The Banking Sector In Hong Kong: Competition, Efficiency, Performance and Risk (Palgrave MacMillan Studies in Banking and Financial Institutions)

Palgrave Macmillan Studies in Banking and Financial Institutions Series Editor: Professor Philip Molyneux The Palgrave Macmillan Studies in Banking and Financial Institutions will be international in orientation and include studies of banking within particular countries or regions, and studies of particular themes such as Corporate Banking, Risk Management, Mergers and Acquisitions, etc. The books will be focused upon research and practice, and include up-to-date and innovative studies on contemporary topics in banking that will have global impact and influence.

Titles include: Yener Altunbas, Blaise Gadanecz and Alper Kara SYNDICATED LOANS A Hybrid of Relationship Lending and Publicly Traded Debt Elena Beccalli IT AND EUROPEAN BANK PERFORMANCE Santiago Carbó, Edward P.M. Gardener and Philip Molyneux FINANCIAL EXCLUSION Allessandro Carretta, Franco Fiordelisi and Gianluca Mattarocci (editors) NEW DRIVERS OF PERFORMANCE IN A CHANGING WORLD Violaine Cousin BANKING IN CHINA Franco Fiordelisi and Philip Molyneux SHAREHOLDER VALUE IN BANKING Hans Genberg and Cho-Hoi Hui THE BANKING SECTOR IN HONG KONG Competition, Efficiency, Performance and Risk Munawar Iqbal and Philip Molyneux THIRTY YEARS OF ISLAMIC BANKING History, Performance and Prospects Kimio Kase and Tanguy Jacopin CEOS AS LEADERS AND STRATEGY DESIGNERS Explaining the Success of Spanish Banks M. Mansoor Khan and M. Ishaq Bhatti DEVELOPMENTS IN ISLAMIC BANKING The Case of Pakistan Mario La Torre and Gianfranco A. Vento MICROFINANCE Philip Molyneux and Munawar Iqbal BANKING AND FINANCIAL SYSTEMS IN THE ARAB WORLD Philip Molyneux and Eleuterio Vallelado (editors) FRONTIERS OF BANKS IN A GLOBAL WORLD Anastasia Nesvetailova FRAGILE FINANCE Debt, Speculation and Crisis in the Age of Global Credit

Dominique Rambure and Alec Nacamuli PAYMENT SYSTEMS From the Salt Mines to the Board Room Andrea Schertler THE VENTURE CAPITAL INDUSTRY IN EUROPE Alfred Slager THE INTERNATIONALIZATION OF BANKS Noel K. Tshiani BUILDING CREDIBLE CENTRAL BANKS Policy Lessons for Emerging Economies

Palgrave Macmillan Studies in Banking and Financial Institutions Series Standing Order ISBN 978- 1–4039–4872–4 You can receive future titles in this series as they are published by placing a standing order. Please contact your bookseller or, in case of difficulty, write to us at the address below with your name and address, the title of the series and one of the ISBNs quoted above. Customer Services Department, Macmillan Distribution Ltd, Houndmills, Basingstoke, Hampshire RG21 6XS, England

The Banking Sector in Hong Kong Competition, Efficiency, Performance and Risk Edited by

Hans Genberg and Cho-Hoi Hui

Selection and editorial matter © Hans Genberg and Cho-Hoi Hui 2008 Chapters © their authors 2008 Foreword © Peter S. T. Pang 2008 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1T 4LP. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The authors have asserted their right to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2008 by PALGRAVE MACMILLAN Houndmills, Basingstoke, Hampshire RG21 6XS and 175 Fifth Avenue, New York, N.Y. 10010 Companies and representatives throughout the world PALGRAVE MACMILLAN is the global academic imprint of the Palgrave Macmillan division of St. Martin’s Press, LLC and of Palgrave Macmillan Ltd. Macmillan® is a registered trademark in the United States, United Kingdom and other countries. Palgrave is a registered trademark in the European Union and other countries. ISBN-13: 978–0–230–20266–5 hardback ISBN-10: 0–230–20266–7 hardback This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin. A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data The banking sector in Hong Kong : competition, efficiency, performance and risk / edited by Hans Genberg and Cho-Hoi Hui. p. cm. Includes bibliographical references and index. ISBN 0–230–20266–7 (alk. paper) 1. Banks and banking—China—Hong Kong. 2. Mortgage loans—China—Hong Kong. 3. Financial risk—China—Hong Kong. I. Genberg, Hans. II. Hui, Cho-Hoi. HG3352.B36 2008 332.1095125—dc22 2008015885 10 17

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Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham and Eastbourne

Contents List of Figures

x

List of Tables

xiii

Foreword

xv

Acknowledgements

xvi

Notes on the Contributors

xvii xviii

Introduction Hans Genberg and Cho-Hoi Hui

Part I: 1

2

Competition, Efficiency and Profitability

1

The Cost Efficiency of Commercial Banks in Hong Kong

3

Jim Wong, Tom Pak-Wing Fong, Eric Tak-Chuen Wong and Ka-Fai Choi 1.1 Introduction 1.2 Methodology 1.3 Data and estimation methods 1.4 The inefficiency estimates 1.5 Efficiency, bank characteristics and macroeconomic conditions 1.6 Conclusion

10 12

Competition in Hong Kong’s Banking Sector: A Panzar-Rosse Assessment

17

Jim Wong, Eric Tak-Chuen Wong, Tom Pak-Wing Fong and Ka-Fai Choi 2.1 Introduction 2.2 The Panzar–Rosse approach 2.3 The empirical specifications 2.4 Data and estimation methods 2.5 Estimation results 2.6 Conclusion

17 18 19 22 24 28

v

3 4 6 8

vi Contents

3

Testing for Collusion in the Hong Kong Banking Sector Jim Wong, Eric Tak-Chuen Wong, Tom Pak-Wing Fong and Ka-Fai Choi 3.1 Introduction 3.2 The conjectural variation approach 3.3 The empirical specifications 3.4 Data and estimation methods 3.5 Estimation results 3.6 Conclusion

4

32

32 33 36 39 39 43

Determinants of the Performance of Banks in Hong Kong

50

Jim Wong, Tom Pak-Wing Fong, Eric Tak-Chuen Wong and Ka-Fai Choi 4.1 Introduction 4.2 Literature review 4.3 The empirical specification 4.4 Data and estimation method 4.5 Estimation results 4.6 Conclusion Appendix 4A Measures of scale inefficiency

50 51 53 56 58 61 62

Part II: Interest Rate and Default Risks in the Mortgage Market

67

5

69

Interest Rate Risk in the Pricing of Banks’ Mortgage Lending Jim Wong, Laurence Kang-Por Fung, Tom Pak-Wing Fong and Cho-Hoi Hui 5.1 Introduction 5.2 Narrowing of spread during the tightening phase of interest rate cycle 5.3 Shift in risk premium 5.4 Potential reduction in interest rate margins 5.5 Conclusion Annex 5A Effective mortgage rates Annex 5B Test of lead-lag relationship between LIBOR and BLR Annex 5C Graphical illustration of the narrowing of interest spread between BLR and HIBOR during the tightening phase of an interest rate cycle Annex 5D Cointegration and error correction model Annex 5E Model specification and estimation results

69 71 72 74 80 82 83

84 85 86

Contents vii

6

Hong Kong Mortgage Rate Setting -- An Alternative Reference Rate? Jim Wong, Cho-Hoi Hui and Laurence Kang-Por Fung 6.1 Introduction 6.2 Overseas experience 6.3 Possible alternative reference rates: an evaluation 6.4 Conclusion Annex 6A Reference rates for pricing mortgage loans in the US, UK and Australia Annex 6B A technical note on the construction of the effective deposit rate and the composite rate Annex 6C Relative features of alternative reference rates Annex 6D A quantitative assessment of the approximation of alternative reference rates as a measure of average cost of funds Annex 6E Simulation of interest margin for the loan portfolio acquired in January 1999 under the scenario of different reference rates

7

Residential Mortgage Default Risk in Hong Kong Jim Wong, Laurence Kang-Por Fung, Tom Pak-Wing Fong and Angela Sze 7.1 Introduction 7.2 Theoretical background and literature review 7.3 Methodology and data 7.4 The model and estimation results 7.5 Default probability and the level of CLTV 7.6 Estimated default probability and macro variables 7.7 The 70 per cent LTV ratio and asset quality 7.8 Conclusion Annex 7A Estimation results for initial model specification with the CLTV ratio and CDSR as core variables Annex 7B Estimation results for initial model specification with the CLTV ratio and mortgage rate (as a proxy for CDSR) as core variables Annex 7C The derivation of the relationship between default probability and the CLTV level

95 95 97 97 108 113 115 122

123

127

132

132 133 134 138 141 141 146 148

149

150 151

viii Contents

Part III: Quantifying Risks, Capital Adequacy and Stress-Testing Framework of Systemic Risk

157

8

159

Determinants of the Capital Level of Banks in Hong Kong Jim Wong, Ka-Fai Choi and Tom Pak-Wing Fong 8.1 Introduction 8.2 Possible determinants of capital holdings of banks 8.3 Conclusion Annex 8A A quantitative analysis of determinants of bank capital in Hong Kong Annex 8B Details of the survey results

9

10

11

159 160 170 172 176

Benchmarking Model of Default Probabilities of Listed Companies

191

Cho-Hoi Hui, Eric Tak-Chuen Wong, Chi-Fai Lo and Ming-Xi Huang 9.1 Introduction 9.2 Structural model of term structures of PDs 9.3 Benchmarking process 9.4 Data and empirical results 9.5 Summary Appendix 9A Appendix 9B Appendix 9C

