 percent) than in Part A (5.70 percent). Consequently, the debt-to-equity ratio is also higher in Part B (i.e., 8.85) than in Part A (8.41), in order to keep the probability of default constant. The expected rate of return on equity is 10.46 percent in Part A, compared to 16.28 percent in Part B. Table 14.4 illustrates the importance of the correlation coefficient. The premise that underlies the first generation RAROC approach—keeping the probability of default constant—is inconsistent with a constant expected rate of return on equity for projects with different volatilities and correlations with the market portfolio. In the second case considered in the CTW paper, the firm undertakes a pure financing decision to achieve a degree of leverage so that the expected rate of return on equity equals some prespecified level. CTW compute the probability of default. They alter the volatility of the firm’s risky assets and adjust the firm’s capital structure so that the expected rate of return on equity is kept constant. It is shown that the probability of default is not invariant to changes in the risk of the firm’s assets even if the expected rate of return on equity is kept constant. So the first generation RAROC approach is flawed in the sense that it is possible to pick a capital structure so as to achieve a required rate of return on equity, but the probability of default will change as the risk of the business changes (Table 14.5). There is a striking difference between the results in the table. The probabilities of default are an order of magnitude higher in Part A than in Part B. An increase in the correlation coefficient, keeping volatility constant, increases the expected rate of return on the risky asset and reduces the degree of leverage necessary to reach the target return on equity. For example, if we increase the correlation coefficient from
0.25 (Case A) to 0.50 (Case B) while keeping the volatility
562 5.70 6.27 7.42 9.71
5 10 20 40
939.8 838.0 661.2 399.4
Face Value of Debt F
893.7 796.8 628.4 379.3
Debt D(0:T)
106.3 203.2 371.6 620.7
Equity S(0)
Market Values
8.41 3.92 1.69 0.61
Ratio of D to E D(0;T) /S(0)
10.46 10.71 11.25 12.48
Expected Rate of Return on Equity (percentage) RS
2:08 PM
Standard Deviation (percentage) A
9/27/00
Expected Rate of Return on the Risky Assets (percentage) A R
9699.Ch.14
Altering the Capital Structure to Keep the Probability of Default Constant: p 1% Part A: Correlation coefficient 0.25
T A B L E 14.4
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. Page 562
1 year
Maturity of debt
Expressed as a discretely compounded rate of return.
1
15.0 percent 1000
Market value of assets
12.0 percent
M Expected rate of return on the market portfolio: 1R
Volatility of the return on the market portfolio: M
1 percent
944.9 847.0 675.3 416.1
5.13 percent
5 10 20 40
Face Value of Debt F 898.5 805.2 641.7 394.9
Debt D(0:T) 101.5 194.8 358.3 605.1
Equity S(0)
Market Values
8.85 4.13 1.79 0.65
Ratio of D to E D(0;T) /S(0)
16.28 16.77 17.81 20.21
Expected Rate of Return on Equity (percentage) RS
2:08 PM
Probability of default: p N (d12 )
6.27 7.42 9.71 14.29
Standard Deviation (percentage) A
9/27/00
Default-free rate of interest: 1RF
Expected Rate of Return on the Risky Assets (percentage) A R
9699.Ch.14
Part B: Correlation coefficient 0.50
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. Page 563
563
564 5.70 6.27 7.42 9.71
5 10 20 40
1024.7 993.8 919.6 728.2
Face Value of Debt F
965.1 927.9 846.7 660.7
Debt D(0:T)
34.9 72.1 153.3 339.3
Equity S(0)
Market Values
27.56 26.73 24.92 20.48
Probability of Default (percentage) p N (d12)
2:08 PM
Standard Deviation (percentage) A
9/27/00
Expected Rate of Return on the Risky Assets (percentage) A R
9699.Ch.14
Altering the Capital Structure to Keep the Expected Rate of Return on Equity Constant: R S 17% Part A: Correlation coefficient 0.25
T A B L E 14.5
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. Page 564
1 year
Market value of assets Maturity of debt Expressed as a discretely compounded rate of return.
1
15.0 percent 1000
Volatility of the return on the market portfolio: M
12.0 percent
952.1 851.4 647.7 239.8 5.13 percent
5 10 20 40
Face Value of Debt F 905.2 809.3 615.8 228.1
Debt D(0:T) 94.8 190.7 384.2 771.9
Equity S(0)
Market Values
1.48 1.15 0.56 0.01
Probability of Default (percentage) p N (d 12)
2:08 PM
Default-free rate of interest: 1RF
6.27 7.42 9.71 14.29
Standard Deviation (percentage) A
9/27/00
M Expected rate of return on the market portfolio: 1R
Expected Rate of Return on the Risky Assets (percentage) A R
9699.Ch.14
Part B: Correlation coefficient 0.50
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. Page 565
565
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 566
CHAPTER 14
566
constant (say, A 5 percent), then the degree of leverage in Case B declines from 27.6 (965.1/34.9) in Part A to 9.55 (905.2/94.8) in Part B, to reach the target return on equity of 17 percent. This reduces the probability of default, which is inversely related to the asset’s expected rate of return and directly related to the face value of debt. It is proposed by CTW to use adjusted RAROC to properly measure the contribution of a marginal project to the risk/return of the firm, where the adjusted RAROC (ARAROC) is defined as: RAROC RF ARAROC E
(1)
where E is the systematic risk of equity and RF is the risk-free rate. They also show that a project will increase shareholder value when ARAROC is greater than the expected excess rate of return on the M RF (where R M denotes the expected rate of return on market, R the market). Four points are worth noting. First, RAROC is sensitive to the level of the standard deviation of the risky asset (Table 14.6). So RAROC may indicate that a project achieves the required hurdle rate, given a high enough volatility ( A), even when the net present value of the project is negative. Second, RAROC is sensitive to the correlation of the return on the underlying asset and the market portfolio. Third, the ARAROC measure is insensitive to changes in volatility and correlation. Fourth, if a fixed hurdle rate is used in conjunction with RAROC, high-volatility and high-correlation projects will tend to be selected.
7. CONCLUDING REMARKS Several trends in the banking industry seem likely to secure a growing role for RAROC analysis. These include a trend toward integrated risk, capital, and balance-sheet management as well as integration of credit risk and market risk. Meanwhile, the regulatory community is moving toward the use of internal models for the calculation of capital charges. This transformation in capital and balance-sheet management is being driven largely by advances in risk management. Approaches to measuring and managing credit, market, and operational risk are merging together into one overall risk framework.
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 567
Capital Allocation and Performance Measurement
567
T A B L E 14.6
Sensitivity of RAROC to Volatility for a Zero Net Present Value Investment Part A: Correlation coefficient 0.25
Expected Rate of Return1 Standard Deviation1 A 5 10 20 40
Risky Asset A R
Equity E R
Economic Capital E
RAROC1
ARAROC1
5.70 6.27 7.42 9.71
10.46 10.71 11.25 12.48
106.3 203.2 371.6 620.7
10.46 10.71 11.25 12.48
6.88 6.88 6.88 6.88
Part B: Correlation coefficient 0.50 Expected Rate of Return1 Standard Deviation1 A 5 10 20 40
Risky Asset A R
Equity E R
Economic Capital E
RAROC1
ARAROC1
6.27 7.42 9.71 14.29
16.28 16.77 17.81 20.21
101.5 194.8 358.3 605.1
16.28 16.77 17.81 20.21
6.90 6.90 6.89 6.88
Default-free rate of interest: 2Rf
5.13 percent
M Expected rate of return on the market portfolio: 2R
12.0 percent
Volatility of the return on the market portfolio: M
15.0 percent
Market value of the risky assets: A(0) ( cost of investment)
1000
Maturity of debt: T
1 year
Probability of default: p
1 percent
1
Expressed in percentage form.
2
Expressed as a discretely compounded rate of return.
Figure 14.20 illustrates how tools developed to measure risk capital in the trading world are being applied to market risk capital in the banking book. Over time, businesses within best-practice banks will find that they have to bid for scarce regulatory capital, balance-sheet limits, and risk limits. Managers will assess these bids by employing RAROC methodologies. The RAROC process will also integrate the entire risk process, as shown in Figure 14.21.
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 568
CHAPTER 14
568
FIGURE
14.20
Integration of Credit and Market Risk
e alu V to in
• Integrated models
for banking book
sk Ri g • Knowledge transfer from in rm trading book to banking book o f ns a Tr • Integrated models for trading book
Increasing Model Sophistication
FIGURE
14.21
The RAROC Process Integrates a Number of Critical Elements
RAROC
Models
Risk Management
BalanceSheet Management
Capital Management
•Market Risk •Credit Risk •Operational Risk
Risk MIS
Performance Management
Pricing
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 569
Capital Allocation and Performance Measurement
569
7.1 RAROC Link to Stakeholders RAROC provides a link between the needs of bank management and a variety of external stakeholders (Figure 14.22). Some stakeholders, such as debt holders, regulators, and rating agencies, are interested in the bank’s solvency in terms of the safety of its deposits. Others, such as shareholders, are interested in the bank’s profitability. RAROC provides a “common language” for risk and measurement that supports each of these interests. 7.2 Regulatory Trends Regulators are finding it increasingly difficult to keep pace with market developments such as credit derivatives. They are also becoming receptive to the use of internal models. Over time, an integrated RAROC framework that links regulatory capital and economic capital might well evolve (Figure 14.23). The BIS 98 regulations, and the consultative paper on a new capital adequacy framework released in 1999 by the Basle Committee (BIS 1999), are important steps toward linking regulatory capital and economic capital.
FIGURE
14.22
How RAROC Balances the Desires of Various Stakeholders
Bank Management
Risk and Capital
Safety • Debt holders • Regulators • Rating agencies
Risk versus Reward
Profitability • Shareholders • Analysts
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 570
CHAPTER 14
570
FIGURE
14.23
Integrated RAROC—Shareholder Value Creation
Tomorrow Regulatory Capital
Economic Capital Integrated RAROC Framework
Market Risk
Credit Risk
Operational Risk
APPENDIX 1: FIRST GENERATION OF RAROC MODEL—ASSUMPTIONS IN CALCULATING EXPOSURES, EXPECTED DEFAULT, AND EXPECTED LOSSES A.1 Methodology A series of assumptions are made in the development of a typical first generation RAROC model. Default data from sources internal to the bank, and external rating agency data, are employed to generate expected loss and credit risk capital factors. Typically it is assumed that default rates are stochastic, but that the loss given default (LGD) is a constant. The results of several Moody’s bond default studies are often used to develop the probability of default statistics, because these provide a link to the market’s perception of credit risk. In addition, Moody’s provides 24 years (1970 to 1993) of data, which allows the analyst to make statements about the probability of default within the remaining term of the asset class (e.g., a loan). (Bank data are typically available only for much shorter periods of time.)
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 571
Capital Allocation and Performance Measurement
571
Loss given default (LGD) is defined as the expected severity of loss given that a default on a credit obligation has occurred. The LGD rate for a defaulted facility represents the ratio of the expected loss that will be incurred over the total gross loan outstanding. A typical analysis might suggest a 40 percent loss given default rate for a loan portfolio, on a portfolio-wide basis. Similarly, a typical analysis might suggest that a 60 percent loss given default for corporate bonds is reasonable, on a portfolio basis. The analysis begins with an assumption of the distribution of the default rate. This assumption allows us to estimate the expected default rate, and the worst case default rates for a given confidence level, as well as the expected loss. From these estimates, and the assumptions concerning the LGD, and risk tolerance, we derive the capital factors to be used in RAROC calculations. For first-generation RAROC models, it is typical to assume that the default rate for a portfolio of loans can be expressed as a simple distribution. Let p be a random variable representing the probability of default for a given risk rating and tenor. If we assume further that the probability of default p is such that z p/ [1 p] is log-normal distributed, then y ln z ln(p/(1 p)) is normally distributed with mean y and standard deviation y (i.e., y N( y, y)). We can express p in terms of the normally distributed variable y: p exp(y)/(1 exp(y))
(A1)
Figure 14.A.1 illustrates how the default distribution varies by tenor for loans that are risk rated 4. A.2 Worst Case Default Rates and Expected Loss Let us denote the mean and standard deviation of the default probability by and , respectively. Then the mean and standard deviation of z p/(1 p) can be approximated,7 respectively, by z /(1 ) and z /(1 )2. The variance of y ln z can be estimated by z (A2) 2y ln 1 2z
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 572
CHAPTER 14
572
FIGURE
14.A.1.1
Default Distribution of RR4 Loans
1 Year 3 Year 5 Year
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
Probability of Default (in percent)
Accordingly, the worst case value of y at the 99.865 percent confidence level, which is three times the standard deviation away from the mean, is given by x: x E(z)exp(3 y 5 2y)
(A3)
The worst-case probability of default corresponding to x is x (1 x)
(A4)
Under the assumption that the loss given default is a constant 40 percent, then: • The expected loss rate is 40 percent of the expected default
rate, :
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 573
Capital Allocation and Performance Measurement
573
Expected loss 40%
(A5)
• The capital factor is 40 percent of the difference between the
worst case default rate and the expected default rate : Capital factors 40% ( )
(A6)
A.3 Illustration of Capital and Expected Loss Model for Loans Accounted for on an Accrual Basis Assume a loan is risk rated RR4 with a tenor of five years. First, one needs to determine the expected default percentage over five years. The cumulative default rate, , as shown in the cumulative default table (Table 14.A.1) is 1.97 percent. The source of the data used to derive the adjusted cumulative default table is Moody’s default history of 1970 to 1993.8 Observe that the expected default percentage in Table 14.A.1 declines from 1.97 percent to 1.46 percent as the tenor of loan declines from five years to four years. Second, the expected loss would be estimated as the default rate times the loss given default. For example, if we assume a T A B L E 14.A.1
“Adjusted Cumulative” Expected Default Rates
Tenor (years) Risk Rating
1
2
3
1 2 3 4 5 6 7 8 9 10 11 12 Note: Only part of the table is shown.
4
5
6
1.46%
0.62% 1.97% 11.85%
2.46%
7
8
9
10
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 574
CHAPTER 14
574
constant 40 percent loss given default, then the expected loss for our five-year, risk rated 4 loan is simply: 1.97% 40% 0.79% The expected loan losses for RR1 to RR6 are calculated by simply multiplying Table 14.A.1 by 40 percent. For convenience, a table of expected loan losses at a 40 percent loss rate is shown in Table 14.A.2. The expected loan loss rates for watch list ratings are mostly judgmental. Next, we determine the worst case default and loss rates. For this we also require an estimate of the standard deviation, , of the default rate. The estimate of the standard deviation of the default rate for a loan that is risk rated 4 and has a tenor of five years is 1.13 percent (Table 14.A.3). Using these values, the equations developed above are: z /(1 ) 1.97%/(1 1.97%) 0.02010 z /(1 )2 1.1347%/(1 1.97%)2 0.01181 and plugging in numbers for z and z, we obtain: T A B L E 14.A.2
Adjusted Cumulative Expected Loan Losses (@40% Loss Rate)
Tenor (years) Risk Rating
1
2
3
1 2 3 4 5 6 7 8 9 10 11 12
Note: Only part of the table is shown.
4
5
6
0.58%
0.25% 0.79% 4.74%
0.98%
7
8
9
10
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 575
Capital Allocation and Performance Measurement
575
T A B L E 14.A.3
Standard Deviation of Default
Tenor (years) Risk Rating 1 2 3 4 5 6 7 8 9 10 11 12
1
3
5
10
0.78%
0.64% 1.13% 5.11%
1.77%
Note: Only part of the table is shown.
0.01181 z 2y ln 1 2 ln 1 z 0.020 10 y 0.54456
2
0.29656
The worst case value of y at the 99.865 percent confidence level (3 ) is then: x zexp(3 y 5 2y) 0.02010 exp(3 0.54456 .5 0.29656) 0.08876 The worst case probability of default at 99.865 percent confidence level (for 3 ) is: x/(1 x) 0.08876/(1 0.08876) 8.15% A table of the worst case probability of default is shown in Table 14.A.4. The capital factor prior to adjusting for loss given default is the unexpected loss defined as the difference between the worst case probability of default and the expected default rate: 8.15 1.97 6.18
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 576
CHAPTER 14
576
T A B L E 14.A.4
Worst Case Probability of Default
Tenor (years) Risk Rating
1
2
3
1 2 3 4 5 6 7 8 9 10 11 12
4
5
6
7.23%
5.34% 8.15% 32.64%
8.97%
7
8
9
10
Note: Only part of the table is shown.
T A B L E 14.A.5
Capital Factor at a 99.856 Percent Confidence Level (Prior to Adjusting for Loss Given Default)
Tenor (years) Risk Rating
1
2
3
1 2 3 4 5 6 7 8 9 10 11 12 Note: Only part of the table is shown.
4
5
6
5.77%
4.72% 6.18% 20.79%
6.51%
7
8
9
10
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
9/27/00
2:08 PM
Page 577
Capital Allocation and Performance Measurement
577
T A B L E 14.A.6
Capital Factors at a 99.865 Percent Confidence Level (at 40 Percent Loss Given Default)
Tenor Risk Rating 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
2.31%
1.89% 2.47% 8.32%
2.60%
7
8
9
10
The capital factors prior to adjusting for loss given default are presented in Table 14.A.5. Note that the capital factor represents the amount of capital that is required to cushion unexpected losses over the life of the transaction. The capital factors adjusted for loss given default 40 percent ( ). For example, the capital factor for a RR4 five-year loan 40 percent (8.15 percent 1.97 percent) 40 percent 6.18 percent 2.47 percent. For convenience, a table of capital factors adjusted for 40 percent loss given default is shown in Table 14.A.6.
NOTES 1.
2.
Figure 14.2 shows the evolution of performance measurement from a practitioner perspective. In Chapter 17 we examine the evolution of RAROC towards a more sophisticated theoretical paradigm. NIFs, RUFs, and GUNs are term commitments by the bank to underwrite different types of public offerings.
This chapter has been withfrom permission from Risk Management, by Michel Crouhy, Galai andRobert Robert Mark. Mark, © Reproduced withreproduced permission Risk Management, by Michel Crouhy, DanDan Galai and published by McGraw-Hill , New York 2001 (© McGraw-Hill, all rights reserved). 2001 The McGraw-Hill Companies, Inc. 9699.Ch.14
578
3.
4.
9/27/00
2:08 PM
Page 578
CHAPTER 14
This section is based on Mark (1999). See Appendix 1 for a detailed analysis of exposures and losses, including tables and assumptions made in quantifying exposures and losses. The average worst case credit risk exposure, integrated from 0 to T, equals: (T0 K t dt)/T (K T3/2)/(3/2) (1/T) 2/3 [K T ] 2/3 WT
For example, the expected credit loss at a given point in time equals CE DR (1 RR) f(CE, DR, RR)dCEdDRdRR, where CE denotes credit risk exposure, DR the default rate, RR the recovery rate, and f(CE, DR, RR) the multivariate probability density function. 6. Portions of this section appeared in Crouhy, Turnbull, and Wakeman (1999). 7. The approximation is based on the Taylor series expansion, and by omitting higher-order terms in the series. 8. The Moody’s data for short tenors are adjusted to reflect the bank’s own experience for large corporate loans. See Chapter 7 for a description of Moody’s and S&P’s data.
5.
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
Reproduced from Portfolio Theory and Performance Analysis, by Noël Amenc and Véronique Le Sourd. 2003. Copyright © John Wiley & Sons Limited. Reproduced with permission.
4 The Capital Asset Pricing Model and its Application to Performance Measurement1 In Chapter 3 we described Markowitz’s portfolio analysis model and presented the empirical market model. The latter was developed by Sharpe in order to simplify the calculations involved in the Markowitz model and thereby render it more operational. The next step in financial modelling was to study the influence of the behaviour of investors, taken as a whole, on asset prices. What resulted was a theory of asset valuation in an equilibrium situation, drawing together risk and return. The model that was developed is called the Capital Asset Pricing Model (CAPM). Several authors have contributed to this model. Sharpe (1963, 1964) is considered to be the forerunner and received the Nobel Prize in 1990. Treynor (1961) independently developed a model that was quite similar to Sharpe’s. Finally, Mossin (1966), Lintner (1965, 1969) and Black (1972) made contributions a few years later. This model was the first to introduce the notion of risk into the valuation of assets. It evaluates the asset return in relation to the market return and the sensitivity of the security to the market. It is the source of the first risk-adjusted performance measures. Unlike the empirical market line model, the CAPM is based on a set of axioms and concepts that resulted from financial theory. The first part of this chapter describes the successive stages that produced the model, together with the different versions of the model that were developed subsequently. The following sections discuss the use of the model in measuring portfolio performance.
4.1 THE CAPM 4.1.1 Context in which the model was developed 4.1.1.1 Investor behaviour when there is a risk-free asset Markowitz studied the case of an investor who acted in isolation and only possessed risky assets. This investor constructs the risky assets’ efficient frontier from forecasts on expected returns, variance and covariance, and then selects the optimal portfolio, which corresponds to his/her level of risk aversion on the frontier. We always assume that the Markowitz assumptions are respected. Investors are therefore risk averse and seek to maximise the expected utility of their wealth at the end of the period. They choose their portfolios by considering the first two moments of the return distribution only, i.e. the expected return and the variance. They only consider one investment period and that period is the same for everyone. 1 Numerous publications describe the CAPM and its application to performance measurement. Notable inclusions are Broquet and van den Berg (1992), Fabozzi (1995), Elton and Gruber (1995) and Farrell (1997).
95
C04
WU058-Amenc
96
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
E (RP) M
A RF
B
σ (RP) Figure 4.1 Construction of the efficient frontier in presence of a risk-free asset
Let us now consider a case where there is a risk-free asset. An asset is said to be risk-free when it allows a pre-determined level of income to be obtained with certainty. We shall write this asset’s rate of return as RF . Its risk is nil by definition. The investor can now spread his wealth between a portfolio of risky assets, from the efficient frontier, and this risk-free asset. We take x to be the proportion of wealth invested in the risk-free asset. The remainder, or (1 − x), is invested in the portfolio of risky assets, denoted as A. The expected return of the investor’s portfolio P is obtained as a linear combination of the expected returns of its component parts, or E(R P ) = x RF + (1 − x)E(R A ) and its risk is simply equal to σ P = (1 − x)σ A since the variance of the risk-free asset is nil and its covariance with the risky portfolio is also nil. We can then eliminate x from the two equations and establish the following relationship: E(R A ) − RF E(R P ) = RF + σP (4.1) σA This is the equation of a straight line linking point RF and point A. To be more explicit, let us see what happens graphically (see Figure 4.1). If we consider the representation of the Markowitz frontier on the plane (σ P , E(R P )), the point corresponding to the risk-free asset is located on the y-axis. We can therefore trace straight lines from RF that link up with the different points on the efficient frontier.2 The equation of all these lines is equation (4.1). Among this set of lines there is one that dominates all the others and also dominates the frontier of risky assets at every point. This is the only line that forms a tangent with the efficient frontier. The point of tangent is denoted as M. The RF M line represents all the linear combinations of the efficient portfolio of risky assets M with a risk-free investment. It characterises the efficient frontier in the case where one of 2 We assume that the return RF is lower than the return on the minimal variance portfolio (located at the summit of the hyperbola). Otherwise, the principle that a risky investment must procure higher revenue than a risk-free investment would not be respected.
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
The Capital Asset Pricing Model
97
E (RP) M
RF
σ (RP) Figure 4.2 Efficient frontier in presence of a risk-free asset
the assets is risk-free. The introduction of a risk-free asset therefore simplifies the result, since the efficient frontier is now a straight line. In addition, the risk of the portfolios is reduced for a given return, since the straight line dominates the efficient frontier of risky assets at every point. Investors therefore benefit from having such an asset in their portfolio. The choice of a particular portfolio on the line depends on the investor’s level of risk aversion. The more risk averse the investor, the greater the proportion of the portfolio that he/she will invest in the risk-free asset. If the opposite is true, then the investor puts most of the portfolio into risky assets. Two cases are possible. (1) The investor has a limitless capacity to borrow, i.e. to invest negatively in the risk-free asset, in order to invest a sum that is greater than his wealth in risky assets. In this case, the efficient frontier is the line to the right of point M. (2) The borrowing is limited, in which case the efficient frontier is a straight line up to the point of tangency with the risky asset frontier and is then the curved portion of the risky asset frontier, since the segment of the line located above no longer corresponds to feasible portfolios (Figure 4.2). The previous study assumed that the borrowing interest rate was equal to the lending interest rate. This assumes that the markets are frictionless, i.e. that the assets are infinitely divisible and that there are no taxes or transaction costs. This assumption will also be used in developing equilibrium theory. It has therefore been established that when there is a risk-free asset, the investor’s optimal portfolio P is always made up of portfolio M with x proportion of risky assets and proportion (1 − x) of the risk-free asset. This shows that the investment decision can be divided into two parts: first, the choice of the optimal risky asset portfolio and secondly the choice of the split between the risk-free asset and the risky portfolio, depending on the desired level of risk. This result, which comes from Tobin (1958), is known as the two-fund separation theorem. This theorem, and Black’s theorem, which was mentioned in Chapter 3, have important consequences for fund management. Showing that all efficient portfolios can be written in the form of a combination of a limited number of portfolios or investment funds made up of available securities greatly simplifies the problem of portfolio selection. The problem of allocating the investor’s wealth then comes down to the choice of a linear combination of mutual funds. The position of the optimal risky asset portfolio M has been defined graphically. We now establish its composition by reasoning in terms of equilibrium.
C04
WU058-Amenc
98
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
4.1.1.2 Equilibrium theory Up until now we have only considered the case of an isolated investor. By now assuming that all investors have the same expectations concerning assets, they all then have the same return, variance and covariance values and construct the same efficient frontier of risky assets. In the presence of a risk-free asset, the reasoning employed for one investor is applied to all investors. The latter therefore all choose to divide their investment between the risk-free asset and the same risky asset portfolio M. Now, for the market to be at equilibrium, all the available assets must be held in portfolios. The risky asset portfolio M, in which all investors choose to have a share, must therefore contain all the assets traded on the market in proportion to their stock market capitalisation. This portfolio is therefore the market portfolio. This result comes from Fama (1970). In the presence of a risky asset, the efficient frontier that is common to all investors is the straight line of the following equation: E(R M ) − RF E(R P ) = RF + σP σM This line links the risk and return of efficient portfolios linearly. It is known as the capital market line. These results, associated with the notion of equilibrium, will now allow us to establish a relationship for individual securities. 4.1.2 Presentation of the CAPM We now come to the CAPM itself (cf. Briys and Viala, 1995, and Sharpe, 1964). This model will help us to define an appropriate measure of risk for individual assets, and also to evaluate their prices while taking the risk into account. This notion of the “price” of risk is one of the essential contributions of the model. The development of the model required a certain number of assumptions. These involve the Markowitz model assumptions on the one hand and assumptions that are necessary for market equilibrium on the other. Some of these assumptions may seem unrealistic, but later versions of the model, which we shall present below, allowed them to be scaled down. All of the assumptions are included below. 4.1.2.1 CAPM assumptions3 The CAPM assumptions are sometimes described in detail in the literature, and sometimes not, depending on how the model is presented. Jensen (1972a) formulated the assumptions with precision. The main assumptions are as follows: 1. Investors are risk averse and seek to maximise the expected utility of their wealth at the end of the period. 2. When choosing their portfolios, investors only consider the first two moments of return distribution: the expected return and the variance. 3. Investors only consider one investment period and that period is the same for all investors. 3 These assumptions are described well in Chapter 5 of Fabozzi (1995), in Cobbaut (1997), in Elton and Gruber (1995) and in Farrell (1997), who clearly distinguishes between the Markowitz assumptions and the additional assumptions.
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
The Capital Asset Pricing Model
99
4. Investors have a limitless capacity to borrow and lend at the risk-free rate. 5. Information is accessible cost-free and is available simultaneously to all investors. All investors therefore have the same forecast return, variance and covariance expectations for all assets. 6. Markets are perfect: there are no taxes and no transaction costs. All assets are traded and are infinitely divisible. 4.1.2.2 Demonstration of the CAPM The demonstration chosen is the one given by Sharpe (1964). See also Poncet et al. (1996). It is the simplest and the most intuitive, since it is based on graphical considerations.4 We take the risk-free asset and the market portfolio. These two points define the capital market line. When the market is at equilibrium, the prices of assets adjust so that all assets will be held by investors: supply is then equal to demand. In theory, therefore, the market portfolio is made up of all traded assets, in proportion to their market capitalisation, even though in practice we use the return on a stock exchange index as an approximation of the market return. We now take any risky asset i. Asset i is located below the market line, which represents all efficient portfolios. We define a portfolio P with a proportion x invested in asset i and a proportion (1 − x) in the market portfolio. The expected return of portfolio P is given by E(R P ) = xE(Ri ) + (1 − x)E(R M ) and its risk is given by 1/2 σ P = x 2 σi2 + (1 − x)2 σ M2 + 2x(1 − x)σi M where σi2 denotes the variance of the risky asset i; σ M2 denotes the variance of the market portfolio; and σi M denotes the covariance between asset i and the market portfolio. By varying x, we construct the curve of all possible portfolios obtained by combining asset i and portfolio M. This curve goes through the two points i and M (see Figure 4.3). The leading coefficient of the tangent to this curve at any point is given by ∂E(R P ) ∂E(R P )/∂ x = ∂σ P ∂σ P /∂ x Now ∂E(R P ) = E(Ri ) − E(R M ) ∂x and 2xσi2 − 2σ M2 (1 − x) + 2σi M (1 − 2x) ∂σ P = ∂x 2σ P 4
The interested reader could refer to a more comprehensive demonstration in Chapter 9 of Briys and Viala (1995).
C04
WU058-Amenc
100
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
E (RP) M
RF
i σ (RP)
Figure 4.3 Curve of all portfolios made of the market portfolio and a risky asset
After simplifying, we obtain the following ∂E(R P ) (E(Ri ) − E(R M ))σ P = 2 ∂σ P x σi + σ M2 − 2σi M + σi M − σ M2 The equilibrium market portfolio already contains asset i since it contains all assets. Portfolio P is therefore made up of an excess of asset i, in proportion x, compared with the market portfolio. Since this excess must be nil at equilibrium, point M is characterised by x = 0 and σ P = σM . When the market is at equilibrium, the slope of the tangent to the efficient frontier at point M is thus given by ∂E(R P ) (E(Ri ) − E(R M ))σ M (M) = ∂σ P σi M − σ M2 Furthermore, the slope of the market line is given by b=
E(R M ) − RF σM
where σ M denotes the standard deviation of the market portfolio. At point M the tangent to the curve must be equal to the slope of the market line. Hence, we deduce the following relationship: (E(Ri ) − E(R M ))σ M E(R M ) − RF = 2 σM σi M − σ M which can also be written as E(Ri ) = RF +
(E(R M ) − RF ) σi M σ M2
The latter relationship characterises the CAPM. The line that is thereby defined is called the security market line. At equilibrium, all assets are located on this line. This relationship means that at equilibrium the rate of return of every asset is equal to the rate of return of the risk-free asset plus a risk premium. The premium is equal to the price of the risk multiplied by the quantity of risk, using the CAPM terminology. The price of the risk
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
The Capital Asset Pricing Model
101
is the difference between the expected rate of return for the market portfolio, and the return on the risk-free asset. The quantity of risk, which is called the beta, is defined by σi M βi = 2 σM Beta is therefore equal to the covariance between the return on asset i and the return on the market portfolio, divided by the variance of the market portfolio. The risk-free asset therefore has a beta of zero, and the market portfolio has a beta of one. The beta thus defined is the one that already appeared in Sharpe’s empirical market model. By using the beta expression, the CAPM relationship is then written as follows: E(Ri ) = RF + βi (E(R M ) − RF ) The CAPM has allowed us to establish that at equilibrium the returns on assets, less the riskfree rate, have a linear link to the return on the market portfolio, with the market portfolio being built according to Markowitz’s principles. This original version of the CAPM is based on assumptions that the financial markets do not completely respect. This first formula was followed by several other versions, which enabled the realities of the market to be taken into account to a greater degree. The different versions will be discussed in Section 4.1.3 below. 4.1.2.3 The contribution of the CAPM The CAPM established a theory for valuing individual securities and contributed to a better understanding of market behaviour and how asset prices were fixed (cf. Chapter 3 of Farrell, 1997). The model highlighted the relationship between the risk and return of an asset and showed the importance of taking the risk into account. It allowed the correct measure of asset risk to be determined and provided an operational theory that allowed the return on an asset to be evaluated relative to the risk. The total risk of a security is broken down into two parts: the systematic risk, called the beta, which measures the variation of the asset in relation to market movements, and the unsystematic risk, which is unique for each asset. This breakdown could already be established with the help of the empirical market model, as we saw in Chapter 3. The unsystematic risk, which is also called the diversifiable risk, is not rewarded by the market. In fact, it can be eliminated by constructing diversified portfolios. The correct measure of risk for an individual asset is therefore the beta, and its reward is called the risk premium. The asset betas can be aggregated: the beta of a portfolio is obtained as a linear combination of the betas of the assets that make up the portfolio. According to the CAPM, the diversifiable risk component of each security is zero at equilibrium, while within the framework of the empirical market model only the average of the specific asset risks in the portfolio is nil. The CAPM provides a reference for evaluating the relative attractiveness of securities by evaluating the price differentials compared with the equilibrium value. We should note that the individual assets are not on the efficient frontier, but they are all located on the same line at equilibrium. The CAPM theory also provided a context for developing manager performance evaluation, as we will show in Sections 4.2 and 4.3, by introducing the essential notion of risk-adjusted return. By proposing an asset valuation model with the exclusive help of the market factor, Sharpe simplified the portfolio selection model considerably. He showed that optimal portfolios are obtained as a linear combination of the risk-free asset and the market portfolio, which, in
C04
WU058-Amenc
102
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
practice, is approximated by a well-diversified portfolio. Equilibrium theory, which underlies the model, favoured the development of passive management and index funds, since it shows that the market portfolio is the optimal portfolio. The model also paved the way for the development of more elaborate models based on the use of several factors. 4.1.2.4 Market efficiency and market equilibrium An equilibrium model can only exist in the context of market efficiency. Studying market efficiency enables the way in which prices of financial assets evolve towards their equilibrium value to be analysed. Let us first of all define market efficiency and its different forms. The first definition of market efficiency was given by Fama (1970): markets are efficient if the prices of assets immediately reflect all available information. Jensen (1978) gave a more precise definition: in an efficient market, a forecast leads to zero profits, i.e. the expenses incurred in searching for information and putting the information to use offset the additional profit procured (cf. Hamon, 1997). There are several degrees of market efficiency. Efficiency is said to be weak if the information only includes past prices; efficiency is semi-strong if the information also includes public information; efficiency is strong if all information, public and private, is included in the present prices of assets. Markets tend to respect the weak or semi-strong form of efficiency, but the CAPM’s assumption of perfect markets refers in fact to the strong form. The demonstration of the CAPM is based on the efficiency of the market portfolio at equilibrium. This efficiency is a consequence of the assumption that all investors make the same forecasts concerning the assets. They all construct the same efficient frontier of risky assets and choose to invest only in the efficient portfolios on this frontier. Since the market is the aggregation of the individual investors’ portfolios, i.e. a set of efficient portfolios, the market portfolio is efficient. In the absence of this assumption of homogeneous investor forecasts, we are no longer assured of the efficiency of the market portfolio, and consequently of the validity of the equilibrium model. The theory of market efficiency is therefore closely linked to that of the CAPM. It is not possible to test the validity of one without the other. This problem constitutes an important point in Roll’s criticism of the model. We will come back to this in more detail at the end of the chapter. The empirical tests of the CAPM involve verifying, from the empirical formulation of the market model, that the ex-post value of alpha is nil.
C04
WU058-Amenc
108
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
4.2 APPLYING THE CAPM TO PERFORMANCE MEASUREMENT: SINGLE-INDEX PERFORMANCE MEASUREMENT INDICATORS7 When we presented the methods for calculating the return on a portfolio or investment fund in Chapter 2, we noted that the return value on its own was not a sufficient criterion for appreciating the performance and that it was necessary to associate a measure of the risk taken. Risk is an essential part of the investment. It can differ considerably from one portfolio to another. In addition, it is liable to evolve over time. Modern portfolio theory and the CAPM have established the link that exists between the risk and return of an investment quantitatively. More specifically, these theories highlighted the notion of rewarding risk. Therefore, we now possess the elements necessary for calculating indicators while taking both risk and return into account. The first indicators developed came from portfolio theory and the CAPM. They are therefore more specifically related to equity portfolios. They enable a risk-adjusted performance value to be calculated. It is thus possible to compare the performance of funds with different levels of risk, while the return alone only enabled comparisons between funds with the same level of risk. This section describes the different indicators and specifies, for each, their area of use. It again involves elementary measures because the risk is considered globally. We will see later on that the risk can be broken down into several areas, enabling a more thorough analysis. 4.2.1 The Treynor measure The Treynor (1965) ratio is defined by TP =
E(R P ) − RF βP
where E(R P ) denotes the expected return of the portfolio; denotes the return on the risk-free asset; and RF βP denotes the beta of the portfolio. This indicator measures the relationship between the return on the portfolio, above the riskfree rate, and its systematic risk. This ratio is drawn directly from the CAPM. By rearranging the terms, the CAPM relationship for a portfolio is written as follows: E(R P ) − RF = E(R M ) − RF βP The term on the left is the Treynor ratio for the portfolio, and the term on the right can be seen as the Treynor ratio for the market portfolio, since the beta of the market portfolio is 1 by definition. Comparing the Treynor ratio for the portfolio with the Treynor ratio for the market portfolio enables us to check whether the portfolio risk is sufficiently rewarded. The Treynor ratio is particularly appropriate for appreciating the performance of a welldiversified portfolio, since it only takes the systematic risk of the portfolio into account, i.e. 7 On this subject, the interested reader could consult Broquet and van den Berg (1992), Elton and Gruber (1995), Fabozzi (1995), Grandin (1998), Jacquillat and Solnik (1997), and Gallais-Hamonno and Grandin (1999).
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
The Capital Asset Pricing Model
109
the share of the risk that is not eliminated by diversification. It is also for that reason that the Treynor ratio is the most appropriate indicator for evaluating the performance of a portfolio that only constitutes a part of the investor’s assets. Since the investor has diversified his investments, the systematic risk of his portfolio is all that matters. Calculating this indicator requires a reference index to be chosen to estimate the beta of the portfolio. The results can then depend heavily on that choice, a fact that has been criticised by Roll. We shall return to this point at the end of the chapter.
4.2.2 The Sharpe measure Sharpe (1966) defined this ratio as the reward-to-variability ratio, but it was soon called the Sharpe ratio in articles that mentioned it. It is defined by SP =
E(R P ) − RF σ (R P )
where E(R P ) denotes the expected return of the portfolio; RF denotes the return on the risk-free asset; and σ (R P ) denotes the standard deviation of the portfolio returns. This ratio measures the excess return, or risk premium, of a portfolio compared with the risk-free rate, compared, this time, with the total risk of the portfolio, measured by its standard deviation. It is drawn from the capital market line. The equation of this line, which was presented at the beginning of the chapter, can be written as follows: E(R P ) − RF E(R M ) − RF = σ (R P ) σ (R M ) This relationship indicates that, at equilibrium, the Sharpe ratio of the portfolio to be evaluated and the Sharpe ratio of the market portfolio are equal. The Sharpe ratio actually corresponds to the slope of the market line. If the portfolio is well diversified, then its Sharpe ratio will be close to that of the market. By comparing the Sharpe ratio of the managed portfolio and the Sharpe ratio of the market portfolio, the manager can check whether the expected return on the portfolio is sufficient to compensate for the additional share of total risk that he is taking. Since this measure is based on the total risk, it enables the relative performance of portfolios that are not very diversified to be evaluated, because the unsystematic risk taken by the manager is included in this measure. This measure is also suitable for evaluating the performance of a portfolio that represents an individual’s total investment. The Sharpe ratio is widely used by investment firms for measuring portfolio performance. The index is drawn from portfolio theory, and not the CAPM like the Treynor and Jensen indices. It does not refer to a market index and is not therefore subject to Roll’s criticism. This ratio has also been subject to generalisations since it was initially defined. It thus offers significant possibilities for evaluating portfolio performance, while remaining simple to calculate. Sharpe (1994) sums up the variations on this measure. One of the most common involves replacing the risk-free asset with a benchmark portfolio. The measure is then called the information ratio. We will describe it in more detail later in the chapter.
C04
WU058-Amenc
110
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
4.2.3 The Jensen measure Jensen’s alpha (Jensen, 1968) is defined as the differential between the return on the portfolio in excess of the risk-free rate and the return explained by the market model, or E(R P ) − RF = α P + β P (E(R M ) − RF ) It is calculated by carrying out the following regression: R Pt − RFt = α P + β P (R Mt − RFt ) + ε Pt The Jensen measure is based on the CAPM. The term β P (E(R M ) − RF ) measures the return on the portfolio forecast by the model. α P measures the share of additional return that is due to the manager’s choices. In order to evaluate the statistical significance of alpha, we calculate the t-statistic of the regression, which is equal to the estimated value of the alpha divided by its standard deviation. This value is obtained from the results of the regression. If the alpha values are assumed to be normally distributed, then a t-statistic greater than 2 indicates that the probability of having obtained the result through luck, and not through skill, is strictly less than 5%. In this case, the average value of alpha is significantly different from zero. Unlike the Sharpe and Treynor measures, the Jensen measure contains the benchmark. As for the Treynor measure, only the systematic risk is taken into account. This third method, unlike the first two, does not allow portfolios with different levels of risk to be compared. The value of alpha is actually proportional to the level of risk taken, measured by the beta. To compare portfolios with different levels of risk, we can calculate the Black–Treynor ratio8 defined by αP βP The Jensen alpha can be used to rank portfolios within peer groups. Peer groups were presented in Chapter 2. They group together portfolios that are managed in a similar manner, and that therefore have comparable levels of risk. The Jensen measure is subject to the same criticism as the Treynor measure: the result depends on the choice of reference index. In addition, when managers practise a market timing strategy, which involves varying the beta according to anticipated movements in the market, the Jensen alpha often becomes negative, and does not then reflect the real performance of the manager. In what follows we present methods that allow this problem to be corrected by taking variations in beta into account. 4.2.4 Relationships between the different indicators and use of the indicators It is possible to formulate the relationships between the Treynor, Sharpe and Jensen indicators. 4.2.4.1 Treynor and Jensen If we take the equation defining the Jensen alpha, or E(R P ) − RF = α P + β P (E(R M ) − RF ) 8
This ratio is defined in Salvati (1997). See also Treynor and Black (1973).
(4.2)
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
The Capital Asset Pricing Model
111
and we divide on each side by β P , then we obtain the following: E(R P ) − RF αP = + (E(R M ) − RF ) βP βP We then recognise the Treynor indicator on the left-hand side of the equation. The Jensen indicator and the Treynor indicator are therefore linked by the following exact linear relationship: TP =
αP + (E(R M ) − RF ) βP
4.2.4.2 Sharpe and Jensen It is also possible to establish a relationship between the Sharpe indicator and the Jensen indicator, but this time using an approximation. To do that we replace beta with its definition, or ρPM σ P σ M βP = σ M2 where ρ P M denotes the correlation coefficient between the return on the portfolio and the return on the market index. If the portfolio is well diversified, then the correlation coefficient ρ P M is very close to 1. By replacing β P with its approximate expression in equation (4.2) and simplifying, we obtain: σP (E(R M ) − RF ) σM
E(R P ) − RF ≈ α P + By dividing each side by σ P , we finally obtain:
E(R P ) − RF αP (E(R M ) − RF ) ≈ + σP σP σM The portfolio’s Sharpe indicator appears on the left-hand side, so SP ≈
αP (E(R M ) − RF ) + σP σM
4.2.4.3 Treynor and Sharpe The formulas for these two indicators are very similar. If we consider the case of a welldiversified portfolio again, we can still use the following approximation for beta: βP ≈
σP σM
The Treynor indicator is then written as follows: TP ≈
E(R P ) − R F σM σP
Hence SP ≈
TP σM
C04
WU058-Amenc
112
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
Table 4.1 Characteristics of the Sharpe, Treynor and Jenson indicators Criticised by Roll
Name
Risk used
Source
Sharpe
Total (sigma)
Portfolio theory
No
Treynor
Systematic (beta)
CAPM
Yes
Jensen
Systematic (beta)
CAPM
Yes
Usage Ranking portfolios with different levels of risk Not very well-diversified portfolios Portfolios that constitute an individual’s total personal wealth Ranking portfolios with different levels of risk Well-diversified portfolios Portfolios that constitute part of an individual’s personal wealth Ranking portfolios with the same beta
It should be noted that only the relationship between the Treynor indicator and the Jensen indicator is exact. The other two are approximations that are only valid for a well-diversified portfolio.
4.2.4.4 Using the different measures The three indicators allow us to rank portfolios for a given period. The higher the value of the indicator, the more interesting the investment. The Sharpe ratio and the Treynor ratio are based on the same principle, but use a different definition of risk. The Sharpe ratio can be used for all portfolios. The use of the Treynor ratio must be limited to well-diversified portfolios. The Jensen measure is limited to the relative study of portfolios with the same beta. In this group of indicators the Sharpe ratio is the one that is most widely used and has the simplest interpretation: the additional return obtained is compared with a risk indicator taking into account the additional risk taken to obtain it. These indicators are more particularly related to equity portfolios. They are calculated by using the return on the portfolio calculated for the desired period. The return on the market is approximated by the return on a representative index for the same period. The beta of the portfolio is calculated as a linear combination of the betas of the assets that make up the portfolio, with these being calculated in relation to a reference index over the study period. The value of the indicators depends on the calculation period and performance results obtained in the past are no guarantee of future performance. Sharpe wrote that the Sharpe ratio gave a better evaluation of the past and the Treynor ratio was more suitable for anticipating future performance. Table 4.1 summarises the characteristics of the three indicators.
4.2.5 Extensions to the Jensen measure Elton and Gruber (1995) present an additional portfolio performance measurement indicator. The principle used is the same as that of the Jensen measure, namely measuring the differential between the managed portfolio and a theoretical reference portfolio. However, the risk considered is now the total risk and the reference portfolio is no longer a portfolio located on
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
The Capital Asset Pricing Model
113
the security market line, but a portfolio on the capital market line, with the same total risk as the portfolio to be evaluated. More specifically, this involves evaluating a manager who has to construct a portfolio with a total risk of σ P . He can obtain this level of risk by splitting the investment between the market portfolio and the risk-free asset. Let A be the portfolio thereby obtained. This portfolio is situated on the capital market line. Its return and risk respect the following relationship: E(R M ) − RF E(R A ) = RF + σP σM since σ A = σ P . This portfolio is the reference portfolio. If the manager thinks that he possesses particular stock picking skills, he can attempt to construct a portfolio with a higher return for the fixed level of risk. Let P be his portfolio. The share of performance that results from the manager’s choices is then given by E(R M ) − RF E(R P ) − E(R A ) = E(R P ) − RF − σP σM The return differential between portfolio P and portfolio A measures the manager’s stock picking skills. The result can be negative if the manager does not obtain the expected result. The idea of measuring managers’ selectivity can be found in the Fama decomposition, which will be presented in Chapter 7. But Fama compares the performance of the portfolio with portfolios situated on the security market line, i.e. portfolios that respect the CAPM relationship. The Jensen measure has been the object of a certain number of generalisations, which enable the management strategy used to be included in the evaluation of the manager’s value-added. Among these extensions are the models that enable a market timing strategy to be evaluated. These will be developed in Section 4.3, where we will also discuss multi-factor models. The latter involve using a more precise benchmark, and will be handled in Chapter 6. Finally, the modified versions of the CAPM, presented at the end of Section 4.1, can be used instead of the traditional CAPM to calculate the Jensen alpha. The principle remains the same: the share of the return that is not explained by the model gives the value of the Jensen alpha. With the Black model, the alpha is characterised by E(R P ) − E(R Z ) = α P + β P (E(R M ) − E(R Z )) With the Brennan model, the alpha is characterised by E(R P ) − RF = α P + β P (E(R M ) − RF − T (D M − RF )) + T (D P − RF ) where D P is equal to the weighted sum of the dividend yields of the assets in the portfolio, or DP =
n
xi Di
i=1
xi denotes the weight of asset i in the portfolio. The other notations are those that were used earlier. We can go through all the models cited in this way. For each case, the value of α P is estimated through regression.
C04
WU058-Amenc
114
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
4.2.6 The tracking-error The tracking-error is a risk indicator that is used in the analysis of benchmarked funds. Benchmarked management involves constructing portfolios with the same level of risk as an index, or a portfolio chosen as a benchmark, while giving the manager the chance to deviate from the benchmark composition, with the aim of obtaining a higher return. This assumes that the manager possesses particular stock picking skills. The tracking-error then allows the risk differentials between the managed portfolio and the benchmark portfolio to be measured. It is defined by the standard deviation of the difference in return between the portfolio and the benchmark it is replicating, or TE = σ (R P − RB ) where RB denotes the return on the benchmark portfolio. The lower the value, the closer the risk of the portfolio to the risk of the benchmark. Benchmarked management requires the tracking-error to remain below a certain threshold, which is fixed in advance. To respect this constraint, the portfolio must be reallocated regularly as the market evolves. It is necessary however to find the right balance between the frequency of the reallocations and the transaction costs that they incur, which have a negative impact on portfolio performance. The additional return obtained, measured by alpha, must also be sufficient to make up for the additional risk taken on by the portfolio. To check this, we use another indicator: the information ratio. 4.2.7 The information ratio The information ratio, which is sometimes called the appraisal ratio, is defined by the residual return of the portfolio compared with its residual risk. The residual return of a portfolio corresponds to the share of the return that is not explained by the benchmark. It results from the choices made by the manager to overweight securities that he hopes will have a return greater than that of the benchmark. The residual, or diversifiable, risk measures the residual return variations. Sharpe (1994) presents the information ratio as a generalisation of his ratio, in which the risk-free asset is replaced by a benchmark portfolio. The information ratio is defined through the following relationship: IR =
E(R P ) − E(RB ) σ (R P − RB )
We recognise the tracking-error in the denominator. The ratio can also be written as follows: αP IR = σ (e P ) where α P denotes the residual portfolio return, as defined by Jensen, and σ (e P ) denotes the standard deviation of this residual return. As specified above, this ratio is used in the area of benchmarked management. It allows us to check that the risk taken by the manager, in deviating from the benchmark, is sufficiently rewarded. It constitutes a criterion for evaluating the manager. Managers seek to maximise its value, i.e. to reconcile a high residual return and a low tracking-error. It is important to look at the value of the information ratio and the value of the tracking-error together. For the same information ratio value, the lower the tracking-error the higher the chance that the manager’s performance will persist over time.
C04
WU058-Amenc
July 17, 2003
17:48
Char Count= 0
The Capital Asset Pricing Model
115
The information ratio is therefore an indicator that allows us to evaluate the manager’s level of information compared with the public information available, together with his skill in achieving a performance that is better than that of the average manager. Since this ratio does not take the systematic portfolio risk into account, it is not appropriate for comparing the performance of a well-diversified portfolio with that of a portfolio with a low degree of diversification. The information ratio also allows us to estimate a suitable number of years for observing the performance, in order to obtain a certain confidence level for the result. To do so, we note that there is a link between the t-statistic of the regression, which provides the alpha value, and the information ratio. The t-statistic is equal to the quotient of alpha and its standard deviation, and the information ratio is equal to the same quotient, but this time using annualised values. We therefore have tstat IR ≈ √ T where T denotes the length of the period, expressed in years, during which we observed the returns. The number of years required for the result obtained to be significant, with a given level of probability, is therefore calculated by the following relationship:
tstat 2 T = IR For example, a manager who obtains an average alpha of 2.5% with a tracking-error of 4% has an information ratio equal to 0.625. If we wish the result to be significant to 95%, then the value of the t-statistic is 1.96, according to the normal distribution table, and the number of years it is necessary to observe the portfolio returns is
1.96 2 T = = 9.8 years 0.625 This shows clearly that the results must persist over a long period to be truly significant. We should note, however, that the higher the manager’s information ratio, the more the number of years decreases. The number of years also decreases if we consider a lower level of probability, by going down, for example, to 80%. The calculation of the information ratio has been presented by assuming that the residual return came from the Jensen model. More generally, this return can come from a multi-index or multi-factor model. We will discuss these models in Chapter 6. 4.2.8 The Sortino ratio An indicator such as the Sharpe ratio, based on the standard deviation, does not allow us to know whether the differentials compared with the mean were produced above or below the mean. In Chapter 2 we introduced the notion of semi-variance and its more general versions. This notion can then be used to calculate the risk-adjusted return indicators that are more specifically appropriate for asymmetrical return distributions. This allows us to evaluate the portfolios obtained through an optimisation algorithm using the semi-variance instead of the variance. The best known indicator is the Sortino ratio (cf. Sortino and Price, 1994). It is defined on the same principle as the Sharpe ratio. However, the risk-free rate is replaced with
C04
WU058-Amenc
116
July 17, 2003
17:48
Char Count= 0
Portfolio Theory and Performance Analysis
the minimum acceptable return (MAR), i.e. the return below which the investor does not wish to drop, and the standard deviation of the returns is replaced with the standard deviation of the returns that are below the MAR, or Sortino ratio = 1 T
E(R P ) − M A R T t=0 R Pt <M A R
(R Pt − M A R)2
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Reproduced from Portfolio Theory and Performance Analysis, by Noël Amenc and Véronique Le Sourd. 2003. Copyright © John Wiley & Sons Limited. Reproduced with permission.
6 Multi-Factor Models and their Application to Performance Measurement1 In Chapter 4 we described the Capital Asset Pricing Model (CAPM) and presented the associated criticisms. The model is based on very strong theoretical assumptions which are not entirely respected by the markets in practice. We have seen that the model assumes that the market portfolio is efficient in the mean–variance sense. However, the efficiency can only be ensured if the portfolio returns are normally distributed, or if the investors have a quadratic utility function. These assumptions are restrictive and difficult to justify. It has therefore not been possible to validate the model empirically in a rigorous fashion. The modified versions of the CAPM only provided partial solutions. The theorists thus sought to develop a more general model, while at the same time simplifying the assumptions. The result was a family of models that was referred to collectively as multi-factor models. These models constitute an alternative theory to the CAPM, but do not replace it. They are also linear models but, unlike the CAPM, there are no assumptions about the behaviour of investors. They also allow asset returns to be explained by factors other than the market index, and thus provide more specific information on risk analysis and the evaluation of manager performance. In this chapter we begin by presenting multi-factor models from a theoretical point of view, and then describe the methods for choosing the factors and estimating the model parameters. Finally, we present the two main applications of these models, namely risk analysis and evaluation of portfolio performance.
6.1 PRESENTATION OF THE MULTI-FACTOR MODELS The earliest model, which comes from Ross, is based on a key concept in financial theory: arbitrage valuation. A second category of models, based only on empirical considerations, was developed later. This section presents the structure of these two types of model. 6.1.1 Arbitrage models In 1976, Ross proposed a model based on the principle of valuing assets through arbitrage theory (see also Roll and Ross, 1980). This model, called the Arbitrage Pricing Theory (APT) model, is based on less restrictive assumptions than the CAPM. While the CAPM assumes that asset returns are normally distributed, the APT does not hypothesise on the nature of the distribution. The APT model does not include any assumptions on individuals’ utility functions either, but simply assumes that individuals are risk averse. This simplification of the assumptions allows the model to be validated empirically. 1 For more details, the interested reader could consult Batteau and Lasgouttes (1997), Fedrigo et al. (1996), Marsh and Pfleiderer (1997), Chapters 8 and 16 of Elton and Gruber (1995), Chapter 4 of Farrell (1997) and Fontaine (1987).
149
c06
WU058-Amenc
150
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
The APT model still seeks to explain asset returns through common factors, but instead of the well-defined single factor in the CAPM, the model employs K factors and consequently constitutes a more general theory. The problem then consists of determining the value of K and the nature of the factors. That will be the subject of Section 6.2 of this chapter. The present section simply describes the theory underlying the model. The APT model first postulates that a linear relationship exists between the realised returns of the assets and the K factors common to those assets, or K
Rit = E(Ri ) +
bik Fkt + εit
k=1
where Rit denotes the rate of return for asset i; E(Ri ) denotes the expected return for asset i; bik denotes the sensitivity (or exposure) of asset i to factor k; Fkt denotes the return of factor k with E(Fk ) = 0; and εit denotes the residual (or specific) return of asset i, i.e. the share of the return that is not explained by the factors, with E(εi ) = 0. The APT model assumes that markets are perfectly efficient and that the factor model for explaining the asset returns is the same for all individuals. The number of assets n is assumed to be very large compared with the number of factors K. The residual returns of the different assets are independent from each other and independent from the factors. We therefore have cov(εi , ε j ) = 0, cov(εi , Fk ) = 0,
for i = j for all i and k
Arbitrage reasoning then allows us to end up with the following equilibrium relationship: E(Ri ) − RF =
K
λk bik
k=1
where RF denotes the risk-free rate. The details that allow us to obtain this relationship are presented in Appendix 6.1 at the end of this chapter. This relationship explains the average asset return as a function of the exposure to different risk factors and the market’s remuneration for those factors. λk is interpreted as the factor k risk premium at equilibrium. We define δk as the expected return of a portfolio with a sensitivity to factor k equal to 1, and null sensitivity to the other factors. We then have the following relationship: λk = δk − RF which allows us to write the arbitrage relationship in the following form: E(Ri ) − RF =
K k=1
(δk − R F )bik
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
151
This relationship can be interpreted as the equation of a linear regression, where the bik are defined as bik =
cov(Rit , δk ) var(δk )
The bik are the sensitivities to the factors (factor loadings). This formula shows the CAPM as a specific case of the APT model, as long as we assume that the returns are normally distributed. We then simply take the market portfolio as the only factor. The APT model allows us to use several factors to explain the returns, which gives it an advantage, in theory, over the CAPM. The market portfolio no longer has any particular role. It is simply one factor among many. The APT model does not require it to be efficient, as was the case for the CAPM. Finally, the APT model can be extended to the case of investment over several periods, while the CAPM only considers a single period. Since the theory does not give the number and the nature of the factors, this model has been the object of numerous empirical validation tests to identify the most significant factors. The results of these tests will be presented in Section 6.2, which discusses the choice of factors and model estimation. The models in this category are called longitudinal, or chronological, models, a reference to the fact that the returns are explained for each period. 6.1.2 Empirical models The models drawn from arbitrage theory associate a risk premium λk with each factor. This risk premium is a characteristic of the factor and is completely independent from the securities. Another approach, which is empirical, proposes making the expected returns dependent on security-specific factors. In the first case the risk premiums constitute responses to outside influences. They reflect the link that exists between economic forces and the securities markets. The sensitivity of assets is evaluated in relation to factors that are qualified as macroeconomic, such as the return on the bond market, unanticipated changes in inflation, changes in exchange rates and changes in industrial production. In the second case the factors are security-specific attributes and are not linked to the economy. This type of factor will be described more precisely later in the chapter, when the Barra model is presented. The empirical models make less restrictive assumptions than the APT-type models and no longer use arbitrage theory. They do not presume that there is an explanatory factorial relationship for the returns realised in each period t. They directly postulate that the average returns on the assets, or more precisely the average risk premiums, can be decomposed with the help of factors. Therefore, only one calculation stage remains, while the APT model required two. For each asset i, the relationship is written as follows: E(Ri ) − RF =
K
bik αk + εi
k=1
where bik denotes the value of factor k that is specific to firm i; αk denotes the coefficient associated with factor k, corresponding to the market’s remuneration for that factor; and εi denotes the specific return on asset i.
c06
WU058-Amenc
152
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
The factors that are used in this model are derived from financial analysis. They consist of financial ratios such as the P/E ratio, the dividend growth rate, the dividend yield, the earnings yield, and also the return for a past period and the market capitalisation. They are given the general term of fundamental factors. These models are called cross-sectional or fundamental, in reference to the factors. In Section 6.2 we will present the model developed by the firm Barra, which is the best known in this category of model. The CAPM can also be seen as a specific case of this type of model. In this case the only factor that explains the security’s risk premium is its beta, which does indeed constitute a security-specific factor. 6.1.3 Link between the two types of model From a formal point of view, the relationship that gives the factorial expression of an asset’s average return is similar to the second APT equation, apart from the fact that it contains an additional residual return term. As we saw previously, the empirical model is written as follows: E(Ri ) − RF =
K
bik αk + εi
k=1
and the second APT equation is written as E(Ri ) − RF =
K
λk bik
k=1
These two equations are cross-sectional. All that would be needed for the two equations to be strictly identical, apart from the names of the variables, would be to add a residual term to the APT equation. The empirical model is therefore drawn directly from the arbitrage model formula. The difference between the two models is in the interpretation of the variables. In the case of the APT model, bik denotes the sensitivity of asset i to factor k. These bik have been estimated through regression with the help of the first APT equation. In the case of the empirical models, bik denotes the value of factor k specific to firm i. These bik factors are actually interpreted as the assets’ exposures to the attributes. The bik are known beforehand. The αk in the empirical model and the λk in the APT model are then estimated through similar procedures. These variables, called risk premiums, represent the market’s remuneration for the factors. We should stress that the variables that dominate in each of the two models are not the same. The second APT equation focuses on the risk premiums (the lambdas) associated with the economic factors that describe the market. The empirical models, for their part, favour the betas, i.e. the exposures, that are characteristic of the firms. The two approaches thus correspond to different philosophies.
6.2 CHOOSING THE FACTORS AND ESTIMATING THE MODEL PARAMETERS As we mentioned in Section 6.1, multi-factor model theory does not specify the number or nature of the factors. That is where the main difficulty resides. The use of these models therefore requires a prior phase for seeking and identifying the most significant factors, as well as estimating the associated risk premiums. A certain number of empirical studies have been
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
153
carried out on this subject. They give guidance on the choices, but the combinations of factors that allow the returns on a group of assets to be explained are not necessarily unique. In addition, two major techniques are opposed in identifying the common factors for the assets. A first method, which is called an exogenous or explicit factor method, consists of determining the factors in advance. The choice of factors at that stage is arbitrary and tests are then carried out to conserve the most significant factors only. A second method, which is called an endogenous or implicit factor method, involves extracting the factors directly from the historical returns, with the help of methods drawn from factor analysis. Although the second method enables the evolution of returns to be monitored, the problem of interpreting the factors is posed. In view of the nature of the factors considered and the identification method chosen, the multi-factor models used in practice can be grouped into three categories: 1. The first category brings together models where the factors are macroeconomic variables. The choice of these variables comes from empirical studies carried out to test the APT model. The factor loadings are calculated through regression. 2. The second category comprises models where the factor loadings are functions of the firms’ attributes and the factors are estimated through regression. This is the approach used by the American firm Barra. The factors are said to be fundamental factors. 3. The third category consists of models where the factors are extracted from the return database through factor analysis or principal component analysis. This is the approach that was used for the first tests on the APT model to determine the number of explanatory factors. The principal application of this approach is in portfolio risk analysis and control. It is used by the American firms Quantal and Advanced Portfolio Technology (APT). The latter has a French subsidiary called Aptimum. In the first two categories the factors are explicit. In the third, they are implicit. The empirical formulation common to these models can be written as follows: Rit = bi1 F1t + · · · + bi K FK t + u it where i = 1, . . . , n, with n the number of assets, and t = 1, . . . , T , with T the number of sub-periods. For the first category of models, we know F and we estimate b; for the second, we know b and we estimate F; and for the third, we estimate b and F simultaneously. Note that for the first and third category models an additional stage is necessary to estimate the risk premiums associated with the factors, once the b coefficients are known. In this section we describe the characteristics of each model in detail and present the methods for evaluating the parameters. 6.2.1 Explicit factor models 6.2.1.1 Explicit factor models based on macroeconomic variables These models are derived directly from APT theory. The risk factors that affect asset returns are approximated by observable macroeconomic variables that can be forecast by economists. The choice of the number of factors, namely five macroeconomic factors and the market factor, comes from the first empirical tests carried out by Roll and Ross with the help of a factor analysis method. The classic factors in the APT models are industrial production, interest rates, oil prices, differences in bond ratings and the market factor. In order to be able to use
c06
WU058-Amenc
154
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
them as factors, the series of economic variables must be restated. They must first be centred, so that their mean is null, and then we must calculate the innovations of each series, i.e. the unanticipated changes in the series, which will enable the asset returns to be explained. The innovations are obtained by taking the residuals of the autoregressive processes adapted to each series. The principle behind this method is described clearly in Chen et al. (1986). The procedure for estimating the model for a given market and period can then lead to the retention of certain factors only. This procedure, inspired by that used by Fama and MacBeth (1973) to test the CAPM, is carried out in two stages. The first stage uses the first APT equation, or Rit = αi +
K
bik Fkt + εit
k=1
The Rit returns for a set of assets are observed for a fixed period and with a certain frequency. For example, we could consider the weekly returns on French stocks over the past five years. The number of time periods must be greater than the number of assets. Roll and Ross worked on the American market using daily returns. In view of the large number of assets, they grouped them together into portfolios to perform the study. They constructed around 40 portfolios with 30 securities in each. The criterion chosen for making up the portfolios was a ranking of the securities in descending order of market capitalisation. There was another advantage to grouping the securities together in portfolios, which justified the fact that it was used by Fama and MacBeth: it enabled the error introduced by using the results of the first regression to carry out the second regression to be reduced. The Fkt are the series of innovations of the factors obtained from the economic variables observed for the same period and with the same frequency as the asset returns. The factor loadings bik for each asset are estimated through regression. By developing the contents of the matrices, this regression is written as follows: R11 . . . Rn1 F11 . . . FK 1 b11 . . . bn1 ε11 . . . εn1 . ... .
. . . . . . . . . . . . . . . . . . . . = α1 . . . αn + . . . . . . . . . . + . . . . . . ... . . . . . . . . . . . . . . . . R1T . . . RnT F1T . . . FK T b1K . . . bn K ε1T . . . εnT Roll and Ross (1980) describe the econometric aspects of this regression. The second stage then involves estimating, through regression, the risk premiums λk associated with each factor. A cross-sectional regression of the expected asset returns against the factor loadings obtained during the first regression is then performed. The equation for this regression comes from the second APT equation, or E(Rit ) = λ0 +
K
bik λk
k=1
where λ0 = RF is the rate of return of the risk-free asset. Explicitly, the second regression is written R11 . . . Rn1 λ11 . . . λ K 1 b11 . . . bn1 λ 01 . ... . ... . ... . . . .
. ... . = ... . . ... . + u1 . . . un + . . . . ... . ... . . ... . λ0T R1T . . . RnT λ1T . . . λ K T b1K . . . bn K
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
155
The result of this regression is a time series of λkt . The average premium for the period is obtained by calculating T 1 λ¯ k = λkt T t=1
We then carry out a statistical test to check whether this average premium is significantly positive. At the end of this second stage we only retain, for the model, factors that have a significant risk premium. To be rigorous, it is then necessary to carry out the whole procedure again with the number of factors really identified and recalculate the factor loadings and risk premiums for the factors retained only. Empirical validation studies of the APT2 model highlight the fact that only a small number of factors have a significantly positive risk premium. In addition, the results vary depending on the period studied and the country. The research and identification phase for the model is therefore essential, so that only the “right” factors are retained. It is also necessary to re-evaluate the model periodically to ensure that it corresponds to the returns to be analysed. At the end of the model’s research and identification stage, we have, for a given period, the following relationship: E(Ri ) = λ0 +
K
bik λk
k=1
in which all the parameters are known: the number of factors K, the factor loadings bik and the risk premiums λk . The risk premiums do not depend on the assets, only on the factors. By replacing E(Ri ) with its expression in the first APT equation, we obtain the following: Rit = λ0 +
K k=1
bik λk +
K
bik Fkt + εit
k=1
Assuming that the loadings and risk premiums of the factors are stable, we can forecast, in theory, the return on the asset for the upcoming period with the help of forecasts on the factors, since the factors are well-defined variables. εit then measures the differential between the forecast and realised variable. This should however be used with care, because empirical studies tend to prove that factor loadings and risk premiums are not stable over time. The use of the APT model for analysing portfolio risk and performance is discussed in Section 6.4. 6.2.1.2 Explicit factor models based on fundamental factors This approach is much more pragmatic. The aim now is to explain the returns on the assets with the help of variables that depend on the characteristics of the firms themselves, and no longer on identical economic factors, for all assets. The modelling no longer uses any theoretical assumptions but considers a factorial breakdown of the average asset returns directly. The model assumes that the factor loadings of the assets are functions of the firms’ attributes. The realisations of the factors are then estimated by regression. Here again the choice of explanatory variables is not unique. Studies suggest that only two factors should be added to the market factor: this is the case for the studies carried out by Fama and French. Carhart, 2
See, for example, the Chen et al. (1986) study on American stocks and the Hamao (1988) study on Japanese stocks.
c06
WU058-Amenc
July 17, 2003
156
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
for his part, proposed a four-factor model. Other studies led to a long list of very specific factors: this is the case for those carried out by the authors of the Barra model. For example, an article by Connor (1995) studies the explanatory power of 13 fundamental factors. We have chosen to limit ourselves here to a few examples of models. However, the subject of characterising explanatory factors for returns is vast and research articles on the subject are published regularly. The Journal of Finance, for example, constitutes an interesting source of information on the subject. Fama and French’s three-factor model3 Fama and French have carried out several empirical studies to identify the fundamental factors that explain average asset returns, as a complement to the market beta. They highlighted two important factors that characterise a company’s risk: the book-to-market ratio and the company’s size measured by its market capitalisation. Fama and French (1993) therefore propose a three-factor model, which is formulated as follows: E(Ri ) − RF = bi1 (E(R M ) − RF ) + bi2 E(SMB) + bi3 E(HML) where denotes the expected return of asset i; E(Ri ) RF denotes the rate of return of the risk-free asset; E(R M ) denotes the expected return of the market portfolio; SMB (small minus big) denotes the difference between returns on two portfolios: a smallcapitalisation portfolio and a large-capitalisation portfolio; HML (high minus low) denotes the difference between returns on two portfolios: a portfolio with a high book-to-market ratio and a portfolio with a low book-tomarket ratio; bik denotes the factor loadings. The bik are calculated by regression from the following equation: Rit − RFt = αi + bi1 (R Mt − RFt ) + bi2 SMBt + bi3 HMLt + εi Fama and French consider that the financial markets are indeed efficient, but that the market factor does not explain all the risks on its own. They conclude that a three-factor model does describe the asset returns, but specify that the choice of factors is not unique. Factors other than those retained in their 1993 model also have demonstrable and demonstrated explanatory power. Carhart’s (1997) four-factor model This model is an extension of Fama and French’s three-factor model. The additional factor is momentum, which enables the persistence of the returns to be measured. This factor was added to take into account the anomaly revealed by Jegadeesh and Titman (1993). With the same notation as above, this model is written E(Ri ) − RF = bi1 (E(R M ) − RF ) + bi2 E(SMB) + bi3 E(HML) + bi4 (PR1YR) where PR1YR denotes the difference between the average of the highest returns and the average of the lowest returns from the previous year. 3
Cf. Fama and French (1992, 1995, 1996) and Molay (2000).
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
157
The Barra model4 The Barra multi-factor model is the best known example of the commercial application of a fundamental factor model. Barra disseminates research articles written by members of the firm on its web site. These articles situate the Barra model within the context of multi-factor models and compare it with other approaches. We could, for example, cite Engerman (1993), Grinold (1991), Rosenberg (1987) and Rudd (1992). The Barra model assumes that asset returns are determined by the fundamental characteristics of the firm such as the industrial sector, the size and earnings. The systematic risk of an asset can then be explained by its sensitivity with regard to these characteristics. The characteristics constitute the exposures or betas of the assets. The approach therefore assumes that the exposures are known and then calculates the factors. The returns are characterised by the following factorial structure: Rit =
K
bikt αkt + u it
k=1
where Rit bik αk ui
denotes the return on security i in excess of the risk-free rate; denotes the factor loading or exposure of asset i to factor k; denotes the return on factor k; and denotes the specific return on asset i.
The specific returns on the assets are assumed to be non-correlated with each other and non-correlated with the factor returns. The factors used in this model belong to two categories: factors linked to the industrial sector and the risk indices. The former measure the differences in behaviour among securities that belong to different industries. The latter measure the differences in behaviour among securities for the non-industrial side. Barra’s model for American stocks defines 52 industrial categories. The list of industries is given in Barra (1998). We then determine the exposure of the securities in the universe to those industries: each security is attributed a weighting in the different industries. If the security is only attached to a single industrial sector, then the exposure to the “industry” factor takes a value of one or zero, depending on whether the security belongs to that group of industries or not. The assets of firms whose activity is spread over several industries are split between the different groups concerned with a percentage corresponding to the share of activity in that industry. The “industry” factors are orthogonal in their construction. For the second category of factors, the model uses a precise list of 13 risk indices. Each of these indices is constructed from a certain number of fundamental pieces of information called descriptors, the combination of which best characterises the risk concept to be described. Barra (1998) presents these indices and their descriptors in detail. The list of risk indices, ranked in descending order of importance, is as follows: 1. volatility, a risk index based on both the long-term and short-term measurement of volatility; 2. momentum, an index that measures the variation in returns related to recent behaviour of the stock prices: the stocks that had a positive return in excess of the risk-free rate over the period are separated from those that had a negative return; 4
For more details, one can consult Sheikh (1996).
c06
WU058-Amenc
158
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
3. size, an index that measures the difference in asset returns due to differences in market capitalisation; 4. size non-linearity, an index that measures the deviations from linearity in the relationship between the returns and the logarithm of their market capitalisation; 5. trading activity, an index that measures the volume of trades for each asset (the assets with the most significant trading activity are the most interesting for institutional investors: the returns on those stocks may behave differently than the returns of stocks that are not widely held by the institutions); 6. growth, an index that uses historical growth and profitability measures to forecast future earnings growth; 7. earnings yield, an index that is obtained by combining the historical earnings-to-price ratios with the values that were predicted by analysts: assets with the same earnings yield have returns that behave similarly; 8. value, an index that separates value stocks from growth stocks by using their book-to-price ratio; 9. earnings variability, an index that measure the variability in earnings by using both historical measures and analysts’ forecasts; 10. leverage, an index that measures the financial leverage of the company; 11. currency sensitivity, an index that measures the sensitivity of the stock return to the return on a basket of foreign currencies; 12. dividend yield, an index that gives a forecast of the dividend yield from historical dividend data and the behaviour of the market price of the stock; 13. non-estimation universe indicator, an index for companies that are outside the estimation universe. It allows the factor model to be extended to stocks that are not part of the estimation universe. The exposures to the risk indices are put together by weighting the exposures to their descriptors. The weightings are chosen in such a way as to maximise the explanatory and forecasting power of the model. Since the units and orders of magnitude are different depending on the variables, the exposures to the descriptors and risk indices are normalised according to the following formula: bnormalised =
braw − braw std[braw ]
where braw denotes the mean value of exposure to a risk index for the whole universe of assets; and std[braw ] denotes the standard deviation of the exposure values for the whole universe of assets. The result is that the exposure to each risk index has a null mean and a standard deviation equal to 1. The Barra model therefore contains a total of 65 factors. Using this model in practice implies that we know the risk indices and that they are regularly updated. We therefore start by observing the characteristics of the companies at the beginning of each period. These characteristics are used to calculate the companies’ factor loadings. These loadings or exposures constitute the bikt measured at the beginning of period t. They represent the risk indices and industry groups. The returns on the factors, αkt , and the specific returns, u it , are then estimated through a multiple regression, using the Fama–MacBeth procedure (Fama and MacBeth, 1973). To do this, the asset returns, Rit , in excess of the risk-free rate, are regressed on the factor exposures.
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
159
We obtain time series of factor realisations, for which we calculate the mean. We then test whether the mean is significantly different from zero. The model therefore proceeds in a single step. The model must be updated regularly to integrate the new information that comes from the companies. Barra estimates the returns of the 65 factors monthly. The Barra model can also be used as an APT model in which the macroeconomic factors are replaced with microeconomic factors or fundamental attributes. We then calculate the assets’ factor loadings. The model formulated by Barra is therefore consistent with the APT model. The results are then used to estimate the variance–covariance matrix of asset returns. This aspect will be detailed in Section 6.4 when the Barra portfolio risk analysis model is presented. 6.2.2 Implicit or endogenous factor models5 The idea behind this approach is to use the asset returns to characterise the unobservable factors. It is natural to assume that the factors that influence the returns leave an identifiable trace. These factors are therefore extracted from the asset returns database through a factor analysis method and the factor loadings are jointly calculated. This approach was originally used by Roll and Ross to test the APT model. In this section we discuss the principle of factor analysis and its use in evaluating multi-factor models. Finally, we present a valuation method, called semi-autoregressive, which was developed more recently. The disadvantage of an implicit search for factors, however, is that it does not allow the nature of the factors to be identified. 6.2.2.1 The principle of factor analysis6 Factor analysis is a set of statistical methods that allows the information contained in a group of variables to be summarised, with the help of a reduced number of variables, while minimising the loss of information due to the simplification. In the case of factor models, this technique allows us to identify the number of factors required for the model and to express the asset returns with the help of several underlying factors. The method enables the explanatory factors and the factor loadings to be obtained simultaneously, but it does not give any information on the nature of the factors, which we must then be able to interpret. From a mathematical point of view the returns of n assets considered over T periods are equated with a data cloud in the space R n . The principle involves projecting this cloud into a sub-space of lower dimension, defined by factor axes, while explaining as much of the cloud’s variability as possible. The strong correlations that exist between the returns on the assets enable this result to be reached. The search for factor axes is carried out from the calculation of the eigenvalues and eigenvectors of the asset returns’ variance–covariance matrix. The weight of the factor axes is measured by the factor loadings. There are two factor analysis methods: (1) factor analysis based on the principle of maximum likelihood, which involves an optimal reproduction of the correlations observed, and (2) principal component analysis, which involves extracting the maximum variance. If the number of assets is significant, then we group the assets into portfolios to carry out the study, so that the number of correlations to be calculated remains reasonable. Studies have shown that the results obtained depend on the criterion used to form the portfolios. Moreover, 5 6
Cf. Fedrigo et al. (1996). Cf. Chapter 2 of Fontaine (1987), and Batteau and Lasgouttes (1997).
c06
WU058-Amenc
160
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
the greater the number of securities, the more the number of factors increases. These factors also vary depending on the period considered. Maximum likelihood method This method, which is called classic factor analysis, aims to reproduce the correlation between the variables as well as possible. Each of the variables observed is described linearly with the help of K common factors, which take into account the correlation between the variables, and a specific factor (or residual term), which expresses the share of variance that is specific to each security. The factors are modelled by random variables of normal density. Since the factors are assumed to be independent, the variables have a multivarious normal distribution. In the case that interests us, the variables are asset returns. The method involves expressing the asset returns variance–covariance matrix as the sum of a positive eigenvalue matrix of rank K and a diagonal matrix, or V = B B + D where B, with a dimension of n × K , denotes the factor loading matrix bik , and D denotes the variance–covariance matrix of the residuals. This matrix is diagonal because the residuals are not correlated. The advantage of the procedure is to obtain a value of K that is as small as possible, or at least much smaller than the number of initial variables. Roll and Ross used this method, or more specifically Lawley and Maxwell’s (1963) maximum likelihood method, to identify the number of factors in the APT model and to estimate the bik factor loadings of the assets. Principal component analysis The principle consists of searching for linear combinations of the n initial vectors, such that the new vectors obtained are eigenvalues of the initial variance–covariance matrix. The most widely used algorithm is Hotelling’s (1933). The procedure is as follows. We begin by extracting the index which best explains the variance of the original data. This constitutes the first principal component. We then extract the index which best explains the variance of the original data that was not explained by the first component. The second index is therefore, through its construction, non-correlated with the first. We then proceed sequentially. The iterative procedure can be repeated, in theory, until the number of indices extracted is equal to the number of variables studied: we thereby reproduce the original variance–covariance matrix exactly. In practice, since the components have decreasing explanatory power, we evaluate the quantity of information returned at each stage with the help of the associated eigenvalue, and we stop the procedure when the component obtained is no longer significant. The dimension of the new space for explaining the returns is therefore chosen in such a way as to limit the loss of information. The K explanatory factors retained are the eigenvectors associated with the K largest eigenvalues from the matrix. When the returns are widely dispersed, the number of high eigenvalues is significant, which leads to a space of large dimension. If, on the other hand, there is strong correlation between the returns, then a limited number of components is sufficient to explain most of the variance–covariance matrix. Comparing the two approaches The maximum likelihood method is better adapted to the Ross model. The principal component analysis method, for its part, corresponds more to a description of the returns. This
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
161
method does, however, have an advantage over the first in that it does not make any particular assumptions about the distribution of the returns. Researchers nevertheless prefer the method based on maximum likelihood, which uses Gaussian laws, the properties of which are well known. The real distributions of the returns are not in fact very far removed from a multinormal law and the method provides a more accurate test of the number of factors in the model. 6.2.2.2 Estimating the risk premiums Factor analysis allows us to obtain the number of factors that explain the returns, and simultaneously the value of those factors and an estimation of the matrix of factor loadings. That is the advantage of the method compared with explicit factor models, where it was necessary to have one of the two variables, factors or factor loadings, to estimate the other. For what follows, i.e. estimating risk premiums, the principle remains the same as for explicit factor models: the factor loadings are regressed as a cross-section on the expected asset (or portfolio) returns to obtain the value of the risk premiums and their statistical significance. We thereby obtain the λk , k = 0, . . . , K , such that E(Ri ) = λ0 + bi1 λ1 + · · · + bi K λ K ,
i = 1, . . . , n
where n denotes the number of assets. 6.2.2.3 Interpreting the factors The implicit factor estimation method has the disadvantage of not allowing a direct economic interpretation of the factors obtained. We can simply say that each factor, obtained as a linear combination of the asset returns, is a portfolio with a sensitivity to itself equal to one, and null sensitivity to the other factors. This is due to the orthogonal nature of the factors. Since we are unable to name the implicit factors, we can explain the factors with the help of known indicators and thus come back to an explicit factor decomposition from the implicit decomposition. We proceed in the following manner. Taking Rit as the return on asset i explained by k implicit factors: Rit = µi + βi1 F1t + · · · + βik Fkt + εit where theF jt denote the non-correlated implicit factors. We have cov(Fi , F j ) = 0 and var(Fi ) = 1. We regress an explicit factor on the implicit factors: Rmt = µm + βm1 F1t + · · · + βmk Fkt + εmt By calculating cov(Ri , Rm ) = βi1 βm1 + βi2 βm2 + · · · + βik βmk and 2 2 2 var(Rm ) = βm1 + βm2 + · · · + βmk
and calculating the quotient of these two quantities, we obtain a beta that we can equate with the CAPM beta and which gives us the coefficient of the explicit factor Rmt in the decomposition
c06
WU058-Amenc
162
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
of the return Rit . By doing this for all the explicit factors, we reach an explicit decomposition of the return Rit , having started with its implicit decomposition. 6.2.2.4 Semi-autoregressive approach7 The underlying idea is to postulate that there is an approximate linear relationship between the returns and the factor loadings. If we have more returns than loadings, then the latter can be approximated with the help of a sub-sample of returns. These approximations are then regressed as a cross-section on the returns for a different period to estimate the associated factors. This method differs from the conventional factor extraction techniques, such as factor analysis based on maximum likelihood and principal component analysis, even if the idea used is also the replication of the factors with the help of linear combinations of asset returns. This method does not make any assumptions about the return distributions. It provides a simple asymptotic variance–covariance matrix of the estimated factors, which can be used to control the measurement errors. This is useful both for testing the model and for using it to evaluate the performance of a portfolio compared with a benchmark, while taking the measurement errors into account. The asset returns are assumed to be generated by the following model approximated to K factors: Rit = E(Rit ) + bi1 F1t + · · · + bi K FK t + εit for i = 1, . . . , n and t = 1, . . . , T . The notation and conditions on the variables are those of the APT model, or Fkt , is the unobservable risk factors with E(Fk ) = 0; bik , is the factor loadings, which are assumed to be constant over the period studied; and εit , is the specific risk of each asset with cov(εi , Fk ) = 0 for all i and k and cov(εi , ε j ) = 0 for i = j. The APT equilibrium relationship allows us to write Et (Rit ) = λ0t + λ1t bi1 + · · · + λ K t bi K where (λ1t . . . λ K t ) denotes the vector of the risk premiums associated with the factors; and λ0t denotes the return on a zero-beta portfolio. By combining the two APT equations and expressing: skt = Fkt + λkt we can then write Rit = λ0t + s1t bi1 + · · · + s K t bi K + εit for i = 1, . . . , N and for t = 1, . . . , T . The factor loadings bik are not observable, so they must be constructed through approximations, obtained with the help of the returns. To do so, we write the equation for an asset i for 7
Cf. Mei (1993) and Batteau and Lasgouttes (1997).