191 194 198 200 206 207 208 210

Measuring Provisions for Collateralized Retail Lending

214

Cho-Hoi Hui, Chi-Fai Lo, Eric Tak-Chuen Wong and Po-Kong Man 10.1 Introduction 10.2 Model for measuring provisions 10.3 Empirical analysis 10.4 Numerical results 10.5 Summary Appendix 10A

214 220 223 229 233 235

A Framework for Stress Testing Banks’ Credit Risk

240

Jim Wong, Ka-Fai Choi and Tom Pak-Wing Fong 11.1 Introduction 11.2 Elements of stress test and the common methodology 11.3 The framework 11.4 The model and estimation results 11.5 The simulation of future credit losses and stress testing 11.6 A stress test for banks’ mortgage portfolio 11.7 Conclusion

240 241 242 246 248 253 256

Contents ix

12

Assessing the Risk of Multiple Defaults in the Banking System Ip-Wing Yu, Laurence Kang-Por Fung and Chi-Sang Tam 12.1 Introduction 12.2 Methodology and data 12.3 Empirical results 12.4 Conclusion Appendix 12A Technical details for deriving the default probability based on the structural approach

Index

261 261 262 266 270 271 277

List of Figures 1.1 1.2 2.1 2.2 2.3 3.1 4.1 4.2 5.1 5.2 5.3 5.4 5.5 5C.1 6.1 6.2a

6.2b

6.3 6.4 6B.1 6B.2 6B.3 6B.4 6D.1 6D.2 6D.3 6D.4

Trends of the inefficiency estimates Dispersions of the inefficiency estimates Major changes in market concentration around 2001 Rolling estimates of H statistic of Model A Rolling estimates of H statistic of Model B Degree of oligopolistic coordination before and after structural changes Time series plots of average quarterly ROA and IRS Market concentration and regulatory liberalization Average mortgage rate and BLR Interest spreads and BLR Movements of 3-month HIBOR and 3-month LIBOR Risk premium Flow of influence Illustration of interest spread narrowing Alternative reference rates and BLR ( January 1997 to April 2005, monthly average) Mortgage rates based on possible reference rates (for mortgage loans priced in January 1997 with constant mark-ups throughout the remaining contractual period) Relative monthly fluctuations of selected reference rates (February 1997 to April 2005, monthly average, in absolute terms) Ranking of the reference rate in terms of stability and conduciveness to interest rate risk management Adjustments of the mortgage rate (based on a prescribed triggering rule) and BLR Interest rates of retail market funding Interest rates of wholesale market funding EDR The composite rate Based on the composite rate Based on HIBOR3 Based on EDR Based on BLR

x

9 9 22 27 27 35 57 58 70 71 72 73 74 84 99

104

104 110 111 116 116 119 121 123 124 124 125

List of Figures xi

6D.5 6D.6 6E.1 6E.2 7.1 7.2 7.3 7.4 7.5 7.6 7.7 8.1 8.2 9.1

9.2 9.3 9.4 10.1 10.2

10.3

10.4

Based on EFN3 Based on the base rate Cost of funds represented by the composite rate Cost of funds represented by HIBOR3 Mortgage delinquency rate in Hong Kong Default probability and CLTV ratio by snapshot month (with other explanatory variables held at mean levels) Default probability and CLTV ratio (an enlarged graphical exhibition of Figure 7.2) Default probability and CLTV ratio (all other variables at mean levels) Default probability and CLTV ratio at different unemployment rates Default probability and CLTV ratio at different mortgage rates Default probability and CLTV ratio at different changes of Hang Seng Index CAR and bank size CAR and economic cycles PD term structures generated from the structural model and actual cumulative default rates reported by S&P’s (2002) of ratings of CCC, B, BB and BBB Benchmarking process of benchmark PD estimation Mismatch distribution of benchmark ratings versus S&P’s ratings of 3,943 sample companies Receiver operating characteristic curve and accuracy ratio of the benchmarking model Private domestic price index (V) and problem-loan ratio (D) of residential mortgage loans Provisions of pools of loans with different loan-to-value ratios and volatilities of collateral value for a three-year time horizon Changes in provisions with respect to changes in loan-tovalue ratios (that is δ) under different loan-to-value ratios and volatilities of collateral value for a three-year time horizon Percentage changes in provisions of pools of loans with different correlation between collateral value and PD compared with the provisions with zero correlation under different dynamics of PD

125 126 127 127 137 142 142 145 145 146 146 161 163

197 199 202 204 224

230

231

232

xii List of Figures

10.5

Provision-given-default of pools of loans with different time horizons and correlation between collateral value and PD 11.1a A GDP shock: simulated frequency distributions of credit loss under baseline and stressed scenarios 11.1b A China GDP shock: simulated frequency distributions of credit loss under baseline and stressed scenarios 11.1c An interest rate shock: simulated frequency distributions of credit loss under baseline and stressed scenarios 11.1d A property price shock: simulated frequency distributions of credit loss under baseline and stressed scenarios 11.2a A GDP shock: simulated frequency distributions of credit loss for RMLs under baseline and stressed scenarios 11.2b A property price shock: simulated frequency distributions of credit loss for RMLs under baseline and stressed scenarios 11.2c An interest rate shock: simulated frequency distributions of credit loss for RMLs under baseline and stressed scenarios 12.1 One-year default probability of listed banks 12.2 Aggregate one-year default probability of listed banks 12.3 Monthly asset correlation between banks 12.4 Multiple default risk index (based on one-year probability of at least one default of listed banks) 12A.1 Asset value, default barrier and default probability

233 250 250

251

251

255

255

256 266 267 268 269 272

List of Tables 1.1 1.2 1.3 2.1 2.2 2.3

Some descriptive statistics of retail banks as of 2005 Q4 Inefficiency estimates of retail banks in Hong Kong Panel data regression of inefficiency estimates Competitive structures and the H statistic Summary statistics on the sample (1991 Q1–2005 Q4) Empirical results of the Panzar–Rosse model for the Hong Kong banking sector 2.4 Empirical results of the Panzar–Rosse model for the Hong Kong banking sector (analysis of bank size) 3.1 Empirical results of the conjectural variation parameter for the Hong Kong banking sector 4.1 General features of the data (sample period: 1991 Q1–2005 Q4; no. of observations: 1,418) 4.2 Estimation results of ROA and IRS 5.1 Potential reduction of mortgage spreads (with an increase of 120 bps in US interest rates) 5.2 Simulated impact on net interest margin of currently priced loans and banks’ overall mortgage portfolio (with an increase of 120 bps in US interest rates) 5B.1 Tests of lead-lag relationship between LIBOR and BLR 5E.1 ADF unit root test results 5E.2 ADF unit root test on long-run equilibrium 5E.3 Estimation results of Models A, B and C 6.1 Merits and drawbacks of alternative reference rates 6.2 Volatility of monthly payment burden of possible reference rates 6.3 Changes in monthly average rates and differences between daily high and low of reference rates during two particularly volatile periods 6.4 Variability of margin for banks’ mortgage portfolio of January 1999 (during the period January 1999 to April 2005) 6.5 Estimated squeezes of interest margins resulting from the recent rise in cost of funds under different reference rates (for banks’ mortgage portfolio acquired during January 2005) 6.6 Ranking of possible reference rates xiii

7 8 11 19 23 25 26 40 57 60 76

78 83 87 87 88 101 103

103

107

107 109

xiv List of Tables

6B.1 Major funding sources of banks and interest rates 6B.2 Derivation of EDR (for April 2005) 6B.3 Derivation of the composite rate (for April 2005) 6D.1 Estimation results (from January 1999 to April 2005) 7.1 Explanatory variables for the logit model 7.2 Number of loan cases 7.3 Estimation results 7.4 Estimated default probability at different CLTV levels 7.5 Estimated default probability (%) at different CLTV levels under varying macroeconomic conditions 7.6 Estimated loan defaults with and without a relaxation of the maximum LTV ratio guideline 8A.1 Description of the explanatory variables 8A.2 General features of the data (sample period: 1992 Q1–2004 Q3; No. of banks: 28; No. of observations: 1,221) 8A.3 Determinants of banks’ capital level: GMM estimates 8A.4 A summary of the estimated effects of exogenous changes 8B.1 Response rate of the survey 8B.2 Banks’ replies to question 6.15 9.1 Assignment of ordinal numbers to S&P’s ratings and numbers of sample companies with S&P’s ratings 9.2 Mismatch statistics of benchmark ratings versus S&P’s ratings of 3,943 sample companies 9.3 Degree of association between benchmark ratings versus S&P’s ratings of 3,943 sample companies 10.1 Statistics of the data series of V and D 10.2 Estimation results of alternative models of X (ln D) and Y (ln V ) 11.1 SUR estimates for the equation system (sample period: 1994 Q4 to 2006 Q1) 11.2 The mean and VaR statistics of simulated credit loss distributions 11.3 Post-default operating profit of a hypothetical local bank (in HK$ million) 11.4 SUR estimates for the equation system for RMLs (sample period: 1998 Q2 to 2006 Q1) 11.5 The mean and VaR statistics of the simulated credit loss distributions for RMLs 11.6 Post-default operating profit of a hypothetical local bank for RML (in HK$ million)