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
163
t = 1 to K. We then obtain the following system: s11 . . . s K 1 bi1 Ri1 − λ01 − εi1 . ... . . . . . = . . . . . . ... . . . s1K . . . s K K bi K Ri K − λ0K − εi K or, in a more condensed manner:
bi = γi The matrix is assumed to be non-singular, i.e. with no redundant factors. The system can be transformed by expressing s˜t = ( −1 ) st b˜ i = bi in order to normalise the factors and the factor loadings. With this notation we can write Rit = λ0t + s˜1t b˜ i1 + · · · + s˜ K t b˜ i K + εit where i varies from 1 to n and t varies from K + 1 to T. Since Ri1 − λ01 − εi1 . ˜bi = bi = γi = . . Ri K − λ0K − εi K by replacing b˜ i with its expression for t > K , we have Rit = λ0t + s˜1t (Ri1 − λ01 − εi1 ) + · · · + s˜ K t (Ri K − λ0K − εi K ) + εit By grouping the terms, we finally obtain: Rit = s˜0t + s˜1t Ri1 + · · · + s˜ K t Ri K + ηit with s˜0t = λ0t −
K
s˜ jt λ0 j
j=1
and ηit = εit −
K
s˜ jt εi j
j=1
for t = K + 1, . . . , T. We have therefore transformed a model with K factors into a semi-autoregressive model with K lags. We can then carry out a cross-sectional regression of Rit on (1, Ri1 , . . . , Ri K ) to
c06
WU058-Amenc
164
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
obtain an estimation of the normalised factors s˜kt . The regression is written as follows: s˜ R1t 1 R11 . . . R1K 0t η1t ˜ . . s1t . ... . . . . = . . ... . + . . . . . . ... . . Rnt 1 Rn1 . . . Rnk ηnt s˜ K t for t = K + 1, . . . , T The model is called semi-autoregressive because the autoregressive terms only vary in i and not in i and t. 6.2.2.5 A specific example: the model used by the firm Advanced Portfolio Technology (APT)8 This firm, which has been operating for around 15 years, has developed a model that renders the APT theory operational, with the difficulty being to determine the right factors to explain the returns. The model was drawn from several observations. First, it is not realistic to wish to fix the model’s factors once and for all. Next, the factors that influence asset returns are not directly observable. The factors that make asset prices move are not the economic variables themselves, but the share of unanticipated change in the variables, i.e. the difference between the forecast and the realised value. The best solution for determining the factors is therefore to observe the asset prices. To do that, the asset returns are measured at regular intervals, e.g. every three days, or every week, or every month, over the whole study period. If the universe under consideration contains many assets, then this will lead to a large amount of data. It is then necessary to group the assets together to extract the factors. The founders of the firm APT do not carry out traditional factor analysis, such as, for example, that used by Roll and Ross to test their model. They developed a specific statistical estimation technique which enables the factors to be estimated from a large sample of variables. They carried out tests on their model with the help of Monte Carlo simulations and showed that their procedure enabled the true factorial structure of the model to be obtained, while factor analysis applied to large data samples could pose problems. It again involves an implicit estimation of the factors, since the procedure does not make any initial assumptions about the nature of the factors. The procedure is as follows. From the data observed we calculate the covariances between the assets. We observe at that stage that certain assets behave similarly, while others evolve independently or in the opposite way. The assets can then be grouped into homogeneous classes, i.e. into groups with similar covariances. The common characteristics of each group obtained in this way can be seen as a manifestation of the effect of the factor that we are seeking to measure. By then combining the individual returns of the securities in the group, we calculate the return for each group, which enables us to obtain an index for each group. These indices constitute the factors. They are constructed in such a way as to be non-correlated between themselves, which is an advantage compared with the economic variables, which are often correlated. These indices then allow the factor loading coefficients for each asset to be calculated, together with the specific asset return component that is not taken into account by the factors. These calculations are carried out through regression. For each asset we obtain one 8
See the Internet site http://www.apt.co.uk.
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
165
coefficient per factor and a coefficient that is specific to the asset. The return on the asset is then simply expressed as the weighted sum of the product of each coefficient times the return on the factor, plus the specific component of the asset. In solving this problem the choice of the optimal number of factors is important. The more precise the information we wish to obtain, the more we will tend to increase the number of factors. However, the model is useful insofar as it allows us to retain a limited number of factors. To reach the optimal number of factors, the factor model is then tested for a period that is different from the estimation period to check that no important factors have been omitted. The model obtained uses 20 factors. After identifying the risk factors implicitly, the firm APT also proposes explaining the asset returns with the help of known explicit factors. To do this, the explicit factors are decomposed with the help of implicit factors, in accordance with the principle described in Section 6.2.2.3 concerning the interpretation of implicit factors. We thus calculate the weighting of each explicit factor in the decomposition of the asset returns. For example, the coefficient of the explicit factor, Rmt , is given by k
γim =
βi j βm j
j=1 k j=1
βm2 j
where βi j denotes the coefficients of the decomposition of the return on asset i according to the implicit factors; and βm j denotes the coefficients of the decomposition of the explicit factor m according to the implicit factors. The model can handle all kinds of assets, stocks, bonds, indices, currencies and raw materials and covers all countries, including emerging countries. The calculations are carried out using three and a half years of historical data and weekly returns. 6.2.3 Comparing the different models Comparisons between the different models relate to both the explanatory power of the different types of factors and the methods for estimating the parameters. The first problem that arises is the choice between an explicit factor model and an implicit factor model. The explicit factor models appear, at least in theory, to be simpler to use, but they assume that we know with certainty the number and nature of the factors that allow asset returns to be explained and that the latter can be observed and measured without error. However, we have seen that factor model theory does not indicate the number and nature of the factors to be used. The choice is therefore made by relying on empirical studies, but there is no uniqueness to the factors, nor are the factors necessarily stable over time. Fedrigo et al. (1996) describe the influence of errors on the models fairly thoroughly. They detail the consequences of a measurement error, the omission of a correct factor or the addition of an irrelevant factor. The models are useful, however, to the extent that they allow economic interpretation of the factors, since the factors are known beforehand. As far as the choice of factors is concerned, two trends are opposed, namely economic factors or fundamental factors. From the point of view of the model itself, models that use macroeconomic factors, such as the APT model, focus essentially on the values of the risk premiums associated with the factors, in order to identify the most highly remunerated sources of risk. The fundamental factor models focus on the factors themselves, to identify those
c06
WU058-Amenc
166
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
that have the greatest influence on asset returns. Moreover, certain authors, such as Grinold (1991) and Engerman (1993), affirm that macroeconomic factors are the most appropriate for explaining expected asset returns, but that fundamental factors are preferable for modelling and portfolio risk management. They therefore justify the choices made by Barra. This can be explained by the fact that the fundamental factors depend on the assets and are therefore more liable to take into account the inherent risks of each company. Using an implicit factor model solves the problem of the choice of factors, since the model does not make any prior assumptions about the number and nature of the factors and should therefore enable the true model to be determined. The limitation in using this type of model then comes from the difficulty in interpreting the factors obtained. This is doubtless why those models are far less developed in the literature and seem to have been the subject of fewer applications to date. It is nevertheless possible, as we saw in Section 6.2.2.3, to come back to an explicit decomposition from the implicit decomposition. The implicit models are also very useful for analysing and monitoring portfolio risk, because they are better at taking into account market evolutions. We will return to this subject in Section 6.4. To finish, we note a final advantage of implicit factor models. As we have seen throughout this chapter, it is common to model the dependency of returns compared with the factors through a linear relationship. This is because it is the easiest way to proceed. But the true model may be non-linear. In that case an implicit factor model enables a better approximation of any eventual non-linearities by adding supplementary factors.
6.3 EXTENDING THE MODELS TO THE INTERNATIONAL ARENA9 Extensions to Ross’s arbitrage model, and multi-factor models in general, have been developed for international portfolios in order to respond to criticism of the international CAPM. The factors used in these models come from a longer list of factors: as well as the national factors, international factors are added, along with specific factors for exchange rates. Certain factors can explain both returns and exchange rates. Most models assume that the factorial structure of exchange rates includes both factors that are common to financial assets and exchange rates and factors that are specific to exchange rates. A large number of models assume that the realisation of the factors does not depend on the currency under consideration. Only Fontaine (1987) proposes a model where the factors depend on the currency. It could be justifiable to consider that the factors do not depend on the currency for economic factors such as oil production, which is expressed in barrels, but it is not true for factors that are expressed in monetary units. The international multi-factor models have been the subject of many studies. It is not possible to cite them all here. One could refer to Fontaine (1987) and Fontaine (1997) which constitute a thorough study of the subject. Here we simply present the general form of the models and give some indications about the factors used. 6.3.1 The international arbitrage models The assumptions are those of arbitrage models in the national framework, to which some additional assumptions linked to the international context have been added. Investors make 9
Cf. Fontaine (1997) and Chapter 5 of Fontaine (1987).
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
167
the same forecasts on the exchange rate variations. They assume the same factor model for the asset returns expressed in their domestic currency. In each country, there is a risk-free asset. The return on that asset expressed in the currency of another country is assumed to be generated by the factor model of that country. It is then appropriate to check whether the factor model for explaining the returns depends on the currency in which the returns are expressed or not. We can then establish the capital asset pricing relationship in the international context. The model described is that of Fontaine (1987). This model assumes that there are N + 1 assets and L + 1 countries. The first L + 1 assets are the risk-free assets. The reference country is identified by the index 0. The return on each asset i from the reference country expressed in the currency of that country is written as follows: K 0 0 0 0 Ri0 = E Ri0 bik Fk0 + εi0 + k=1
where 0 denotes the return on asset i from the reference country in the reference currency; Ri0 0 E(Ri0 ) denotes the expected return on asset i from the reference country in the reference currency; 0 denotes the sensitivity (or exposure) of asset i to factor k in the reference currency; bik Fk0 denotes the return on factor k in the reference currency with E(Fk0 ) = 0; and 0 εi0 denotes the residual (or specific) return on asset i from the reference country in the 0 ) = 0. reference currency with E(εi0
The return on an asset i from country j in currency j is written as follows: K j j j j j Ri j = E Ri j + bik Fk + εi j k=1
This model assumes therefore that the Fk factors depend on the currency under consideration, j or Fk0 = Fk . To then be able to express the returns on the assets from the different countries in a common currency, we need the exchange rates. The exchange rates are also governed by a factor model: K
TC 0j = E TC 0j + b0jk Fk0 + ε 0j j k=1
where TC 0j denotes the exchange rate that enables us to switch from currency j to the reference currency. These elements now permit us to study the impact of the exchange rate on the factorial structure of the returns. To do so, let us consider the return on an asset i from country j. The return in the reference currency is written as follows: j
j
Ri0j = Ri j + TC 0j + Ci j j
j
where Ci j denotes the covariance between the exchange rate TC 0j and the return Ri j . By j
replacing TC 0j and Ri j with their expressions, we obtain the following: K K
j j j j j 0 Ri0j = E Ri j + bik Fk + εi j + E TC 0j + bik Fk0 + ε 0j j + Ci j k=1
k=1
c06
WU058-Amenc
168
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
It is then necessary to express all the factors in the same currency. We have 2 j Fk0 = Fk + TC 0j + Ck0j − σ j0 where Ck0j denotes the covariance between the exchange rate TC 0j and the factor Fk0 ; and (σ j0 )2 denotes the variance of the exchange rate TC 0j . This expression comes from Ito’s lemma. j
By replacing Fk with its expression as a function of Fk0 , we obtain: K j 2
j j Ri0j = E Ri j + + εi j + E TC 0j bik Fk0 − TC 0j − Ck0j + σ j0 k=1
+
K
j
0 bik Fk0 + ε 0j j + Ci j
k=1
We can also replace TC 0j with its factorial expression, which gives K K j 0 0 2 j j 0 0 0 0 0 0 + εi j Ri j = E Ri j + bik Fk − E TC j + b jk Fk + ε j j − Ck j + σ j k=1
k=1
K
j 0 + E TC 0j + bik Fk0 + ε 0j j + Ci j k=1
By grouping the terms together, we obtain: K j
2
j j Ri0j = E Ri j + E TC 0j + Ci j + bik −E TC 0j − Ck0j Fk0 + σ j0
+
K
k=1
j bik
+
b0jk
1−
k=1
K
j bik
k=1
Fk0
+ 1−
K
j bik
j
ε 0j j + εi j
k=1
If we define K
j
2 j j Ei0j = E Ri j + E TC 0j + Ci j + bik −E TC 0j − Ck0j Fk0 + σ j0 0 bik =
K
k=1
di0j = 1 −
j
bik + b0jk 1 − K k=1
k=1
K k=1
j
bik
j
bik
then the expression can be written in a more condensed manner: Ri0j = Ei0j +
K
j
0 bik Fk0 + di0j ε 0j j + εi j
k=1
The factorial structure of the model therefore finds itself modified compared with the national case, since an additional factor appears which is common to all assets from country j. This is the term ε 0j j which is specific to the exchange rate in country j. di0j represents the sensitivity of asset i to this factor. This sensitivity is null if asset i does not belong to country j.
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
169
The following conditions are respected: j
cov Fk0 , εi j = 0 j
cov ε0j j , εi j = 0 j j
cov εi j , εi j = 0 for all i = i j
E Fk = 0 j
E εi j = 0
E ε 0j j = 0 The arbitrage relationship is obtained by constructing the risk-free portfolio. It is written as follows: K 0 Ei0j = λ00 + λk0 bik + M 0j di0j k=1
where M 0j denotes the risk premium of the exchange factor; λk0 denotes the risk premium of factor k; and λ00 denotes the return on the risk-free asset of the reference country expressed in the reference currency. If we assume that the returns are hedged against exchange rate risk, then the additional term due to the currency exchange is eliminated and we obtain a relationship of the same form as the arbitrage relationship in the national case. Fontaine’s model assumes that the realisations of the factors depend on the currency. That is therefore the most general case. Other authors assume that the factors do not depend on the j currency, or Fk = Fk . 6.3.2 Factors that explain international returns Marsh and Pfleiderer (1997) studied the importance of two essential factors in international investment: the country and the industrial sector. If the industries are worldwide, i.e. if the markets are integrated, then the country factor should not be significant, because its effect is already contained in the industry factor. If the industries are not worldwide, i.e. if the markets are segmented, then companies that belong to the same industrial sector but different countries have different characteristics and the country factor therefore becomes significant. A model that is classically proposed to study the effects of factors is the following. If we take an asset i belonging to industrial sector j and country k, the return is expressed by R˜ i jkt = E( R˜ i jkt ) + G˜ t + I˜ jt + C˜ kt + e˜i jkt where G˜ t denotes the global market factor represented by an international index; I˜ jt denotes the industrial factor; C˜ kt denotes the country factor; and e˜i jkt denotes the residual return.
c06
WU058-Amenc
170
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
This model assumes that all assets in the same country have the same sensitivity to the country factor and that all assets in the same industrial sector have the same sensitivity to the industry factor. This assumption is not very realistic. Marsh and Pfleiderer therefore propose the following model: R˜ i jkt = Ai + ai G˜ t + bi j I˜ jt + cik C˜ kt + e˜i jkt where each factor is now assigned an asset-specific sensitivity. The model was tested with and without the global market factor. In both cases the country factor outweighs the industry factor. When present, the market factor explains around a third of the returns. Marsh and Pfleiderer’s article cites other studies that reached the same conclusion. This result casts doubt over Barra’s factor model, which gives considerable importance to the industry-based factors. The result is consistent with the risk models used by Quantal, which stipulate that the industrial classification is not generally a good basis for measuring risk. As in the national case, there are several methods for identifying “international” factors: 1. Exogenous methods based on time series. These models use international index-type variables above all, grouping together the effect of several variables. 2. Methods based on factor analysis of asset returns, which enable the factors to be extracted and the factor loadings to be calculated, but which do not allow us to identify the variables represented by the factors. 3. Methods based on company attributes (fundamental factors). Grinold et al. (1989) describe a multi-factor model in the international framework based on the experience of the firm Barra. This model consists of isolating the currency effect and then decomposing the local portfolio return into a market term, an industrial sector term and a common factor term. These factors are company attributes such as, for example, size, volatility or earnings. Grinold et al. find that the country factor is on average more important than the industry factor but that, at a more detailed level, the most important industry factors are more important than the least important country factors.
6.4 APPLYING MULTI-FACTOR MODELS The use of multi-factor models is beginning to be more widespread among professionals, after remaining in the research domain for many years. Roll and Ross’s (1984) article describes, for example, the possible applications of the APT model to portfolio management. The main disadvantage of these models, compared with the CAPM, is that the theory does not define the nature of the factors. In addition, the fact that they are difficult to implement was long considered to be an obstacle to their use. However, their use has now been facilitated by the improved calculation speed. Unlike the models drawn from the CAPM, the multi-factor models do not really allow us to measure the advantage of a particular portfolio for an investor in terms of optimality, as Salvati (1997) explains, because they do not make any particular assumptions about investors’ behaviour. These models are not aimed at comparing the overall levels of portfolio risk. They are, however, explanatory models that study several different areas of risk. They allow us to identify all the sources of risk to which a portfolio is subjected, and to measure the associated remuneration. This results in better control over portfolio management: orienting the portfolio towards the right sources of risk leads to an improvement in its performance.
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
171
Risk analysis and performance evaluation through multi-factor models are therefore connected. The procedure is as follows. A manager seeks to reach a certain level of performance by orienting his portfolio toward the most highly remunerated risk factors. He carries out risk analysis at the beginning of the period to construct his portfolio, then analyses the performance at the end of the period and attributes the contribution of each risk factor to the overall performance. He can thus check whether the result obtained corresponds to his original expectations and then evaluate the decisions that were rewarding and those that were not. It is possible to construct a wide variety of multi-factor models. The choice of a model for studying a particular portfolio depends on the nature of the portfolio. In this section we give details on how the different factor models that were presented at the beginning of the chapter are used to analyse portfolio risk and performance. 6.4.1 Portfolio risk analysis10 Using the factorial structure of asset returns it is easy to calculate the variance and covariance of the securities with the help of the variance and covariance of the factors. This produces a factorial structure for asset risk that measures the standard portfolio risk. This structure separates the risk into a component drawn from the model and a specific component. Risk analysis is important for both passive investment and active investment. Passive investment index funds generally do not contain all the securities in their reference index when there are a large number of securities. The manager must then analyse the portfolio risk regularly to check that it is sufficiently close to the risk of the index. The factorial decomposition of the risk ensures better monitoring of his portfolio’s tracking-error. In active investment, risk analysis allows us to determine the factors that have the greatest influence on asset prices according to the remuneration they produce in a well-diversified portfolio. Highlighting the risk factors also allows us to construct portfolios that are not sensitive to a particular factor. The factorial decomposition of risk therefore allows risk to be managed better. We present examples of risk models below: the Barra model, the model used by the firm Quantal, and application of the firm Aptimum’s model to risk analysis. 6.4.1.1 Barra’s risk model11 The risk analysis model developed by Barra is drawn from their multi-factor model. We saw previously that the asset returns in that model are characterised by the following factorial structure: Rit =
K
bikt αkt + u it
k=1
where Rit bik αk ui
denotes the return on security i in excess of the risk-free rate; denotes the exposure or factor loading of asset i with regard to factor k; denotes the return on factor k; and denotes the specific return of asset i. 10
Cf. Burmeister et al. (1997) and Chapter 4 of Farrell (1997). Cf. Kahn (1995) and Chapter 3 of Grinold and Kahn (1995) with the technical appendix to the chapter, Sheikh (1996), Barra (1998) and Grinold and Kahn (2000). 11
c06
WU058-Amenc
172
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
The specific returns are assumed to be non-correlated between themselves and non-correlated with the factor returns, or cov(u i , u j ) = 0
for all i = j
and cov(u i , αk ) = 0 The next step is to calculate the asset return variance–covariance matrix with the help of the variance–covariance matrix of the risk factor returns that are common to this set of assets, which allows the number of calculations required to be reduced. The variance–covariance matrix for the returns on the securities is therefore given by V = BB T + where denotes the variance–covariance matrix for the factor returns; B denotes the matrix of the assets’ factor loadings; and denotes the variance matrix for the asset-specific returns. This matrix is diagonal because the terms that are specific to each asset are not correlated between themselves. Explicitly, the elements of the assets’ variance–covariance matrix therefore have the following structure: Vi j =
K
bik1 ωk1 k2 b jk2 + i j
k1 ,k2 =1
where Vi j denotes the covariance between asset i and asset j; ωk1 k2 denotes the covariance of factor k1 with factor k2 ; and i j denotes the specific covariance of asset i with asset j. This term is therefore null if i = j. The matrix V is estimated with the help of the matrix B, the securities’ loadings for the common factors, the matrix , the variance–covariance of the factors, and the matrix , the variances of the security-specific returns. Barra’s choice of fundamental factors should integrate evolutions in the composition of the portfolio and its risk characteristics better than macroeconomic factors, because these factors take the evolution of companies’ risk characteristics into account. However, unlike the macroeconomic factor models, where the factors’ variance–covariance matrix is calculated with the help of observed data, the matrix for the fundamental factor models is calculated with estimated data. The portfolio risk is then calculated from the portfolio composition and Vi j . Let h p be the vector of size n defining the asset weightings in portfolio P. The exposures to the factors of portfolio P are given by x P = BTh P The variance of portfolio P is then written σ P2 = h TP V h P = x TP x P + h TP h P
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
173
Barra use the real composition of the portfolio over time by conserving the historical monthly data. We can carry out an identical analysis to calculate the active risk or tracking-error of the portfolio. As a reminder, this is the component of risk due to the differential between the portfolio and its benchmark. It will be denoted in what follows by the variable P2 . Taking h B as the vector of benchmark weightings, we define the differential between the portfolio composition and the benchmark composition as h PA = h P − h B We then have x PA = B T h PA and hence
P2 = h TPA V h PA = x TPA x PA + h TPA h PA The multi-factor risk model allows us to analyse the risk of a portfolio that has already been constituted. The risk is broken down according to the different sources of risk. The residual share of the risk that is not explained by the factors can thus be identified. In the case of active portfolio management, this risk decomposition can be compared with that of a passively managed reference portfolio. The differentials observed indicate that the manager expects higher remuneration for certain factors. With the help of the portfolio risk expressions established from the factors, we can accurately calculate the marginal contribution of each factor to the portfolio risk, for both the total risk of the portfolio and its active risk. This allows us to see the assets and factors that have the greatest impact on the portfolio risk. The marginal contribution of a security to the total risk of the portfolio, written as MCTR, for the marginal contribution to total risk, is defined by the partial derivative of the risk compared with the weighting of the security: MCTR =
∂σ P V hP = T σP ∂h P
The nth component of the MCTR vector is the partial derivative of σ P compared with the nth component of the vector h P . We can see it as the approximate change in portfolio risk given an increase of 1% in the weighting of asset n financed by a 1% decrease in cash. The same type of reasoning can be applied to calculate the marginal contribution of a factor, written FMCTR, to the total risk of the portfolio. The marginal contribution of a factor enables us to measure the change in risk brought about by a modification in the exposure to that factor. We have FMCTR =
∂σ P x P = T σP ∂xP
By noting that x TP FMCTR =
x TP x P h T V h P − h TP h P = P σP σP
then x TP ( j)FMCTR( j) gives the contribution of factor j to the total risk of the portfolio and h TP h P /σ P gives the contribution of the asset-specific risks to the total risk of the portfolio.
c06
WU058-Amenc
174
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
We can use the same reasoning with the active risk of the portfolio and successively calculate the marginal contributions of the assets to that risk, or MCAR =
∂ P V h PA = T
P ∂h PA
and the marginal contributions of the factors, or FMCAR =
∂ P x PA =
P ∂ x TPA
Following this phase, performance analysis will allow us to check whether the portfolio risk choices were judicious. This will be developed later in the chapter. 6.4.1.2 The Quantal risk model12 Quantal developed and use a risk model based on implicit factors extracted from asset returns. These factors are generated by using the most recent four to six months of daily returns and giving more importance to the most recent trends to avoid including irrelevant data from the past. The analysis is carried out at the level of the securities and is not limited by the definition of a country or an industrial sector. The statistical model used is consistent with the APT model. The choice of a short period makes the model very sensitive to recent movements in the market and gives a good view of the portfolio risk and a better forecast of its trackingerror. The choice of an implicit model to explain the risk allows us to determine, in order of importance, the factors that have the greatest influence on the evolution of returns, while the use of predefined factors could lead to improper factors being included or certain factors being omitted. This allows us to carry out a better analysis of portfolio risk. For example, in the case of benchmarked investment, a portfolio can be constructed in such a way as to be exposed to the same risk factors as the reference portfolio, without having to be invested in exactly the same securities, and can thus conserve a minimal tracking-error. 6.4.1.3 The model developed by the firm APT (Advanced Portfolio Technology) We have already discussed this company and its model, which is based on the search for implicit factors, in Section 6.2.2.5. The principle used is the same as Quantal’s. In practice, the calculations are carried out by using historical data on 180 weekly returns with a database of 30 000 securities from different countries. The model extracts 20 factors through the statistical method presented in Section 6.2.2.5. The factors are orthogonal, i.e. independent, and they have strong explanatory power. The estimations are performed again every quarter by integrating the new data for the most recent quarter and eliminating the data from the earliest quarter. This model is used to establish a ranking of mutual funds by risk category in order to be able to compare their performance within a single category. The ranking has appeared in Le Monde and other European newspapers13 since the beginning of 1999. This ranking includes the risks taken by the manager, with the different areas of those risks being studied. The factor model established allows the fund and asset returns to be broken down into a certain number of 12
Cf. Quantal’s web site: http://www.quantal.com. El Pais in Spain, The Guardian / Money Observer in the United Kingdom, Le Soir in Belgium, La Stampa in Italy, S¨uddeutsche Zeitung in Germany, Tageblatt in Luxembourg, Le Temps in Switzerland and Der Standard in Austria. 13
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
175
coefficients of sensitivity to the risks that are common to all the assets. The values of these coefficients allow the risks of the funds to be evaluated. Precise knowledge of the risks then allows the mutual funds to be grouped into peer groups with very similar risk profiles. The ranking can then be established within each group. APT compare their method with that of arbitrarily chosen explicit factor models. The explicit factors can be interpreted, but they are liable to be correlated. APT prefer to favour the explanatory power of the returns rather than interpretation of the factors. In addition, as we indicated in Section 6.2.2.3, a transition from implicit factors to explicit factors is then possible. In this section we have presented three types of risk analysis model: one based on explicit factors and the other two based on implicit factors. Implicit factor models are particularly interesting for monitoring the risk, and, by extension, the performance, of an index portfolio, because they allow the exposure to different risk factors to be controlled accurately. To do that, we analyse the index to be replicated. We can then construct the index portfolio so that it is as close as possible to the index by exposing it to the same risks, with the same factor loadings as the index. This allows us to conserve the minimal portfolio tracking-error and to achieve the desired performance. Since the implicit factor models integrate evolutions in the market better than the explicit factor models, they allow more reliable results to be obtained. 6.4.2 Choice of portfolio The simplified structure of the asset returns’ variance–covariance matrix allows the portfolio optimisation methods to be implemented with fewer calculations. This point was addressed in Section 3.4 of Chapter 3. 6.4.3 Decomposing the performance of a portfolio14 The multi-factor models have a direct application in investment fund performance measurement. The models contribute more information to performance analysis than the Sharpe, Treynor and Jensen indices. We have seen that the asset returns could be decomposed linearly according to several risk factors common to all the assets, but with specific sensitivity to each. Once the model has been determined, we can attribute the contribution of each factor to the overall portfolio performance. This is easily done when the factors are known, which is the case for models that use macroeconomic factors or fundamental factors, but becomes more difficult when the nature of the factors has not been identified. Performance analysis then consists of evaluating whether the manager was able to orient the portfolio towards the most rewarding risk factors. Ex post observation of the level of returns compared with the consensus returns allows us to evaluate whether the manager was right or not to deviate from the benchmark by orienting the portfolio towards certain factors. Analysis of portfolio performance with the help of a multi-factor model is applied to relatively homogeneous asset classes, for example French stocks, or international stocks, or a category of bonds. The factors identified depend on the type of asset under consideration. All the models presented below generalise the Jensen measure. The share of return that is not explained by the factors constitutes the residual return and allows us to calculate the information ratio, as it was defined in Chapter 4. 14
Cf. Roll and Ross (1984).
c06
WU058-Amenc
July 17, 2003
176
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
6.4.3.1 The multi-index model: Elton, Gruber, Das and Hlavka’s model15 This model constitutes the first improvement compared with the single-index model. The indices quoted on the markets are indices that are specialised by asset type. The use of several indices therefore gives a better description of the different types of assets contained in a fund, such as stocks or bonds, but also, at a more detailed level, the large or small market capitalisation securities and the assets from different countries. The multi-index model is simple to use because the factors are known and easily available. The empirical validation studies are however more recent than those carried out on the APT model. The Elton et al. model is a three-index model that was developed in response to a study by Ippolito (1989) which shows that performance evaluated in comparison with an index that badly represents the diversity of the assets in the fund can give a biased result. Their model is presented in the following form: R Pt − RFt = α P + β PL (RLt − RFt ) + β PS (RSt − RFt ) + β PB (RBt − RFt ) + ε Pt where RLt RSt RBt ε Pt
denotes the return on the index that represents large-cap securities; denotes the return on the index that represents small-cap securities; denotes the return on a bond index; and denotes the residual portfolio return that is not explained by the model.
Elton et al. position themselves within the framework of the efficient market hypothesis defined by Grossman and Stiglitz (1980), which assumes that the markets are efficient if the additional return produced by the active management of a portfolio simply compensates for the management fees. The manager’s performance corresponds to the excess return that is not explained by the three indices. The model allows for better integration of the nature of the fund and identification of the manager’s style as a function of the significance of each index in the performance result. This model can be used to evaluate the manager’s market timing capacity with regard to each of the market sectors by adding a quadratic term for each index. We then obtain a generalisation of the Treynor and Mazuy model. 6.4.3.2 The APT model16 The use of the APT model to analyse performance was developed for the first time by Connor and Korajczyk (1986). The principle is the same as for the Jensen measure or the multi-index model, namely to separate the predictable part of performance, explained by the model, from the manager’s contribution. If the factors have been chosen well, then this model should enable the strategy followed by the manager to be described more accurately than by the three-index model presented above. As we mentioned during the theoretical presentation of this model, the essential difficulty is in choosing the right factors. Connor and Korajczyk use macroeconomic factors. They selected the following five factors: the forward structure of rates, the bond premium, the unanticipated unemployment rate, unanticipated inflation and the residual market factor. 15 16
Cf. Elton et al. (1993), and also Elton and Gruber (1995), Fabozzi (1995) and Grandin (1998). Cf. Elton and Gruber (1995), Grandin (1998), and Roll (1997) who cites the method used by Connor and Korajczyk.
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
177
Once the average return decomposition model has been established for each asset over a given period, we can study the performance of a portfolio made up of n assets, chosen from among the assets that were used to construct the model. We have E(Rit ) − RF =
K
βik λk
k=1
where βik and λk are known. The return on the portfolio is written as follows: R Pt =
n
xi Rit
i=1
with xi being the weightings of the assets in the portfolio. The composition of the portfolio is assumed to be fixed over the period under consideration. The study period actually has to be broken down into as many sub-periods as there are modifications to the portfolio and the results then have to be aggregated over a complete period. By aggregating the results obtained for each asset at the portfolio level, we can then decompose its total return according to the risk factors. The return forecast by the model is therefore: E(R P ) = RF +
K
λk β Pk
k=1
where β Pk =
n
xi βik
i=1
The differential between the observed portfolio return and its expected return, or R Pt − E(R P ), gives the share of return that is not explained by the model, and therefore attributable to the manager. The share of return explained by factor k is given by λk β Pk . This decomposition allows the performance differential between two portfolios to be explained by the different exposure to the factors. Since the performance analysis is carried out ex post, the study period can be included in the period that was used to establish the model. It is then necessary to update the model regularly by continually taking, for example, five-year rolling periods of historical data. 6.4.3.3 Barra’s model for analysing the performance of equity portfolios17 Barra promote a performance analysis and attribution model called Equity Portfolio Performance Analysis, based on their risk model. It involves evaluating performance in relation to the risks taken, with the help of the multi-factor risk analysis model, and identifying the sources of portfolio performance. The model uses the historical monthly composition of the portfolio. Performance attribution allows us to identify the management decisions and asset allocation 17 Cf. Barra’s internet site: http://www.barra.com, and Meier (1991, 1994). The models for bond portfolios will be presented in Chapter 8.
c06
WU058-Amenc
July 17, 2003
178
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
strategies that made the greatest contribution to the portfolio return and to determine whether the return is sufficient with regard to the risk taken to achieve it. We can therefore evaluate the manager’s skill in achieving returns for the different categories of risk. In Barra’s performance attribution model the multi-factor models are integrated in a very thorough analysis that also handles evaluation of the investment management process, an aspect that will be detailed in Chapter 7. The performance of the portfolio is compared with that of a benchmark which can be chosen from among a list of specific benchmarks or can be custom built. The asset allocation component is separated from the stock picking component for each market sector, with the latter then being analysed with the help of a factor model. For the moment, we only describe the application of multi-factor models to analysis for each market sector. Using the model’s risk indices and calculated risk premiums, the portfolio return is decomposed according to the same principle as that used for the APT model. We thereby determine the share of return that comes from each of the risk factors. With the notation being the same as that used in Section 6.4.1.1, in which we described Barra’s risk model, we recall that the return on a portfolio made up of n assets is written as follows: R Pt =
K
x Pkt αkt + u Pt
k=1
where x P = BTh P and u Pt =
n
h Pit u it
i=1
and where αk ui B hP
denotes the return on factor k; denotes the specific return on asset i; denotes the factor loading matrix; and denotes the vector that defines the weightings of the assets in the portfolio.
The coefficients x Pkt denote the portfolio’s exposures to the factors at the beginning of the period studied. R Pt and αkt . denote the returns realised by the portfolio and the factors, respectively. The return attributed to factor k is therefore written as follows: R Pkt = x Pkt αkt and the portfolio-specific return is given by u Pt . This specific return measures the manager’s skill in selecting individual securities. The performance decomposition can also be performed on the portfolio’s active return. Studying the performance and interpreting the results then leads to a review of the investment plan. Performance attribution thus allows for a better understanding of the results and improved portfolio management. Barra initially developed multi-factor models for each country and then developed a model that was adapted to international multi-currency portfolios. The latter model analyses portfolio performance as a function of the allocation by country, and then uses a specific model for each
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
179
country. In the case of international portfolios, the major source of performance identified is the choice of allocation by country and by currency. 6.4.3.4 Implicit factor model for performance analysis Once the model has been identified, we obtain a decomposition of the expected return on each asset according to the different factors. We can then explain the share of the portfolio return that is due to each factor and isolate its residual return. The principle is then the same as for an APT-type explicit factor model, apart from the fact that we cannot necessarily name the factors and the factors thus remain difficult to interpret. For that reason the models actually are more often used to manage portfolio risk than to explain portfolio performance. However, as we already indicated in Section 6.4.1.3, the firm APT’s implicit factor model is used to rank the performances of mutual funds and investment funds. Once the funds have been split into groups with similar risk profiles, they are ranked by level of performance within each group. The ranking obtained presents a restated performance on which a judgement is expressed. The level of risk taken in comparison with funds in the same category is also qualified with a system of stars. We can therefore evaluate the quality of management for each fund and analyse the source of the performance according to the risks taken to achieve it. 6.4.4 Timing analysis The timing analysis methods, which were presented in Chapter 4 and which allow us to analyse the evolution of the portfolio’s exposure to market risk, are generalised in the case of a multifactor model. To do so, one simply adds a quadratic term to the equation for each of the factors. We thus obtain a Treynor and Mazuy-type formula. This allows us to study the variation in the portfolio’s exposure to the different risk factors in correlation with the factor trends. 6.4.5 Style analysis The concept of management style has become more and more prominent in recent years in equity management services. We observe that securities produce different performances according to the category to which they belong and the time periods considered. In Chapter 1 we presented the different investment styles and described the usefulness of the multi-style approach. Managers can construct portfolios based on a pure investment style or else spread the portfolio over several investment styles. Multi-style portfolios can also be obtained by combining funds where the managers follow well-defined styles. It is then necessary to have an appropriate model to analyse the performance of those portfolios and a benchmark that corresponds to the structure of the portfolio. The choice of benchmark is very important. It would not be fair to compare the performance of a manager who follows a very precise style with that of a benchmark representing the whole of the market, or that corresponds to a style that is different from his. A manager may, for example, produce a performance that is worse than the performance of the market as measured by a broad index if the style that he employs is not the most favourable over the period under consideration. He could nevertheless display particular skill within his style by producing a performance that is better than the benchmark that corresponds to his specific style; we should not consider in that case that the manager has performed badly. The opposite situation may also arise. A manager may produce a performance that is better than the broad index, but worse than the index corresponding to his style; he
c06
WU058-Amenc
180
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
should not in that case be considered to be a good manager in the style that he employs. Studying performance in comparison with a specific benchmark allows us to avoid those kinds of errors. Two types of method allow the style of a portfolio to be analysed. The first, called returnbased style analysis, is based solely on the study of past portfolio returns. It does not require the composition of the portfolio to be known. It is drawn from the style analysis model developed by Sharpe (1992). The second method, called portfolio- or factor-based style analysis, analyses the style of the portfolio by studying each of the securities that make up the portfolio. We shall present these two types of analysis while specifying their respective advantages and disadvantages. Before that, however, we introduce and examine the issue of style indices on which the whole analysis is based. 6.4.5.1 Style indices18 The need to measure the performance of different investment styles led to the development of style indices. The style indices for the American market are principally developed by four companies: Frank Russell, Wilshire Associates, Barra, in association with Standard & Poor’s, and Prudential Securities International. The Frank Russell Company produces three types of style index: a large-cap index based on the Russell 1000 index, the Russell 3000 index and the Russell Top 200 index, a mid-cap index, and a small-cap index using both the Russell 2000 and Russell 2500 indices. Standard & Poor’s publish large-cap indices for growth and value stocks in partnership with Barra. These indices are based on the S&P Composite, MidCap 400 and SmallCap 600 indices. Wilshire Associates and Prudential Securities publish style indices for the following three categories: large-cap, mid-cap and small-cap. There are also international style indices. Boston International Advisors (BIA) created style indices for 21 countries and seven regions for the following four major style categories: large value, large growth, small value and small growth. Parametric Portfolio Associates (PPA) have also developed a similar set of international indices. We will describe the main indices in more detail below. The Russell Growth and Value indices are available for the three Russell large-cap indices: the Top 200 index, the Russell 1000 index and the Russell 3000 index. The mid-cap style indices are based on the Russell MidCap index and the small-cap style indices are based on the Russell 2000 index and the Russell 2500 index. These three indices use the same calculation method. The securities are ranked on the basis of their P/E ratio and their long-term growth rate. This ranking determines whether a stock tends to be a growth stock or a value stock. Around 30% of the securities in the large-cap index appear in both the growth and value indices, but in different proportions. The rest of the stocks appear in only one index. The Russell 3000 index contains the 3000 largest companies in the United States, which together represent 98% of American stock market capitalisation. The Russell 2000 index corresponds to the bottom two-thirds of the list of the 3000 largest American corporations. The Russell 1000 index contains the 1000 largest companies. The Russell 2500 corresponds to the Russell 3000 index with the 500 largest capitalisations taken away. The Top 200 index contains the 200 largest firms. The MidCap index contains the 800 firms that come after the 200 largest firms in descending order of market capitalisation. The combination of the Top 200 index and the MidCap index constitutes the Russell 1000 index. 18
Cf. Brown and Mott (1997) and Mott and Coker (1995).
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
181
The S&P/Barra Growth and Value indices are constructed from the S&P500 index on the basis of the P/E ratios of the securities. The securities with the lowest P/E ratios are integrated into the value index and the securities with the highest P/E ratios go into the growth index. The two indices are constructed in such a way as to have approximately the same capitalisation. Since the companies in the growth index have a larger market capitalisation, this index only contains 40% of the securities. The rest of the securities make up the value index. The same methodology is used to construct the S&P MidCap and SmallCap indices. The S&P500 index, which is also called the S&P Composite, is constructed so as to be representative of the New York Stock Exchange in terms of industrial sectors. The stocks in the S&P MidCap 400 index are chosen according to their size and their industrial characteristics. The S&P SmallCap 600 index was introduced in October 1994. It contains companies chosen according to their size, their industrial characteristics and their liquidity. The SmallCap, MidCap and S&P Composite indices do not overlap. Certain companies in the MidCap index have a larger market capitalisation than those in the S&P500 and certain companies in the SmallCap index have a larger market capitalisation than those in the MidCap index. The Wilshire Growth and Value indices are constructed from the Top 750 large-cap index, the MidCap 750 index and the Next 1750 small-cap index, eliminating securities that do not have growth characteristics for the former, or value for the latter. The Wilshire Top 750 index contains the securities with the largest market capitalisation in the Wilshire 5000 index, an index that had over 7000 securities halfway through the year 1996. The Wilshire MidCap index is a little smaller than the Russell MidCap and S&P MidCap indices. It contains the 250 smallest market capitalisation securities in the Top 750 index and the 500 largest market capitalisation securities in the Next 1750 index. For the same style we therefore have several indices. However, we observe that the performance of these indices is different, even though they represent the same investment style. The differences observed are anything but negligible, as they can reach several basis points. The reason for this is that the indices are based on different universes of securities and are calculated using different methods. For example, Russell and Standard & Poor’s create their indices on the basis of the P/E ratio, while Wilshire and PSI use a scanning technique based on several criteria. The choice of a particular index from among the different indices available for the same style is therefore difficult, and all the more so because the resulting performance analysis depends on the reference index chosen. To solve this problem we can seek to identify pure style indices. To do this, we carry out factorial analysis on the returns of the style indices that belong to the same style category. The first component then constitutes a pure style component, which can be seen as the intersection of the indices under consideration. By proceeding in that way for each style category, we obtain a set of pure style indices19 . These indices can then be used as a basis for constructing normal portfolios made up of several style indices. 6.4.5.2 Sharpe’s style analysis model20 The theory developed by Sharpe stipulates that a manager’s investment style can be determined by comparing the returns on his portfolio with those of a certain number of selected indices. Intuitively, the simplest technique for identifying the style of a portfolio involves successively 19 20
On the subject of implementing the technique for constructing “pure” indices, see Amenc and Martellini (2001). Cf. Sharpe (1992), Fabozzi (1995) and Hardy (1997).
c06
WU058-Amenc
182
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
comparing his returns with those of the different style indices. The goodness of fit between the portfolio returns and the returns on the index is measured with the help of a quantity called R 2 , which measures the proportion of variance explained by the model. If the value of R 2 is high, then the proportion of unexplained variance is minimal. The index for which the R 2 is highest is therefore the one that best characterises the style of the portfolio. But managers rarely have a pure style, hence Sharpe’s idea to propose a method that would enable us to find the combination of style indices which gives the highest R 2 with the returns on the portfolio being studied. The Sharpe model is a generalisation of the multi-factor models, which is applied to classes of assets. Sharpe presents his model with 12 asset classes. These asset classes include several categories of domestic stocks, i.e. American in the case of the model: value stocks, growth stocks, large-cap stocks, mid-cap stocks and small-cap stocks. They also include one category for European stocks and one category for Japanese stocks, along with several major bond categories. Each of these classes corresponds, in the broad sense, to a management style and is represented by a specialised index. The model is written as follows: R Pt = b P1 F1t + b P2 F2t + · · · + b P K FK t + e Pt where Fkt denotes the return on index k; b Pk denotes the sensitivity of the portfolio to index k and is interpreted as the weighting of class k in the portfolio; and e Pt represents the portfolio’s residual return term for period t. In this model the factors are the asset classes, but unlike ordinary multi-factor models, where the values of the coefficients can be arbitrary, here they represent the distribution of the different asset groups in the portfolio, without the possibility of short selling, and must therefore respect the following constraints: 0 ≤ b Pk ≤ 1 and K
b Pk = 1
k=1
These weightings are determined by a quadratic program, which consists of minimising the variance of the portfolio’s residual return. The style analysis thus carried out allows us to construct a customised benchmark for the portfolio. To do so, we simply take the weightings obtained for each style index. This type of benchmark is called a Sharpe benchmark. We referred to it previously in Chapter 2. It corresponds to a passive portfolio of the same style as the portfolio to be evaluated. The difficulty lies in choosing a period of suitable length to be representative of the manager’s style. A period that is too short is insufficient for evaluating a manager’s style, but a benchmark constructed from a period that is too long may not fully reflect recent changes in the manager’s style. Using a period of three years for constructing a benchmark is recommended. The benchmark established in that way is created ex post, although it would be useful for it to exist at the beginning of the period for which we are evaluating the manager. In order to have an appropriate benchmark
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
183
for the manager’s portfolio available permanently, we can proceed in rolling periods by always using the last three years of historical data to construct the reference for the upcoming period. We then update the benchmark by continually advancing it by one period (a quarter or a month) over time. Once the coefficients of the model have been determined for a representative period and the benchmark has been constructed, the manager’s performance is calculated as being the difference between the return on his portfolio and the return on the benchmark. We thereby isolate the share of performance that comes from asset allocation and is explained by the benchmark. The residual share of performance not explained by the benchmark constitutes the management’s value-added and comes from the stock picking, within each category, that is different from that of the benchmark. It is the manager’s active return. The proportion of the variance not explained by the model, i.e. the quantity 1 − R 2 , measures the importance of stock picking quantitatively. When a fund is assigned to several managers, the style for the whole fund is obtained by aggregating the styles obtained for each manager with their respective weightings. In the case of international portfolios, the style analysis can be carried out by country, by considering the different style indices within each country, or else globally, by using international style indices. The Sharpe model uses an analysis that is called return-based, i.e. based solely on the returns. The advantage of this method is that it is simple to implement. It does not require any particular knowledge about the composition of the portfolio. The information on the style is obtained simply by analysing the monthly or quarterly returns of the portfolio through multiple regression. The sources of the historical portfolio returns are explained by the combination of style indices that best represents the returns on the portfolio as a whole. The necessary data are the historical portfolio returns and the returns on a set of specified indices. But the major disadvantage of this method lies in the fact that it is based on the past composition of the portfolio and does not therefore allow us to correctly evaluate the modifications in style to which it may have been subjected during the evaluation period. This method therefore assumes that the managers have a consistent style during the period, or that only minimal and progressive style modifications occurred. As long as these conditions are respected, the method described works well. When the study period is fairly long, there can be no certainty about style consistency over time. Past data may not be representative of the current portfolio. In this case the result obtained is actually the average style of the portfolio over the period. If style modifications occur, then the method tends to detect them late or sometimes not detect them at all. When several groups of indices are available for analysing the style, the results can differ according to the group of indices used. To get a view of the evolution of the portfolio style over time, we can carry out the analysis again for rolling sub-periods, after carrying out the analysis for the complete period. With quarterly returns we take, for example, three-year periods by rolling over one quarter. The successive results show the evolution in the manager’s style. This is a quick way to analyse the evolution of the style without having to know the portfolio composition in detail. Certain managers seek to add value by switching from one style and/or sector to another and by predicting the style or sector that will be favourable in the upcoming period. These managers are called sector rotators or style rotators. The style analysis and benchmark creation described in this section are not suitable for analysing this type of manager. It is better in that case to use a broad benchmark. However, the analysis presented allows us to identify this type of manager rapidly. The rolling period analysis gives results that are spread over all styles instead of tending towards a specific style. The style is therefore inconsistent. The
c06
WU058-Amenc
184
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
R 2 calculated to validate the benchmark is low and it is virtually impossible to predict the future on the basis of the past. The benchmark evaluated by rolling period evolves greatly from one period to another. While the average style benchmark turnover in one year is between 20% and 30%, that of a style rotator can reach 100%. We have seen that the main disadvantage of the return-based method was that it was essentially based on past data. Furthermore, linear statistic modelling poses the problem of the meaning of the term “residual”. We must consider that the classic assumptions of the linear model are always true and, consequently, that the optimality properties of the linear regression estimators will always remain valid. In particular, it is classic to rely on the “central limit” theorem to justify the fact that the random residual of the model (an effect that results from the addition of multiple unspecified random factors) has a distribution that is similar to the Laplace–Gauss law. This allows the parameters of the estimated model to be “Studentised” and thus allows their “significance” to be qualified statistically. Apart from that statistical assumption, style analysis presents other statistical difficulties: 1. The linear regression uses past data and the past cannot be representative of the future (the problem with the non-stationarity of the processes). 2. The constraint imposed by the Sharpe model on the weight of the factors (positive and with a sum equal to 1) tends to distort the regression results obtained (DeRoon et al., 2000). The correlation between the error term and the benchmark or benchmarks chosen may not be equal to 0. 6.4.5.3 Portfolio-based analysis The principle of portfolio-based analysis is to analyse each of the securities that make up the portfolio (cf. Borger, 1997). The securities are studied and ranked according to the different characteristics that allow their style to be described. The results are then aggregated at the portfolio level to obtain the style of the portfolio as a whole. This method therefore requires the present and historical composition of the portfolio, together with the weightings of the different securities that it contains, to be known precisely. The analysis is carried out regularly in order to take account of the evolution of the portfolio composition and the evolution of the characteristics of the securities that make up the portfolio. The results obtained therefore correspond to the characteristics of the portfolio currently held by the manager and thus liable to influence his future performance, while the method described previously was based on the past characteristics of the portfolio. This method therefore enables better monitoring of the evolution of the portfolio. The method is partly drawn from the work of Fama and French, which we presented earlier in the chapter, who showed that asset returns could be explained by a small number of fundamental factors. In particular, Fama and French identified the size, measured by the market capitalisation, and the book-to-market ratio. As we saw in Chapter 1, the style is essentially analysed according to two facets. Assets are classified, on the one hand, according to their market capitalisation, and, on the other, according to whether they are growth stocks or value stocks. For the size criterion, they are generally separated into two groups: large-cap securities and small-cap securities. To do this, all securities are ranked in decreasing order of market capitalisation. We can then define the two groups so that the total market capitalisation of each group is the same. In this case the small-cap stock group will contain more securities than the large-cap stock group. We can also choose to separate the two groups by observing the level at which the performance differences
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
185
between the securities become significant. In addition, we can define a third intermediate category containing mid-cap securities. We observe that the investment styles and the fundamental factors are linked: a style can be described by a set of fundamental factors. The stocks can be split into value stocks and growth stocks by observing the values of the securities’ fundamental characteristics. Value stocks are characterised by high returns. Several variables allow them to be identified. The first is the book/price (B/P) ratio, which measures the book value compared with the market value. Value stocks are characterised by a high B/P ratio, but it is more difficult to justify stocks with a low B/P ratio being growthstocks. Value stocks are also characterised by a high earnings/price (E/P) ratio. This ratio measures the amount of earnings compared to the market value. We can also identify value stocks on the basis of the yield/priceratio, which measures the value of the dividend compared to the market value, i.e. the return on the security. Certain securities cannot be included in either the growth or the value category. This is the case, for instance, for companies that have made a loss. The different securities are therefore classified in line with the value of the fundamental characteristics that are chosen to describe the styles. We can then check whether the different groups obtained do have different performance characteristics. Once the study has been carried out security by security, the results are used to evaluate the style of the portfolio as a whole. The portfolio’s market capitalisation is obtained, for example, by calculating the weighted mean of the market capitalisation of the securities that make up the portfolio. We proceed in the same way for all the fundamental characteristics of the portfolio. The study must be carried out regularly, because the characteristics of the securities are liable to evolve over time. It is also possible to turn to factor analysis for implicit identification of the factors that characterise the style of the portfolios, rather than presupposing the nature of the fundamental factors associated with each style (cf. Radcliffe, 2000). This approach, which is not very widely used today in practice, is an attempt to respond to a criticism, which is difficult to refute, of the security characteristic-based style analysis techniques. Numerous studies (notably Lucas and Riepe, 1996) have highlighted the difficulty of a priori classification of securities according to their characteristics. On the one hand, commonly used attributes such as the book/price or earnings/price ratios are unstable and depend as much on market conditions as on company-specific qualities. On the other hand, the characteristics of a large number of securities do not allow satisfactory discriminatory analysis to be carried out. In a Bienstock and Sorensen (1992) study, it appears that only 20% of the stocks, from a sample of 3000, can, to a significant degree, be classified as value or growth. Such a limitation would lead to the construction of style benchmarks that would be too narrow and would either not correspond to the actual investment management carried out or, if the manager wished to guarantee his style by respecting this constraint, significantly restrict the investment opportunities. Finally, when the investor chooses stocks that present the desired characteristics, he selects other undesired attributes, which should be analysed, with the stocks (exposure to a country, to a sector, etc.). This complicates the a priori construction of the benchmark or portfolio that is representative of the allocation desired. 6.4.5.4 Comparing the two methods The return-based method is the most widely used because it is the simplest to implement. There is no need to know the securities that make up the portfolio, nor their proportions. It is therefore the only method that can be used when there are no data available on the composition
c06
WU058-Amenc
186
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
of the portfolio21 . This ex post analysis does not however allow the managers’ a priori respect of investment constraints to be managed. In addition, this technique has the disadvantages of the methods that use regression, namely a risk of the model being wrongly specified when the style indices are chosen. The return-based approach nevertheless has allowed the use of customised benchmarks to be developed and generalised, where previously one merely tended to compare portfolios with broad indices. The portfolio-based method requires more information on the portfolio, but in exchange it provides more precise information. It is based on the style characteristics used by the manager to construct and maintain his portfolio and allows the investment strategies followed to be studied. The manager therefore has the possibility of evaluating the results of his forecasts and gaining a better understanding of the reasons for the over- or underperformance highlighted by performance attribution. The portfolio-based approach integrates the evolution of the portfolio style over time to a greater degree. While the return-based method could simply reveal a style differential sustained by the portfolio, the decomposition of the portfolio makes it possible to understand the security in the portfolio or the investment strategy that created the differential. This technique allows us to notice rapidly that a manager is holding securities that do not correspond to his style. But the main weakness of this approach is the frequently subjective character of the classifications. Since the style analyses performed within this approach are specific to each manager, it is difficult for them to be reproduced by an external third party. This can turn out to be a major disadvantage when an external consultant is used to certify or evaluate the quality of the management performance analysis provided to the institutional investor. As a result, we often see objectives shared between the methods22 . The techniques that rely on the portfolio-based analysis approach are used for the internal implementation of the monitoring process for risks, compliance with investment constraints and performance attribution. Since an analysis that is exclusively based on the returns is considered to be more objective, it is more often used for an external view of performance measurement and its adjustment in relation to the risk taken and the style used by the manager over the analysis period. Within the area of multimanagement, we find this breakdown again. Only multimanagers who have access, through their information system, to all the daily operations of their delegated managers favour portfolio-based analysis. Managers of funds-of-funds use techniques that are only based on returns. 6.4.5.5 Style benchmarks In Chapter 2 we defined normal benchmarks. This type of benchmark allows more accurate performance evaluation of a portfolio that is managed according to a particular style. The two methods for analysing the portfolio style that we have just described are used to construct appropriate normal portfolios for the managers’ styles. The manager’s portfolio can then be represented as a weighted combination of style indices. In order to determine the weightings to assign to each style index, we analyse the style of the manager over a given period using one of the two methods described above. We thus obtain a set of weights that represent the manager’s style at the end of the time period. The reference 21 In 1995, a survey of data from two major mutual fund information providers in the United States showed that only one-fifth (Morningstar) and one-half (Value Line) of the fund compositions present in the marketed databases had been updated in the previous three months. 22 For more details on the conditions of use of the two approaches, it would be beneficial to refer to Trzcinka (1997).
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
187
portfolio for evaluating the manager is a portfolio made up of the style indices in proportions defined by the portfolio style analysis. This portfolio is the normal portfolio weighted by the style. Formally, it is calculated in the following way: R Nt = w1,t−1 S1t + w2,t−1 S2t + · · · + wn,t−1 Snt + εnt where RNt denotes the return of the style-weighted normal portfolio at date t; wn,t−1 denotes the weight of style index n at the beginning of the time period or the end of the last time period; Snt denotes the return of style index n at time t or over the interval from t − 1 to t; εnt denotes the residual return non-correlated with the n style indices; and n denotes the number of style indices in the analysis. The portfolio with return RNt is the reference portfolio for evaluating portfolio management and portfolio performance. We note that the manager’s alpha is integrated in the error term, whatever the specific portfolio risk. Any return that is not taken into account by the style indices is integrated in the error term. That is the disadvantage of using this method to create normal portfolios compared with the methods based on defining a manager-specific list of securities, which were described in Chapter 2. When we create a normal portfolio it can track the portfolio of the manager under evaluation with a certain degree of accuracy. The closer the normal portfolio is to the manager’s portfolio, the better it will capture his style, but in that case the normal portfolio will only be adapted to a single manager. If, on the other hand, we create a normal portfolio that is a bit more general, it will allow us to evaluate and compare managers with different portfolios but fairly similar styles. 6.4.5.6 Management style characteristics and other methods of classification Roll (1997) presents an interesting study that allows the relative risk of different management styles to be analysed. The securities were first classified according to the following three style characteristics: size, B/P ratio and E/P ratio. Each security is then given a label, L for low and H for high, for each of the three criteria, depending on whether it is found in the top half or the bottom half of the list. We then construct portfolios containing securities with the same characteristics, i.e. with the same series of labels. This leads to eight portfolios, the first being characterised by three H labels, the last by three L labels, and the intermediate portfolios by different combinations of H and L. This classification is redone each month. The composition of the portfolios is therefore liable to evolve from one month to the next. The portfolio returns are evaluated on a monthly basis. The goal of the study is to see if the observed differences in returns between the portfolios, which correspond to different styles, are statistically significant. If the response is positive, then we can deduce that the different styles are characterised by different levels of risk. The study was carried out by successively using the CAPM model and a five-factor APT model to explain the returns of the different portfolios. In both cases the results show significant differences in returns between the styles, and hence different levels of risk. In addition, the APT model’s risk factors do not allow the performance resulting from the portfolio style to be explained completely. We also observe that the specific returns associated with the style are not stationary over time.
c06
WU058-Amenc
188
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
We described the methods that allow the asset styles to be identified with the help of fundamental factors a little earlier. Another useful technique for classifying assets according to their style involves defining style betas (cf. Quinton, 1997) using the same principle as the market betas in Sharpe’s CAPM. The return of each asset is described in the following way: Rstock = α + βM RM + βG−V RG−V + βL−S RL−S where α RM RG−V RL−S βM βG−V βL−S
denotes the return not explained by the model; denotes the monthly market return measured by an index representing the market as a whole; denotes the difference between the monthly return of the growth index and the monthly return of the value index; denotes the difference between the monthly return of the large-cap index and the monthly return of the small-cap index; denotes the security’s sensitivity to the market index; denotes the security’s sensitivity to the difference between the growth index and the value index; and denotes the security’s sensitivity to the difference between the large-cap index and the small-cap index.
The coefficients of this equation are estimated through regression. The stocks for which βG−V is positive are growth stocks and those for which βG−V is negative are value stocks. In the same way, stocks with a positive βL−S are large-cap stocks and those with a negative βL−S are small-cap stocks. This model defines an APT-type relationship between the returns of the stocks and the returns of the style indices. The betas also provide an accurate measure of the sensitivity of each stock to the different investment styles. Using this analysis we can evaluate the investment style of a portfolio as the weighted mean of the investment styles of the different assets that make up the portfolio. Brown and Goetzmann (1996) developed an algorithm for classifying funds by category of style which differs from the traditional methods. According to them, the traditional methods do not allow a certain number of problems to be solved satisfactorily, namely explaining future returns of funds, giving indications on the managers’ strategies and providing useful benchmarks for evaluating relative performance. The authors indicate that the method that they have developed gives better results for those questions. The algorithm that they developed is consistent with the APT model. The funds are grouped together on the basis of series of past returns and on the responses to specified exogenous factors and endogenous stochastic variables. The results consist of styles that differ from the standard classifications. Their conclusion is that their method would not replace Sharpe’s style analysis, but would complement it. 6.4.5.7 Investment style and performance persistence We saw in Chapter 1 that performance persistence studies do not give very conclusive results as to whether persistence really exists. Over a long period, there is a greater tendency to observe underperformance persistence on the part of poor managers than overperformance persistence from good managers. However, the studies do not take into account the investment
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
189
style followed by the managers. We do, nevertheless, observe that different investment styles are not all simultaneously favoured by the market. Markets are subject to economic cycles and a style that is favourable for one period, i.e. that offers a performance that is better than that of the market, can be less favourable over another period and lead to underperformance compared with the market. This can be measured by comparing the returns of the different style indices with the returns of a broad market index. The fact that an investment style performs well or badly should not be confused with the manager’s skill in picking the right stocks within the style that he has chosen. As we mentioned earlier, a manager’s skill in practising a well-defined style should be evaluated in comparison with a benchmark that is adapted to that style. Few studies have addressed the subject of performance persistence for managers who specialise in a specific style. The results of the studies that have been performed are contradictory and do not allow us to conclude that persistence exists. For example, Coggin et al. (1993) carried out a study on American pension funds over the period from 1983 to 1990. Their study relates to identification of both the market timing effect and the selectivity effect. They used two broad indices: the S&P500 index and the Russell 3000 index, and four specialised indices: the Russell 1000 index for large-cap stocks, the Russell 2000 index for small-cap stocks, a Russell index specialised in value stocks and a Russell index specialised in growth stocks. They showed that the timing effect and the selectivity effect were both sensitive to the choice of benchmark and the period of the study. They found a positive selectivity effect compared with the specific indices, while that effect was negative compared with the broad indices. However, they found a negative market timing effect in both cases. The study shows, therefore, that specialisation is a source of value-added. Managers succeed in performing better than their reference style index, even if they do not manage to beat the market as a whole. Over the period studied, the different style indices did not all perform in line with the market. The performance of the value stock index was approximately equal to that of the market, which implies that the study period was favourable for value stocks. The performance of the growth stock index was slightly worse. As far as the small-cap stock index was concerned, its performance was half as good as that of the market index. However, Kahn and Rudd (1995, 1997) concluded that fund performance was not persistent for a sample of 300 US funds over the period from October 1988 to October 1995. A final interesting study is that of Chan et al. (1999). This study concerns Morningstar funds. The study shows that on the whole there is a certain consistency in the style of the funds. Nevertheless, funds that have performed badly in the past are more liable to modify their style than others. This study shows that it is preferable to avoid managers who change style regularly. They make it more difficult to optimise a portfolio that is shared between several managers and produce worse performances than managers whose style is consistent.
6.5 SUMMARY AND CONCLUSION Throughout this chapter we have presented the different categories of multi-factor models and their application to portfolio management. The common denominator between all these models is to allow the number of terms employed in calculating the asset variance–covariance matrix to be reduced. By analysing the assets through a reduced number of factors we can express this matrix as a function of the variance–covariance matrix of the factors and the variance– covariance matrix of the asset-specific risks. It therefore becomes easier to analyse large portfolios. In relation to analysing the results of portfolio management, multi-factor models
c06
WU058-Amenc
190
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
allow us to identify the factors that made the most significant contribution to the performance of a portfolio over a given period. This chapter also allowed us to appreciate the difficulties linked to the choice and construction of the correct factor model. The results depend above all on the correct fit between the models used and the portfolios studied. Determining the model is therefore a step that should not be neglected. For a long time the models that dominated the market used explicit factors. These models are easier for users to understand because the factors are expressed clearly. But, as we have seen, these models cannot guarantee that the choice of factors is optimal. That is why recent research favours implicit factors, and all the more so since progress in calculating speed and database management allow the factors to be extracted more easily. These models allow the evolution of returns over time to be monitored better, which is why they are very useful for monitoring and managing portfolio risk. If we wish, for example, to use past results to modify the portfolio composition for the following period, or construct a portfolio with levels of risk specified in relation to the different factors with an explicit factor model, we cannot be sure that the model is stable. It is better in that case to be able to turn to an implicit factor model. However, as far as ex post portfolio performance analysis is concerned, we will continue to prefer explicit factor models that allow the sources of portfolio performance to be described by name. They then allow us to produce reports attributing the contribution of each identified risk factor to the total performance of the portfolio. At the end of this chapter it is interesting to return to the contribution of the APT model and multi-factor models in general, compared with the CAPM. The superiority of these models from a theoretical point of view is unquestionable and unquestioned. However, in practice we observe that the CAPM remains very widely used. Its strength is its great simplicity, even though it has not been the object of rigorous empirical validation. In comparison, the multifactor models are more cumbersome to implement. Certain models presented in this section are appropriate for portfolios that are diversified between several asset classes. This is the case for Sharpe’s style analysis model and the multiindex model. Others, such as the APT model or the Barra model are more appropriate for analysing a homogeneous class of assets that determines the choice of factors. In Chapter 8, which is devoted to bond investment, we will present versions of these models that are more appropriate for bond portfolios.
APPENDIX 6.1 THE PRINCIPLE OF ARBITRAGE VALUATION The principle of arbitrage valuation is based on the following reasoning: any portfolio constructed with no capital invested and no risk taken should obtain a null return on average. Such a portfolio is called an arbitrage portfolio. This portfolio is constructed by considering an investment spread over n assets. It is possible to modify the proportions invested in the different assets without changing the total value of the portfolio, i.e. with no new capital outlay. To do so, we buy and sell in such a way that the total sum of the movements is null. If we take wi to be the change in the proportion invested in asset i, then the portfolio defined by the weightings, (wi )1≤i≤n , respects the following condition: n i=1
wi = 0
(A.1)
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
191
The return obtained by this portfolio is written as follows: RP =
n
wi Rit
i=1
By using the factor relationship assumed by the APT model, or Rit = E(Ri ) +
K
bik Fkt + εit
k=1
we obtain the following expression through substitution: RP =
n i=1
wi E(Ri ) +
n
wi bi1 F1 + · · · +
i=1
n i=1
wi bi K FK +
n
wi εit
i=1
Let us now render explicit the conditions that must be respected by the portfolio. The portfolio must be risk-free, which implies that both the systematic and the non-systematic risk are to be eliminated. The systematic risk in relation to each factor k is given by the vector bk . To cancel this risk, it is necessary to make the terms containing bik disappear from the R P expression. To do that we choose the wi in such a way that the weighted sum of the components of bk is null for each factor k, or n
wi bik = 0
(A.2)
i=1
for all k. The non-systematic risk is eliminated by applying the principle of diversification. The number of assets n contained in the portfolio must therefore be large. And the changes in the percentages invested must be small, or wi ≈ 1/n Since the error terms εi are independent from each other, the law of large numbers allows us to write that their weighted sum tends towards 0 when n becomes large. Diversification therefore allows us to make the last term of the R P expression disappear. Furthermore, since the wi have been chosen such that n
wi bik = 0
for all k
i=1
all the terms containing the factors have thus been eliminated and the R P expression becomes simply RP =
n
wi E(Ri )
i=1
The return on this portfolio is null by definition since it is an arbitrage portfolio. We thus have n i=1
wi E(Ri ) = 0
(A.3)
c06
WU058-Amenc
192
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
We have just established that the vector (wi )1≤i≤n had to respect the following three conditions: A.1. A.2. A.3.
n i=1 n i=1 n
wi = 0 wi bik = 0 wi E(Ri ) = 0
i=1
These three conditions mean that the vector (wi )1≤i≤n must be orthogonal to the following three vectors: the column vector with all its components equal to 1, the vector of factor loadings, and the vector of expected returns. This last vector must therefore be a linear combination of the other two, or E(Ri ) = λ0 + λ1 bi1 + · · · + λk bik with λ0 = R F We thus obtain the so-called arbitrage valuation relationship: E(Ri ) − R F = λ1 bi1 + · · · + λk bik
BIBLIOGRAPHY Amenc, N. and Martellini, L., “The Brave New World of Hedge Fund Indices”, ACT-Edhec, Working Paper, September 2001. Barra, “The Barra E2 Multiple-Factor Model”, Barra web site, April 1996. Barra, “US Equity Model Version 3”, 1998. Batteau, P. and Lasgouttes, V., “Mod`eles multifacteurs des rentabilit´es boursi`eres”, in Encyclop´edie des march´es financiers, Economica, 1997, pp. 1221–1257. Bienstock, S. and Sorensen, E., “Segregating Growth from Value: It’s not Always Either/Or”, Salomon Brothers, Quantitative Equities Strategy, July 1992. Borger, D.R., “Fundamental Factors in Equity Style Classification”, in The Handbook of Equity Style Management, T.D. Coggin, F.J. Fabozzi and R.D. Arnott, eds, 2nd edn, Frank J. Fabozzi Associates, 1997. Brown, S.J. and Goetzmann, W.N., “Mutual Fund Styles”, Working Paper, NYU Leonard Stern School of Business, 1996. Brown, M.R. and Mott, C.E., “Understanding the Differences and Similarities of Equity Style Indexes”, in The Handbook of Equity Style Management, T.D. Coggin, F.J. Fabozzi and R.D. Arnott, eds, 2nd edn, Frank J. Fabozzi Associates, 1997. Burmeister, E., Roll, R. and Ross, S., “Using Macroeconomic Factors to Control Portfolio Risk”, Working Paper, BIRR Portfolio Analysis, Inc., March 1997. This article is based on the previous version of “A Practitioner’s Guide to Arbitrage Pricing Theory”, a contribution to A Practitioner’s Guide to Factor Models for the Research Foundation of the Institute of Chartered Financial Analysts, 1994. Carhart, M.M., “On Persistence in Mutual Fund Performance”, Journal of Finance, vol. 52, no. 1, March 1997, pp. 57–82. Chan, L.K.C., Chen, H.-L. and Lakonishok J., “On Mutual Fund Investment Styles”, Working Paper no. 7215, National Bureau of Economic Research, 1999.
c06
WU058-Amenc
July 17, 2003
18:8
Char Count= 0
Multi-Factor Models
193
Chen, N.-F., Roll, R. and Ross, S., “Economic Forces and the Stock Market”, Journal of Business, vol. 59, no. 3, 1986. Coggin, T.D., Fabozzi, F.J. and Arnott, R.D., The Handbook of Equity Style Management, 2nd edn, Frank J. Fabozzi Associates, 1997. Coggin, T.D., Fabozzi, F.J. and Rahman, S., “The Investment Performance of U.S. Equity Pension Fund Managers: An Empirical Investigation”, Journal of Finance, vol. 48, no. 3, July 1993, pp. 1039– 1055. Connor, G., “The Three Types of Factor Models: A Comparison of their Explanatory Power”, Financial Analysts Journal, May–June 1995. Connor, G. and Korajczyk, R.A., “Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis”, Journal of Financial Economics, March 1986, pp. 373–394. Copeland, T.E. and Weston, J.F., Financial Theory and Corporate Policy, 3rd edn, Addison-Wesley, 1988. DeRoon, F., Nijman T., and ter Horst, J., “Evaluating Style Analysis”, Working Paper, Quantitative Investment Research Europe, 2000. Eichholtz, P., Op’t Veld, H. and Schweitzer, M., “Outperformance: Does Managerial Specialization Pay?”, Working Paper, Linburg Institute of Financial Economics, 1997. Elton, E.J. and Gruber, M.J., Modern Portfolio Theory and Investment Analysis, 5th edn, Wiley, 1995. Elton, E.J., Gruber, M.J., Das, S. and Hlavka, M., “Efficiency with Costly Information: A Reinterpretation of Evidence from Managed Portfolios”, Review of Financial Studies, vol. 6, no. 1, 1993, pp. 1–22. Engerman, M., “Using Fundamental and Economic Factors to Explain Stock Returns: A Look at Broad Factors that Affect many Stocks”, Barra Newsletter, fall 1993. Fabozzi, F.J., Investment Management, Prentice Hall International Editions, 1995. Fama, E.F. and French, K.R., “The Cross Section of Expected Returns”, Journal of Finance, vol. 47, June 1992, pp. 427–465. Fama, E.F. and French, K.R., “Common Risk Factors in the Returns on Stocks and Bonds”, Journal of Financial Economics, vol. 33, 1993, pp. 3–56. Fama, E.F. and French, K.R., “Size and Book-to-Market Factors in Earnings and Returns”, Journal of Finance, vol. 50, no. 1, March 1995, pp. 131–155. Fama, E.F. and French, K.R., “Multifactor Explanations of Asset Pricing Anomalies”, Journal of Finance, vol. 51, no. 1, March 1996, pp. 55–84. Fama, E.F. and MacBeth, J.D., “Risk, Return, and Equilibrium: Empirical Tests”, Journal of Political Economy, vol. 81, 1973. Farrell, Jr. J.L., Portfolio Management, Theory and Application, McGraw-Hill, 2nd edn, 1997. Fedrigo, I., Marsh, T.A. and Pfleiderer, P., “Estimating Factor Models of Security Returns: How Much Difference does it Make?”, Working Paper, December 1996. Fontaine, P., Arbitrage et e´ valuation internationale des actifs financiers, Economica, 1987. Fontaine, P., “Mod`eles d’arbitrage et multifactoriels internationaux”, in Encyclop´edie des march´es financiers, Economica, 1997, pp. 1164–1185. Grandin, P., Mesure de performance des fonds d’investissement, M´ethodologie et r´esultats, Economica, Gestion poche, 1998. Grinold, R.C., “The APT, the CAPM, and the Barra Model: How does Barra’s Model of Asset Risk Fit the APT and CAPM Models?”, Barra Newsletter, November–December 1991. Grinold, R.C. and Kahn, R.N., Active Portfolio Management, Irwin, 1995. Grinold, R.C. and Kahn, R.N., Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk, Irwin, 2nd edn, 2000. Grinold, R.C., Rudd, A. and Stefek, D., “Global Factors: Fact or Fiction?”, Journal of Portfolio Management, fall 1989. Grossman, S.J. and Stiglitz, J., “On the Impossibility of Informationally Efficient Markets”, American Economic Review, 1980, pp. 393–408. Hamao, Y., “An Empirical Examination of the Arbitrage Pricing Theory: Using Japanese Data”, Japan and the World Economy, vol. 1, 1988, pp. 45–61. Hardy, S., “Return-Based Style Analysis”, in The Handbook of Equity Style Management, T.D. Coggin, F.J. Fabozzi and R.D. Arnott, eds, 2nd edn, Frank J. Fabozzi Associates, 1997. Hotelling, H., “Analysis of a Complex of Statistical Variables into Principal Components”, Journal of Educational Psychology, vol. 24, 1933, pp. 417–441.
c06
WU058-Amenc
194
July 17, 2003
18:8
Char Count= 0
Portfolio Theory and Performance Analysis
Ippolito, R., “Efficiency with Costly Information: a Study of Mutual Fund Performance, 1965–84”, Quarterly Journal of Economics, vol. 104, 1989, pp. 1–23. Jegadeesh, N. and Titman, S., “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency”, Journal of Finance, vol. 48, 1993, pp. 65–91. Kahn, R.N., “Macroeconomic Risk Perspective”, Barra Newsletter 161, summer 1993. Kahn, R.N., “Quantitative Measures of Mutual Fund Risk: An Overview”, Barra Research Publications, July 1995. Kahn, R.N. and Rudd, A., “Does Historical Performance Predict Future Performance?”, Financial Analysts Journal, November–December 1995, pp. 43–52. Kahn, R.N. and Rudd, A., “The Persistence of Equity Style Performance: Evidence from Mutual Fund Data”, in The Handbook of Equity Style Management, T.D. Coggin, F.J. Fabozzi and R.D. Arnott, eds, 2nd edn, Frank J. Fabozzi Associates, 1997. Lawley, D.N. and Maxwell, E., Factor Analysis as a Statistical Method, Butterworths, 1963. Lucas, L. and Riepe, M.W., “The Role of Returns-Based Style Analysis: Understanding, Implementing and Interpreting the Technique”, Ibbotson Associates, May 1996. Marsh, T. and Pfleiderer, P., “The Role of Country and Industry Effects in Explaining Global Stock Returns”, Working Paper, September 1997. Mei, J., “A Semi-Autoregressive Approach to the Arbitrage Pricing Theory”, Journal of Finance, vol. 48, July 1993, pp. 599–620. Meier, J., “Performance Attribution and the International Portfolio”, Barra Newsletter, September– October 1991. Meier, J., “Global Equity Performance Attribution”, Barra Newsletter, spring 1994. Molay, E., “Le mod`ele de rentabilit´e a` trois facteurs de Fama et French (1993): une application sur le march´e fran¸cais”, Banque et March´es, no. 44, January–February 2000. Mott, C.E. and Coker, D.P., “Understanding the Style Benchmarks”, in Equity Style Management, Evaluating and Selecting Investment Styles, R.A. Klein and J. Lederman, eds., Irwin, 1995. Quinton, K., “Style Betas: An Approach to Measuring Style at the Security Level”, in The Handbook of Equity Style Management, T.D. Coggin, F.J. Fabozzi and R.D. Arnott, eds, 2nd edn, Frank J. Fabozzi Associates, 1997. Radcliffe, R.C., “Equity Style Information”, Working Paper, Department of Finance, Insurance and Real Estate, University of Florida, January 2000. Roll, R., “Style Return Differentials: Illusions, Risk Premiums, or Investment Opportunities”, in The Handbook of Equity Style Management, T.D. Coggin, F.J. Fabozzi and R.D. Arnott, eds, 2nd edn, Frank J. Fabozzi Associates, 1997. Roll, R. and Ross, S., “An Empirical Investigation of the Arbitrage Pricing Theory”, Journal of Finance, vol. 35, no. 5, December 1980, pp. 1073–1103. Roll, R. and Ross, S., “The Arbitrage Pricing Theory Approach to Strategic Portfolio Planning”, Financial Analysts Journal, May–June 1984, pp. 14–26. Rosenberg, B., “Choosing a Multiple Factor Model”, Investment Management Review, November– December 1987, pp. 28–35. Ross, S.A., “The Arbitrage Theory of Capital Asset Pricing”, Journal of Economic Theory, vol. 13, December 1976, pp. 341–360. Rudd, A., “On Factor Models”, Barra Newsletter, September–October 1992. Salvati, J., “Mesure de performance et gestion de portefeuille”, in Encyclop´edie des march´es financiers, Economica, 1997, pp. 1122–1139. Sharpe, W.F., “Asset Allocation: Management Style and Performance Measurement”, Journal of Portfolio Management, vol. 18, winter 1992, pp. 7–19. Sheikh, A., “Barra’s Risk Model”, Barra Research Insights, 1996. Simon, Y., Encyclop´edie des march´es financiers, Economica, 1997. Trzcinka, C., “Is Equity Style Management Worth the Effort?: Some Critical Issues for Plan Sponsors”, in The Handbook of Equity Style Management, T.D. Coggin, F.J. Fabozzi and R.D. Arnott, eds, 2nd edn, Frank J. Fabozzi Associates, 1997.
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Reproduced from Portfolio Theory and Performance Analysis, by Noël Amenc and Véronique Le Sourd. 2003. Copyright © John Wiley & Sons Limited. Reproduced with permission.
8 Fixed Income Security Investment All the developments presented up to this point have been more particularly related to the management of equity portfolios because, historically, modern portfolio theory and the quantitative methods that were drawn from it were developed in order to study equity portfolios. Nevertheless, investors generally hold portfolios that are diversified among several asset classes so as to spread their risk and ensure a certain level of consistency in the performance of their investments. Just as it is useful to practise diversification within each asset class to reduce the portfolio risk, diversification between classes also leads to risk reduction. Moreover, a study by Dietz showed that portfolios containing 35%–60% bonds and 40%–60% stocks are those for which the risk-related expected return is optimal. This is explained by the fact that certain periods are more favourable for stock markets, while others are more favourable for bond markets. The use of quantitative methods for managing bond portfolios is more recent than for equities, but it is more and more prevalent. In the previous chapter we presented the investment management process as a whole and studied the performance of a diversified portfolio. Here we describe the particular characteristics of bond investment and the specific performance analysis models used for this type of investment. Before defining the risk and return characteristics of bond portfolios, we first present the yield curve modelling methods that are the basis of bond management.
8.1 MODELLING YIELD CURVES: THE TERM STRUCTURE OF INTEREST RATES The yield curve or term structure of interest rates is the function that associates the level of the interest rate with each maturity. Let r(t) be this function. The term structure of interest rates conditions the prices of bond instruments. Measuring the current rates, forecasting future rates and anticipating shifts in the yield curves allow the future value of rate instruments to be predicted. Modelling the yield curve is therefore essential. The yield curve can be constituted through observation of the prices of financial instruments, by establishing a relationship between the maturities of the securities and the levels of rates. Two alternatives exist: using yield to maturity or using zero-coupon rates. 8.1.1 Yield to maturity and zero-coupon rates1 The yield to maturity r of a bond is defined as the rate that makes its quotation price P equal to the discounted sum of its future cash flows (Fi )i=1,...,n , or P=
n i=1
1
Fi (1 + r )i
Cf. Fitoussi and Sikorav (1991) and Bayser and Pineau (1999).
229
C08
WU058-Amenc
230
July 17, 2003
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
r constitutes the bond’s internal rate of return, but the use of r to define the return that is actually obtained for the bondholder presents a certain number of disadvantages. In order for the rate to correspond to the return obtained at maturity, we must be able to reinvest the coupons at the same rate as r, which is not necessarily the case. In addition, this definition of the rate assumes that the yield curve is flat and that each bond has its own interest rate, while we would wish to have a term structure for the rates with a single rate associated with each maturity. To achieve this, we turn to zero-coupon bonds. A zero-coupon security is a security that only pays out a single cash flow at its expiry date. Let Bt be the elementary zero-coupon security paying out one euro at date t. The zero-coupon price and its t maturity rate of return respect the following relationship: Bt =
1 (1 + rt )t
assuming that the reference date is 0. The complete set of rates rt for the different zero-coupon maturities allows us to define the range of zero-coupon rates. The use of zero-coupon rates allows us to construct a yield curve that associates a single rate with each maturity. The curve that is thereby obtained is then used as a basis for valuing rate instruments and measuring the risks. Any bond that pays out Fi cash flows at dates ti , i = 1, . . . , n, can be modelled by a portfolio of zero-coupon securities, with each cash flow considered to be a zero coupon. The number of zero-coupon securities traded on the markets is not sufficient to allow a direct estimate of the yield curve using those securities. Several models have therefore been proposed using government bonds with maturities that allow all yield curves to be covered. These bonds are coupon bonds. In this case, each coupon is equated to a zero-coupon security with a maturity that corresponds to the date on which the coupon falls. We present the models that allow the zero-coupon rates to be constructed theoretically below. We distinguish between static models (Vasicek–Fong), where the rates are constructed using the coupon bond prices or the yield to maturity, and dynamic models (Vasicek, Cox–Ingersoll and Ross) which model the range of rates with the help of state variables such as the short rate, the long rate and the spread between the long rate and the short rate. 8.1.2 Estimating the range of zero-coupon rates from the range of yields to maturity2 8.1.2.1 Direct method We assume that we observe the range of yields to maturity (an )n=1,...,N . A step-by-step calculation allows us to deduce the range of zero-coupon rates (rn )n=1,...,N . We recall that a bond’s yield to maturity a is defined as the rate that renders its quotation price P equal to the discounted sum of its future cash flows (Fi )i=1,...,n , or P=
n i=1
Fi (1 + a)i
By using the zero-coupon rates we have P=
n i=1
2
Cf. Poncet et al. (1996) and Fabozzi and Fong (1994).