115 118 120 123 136 138 140 143 147 148 172

174 175 175 176 180 200 201 206 224 226 248 252 253 254 257 257

Foreword Financial innovations steadily increase the complexity of financial markets creating new challenges for monetary authorities whose responsibility is to safeguard financial stability. In this environment it is essential that central banks stay at the forefront of research in order to be in a position to evaluate possible sources of fragility and signs of instability. The Hong Kong Monetary Authority is Hong Kong’s central banking institution, and one of its responsibilities is to promote the safety of Hong Kong’s banking system. The Research Department of the HKMA supports this function by conducting research that serves as an input to the surveillance of the Hong Kong economy in general and the banking sector in particular. The papers included in this volume were written by staff of the Market Research Division of the Research Department as part of this process. Together they present an up-to-date view of the degree of competition, efficiency, and profitability in the banking sector; of interest-rate and default risk in the mortgage market; and of measuring risk and capital adequacy as well as conducting stress testing in the context of the implementation of the Basel II regulatory framework in Hong Kong. By promoting research on banking issues and by encouraging its dissemination to a wide audience the HKMA seeks to contribute to an understanding of the banking sector in Hong Kong as well as to scholarly research on banking and risk assessment issues more generally. We hope that the papers collected in this volume will stimulate others to carry out similar research for other economies and to conduct further research on banking and financial issues in Hong Kong. Peter S. T. Pang Deputy Chief Executive Hong Kong Monetary Authority

xv

Acknowledgements We are very grateful for the advice and encouragement received from Joseph Yam, Chief Executive of the Hong Kong Monetary Authority. We also wish to thank Peter Pang, Deputy Chief Executive of the Hong Kong Monetary Authority, who oversees researches in the authority, for his strong support and providing the inspirations for many of the studies in this book. Colleagues of the Banking Departments of the Hong Kong Monetary Authority, in particular Y.K. Choi, Deputy Chief Executive, and Raymond Li and Arthur Yuen, Executive Directors of Banking Development and Supervision respectively, have our gratitude for their invaluable comments and suggestions on the analyses in this volume. We would like to extend our thanks to authors of the papers, as well as colleagues of the Market Research Division of the Research Department for their contributions to the production of this volume. Special thanks are due to Bloomberg L.P., CEIC Data Company Ltd, Standard and Poor’s, Thomson Financial, the Hong Kong Mortgage Corporation Limited, and the Census and Statistics Department and the Rating and Valuation Department of the Hong Kong SAR Government, for the permission of the use of their data. Last but not least, we would like to thank Lisa von Fircks and Nick Brock of Palgrave Macmillan for their excellent works in coordinating and seeing through the production of this volume.

Hans Genberg and Cho-Hoi Hui

xvi

Notes on the Contributors Ka-Fai Choi was Manager Trainee, Market Research Division of Research Department at the Hong Kong Monetary Authority. Tom Pak-Wing Fong is Manager, Market Research Division of Research Department at the Hong Kong Monetary Authority. Laurence Kang-Por Fung is Manager, Market Research Division of Research Department at the Hong Kong Monetary Authority. Hans Genberg is Executive Director, Research Department at the Hong Kong Monetary Authority. He is also the Director of the Hong Kong Institute for Monetary Research. Ming-Xi Huang was Research Associate, Department of Physics at the Chinese University of Hong Kong. Cho-Hoi Hui is Head, Market Research Division of Research Department at the Hong Kong Monetary Authority. Chi-Fai Lo is Associate Professor, Department of Physics at the Chinese University of Hong Kong. Po-Kong Man was Research Associate, Department of Physics at the Chinese University of Hong Kong. Angela Sze was Research Analyst, Market Research Division of Research Department at the Hong Kong Monetary Authority. Chi-Sang Tam was Research Analyst, Market Research Division of Research Department at the Hong Kong Monetary Authority. Jim Wong is Senior Manager, Market Research Division of Research Department at the Hong Kong Monetary Authority. Eric Tak-Chuen Wong is Manager, Market Research Division of Research Department at the Hong Kong Monetary Authority. Ip-Wing Yu is Senior Manager, Market Research Division of Research Department at the Hong Kong Monetary Authority.

xvii

Introduction Hans Genberg and Cho-Hoi Hui

The banking sector in Hong Kong has undergone significant changes and developments over the past decade. A series of market liberalization measures took place during this period. In particular, the interest rate deregulation was fully completed by July 2001, and the restriction on the number of branches and offices for foreign banks was completely removed in 2001. At the same time, there were major mergers and acquisitions in the industry, resulting in a higher degree of market concentration. How these changes may have affected competition, efficiency and the performance of banks are issues of interest. Market liberalization has also brought about increased price competition, which calls for greater attention to interest rate and credit risks. In this regard, one main area of interest has been the interest rate risk of mortgage lending, which accounts for about 24 per cent of banks’ domestic loan portfolios. Internationally, an important initiative regarding the adequacy of capital under the Basel New Capital Framework, also known as Basel II, has begun to replace the current Basel Accord in various jurisdictions since 2007. Under the internal ratings-based (IRB) approach in Basel II, credit risk measures are estimated by banks. Quantifying risks and capital requirements have thus also become an important field of banking studies. To cover each of these three areas of interest, the chapters in this book is grouped into three respective parts.

Part I: Competition, Efficiency and Profitability Chapters 1 to 4 assess the current levels and trends of competition and efficiency in the banking industry, whether collusion exists, and whether large banks are benefiting from scale economies and have substantial pricing power over smaller banks. While each of the chapters is by itself a stand-alone study and examines specific issues, together they present a consistent picture for the industry. Four themes are highlighted: cost efficiency, market structure, effects of mergers and acquisitions on competition, and the pricing power of large banks. The main conclusions of each will be described briefly. xviii

Introduction xix • Cost Efficiency

Given banks’ special role in channelling funds from savers to investors, their cost efficiency has a significant effect on the supply of credit and, in turn, on overall economic performance. In addition, inefficiency would affect banks’ earnings, thus hampering their ability to withstand shocks. Using the stochastic frontier approach and a panel dataset of retail banks, Chapter 1 assesses the cost efficiency of the banking sector in Hong Kong. The average cost inefficiency during the period 1992–2005 is found to be about 15 per cent to 29 per cent of observed total costs, which is largely in line with the experience of US and European banks. Cost efficiency is found to be correlated with macroeconomic conditions, with a significant rise in cost inefficiency triggered by the Asian financial crisis and the outbreak of Severe Acute Respiratory Syndrome (SARS) during the period 1998–2003, partly due to the lack of perfect flexibility by banks to adjust their factor inputs (labour, funds and capital) in response to falling outputs. Additional resources spent on risk control, new business initiatives and strengthening customer relationships may also have contributed. Nevertheless, the cost efficiency has started to improve by 2004 Q1, along with the recovery of the economy. This suggests also that the adjustments and streamlining by the banks in recent years may have begun to bear fruit. Empirical results also indicate that cost efficiency is positively correlated with bank size, suggesting large banks are on average more efficient than smaller banks. • Market Structure, Competition and Collusion

Competition could have a significant impact on efficiency and profitability. The degree of competition in the banking industry is therefore always of interest. This is particularly the case for Hong Kong, where the industry is characterized by a few major banking groups and a relatively high degree of market concentration. Evidence of co-movements of the best lending rates and fee setting among banks, even after the removal of the interest rate agreement, has also caused some concerns about the possible existence of oligopolistic coordination among banks. Whether such a phenomenon reflects collusive pricing behaviour or is simply the result of price competition is of interest to policy markers. To examine the issue, three different approaches have been employed: (i) The first is the Panzar-Rosse approach in Chapter 2 which reveals the market structure by investigating the responsiveness of revenues

xx Introduction

to changes in input costs of banks. The relationship between the responsiveness and market structure is directly derived from standard economic theories. (ii) In Chapter 3, the conjectural variation approach is adopted, which reveals the degree of price coordination among banks by estimating price inter-dependence from a system of equations that describes the demand, supply and cost structures of banks. (iii) In Chapter 4, the third approach, due to Berger and Hannan, provides estimates of how market structure (such as market concentration and market shares of banks) and efficiency affect the profitability and pricing power of banks.

The empirical results all suggest that the degree of competition in the banking sector was fairly high during the period 1992–2002, with banks operating in a competitive fashion without any significant sign of collusion on pricing. This situation was largely maintained from 2003 to 2005, notwithstanding significant changes in the operating conditions, in particular a number of mergers and acquisitions. The studies show that the market structure of Hong Kong’s banking sector is one of monopolistic competition, which is similar to most other banking centres, including Germany, Japan, Switzerland, the UK, the US and many other OECD countries. Such a market structure has the following characteristics: (a) Each bank provides some products which are differentiated from other banks (that is imperfect substitution of products), implying that any particular bank would find it difficult to get the entire market share of a particular product. (b) There is free entry and exit of banks in response to profit. If any bank is making significant profit with a particular product, it signals to other banks to produce similar products. Other banks which are not then present will also be attracted to the market. Because of the large number of suppliers and choices available in the market, high competitive pressures are maintained, and they force abnormal profit to zero in the long-run. In reality, while bank entries and exits are not frequently observed in Hong Kong, it is not difficult to observe that if a bank launches a new product which draws positive responses from customers, other banks will usually offer very similar (but not exactly the same) products to compete in a very short period of time (for example, HIBOR-based mortgages). This observation is consistent with the finding that the banking market in Hong Kong is one of monopolistic competition.

Introduction xxi • How Have Recent Mergers and Acquisitions Affected Competition?