Fi (1 + ri )i
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
231
We consider a fixed-rate bond issued at par, i.e. with a market value equal to its face value. We have the following relationship linking the yields to maturity with the zero-coupon rates: 1=
k i=1
1 ak + , i (1 + ri ) (1 + rk )k
k = 1, . . . , n
where k represents the maturity. For k = 1 we have 1=
a1 1 + 1 + r1 1 + r1
and hence r 1 = a1 For k = 2 we have 1=
a2 1 + a2 + 1 + r1 (1 + r2 )2
from which (1 + r2 )2 =
(1 + a2 )(1 + r1 ) 1 + r 1 − a2
which allows us to calculate r2 . More generally, we can calculate rn as a function of an and the rates (ri )i=1,...,n−1 by considering a security at par with maturity n whose value is written as follows: 1=
n−1 i=1
an 1 + an + (1 + ri )i (1 + rn )n
Hence (1 + rn )n = 1−
1 + an n−1 an i=1
(1 + ri )i
The yield curve for any maturity can then be generated through cubic or linear interpolation methods. These direct methods are theoretically simple and very easy to implement. Unfortunately, significant difficulties prevent us from using them in reality:
r in the markets there are rarely distinct bonds with the same coupon dates, and which also present linearly independent cash flow vectors;
r the method is not robust if the sample of coupon bonds is modified. 8.1.2.2 Indirect methods These difficulties lead us to consider alternative methods that are often called “indirect methods”. The common factor between indirect methods is that they require the market data to be adjusted to a previously specified shape of the yield curve. Although these methods alleviate the practical difficulties mentioned above, they suffer from an eventual specification risk, or model risk. If we choose an inappropriate shape for the yield curve, adjusting the market data to the model will not provide a truly reliable result. A large number of models are used in practice. Here we shall simply present the Vacisek and Fong (1982) model, and, for more details,
C08
WU058-Amenc
July 17, 2003
232
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
we encourage the reader to refer to the work of Martellini and Priaulet (2001) in the same collection. The price of a bond is written as follows: P=
n
Fi Bti
i=1
with Bti =
1 (1 + rti )ti
where Bt represents the discounting factor at time t which is interpreted as the present value of a cash flow amount of 1 paid out at date t or as the present value of a zero-coupon bond with a face value of 1 paid out at time t; and Fti denotes the cash flow paid out at time ti . The proposal from the model is to write the discounting factor in the following form: Bt =
m
βi (1 − e−αt )i
i=1
and to use this expression to calculate the value of the zero-coupon rate. The α and βi parameters are determined using the prices of bonds quoted on the market. Statistical regression allows a yield curve to be constituted using discrete data. These rates can then be used to discount the cash flow of any bond and therefore to calculate its theoretical price. 8.1.3 Dynamic interest rate models3 Empirical studies on the yield curve have highlighted a certain number of characteristics that must be satisfied by any logical model of interest rate dynamics. In particular: 1. The rates cannot become negative. 2. From an historical viewpoint, high rate values tend to be followed, more often than not, by downward movements, which leads us to consider return to the mean effects. 3. Rate volatility tends to be higher for short rates than for long rates; moreover, the level of volatility seems to vary as a function of the absolute level of the rates. These studies have made a positive contribution to our understanding of the process followed by the short rate. Here we present some of the models that are most frequently used in practice. 8.1.3.1 The Vasicek model Vasicek (1977) assumes that only the short rate explains shifts in the zero-coupon yield curve. The short rate follows a diffusion process of the following form: drt = β(α − rt )dt + σ dWt where α denotes the mean interest rate; β denotes the speed of return to the mean; 3
Cf. Joshi and Swertloff (1999).
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
233
σ denotes the volatility of the interest rate; and Wt denotes a real value Brownian motion representing a shock for short rates. While the previous model was a static model, this model is a dynamic model. The interest rate is modelled as a random process that oscillates around the level of the long-term interest rate. The short rate converges towards its assumed long-term value of α at a speed of β. The oscillations around the long-term value have an amplitude of σ . The most widely used method for estimating the model parameters involves extracting them from the price of quoted assets. The model has been presented with constant volatility, but this can be replaced with stochastic volatility. Apart from the difficulty in estimating the parameters, the Vasicek model can produce negative interest rates. 8.1.3.2 The Cox–Ingersoll–Ross (CIR) model The Cox, Ingersoll and Ross (CIR) (1985) model is again a stochastic interest rate model which models a rate that oscillates around its mean. This model is written as follows: √ drt = β(α − rt )dt + σ rt Wt where α β σ Wt
denotes the mean interest rate; denotes the speed of return to the mean; denotes the volatility of the interest rate; and is a Brownian motion which characterises a random shock.
The contribution in comparison with the Vasicek model is that the interest rate volatility is heteroskedastic. When the level of rates increases, the volatility also increases, and when the level decreases, the volatility decreases as well. This ensures that the interest rates produced by the model are always non-negative. 8.1.3.3 The Heath–Jarrow–Morton (HJM) model The approach is analogous to that developed by Black and Scholes (1973) for valuing equity options. By using the spot curve observed on the market, the idea is to equate the underlying with the whole yield curve. This approach is better known as the arbitrage approach. The Heath–Jarrow–Morton (1992) model uses the current forward interest rates to forecast the future short-term interest rates, instead of modelling the rates’ dynamics. By considering a model with a dimension of one, i.e. in which a single forward rate explains the whole rate structure, and by denoting the instantaneous forward rate at time t for maturity T as f (t, T ), we have the following relationships: d f (t, T ) = α1 (t, T )dt + σ1 (t, T )dWt dB(t, T ) = α2 (t, T )dt − σ2 (t, T )dWt B(t, T ) where α1 and α2 denote given functions; σ1 denotes the volatility of the forward rate;
C08
WU058-Amenc
234
July 17, 2003
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
σ2 denotes the volatility of the zero-coupon bond; and Wt is a Brownian motion with a dimension of one. The volatilities σ1 and σ2 respect the following relationship: T σ2 (t, T ) = σ1 (t, u)du t
Implementation of this model is complex.
8.2 MANAGING A BOND PORTFOLIO The first section of this chapter gave us an overview of the yield curve estimation models, which condition bond prices. We now come to the actual management of bond portfolios. The investment strategy adopted by the manager conditions the performance of the portfolio. It is necessary to dispose of and evaluate the risk factors to which the portfolio is subjected in order to analyse the strategy. Before turning to the definition of the different types of risks for bond portfolios and the analysis of the risks, by studying yield curve shifts, we first describe the quantitative analysis framework for bond portfolios. 8.2.1 Quantitative analysis of bond portfolios4 The use of quantitative techniques for managing bond portfolios is becoming more and more widespread. Quantitative techniques are applied to virtually all stages in the portfolio management process. The first stage is to define asset allocation: we choose to divide the portfolio between different asset classes, while taking into account constraints on the duration, the active–passive profile and the diversification and liquidity requirements. The next stage involves choosing the benchmark, or defining a bespoke benchmark. The final stage consists of analysing the performance obtained. In Chapter 2 we discussed the usefulness of benchmarks and the construction of benchmarks for equity portfolios in particular. Defining a benchmark is also essential for managing a bond portfolio. The benchmark can be a broad bond index or a sector index. This type of index is produced by specialised firms. In the United States, Lehman Brothers produce the Lehman Aggregate index, Salomon Brothers the Salomon Broad Investment Grade (BIG) index and Merrill Lynch the Merrill Lynch Domestic Master index. However, these indices may not correspond to the needs of investors who will prefer, if that is the case, to produce customised benchmarks that accurately reflect the composition of their portfolio. A customised benchmark can be defined using a standard benchmark by only keeping certain sectors, for example. It can also be defined by modifying the percentages of the different categories of bonds compared with an index quoted on the market. Finally, it can be constructed more accurately by using individual investment specifications, in terms of sector allocation, choice of bond categories, the active–passive balance and liquidity, for each investor. Each portfolio has its own objectives and constraints. This can be translated into risk and return terms and conditions the choice of assets that can be included in the portfolio. For the evaluation to be correct, it is therefore important to dispose of a benchmark that is subject to the same constraints as the portfolio to be 4
Cf. Dynkin and Hyman (1998).
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
235
evaluated. Once the benchmark has been defined, investors can express their return objectives and risk constraints in terms of deviation from the benchmark. In Section 8.3 we shall see that performance measurement also relies on the portfolio’s benchmark. The evaluation methods for the securities must therefore be consistent, for both the portfolio and its benchmark. This is now ensured by the existence of the AIMR standards. 8.2.2 Defining the risks A bond is a security with a limited life span. It is a less risky product than a stock. It is however subject to two types of risk that explain the variations in bond returns: the default risk (or spread risk) and the market risk (or risk of interest rate fluctuations). The risk factors for bonds are different from the risk factors for stocks, even though we can draw some comparisons. The duration of a bond, which measures the market risk, can be compared to the beta of a stock, for example. 8.2.2.1 Default risk The spread risk is connected to the risk of the issuer defaulting. The quality of the issuer is measured through a rating attributed to the bond by the rating agencies. A modification in the rating leads to a variation in the price of the bond and therefore to a modification in its spread. It should be noted that the bonds with the best ratings are those that pay out the lowest coupons, in line with the risk premium principle. In what follows we offer an overview of the methods for approaching the question of default risk. From a schematic point of view, these methods are of two different types: value of the firm-based models (which are also called structural models) and intensity-based models (which are also called reduced-form models). The value of the firm-based models are characterised by the fact that the default date is determined by the date at which the process describing the value of the firm reaches a frontier. In the seminal works of Black and Scholes (1973) and Merton (1974) it is in fact assumed that the default can only occur on the bond security’s maturity date. This framework was generalised by Black and Cox (1976), who consider a default date that is triggered when the value of the firm’s assets reaches a given threshold. The reduced-form models, on the contrary, do not seek to analyse the default process. They prefer to focus on modelling a default that occurs at a random date, which is defined as the first jump date of a Poisson process. This approach has been the subject of a large amount of recent work (Jarrow and Turnbull, 1995; Madan and Unal, 1995; Duffie et al., 1996; Duffie and Singleton, 1997; Duffie and Lando, 1997; and Lando, 1996; for example). 8.2.2.2 Market risk The risk of a shift in the yield curve is evaluated as a first approximation by the duration. The duration measures the average weighted duration of the time period required for the value of a bond to be paid back by the cash flow that it generates. The duration is the average life span of a bond. In general, it is shorter than the maturity, except in the case of a zero-coupon bond.
C08
WU058-Amenc
236
July 17, 2003
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
For a bond P with a price defined by the yield to maturity r, or P=
n i=1
Fi (1 + r )i
the duration is written as follows: n
D=
i Fi (1 + r )i i=1
P A portfolio’s exposure to movements in the yield curve is measured by the modified duration (or sensitivity). The sensitivity is written as follows: S=−
n 1 1 dP i Fi = P dr P i=1 (1 + r )i+1
We can also calculate the convexity, defined by C=
n 1 d2 P i(i + 1)Fi 1 = P dr 2 P i=1 (1 + r )i+2
The duration assumes that the yield curve is only subject to parallel shifts. However, the yield curve may be subject to three types of shift: a parallel shift, a butterfly shift or a twist. A factor model allows all the possible shifts to be explained completely. 8.2.3 Factor models for explaining yield curve shifts The factor decomposition methods for the risk rely on statistical analysis of zero-coupon yield curve shifts observed in the past. Several models have been proposed. Since a bond portfolio can be modelled by a set of zero-coupon bonds, which depend on the structure of spot rates, we will show how to describe the spot rates with the help of a factor structure and deduce from this a factorial characterisation of the portfolio’s risk and return. 8.2.3.1 Litterman and Scheinkman model5 The Litterman and Scheinkman model uses past data to construct a factorial structure for decomposing the shifts in the yield curve. The factors, which cannot be observed, are extracted from the variance–covariance matrix of changes to the spot rates, with the help of a principal component analysis method. We outlined the principles of this method in Chapter 6. Litterman and Scheinkman identify three explanatory factors, with each factor corresponding to a possible shift in the yield curve. The first factor is a level factor which takes into account the parallel shifts in the yield curve. This initial factor is not sufficient to describe the yield curve completely, which is why it is necessary to add other factors. A second factor takes into account a change in the slope of the yield curve. The third factor characterises the curvature. These three factors have decreasing degrees of explanatory power. The first factor explains on average 73% of the variations. Studies have shown that the three factors explained around 95% of the yield curve movements for the United States. 5
Cf. Knez et al. (1994).
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
237
Some criticisms have been formulated with regard to this method. The first is that since the principal components are linear combinations of movements in the yield curve taken as a whole, they are difficult to forecast. The second criticism is that if the analysis is carried out for a non-American market, then there is no guarantee that the principal components identified will be of the same nature as those proposed in the model. Finally, this approach does not provide a direct measure of a bond or a bond portfolio’s sensitivity to changes in the factors. These criticisms are formulated in JP Morgan (1996a), who proposes another method. 8.2.3.2 JP Morgan method The method proposed by JP Morgan (1996a) should allow us to determine the sensitivity of a bond, or any bond portfolio, to non-parallel shifts in the yield curve, while avoiding the disadvantages of the other methods. The result is a characterisation of the risk of a portfolio in terms of sensitivity to rate movements at different points on the curve. The spot rate is influenced by a certain number of factors, which are the same for all maturities, but their impact on the portfolio will vary depending on the maturity. The variation in these factors leads to modifications in the value of the rates, depending on the sensitivity of the rates to each of the factors. The variation in the spot rate with maturity m, in country j and at time t, as a function of the factors is given by j
St (m) =
K
j
j
βk (m)Fkt
k=1
where m denotes the maturity; βk (m) denotes the sensitivity in relation to factor k; the sensitivities are functions of the maturity; and Fk denotes the change in factor k. The instantaneous change in the price of a zero coupon resulting from a small change in the spot rate is equal to the change in the spot rate multiplied by the duration of the zero coupon. This duration is equal to its maturity. We therefore have j
Z t (m) j
Z t (m)
j
= −mSt (m)
j
where Z t (m) denotes the price of the zero-coupon with maturity m, in country j and at time t. By replacing the variation in the spot rate as a function of its factorial expression in this expression, we obtain: j
Z t (m) j Z t (m)
= −m
K
j
j
βk (m)Fkt
k=1
We define the duration of the zero-coupon bond with maturity m in relation to the kth factor as j
j
Dk (m) = mβk (m)
C08
WU058-Amenc
July 17, 2003
238
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
which allows us to write j
Z t (m) j
Z t (m)
=−
K
j
j
Dk (m)Fkt
k=1
Any bond or bond portfolio can be represented by a portfolio of zero-coupon bonds, where each zero-coupon bond corresponds to a cash flow from the bond. The variation in the value of the bond portfolio can therefore be written as a linear combination of the variations in the value of the zero-coupon bonds, or j
Bt j
Bt
=
n i=1
j
xi
Z t (m i )
=−
j
n
xi
K
Z t (m i ) i=1 k=1 K n j j =− xi Dk (m i )Fkt
j
j
Dk (m i )Fkt
k=1 i=1 j Bt
where denotes the value of the bond portfolio at time t, in country j; and xi denotes the proportion represented by the current value of the ith cash flow in relation to the total value of the portfolio. We define the duration of the bond portfolio in relation to the kth factor as n
j
Dk (B) =
j
xi Dk (m i )
i=1
Hence j
Bt j
Bt
=−
K
j
j
Dk (B)Fkt
k=1
We therefore establish that the return of a bond portfolio depends only on a finite number of factors, rather than a complete spot rate structure. The coefficients of the factorial decomposition are the duration of the portfolio in relation to each of the three shifts in the yield curve. It is then necessary to construct the explanatory factors. The method used by JP Morgan is based on Ho’s (1992) key observable rates approach, but removes the assumption of rate independence and therefore takes into account the correlation between the rates for the different maturities. The factors are obtained by linearly combining the key rates and are orthogonal by construction. 8.2.4 Optimising a bond portfolio6 The construction of a bond portfolio relies more on the choice of a category of bonds presenting the same characteristics (duration, maturity, etc.) than on the choice of individual securities. The factorial structure defined in the previous section allows us to characterise the risk and return of a bond portfolio according to its sensitivity to variations in the factors. The return of a portfolio is written as follows: R Pt − RFt =
K k=1
where RFt denotes the risk-free rate. 6
Cf. JP Morgan (1996b).
j
j
Dk (B)Fkt
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
239
When we know the current rates and the expected future rates, the optimisation involves determining the portfolio that allows a given level of out-performance to be reached in relation to a benchmark specified in advance with a minimum tracking-error. The performance of the portfolio in excess of that of the benchmark can be characterised in terms of the duration differential between the two portfolios, or R Pt − R Bt =
K
j j j Dk (B) − dk (B) Fkt
k=1
where
j dk (B)
denotes the duration of the benchmark compared with the kth factor.
8.2.5 Bond investment strategies As a consequence of the particular nature of fixed income securities, the strategies used to manage fixed income portfolios differ from those used to manage equity portfolios. Bonds are characterised by their maturity, the spread, the quality of the security and the coupon rate. A fixed income portfolio could be managed according to a duration strategy, a sector weighting strategy or a maturity distribution strategy. The rate risk indicators such as the duration, the sensitivity and the convexity allow the impact on bonds of variations in interest rates to be measured. The objective is always to obtain the best return for a given level of risk. The portfolio is constructed in accordance with the characteristic bond indicators. The investment strategies used can be passive, such as replicating an index or immunising the portfolio against interest rate risk, or active. Active investment involves forecasting interest rates to anticipate movements in the bond market as a whole or carrying out an analysis of the market in order to identify the sectors or securities that have been incorrectly valued. In an interest rate strategy the positioning of the portfolio on the maturity spectrum will depend on the anticipated evolution of the yield curve. The security or sector selection requires the preferences to be quantified in accordance with the individual characteristics of the securities. The securities can be classified according to their default risk or according to their spread. The default risk is the likelihood that the issuer will not respect his contractual obligation, i.e. that he will not be able to redeem the security at its expiry date or that he will no longer be in a position to pay the coupons. A rating is attributed to bonds according to the quality of the issuer. When an issuer’s default risk increases, the ranking of the security may be lowered. Bonds can be grouped together by sector, i.e. by sub-classes that behave in a similar manner. For example, bonds with the same level of ranking will have prices and returns that evolve in the same way. The price differential between bonds in different sectors can undergo modifications in several situations: if the sector’s default risk increases, if the market’s evaluation of the attributes and characteristics of the securities in the sector is modified or if there are modifications in supply and demand. The difference in return between two sectors, which is usually measured in basis points, is called the spread. Analysing the spread gives a relative evaluation of the interesting sectors. This is useful for investing in the sectors where the securities will have the strongest rate of appreciation. Individual securities are analysed by evaluating their risk premium, i.e. the difference between the return of the bond and that of the risk-free rate. This risk premium is the investor’s compensation for the risk taken. The manager’s investment choices in relation to the maturity of the securities indicate how he has positioned his portfolio on the yield curves and the returns of each maturity class then
C08
WU058-Amenc
240
July 17, 2003
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
show the evolution of the rates over the investment period. Choosing securities according to the value of their coupons is also linked to the manager’s anticipation of the level of future rates. If he anticipates a rise in rates, then he will choose securities with a high coupon. 8.2.6 International fixed income security investment7 In the same way as for equities, international investment widens the field of investment and increases the expected return of the portfolio while limiting the risks. In this case we use an international benchmark. An international fixed income security portfolio’s risk is made up of the risk of each local market and a significant share of exchange rate risk. As for equities, the return can be divided into the local return and the currency return. This decomposition has an impact on the variance–covariance matrix, which is broken down into two blocks: one block for the local market and one block for the currency. The two blocks in the matrix are estimated separately. Although exchange rate risk has little impact on equity investments, it affects fixed income security investments considerably, because the evolution of interest rates and exchange rates is linked. Interest rates influence exchange rates in the short term and exchange rates influence interest rates. To avoid an unfavourable turn in the exchange rates overriding the risk reduction advantage procured through diversification, it is desirable to hedge against exchange rate risk and use a hedged benchmark.
8.3 PERFORMANCE ANALYSIS FOR FIXED INCOME SECURITY PORTFOLIOS The most thorough studies on performance analysis relate to equity portfolios. The first models were developed from the Capital Asset Pricing Model (CAPM), which only concerns portfolios invested in equities and cash. In addition, portfolio analysis originated in the United States, where portfolios are principally invested in equities. In France, the market for fixed income securities is considerable, but traditional models lead to inappropriate conclusions if the funds contain bonds because the characteristics of bonds are very different from the characteristics of equities. This is why it is necessary to look at specific performance analysis for portfolios, or parts of portfolios, that are invested in bonds. As for equity portfolios, analysing the performance of bond portfolios initially involves measuring their return and comparing the result with that of the benchmark associated with the portfolio. The performance can then be decomposed and explained. Performance attribution for fixed income securities is still the subject of a large amount of research. The analysis can involve an approach by strategy or a factor approach. The factor approach consists of explaining the return of the portfolio through the return of the identified factors. A multi-factor model allows us to forecast the ex ante risk associated with each factor and to measure the return generated by the factors. An approach of this type allows the sources of the portfolio return to be identified in detail, and also allows the statistical significance of the returns to be measured. It is possible to carry out several types of analysis to study portfolio performance, depending on whether we study the portfolio return in an absolute manner, or in a relative manner compared with a benchmark. In this section we present the different types of portfolio performance analysis and decomposition. We initially describe performance analysis in comparison with 7
Cf. Murphy and Won (1995) and Faillace and Thomas (1997).
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
241
a benchmark, and then we give additive decompositions of bond portfolio returns that do not use a multi-factor approach. We then present models that use a multi-factor approach. In Section 8.2 we presented a factorial decomposition of the price of a bond. There are other possible decompositions. The bond performance attribution models are then modelled on these decompositions. 8.3.1 Performance attribution in comparison with a benchmark Performance attribution in relation to a benchmark involves comparing the portfolio’s rate of return with that of its benchmark and evaluating the difference. The benchmark’s return is provided by a specialised firm in the case of a standard benchmark. For customised benchmarks, the firms provide returns for each component of the benchmark. The portfolio return is calculated by the manager. Using uniform methods is therefore very important and that is why the AIMR calculation standards are useful. This analysis takes place within the framework of benchmarked fixed income security investment. The performance differential between the portfolio and its benchmark can then be analysed in order to understand the source of the differential and interpret it in relation to the investment strategy chosen by the manager and his exposure to the different risk factors. Performance attribution allows us to explain the differences in return between the portfolio and its benchmark, rather than the returns themselves. It does not explain the total return of each security, but rather the relative performance of the portfolio compared with the benchmark in terms of the allocation differences between the two. This allows us, therefore, to analyse the manager’s allocation decisions and the benefits procured by the over- or underweighting of the different sectors in the portfolio. For example, if each asset class in the portfolio has had the same return as the asset class in the corresponding benchmark, then the difference in performance between the portfolio and its benchmark will only be due to a different choice of weightings between the portfolio and its benchmark, i.e. the manager’s allocation choices. The analysis can be carried out on several levels. We can, for example, analyse the portfolio by portion of duration, and then analyse the composition by sector within each portion of duration. The excess performance of the portfolio compared with its benchmark can be explained in terms of positioning on the yield curve, sector allocation and security selection. A little later in this chapter we give a detailed presentation of performance decomposition for fixed income security portfolios which corresponds to the stages in the investment management process. We should mention that there is an additional difficulty for bond portfolios compared with equity portfolios. Since bonds have a limited life span, the composition of the portfolio evolves over time, which gives additional reasons for the portfolio to deviate from its benchmark. 8.3.2 The Lehman Brothers performance attribution model8 Lehman Brothers developed a performance attribution model that allows the return of each asset to be decomposed and the different portions of performance to be attributed to the following factors: the passing of time; shifts in the yield curve; changes in volatility and changes in spreads. The results, security by security, of the decomposition are then aggregated at the portfolio level, thereby allowing the portfolio performance to be explained. 8
Cf. Dynkin et al. (1998).
C08
WU058-Amenc
242
July 17, 2003
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
The prices of fixed income securities are affected by the passing of time and yield curve movements, with the latter factor accounting for the largest share. The model developed by Lehman Brothers produces an approximation of the real movements in the yield curve by using a combination of the three basic movements: the parallel shift, the twist and the butterfly shift. For a given month, the model first identifies all the modifications in the market and then divides the return of each security into several components, each being associated with a modification in the market. The model defines the components of the yield curve movements as intuitively as possible and attempts to attribute the realised returns to each component as accurately as possible. The model is based on changes in the official market rates, which can be observed on the market, rather than rates obtained through calculation. For each month, the real changes in the yield curve are described with the help of the three basic movements. Each of these components is a linear function by portions using two-, five-, 10- and 30-year variations in rates. The return that comes from a parallel shift in the yield curve (the shift return) is expressed as the average change in the official two-, five-, 10- and 30-year market rates, or s = 1/4(y2 + y5 + y10 + y30 ) The slope of the yield curve can undergo modifications, such as a flattening or, on the contrary, an increase in the slope around the five-year rate. The resulting return (the twist return) is quantified through the change in the spread between the official two- and 30-year market rates, or t = y30 − y2 The slope of the yield curve may also be subject to a butterfly shift when the middle of the curve moves in the opposite direction to its extremities. The resulting return (the butterfly return) is determined through the differential between the average of the two- and 30-year rates and the five-year rate, or b = 1/2(y2 + y30 ) − y5 The residual return, or shape return, is the yield curve return that is not explained by the three types of yield curve shift. The Lehman Brothers model constructs a sequence of progressive changes to move from the environment at the start of the month to the environment at the end of the month. The bonds are valued at each of these stages. Each component of return is given by the difference in price between two successive valuations. The Lehman Brothers method presents an advantage over methods that use the sensitivities at the start of the month. The methods that use the start of the month parameters do not integrate the fact that changes in the yield curve modify the risk characteristics of all securities with cash flow that depends on the interest rates, which can lead to significant errors when calculating the components of the return. The yield curve shift decomposition in the Lehman Brothers model was developed on the basis of statistical studies on the historical behaviour of government loans. Tests were carried out to validate the model. The tests showed that the model gave more accurate explanations of shifts in the yield curve than other models such as principal component analysis. This decomposition applied to the return of a portfolio and that of its benchmark allows the performance of the portfolio to be analysed within the framework of both passive investment and active investment. In active investment, the manager seeks to obtain a higher return for
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
243
his portfolio by choosing a strategy based on his anticipations for the market in terms of yield curve evolution. To do this, the portfolio will voluntarily deviate from the benchmark on one or more aspects. Separating the portfolio return into several components allows us to analyse the effect of the different investment strategies on the overall performance of the portfolio. In the case of passive investment, where the objective is to track the performance of the benchmark, the return differentials between the portfolio and the benchmark must be monitored closely. It is therefore useful to have a precise understanding of the origins of the return differences between the portfolio and the benchmark, in the case of underperformance, so as to carry out the necessary modifications to the portfolio. 8.3.3 Additive decomposition of a fixed income portfolio’s performance9 We have seen that the study of performance attribution for fixed income portfolios must be based on indicators that are characteristic of this class of assets, such as the duration, the maturity and the spread. These indicators can be tricky to estimate. Fong et al. (1983) proposed a solution for decomposing the return of a fixed income portfolio. The principle consists of separating the portfolio return into two components: a component that comes from the financial environment, over which the manager has no control, and a component that corresponds to the manager’s value-added, or R = I +C where I denotes the effect of the interest rates’ financial environment; and C denotes the manager’s contribution. Each of these two terms can be decomposed again. I corresponds to the return of the bond market considered globally. It can be decomposed into two terms: a predictable component and an unanticipated component, which comes from changes in the interest rates, or I = E +U where E denotes the share of return obtained in the absence of modifications to the rate structure; and U denotes the share of return that comes from a modification in the rate structure. The value of I is observed on the market: it is given by the value of a fixed income security index. The value of E must be estimated and the value of U is then obtained by calculating the difference between I and E. The manager’s value-added is obtained globally as the difference between the portfolio return and the return I of the fixed income security index. This component can then be divided into three terms: a term linked to the choice of maturity, a term linked to the choice of sector and finally a security selection term, or C =M+S+B where M denotes the share of return that comes from managing the maturity (or managing the duration); S denotes the share of return that comes from managing the spreads; and B denotes the share of return that comes from the choices of individual securities. 9
Cf. Fabozzi and Fong (1994), la Bruslerie (1990), Elton and Gruber (1995), Fabozzi (1995) and Grandin (1998).
C08
WU058-Amenc
July 17, 2003
244
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
The management of the maturity has the greatest impact on portfolio performance. The success of the manager’s decisions depends on his capacity to anticipate evolutions in interest rates. To estimate this component, we simulate the portfolio result by eliminating the effects of the other two components. Managing the sector and the quality relates to how the portfolio is divided between the different compartments of the fixed income security market. It involves measuring the manager’s capacity to identify the right sector at the right time. This component is estimated by carrying out a simulation in which the other two effects are neutralised. The individual selection of securities consists of choosing, within each bond category, the securities for which we anticipate the best performance. This effect is measured as the difference between the overall portfolio return and all the other effects identified. This performance decomposition method is suitable for a portfolio that is solely invested in domestic assets. Solnik proposed a decomposition model in the international framework, which we present in the following section. 8.3.4 International Performance Analysis (IPA)10 This model was developed by Solnik. It focuses on the effect on performance of the choices between the different international markets, without entering into performance decomposition within each market. The return of each portfolio currency compartment is initially evaluated independently. If we take V jt as the value of the assets held in currency j at time t, then the return on the portfolio compartment in currency j is given by Rj =
V jt
−1
V jt−1
Part of the value of V j is made up of income such as the coupons cashed in during the period. The overall return can therefore be decomposed into two terms: R j = Pj + C j − 1 where P j denotes the gain or loss of capital, as a relative value; and C j denotes the current return, which comes from the income. The return can be converted into the reference currency by using the exchange rate S j for currency j, or R Ref = j
S tj V jt t−1 S t−1 j Vj
−1
We define the percentage currency gain, or loss, over the period as s, which gives us 1 + sj =
S tj S t−1 j
Hence R Ref = (1 + s j )(1 + R j ) − 1 j 10
This model is described in la Bruslerie (1990) and in Solnik (1999).
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
245
and by replacing R j with its decomposition: = P j + C j + s j (P j + C j ) − 1 R Ref j This expression reveals a term that measures the impact of exchange rate fluctuations on the return expressed in the reference currency. We shall call this term e j . We have e j = s j (P j + C j ) and hence R Ref = Pj + C j + e j − 1 j Let us now consider the return of our entire portfolio. It is equal to the weighted sum of the investment returns in each currency. Taking x j as the weighting of each compartment in the portfolio, the overall portfolio return is given by RP = x j Pj + xjCj + xjej − 1 j
j
j
The portfolio performance realised on a market j can be compared with the performance I j of an index on that market. The overall portfolio performance can then be rewritten in the following manner: RP = xj Ij + x j (P j + C j − I j ) + xjej − 1 j
j
j
The first term represents the weighted mean of the local market indices. It gives the return of a well-diversified international portfolio. The second term measures the manager’s selection capacity in each market. The third term corresponds to the contribution of the exchange rate gains or losses to the overall portfolio performance. This analysis considers that the portfolio weightings remain constant, but in practice the manager regularly adjusts his portfolio between the different markets, which contributes to the performance result. By introducing the weighting differentials between the managed portfolio and an international reference index, we can identify three terms in the performance evaluation: strategic allocation, tactical allocation or timing, and stock picking. This was presented in detail in Chapter 7. We discuss an adaptation of the model presented in Chapter 7 to the specific case of bonds below. 8.3.5 Performance decomposition in line with the stages in the investment management process Decomposing performance in accordance with the stages in the investment management process, as it was presented in Chapter 7, is valid for all asset classes, but the particular nature of bonds has led to the development of more appropriate decompositions. In the case of bonds, the asset allocation term remains useful because it measures the contribution to the excess return that comes from the portfolio’s exposure to a given risk. But the stock picking term provides little information. It is more useful to replace it with a decomposition term according to the sensitivities to the risk factors. The share of return that is not explained by the risk factors constitutes a residual stock picking term.
C08
WU058-Amenc
July 17, 2003
246
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
The complete decomposition identifies the following terms (see Kuberek, 1995): 1. A return term that comes from the currency effect, which is written as follows: (w ph − wbh )x˜ h h
where w ph denotes the weight of currency h in the portfolio; wbh denotes the weight of currency h in the benchmark; and x˜ h denotes the hedged return of currency h. 2. A return term that comes from asset allocation, which is written as follows: (w pi − wbi )H˜ i i
where w pi denotes the weight of class i in the portfolio; wbi denotes the weight of class i in the benchmark; and H˜ i denotes the excess return of class i. The asset classes are represented by specific indices. 3. A term that comes from the decomposition of the return according to the risk factors within each asset class, which is written as follows: w pi (b pi j − bbi j ) Q˜ i j i
j
where w pi b pi j bbi j Q˜ i j
denotes the weight of class i in the portfolio; denotes the portfolio’s exposure to risk factor j for class i; denotes the benchmark’s exposure to risk factor j for class i; and denotes the excess return compared to risk factor j.
The risk factors used are characteristic of fixed income securities and can be the duration, the maturity or the sector. This term allows the performance to be explained precisely by groups of bonds with the same characteristics. 4. Finally, an ultimate residual term that comes from security selection, once all the other effects have been eliminated, which is written: R˜ P − w ph x˜ h − w pi H˜ i − w pi (b pi j − bbi j ) Q˜ j h
i
i
j
where R˜ P denotes the total portfolio return. As in all the decompositions presented, the size of the study periods chosen is important. Originally monthly or quarterly, performance attribution is evolving in the direction of daily analysis, which ensures that the portfolio composition is fixed over the calculation period.
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
247
8.3.6 Performance decomposition for multiple currency portfolios To complement the performance decomposition model proposed by Kuberek, we present the model developed by McLaren (2002), which gives details on performance attribution for a multiple-currency portfolio. This model provides a precise explanation for the relationship between portfolio performance and the manager’s investment decisions and explicitly accounts for the duration decisions. The model is initially described from a single-currency perspective and then a currency return analysis is performed. The portfolio analysis is carried out sector by sector, where a sector represents any grouping of assets (for example, type of issuer, credit quality or industrial sector). The total performance is then obtained by adding together the performance of each sector. Comparing the performance of the portfolio with that of the benchmark allows us to identify four effects: the duration contribution, the spread contribution, the selection effect and the interaction effect. We define the following variables: L ai L pi L yi Wai W pi
is the local return of the fund for sector i; is the local return of the benchmark for sector i; is the local return of the yield curve for sector i; is the weight of the fund for sector i; and is the weight of the benchmark for sector i.
Using this notation, the return of sector i is given by Wai L ai for the portfolio and by W pi L pi for the benchmark. The analysis involves decomposing the difference between these two terms into several components. Initially, we will only consider single-currency analysis. The duration contribution is defined as that part of the total contribution that would have been achieved if the fund were invested in bonds that have no risk premium or credit component. The duration contribution is then the result of under- or overweighting segments of the yield curve relative to the normal weights identified by the benchmark or policy: (Wai − W pi ) L yi The spread contribution is that part of the total contribution that is not explained by the duration contribution. Its value is obtained by under- or overweighting the various spreads relative to the normal weights identified by the benchmark or policy: (Wai − W pi )(L pi − L yi ) The selection term measures the active investment decisions concerning the bonds within each sector: Sri = W pi (L ai − L pi ) The interaction term is due to the interaction between the allocation and bond selection contributions: Ii = (L ai − L pi )(Wai − W pi ) Using these four terms, we can write the following decomposition: Wai L ai − W pi L pi = (Wai − W pi ) L yi + (Wai − W pi )(L pi − L yi ) + W pi (L ai − L pi ) + (L ai − L pi )(Wai − W pi )
C08
WU058-Amenc
248
July 17, 2003
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
This model can be extended to analyse multiple-currency portfolios by adding a currency component. McLaren describes two different ways of analysing this component: comparing the fund currency returns with the benchmark currency returns, and comparing the fund currency returns with forward currency returns. We have chosen to limit the presentation to the benchmark analysis. The reader interested in further analysis should refer to McLaren’s article. We define the following variables: CRai is the currency return of the fund for sector i; and CR pi is the currency return of the benchmark for sector i. Using this notation, the currency contribution of the fund sector is given by Cai = Wai CRai and the currency contribution of the benchmark is given by C pi = W pi CR pi . The outperformance of the portfolio as a result of currency decisions is the difference between these two terms. We identify the following two components: 1. The currency allocation, defined as that part of the outperformance resulting from allocation decisions: (Wai − W pi )CR pi 2. The currency timing, measuring the difference between the fund and benchmark currency returns encountered when trading occurred during the period. Here the interaction between allocation and timing has been added to the pure currency timing term: CTri = Wai (CRai − CR pi ) We can then write the following decomposition for the currency term: Cri = Wai CRai − W pi CR pi = (Wai − W pi )CR pi + Wai (CRai − CR pi )
8.3.7 The APT model applied to fixed income security portfolios This model, which was developed by Elton et al. (1995), uses both indices and macroeconomic variables to explain the returns and expected returns of bonds. The authors underline the fact that, in spite of the importance of the fixed income security markets, little attention has been given to applying models based on Ross’s APT to the valuation of bonds. Nevertheless, the APT model, which was presented in detail in Chapter 6, can also be used for fixed income security portfolios. The factors used are indices traded on the markets and factors measuring the unanticipated variations in economic variables. The return of a security is given by Rit = E(Ri ) +
J
βi j (R jt − E(R j )) +
j=1
where Rit denotes the return on asset i at time t; R jt denotes the return on a tradable portfolio j at time t;
K k=1
γik gkt + ηit
(8.1)
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
gkt βi j γik ηit
249
denotes the unexpected change in the kth economic variable at time t with E(gk ) = 0; denotes the sensitivity of asset i to the innovation of the jth portfolio; denotes the sensitivity of asset i to the innovation of the kth economic factor; and denotes the return on asset i at time t, not explained by the factors and the indices, with E(ηi ) = 0.
Arbitrage reasoning allows us to write the following: E(Ri ) = RFt +
J
βi j λ j +
j=1
K
γik λk
k=1
where RFt denotes the return of the risk-free asset; λ j denotes the risk premium of index j; and λk denotes the risk premium of the kth economic variable. When the variables are indices traded on the markets, the risk premium is written as follows: λ j = E(R j ) − RF Through substitution, we obtain the following: E(Ri ) = RFt +
J
βi j (E(R j ) − RF ) +
j=1
K
γik λk
k=1
By bringing this expression into equation (8.1) we obtain: Rit = RFt +
J
βi j (R jt − RFt ) +
j=1
K
γik (λk + gkt ) + ηit
k=1
which can also be written Rit − RFt = αi +
J
βi j (R jt − RFt ) +
j=1
K
γik gkt + ηit
k=1
where αi =
K
γik λk
k=1
This model is a multi-factor model in which αi must respect a particular relationship. The model was tested with several series of factors. Once the model has been developed and the parameters set, it can be used to evaluate the performance of fixed income security portfolios. 8.3.8 The Khoury, Veilleux and Viau model This model is a performance attribution model for fixed income security portfolios. The form of the model is multiplicative, so as to be able to handle investments over several periods. The model identifies 11 factors that are liable to influence the value of bonds. For the moment, the model has been studied more often than it has been applied.
C08
WU058-Amenc
July 17, 2003
250
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
Traditionally, multi-factor models are formulated in the following way: R Pt =
K
βPk Fkt + uPt
k=1
where R Pt βPk Fkt u Pt
denotes the return of portfolio P for period t; denotes the sensitivity of the portfolio to factor k; denotes the return of factor k over period t; and denotes the specific return of the portfolio over period t.
In order to be able to combine the returns over time, the model can be written in multiplicative form, or (1 + R Pt ) =
K
(1 + βPk Fkt )(1 + uPt )
k=1
The factors proposed are divided between factors linked to the spread risk and factors linked to the risk of yield curve shift. The latter factors take into account the different types of possible shift: parallel shifts, changes in curvature and butterfly risk. With this formula, the portfolio and benchmark performance results are compared by calculating their return ratio, or K
(1 + R Pt ) k=1 = K (1 + R Bt )
(1 + βPk Fkt )(1 + uPt ) (1 + βBk Fkt )(1 + uBt )
k=1
where the benchmark is decomposed in the same way as the portfolio. The Khoury et al. (1997) article presents the construction of the explanatory factors in detail. 8.3.9 The Barra model for fixed income security portfolios11 Kahn (1991) describes the performance attribution model for bond portfolios used by Barra. It is a multi-factor model. The factors used to explain the return of the portfolio for each period are the usual specific factors for bonds, linked to the maturity, the spread, the quality of the issuer and the risk of yield curve shift. Applied to a single period, this model allows us to identify the sources of portfolio performance period by period. The results for each period can then be combined to evaluate the manager and separate the share of performance due to luck from the share of performance due to skill. This multi-period analysis involves studying the series of returns attributed to each factor. The study allows us to check whether the return attributed to a factor for a period remains significant over time. To do so, we evaluate the t-statistic of the series, a notion that we defined in Chapter 4. 11
Cf. Algert and Leverone (1992), Davis (1991) and Kahn (1991).
C08
WU058-Amenc
July 17, 2003
18:18
Char Count= 0
Fixed Income Security Investment
251
8.3.10 Decomposition with hedging of the exchange rate risk The excess return, compared with a benchmark portfolio, of an international fixed income portfolio that is hedged against exchange rate risk can be decomposed into three terms. The first term measures the return linked to the allocation by country. It measures the impact of a different benchmark allocation in terms of countries by assuming that the durations in each country are equal to their optimal levels. The second term measures the return that comes from a different allocation within each country and gives the excess return of a portfolio invested, like the benchmark, in terms of allocation by country, but with different durations within each country. The final term measures the return compared with the different exchange rate hedging parameters. The precise formula is described in the appendix to JP Morgan (1996b). We discussed this point in the previous chapter, when analysing the investment management process for an international portfolio.