The impact of industry consolidations on market concentration is apparent. As shown in the studies, the degree of market concentration measured by the Herfindahl-Hirschman index increased sharply around the second half of 2001, reflecting merger and acquisition activities. Unfortunately, the precise effect of increased market concentration on competition cannot in this case be clearly estimated econometrically, as the major mergers and acquisitions around 2002 happened to coincide with major regulatory liberalization, including the full implementation of interest rate deregulation. This has resulted in a close resemblance of the time series data representing de-regulation and those representing market concentration. As a result, our analysis in Chapter 2 can only estimate the net effect of these two developments, but not their separate impacts. On the whole, the results indicate that market concentration either has not had a significant negative impact on competition, or that its adverse effect has been largely offset by regulatory liberalization (and technological progress). The emergence of a number of larger banks through mergers and acquisitions which should be more capable of competing with existing large banks may have also contributed. Given the uncertainties surrounding the estimates of the effect of market concentration on competition, the consequence of ongoing industry consolidations should be monitored closely in the years to come. • Do Large Banks Have Substantial Pricing Power Over Smaller Banks?

Chapter 4 assesses the main determinants of banks’ profitability and finds that banks’ profits and margins are mainly determined by their cost efficiency and the macroeconomic environment. The empirical results suggest that banks with lower production costs may earn higher profits through optimizing the input mix. Combined with findings in Chapter 1 that larger banks are in general more cost efficient than smaller banks, this finding suggests that larger banks can offer services at lower prices than smaller banks, yet attaining a similar or even higher level of profit. Smaller banks are therefore more vulnerable to intense competitions than larger banks.

Part II: Interest Rate and Default Risks in the Mortgage Market Part II examines the issue of interest rate and default risks in relation to banks’ mortgage portfolios. In Hong Kong, mortgage loans extended by

xxii Introduction

banks are primarily adjustable rate mortgages, which are largely priced with reference to the best lending rate, while banks’ cost of funds is determined by a mix of interest rates including customers’ savings and time deposit rates and Hong Kong Interbank Offered Rates (HIBORs). Under Hong Kong’s Linked Exchange Rate system, local interest rates tend to largely follow their US counterparts. However, due to the interest rate and market structures of Hong Kong’s banking system, the various local interest rates have shown different responses to changes in US rates, in terms of speed and magnitude. This gives rise to possible interest rate risks to banks’ mortgage loan portfolios. During periods when the upward adjustments by banks of the best lending rate (BLR) lag significantly behind the rises in HIBORs and time deposit rates, banks’ interest rate margin could be squeezed. Such risk in fact materialized in early 2005. Strong price competition in Hong Kong’s mortgage market, coupled with the abundance of liquidity, resulted in a significant reduction in the effective mortgage rates by late 2004 to a level which was not sufficient to buffer for a possible sharp rise in the funding cost (due to a possible sharp increases in HIBORs arising from the liquidity situation returning to normal) along with a more moderate rise in the BLR. As a result, as HIBORs rose sharply during the first half of 2005, some banks which relied heavily on time deposits and interbank borrowing as funding sources had suffered from a squeeze of the interest rate margin of their mortgage loans. In Chapter 5, a stress-testing framework is developed to assess this particular type of interest rate risk to which banks in Hong Kong are exposed. The framework utilizes a model that describes the dynamics of the BLR and therefore the net interest margin of banks in Hong Kong in response to variations in US interest rates and the differential between Hong Kong dollar and US dollar interest rates (resulting from changes in the liquidity situation). The framework can be employed to assess the impact of interest rate shocks on the interest income of banks in Hong Kong. The use of BLR as the reference rate for setting mortgage rates has been adopted by banks for many years. However, the analysis in Chapter 5 suggests that such a practice may not be conducive to banks’ management of interest rate risk, as the movement of BLR may deviate significantly from banks’ cost of funds. Drawing on overseas experience, Chapter 6 examines several local interest rates in order to assess their relevance as alternative reference rates. The assessments are made by evaluating the appropriateness of each rate based on criteria of importance to consumers and factors relevant to banks. Together with other factors, the two key criteria for the assessment are (i) the stability of mortgage rates over time which is regarded as important by both borrowers and banks, and

Introduction xxiii

(ii) conduciveness to interest rate risk management which is important for banking stability. A comparative analysis suggests that a composite rate reflecting movements in various deposit rates, interbank and other interest rates is probably the best as it tracks closely the cost of funds of most local banks and is more stable than the interbank rates and the yield of exchange fund notes. These findings have later resulted in the compilation of a composite interest rate by the Hong Kong Monetary Authority (HKMA), which is now updated and released regularly on a monthly basis, and has become an important indicator of the average funding cost of Hong Kong banks. In the mortgage loan market, the importance of underwriting standards has been highlighted vividly by the subprime loan problems which are currently plaguing global financial markets. In addition to proper assessment of repayment capability, Chapter 6 examines what other factors are crucial to residential mortgage default risk. The empirical analysis reveals the role of current loan-to-value ratio (CLTV) as a major determinant for mortgage default decisions. It also finds that the default probability is positively correlated with the level of interest rates and the unemployment rate, and negatively correlated with financial market sentiment. Given the importance of the CLTV for defaults, this study lends strong support to Hong Kong’s prudential policy of encouraging the adoption of a maximum 70 per cent LTV ratio in residential mortgage lending.

Part III: Quantifying Risks, Capital Adequacy and Stress-testing Framework of Systemic Risk While banks have faced difficulties over the years for a multitude of reasons, the major cause of serious banking problems continues to be directly related to lax credit standards for borrowers, poor portfolio risk management, or a lack of attention to changes in economic conditions and interest rates or other circumstances that can lead to a deterioration in the credit standing of their counterparties and narrowing of banks’ net interest incomes. The Basel Committee on Banking Supervision has played a leading role by fostering an appropriate credit risk assessment approach and by setting out principles for sound banking practices. The Basel Committee is responsible for proposing regulatory requirements, including capital and provisioning requirements, for internationally active banks. Typically, bank supervisors around the world adopt the guidelines put forth by the committee. These practices should be applied in conjunction with a system of quantitative risk

xxiv Introduction

measures for determining the adequacy of capital and provisions and for assessing interest rate risk. Such development has been supported by an enormous expansion in the areas of financial economics including equilibrium analysis in financial markets, asset-pricing theory and option-pricing theory during the last two decades. Under the initiative regarding the adequacy of capital under Basel II, banks are allowed to calculate regulatory capital charges for their credit exposures using the standardized approach based on supervisory risk weights or the IRB approach. Over time, banks are expected to evolve to the IRB approach, which relies on the banks’ own measures in determining the risk components of various asset classes. In Hong Kong, banks generally maintain capital adequacy ratios well above the regulatory requirement. Chapter 8 shows that such buffers are largely determined by internal considerations of the banks, their responses to market discipline, and the regulatory framework. The chapter also argues that to the extent that part of the high capital buffer is due to the agency problem, information asymmetries, or a mismatch between the expectation of the regulator and banks over the approach to maintaining a capital buffer, action could be taken to improve the use of capital. In this connection, the initiative under Basel II is expected to help. Under the IRB approach in Basel II, credit risk measures are estimated by banks. Systematic underestimation of such measures and the corresponding regulatory capital in a bank (or a number of banks) will increase the bank’s vulnerability to adverse changes in market conditions, in particular during a financial or banking crisis. Therefore, the validation of IRB systems has emerged as one of the important issues of the implementation of Basel II. For validation purposes, Chapter 9 uses an approach pioneered by Merton to provide structural model-based methodology for credit risk assessment (probability of default) and capital requirements under Basel II. Benchmark probability of default obtained from the model could be used as external and independent probability of default estimates for comparisons with banks’ internal probability of default estimates of listed companies. Significant deviations from this benchmark provide a reason to review the banks’ internal estimates and their credit rating processes. Apart from capital adequacy, the development of the methodologies of determining provisions has also emerged as an important research area. Chapter 10 develops a simple model for measuring the provision for a pool of collateralized retail loans with homogenous characteristics, where the collateral coverage is treated as a put option with the

Introduction xxv

strike price equal to the outstanding loan amount of the pool. The collateral value and the probabilities of default of borrowers in the pool are the two correlated stochastic variables in the model. As the information associated with these factors is in general available in banks’ retail portfolios, the model can be readily incorporated into their internal risk management systems as a useful quantitative tool for measuring provisions. To monitor stability of the Hong Kong banking system, stress testing and vulnerability indicators are important tools for assessing systemic risk. Chapter 11 introduces a stress-testing framework that involves the construction of macroeconomic credit risk models, each consisting of a multiple regression model explaining the default rate of banks’ credit exposures, and a set of autoregressive models explaining the macroeconomic environment estimated by the method of seemingly unrelated regression. Chapter 12 derives a multiple default risk index based on an optionpricing model to assess the multiple default risk of a portfolio of publicly-listed banks in Hong Kong during the period of January 1997 to January 2006. The index jumped in advance of the Asian financial crisis in 1997, indicating its early-warning capability. By incorporating asset correlations between banks, this indicator has the advantage of providing high frequency information that can be used to assess the systemic risk in the banking system.