BIBLIOGRAPHY Algert, S. and Leverone, M., “Fixed Income Performance Analysis Over Time”, Barra Newsletter, January–February 1992. Banque Strat´egie, “Les march´es obligataires”, January 1999. Bayser, X. (de) and Pineau, F., “La gestion obligataire quantitative mod´elis´ee”, Banque Strat´egie no. 156, January 1999, pp. 19–22. Black, F. and Cox, J.C., “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions”, Journal of Finance, vol. 31, May 1976, pp. 351–367. Black, F. and Scholes, M., “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, vol. 81, 1973, pp. 637–659 la Bruslerie, H. (de), Gestion obligataire internationale, tome 2 : Gestion de portefeuille et contrˆole, Economica, 1990. Cox, J.C., Ingersoll, J.E. and Ross, S.A., “A Theory of the Term Structure of Interest Rates”, Econometrica, vol. 53, no. 2, 1985, pp. 385–407. Davis, M., “Fixed Income Performance Attribution”, Barra Newsletter, July–August 1991. Duffie, D. and Lando, D., “Term Structures of Credit Spreads with Incomplete Accounting Information”, Working Paper, Stanford University, 1997. Duffie, D. and Singleton, K., “Modeling Term Structures of Defaultable Bonds”, Working Paper, Stanford University, 1997. Duffie, D., Schroder, M. and Skiadas, C., “Recursive Valuation of Defaultable Securities and the Timing of Resolution of Uncertainty”, Annals of Applied Probability, vol. 6, 1996, pp. 1075–1090. Dynkin, L. and Hyman, J., “Quantitative Analysis of Fixed Income Portfolios Relative to Indices”, in Handbook of Portfolio Management, F.J. Fabozzi, ed., Frank J. Fabozzi Associates, 1998. Dynkin, L., Hyman, J. and Konstantinovsky, V., “A Return Attribution Model for Fixed Income Securities”, in Handbook of Portfolio Management, F.J. Fabozzi, ed., Frank J. Fabozzi Associates, 1998. Elton, E.J. and Gruber, M.J., Modern Portfolio Theory and Investment Analysis, 5th edn, Wiley, 1995. Elton, E.J., Gruber, M.J. and Blake, C.R., “Fundamental Economic Variables, Expected Returns, and Bond Fund Performance”, Journal of Finance, vol. 50, no. 4, September 1995, pp. 1229–1256. Fabozzi, F.J., Investment Management, Prentice Hall International Editions, 1995. Fabozzi, F.J., Handbook of Portfolio Management, Frank J. Fabozzi Associates, 1998. Fabozzi, F.J. and Fong, G., Advanced Fixed Income Portfolio Management, The State of the Art, Irwin, 1994. Faillace, A.L. and Thomas, L.R., “International Fixed Income Investment: Philosophy and Process”, in Managing Fixed Income Portfolios, F.J. Fabozzi, ed., Frank J. Fabozzi Associates, 1997. Fitoussi, B. and Sikorav, J., “Courbe de taux et z´ero-coupons : quel prix pour l’argent ?”, Quants, CCF, 1991.
C08
WU058-Amenc
252
July 17, 2003
18:18
Char Count= 0
Portfolio Theory and Performance Analysis
Fong, G., Pearson, C. and Vasicek, O., “Bond Performance Analyzing Sources of Return”, Journal of Portfolio Management, spring 1983, pp. 46–50. Grandin, P., Mesure de performance des fonds d’investissement, M´ethodologie et r´esultats, Economica, Gestion poche, 1998. Heath, D., Jarrow, R. and Morton, A., “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation”, Econometrica, vol. 60, 1992, pp. 77–105. Ho, T.S.Y., “Key Rates Durations: Measures of Interest Rate Risks”, Journal of Fixed Income, 1992. Jarrow, R. and Turnbull, S., “Pricing Derivatives on Financial Securities Subject to Credit Risk”, Journal of Finance, vol. 50, March 1995, pp. 53–85. Joshi, J.P. and Swertloff, L., “A User’s Guide to Interest Rate Models: Applications for Structured Finance”, Journal of Risk Finance, fall 1999, pp. 106–114. Kahn, R.N., “Bond Performance Analysis: A Multifactor Approach”, Barra Newsletter, July–August 1991 and Journal of Portfolio Management, fall 1991. Kahn, R.N., “Fixed Income Risk Modeling”, in The Handbook of Fixed Income Securities, F.J. Fabozzi, ed., 5th edn, Frank J. Fabozzi Associates, 1997. Khoury, N., Veilleux, M. and Viau, R., “A Performance Attribution Model for Fixed-Income Portfolios”, Working Paper, 1997. Knez, P.J., Litterman, R. and Scheinkman, J., “Explorations into Factors Explaining Money Market Returns”, Journal of Finance, vol. 49, no. 5, December 1994, pp. 1861–1882. Kuberek, R.C., “Attribution Analysis for Fixed Income”, Performance Evaluation, Benchmarks, and Attribution Analysis, AIMR, 1995. Lando, D., “Modeling Bonds and Derivatives with Default Risk”, Working Paper, University of Copenhagen, 1996. McLaren, A., “A Framework for Multiple Currency Fixed Income Attribution”, Journal of Performance Measurement, vol. 6, no. 4, summer 2002. Madan, D. and Unal, H., “Pricing the Risks of Default”, Working Paper, College of Business and Management, University of Maryland, 1995. Martellini, L. and Priaulet, P., Fixed-Income Securities: Dynamic Methods for Interest Rate Risk Pricing and Hedging, Wiley, 2001. JP Morgan, “Multi-Factor Duration”, Internal documents, Capital Market Research, London, 1996a. JP Morgan, “Fixed Income Optimization”, Internal documents, Capital Market Research, London, 1996b. Merton, R.C., “On the Pricing of Corporate Debt: the Risk-Structure of Interest Rates”, Journal of Finance, vol. 29, 1974, pp. 449–470. Munro, J., “Performance Attribution for Global Fixed Income Portfolios”, Global Investor, November 1996. Murphy, B.P. and Won, D., “Valuation and Risk Analysis of International Bonds”, in The Handbook of Fixed Income Securities, F.J. Fabozzi, ed., 4th edn, Frank J. Fabozzi Associates, 1995. Poncet, P., Portait, R. and Hayat, S., Math´ematiques financi`eres : Evaluation des actifs et analyse du risque, 2nd edn, Dalloz, 1996. Solnik, B., International Investments, 4th edn, Addison-Wesley, 1999. Vasicek, O.A., “An Equilibrium Characterisation of the Term Structure”, Journal of Financial Economics, vol. 5, 1977, pp. 177–188. Vasicek, O.A. and Fong, H.G., “Term Structure Modeling using Exponential Splines”, Journal of Finance, vol. 37, no. 2, May 1982, pp. 339–348.
Chapter 6
Funds of hedge funds Sohail Jaffer
Premium Select Lux SA, Luxembourg1 This chapter has been reproduced with permission from The New Generation of Risk Management for Hedge Funds and Private Equity Investments, edited by Lars Jaeger, published by Euromoney Books, London 2003 (© Euromoney Institutional Investor plc, all rights reserved).
Introduction The main purpose of this chapter is to share some insight and perspectives on the fast-growing proliferation of funds of hedge funds, their set-up and value added. There is a consideration of evolving institutional investor demand, and concerns relating to investment and risk transparency, liquidity, leverage, disclosures, and reporting. Institutional investors are drawn to funds of hedge funds due to their diversification benefits, attractive risk-return characteristics and low correlations to traditional asset classes. However, they are more risk-averse than some endowments, foundations and private investors, who demand a greater degree of transparency and expect a steady pattern of returns. They are familiar with Value-at Risk (VaR), stress testing, scenario analysis and other quantitative tools used for risk management in their traditional asset portfolios, and invariably seek to apply these risk monitoring tools when investing in funds of hedge funds. One crucial aspect of an increase in the flow of institutional assets into funds of hedge funds is comprehensive risk monitoring, control, a significant improvement in existing risk management practices, effective disclosures and timely reporting. The funds of hedge funds industry stands at an interesting crossroads, with the rapid institutionalisation of both the buy and supply sides, and advances in risk management technology.
The set-up and value added of funds of hedge funds A fund of funds is designed to blend different hedge fund styles and spread the risks over a wide variety of funds. A large number of funds of hedge funds aimed at institutional investors tend to target a 10–15 per cent annual net return objective with a volatility averaging between 5 and 10 per cent.2 Due to the difficult market environment of the past three years, the achievement of this performance objective has not proved easy and has tested the skills of several funds of hedge funds managers. The challenge for the fund of funds manager is to deliver a more consistent return than any single underlying hedge fund. This return objective may be achieved by careful manager selection, portfolio construction, risk monitoring and portfolio rebalancing. A skilful mix across individual investment styles, with low correlation, strategic and tactical asset allocation including sectors and geographical regions, proactive portfolio rebalancing, and timely manager changes, forms part of the competitive strength of a successful fund of funds oper-
88
FUNDS OF HEDGE FUNDS
ation.3 Investors in funds of hedge funds include banks, insurance companies, pension funds, endowments and foundations, family offices, and high-net-worth individuals. In 2003, Deutsche Bank surveyed 376 institutions with hedge fund assets totalling more than US$350 billion.4 The most significant findings were contained in a two-part survey, released in January and March 2003, which revealed the following. • Allocations into funds of hedge funds were larger than those made directly into hedge funds. More than one third of investors made allocations of more than US$20 Exhibit 6.1 million into funds of hedge funds. Funds of hedge funds greater than • For the second consecutive year funds of US$1 billion, 2001 hedge funds investors and direct hedge Assets (US$ billion) funds investors had similar holding peri- Fund of funds ods. Two thirds of funds of hedge funds RMK 8.5 investors had held their positions for three Ivy Asset Management 6.3 years or more. Quellos 6.2 • Fees, transparency and risk remained Asset Alliance 4.5 the main concerns investors had when Haussman Holdings NV 3.4 considering allocations into funds of Mesirow 3.2 Ramius 2.8 hedge funds. 2.5 • 60 per cent of investors took between two Brummer & Partners GAM Diversity Inc 1.9 and six months to complete due diligence JP Morgan Multi-Strategy Fund, Ltd. 1.8 on a hedge fund. Xavex HedgeSelect Certificates 1.8 • With large investment staffs it is not surOptima Fund Management 1.6 prising that funds of hedge funds are UBS O'Connor 1.6 capable of making an investment decision Arden 1.5 in less than one month. Permal Investment Holdings N.V. 1.5 • 81 per cent of investors were willing to Arden 1.5 lock up their capital for at least one year. Pamio 1.5 • Capacity guarantees were one of the main Lighthouse Partners 1.3 reasons why investors allocate capital to Mesirow Alternative Strategies Fund, LP 1.2 Longchamp Group 1.2 start up hedge funds. 1.1 • More than half of the investors surveyed GAM Global Diversity Inc 1.1 reviewed their hedge fund portfolio of Man-Glenwood Multi-Strategy Fund Ltd. Olympia Stars 1.1 hedge funds monthly. 1.1 • Risk and strategy drift monitoring were Select Invest K-2 1.1 paramount concerns for investors. Mezzacappa Partners, LP 1.0 • Investors were turning to prime brokers Mesirow Alternative Strategies Fund, LP 1.0 for additional help with capital introduc- Meridian Horizon Fund, LP 1.0 tion and risk management. Leveraged Capital Holdings 1.0 • Investors wanted fund administrators to Meridian Horizon 1.0 offer improved risk reporting for hedge Total 66.3 fund investments. The fund of hedge funds market has evolved, and is polarised between the large ‘mega’
Sources: Altvest, Tuna, Tass, HFR, Directory of Fund of Hedge Funds Investment Vehicles (2001), CMRA Research.
89
PART I: HEDGE FUND RISK
funds and the medium- to small-sized funds. The threshold for large-sized funds is assets in excess of US$500 million. According to a list supplied by Capital Market Risk Advisors (CMRA), the assets of some 30 large-sized funds of hedge funds aggregated to some US$66.3 billion in 2001 (see Exhibit 6.1). The list was based on funds of funds with assets exceeding US$1 billion each and was sourced mainly from a US funds of funds manager universe. Due to their capital clout, the large-sized funds tend to provide a wider range of diversification across managers, and offer economies of scale in research and administration. They can also attract new manager talent, as they can provide seed capital. The challenges encountered by such giant funds of funds include the optimal deployment of capital; limited scope of flexibility to actively allocate assets between the different strategy sectors and switch between individual managers; and controlling the potential risks of over diversification. In July 2002, a study by François-Serge Lhabitant and Michelle Learned observed that, since most of the diversification benefits are reached for small-sized portfolios (typically 5–10 hedge funds), it seems that hedge fund portfolios should be rather cautious on their allocations past this number of funds.5 In addition, maintaining a close in-depth relationship with a relatively large group of managers may also strain the capacity and resources of portfolio and risk management. In contrast to the large-sized fund of hedge funds, the small- to medium-sized funds are focused on generating alpha through active management across a more concentrated pool of managers; identification and selection of niche investment strategies; potential access to a faster decision-making process; and quicker ability to react to changes in varying market environments. The average hedge fund size by strategy as of the third quarter of 2001 is summarised in Exhibit 6.2. Interestingly, the average hedge fund size of individual macro global, relative value arbitrage and event-driven hedge funds show that they continued to attract fund of funds allocations. Exhibit 6.2 Average hedge fund size by 3Q-01 Areas of investment of funds of funds
250 200 150 100
90
Market timing
Short selling
Emerging markets
Managed futures
Regulation D
Sector
Merger arbitrage
Convertible arbitrage Distressed securities
Fund of funds
Fixed income
Statistical arbitrage
Source: Hedge Fund Research, Inc.
Equity market neutral
Equity hedge
Event driven
0
Macro
50 Relative value arbitrage
Average assets (US$ million)
300
FUNDS OF HEDGE FUNDS
The litmus test applied to the value proposition of a fund of funds manager should take into consideration the following criteria of an ability to: • successfully identify, evaluate, invest and maintain in-depth relationships with a group of high-performing managers (the fund of fund manager will most probably build a proprietary database to maintain such an important competitive advantage); • establish an experienced portfolio management team that can thoroughly understand the diverse range of hedge fund strategies and the underlying risk/return characteristics of each strategy implemented, and assess the risk of the different types of securities and derivatives used by the hedge fund managers; • analyse and understand the impact of different market conditions on the portfolio; • focus on both qualitative and quantitative variables of due diligence; • maintain an efficient and reliable back-office infrastructure capable of monitoring risks, compliance with investment guidelines, detecting style drift, and proactively spotting and resolving operational issues; • target absolute returns and low volatility when compared with the traditional asset classes (a vital aspect is capital preservation and liquidity); • provide risk transparency, accurate reporting and timely disclosures; and • align own interests with those of investors, and adhere to the highest standards of ethics and integrity.
Portfolio management strategies The array of skills and experience of both fund of hedge funds managers and individual hedge fund managers varies enormously. Due to the different objectives and risk/reward attributes of the specific portfolio, the tilt and mix of portfolio management strategies tend to vary. Exhibit 6.3 Correlations in best and worst 48 S&P 500 ranked months, January 1990–December 2002 0.15
Correlation in 48 best S&P 500 months
0.10
CTA US$ Weighted Index
Global asset allocators
0.05 Equity hedge
0.00 -0.05 -0.10
Relative value
-0.15 -0.20 -0.25 -0.6
Event driven
-0.4
-0.2 0.0 0.2 0.4 Correlation in 48 worst S&P 500 months
0.6
0.8
Sources: EACM, Datastream, CISDM.
91
PART I: HEDGE FUND RISK
Some portfolios may display a stronger bias towards directional strategies and others towards non-directional strategies. The fund of funds manager evaluates the return, volatility and correlation for a selection of hedge fund strategies. A historical performance summary of the main hedge fund strategies and traditional assets for the period January 1990 to December 2002 is provided in Exhibit 6.3. However, as the return and risk characteristics, and correlation pattern, of individual strategies vary significantly over time, as well as in different market conditions, pure quantitative analysis based on past performance and correlation data is of limited importance. The critical aspects are the weights of the individual strategy sectors; correlation between the different strategies; and the selection of the specific managers within each sector. The choice of strategies may include equity market neutral, convertible arbitrage, fixed income arbitrage, risk arbitrage, distressed securities, macro, equity hedge, equity non-hedge and emerging markets. The three core building blocks underpinning the integrated investment process of the fund of hedge funds manager comprise: • strategy sector selection and allocation; • manager selection, evaluation and ongoing due diligence; and • continuous manager monitoring and proactive risk management. Given the wide dispersion of returns among hedge fund managers, huge diversity in individual skill sets and the inefficient nature of the hedge fund market, an experienced fund of hedge funds manager should have a substantial edge over less skilled and less experienced providers. Quality hedge fund talent is scarce and investing in hedge funds is mainly a people business. The turnover of skilled managers and, in some cases, experienced investment pairs or teams needs to be monitored carefully. Portfolio construction tends to combine bottom-up manager selection and top-down asset allocation approaches. The diversification across the mix of strategy sectors, managers and Exhibit 6.4 Classification of hedge funds by diversification characteristics Classification
Characteristics
Examples
Return-enhancer
High return, high correlation with stock/bond portfolio
Equity market-neutral, convertible bond arbitrage
Risk-reducer
Lower return, low correlation with stock/bond portfolio
Merger arbitrage, distressed securities, long/short equity
Total diversifier
High return and low correlation with stock/bond portfolio
Global asset allocation
Pure diversifier
Low or negative return with high negative correlation with stock/bond portfolio
Short seller
Source: Schneeweis, Thomas, and Richard Spurgin (31 July 2000), Hedge Funds: Portfolio Risk Diversifiers, Return Enhancers or Both?, CISDM Working Paper.
92
FUNDS OF HEDGE FUNDS
Exhibit 6.5 Correlations in best and worst 48 S&P 500 ranked months, January 1990–December 2002 0.15
Domestic long
0.10 Correlation in 48 best S&P 500 months
Systematic
0.05 -0.00 -0.05
Arbitrage
Market neutral Long/short
-0.10 -0.15 -0.20
Convertible hedge
-0.25 -0.30 -0.4
-0.2
0.0
0.2
0.4
Event driven Bankruptcy Bond hedge
0.6
0.8
Correlation in 48 worst S&P 500 months Sources: EACM, Datastream, CISDM.
styles ultimately differentiates one fund of funds portfolio from another. Exhibit 6.4 summarises the classification of hedge funds by diversification characteristics. Fund of funds managers also allocate assets to systematic managed futures strategies and, given their diversification properties, they view them as pure diversifiers. Normally a critical success factor in a conventional portfolio design is to estimate the return, volatility and correlation, and to combine the variables to construct a mean-variance efficient portfolio. However, due to the heterogeneous nature of hedge fund strategies, the performance variability of managers within a single strategy sector, and the latent risks of low liquidity, credit and event risks, there are several limitations in employing a conventional mean-variance efficient portfolio for creating a fund of hedge funds. Since fund of funds managers’ future estimates of such variables tend to differ, they invariably result in different types of portfolios. As an example, the correlations in the best and worst 48 S&P 500 months for the period January 1990 to December 2002 are summarised on Exhibits 6.5. Some managers might place more weight on past factors and others might try to select the strategy that is expected to perform the best over the next six to 12 months.
Style risks and diversification: the selection of strategy sectors An important source of alpha in a fund of funds portfolio depends on sector allocation and the right selection of strategies. The main aims of sector allocation are to achieve and maintain effective diversification, and match the targeted risk/reward profile. The important elements of diversification include sector and strategy correlations across the different sources of return (see Hedge Fund Research’s strategy sector correlation matrix table in Exhibit 6.6). A truly diversified portfolio should be able to achieve its targeted performance across the different sources of return.
93
-0.07 0.31 -0.18 -0.24 -0.10 0.25
HFRI Event-Driven Index
HFRI Fixed Income Arbitrage Index
HFRI Macro Index
HFRI Merger Arbitrage Index
HFRI Relative Value Arbitrage Index
HFRI Sector (total)
HFRI Short Selling Index
-0.21 -0.19
MSCI Indices US$ World Index
S&P 500 w/ dividends
Source: Hedge Fund Research.
0.24
Credit Aggregate Bond Index
Lehman Brothers Government/
0.11 -0.22
HFRI Equity Market Neutral Index
-0.11 -0.10
HFRI Distressed Securities Index
HFRI Equity Hedge Index
-0.19
HFRI Convertible Arbitrage Index
HFRI Emerging Markets (total)
1.00 -0.12
HFR Managed Futures Index
HFR Managed Futures Index
Fund/fund
HFRI Convertible Arbitrage Index 0.31
0.29
0.18
-0.35
0.36
0.56
0.45
0.39
0.11
0.61
0.13
0.46
0.43
0.60
1.00
-0.12
HFRI Distressed Securities Index 0.37
0.34
0.04
-0.47
0.50
0.70
0.51
0.46
0.36
0.78
0.18
0.58
0.63
1.00
0.60
-0.19
HFRI Emerging Markets (Total) 0.57
0.61
0.01
-0.57
0.58
0.49
0.42
0.59
0.27
0.69
0.07
0.64
1.00
0.63
0.43
-0.11
HFRI Equity Hedge Index 0.66
0.62
0.09
-0.79
0.83
0.52
0.47
0.58
0.06
0.76
0.34
1.00
0.64
0.58
0.46
-0.10
0.12
0.10
0.21
-0.11
0.24
0.21
0.19
0.23
0.06
0.20
1.00
0.34
0.07
0.18
0.13
0.11
HFRI Equity Market Neutral Index
94
Strategy sector correlation matrix, January 1990 – March 2003
Exhibit 6.6
HFRI Event-Driven Index 0.63
0.58
0.08
-0.63
0.66
0.64
0.73
0.54
0.17
1.00
0.20
0.76
0.69
0.78
0.61
-0.22
HFRI Fixed Income Arbitrage Index -0.07
-0.01
-0.21
-0.03
0.07
0.30
-0.02
0.12
1.00
0.17
0.06
0.06
0.27
0.36
0.11
-0.07
HFRI Macro Index 0.37
0.40
0.37
-0.39
0.47
0.37
0.28
1.00
0.12
0.54
0.23
0.58
0.59
0.46
0.39
0.31
HFRI Merger Arbitrage Index 0.46
0.41
0.09
-0.37
0.38
0.43
1.00
0.28
-0.02
0.73
0.19
0.47
0.42
0.51
0.45
-0.18
HFRI Relative Value Arbitrage Index 0.35
0.35
0.04
-0.38
0.44
1.00
0.43
0.37
0.30
0.64
0.21
0.52
0.49
0.70
0.56
-0.24
HFRI Sector (Total) 0.58
0.56
0.01
-0.80
1.00
0.44
0.38
0.47
0.07
0.66
0.24
0.83
0.58
0.50
0.36
-0.10
0.25
-0.69
-0.65
-0.02
1.00
-0.80
-0.38
-0.37
-0.39
-0.03
-0.63
-0.11
-0.79
-0.57
-0.47
0.18
0.13
1.00
-0.02
0.01
0.04
0.09
0.37
-0.21
0.08
0.21
0.09
0.01
0.04
0.18
0.24
0.83
1.00
0.13
-0.65
0.56
0.35
0.41
0.40
-0.01
0.58
0.10
0.62
0.61
0.34
0.29
-0.21
HFRI Short Selling Index Lehman Brothers Government/Credit Aggregate Bond Index MSCI Indices US$ World Index -0.35
S&P 500 w/ dividends 1.00
0.83
0.18
-0.69
0.58
0.35
0.46
0.37
-0.07
0.63
0.12
0.66
0.57
0.37
0.31
-0.19
PART I: HEDGE FUND RISK
FUNDS OF HEDGE FUNDS
The risks and premiums vary among different strategies. A comprehensive analysis of the different sources of returns for each strategy is described in Chapter 3 of this Euromoney publication. In addition, Chapter 3 of Managing Risk in Alternative Investment Strategies by Lars Jaeger also describes each strategy, sources of return and relevant risk factors.6 Increasingly investors are searching for a ‘four seasons portfolio’ that can weather global volatility spikes and sudden market stress events. The challenge for an experienced fund of funds manager is to find the balance between a predetermined sector allocation and an opportunistic switching between strategies. According to the Deutsche Bank Alternative 2003 Investment Survey (Part 1), some of the expected investor shifts in portfolio allocation by strategy were as follows: • more than 50 per cent of investors planned to increase allocations to long/short managers; • 44 per cent of investors said that they would increase their portfolio allocation to distressed debt; • macro hedge funds should see increased investments in 2003; • investors planned to hold or increase their exposure to multi-strategy hedge funds in 2003; and • in 2002 strong managed futures (CTA) returns would influence investors to increase allocations in 2003. Finding the right sector allocation for a multi-manager portfolio is often a difficult task. Due to the high variability of returns of individual hedge fund managers, and the changing correlation features of individual strategies over time and in different market environments, the use of past performance and historical correlation data has its limitations. An analysis of the variExhibit 6.7 Summary of fund of funds return and volatility assumptions using HFR historic data, 1990–2001 (%) Strategies analysed Equity Hedge Equity Market Neutral Equity Non-hedge Sector Convertible Arbitrage Merger Arbitrage Relative Value Arbitrage Statistical Arbitrage Fixed Income Macro Event Driven Short Selling Distressed Securities Market Timing Regulation D Emerging Markets
11.83 years mean return
Volatility
20.2 11.2 16.9 22.2 12.0 12.2 13.8 0.8 11.2 17.8 15.9 3.0 15.2 14.4 11.1 13.5
9.4 3.3 14.9 14.6 3.4 4.5 3.9 4.0 3.7 9.0 6.7 23.2 6.5 7.0 6.1 16.2
Sources: HFR Database, CMRA Analysis.
95
PART I: HEDGE FUND RISK
Exhibit 6.8 Equity-driven strategies, 1990–2001 (%)
2000
2001
2000
2001
1998
1999
1997
1996
1995
1993
1994
1998
1999
1997
1996
1995
1994
Sector 11.8 year mean return = 22.17% Standard deviation = 14.57%
1993
2001
2000
1998
1999
1997
1996
1995
1994
1993
80 70 60 50 40 30 20 10 0 -10 -20
1991
2001
2000
1998
1999
1997
1996
1995
1994
1993
1992
Equity non-hedge 11.8 year mean return = 16.87% Standard deviation = 14.94%
1991
1990
70 60 50 40 30 20 10 0 -10 -20
1992
1990
-10
1991
0
1992
10
1991
20
1990
30
1990
40
Equity market-neutral 11.8 year mean return = 11.21% Standard deviation = 3.32%
20 18 16 14 12 10 8 6 4 2 0
1992
Equity hedge 11.8 year mean return = 20.25% Standard deviation = 9.44%
50
Sources: HFR Database, Altvest, Bloomberg, CMRA Analysis, Fund of Funds.
ability of returns and standard deviations of equity driven, arbitrage-related and other strategies over the period 1990–2001 compiled by Hedge Fund Research, Inc. are summarised in Exhibits 6.7 to 6.10. Hence a qualitative understanding of the key performance drivers (eg, corporate earnings, yield curves and credit spreads) as well as the main strengths and weaknesses of the relevant strategy sectors is needed to select the appropriate mix of strategies in a portfolio. The factor sensitivities of the different hedge fund strategies are well described in the following studies and reports: • Schneeweis, Kazemi and Martin of the Centre for International Derivatives and Securities Markets (CISDM), Lehman Brothers report titled Understanding Hedge Fund Performance: Research Results and Rules of Thumb for the Institutional Investor, November 2001; • Fung, W., and D. Hsieh (September/October 2002), ‘Asset Based Style Factors for Hedge Funds’, Financial Analyst Journal, pp. 16–27; • Fung, W., and D. Hsieh (1997), ‘Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds’, Review of Financial Studies, Vol. 2, No. 10, pp. 275–302; and • Agarwal, V., and N. Naik (September 2000), Performance Evaluation of Hedge Funds with Option Based and Buy-and-Hold Strategies, Working Paper. The dynamic risk/return profile of the different strategy sectors and the correlations between strategies needs to be actively monitored and reassessed. Due to the changes in economic
96
FUNDS OF HEDGE FUNDS
Exhibit 6.9 Arbitrage-driven strategies, 1990–2001 (%) Convertible arbitrage 11.8 year mean return = 11.99% Standard deviation = 3.42%
30 25 20
25 20
15 10
15 10
5 0
5 2001
1999
1998
1997
1995
1996
1994
1993
2000
10
2001
15 10
1992
1991
25 20 15 5
1999
1998
1997
1996
1995
1994
1993
1991
1990
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
-5
1992
0
5 0 1990
Statistical arbitrage 11.8 year mean return = 10.77% Standard deviation = 3.99%
30
25 20
2000
Relative value arbitrage 11.8 year mean return = 13.82% Standard deviation = 3.91%
35 30
1990
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
0 1991
1990
-5
Merger arbitrage 11.8 year mean return = 12.24% Standard deviation = 4.53%
30
Sources: HFR Database, Altvest, Bloomberg, CMRA Analysis, Fund of Funds.
environment and market conditions, the attractiveness of particular strategies may diminish, while certain strategies may complement one another in defined market conditions and potentially enhance portfolio diversification.
Risks of fund of funds manager selection: the due diligence process The institutional investor needs a disciplined approach in identifying a top-quartile fund of funds manager; they require an approach that can enable them to assess the large diversity in individual skill sets as well as experience levels among the different funds of funds.7 The fund of funds team’s investment credentials, knowledge and understanding of the different strategy sectors, the depth of their relationships with top-tier individual hedge fund managers, their allocation and risk management expertise, their ability to obtain and monitor individual manager positions in real time, their operational competence, and their experience of handling significant market stress events are some of the aspects that need to be taken into account when assessing and differentiating a fund of funds operation. The due diligence summary prepared by Jon Lukomnik of Capital Market Risk Advisors (CMRA), which features as Appendix 3 in the publication Hedge Fund Risk Transparency by Leslie Rahl, is very valuable.8 The art and science of identifying and evaluating a top-quartile fund of hedge funds manager should therefore include a review and analysis of the investment process, the business model, and the quality and depth of resources.9
97
PART I: HEDGE FUND RISK
Exhibit 6.10 Other strategies, 1990–2001 (%)
2000
2001
1999
1998
1997
1995
Event driven 11.8 year mean return = 15.94% Standard deviation = 6.74%
40 30
30
2001
40
2000
Distressed securities 11.8 year mean return = 15.23% Standard deviation = 6.46%
50
1996
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1990
-5
1991
5 0
1994
10
1993
15
1991
20
1990
25
Macro 11.8 year mean return = 17.83% Standard deviation = 9.04%
70 60 50 40 30 20 10 0 -10
1992
Fixed income 11.8 year mean return = 11.22% Standard deviation = 3.72%
30
20
20
1999
1998
1997
1995
1996
1994
1993
1992
1990
2001
2000
1999
1998
1997
1996
1995
1994
1993
-10
1992
-10
1991
0
1990
0
1991
10
10
Short selling 11.8 year mean return = 2.99% Standard deviation = 23.22%
40 30 20 10 0 -10
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1990
-30
1991
-20
Sources: HFR Database, Altvest, Bloomberg, CMRA Analysis, Fund of Funds.
The investment process The main ingredients of a dynamic investment process focus on strategy sector selection and allocation; manager selection, evaluation and ongoing due diligence; and continuous risk monitoring. Successful fund of fund managers prefer to create and maintain proprietary databases of individual hedge fund managers. Considerable time and resources are dedicated to identifying and contacting emerging new manager talent that does not feature on other fund of funds managers’ radar screens. A competitive advantage may also be sought by using the fund of fund manager’s personal network in the industry and reserving capacity at the individual hedge fund manager level.10
98
FUNDS OF HEDGE FUNDS
Funds of hedge funds tend to use either wholly external or wholly in-house talent, or in some cases an intelligent mixture of both. The institutional investor needs to satisfy himself/herself about potential conflicts of interest. In some cases fund of funds managers may have negotiated exclusive third-party marketing rights to promote new external hedge fund managers; and in certain instances the institutional investor may perceive the manager’s selection process to be influenced by their need to fulfil capacity commitments.11 Most portfolio construction tends to blend bottom-up manager selection and top-down asset allocation approaches. The investment objectives, risk/return expectations, capital preservation and risk tolerance of the target investor base all influence the portfolio design. The institutional investor should assess the extent and frequency of the information disclosed by the individual hedge fund managers. The quality and type of information available to the fund of funds manager regarding the underlying portfolio could have a significant bearing on the rebalancing of the portfolio and the monitoring of risk. The risk parameters, including the stress test models and general monitoring systems employed, as well as the frequency and scale of action taken by the fund of funds manager, should add a layer of comfort from the investor’s perspective.12
The business model The institutional investor should carefully assess and analyse the business model used by a fund of hedge funds manager. Areas to consider include: • • • • • • • • • • • •
the scope of the firm’s asset management activities; the mix with other non-asset management activities; the target group of clients; capacity constraints; liquidity and redemption provisions; the extent of economic dependence on a limited number of clients; the investment rules for a manager’s own capital; remuneration structures for key investment professionals; rebates received from individual hedge funds/brokers; ethical and compliance record; conflict of interest policies; and quality of service providers.
The list above is not provided in a particular order and is by no means exhaustive, but is given to raise the institutional investor’s awareness that the type of business model a manager employs could have serious implications for a fund of funds’ performance going forward.13
Quality and depth of resources The institutional investor should also pay particular attention to the credentials, experience and the incentives used to attract and retain top industry talent by the fund of funds manager. The ability to build, motivate, manage and retain a talented team of professionals is an important success factor in distinguishing a successful fund of funds manager. The qualifications and depth of relevant experience of the individual portfolio and risk managers, business
99
PART I: HEDGE FUND RISK
development and product managers, investment and systems analysts, and in-house legal and compliance professionals can also contribute to the top-quartile performance ranking of the fund of funds manager. 14 Institutional investors may also find the illustrative due diligence questionnaire of fund of funds managers prepared by the Alternative Investment Management Association (AIMA) useful. This is available at no charge to AIMA members and institutional investors, on application to AIMA at
[email protected]
The post-investment risk management process for multi-manager portfolios The three most important pillars underlying successful and profitable hedge fund investing are: • astute strategy sector selection and allocation; • pragmatic manager due diligence; and • proactive and systematic manager risk monitoring. Fund of funds managers are increasingly seeking to enhance their active risk management capabilities, and strengthen their manager monitoring and control systems, with a view to differentiating them and adding real value. The main purposes of continuous and independent monitoring are to analyse the application of the manager’s strategy in different market environments; evaluate the impact of adverse market trends on the portfolio; identify abnormal market exposure, undue portfolio concentration, flash ‘liquidity dry up’ situations, any significant style drifts or sudden spikes in leverage; and judge the adverse impact of a single market stress event on the portfolio. Effective post-investment risk management involves a combination of an independent monitoring of the activity in the relevant financial markets, and maintaining a close dialogue and frequent exchange of information with the manager. Any changes in the manager’s core investment process, risk management and operational procedures, reporting of unexpected investment gains or losses, turnover of key personnel, impact of large subscription or redemptions or shifts in volatility pattern, correlation, leverage or other risk indicators should be investigated promptly. Remedial action by the fund of funds manager may include reallocation of assets or excluding the manager from the portfolio. A sample generic post-investment equity risk management report provided by Fauchier Partners is shown in Exhibit 6.11. To ensure the integrity of the performance analysis and attribution, the fund of funds manager should obtain pricing of manager’s positions and investment activities from independent sources, which may include information vendors, market-makers, prime brokers and custodian banks. The real challenge faced by fund of funds managers today is actually getting the underlying manager’s individual positions and obtaining such data on a real-time basis. Performance attribution should decompose the investment results arising from individual asset classes and strategy sectors (eg, convertible bonds, mortgage-backed securities, distressed debt), and also analyse results with respect to different investment styles. A systematic risk monitoring discipline includes analyses of portfolio concentrations, correlation and volatility deviations from the historical norm, liquidity assessment, stress testing, and scenario analysis.
100
FUNDS OF HEDGE FUNDS
Exhibit 6.11 Monthly exposure and asset report Fund name Completed by E-mail address
Month Fund ID Please add contact name and e-mail address.
Fund exposure (%)
Fund ID should be left blank.
High
Low
Average
Close
Long exposure Short exposure Net futures Net options Gross Net Cash
Please note that the highest gross exposure, net exposure, long exposure and short exposure may not necessarily occur on the same day.
Month end – industry sector/asset type/credit exposure Top five sectors 1 2 3 4 5
Long
Short
Gross
Net
Gross
Net
Sum Month end – country exposure Top five countries 1 2 3 4 5
Long
Short
Concentration at month end Long portfolio top five Names
Short portfolio top five % by value
1 2 3 4 5 Sum #Long Long beta
% by value 1 2 3 4 5 Sum #Short Short beta
Stock names are not required for the top five short positions, only the percentages held.
Total number of positions
101
PART I: HEDGE FUND RISK
Exhibit 6.11 continued Monthly exposure and asset report Market cap distribution Lower limit
Upper limit
%
Small Mid Large
Capitalisation analysis of portfolio: please define the ranges you use for small-, mid- and large-cap stocks.
Performance attribution – month Month Long Short Futures/options Currency
Year to date Gross (Y/N)? Net (Y/N)?
Please also indicate that the calculations have been made on a gross basis, ie, gross of fees.
Intra month variation High
Performance attribution into long and short components to show the contribution of each side of the portfolio to the return of the fund.
Fund equity at month end Net change (US$ million) (US$ million)
Low
Daily NAV
Equity
Hedge fund asset position Turnover For closed positions Turnover #Closed Max weighting at close Long side Short side P/L Max Long side Short side
Please provide highest and lowest NAV values intra-month.
Min
Fund name Value date Completed by Date completed Currency
Units (eg, M) Value date
Vehicle1 Hedge fund strategy2 All hedge fund strategies3 Total assets in group4 Definitions 1 The vehicle in which Fauchier Partners clients have invested. 2 Total for all vehicles employing the same investment strategy. 3 Total for all hedge fund strategies. 4 Total of all funds managed by the group; to include long only, private equity, hedge funds,etc. Source: Fauchier Partners.
102
FUNDS OF HEDGE FUNDS
Defining and managing hedge fund portfolio risk In May 2003 KPMG Financial Advisory Services Luxembourg completed and released an interesting survey on financial risk management for hedge funds.16 The sample comprised 19 hedge fund and fund of hedge funds managers with combined assets under management of €38.5 billion, and 18 fund administrators with combined hedge fund and funds of hedge fund assets under administration of €23.7 billion. Highlights from survey include the following. • Fund of hedge funds dominated hedge funds in terms of both assets and the number of funds among the participants. • Overall the breakdown of fund of hedge funds assets per investment style was similar between European fund of hedge funds managers and Luxembourg fund administrators. The most common investment styles were multi-strategy and short selling. • a majority of participants (55 per cent) distributed fund of hedge funds across several jurisdictions. • Funds of hedge funds’ net asset values (NAV) were mostly reported on a monthly basis and to a lesser extent on a weekly basis, while redemptions of fund of hedge funds shares were accepted by participants primarily on a monthly basis and, to a much lower extent, on either a quarterly basis or a weekly basis. • Only half the risk management systems in use by fund of hedge funds managers accepted data feeds in different formats and contents from different sources. Most fund of hedge funds managers indicated that they used both an in-house system and one of the most common risk management packages to monitor hedge fund risk. • Concentration measures (71 per cent), sensitivities (62 per cent) and VaR (54 per cent) were the most common risk management measures provided by fund of hedge funds managers to investors. A majority of fund administrators were not informed about the risk management information provided to investors. • Fund of hedge funds managers (69 per cent) tended to be more satisfied with the quality and frequency of pricing of the fund of hedge funds investments relative to fund administrators (40 per cent). • A majority of fund of hedge funds managers (56 per cent) used software programs to price some of the fund of hedge funds investments. • CSFB Tremont Index (26 per cent) and Hedge Fund Research (HFR) (29 per cent) were the most common benchmarks used among fund of hedge funds managers, but a significant number did not use a benchmark (23 per cent) or measured performance relative to long-only indices (16 per cent) (MSCI world index). Generally, fund administrators did not use benchmarks for fund of hedge funds. • When accepting a new fund of hedge funds promoter, experience of the fund of hedge funds manager (23 per cent), and the reputations of both the manager (19 per cent) and the institution employing the manager (16 per cent), were considered critical by fund administrators.