Disclaimer The views and analysis expressed in this book are those of the authors, and do not necessarily represent the views of the Hong Kong Monetary Authority

Part I Competition, Efficiency and Profitability

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1 The Cost Efficiency of Commercial Banks in Hong Kong Jim Wong, Tom Pak-Wing Fong, Eric Tak-Chuen Wong and Ka-Fai Choi

1.1 Introduction In recent years, the cost efficiency of banks, along with scale and scope economies, has attracted much attention from both academics and policy makers. Given their special role in channelling funds from savers to investors, poor cost efficiency of banks would restrain the creation of credit, thus jeopardizing the level of economic performance. In addition, inefficiency would affect banks’ earnings, hampering their ability to withstand shocks. The cost efficiency of the US and European banking industries has been examined intensively.1 As for the banking sector in Hong Kong, the issue has only recently been studied by Kwan (2002, 2006) and Drake et al. (2006a, 2006b). By using a non-parametric approach, Drake et al. (2006a) analysed the potential impact of environmental and market factors on the efficiency of the Hong Kong banking system. Many institutions were found to have a high level of technical inefficiency, and there were considerable variations in efficiency levels and trends across size groups and banking sectors. Their results also suggested that the efficiency of banks in Hong Kong had been affected by external factors, mainly macroeconomic and housing market factors.2 Kwan (2002, 2006), based on quarterly data from 1992 to 1999 of 51 banks in Hong Kong and using the stochastic cost frontier approach, found that the X-efficiency was about 16 per cent to 30 per cent of observed total costs. Kwan also found that the average large bank was less efficient than the average small bank, but the size effect appeared to be related to differences in portfolio characteristics among different sized banks. After controlling for on- and off-balance sheet characteristics and loan growth, Kwan (2002, 2006) showed that large banks had higher cost efficiency than smaller banks.3 This suggests that empirical results on the 3

4 The Banking Sector in Hong Kong

size–efficiency relationship are sensitive to the specification employed, in particular the specification on how banks’ outputs are measured.4 As for the evolution of efficiency over time, Kwan (2002, 2006) found that between 1992 and 1997 banks were becoming more efficient, but they were less efficient in 1998 and 1999. The deterioration after 1997 may be explained by the effects of the Asian financial crisis. It is, therefore, of interest to see how the banks have fared in recent years. This chapter reassesses the efficiency level of banks in Hong Kong and the size–efficiency relationship by incorporating off-balance sheet (OBS) outputs into the analysis, in view of the increasing importance of OBS business as a source of banks’ incomes.5,6,7 It also examines the relationship between cost efficiencies, bank characteristics and macroeconomic conditions. In addition, the efficiency estimates are extended to cover the period up to 2005, with the focus on retail banks. The rest of the chapter is organized as follows. The next section discusses the methodology of evaluating banks’ cost efficiency. This includes an exposition of the stochastic cost frontier approach as originated from Aigner et al. (1977). Section 1.3 describes the data employed and the estimation methods, and presents summary statistics of the dataset. Section 1.4 presents the efficiency estimates and section 1.5 examines the relationships between efficiency, bank characteristics and macroeconomic conditions. Finally, section 1.6 concludes.

1.2 Methodology There are two main approaches to the estimation of efficiency – the stochastic frontier approach (SFA) and the data envelopment approach (DEA).8 In this chapter, we adopt the stochastic cost frontier approach developed by Aigner et al. (1977), a technique that is commonly used in banking studies.9 In this framework, the banking firm is viewed as an intermediary that combines various factor inputs to produce a number of outputs. The log of production cost is assumed to take the following general form: ln Ci = f ( ln yji , ln wki ) + εi ,

(1.1)

where Ci is the total production cost of the ith bank, yji is the jth output of the ith bank, and wki is the price of the kth input of the ith bank. With the functional form of f in equation (1.1) specified as a multi-product translog with the usual symmetry restrictions based on

Wong, Fong, Wong and Choi 5

the duality theorem, equation (1.1) can be written as10,11 ln Ci = α0 +

J 

τj ln yji +

j=1

+

1 2

K  K  k=1 h=1

K 

1 γjl ln yji ln yli 2 J

φk ln wki +

J

j=1 l=1

k=1

K  J

ϕkh ln wki ln whi +

ωjk ln yji ln wki + εi .

(1.2)

j=1 k=1

The error term εi has two independently distributed components: εi = vi + ui .

(1.3)

The first component, vi , is a statistical noise and is assumed to be distributed as a symmetric normal N(0, σv2 ). The second component, ui , is bank-specific and is assumed to be distributed as a half-normal |N(0, σu2 )|. Given the above, the lowest attainable production cost is f ( ln yji , ln wki ) + vi . This is precisely the stochastic cost frontier of the ith bank.12 With the estimated cost frontier of banks, the level of cost inefficiency can be assessed. In this chapter, what cost inefficiency refers to is the situation in which the bank can reduce the production cost in obtaining the same quantities of outputs, given the input prices, but it has failed to do so. This means the production cost is not on the stochastic cost frontier. In other words, ui is positive. Cost inefficiency is therefore an estimate of the percentage by which total production cost could have been reduced if the bank had operated on the stochastic cost frontier, holding the output levels and input prices constant. In the analytical apparatus of the standard production theory, such a deviation occurs when the bank does not choose the right mix of inputs to produce the target output or employs excessive quantities of the factor inputs to produce the same amount of output.13 Following Jondrow et al. (1982), we estimate the observation-specific cost inefficiencies by computing the conditional expected values. For the nth bank, the inefficiency estimate (IE estimate), represented by the conditional expectation of un , can be derived as:   g(εn λ/σ) εn λ σλ + , (1 + λ2 ) G(εn λ/σ) σ

(1.4)

where λ is σu /σv , σ 2 is σv2 + σu2 , g and G are the standard normal density and cumulative distribution functions respectively.

6 The Banking Sector in Hong Kong

1.3 Data and estimation methods In the estimation we employ a panel dataset that involves 38 retail banks in Hong Kong and covers the period from 1992 Q1 to 2005 Q4.14 Retail banks are the locally incorporated banks plus a number of larger foreign banks whose operations are similar to those of the locally incorporated banks in that they operate a branch network and are active in retail banking. The banking data are obtained from the regulatory returns that Authorized Institutions in Hong Kong must file with the Hong Kong Monetary Authority (HKMA). Since our purpose is to examine the cost efficiency in Hong Kong, the sample is restricted to incorporate only data on the Hong Kong offices of retail banks. Following past literature (see Clark and Siems 2002 and Kwan 2006), the banking cost function is dependent upon input prices and the level of output. As for the banks’ output variables, we adopt the intermediation approach by Sealey and Lindley (1977), which views banks as an agent to employ labour, funds and capital to produce interest-bearing assets. Outputs are measured by the amount of interest-bearing assets generated by the banks. We follow Kwan (2006) to define outputs which relate to banks’ intermediation function. Accordingly, they are (1) loans to finance imports, exports, re-exports, and merchandising trade (y1 ); (2) loans for non-trade-related financing (y2 ); and (3) non-loan earning assets including negotiable certificates of deposit, all other negotiable debt instruments and equity investments (y3 ). Since many banks have moved to provide financial services off the balance sheet, the traditional measures of on-balance sheet output based on the intermediation approach tend to underestimate output levels of banks. Following the specification of Rogers (1998) and Clark and Siems (2002), non-interest incomes are added into the estimation to serve as a proxy for OBS outputs generated by banks.15 With regard to the input variables, banks are considered as employing three factor inputs: labour, funds and capital. The unit price of labour is computed as the ratio of staff expense to total assets. The unit price of funds is proxied by the ratio of interest expense to total funding (the sum of deposits from customers, due to banks, amount payable under repos and negotiable debt instruments issued and outstanding). The unit price of capital is derived as the ratio of expenses, other than staff and interest expenses, to fixed assets. Table 1.1 provides some descriptive statistics of retail banks. In 2005 Q4, the average values of the three groups of interest-earning outputs (trade-related loans, non-trade-related loans, other non-loan-earning assets) and non-interest incomes per retail bank were about HK$5.0

Wong, Fong, Wong and Choi 7 Table 1.1 Some descriptive statistics of retail banks as of 2005 Q4 Mean

Median

Amount % change Amount % change from 1999 Q4 from 1999 Q4 Average output values per bank (HK$ million) Loans to finance trade Non-trade-related loans Other earning assets Non-interest incomes

4,997 68,876 47,394 539

124.7 107.5 310.5 6.5

2,475 34,949 20,842 127

82.1 76.8 383.8 −0.9

1,645

−4.4

1,442

0.9

8,431

−36.3

7,601

−42.7

1,397

106.7

896

56.8

Others (HK$ million) Average total assets per bank 190,902 Average total costs per bank 1,732

120.9 47.4

81,062 766

97.4 28.7

Input prices (HK$) Labour (per HK$1 million of total assets) Borrowed funds (per HK$1 million of total funding) Capital (per HK$1,000 of fixed assets)

billion, HK$68.9 billion, HK$47.4 billion, and HK$539 million respectively. On the input side, the average cost of labour per HK$1 million of total assets, and borrowed funds per HK$1 million of interest-bearing liabilities were HK$1,645 and HK$8,431 respectively, and the average cost of capital per HK$1,000 of fixed assets was HK$1,397. Compared with 1999 Q4, all interest-bearing output values increased significantly by over 100 per cent, and non-interest incomes rose by an average 6.5 per cent. On the input side, while the average price of capital also increased, the average cost of labour and borrowed funds registered reductions. The stochastic cost frontier can be estimated by the pooled time-series cross-section observations of the dataset with the assumption that all banks have the access to the same production technology. By using the maximum likelihood method, the coefficients of the cost function are obtained. The conditional expectation of inefficiency in equation (1.4) for each bank and of each period is obtained by using the residuals and their variances derived by the estimated stochastic cost frontier.

8 The Banking Sector in Hong Kong Table 1.2 Inefficiency estimates of retail banks in Hong Kong

1992 Q4 1993 Q4 1994 Q4 1995 Q4 1996 Q4 1997 Q4 1998 Q4 1999 Q4 2000 Q4 2001 Q4 2002 Q4 2003 Q4 2004 Q4 2005 Q4

Weighted average

Median

Average

28.9 23.9 21.7 20.1 17.1 15.1 16.1 15.1 19.9 25.0 25.8 26.3 23.9 18.0

19.7 19.5 19.6 16.1 12.8 10.0 11.3 12.2 15.1 15.4 17.7 17.9 15.3 11.7

21.8 21.3 19.9 17.7 14.9 13.8 13.4 14.0 17.9 20.4 19.0 21.2 19.6 17.2

Notes: 1. The figures are in percentage terms. 2. The weighted averages are calculated with banks’ efficiency estimates being weighted by their asset sizes.

1.4 The inefficiency estimates The inefficiency estimates (IE estimates) are presented in Table 1.2. Figures 1.1 and 1.2 depict the time series of some descriptive statistics of the IE estimates. A higher IE estimate will be observed when higher input costs or lower levels of output value take place, resulting in a larger deviation from the minimum cost. In other words, a higher IE estimate means lower efficiency, and vice versa. As can be seen from the table and figures, the weighted average IE estimate started to increase by 1998 and reached 26.3 per cent in 2003 Q4, after declining gradually from 28.9 per cent in 1992 Q4 to 15.1 per cent in 1997 Q4. Nevertheless, since 2004 the IE estimate has resumed its declining trend and improved to 18.0 per cent by 2005 Q4.16 An examination of the evolution of the IE estimates over time shows that the estimates systematically relate to economic cycles. During the period when Hong Kong suffered from two significant economic shocks – the Asian financial crisis and the outbreak of SARS – the IE estimates deteriorated significantly. However, as the economy recovered in recent years, the IE estimates began to decline. The positive correlation between the cost efficiency of banks and economic performance will be tested formally in section 1.5.

Wong, Fong, Wong and Choi 9 (%) 40 Weighted average 30

20

10

Median Average 2003Q2

2004Q3

2005Q4

2004Q3

2005Q4

2002Q1

2000Q4

1999Q3

1998Q2

1997Q1

1995Q4

1994Q3

2003Q2

Figure 1.1

1993Q2

1992Q1

0

Trends of the inefficiency estimates

(%) 100 80 Upper quarter 60 40 20 0

2002Q1

2000Q4

1999Q3

1998Q2

Median 1997Q1

1995Q4

1994Q3

1992Q1 Figure 1.2

1993Q2

Lower quarter

20

Dispersions of the inefficiency estimates

Notes: 1. The shaded area covers all the obtained estimates of retail banks’ inefficiencies. 2. The weighted average is weighted by total assets.

A possible reason for this time-series property is that as risks are more likely to materialize during economic downturns, banks may have to spend additional resources (factor inputs) or to reduce the amount of outputs (such as credit) in order to better control the risks. In addition, banks may incur more costs on new business initiatives and strengthening customer relationships. In consequence, they would be using more

10 The Banking Sector in Hong Kong

inputs to produce the same quantity of output, or to produce a smaller quantity of output with the same amount of inputs, giving rise to higher IE estimates. Another possible reason is that there are fixities in the factor inputs. The quantity of physical capital is obviously not easy to adjust and, with the existence of recruitment cost and investment in specific human capital, labour is likely to be quasi-fixed.17 Moreover, banks generally do not have perfect control over the quantity of deposits. With such fixities, banks may be unable to reduce by an enough extent the input quantities when the demand for banking services is weakened by an economic downturn. Even if such fixities may not be very rigid, it would take time for banks to adjust and streamline their operation. As a result, in economic downturns, some factor inputs may become idle, thereby deteriorating the cost efficiency. Apart from the time-series variations, the IE estimates also differ substantially among banks. Figure 1.2 displays the range and interquartile range of the IE estimates. It can be seen that the cost efficiency of banks was rather diverse, for example, it ranged from 10 per cent to 80 per cent during 2003. It is worth noting that banks with very high IE estimates were also found to have a very low loan-to-asset ratio. Another interesting finding is that the distributions shown in Figure 1.2 are skewed significantly. Both the upper and lower quartiles and the median were very close to the minimum, indicating there were more relatively efficient than inefficient banks.

1.5 Efficiency, bank characteristics and macroeconomic conditions To examine the relationship between cost efficiencies, bank characteristics and macroeconomic conditions, we estimate a panel data regression model to relate the IE estimate to a number of variables, including bank size, funding sources, business mix, loan quality, and real GDP growth rates.18 The regression model, Model A, is as follows: IEit = β0 + β1 log (TAit ) + β2 + β5 GDPGit + f (eit ),

      Depit y1it + y2it LLossit + β3 + β4 TAit TAit TLoanit (1.5)

where TA is total assets, Dep is customers’ deposits, y1 and y2 are loans to finance imports, exports, re-exports, and merchandising trade and loans for non-trade-related financing respectively, LLoss is loan loss provisions, TLoan is total loans, GDPG is the real GDP growth rate, and the

Wong, Fong, Wong and Choi 11

Table 1.3 Panel data regression of inefficiency estimates

Constant Log(TA) Dep/TA (y1 + y2 )/TA LLoss/TLoan GDPG Adj. R2 DW

Model A

Model B

1.0361** −0.0347** −0.0114 −0.5333** 0.4344** −0.2777**

1.0237** −0.0344** − −0.5328** 0.4232** −0.2785**

0.6661 1.9080

0.6659 1.9082

Notes: ∗∗ denotes statistical significance at the 1% level.

function f (e) consists of autoregressive terms of a white noise process to capture autocorrelation in residuals.19 The variable TA is used to proxy the bank size. The variables of deposits and loans to total assets ratios Dep/TA and (y1 + y2 )/TA capture banks’ funding mix and asset portfolio composition respectively. Regarding the sign of their coefficients, literature does not have a priori expectation. The loan-loss provisions capture the quality of banks’ loan portfolio.20 There are different views about the expected sign of the coefficient of this variable.21 Finally, the growth of GDP tests the relationship between banks’ operating results and the overall economic performance. The sign of the coefficient estimate should be negative, since banks operate in poor economic conditions are likely to incur higher costs or produce less outputs. Applying the method of generalized least squares with fixed effects and cross-section weights, equation (1.5) is estimated with the IE estimates obtained from section 1.4. The results are reported in Table 1.3. The diagnostic test statistics show that the multiple regression model adequately fits the data, with the adjusted R-squares at 0.67 and the DW statistic close to two. With the exception of the ratio of deposits to assets, all coefficients of the explanatory variables are significant and the coefficient for GDPG has the expected sign. As the deposits to assets ratio is not significant, another model (Model B) which excludes it is considered. The estimation results show that all variables remain significant and the signs of their estimated coefficients are unchanged. Key findings from the estimation results are as follows: 1. The level of efficiency of banks is found to be positively correlated with bank size. In other words, large banks are on average more efficient than smaller banks. This is consistent with Kwan (2006) and

12 The Banking Sector in Hong Kong

2.

3.

4.

5.

6.

Drake et al. (2006a) that there is a strong size–efficiency relationship, with larger banks outperforming their smaller competitors. Drake et al. (2006a) commented that such results may have important implications for policy analysis on the area of mergers and consolidation. Similar observations were found in the US banking industry (Berger et al. 1993). Efficiency is also found to be positively correlated with the ratio of loans to total assets, suggesting that banks’ efficiency level may be sensitive to their business mix, with banks which focus more on lending business exhibiting a lower level of inefficiency.22 Banks with higher loan loss provisions appeared to be less efficient. Banks with more provisions indicate poor loan quality, which may call for higher operation costs relating to credit risk and loan loss management, such as credit approval control, foreclosing bad loans, debt recovery expenses, and other loan-restructuring expenses.23 Efficiency is positively correlated with economic performance, with banks found to be less efficient during economic downturns. As discussed in section 1.4, this may be partly due to the fixities in factor inputs, and additional required resources spent on risk control, new business initiatives and customer relationships during economic downturns. The funding structure is found to be not statistically significant. This suggests that while banks with a stronger deposit base could fund their assets less costly, the high cost arising from maintaining a large branch network may have offset such comparative benefit. The relative magnitudes of coefficient estimates suggest that the changes in cost efficiency due to a one standard deviation change in business mix, total assets and economic performance are 7.1 per cent, 4.7 per cent and 1.3 per cent points respectively.24

1.6 Conclusion Using the stochastic frontier approach and a panel dataset of retail banks, this chapter assesses the cost efficiency of the banking sector in Hong Kong. The average cost inefficiency during the period 1992–2005 is found to be about 15 per cent to 29 per cent of observed total costs, which is close to the findings of Kwan (2002, 2006), and is largely in line with the experience of US and European banks.25 Cost efficiency is found to be correlated with macroeconomic conditions, with a significant rise in cost inefficiency triggered by the Asian financial crisis and the outbreak of SARS during the period 1998–2003,

Wong, Fong, Wong and Choi 13

partly due to the lack of perfect flexibility by banks to adjust their factor inputs (labour, funds and capital) in response to falling outputs. Additional resources spent on risk control, new business initiatives and strengthening customer relationships may have also contributed. Nevertheless, the cost efficiency has started to improve by 2004 Q1, along with the recovery of the economy. This suggests also that the adjustments and streamlining by the banks in recent years may have begun to bear fruit. Empirical results also indicate that cost efficiency is positively correlated with bank size, suggesting large banks are on average more efficient than smaller banks. Efficiency is observed to be sensitive to banks’ business mix, with banks which focus more on lending business exhibiting a higher level of efficiency compared to banks which focus relatively less on loans. In addition, banks suffering from larger loan loss provisions are found to be less efficient, probably as a result of higher operational costs relating to credit risk and loan loss management.