The issue of transparency The survey also confirmed that hedge funds transparency remained one of the most significant challenges for the industry. While about 36 per cent of all participants concluded that more hedge fund transparency would have a minimal impact on investors’ confidence, 28 per cent shared the opinion
103
PART I: HEDGE FUND RISK
that it would have a material impact and 17 per cent a significant impact. Finally, 19 per cent stated that the impact of more hedge fund transparency would depend on the hedge fund strategies. Most of the participating fund of hedge funds managers (71 per cent) provided, at least to some extent, consolidated risk profile and position level transparency to investors. The discussion relating to hedge fund transparency, reporting and disclosures continues to evolve, and more recently has been the focus of the Investor Risk Committee (IRC) of the International Association of Financial Engineers (IAFE).17 The IAFE is a non-profit professional society dedicated to fostering the profession of quantitative finance by providing platforms to discuss cutting-edge and pivotal issues in the field. The IAFE seeks to foster frank discussions of current policy issues, and sponsors programmes to educate the financial community and recognise outstanding achievements in the field. The IAFE launched the Investor Risk Committee in January 2000 to provide a forum for participants, teachers and students in the field of investing to study risk and related issues. The IAFE Investor Risk Committee (IRC) consists of individuals from hedge fund investment managers and a variety of institutional investors, including pension funds, endowments, foundations, insurance companies, funds of funds and others. The IRC also includes regulators, software and technology vendors, consultants, prime brokers, custodians, and others who are active in the investor arena. The goal of the IRC is to provide results that will be useful to investors and managers alike to benchmark their practices relative to their peers. The main IAFE Investor Risk Committee findings with respect to hedge fund managers were described in a press release of 27 July 2001, which is reproduced here with the kind permission of the IAFE. The IRC defined that investors have three primary objectives in seeking disclosure from hedge fund managers. • Risk monitoring to ensure that managers are not taking on risks beyond represented levels in terms of allowable investments, exposures, leverage, etc; • Risk aggregation to ensure the investors’ ability to aggregate risks across their entire investment programme in order to understand portfolio-level implications; • Strategy drift monitoring to ensure the investors’ ability to determine whether a manager is adhering to the stated investment strategy or style. IRC members agreed that full position disclosure by managers does not always allow them to achieve their monitoring objectives and may compromise a hedge fund’s ability to execute its investment strategy. Despite the fact that many investors receive full position disclosure for many of their investments, the members of the IRC who have participated in the meetings to date were in agreement that full position disclosure by managers is not the solution. Managers expressed significant concerns over the harm that full position disclosure could cause for many common hedge fund strategies (for example macro and risk arbitrage). Investors agreed that they did not wish to force disclosure that would be adverse to the manager and therefore to their investment. In addition, many investors expressed concern over the operational difficulties associated with processing such vast quantities of diverse data. Source: IAFE Investor Risk Committee Consensus Document of 27 July 2001 included with the kind permission of IAFE.
104
FUNDS OF HEDGE FUNDS
IRC members agreed that the reporting of summary risk, return and position information can be sufficient as an alternative to full position disclosure. Such summary information should be evaluated on four dimensions: content, granularity, frequency and delay. • Content describes the quality and sufficiency of coverage of the manager’s activities. This dimension covers information about the risk, return and positions on an actual as well as on a stress-tested basis. • Granularity describes the level of detail. Examples are NAV disclosure, disclosure of risk factors, for instance, arbitrage pricing theory (APT) and VaR, disclosure of tracking error or other risk and return measures at the portfolio level, by region, by asset class, by duration, by significant holdings. • Frequency describes how often the disclosure is made. High-turnover trading strategies may require more frequent disclosure (for example, daily) than private or distresseddebt investment funds, where monthly or quarterly disclosure is more appropriate. • Delay describes how much of a lag occurs between when the fund is in a certain condition and when that fact is disclosed to investors. A fund might agree to full or summary position disclosure, but only after the positions are no longer held. IRC members agreed that usability of any alternative disclosure depends upon sufficient understanding of the definitions, calculation methodologies, assumptions and data employed by the manager. This may be accomplished in a variety of fashions, including discussions between investors and managers, by the manager providing for adequate transparency of their process or via independent verification. IRC members should benchmark their practices relative to their peers. IRC members agreed that a major challenge to peer group performance and risk comparisons, as well as aggregation across managers, is the use of a variety of calculation methodologies, assumptions and data employed in the marketplace. IRC members did not, however, feel that one size fits all, and felt that multiple peer groups may be relevant, depending on the nature of the investor, as well as the strategies employed by the manager. Investors and managers believe that an industry effort should be made to improve the ability to conduct comparisons across managers, as well as multi-manager portfolio analysis. IRC members agreed that detailed reporting is not a substitute for initial and ongoing due diligence reviews, on-site visits, and appropriate dialogue between investors and managers. IRC members also agreed that market, credit, leverage, liquidity and operational risks are interrelated. Accordingly, exposure to these risks in combination should be included in the dialogue between investors and managers.18 Source: IAFE Investor Risk Committee Consensus Document of 27 July 2001 included with the kind permission of IAFE.
Active risk management and the issue of liquidity Active risk management forms an integral part of the dynamic portfolio management process. It involves the optimal allocation of risk among different strategy sectors and managers. The
105
PART I: HEDGE FUND RISK
fund of funds manager needs to carefully monitor individual managers particularly as regards whether leverage limits are exceeded; stop losses are triggered; any significant style drifts occurred; or credit, liquidity and event risks emerged. The portfolio risk management team needs to identify, evaluate and monitor exposure limits to individual sectors and managers; discuss and agree with each manager the appropriate amount of leverage; establish ‘amber’ alerts and final stop-loss limits beyond which the manager is excluded from the portfolio; and implement controls designed to detect style drift and other significant deviations. It is crucial for fund of funds managers to carefully monitor the underlying market, liquidity and credit risks. Frequent contacts with the individual hedge fund managers are desirable to review and identify any changes in a strategy’s risk structure on a timely basis. Fund of funds managers need to focus and assess both the qualitative and quantitative aspects of risk management. Active risk management practices of fund of hedge funds continue to evolve, and experience and judgement are necessary to exercise timely and effective control. Fund of funds managers need to carefully assess the liquidity risk relating to the particular strategy sector and the underlying investment instruments. A sudden change in market conditions, as observed in 1998, can adversely affect the price of the underlying securities and the financing of the individual leveraged positions. Investment banks and prime brokers control the amount of leverage and margin requirements by applying a haircut on the price of the securities held as collateral. Haircut policies vary depending on market conditions and the credit appetite of the lender. In times of market volatility and stress, credit is rationed more stringently and may force individual hedge fund managers to reduce their leverage by selling securities in a falling market. Generally the redemption provisions of a fund of funds tend to mirror the liquidity offered by the underlying managers that the fund invests with. Typically fund of funds managers offer either monthly or quarterly redemption linked to a notice period of one to three months. In cases of market turmoil the fund of funds manager may use the caveat emptor embedded in the fund prospectus to further extend the redemption period.
Conclusion Several institutional investors have acquired the savoir faire of investing in funds of hedge funds. Increasingly more experienced investors have developed a reasonable level of comfort about investing directly with single-manager and multi-strategy hedge funds. Despite some popular misconceptions and certain hedge fund accidents, the fund of hedge funds industry segment is poised to grow over the next 10 years. The growing understanding of strategy assessment, more effective risk control and tighter manager monitoring, position disclosure and enhanced standards of transparency among funds of funds managers, meaningful disclosures to investors, and improved levels of liquidity should contribute to aligning investor expectations with manager’s interests and pacing future industry growth. Market-practitioner-led groups such as the AIMA, the IAFE or the CISDM and others continue to make valuable contributions to ongoing research, education and enhancement of best-practice standards.
References Alternative Investment Management Association (AIMA) (October 2002), A Guide to Fund
106
FUNDS OF HEDGE FUNDS
of Hedge Funds Management and Investment, London, AIMA. Ineichen, Alexander (September 2001), ‘Global Equity Research – The Search for Alpha Continues: Do Fund of Hedge Funds Managers Add Value?’, London, UBS Warburg. Jaeger, Lars (2002), Managing Risk in Alternative Investment Strategies, London, Financial Times Prentice Hall. Jaffer, Sohail, Ed. (2003), Funds of Hedge Funds For Professional Investors and Managers, London, Euromoney Books. Lhabitant, François-Serge (February 2003), Hedge Funds: Myths and Limits, New York and London, John Wiley & Sons. Nicholas, Joseph G. (1999), Investing in Hedge Funds: Strategies for the New Marketplace, Bloomberg Personal Bookshelf. Rahl, Leslie (2003), Hedge Fund Risk Transparency: Unravelling the Complex and Controversial Debate, London, Risk Books. Schneeweis, Thomas, Hossein Kazemi and George Martin (2001), Understanding Hedge Fund Performance: Research Results and Rules of Thumb for the Institutional Investor, New York, Lehman Brothers. 1
This chapter does not address specific investment objectives, financial situations or needs of any specific reader. The chapter is published solely for informational purposes and is not to be construed as a solicitation or an offer to buy or sell any hedge funds, specific sectors, strategies, securities or related financial instruments. The type of transactions described herein for illustrative purposes may not be eligible for sale in all jurisdictions or to certain categories of investors. The content of this chapter is based on information obtained from sources believed to be reliable but is not guaranteed as being accurate, nor is it a complete statement or summary of the hedge funds, sectors, strategies, securities, markets or developments referred in the chapter. The content of this chapter should not be regarded by readers as a substitute for the exercise of their own judgement. The author accepts no liability whatsoever for any loss or damage of any kind arising out of the use of all or any part of this chapter. 2 Based on Sohail Jaffer (August 2002), ‘Art Mirrors Science’, Global Pensions Hedge Funds Supplement. 3 Ibid. 4 Dyment, John, and Eamon Heavey, Equity Prime Services: Alternative Investment Survey Results Part 1: Investment Trend, Deutsche Bank, January 2003; and Part 2: Inside the Mind of the Hedge Fund Investor, Deutsche Bank, March 2003. 5 Lhabitant, François-Serge, and Michelle Learned, ‘Hedge Fund Diversification: How Much is Enough?’, Journal of Alternative Investments. 6 Jaeger, Lars (2002). 7 Based on Jaffer (2002) cited in note 2 above. 8 Rahl, Leslie (2003). 9 Based on Jaffer (2002) cited in note 2 above. 10 Ibid. 11 Ibid. 12 Ibid. 13 Ibid. 14 Ibid. 15 Ibid. 16 Yves, Courtois (May 2003), Financial Risk Management for Hedge Funds Survey, KPMG, Luxembourg. 17 Details of the IAFE’s Investor Risk Committee can be found at www.iafe.org. 18 Source: IAFE Investor Risk Committee Consensus Document of 27 July 2001. Reproduced with the kind permission of IAFE.
107
Chapter 27
Style drifts: monitoring, detection and control Pierre-Yves Moix, RMF Investment Management, Man Group, Pfaeffikon This chapter has been reproduced with permission from The New Generation of Risk Management for Hedge Funds and Private Equity Investments, edited by Lars Jaeger, published by Euromoney Books, London 2003 (© Euromoney Institutional Investor plc, all rights reserved).
Introduction The detection, monitoring and control of style drifts is perceived as a key preoccupation by hedge fund investors. A recent survey conducted by Deutsche Bank revealed that 73 per cent of hedge fund investors wanted managers to disclose strategy drift monitoring, which was the second most cited transparency issue after reporting on the amount of leverage used.1 Even though style drifts do not necessarily have a negative impact on performance, they should be avoided. They may distort several decisions made during the investment process, such as asset allocation and manager selection. The discussion of style drifts is not only specific to hedge fund investing, but a subject of concern for mutual fund investors. Accordingly, various financial information vendors assess the style purity of the constituents of the mutual fund universe. In the long-only world, style drifts can be identified relatively easily and measured precisely, either from portfolio holding information or by making use of standard quantitative techniques based on portfolio returns. The peculiarity of style drift analysis in hedge fund investment lies in its complexity. First, the definition of ‘investment style’ is ambiguous. The essence of hedge fund investing is the focus on absolute returns, as opposed to performance relative to a benchmark. As a result, hedge fund managers do not try to mimic the performance of a given asset class or set of asset classes. Moreover, in sharp contrast to long-only portfolios, hedge fund managers face few, if any, investment guideline restrictions and operate very opportunistically. Second, due to the dynamic nature of their trading strategies, hedge fund managers frequently change their portfolio holdings and monitoring of potential style drifts is thus made difficult. This chapter is organised as follows. The initial section defines the concepts of investment style and strategy within the context of hedge fund investing. The importance of style and strategy drift monitoring is discussed in the subsequent section. Following this, there is a review of the main reasons that drive managers to drift away from their styles. The analysis of the main rationales for potential style drifts helps in the implementation of adequate approaches for the monitoring, detection and control of style and strategy drifts. These approaches are then explained, followed by the conclusion.
On styles and strategies The detection of style drifts presupposes that investment styles may be identified according to certain parameters and that these parameters may be monitored by the investor on an ongo-
387
PART IV: RISK MANAGEMENT TECHNIQUES
ing basis. As discussed, the freedom given to hedge fund managers and the complexity of their investment strategies make the identification of hedge fund styles difficult. One can even question whether the definition of ‘style’ for hedge fund investing is pertinent. We believe that the definition of style and strategy is possible, but has to be addressed in a different way compared to traditional asset classes. Moreover, as discussed in the next section, the definition of style and strategy is not only an academic exercise, but also a prerequisite of a structured approach to investing. Note that the term ‘hedge fund style’ refers either to a generic classification of hedge fund managers according to given criteria or to the specific investment approach of a particular hedge fund manager. To avoid confusion, we use ‘style’ to refer to the generic and ‘strategy’ to refer to the specific approach of a manager. The notion of style assumes that a non-negligible part of hedge fund performance can be explained by attributes common to a specific investment approach. The notion of strategy reflects the fact that hedge fund investing is heterogeneous by nature and therefore style attributes capture only some of the characteristics of a particular hedge fund strategy. Traditional asset managers such as mutual funds typically hold long positions in predefined types of asset classes and are constrained to very little or no leverage. Their performance is generally highly correlated to the returns on indices of standard asset classes. Sharpe (1992) showed that the performance of mutual funds may be replicated with a high level of precision by modelling a linear exposure to a limited number of standard asset classes. As a result, a mutual fund style may be adequately described by appropriate information on the markets and instruments traded. In other words, the key attribute of a mutual fund style is the nature of its holdings. The conventional style analysis of Sharpe is not appropriate when applied without modification to hedge funds. This means that knowledge of portfolio holdings is not sufficient to identify hedge fund styles and therefore to monitor potential drifts. This is not surprising, since Sharpe’s analysis does not account for the increased flexibility of hedge fund strategies. Hedge fund managers can not only choose among a larger set of asset classes, but implement dynamic trading strategies, hold long and short positions, and use leverage in a discretionary way. To capture the flexibility of hedge fund investing, several researchers have extended or modified the initial work of Sharpe, mostly using returns-based information to identify and explain the factors driving the performance of hedge funds. Good references are the materials by Fung and Hsieh (1997, 1999, 2003), Schneeweis and Spurgin (1998), Agarwal and Naik (2000 a,b,c), and Brealey and Kaplanis (2001). The above list is by no means exhaustive. A review of the literature is beyond the scope of this chapter, but some of its main findings are important for style drift analysis. First, stylistic differences explain a part of the observed performance differences among hedge funds. Brown and Goetzmann (2003) find that more than 20 per cent of the variability of fund returns can be explained solely by the style of management. The notion of style is therefore meaningful to investors. Second, return may be interpreted as a premium for an exposure to risk and therefore the nature of the risk factors that funds are exposed to enables the description of an investment style. Third, the performance-generating process of hedge funds is complex and a linear exposure to factors based on the returns of standard asset classes is not sufficient to describe the risk taken by hedge funds. A description of the main risk factors affecting the performance of the most common hedge fund styles can be found in the article by Moix and Scholz (2003). For hedge fund style drift analysis, the monitoring of exposures to identified risk factors is more important than the
388
STYLE DRIFTS: MONITORING, DETECTION AND CONTROL
review of position holdings. This is particularly true since hedge fund managers can combine financial instruments in many different ways to achieve a given risk exposure. It is interesting to note that the style classification based on self-reporting and used by data vendors performs almost as well as the latest returns-based academic studies in explaining stylistic differences among managers. However, the academic studies have the advantage of giving an analytical framework to support the definition of styles, by explicitly identifying the risk factors affecting the performance of the different hedge fund styles, and can provide insight into the nature of the exposures to the identified risk factors. We believe that further research will be able to give more insight into the risk factors explaining stylistic differences by considering some of the following points: • not only using factors derived from financial data (for example, returns, volatilities and credit spreads) but also considering macroeconomic factors (for example, liquidity, GDP growth and central bank activities) and microeconomic factors; • including for each style a set of factors unique to the corresponding style (for example, trading volumes, new issuances, and mergers and acquisitions), since the degree of overlap of the different strategies is relatively small; and • using more than returns-based information from the manager, such as risk exposure and performance attribution reports. Another important aspect of hedge fund investing, which partly explains the difficulty faced by academic researchers when trying to uncover the link between hedge fund styles and risk factors, is the heterogeneity of hedge fund investing on the strategy level. There are many niche styles in the hedge fund universe and every hedge fund follows its own proprietary strategy, that is, every manager implements an investment style in a very specific way in a real portfolio. As a result, style analysis is not sufficient for investment purposes, but should be complemented by a detailed analysis of the particular investment strategy of the hedge fund of interest. This is one of the key goals of due diligence. During the due diligence process, the potential investor has to understand the types of trade ideas the manager generates; the performance characteristics of the manager’s strategy; and how it relates to different types of market conditions. Strategies that cannot be followed in detail should be avoided.
Style drift: definition and importance Style or strategy drift may be generally defined as the manager’s departure from his area of competence. Hedge fund investing deals primarily with skill-based investing. The skill of a manager consists mainly in finding an investment idea with an attractive risk and return profile; understanding and being able to control the profile in the various types of market environments, and to be able to implement the trading idea in a real portfolio. The potential investor has to understand the particular skill set of a manager and decide whether this skill set is compatible with, and sufficient for running, the investment strategy. In addition, the investor has to assess whether the strategy of the manager fits in with their investment objectives. As discussed earlier, the flexibility of hedge fund investing has many consequences for the analysis of style and strategies. Position checks, that is, types of assets in the portfolio, are not sufficient and probably not the most important part of the analysis. Rather, understanding the types of risk factors a strategy is exposed to and the nature of the corresponding exposure
389
PART IV: RISK MANAGEMENT TECHNIQUES
is essential. Once this has been achieved, the type of market environments in which the manager makes or loses money may be understood and monitored. Style and/or strategy drift can therefore be defined as the following. • Drift in the exposure to a predefined set of risk factors. This may occur in two ways. First, the manager can take exposure to risk factors outside the scope of his investment strategy. For example, we do not want a merger arbitrage manager to be exposed to the significant liquidity and credit risk associated with distressed debt investing. Second, the manager can take a different type of exposure to the predefined risk factors as expected. For example, a market-neutral manager should have significant long and short exposures, but only a residual net exposure to equity indices. A significant net long or net short exposure is therefore a style drift. The risk taken by a market neutral manager should be spread risk and not market risk. • Change in the overall quantity of risk of the fund, mostly through the level of leverage used. The adequate level of leverage depends on the style/strategy implemented and also on the current market environment. Note that the use of specific types of assets or the coverage of particular markets may represent a style drift only if specific guidelines or restrictions have been imposed on the manager. In this case the monitoring of positions is necessary. Not all style and strategy drifts are undesirable. On the contrary, the ability of some hedge fund managers to change their strategies in response to economic circumstances may be very beneficial to investors. This potential ability should, however, be analysed in detail before investing and should then be considered as part of the manager’s strategy. It is also not unusual for a hedge fund manager to implement a new style or strategy. In most cases, the manager does it in a transparent way by informing existing clients proactively. Moreover, the new strategy is tested prior to being offered to a broad range of investors. To this end the strategy is typically implemented in separate accounts, most often with proprietary money or with money from investors willing to sponsor it. In fact, the kinds of style drifts that have to be avoided are the unexpected style drifts that have not been communicated to, and agreed with, the investors. Even unexpected style drifts may not necessarily have a negative impact on performance. A recent study by Wermers (2002) covering the US equity mutual fund industry points out that managers who tend to have an above-average level of style drift deliver superior future portfolio performance. However, unexpected style drifts have to be avoided for at least two reasons. First, from the bottom-up perspective of manager selection and monitoring, style drifts make part of the analyses conducted and the conclusions drawn during due diligence useless. Second, from the top-down view of asset allocation and portfolio construction, style drifts invalidate the assumptions made about risk-return profiles and may therefore destroy the expected diversification benefits resulting from style and manager mix.
Due diligence Investors should spend considerable time evaluating and selecting hedge funds. To this end they should review all factors relevant to making a prudent investment decision. This involves not only the understanding of the investment strategy, but the assessment of the manager’s ability to address the associated strategy and structural risks. The ultimate goal of due diligence is to assess not only whether a given hedge fund manager is a good asset manager,
390
STYLE DRIFTS: MONITORING, DETECTION AND CONTROL
but whether they have an edge in a particular strategy, and possess the necessary infrastructure and experience for running this strategy. Some aspects of due diligence, such as the assessment of the manager’s business model, are common to all hedge funds, whereas others are style-specific. These style-specific components naturally entail a review of the factors explaining the risk and return profile of a hedge fund. For example, leverage is not really an issue for long-only distressed debt managers, while liquidity risk is not the main concern of commodity trading adviser (CTA) managed futures investors. Other aspects of the due diligence process are also related to a specific style, such as the trading experience of a manager, the implemented risk strategies, the risk management infrastructure, the administration and so on. As a result, due diligence questionnaires are style-specific and the lion’s share of manager interviews covers style-related issues. This focus on style-relevant issues avoids wasting the involved parties’ time. In the event of an unexpected style drift, the significant style-specific components of due diligence become useless. In theory, the manager should be reassessed with respect to the newly implemented strategy. In practice, the occurrence of an unexpected style drift raises a warning signal and the most common consequence is redemption.
Asset allocation and portfolio construction The identification of styles is essential for investors using a top-down approach as a building block in the investment process. It allows them to perform an effective asset allocation, that is, to define the optimal style mix for a given risk and return profile. Style diversification has proved to be very effective in delivering consistent performance in various market conditions. In general, the asset allocation comprises two levels. The strategic level defines a neutral style mix based on the performance characteristics of the different styles under different market environments and their correlation structure. The tactical asset allocation is a forward-looking process that adapts the neutral allocation to prevailing market conditions. Portfolio construction consists of investing in hedge funds that have successfully passed the due diligence process according to the defined tactical asset allocation. Portfolio construction is not a mechanical implementation of asset allocation. Asset allocation is based on the aggregated information at the style level. Portfolio construction makes use of the additional strategy-specific information at the hedge fund level in order to understand the way in which risks of individual managers interact. Independently, from the level of technicality used for style and portfolio diversification, that is, qualitative judgement, correlation analysis or diversification with respect to a given set of risk factors, the investor has to implicitly or explicitly assume a given behaviour of the underlying hedge funds in different market environments. An unexpected style drift, even from a positive performance point of view, alters the risk and return characteristics of the corresponding fund, resulting in a violation of the original set of assumptions used for asset allocation and portfolio construction. As a result, the diversification benefits of the asset mix may be seriously compromised.
Main reasons for style drifts Understanding the motivations that drive a manager to operate outside their area of expertise is very useful for the early detection of potential drifts. The main reasons for style and strategy drifts that we have identified include the following.
391
PART IV: RISK MANAGEMENT TECHNIQUES
• Poor market environment. The compensation of hedge fund managers is mostly a function of the absolute performance they deliver. In the case of a challenging style-specific market environment, the temptation is therefore high to opportunistically change the strategy in order to increase performance. Variants on this type of style drift are an increase in leverage or investment in lower-quality assets or trades. • Asset flows and limited capacity of the strategy. Successful managers often have the opportunity to attract more money than their strategy may sustain. Where they accept too much money relative to the trading opportunities, one possible consequence, besides a degradation of performance, is a drift away from the core strategy. • Underperformance with respect to their peers. Hedge fund investing is a very competitive business. Hedge fund managers are on the radar screens of an increasing number of investment professionals, fund of funds managers or institutional investors, who compare their performance with that of their peers. In order to improve their ‘peer group ranking’ hedge fund managers may be tempted to change their investment style or to increase the level of risk. • Large drawdown. The occurrence of a large drawdown may influence the way in which the manager runs their portfolio. They may be tempted to increase the risk level and/or even to take additional bets with the hope of retrieving the losses. Conversely, they may attempt to reduce the overall risk exposure in order to avoid further losses. In both cases the alteration of the risk and return profile leads to a style drift. • Change in key investment professionals. The departure of key investment professionals may alter the strategy of the fund, since specific skills are not transferable. • Changes in market structure or regulatory environment. Market structure or regulatory changes may hit hedge fund strategies that exploit specific opportunities. An example is the arbitraging by mutual fund timers of stales prices due to the time lag involved in international mutual funds. The strategy is confronted to both the resistance of mutual fund managers and the introduction of improved portfolio valuation procedures.
How can a style drift be detected, monitored and controlled? The detection and monitoring of style drifts is embedded in the ongoing due diligence and risk management processes of a hedge fund investor. The different approaches mentioned in this section therefore contribute to, but do not serve, the sole purpose of drift analysis. These approaches are different pieces of the puzzle, which include understanding and monitoring the manager’s strategy, and assessing their risk and return profile in an absolute way, with respect to their peer group and in light of the prevailing market conditions. No single analysis gives the investor sufficient comfort to make a definitive judgement; it is the combination of information obtained with the different approaches that gives a good picture of a portfolio. As usual with investment and risk management, systematic and disciplined processes are prerequisites for success. As discussed in the above section, the main rationales for potential style drifts are a poor market environment, the imbalance between the asset flows and the capacity of the style and strategies, the underperformance of the manager, the occurrence of a large drawdown, the departure of key investment professionals, and changes in market structure or regulatory environment. These indicators of potential style drifts have to be monitored with particular attention in the spirit of proactive risk management. The avoidance of undesired risks such as style drifts is always more desirable than the management of their consequences. Almost all
392
STYLE DRIFTS: MONITORING, DETECTION AND CONTROL
indicators of style drift are monitored during the analyses (which are discussed below). One exception is monitoring change in key investment professionals, which is covered by ongoing due diligence. Another exception is the analysis of potential imbalances between style and strategy capacity and money flows. At the style level, timely estimates of asset flows to the different hedge fund styles are provided by specialised suppliers of hedge fund data. The assessment of the corresponding capacity is a function of the current market opportunities that are assessed during the monitoring of risk factors (discussed below). At the strategy level, the analysis and monitoring of the strategy capacity and asset flows to the single hedge funds are parts of the ongoing due diligence effort. Finally, changes in market structure or regulatory environment are followed closely by professional participants in the hedge fund industry. The detection of style drifts using due diligence and risk management processes is therefore still dependent on the information available on the different managers and their portfolios. Needless to say, a certain level of transparency is key to the successful detection of style drifts.
The buzz word: transparency Although almost everyone agrees on the fact that transparency is a prerequisite of prudent investing, the definition of transparency varies considerably among practitioners and academics, ranging from communication with a manager to full disclosure of positions. Substantial and controversial contributions to the topic may be found in the materials by Rahl (2003), Reynolds Parker (2000) and Jaeger (2002). A detailed discussion of transparency is beyond the scope of this chapter; our conception of transparency has been described in Moix’s article (2003). In short, investors need at least full business and investment process transparency as well as adequate portfolio transparency. Business transparency entails detailed information about all factors needed for the success of a hedge fund, for example, people, infrastructure and client structure, as well as legal and organisational framework. Investment process transparency involves the disclosure of investment strategy, asset selection and allocation procedures, portfolio construction methodology, and risk management strategies and processes. Both business and investment process transparency allow an understanding of the market conditions that place stress on the investment strategy, as well as assessing the ability of the organisation to address the strategy and structural risks. Adequate portfolio transparency (defined below) is necessary for the ongoing review of investments. In order to detect style drifts, investment process and portfolio transparency are needed. During the due diligence process, the following aspects of the investment strategy should at least be covered: • • • • • • • • • •
rationale for the strategy and trade examples; main risk factors; types of exposure to the risk factors; performance and risk attribution; target risk and return; expected maximum drawdown and the largest experienced drawdowns; portfolio turnover; liquidity distribution; portfolio concentration; and identification of market scenarios significantly affecting performance.
393
PART IV: RISK MANAGEMENT TECHNIQUES
Clearly, the above list is not exhaustive and omits style specific issues. As mentioned, one of the main goals of due diligence is the complete understanding of factors driving the performance of a portfolio, as well as the impact on performance of different types of market environments. The experienced investor, after careful due diligence, can assess the attractiveness of the investment strategy and the ability of the manager to successfully implement the strategy. From a style drift perspective, the information obtained during the due diligence gives detailed information on the risk and return characteristics of the investment mandate. These characteristics have to be validated during the initial due diligence and verified regularly after investment. Portfolio-specific information should be updated on a regular basis and at least monthly. In addition to net asset values (NAVs), adequate portfolio transparency should entail profit-and-loss attribution, and exposure to a predefined set of risk factors. This should relate to several dimensions such as asset classes, region and currency. The nature of the exposures should also be disclosed. As a minimum, gross long and short exposures should be reported separately, which is particularly important for market-neutral strategies. Finally, managers should disclose concentration and liquidity figures. To process this information efficiently the profit and loss attribution and exposures reports should be standardised. Moreover, this standardisation helps the investor to analyse all hedge funds in a consistent way and, therefore, to compare the managers. The Investor Risk Committee of the International Association of Financial Engineers (IAFE) has made an important first step towards standardisation in its published report Hedge Fund Disclosure for Institutional Investors. Managers are more and more willing to provide this kind of information to their clients. Note that it is difficult to map all hedge fund styles onto a common set of risk factors, so the mapping scheme should entail style-specific components.
Monitoring the factors driving the performance of styles and strategies The careful monitoring of the evolution and levels of the identified style- and strategy-specific risk factors is an integral part of the asset allocation process, whose goal is to deliver consistent performance in various market conditions. For factors derived from financial data, such as returns, volatilities and credit spreads, the appropriate information can be found in the usual financial information sources. The acquisition of data for macroeconomic and style specific factors presupposes the sometimes tedious search of various highly specialised data sources. The monitoring of risk factors has several uses in the detection of style drift. First, the analysis of the recent evolution of risk factors helps investors to understand in which market environment hedge fund managers have operated, and therefore serves to crosscheck the realised profit and losses. Second, the analysis of the current levels of the risk factors provides an insight into the current market environment. As mentioned previously, a poor market environment is a leading indicator for potential drifts. The prevailing market conditions do not affect the different styles equally. It is particularly useful to compare the current levels of, and changes in, the risk factors with their long-term historical averages, as well as with historical periods of stress. It should also be taken into account that many styles exhibit asymmetric sensitivities to risk factors in different environments. For instance, as shown in the article by Fung and Hsieh (1999), CTA funds tend to perform well during extreme moves in the US equity market and less well during calmer times in US equities.
394
STYLE DRIFTS: MONITORING, DETECTION AND CONTROL
Returns-based analysis A returns-based analysis is a time series analysis that confirms that the hedge fund has performed consistently with its stated investment objectives in terms of risk, return, correlation with predefined asset classes and benchmarks. This analysis is generally performed during the initial due diligence and updated within the context of ongoing due diligence and risk management. It should take into account the prevailing market conditions and assess whether the realised performance is compatible with the current market opportunities. To this end, the monitoring of the risk factors and the due-diligence-related review of market scenarios affecting performance are very helpful. The analysis of time-varying risk and return statistics gives a good picture of the dynamic nature of hedge fund strategies. The construction and analysis of empirical confidence intervals for the monitored risk and return statistics gives an indication of potential strategy drifts or an increase in the general risk level. To this end, the reasons for each figure lying outside its confidence interval have to be understood. Note that an increase in risk or a change in style does not necessarily have a negative impact on performance. Positive break-outs, that is, abnormal positive returns, should therefore be considered as being just as suspect as negative ones. Unusual high positive returns should be interpreted as a strong warning signal for investors, who often tend to invest in past high performers. A recent example is the Eifuku master fund, an Asian equity long/short hedge fund that collapsed at the beginning of 2003. The fund posted an astonishing return of 76 per cent in 2002, which was not in relation to the strategy followed. As discussed previously, drawdowns are leading indicators for potential strategy drifts. If a fund exhibits a drawdown, its size and length give an indication of the sentiment of the corresponding hedge fund manager. This should be compared with the expected worst drawdown and the historical largest drawdowns, in light of the current market environment. The absolute size of the drawdown must also be analysed with respect to the risk management strategy, that is, the loss-cutting strategy of the fund. A large drawdown should imply frequent and detailed communication with the manager.
Analysis of performance attribution and risk exposures Whereas the return-based analysis of potential style drifts facilitates both the assessment of overall hedge fund performance over time and whether it is compatible with the strategy of the manager, the analysis of profit and loss attribution gives insight into where the performance is coming from. To this end, profit and loss numbers have to be analysed across several dimensions such as asset classes, region and currency. First, it verifies whether the manager has been active in the asset classes and regions corresponding to his strategy, and to the skills assessed during the due diligence process. Second, in combination with monitoring the risk factors it enables the assessment of whether the performance level in the different dimensions is compatible with the strategy. It is, for example, difficult for a long-term trend follower to generate a highly profitable performance in US equities in times of strong reversals in the US equity market. Whereas the performance attribution analysis is based on realised performance and helps to detect style drifts retrospectively, the analysis of the current exposures in the different dimensions discussed above provides an insight into potential style drifts. Analysing exposure trends and comparing exposures between managers of the same style provides a cross-sectional and dynamic view of the risks taken by a manager.
395
PART IV: RISK MANAGEMENT TECHNIQUES
Peer group analysis In a peer group analysis, managers are continuously assessed against their peers, and ranked with respect to the various risk, return and performance measures. The assumption made is that the constituents of a well-constructed peer group should have the same kind of exposure to the same set of risk factors. This can be validated by the means of linear regressions of the single hedge fund returns on the peer group average. If the assumption is verified, the explanatory power of the regression will be high. In this case the alpha can be interpreted as the manager’s skill with respect to the strategy’s implementation and the beta can serve as a proxy for the level of leverage used relative to the peer group. As mentioned earlier, underperformance with respect to peers is a leading indicator of a potential style drift. Moreover, relative overperformance may be an ex-post indicator of abnormal risk level. Accordingly, the ranking of a manager with respect to risk and return measures and, most importantly, the changes in ranking have to be observed regularly. The peer group analysis is an ideal complement to the returns-based approach: whereas the returns-based analysis reviews the performance of a single manager in different types of market environments, the peer-group approach is a cross-sectional analysis of different managers sharing a common investment style in exactly the same market environment. A good example of the complementary use of the returns-based and peer group analyses is the assessment of return break-outs, that is, returns that lie outside a predefined confidence interval. The return break-outs detected during a returns-based analysis may be caused by a change in market conditions or by a change in the type and/or level of risk taken by the hedge fund manager. The latter clearly represents a strategy drift. In the case of a break-out caused by a change in market conditions several peer group members will exhibit a corresponding break-out.
Analysis of positions The analysis of single positions cannot help to avoid style drifts. However, it may accelerate the detection of drifts and help to validate the accuracy of a manager’s reported numbers. The checking of positions requires full portfolio transparency, for which managed accounts are the ideal vehicle. A managed account set-up requires a large infrastructure. Besides legal issues, a managed account platform necessitates a large investment in staff and systems. This facilitates position-gathering from the manager, different prime brokers and counterparties. Positions can then be reconciled on a daily basis and all types of financial instruments that are not necessarily exchange-traded can be priced. Our daily experience with the risk management of managed accounts representing all main investment styles for a total investment of several billions of US dollars makes us aware of the difficulty, and the importance, of accurate and timely reconciliation and valuation procedures. Moreover, the large amount of available data has to be processed accurately and efficiently in order to become valuable information, for example, the calculation of the exposures to a predefined set of risk factors. This requires an in-depth understanding of the different strategies to aggregate the positions belonging to the same trade, and to understand the risks inherent in the different trades and strategies. Position transparency is necessary if guidelines and restrictions concerning specific types of assets or markets have been imposed on the manager. This is, however, rather unusual.
396
STYLE DRIFTS: MONITORING, DETECTION AND CONTROL
Talk to your manager Ongoing communication with a manager allows warning signals of style drifts to be detected. Although hedge fund managers may be reluctant to send data with portfolio-holding information, we have never invested money with a manager who was not willing to share as much information as we needed to understand their trading ideas. Managers do not like to waste time with inexperienced investors armed with a questionnaire full of irrelevant questions. When dealing with a professional investor who has already completed the analyses discussed above and really understands the strategy, managers are generally willing to provide detailed information on specific trades. The investor can then make a rational judgement as to the suitability of these trades with respect to the strategy.
Conclusion The assessment of style drift in hedge fund investing is a difficult exercise. This is due to the large freedom given to hedge fund managers, the complex and dynamic nature of their investment strategies, and the large range of instruments used. In contrast to mutual fund investment, the detection of style drift goes beyond the usual position checks, and requires the understanding and monitoring of risk factors driving performance. Even if unexpected style drifts do not necessarily have a negative impact on performance, they should be avoided. In the event of a style drift, style-specific components of due diligence are useless and the overall asset allocation could be invalidated. The main reasons driving managers to drift away from their area of expertise are a poor market environment, imbalance between asset flows and the capacity of the strategy, underperformance with respect to direct competitors, the occurrence of a large drawdown, the departure of key investment professionals, and changes in market structure or regulatory environment. The occurrence of these events has to be monitored on an ongoing basis. The procedures and analyses used for the detection of style drifts are part of the investment and risk management processes. The monitoring of style-specific risk factors and market environments represents an important decision basis for the tactical asset allocation, whose aim is to spread the portfolio exposures across a range of styles and therefore of risk factors. Returns-based analysis, performance attribution, risk exposure monitoring and peer group comparisons are all elements in ongoing due diligence and risk management efforts. Each analysis uncovers a different aspect of the hedge fund strategy characteristics and related risks, and helps in the avoidance or the control of style drifts. Having conducted these analyses, the investor is armed with a detailed understanding of the manager’s strategy, and a deeper insight into the portfolio’s current composition and exposures. This is of great value when asking appropriate questions and obtaining the right answers from a manager during the regular interviews that are conducted as part of ongoing due diligence.
References Agarwal, V., and N. Y. Naik (2000a), Performance Evaluation of Hedge Funds with Optionbased and Buy-and-Hold Strategies, Working Paper, London, London Business School. Agarwal, V., and N. Y. Naik (2000b), ‘On Taking the Alternative Route: The Risks, Rewards, and Performance Persistence of Hedge Funds’, Journal of Alternative Investments, Vol. 2, No. 4, pp. 6–23.
397
PART IV: RISK MANAGEMENT TECHNIQUES
Agarwal, V., and N. Y. Naik (2000c), ‘Generalised Style Analysis of Hedge Funds’, Journal of Asset Management, Vol. 1, No. 1, pp. 93–109. Brown, S. J., and W. N. Goetzmann (2000), ‘Hedge Funds with Style’, Journal of Portfolio Management, 2003, Vol. 29, No. 2, pp. 101–112. Brealey, R. A., and E. Kaplanis (2001), ‘Hedge Funds and Financial Stability: An Analysis of their Factor Exposures’, International Finance, Vol. 4, No. 2, pp. 161–187. Fung, W., and D. A. Hsieh (1997), ‘Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds’, Review of Financial Studies, Vol. 10, No. 2, pp. 275–302. Fung, W., and D. A. Hsieh (1999), ‘A Primer on Hedge Funds’, Journal of Empirical Finance, Vol. 6, pp. 309–331. Fung, W., and D. A. Hsieh (2003), ‘Asset-Based Style Factors for Hedge Funds’, Financial Analyst Journal, Vol. 58, No. 5, pp. 16–27. International Association of Financial Engineers (IAFE), Investor Risk Committee (2001), Hedge Fund Disclosure for Institutional Investors. Jaeger, L. (2000), Managing Risk in Alternative Investment Strategies: Successful Investing in Hedge Funds and Managed Futures, Harlow, Prentice Hall. Moix, P. Y., and S. Scholz (2003), ‘Risk control strategies: the manager’s perspective’, Funds of Hedge Funds, Ed. S. Jaffer, London, Euromoney Books, pp. 219–233. Moix, P. Y. (April 2003), ‘Transparency for Hedge Fund Investors – Contribution to a Major Discussion’, AIMA Journal, AIMA. Rahl, L. (2003), Hedge Fund Risk Transparency: Unravelling the Complex and Controversial Debate, London, Risk Books. Reynolds Parker, V. (2000), ‘The Critical Path to Effective Hedge Fund Risk Management: Control, Transparency and Risk and Performance Measurement’, Managing Hedge Fund Risk, Ed. V. Reynolds Parker, London, Risk Books. Schneeweis, T., and R. Spurgin (1998), ‘Multifactor Analysis of Hedge Fund, Managed Futures and Mutual Fund Return and Risk Characteristics’, Journal of Alternative Investments, Vol. 1, No. 2, pp. 1–24. Sharpe, W. (1992), ‘Asset Allocation: Management Style and Performance Measurement’, Journal of Portfolio Management, Vol. 18, No. 2, pp. 7–19. Wermers, R. (2002), A Matter of Style: The Causes and Consequences of Style Drift in Institutional Portfolios, Working Paper, University of Maryland. 1
Deutsche Bank, Alternative Investment Survey, March 2002.
398
Chapter 17
Risk control strategies: the manager’s perspective Pierre-Yves Moix, PhD, CFA, FRM and Stefan Scholz, PhD RMF Investment Products, Pfaeffikon, Switzerland This chapter has been reproduced with permission from Funds of Hedge Funds for Professional Investors and Managers, edited by Sohail Jaffer, published by Euromoney Books, London 2003 (© Euromoney Institutional Investor plc, all rights reserved).
Introduction In its September 2001 study Funds of Hedge Funds: Rethinking the Resource Requirements, the Barra Strategic Consulting Group stated that risk management is becoming the most important differentiating factor when investors look at funds of hedge funds. This is due to the fact that a growing number of institutional investors are becoming interested in alternative investment strategies, so that the proportion of institutional investors as compared to high net worth individuals is increasing. In comparison to private clients, institutional investors have to comply with a larger number of laws and regulations. Moreover, they want hedge funds to fit into their traditional asset allocation and risk management framework. In addition, institutional investors face a huge headline risk, in that they cannot afford to be involved in a major hedge fund collapse such as LTCM. As a result, investors are becoming more demanding with respect to transparency and risk management, and self-regulation of the industry is starting to occur. Nevertheless, it should be pointed out that the perception of hedge fund risk is somewhat biased and, often, hedge funds are perceived as ‘black boxes’. The same is certainly true for the proprietary trading desks of the investment banks. However, no one would dare to ask them to disclose their positions even though they are the largest hedge funds in the world. In fact, investment banks lost more money than most hedge funds in the course of the LTCM disaster. Looking at the role of a traditional fund of hedge funds, it is apparent that risk management plays a crucial role at three different levels. First, there are the underlying hedge fund investments, which have to be carefully selected and monitored on an ongoing basis. Secondly, there is the portfolio level – a particular fund of funds, which consists of several of the underlying funds. Clearly, it faces the same risks as the hedge funds while providing some additional potential for risk control. Finally, there is the level of the fund of funds firm itself, mainly dealing with operational and business risks that are beyond the scope of this chapter. Thus, in this context, risk control involves the gathering of information, the aggregation of this information, the definition of rules and procedures for taking appropriate action and the communication of relevant information to clients. The transparency of the underlying hedge fund investments is at the heart of the discussion. These comments define the structure of the remainder of this chapter, which first outlines our classification of the risk types and factors inherent in a hedge fund investment. Leverage
219
PERFORMANCE MEASUREMENT AND RISK CONTROL
in itself is not a risk type but a means to scale the profit and loss distribution. Nevertheless, it has to be analysed in the context of market and liquidity risk. The discussion about risk types serves as the basis for the final main section of the chapter where risk monitoring and management are covered. As mentioned, transparency is at the heart of every risk control effort.