Notes 1. For example, Berger and Humphrey (1991), Kaparakis et al. (1994) and Clark and Siems (2002) studied the cost efficiency of the US banking industry, and Altunbas et al. (2001) and Vennet (2002) studied that of the European banking industry. 2. Drake et al. (2006b) presented their further work on the issue in a Hong Kong Institute for Monetary Research (HKIMR) seminar in April 2005. In their study, they examined both cost and profit efficiencies for financial institutions in Hong Kong by using a parametric approach. They found that both profit and cost efficiencies revealed a secular decline over the whole sample period, but a much smaller deterioration in profit efficiency levels was observed. It suggested that Hong Kong’s financial institutions were able to generate significant improvements in revenues relative to costs. Note that the paper is not yet publicly released. 3. Drake et al. (2006a) based on the non-parametric approach and a panel dataset of banks in Hong Kong for the period 1995–2001 also showed that large banks were more efficient than their smaller competitors. The existing literature in this area also suggests that larger banks are in general more efficient. For example, Berger et al. (1993) reported evidence that larger banks were more X-efficient than smaller banks in the US banking industry. 4. Similar observations were found in the US banking industry. While Kaparakis et al. (1994) found that banks generally became less efficient with increasing size for the US banking industry, they noted that the findings would alter if off-balance sheet activities were included in the analysis. 5. Instead of using a non-parametric approach as in Drake et al. (2006a), this chapter adopts the stochastic frontier approach, similar to Kwan (2002, 2006). However, the output variable is represented by the sum of both on-balance

14 The Banking Sector in Hong Kong

6.

7.

8.

9. 10.

11.

12.

13.

14.

sheet and off-balance sheet items. The initial set of input variables included in the estimation is similar to Kwan (2002, 2006). Another possible extension of the current approach, which can be considered in future research, is to take a similar approach to Drake et al. (2006b), in that both the cost and profit efficiencies were estimated and the productivity growth was decomposed into two portions: one due to changes in business conditions and the other due to changes in the best practice and inefficiency. Omitting off-balance sheet (OBS) outputs in the cost efficiency estimation not only affects the size-efficiency relationship estimates, it also affects estimates of the efficiency level. Rogers (1998) and Clark and Siems (2002), by comparing the results which included proxies for the OBS outputs in the estimation, such as non-interest incomes, with those without incorporating OBS outputs in the estimation, showed that omitting OBS activities in the cost efficiency estimation could seriously understate actual bank outputs and efficiency levels. The Data Environment Analysis approach is a non-parametric method that applies mathematical programming technique to envelop the input/ output data. See, for example, Kaparakis et al. (1994), Goldberg and Rai (1996), Vennet (2002) and Kwan (2002, 2006). The translog cost function can be viewed as a logarithmic second-order approximation of the true cost function, assuming that the true cost function is twice continuously differentiable (see Greene 1998). Thus, it is a flexible functional form that is less prone to the problem of specification error. The usual symmetry restrictions γjl = γlj , ϕkh = ϕhk and ωjk = ωkj are imposed to help circumvent the multicollinearity problem arising from the fact that the same interactive explanatory variable enter into the regression equation twice in the translog specification. Conceptually, the reduced form f in equation (1.1) corresponds to the cost function of the standard production theory which assumes that given the target output levels the firm chooses the quantities of inputs to minimize production cost. Therefore, in the absence of ‘luck’, so that vi is non-zero, the production cost of the ith bank when it is fully cost efficient is f ( ln yji , ln wki ). However, vi may not equal zero because in reality there could be random factors that are beyond the bank’s control but influence its production cost. Given this, the stochastic cost frontier becomes f ( ln yji , ln wki ) + vi . Why the banks may not minimize the production cost is in itself an interesting question. The explanation offered by Leibenstein (1966) is that the management may have objectives other than profit maximization, which is known as X-efficiency. Apart from psychological reasons, this can result from a principal–agent problem. Aigner et al. (1977) attributed such deviation to productive inefficiency arising from factors such as technical and economic inefficiency, and the will and effort of the producer and his employees. Initially, there were a total of 45 banks in various periods covered by the study. After removing samples with missing information, 38 retail banks remained in the estimation. Note that the number of banks covered by the study varied in different periods. After the major mergers and acquisitions, the number fell from 38 during 2001 Q2 to 28 during 2005 Q4.

Wong, Fong, Wong and Choi 15 15. An estimation which excludes non-interest incomes as an output was also tried. Consistent with other studies (Rogers 1998 and Clark and Siems 2002), the estimated efficiency level is lower when the non-interest income variable is excluded, indicating that omitting OBS activities in the cost efficiency estimation could understate actual bank outputs and efficiency levels. 16. The Mann–Kendall test suggests that there exists a significant declining trend for the time series of IE estimates from 2003 Q4 to 2005 Q4 at the 0.05 level of significance. 17. See Oi (1962) and Rosen (1968) for a discussion on the fixity of labour input. 18. Note that the statistical relationship needs not imply causality. 19. Data on provisions from banks’ returns are used to proxy loan loss provisions. The data may include some items unrelated to loan loss such as provisions against the values of other claims and investments. 20. Another variable CAR which represents either the respective risk level or banks’ leverage is found to be insignificant. 21. This is to be discussed in details in the following section on key findings from the estimation results. 22. This appears to be in line with banks’ conventional role. It suggests that banks specializing in their main intermediation function are more cost efficient. 23. In this case, both the management board and bank supervisors may require banks to increase their resources in credit assessment and approval. Alternatively, as noted by Kwan (1997), the correlation between poor asset quality and inefficiency may be an indication of poor management of banks, or a direct consequence of the tendency of inefficient firms to make risky loans. On the other hand, to the extent that the efficiency benefit of larger revenue generated through more aggressive lending (with less stringent credit risk control) may more than offset the increased cost arising from greater resources required for the credit risk and loan loss management, the coefficient estimate may have a negative sign. 24. As both GDP growth and loan loss provisions correlate to the business cycle, their estimated coefficients are combined to represent economic performance in the calculation. 25. See Kwan (2002, 2006).

References D. Aigner, C. K. Lovell and P. Schmidt, ‘Formulation and Estimation of Stochastic Frontier Production Function Models’, Journal of Econometrics, 6 (1977) 21–37. A. Altunbas, L. Evans and P. Molyneux, ‘Bank Ownership and Efficiency’, Journal of Money, Credit and Banking, 33 (2001) 926–54. A. N. Berger, ‘Distribution-free Estimates of Efficiency in the US Banking Industry and Tests of the Standard Distributional Assumptions’, Journal of Productivity Analysis, 4 (1993) 61–92. A. N. Berger and D. B. Humphrey, ‘The Dominance of Inefficiencies over Scale and Product Mix Economies in Banking’, Journal of Monetary Economics, 28 (1991) 117–48.

16 The Banking Sector in Hong Kong A. N. Berger, W. C. William and S. G. Timme, ‘The Efficiency of Financial Institutions: a Review and Preview of Research Past, Present, and Future’, Journal of Banking and Finance, 17 (1993), 221–49. J. A. Clark and T. F. Siems, ‘X-efficiency in Banking: Looking beyond the Balance Sheet’, Journal of Money, Credit and Banking, 34 (2002) 987–1013. L. Drake, M. J. B. Hall and R. Simper, ‘The Impact of Macroeconomic and Regulatory Factors on Bank Efficiency: A Non-parametric Analysis of Hong Kong’s Banking System’, Journal of Banking and Finance, 30 (2006a) 1443–66. L. Drake, M. J. B. Hall and R. Simper, ‘Efficiency and Productivity Change in Hong Kong Banking’, HKIMR’s seminar in 2004/2005, (2006b). L. G. Goldberg and A. Rai, ‘The Structure-performance Relationship for European Banking’, Journal of Banking and Finance, 20 (1996) 745–71. W. H. Greene, Econometric Analysis, 3rd edn (Englewood Cliffs, NJ: Prentice Hall, 1998), pp. 693–6. J. Jondrow, C. A. K. Lovell, I. S. Materov and P. Schmidt, ‘On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model’, Journal of Econometrics, 19 (1982) 233–8. E. I. Kaparakis, S. M. Miller and A. G. Noulas, ‘Short-run Cost Inefficiency of Commercial Banks: A Flexible Stochastic Frontier Approach’, Journal of Money, Credit and Banking, 26 (1994) 875–93. S. Kwan, ‘Efficiency of U.S. Banking Firms – An Overview’, FRBSF Economic Letter, Federal Reserve Bank of San Francisco, (1997). S. Kwan, ‘The X-efficiency of Commercial Banks in Hong Kong’, HKIMR working paper, 12/2002. S. Kwan, ‘The X-efficiency of Commercial Banks in Hong Kong’, Journal of Banking and Finance, 30 (2006) 1127–47. H. Leibenstein, ‘Allocative Efficiency vs. “X-efficiency”’, American Economic Review, 56 (1966) 392–415. W. Oi, ‘Labour as a Quasi-fixed Factor’, Journal of Political Economy, 70 (1962) 538–55. K. E. Rogers, ‘Nontraditional Activities and the Efficiency of US Commercial Banks’, Journal of Banking and Finance, 22 (1998) 467–82. S. Rosen, ‘Short-run Employment Variation on Class-I Railroads in the US, 1947– 1963’, Econometrica, 36 (1968) 511–29. C. W. Sealey and J. T. Lindley, ‘Inputs, Outputs and Theory of Production Cost at Depository Financial Institutions’, Journal of Finance, 32 (1977) 1251–66. R. V. Vennet, ‘Cost and Profit Efficiency of Financial Conglomerates and Universal Banks in Europe’, Journal of Money, Credit and Banking, 34 (2002) 254–82.