Risk types and leverage Due to the special characteristic of hedge funds – their greater freedom in choosing investment strategies – we distinguish two generic types of risks: strategy risks and structural risks. Contrary to common belief, leverage in itself is neither a risk type nor a risk measure but a means to gear performance and risk equally. However, because leverage has to be analysed in the context of liquidity and market risk of the underlying assets, it will be examined in this section.
Structural risks Structural risks are risks arising from a hedge fund’s business structure, its operation and management. In the classic categorisation of risk types, many of these risks are summarised under the heading ‘operational risk’. Traditionally, operational risk is defined as the risk of direct or indirect loss resulting from inadequate or failed internal processes, people and systems, or from external events. This definition is also used by the IAFE’s Committee on Operational Risk in its latest report on evaluating operational risk controls. In that context, there is much emphasis on the importance of a broad definition of operational risk. Significantly, issues such as reputational damage, which is difficult to quantify, have to be taken into account in addition to quantifiable risks. As mentioned in the introduction, headline risk is by far the greatest concern of large institutional investors. Thus, structural risks have to be addressed very carefully by the fund of funds manager through proactive risk management, and ongoing risk monitoring and management. These will be examined in the section ‘Risk monitoring and management’ later in this chapter.
Strategy risks Strategy risks are inherent in the investment strategy and its execution. The investment strategy determines how the manager invests, which markets and instruments are used, and which opportunity and return source are targeted. These risks are usually subsumed under the following risk types: market risk, liquidity risk and credit risk. Market risk is the risk arising from changes in financial asset prices. Credit risk is the risk that a borrower or counterparty will fail to meet its obligations in accordance with agreed terms. Liquidity risk has to be subdivided into two categories: trading liquidity risk and funding liquidity risk. The former is the risk arising from the inability, due to prevailing market conditions, to rapidly execute largevolume transactions at all or without a negative impact on market prices. Funding liquidity risk arises from the inability to meet contractual payments, either through borrowing or through the sale of financial assets, at all or without high transaction costs. As illustrated in Exhibit 17.1, these risk types are not isolated but closely interrelated. This is especially pronounced in times of market crisis. Therefore, they have to be addressed in a unified and integrated manner. Initially, we shall analyse two specific relations of the various risk types. First, when
220
RISK CONTROL STRATEGIES: THE MANAGER’S PERSPECTIVE
Exhibit 17.1 The interrelation of risk types Market risk
Credit risk associated with investments
Credit risk Asset liquidity
Credit risk associated with counterparties
Funding liquidity
Operational risk Liquidity risk
Source: Adapted from Sound Practices for Hedge Fund Managers (see References for details).
investors start to withdraw their money from a hedge fund, there is a funding liquidity risk: that is, the manager might be forced to sell assets. If the market liquidity is insufficient to do so, the fund manager faces additional trading liquidity risk that might very well translate into market risk once the asset prices start dropping due to the forced selling. As outlined in the next section, this effect is even more pronounced when the manager uses leverage. Therefore, it is of crucial importance that the redemption and notice periods of a fund match the liquidity of the instruments that the fund manager trades in. It is not in the investor’s interest, for example, to have a fund manager offer monthly liquidity when he deals in highly illiquid securities. Even if an investor is aware of this and behaves accordingly, there remains the risk of co-investors damaging the fund by insisting on the legal liquidity instead of economic liquidity. The same argument can be made for funds of funds. The liquidity that is offered to investors has to match the liquidity of the underlying hedge fund investments unless there are sufficient credit lines and reserve pools in place. Secondly, there is generally a trade-off between market risk and liquidity risk: non-directional strategies are more prone to liquidity risk, whereas directional strategies are more prone to market risk. The reason is that relative value strategies typically have an edge in pricing contracts and therefore take positions when contract complexity is high or market liquidity is low. As a consequence, these strategies are mainly implemented by using over-the-counter contracts. This implies that relative value strategies primarily earn a liquidity risk premium. Directional strategies typically have an edge in identifying market trends and thus primarily earn market risk premiums. Liquidity risks are low as they are implemented using highly transparent and liquid contracts (for example, exchange-traded instruments). A market stress situation typically leads to the deterioration of long-term expectations and, as a consequence, increases the demand for liquidity. In effect, the risk aversion of investors will rise, leading to an increase in market risk, while market liquidity dries up on the bid side. Such a ‘flight to quality’ negatively affects long-duration fixed-income and
221
PERFORMANCE MEASUREMENT AND RISK CONTROL
Exhibit 17.2 Strategy-specific risk factors Style
Strategy
Main risk factors
Equity hedged
Long/short equities
Stocks, event risk (11 September)
Market-neutral/ statistical arbitrage
Volatility, bid-ask spreads, trading volume, trendless markets, model risk, time to reversion, consistent momentum, earnings-related GAP risk, event risk (11 September)
Short-selling Event-driven
Merger arbitrage
Stocks, event risk (11 September) Broken deals, time until deal completion, regulatory environment
Distressed securities
Default rates and losses, recovery rates, liquidity, legal environment
High-yield
Yield and spreads, default rates, recovery rates
Bank loans
Yield and spreads, default rates, recovery rates
Mutual fund timing
Number of days invested, stocks, interest rates, trendless markets
Special situations
Default rates and losses, recovery rates, liquidity, legal environment
Relative value
Multi-strategies
All of the above
Convertible bond arbitrage
Volatility, credit spreads, liquidity
Fixed-income arbitrage
Volatility within yield curve, liquidity, credit spreads
Derivative arbitrage
Volatility, liquidity, model risk
Emerging markets
Country, political conflicts, FX, interest rates
Mortgage-backed securities
Interest rates, consumer attitudes/confidence, liquidity, financing, model risk
Multi-strategies Global macro
All of the above
Emerging markets
Country, political conflicts, FX, interest rates
Currency trading
FX, country
Global trading
All of the above
Managed futures Discretionary trading Systematic trading: short-term traders Systematic trading: long-term trend followers
Stocks, commodities, interest rates, currencies Stocks, commodities, interest rates, currencies, model risk Stocks, commodities, interest rates, currencies, trendless markets, model risk
Source: RMF Investment Products.
growth equity assets, while short-duration and value investments become more attractive. Yield curves will steepen as banks are expected to supply liquidity or investors start shifting assets into shorter-term income assets. During such stress scenarios, long-gamma hedge fund strategies such as managed futures (CTAs) and global macro hedge funds normally gain. In contrast, short-gamma strategies such as event-driven, equity hedged and relative value lose. Such difficult hedge fund periods occurred during the autumn of 1998 and the autumn of 2001.
222
RISK CONTROL STRATEGIES: THE MANAGER’S PERSPECTIVE
Exhibit 17.3 The risk framework Level of aggregation
Strategy risks
Structural risks
Market risk
Liquidity risk
Credit risk
Operational risk
Risk factor 1
Risk factor 2
Risk factor 3
Risk factor n
Source: RMF Investment Products.
This illustrates the point that the concept of the risk types has to be taken one step further: the underlying risk factors have to be identified in order to be able to assess and manage the risk of a given hedge fund accordingly. Clearly, the risk factors are highly dependent on style and strategy. Therefore, Exhibit 17.2 lists the main risk factors according to our style and strategy classification. Note that the different strategies not only have exposures to different risk factors but also have different kinds of exposures to the risk factors. They may be long only, long-short, non-linear, etc. In order to address the risk factors, we propose to map them to the risk types. In the section ‘Risk monitoring and management’ later in the chapter we outline how the risk types are addressed. Our whole risk framework is summarised in Exhibit 17.3.
Leverage Leverage is widely used by hedge fund managers and is a major source of concern for the investor. However, leverage by itself is not a risk type but a means to scale the profit and loss distribution of a portfolio. As is common in the financial services industry, we differentiate between gross and net leverage. The former is given by the sum of long market value and short market value divided by equity. The latter is defined as the difference between long market value and short market value (ie, net exposure) divided by equity. Note that these definitions assume that short market value is expressed as a positive figure. All styles have their specific leverage profile, as illustrated in Exhibit 17.4. It is often argued that hedge funds using high levels of leverage are riskier than those using low levels of leverage. However, this is only true within homogeneous investment styles because leverage gears performance and risk equally. As such, it is not a measure of risk. For some strategies, such as convertible arbitrage, leverage is necessary to assure profitability. Thus leverage must always be analysed in the proper context. We suggest distinguishing between balance-sheet and instrument leverage. The former is achieved through repo transactions or outright credit and the latter through financial derivatives such as futures.
223
PERFORMANCE MEASUREMENT AND RISK CONTROL
Exhibit 17.4 Gross leverage versus net exposure Gross leverage Relative value
Each style has a specific leverage profile
Global macro Eventdriven Equity hedged
Eventdriven
CTA
Net exposure
Source: RMF Investment Products.
Exhibit 17.5 Gross leverage versus instrument volatility and liquidity risk versus market risk Gross leverage
Liquidity risk
Relative value Global macro
Each style has a distinct risk profile
Equity hedged
Eventdriven
CTA
Market risk
Eventdriven
Instrument volatility Source: RMF Investment Products.
The distinction is important as both measures lead to different conclusions with regard to the risk profile of a specific strategy. Relative value strategies use the highest balance-sheet leverage as the equity portion of a typical relative value hedge fund is low. Event-driven, global macro, and equity hedged hedge funds use medium balance-sheet leverage levels, whilst CTAs use no balance-sheet leverage at all. Thus one might conclude that relative value strategies bear the highest risks.
224
RISK CONTROL STRATEGIES: THE MANAGER’S PERSPECTIVE
From the perspective of individual securities, however, relative value hedge funds are generally the least risky funds as they invest in low-volatility instruments such as bonds, while directional hedge fund styles invest in high-volatility instruments such as equities or commodities. In conclusion, the true risk level depends not only on the balance-sheet leverage but also on the instruments’ volatilities and liquidity (see Exhibit 17.5). The effect of leverage on liquidity risk can best be illustrated by taking the liquidity crisis cycle as an example. Initially, a loss (typically a market risk event) occurs as a triggering event. This forces a hedge fund to sell positions in order to meet a creditor’s margin requirements (case of instrument leverage) or to pay back short-term credit lines (case of balance sheet leverage). If the speed and quantity of the liquidation are too large compared to the market liquidity, prices will drop even further, thereby triggering another round of the circle. If the drop in market prices caused by one market participant is so severe that others are forced to liquidate their positions as well, the liquidity crisis cycle becomes a fully fledged market crisis. It is important to stress that the risk in the context of this example is not the leverage itself but the forced selling that results in trading liquidity risk. As outlined in the previous section, investor redemptions (ie, funding liquidity risk) may be a catalyst speeding up the liquidity crisis cycle.
Risk monitoring and management In the previous section we identified the different potential risks and risk exposures inherent in fund of hedge funds investment. A systematic process for identifying and evaluating risks is the foundation of effective risk control. Once potential risks have been identified, they have to be managed. Strategies for managing risks include acceptance, transfer, elimination and control. Acceptance, transfer and elimination are covered by the proactive risk management process, whereas risk control is the objective of ongoing risk management and monitoring. Risk monitoring is the process of measuring the degree of risk inherent in a given portfolio. As such, it is a passive, backward-looking approach much like an accounting view. Risk management is more than risk monitoring: it employs one set of risk measures to allocate risk optimally among various assets, and uses another type of risk measure to monitor exposures and make adjustments. It can only be applied if the fund liquidity allows one to do so. This distinction will be made throughout the remainder of this chapter as it is crucial due to the nature of the different types of hedge fund investments. However, to start with we shall examine the issue of transparency, the extent and degree of which is at the heart of any risk monitoring and management effort.
Transparency The perception of the traditional investment community is that a hedge fund investment is a ‘black box’. We do not share this opinion. Often, it is the lack of understanding and the lack of differentiation capability of certain investors or money allocators that make hedge fund investments look non-transparent. Transparency allows one to review the factors material to making prudent investment decisions. We believe that reaching a satisfactory level of transparency and achieving a proper understanding of the investment strategy is paramount in investment decisions. However, it is necessary, in order to understand the nature of hedge fund investing, to understand what degree of transparency an investor can expect and should require.
225
PERFORMANCE MEASUREMENT AND RISK CONTROL
In hedge fund investing specialist managers apply specialised knowledge to generate returns by investing in arbitrage opportunities, price–value disparities, misunderstood situations, complex-to-value instruments and temporary price dislocations, and by accepting certain risks that other market participants are less adept at handling. Managers who distinguish themselves do so by acting not where profit was generated in the past, but where profit will be generated in the future. Those who correctly anticipate profit potential search in overlooked, complicated or misunderstood situations, and employ the tools and techniques necessary to realise them. Some of these opportunities are short-lived and therefore require secretive investing (eg, arbitrage). Other strategies require managers to position themselves opportunistically in markets and instruments where profit margins are rich (eg, macro investing). Again others use risk management tools that need to be invisible to other market participants in order to remain effective (eg, stop-loss limits). Therefore, it cannot be in investors’ interests to have managers of information-sensitive strategies provide complete transparency through full disclosure of all position details. For example, the risks of a short squeeze or a ‘duplication effect’ demonstrate that the call for total transparency can increase the risks of a strategy and at worst be very destructive to investment performance. Hence the call for total transparency for all hedge funds must be replaced by a demand for appropriate transparency that matches the underlying strategy. In some cases this may mean total transparency. In others, however, transparency may be very limited, barely meeting some minimum requirements to be outlined below. Generally, the level of transparency depends on the liquidity and speed of the strategy. Whereas the CTA industry is fully transparent, more complex strategies tend to be less so. This fact is mirrored in the types of hedge fund investments that are available to investors: fund investments and managed accounts. Fund investments are investment vehicles that are managed by trading advisers. They are organised as either limited liability companies (some 90 per cent) or limited partnerships (around 10 per cent) and the investment manager makes the investment decision. The main features of fund investments include limited liability and liquidity, and restricted transparency with leverage coming under the manager’s control. Managed accounts have the same structure as fund investments but are fully owned and controlled by the investor. The investment manager is hired only to execute investments in pre-agreed strategies. The main features are potential full liability of the investor, no lock-up periods and full transparency. The leverage is partly at the investor’s discretion. In other words, a fund investment is a retail product (ie, there are multiple investors) while a managed account is a customised product (ie, there is a single investor). In the context of this section, full transparency is the most important feature of managed accounts. From a risk management point of view this is clearly desirable, because information at the position level allows risk management rather than risk monitoring, which is illustrated in Exhibit 17.6. Still, it has to be stressed once more that it is not in investors’ interests if the transparency harms the success of the trading strategy. This is one of the reasons why managed accounts do not make much sense in certain strategies and why some managers are not willing to accept managed accounts. In addition, there are other issues that have to be taken into consideration. Full transparency requires, among other things, technological expertise in handling large data sets and in pricing complex financial instruments. Thus the managed account platform is resource-intensive, which implies higher costs. Moreover, transparency is not equal to economic liquidity; that is, as stated earlier,
226
RISK CONTROL STRATEGIES: THE MANAGER’S PERSPECTIVE
Exhibit 17.6 Degree of in-house risk function versus transparency Risk management
Degree of in-house risk function
Managed account
Fund investment
Risk monitoring Low Source: Risk Management and Investment Products.
Transparency
High
it does not make sense to have daily transparency if the underlying investments do not admit appropriate actions on a daily basis. In other words, the action time must be in line with the detection time. This is yet another reason why managed accounts are not appropriate for certain strategies. Given these issues, we are convinced that a fund of funds needs both investment platforms in order to meet its clients’ needs with respect to risk and performance. This is especially true because the LTCM collapse and the institutionalisation of the asset class have increased the pressure on hedge fund managers to provide adequate transparency. The Investor Risk Committee of the IAFE, composed of hedge fund investment managers and a variety of institutional investors, recently published a report entitled Hedge Fund Disclosure for Institutional Investors. Instead of asking for full transparency, it proposes disclosure along four dimensions: content (quality and sufficiency of coverage), granularity (level of detail), frequency of disclosure, and delay (lag time between disclosure and the date to which it refers). In our opinion, content and granularity should cover aggregate exposures to various risk factors such as asset class, sector, currency, region, yield curve, capitalisation, hedge fund strategy, credit quality, liquidity, etc. The way in which this information can be used in a meaningful manner will be outlined later in the chapter. In addition, strategy-specific risk factors (see Exhibit 17.2) should be covered by the Greeks correlation, etc. The adequate frequency of transparency depends on asset turnover: strategies with a high turnover call for a higher frequency than those that hold assets for a long time. If the information that is disclosed does not put the success of the trading strategy at risk there is no need to delay the disclosure. Therefore the delay should match the normal processing time at the hedge fund level and at the fund of funds level. In this framework, we think that most hedge fund managers will be able and willing to provide the information discussed without compromising their returns. Clearly, large funds of funds have a competitive advantage in receiving and processing this information.
227
PERFORMANCE MEASUREMENT AND RISK CONTROL
Proactive risk management Proactive risk management is an integral part of the investment decision. It involves asset allocation (the choice of the optimal mix of hedge fund strategies) and due diligence (the selection of hedge funds that qualify for investment). The results of the asset allocation decision and of the due diligence are implemented through portfolio construction. The end result is a portfolio with a specific risk profile. This profile should correspond to the particular needs of investors. Furthermore, risks in hedge fund investment can be divided into strategy risks and structural risks. Investors are generally willing to bear the strategy risks because they expect to receive a risk premium and to obtain diversification benefits. However, they are not compensated for bearing structural risks and are therefore unwilling to accept them. The asset allocation has a major impact on the risk profile of a fund of funds whereas the due diligence process minimises the structural risks. Asset allocation The main objective of the asset allocation is to design a portfolio the risk profile of which meets client expectations. To this end, the adequate combination of hedge fund strategies is determined by taking into account the portfolio effects. The diversification of strategies serves the mitigation of exposures to market, credit and liquidity risk. To be efficient, this topdown approach requires not only a careful determination of the strategy risks but also an assessment of the types of risk factors. The asset allocation harbours quantitative and qualitative aspects. Quantitative methods, mainly optimisation algorithms, admit the assessment of diversification benefits obtained by the combination of hedge fund styles. However, to be helpful, quantitative methods should take into consideration the characteristics of hedge fund strategies. • Hedge fund strategies are dynamic and may display an option-like payoff. As a result, hedge fund returns are not normally distributed. Therefore volatility is not a good proxy for risk. Risk measures focusing on the loss part of the return distribution are more adequate. • Most quantitative methods, including prediction methods, need historical data on hedge funds. Hedge fund data is of low frequency, exhibits a short history and is not exhaustive because performance reporting is not mandatory. A successful quantitative analysis should correct for the different biases occurring in hedge fund data. These biases do not affect all strategies equally and are not constant over time. Moreover, hedge fund data have been mostly recorded during the longest-ever equity bull market. Optimisations should be run for different time periods and market environments in order to assess the robustness of the results. • As discussed above, non-directional strategies are especially affected by liquidity risk, which is not generally assessed by traditional quantitative risk measures. As a result, these strategies tend to exhibit an artificially high risk/return profile and low correlation, and optimisation algorithms tend to overweight them. As historical returns are poor predictors of future performance, asset allocation is most effective when forward-looking estimates of returns and risk are used. This involves the qualitative analysis of the attractiveness of the different strategies. The assessment of the attractiveness requires a deep understanding of the economic and financial variables that drive the performance of single strategies. These performance drivers are multiple, and
228
RISK CONTROL STRATEGIES: THE MANAGER’S PERSPECTIVE
include market levels and directions, estimates of GDP growth, central bank activities, credit spreads, implied and historical volatilities, asset flows and market liquidities, trading volumes, new issuance, M&A activities, etc. As performance is in essence a premium for a given risk exposure, this exercise is closely related to the identification of risk factors. In order to understand the impact of identified drivers on the performance of hedge fund strategies, the analysis of various market cycles and crises is necessary. The qualitative understanding may be validated by the implementation of multi-factor models. Due diligence The essence of due diligence is the evaluation and selection of hedge fund managers. In the proactive risk management framework, due diligence serves to minimise structural risks and the assessment of the strategy risks specific to each fund, as well as of the manager’s ability to cope with them. With respect to strategy risks, due diligence allows one to have a clear view of the factors that influence the performance and therefore the specific risk profile of the individual manager. This is crucial, as single hedge funds generally do not perfectly fit into a general style classification. This requires skills to understand and evaluate manager trading strategies. Strategy evaluation is not equivalent to the review of positions or risk exposures. It requires a profound knowledge of the different markets, assets and opportunities. However, the due diligence process is much more than the assessment of a trading strategy. It involves complete analysis of the business model to avoid structural risks. A very successful proprietary trader with an outstanding track record is not necessarily a good hedge fund manager. A hedge fund manager not only has to successfully manage his or her portfolio but also has to set up and monitor a business strategy, attract and retain the necessary talented people, and build a complete infrastructure involving sales, IT, administration, risk management, etc. Therefore, the selection process implies considering the following criteria: • people. Hedge funds are skill-based strategies and hence people are the key success factor. The background, the experience and the integrity of key people have to be investigated, as well as the potential to attract talented individuals and to retain them. The incentives of partners and employees should be aligned with those of investors. Moreover, the concentration of decision-making authority has to be examined; • legal and organisational setting. Information on regulatory authorities, past and pending lawsuits, and rules for the trading of own accounts should be available; • client base. The objectives and time horizons of co-investors have to be assessed. Generally, institutional investors are longer-term-oriented, and act less emotionally and less opportunistically than private investors. The concentration of investors, the existence of sponsors and the existence of side-letters should be examined; • risk management. The quality of risk management processes and methods, and the independence of the risk management unit and of pricing sources, have to be analysed; • infrastructure. The logistical set-up plays a fundamental role in running a hedge fund. A particular emphasis should be put on IT and administration. A proper continuity plan should be in place; and • prime broker structure. Prime brokers offer many services to hedge funds, such as financing for leverage and security lending. Prime brokers are not custodians for best trade execution and may liquidate positions against investors’ interests.
229
PERFORMANCE MEASUREMENT AND RISK CONTROL
Due diligence is mostly qualitative by nature. The quantitative analysis of past performance may be valuable if adequate data are available. A careful analysis of a track record, particularly if it covers at least a whole economic cycle, provides some insight into how successfully the hedge fund manager manages risks. However, it should be noted that the predictive power of past performance is very limited. The nature of structural risks changes with the stages of a hedge fund operation. While the analysis of the business strategy is paramount for early-stage hedge funds, the ability to manage potential growth is a key success factor for more mature funds. Portfolio construction Portfolio construction consists of investing in hedge funds that have successfully passed the due diligence process according to the defined asset allocation. The manager diversification serves the mitigation of the residual structural risks not captured by due diligence. To this end, allocation limits for single hedge funds should be set. These limits depend on the seniority of the hedge fund manager and the quality of the relationship with him. Portfolio construction is not a purely mechanical process. To properly diversify strategy risks, it is paramount to understand the way in which risks of individual managers interact. Manager diversification does not necessarily mean strategy risk diversification. Moreover, the portfolio should be designed to have the desired risk profile over the investors’ time horizon. To achieve this, judgement and experience are more important than the analysis of single positions or exposures. Positions and exposures are snapshots, and their information content is generally short-lived with respect to the time horizon of investors. However, exposure analysis and monitoring are important for concentrated strategies, such as merger arbitrage, where diversification requires a careful analysis of the single trades followed by the hedge fund managers. Finally, portfolios have to follow specific constraints such as the type of strategy exposures or minimal liquidity requirements.
Ongoing risk monitoring and management Ongoing risk management and monitoring serve the continuous assessment of the current structural and strategy risks, at both the investment and the portfolio level. Continuous monitoring and management form a critical part of a sound control system. They require discipline, the implementation of processes and the ex ante definition of corrective actions in case of a risk event. At the investment level, the monitoring of the residual structural risks is the objective of ongoing due diligence. The following factors should be analysed with particular care: • change in key people. The departure of key people may compromise business continuity because specific skills are unique and not transferable; • assets under management. The size of the portfolio should be analysed in the light of the capacity of the trading strategy. Furthermore, rapid growth in portfolio size may be sustained only if the business model is scalable; and • change in client base. Client concentration and structure have to be monitored. Reasons for redemptions should be reported. Ongoing due diligence also represents a dynamic review of the strategy risks of the hedge fund. Particular attention should be paid to potential changes of trading methods and algorithms, extensions of traded instruments, and changes in geographical exposures.
230
RISK CONTROL STRATEGIES: THE MANAGER’S PERSPECTIVE
Additionally, the strategy risks have to be monitored and managed extensively inhouse, at the fund level, in order to obtain early warnings of style drifts and performance deterioration. The analysis of style drifts is important because hedge fund managers should take risks in their areas of expertise. Style drifts are more frequent for strategies the attractiveness of which declines. In a bad environment hedge fund managers are prone to make changes in the investment strategies, to invest in other asset classes or to take higher levels of risk. The way risk exposures are controlled depends on the type of investment. Fund investments typically have limited transparency and their liquidity is on the low side (ie, the redemption period is at least one month). Therefore, a careful risk monitoring approach is more appropriate and feasible than a risk management approach. In contrast, managed accounts offer full transparency and daily liquidity. As such, they are perfectly suited for an active risk management approach. For fund investments, risk monitoring entails an in-depth review of the funds’ risk and return characteristics. The consistency and distribution of returns, the behaviour of the fund in market drawdowns, and the evolution of risk measures should be analysed. As discussed above, risk measures focusing on the loss part of the distribution are more insightful. Particular attention should be paid to return breakouts (ie, returns that lie outside a predefined confidence interval). Return breakouts may be caused by a change in market conditions for a specific strategy or by a change in the type and/or level of the risk taken by the hedge fund manager. The latter represents a strategy drift and should be avoided. Strategy drifts can be assessed by analysing the performance of a given fund in relation to funds following the same trading strategy. In case of a change in market conditions, several such funds will exhibit a corresponding breakout. Also, a regression of the returns of a particular fund on the returns of its peers helps to identify strategy shifts. Peer group analysis is also a valuable method with which to detect relative performance drifts. Whenever predefined trigger points are hit, predefined corrective actions have to be taken. First, the corresponding hedge fund manager is asked to provide additional information and an explanation for the risk event. The information should be validated by the disclosure of all exposures and positions necessary to fully understand the risk event. If this information is not satisfactory or if there is no improvement in the near future, a redemption is put in. For the ongoing risk management of managed accounts, additional tools make full use of the information available. Exposure reports quickly identify undesirable positions that do not match the risk profile. For directional strategies, Value at Risk (VaR) analysis permits a consistent measurement of market and credit risk across instruments. VaR analysis can be performed at different levels of aggregation and along various dimensions. VaR analysis should be complemented by stress testing in order to assess the portfolio’s sensitivity to adverse scenarios. This is particularly important for strategies prone to liquidity risk, as current VaR methods are poorly designed to capture this type of risk. It should be pointed out that the mission of funds of funds is not the trading of managed accounts. Hedge fund managers are adequately compensated to do this. Risk management should focus on exceptional risk levels. For managed accounts the first step is generally a reduction in the trading level. Then follows a redemption when the situation deteriorates even further. At the portfolio level, ongoing risk monitoring and management involve the review of asset allocation. To this end, the evolution of the performance drivers has to be monitored systematically. The frequency of the review is a function of the liquidity of the underlying strate-
231
PERFORMANCE MEASUREMENT AND RISK CONTROL
gies. Particular emphasis should be put on the analysis of asset flows towards hedge fund strategies. Significant money inflows into strategies with limited capacity, such as arbitrage strategies, may destroy the sources of returns. Further, the suitability of the constituting hedge funds has to be assessed. Correlation shifts or concentrations of risk exposures may lead to changes in portfolio composition. Finally, risk monitoring at the portfolio level also involves the ongoing aggregation of the risk exposures. As noted by the Investor Risk Committee of the IAFE, this ensures the investors’ ability to aggregate risk across their entire investment programme in order to understand the implications at the portfolio level. As examined above, in addition to hedge funds investing in various asset types, the type of their exposures is heterogeneous. To be informative the nature of the exposures should be analysed. As a minimum, long and short positions should be reported separately. For non-linear exposures, aggregation is a difficult exercise. Summary statistics such as the Greeks can be very helpful but their aggregation may be misleading. Moreover, they are generally time-dependent, which means that their information content is short-lived. Thus we see this information as being more suitable to gain a better understanding of hedge fund strategies.
Conclusion The primary mission of funds of hedge funds with respect to risk control is the avoidance of structural risks and the delivery of the strategy risk profile that investors require. Structural risks should be avoided because there is no compensation for bearing them. Careful due diligence minimises these risks through analysis of the business model, whereas manager diversification mitigates the residual ones. The asset allocation decision has the biggest impact on the risk profile of a fund of funds. This requires a profound understanding of the different strategies and of their risk/return drivers. To this end, we can broadly classify hedge fund styles with respect to their largest strategy risks. Directional strategies are primarily exposed to market risks whereas the non-directional ones are more prone to liquidity risk. For strategies that may offer full transparency without putting their returns at risk and that exhibit adequate liquidity, managed accounts are the ideal platform from an ongoing risk management point of view. Real-time access to the portfolio enables appropriate actions to be taken on a daily basis. For strategies that exhibit limited liquidity or that require a certain level of confidentiality, fund investments represent the most efficient way of gaining exposure to a particular strategy. Hence the call for total transparency for all hedge funds must be replaced by a demand for appropriate transparency that matches the underlying strategy. Careful due diligence and risk monitoring give sufficient insight into the risk profile of fund investments. Therefore, we are convinced that funds of funds need both investment platforms in order to meet investors’ expectations with respect to return and risk management. From the above it is obvious that risk management is much more than reporting or the fulfilment of regulatory requirements. It is embedded in the whole investment process and represents a company-wide effort. Risk is the other face of return. Hedge fund selection serves risk identification and assessment, whereas asset allocation and portfolio construction represent a risk attribution exercise. Within this framework the risk management group, backed by senior management, has the crucial function of ensuring the consistency and appropriateness of the risk management effort. It is an independent unit that takes the responsibility for implementing and monitoring
232
RISK CONTROL STRATEGIES: THE MANAGER’S PERSPECTIVE
the risk management strategy, and the processes for developing risk management methods and standards, and for providing a risk management infrastructure.
References Barra Strategic Consulting Group (2001). Funds of Hedge Funds: Rethinking Resource Requirements. (September). Bookstaber, R. (2000). ‘Understanding and Monitoring the Liquidity Crisis Cycle’. Financial Analysts Journal, Vol. 56, No. 5 (September/October), pp. 17–22. International Association of Financial Engineers (2001a). Hedge Fund Disclosure for Institutional Investors. Investor Risk Committee. (July). International Association of Financial Engineers (2001b). How Should Firms Determine the Effectiveness of their Operational Risk Controls? Report of the Operational Risk Committee: Evaluating Operational Risk Controls. (November). Caxton Corporation, Kingdom Capital Management, Moore Capital Management Inc., Soros Fund Management LLC, Tudor Investment Corporation (2000). Sound Practices for Hedge Fund Managers. (February).
233
APPENDIX
FRM Suggested Readings for Further Study* [1] Chapter 17—“Estimating Volatilities and Correlations,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [2] Chapter 2—“Mechanics of Futures Markets,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [3] Chapter 3—“Determination of Forward and Futures Prices,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [4] Chapter 4—“Hedging Strategies Using Futures,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [5] Chapter 5—“Interest Rate Markets,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [6] Chapter 6—“Swaps,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [7] Chapter 7—“Mechanics of Options Markets,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [8] Chapter 8—“Properties of Stock Options,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [9] Chapter 9—“Trading Strategies Involving Options,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003).
*This list includes all Core Readings from the 2005 FRM Examination Study Guide that are not on either this CD-ROM or the first Readings for the Financial Risk Manager CD-ROM.
1
2
READINGS FOR THE FINANCIAL RISK MANAGER
[10] Chapter 10—“Introduction to Binomial Trees,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [11] Chapter 11—“Model of the Behavior of Stock Prices,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [12] Chapter 12—“The Black-Scholes Model,” John Hull, Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [13] Chapter 14—“The Greek Letters,” John Hull,” Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [14] Chapter 15—“Volatility Smiles,” John Hull,” Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [15] Chapter 19—“Exotic Options,” John Hull,” Options, Futures and Other Derivatives, 5th ed. (New York: Prentice Hall, 2003). [16] Chapter 11—“Implementing Delta-Normal VaR,” Philippe Jorion, Value at Risk, 2nd ed. (New York: McGraw-Hill, 2001). [17] “Measuring and Marking Counterparty Risk,” Eduardo Canabarro and Darrell Duffie, in ALM of Financial Institutions, ed. Leo Tilman (New York: Institutional Investor Books, 2004).* [18] Chapter 6—“Backtesting VaR Models,” Philippe Jorion, Value at Risk, 2nd ed. (New York: McGraw-Hill, 2001). [19] “Demystifying Securitization for Unsecured Investors,” Moody’s Investors Service, January 2003.* [20] “Recommendations for Dealers and End-Users,” in Derivatives: Practices and Principles (Washington, D.C.: Group of Thirty, 1993).* [21] Chapter 3—“Risk Budgeting: Managing Active Risk at the Total Fund Level,” Kurt Winklemann, in Risk Budgeting: A New Approach to Investing, ed. Leslie Rahl (London: Risk Books, 2000). [22] Chapter 6—“Risk Budgeting for Pension Funds and Investment Managers Using VaR,” Michelle McCarthy, in Risk Budgeting: A New Approach to Investing, ed. Leslie Rahl (London: Risk Books, 2000). [23] Chapter 7—“Risk Budgeting for Active Investment Managers,” Robert Litterman, Jacques Longerstaey, Jacob Rosengarten, and Kurt Winklemann, in Risk Budgeting: A New Approach to Investing, ed. Leslie Rahl (London: Risk Books, 2000). [24] Chapter 11—“Risk Budgeting in a Pension Fund,” Leo de Bever, Wayne Kozun, and Barbara Zvan, in Risk Budgeting: A New Approach to Investing, ed. Leslie Rahl (London: Risk Books, 2000).
*A copy of this article is available at www.garp.com under the FRM link.
FRM Suggested Readings for Further Study
3
[25] “Sound Practices for Hedge Fund Managers,” in Managing Hedge Fund Risk, ed. Virginia Reynolds Parker (London: Risk Books, 2003). [26] “The Risk of Hedge Funds,” Alexander M. Ineichen, in Managing Hedge Fund Risk, ed. Virginia Reynolds Parker (London: Risk Books, 2003). [27] “Sifting Through the Wreckage: Lessons from Recent Hedge Fund Liquidations,” Mila Getmansky, Andrew Lo, and Shauna Mei, Journal of Investment Management (November 14, 2004): 1–27.* [28] “The Risk in Fixed Income Hedge Fund Strategies,” David Hsieh and William Fung, Journal of Fixed Income, 12 (2002): 6–27.*
*A copy of this article is available at www.garp.com under the FRM link.
Credits
Readings 57–59 Reproduced with permission from Value at Risk, 2nd ed., by Philippe Jorion. © 2001 The McGraw-Hill Companies, Inc.
Reading 60 Source: Risk Management and Derivatives, 1st ed., by René M. Stulz. © 2003. Reproduced with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax: (800) 730-2215.
Reading 61 Reproduced with permission from Understanding Market, Credit and Operational Risk: The Value at Risk Approach, by Linda Allen, Jacob Boudoukh, and Anthony Saunders. © 2004 Blackwell Publishing.
Reading 62 Reproduced with permission from Risk Management and Capital Adequacy, by Reto Gallati. © 2003 The McGraw-Hill Companies, Inc.
Readings 63–66 Reproduced with permission from Managing Operational Risk: 20 Firmwide Best Practice Strategies, by Douglas G. Hoffman, Chapters 3, 9, 12, and 16. © 2002 Hoffman. Reproduced with permission of John Wiley & Sons, Inc.
Reading 67 Reproduced with permission from Risk Management, by Michel Crouhy, Dan Galai, and Robert Mark. © 2001 The McGraw-Hill Companies, Inc.
Readings 68–70 Reproduced with permission from Portfolio Theory and Performance Analysis, by Noël Amenc and Véronique Le Sourd, Chapters 4 (sections
1
2
READINGS FOR THE FINANCIAL RISK MANAGER
4.1.1, 4.1.2, and 4.2.1–4.2.8), 6, and 8. © 2003 John Wiley & Sons Ltd. Reproduced with permission of John Wiley & Sons, Inc.
Readings 71–72 Reproduced with permission from The New Generation of Risk Management for Hedge Funds and Private Equity Investments, edited by Lars Jaeger. © 2003 Euromoney Books/Euromoney Institutional Investor PLC.
Reading 73 Reproduced with permission from Funds of Hedge Funds, edited by Jaffer Sohail. © 2003 Euromoney Books/Euromoney Institutional Investor PLC.
About the CD-ROM
INTRODUCTION he objective of this volume is to provide core readings recommended by the Global Association of Risk Professionals’ Financial Risk Manager (FRM®) Committee for the 2005 exam that are not available on the first Readings for the Financial Risk Manager CD-ROM. The FRM Committee, which oversees the selection of reading materials for the FRM Exam, suggests 100 readings for those registered for the FRM Exam and any other risk professionals interested in the critical knowledge essential to their profession. Fifty-five of these recommended readings appear on the Readings for the Financial Risk Manager CD-ROM and 17 appear on this CDROM.
T
MINIMUM SYSTEM REQUIREMENTS Make sure that your computer meets the minimum system requirements listed in this section. If your computer doesn’t match up to most of these requirements, you may have a problem using the contents of the CD. For Windows 95, 98, 9x, Windows 2000, Windows NT4 (with SP 4 or later), Windows Me, or Windows XP: ■ PC with a Pentium processor running at 120 Mhz or faster. ■ At least 32 MB of total RAM installed on your computer; for best performance, we recommend at least 64 MB. ■ Adobe Acrobat Reader (included). ■ A CD-ROM drive. For Macintosh: ■ Mac running OSX. ■ Adobe Acrobat Reader (included). ■ A CD-ROM drive.
1
2
READINGS FOR THE FINANCIAL RISK MANAGER
USING THE CD WITH WINDOWS To open and use each model worksheet from the CD, follow these steps: 1. Insert the CD into your computer’s CD-ROM drive. 2. A window will appear with the following options: Install, Explore, and Exit. Install: Gives you the option to install the supplied files on the CDROM. Explore: Enables you to view the author-created samples on the CDROM in a directory structure. A menu should bring you directly to a list of chapter links. Each of these chapter links should lead you to the pertinent readings. Exit: Closes the autorun window. If you do not have autorun enabled, or if the autorun window does not appear, follow these steps to access the CD: 1. Click Start, select Run. 2. In the dialog box that appears, type d:\setup.exe, where d is the letter of your CD-ROM drive. This brings up the autorun window described in the preceding set of steps. 3. Choose the Install, Explore, or Exit option from the menu. (See Step 2 in the preceding list for a description of these options.)
USING THE CD WITH THE MAC OS To install the items from the CD to your hard drive, follow these steps: 1. Insert the CD into your CD-ROM drive. 2. Double-click the icon for the CD after it appears on the desktop. 3. Most programs come with installers; for those, simply open the program’s folder on the CD and double-click the Install or Installer icon. Note: To install some programs, just drag the program’s folder from the CD window and drop it on your hard drive icon.
USING THE SOFTWARE Select the chapters using the table of contents interface. Readings are presented in PDF format.
About the CD-ROM
3
TROUBLESHOOTING If you have difficulty installing or using any of the materials on the companion CD, try the following solutions: ■ Turn off any antivirus software that you may have running. Installers sometimes mimic virus activity and can make your computer incorrectly believe that it is being infected by a virus. (Be sure to turn the antivirus software back on later.) ■ Close all running programs. The more programs you’re running, the less memory is available to other programs. Installers also typically update files and programs; if you keep other programs running, installation may not work properly. ■ Reference the ReadMe. Please refer to the ReadMe file located at the root of the CD-ROM for the latest product information at the time of publication. If you still have trouble with the CD-ROM, please call the Wiley Product Technical Support phone number: (800) 762-2974. Outside the United States, call 1(317) 572-3994. You can also contact Wiley Product Technical Support at http://support.wiley.com. Wiley Publishing will provide technical support only for installation and other general quality control items; for technical support on the applications themselves, consult the program’s vendor or author. To place additional orders or to request information about other Wiley products, please call (800) 225-5945.
CUSTOMER NOTE PLEASE READ THE FOLLOWING. By opening this package, you are agreeing to be bound by the following agreement: This software product is protected by copyright and all rights are reserved by the Global Assocation of Risk Professionals and John Wiley & Sons, Inc., and the original copyright holders whose materials are reprinted on the CD-ROM by permission. You are licensed to use this software on a single computer. Copying the software to another medium or format for use on a single computer does not violate the U.S. Copyright Law. Copying the software for any other purpose is a violation of the U.S. Copyright Law.
4
READINGS FOR THE FINANCIAL RISK MANAGER
This software product is sold as is without warranty of any kind, either express or implied, including but not limited to the implied warranty of merchantability and fitness for a particular purpose. Neither Wiley nor its dealers or distributors assumes any liability for any alleged or actual damages arising from the use of or the inability to use this software. (Some states do not allow the exclusion of implied warranties, so the exclusion may not apply to you.)