2 Competition in Hong Kong’s Banking Sector: A Panzar–Rosse Assessment Jim Wong, Eric Tak-Chuen Wong, Tom Pak-Wing Fong and Ka-Fai Choi

2.1 Introduction The operating environment of the banking sector in Hong Kong has undergone major changes in recent years, including regulatory liberalization, technological progress and industry consolidation.1 These structural developments could have implications for competitive conditions in the sector. Competition could lower financial intermediation costs and contribute to improvements in economic efficiency. However, since it may also reduce the market power and profitability of banks, it could weaken their ability to withstand adverse developments. It is important for policy makers to know the extent of competition in the sector and how it has evolved over time. Jiang et al. (2004)2 examined the evolution of the market structure of Hong Kong’s banking sector during the period 1992 to 2002 by using the Panzar–Rosse assessment.3 The study suggested that while there was evidence that competitive pressures in the sector may have eased somewhat in the latter years, the sector remained highly competitive. However, the analysis which is based on aggregate data of the banking sector was significantly restrained by data limitations, in particular the relatively small number of observations. To address such drawback, this chapter re-visits the issue of the competitive structure of the banking industry in Hong Kong, adopting also the Panzar–Rosse approach as in the previous study, based on a panel dataset which covers all retail banks in Hong Kong for the period of 1991 Q1 to 2005 Q4. The use of a panel dataset not only enhances the efficiency of the estimates,4 thus allowing the drawing of a more precise inference on the population characteristics of the market structure, but also facilitates the construction and testing of more complicated models, 17

18 The Banking Sector in Hong Kong

such as the relationship between competitive pressures and bank size in Hong Kong, which was difficult to achieve in the past study due to the data constraint. Moreover, in this chapter, the data available for analysing the impact of the recent developments on the competitive structure in the banking sector are extended from 2002 Q4 to 2005 Q4. As the interest rate deregulation was only completed in July 2001 and a number of other significant market liberalization moves and substantial bank consolidation only took place around 2001 and 2002, the overall impact on the competitive conditions in the banking sector of these structural developments may not have been fully visualized in Jiang et al. (2004), the study period of which only covered up to 2002. It is important to assess properly how the extent of competition in the sector has changed in the subsequent years, with the effects of both market liberalization and consolidation being more fully realized. With longer time series of data, this chapter should provide a more accurate assessment. The rest of the chapter is organized as follows. The Panzar-Rosse approach will be discussed in the next section. Sections 2.3 and 2.4 describe the empirical specifications, and data and estimation methods respectively. Section 2.5 presents the estimation results. Finally, section 2.6 concludes.

2.2 The Panzar–Rosse approach The Panzar–Rosse approach estimates the sum of elasticities (H statistic) of a firm’s revenue with respect to input prices in a reduced form revenue equation. The measure is grounded in the idea that competitive firms are price takers and must pass through cost changes to customers, while a monopoly can vary output to maximize profits in the face of higher input prices. Let R be the revenue function of a vector of k input prices, w = (w1 , w2 , . . . , wk ) and a vector exogenous variables x that shift the revenue function: R = R (w, x) H=

 ∂R wk ∂wk R k

Panzar and Rosse showed that the H statistic indicates the nature of market structure under certain assumptions5 (Table 2.1). In a monopoly

Wong, Wong, Fong and Choi 19 Table 2.1 Competitive structures and the H statistic Competitive structure

Values of H

Monopoly Monopolistic competition Perfect competition

H ≤0 0
market, H is negative, as an increase in input prices will increase marginal costs and reduce equilibrium output, and subsequently a decline in total revenue given the profit maximization hypothesis. In contrast, in a perfectly competitive market, H is equal to one, as any increase in input prices raises both marginal and average costs and in turn leads to a oneto-one increase in total revenue, without changing the optimal output of banks. This is true since those institutions that cannot cover the increase in input prices through increased revenue will be forced to exit the market. If the market structure is characterized by monopolistic competition, H will be between zero and one, with the total revenue rising less than proportionally to the changes in input prices. The Panzar–Rosse approach has been widely applied to assess competitive conditions in the banking systems of the United States, Canada and Japan since the early 1980s, with later work focusing on European countries. Most of these banking systems exhibited characteristics of monopolistic competition (Bikker and Haaf 2002).

2.3 The empirical specifications In our application of the Panzar–Rosse approach, the following equation is estimated to derive the H statistic from a panel dataset of banks in Hong Kong:  log

Rit TAit

 = α0 +

K 

αk log wkit + xit β + εit

(2.1)

k=1

where R is the revenue; TA is the total assets; wk is the unit price of factor k; x is a vector of control variables; ε is the disturbance term; i and t denote bank and time respectively. The H statistic is the sum of α1 to αK in this specification.

20 The Banking Sector in Hong Kong

In addition to equation (2.1), an equation for unscaled total revenue will also be estimated by:

log (Rit ) = α0 +

K 

αk log wkit + xit β + βTA log TAit + εit

(2.2)

k=1

with the variable TA controlled as an explanatory variable. Equation (2.1) is a special case of equation (2.2) if βTA equals to one. In this regard, equation (2.1) is a restricted model of equation (2.2). The consideration of equation (2.2) follows the idea in Gelos and Roldos (2002). With the specification in equation (2.2), the value of the coefficient of TA can identify the presence or absence of scale economies. We measure the revenue as total revenue6 rather than the gross interest revenue to account for also the growing off-balance sheet business in the banking sector which mainly generates fees and commission-based incomes. Taking total revenue as the dependent variable is consistent with other studies such as Shaffer (1982), Nathan and Neave (1989), Hempell (2002) and Claessens and Laeven (2004). In this study, banks are considered as employing three factor inputs: labour, funds, and capital. The unit price of labour is computed as the ratio of staff expense to total assets.7 The unit price of funds is proxied by the ratio of interest expense to total funding (the sum of deposits from customers, due to banks, amount payable under repos and negotiable debt instruments issued and outstanding). Finally, the unit price of capital is derived as the ratio of expense other than staff and interest expenses to fixed assets. Bank-specific factors which reflect differences in risk and funding structures are incorporated to control for other heterogeneities in the samples. Capital adequacy ratio (CAR) is considered as a proxy for bank risk. The coefficient estimate is expected to be negative, as a lower level of bank risk (that is a higher value in CAR) should lead to lower bank revenue. To capture differences in the funding structure, bank’s deposit mix (DM) as measured by the ratio of deposits from customers to bank’s total funding (the sum of deposits from customers, due to banks, amount payable under repos and negotiable debt instruments issued and outstanding) is included in the estimation. Regarding the sign of the coefficient of DM, literatures do not have a priori expectation. In addition to the bank characteristics, certain macroeconomic variables are included. We incorporate the real GDP growth rate in Hong Kong into equations (2.1) and (2.2) to control for the influence

Wong, Wong, Fong and Choi 21

of economic cycles. Generally, banks should generate larger revenue with the same quantities of inputs under good economic conditions. Inflation rate is incorporated to avoid obtaining a spurious relationship between revenue and factor prices, as their movements are to some extent driven by inflation.

2.3.1 The models A total of six models are specified for estimation: 1. To provide insights on the overall competitive condition during 1991– 2005, Models A and B are specified as equations (2.1) and (2.2) respectively – specifically, scaled R and unscaled R are regressed on the explanatory variables with a constant H statistic for the entire sample period. 2. To study how the degree of competition has evolved over time, two models (Models C and D) will be estimated for scaled R and unscaled R with time-varying H statistic. Models C and D are modified from Models A and B, respectively, to include the interactions between the input-price variables and a dummy variable, DUM. DUM is defined as one after 2001 Q2, and zero otherwise. DUM is so specified as to examine the effect of the structural changes in the banking sector in Hong Kong on the competitive condition in the sector. The time point 2001 Q2 is so chosen to distinguish the two periods as major structural changes either completed or took place around this time: (a) The interest rate deregulation was fully completed by July 2001, with interest rate restrictions on current and savings accounts also removed8 ; (b) the restriction on the number of branches and offices for foreign banks was completely removed in 2001, (c) the market entry criteria have been relaxed since 2002, and (d) most major bank consolidations took place in 2001 and 2002, including the forming of the Bank of China Group, and DBS Bank (Hong Kong) through mergers and acquisitions.9 The impact of industry consolidation on market concentration is apparent. As can be seen in Figure 2.1, the market concentration measured by the Herfindahl–Hirschman index (HHI)10 increased sharply around the second half of 2001, largely due to the merger and acquisition activities.

22 The Banking Sector in Hong Kong HHI 0.16 0.14 0.12 0.10 0.08 0.06 0.04 HHI*

0.02

Figure 2.1

2005/03

2004/03

2003/03

2002/03

2001/03

2000/03

1999/03

1998/03

1997/03

1996/03

1995/03

1994/03

1993/03

1992/03

1991/03

0.00

Major changes in market concentration around 2001

Note: *The HHI is the sum of the squared market shares of assets of all the retail banks in the market, ranging from zero to one. Source: HKMA.

In addition to Models C and D, time series of rolling estimates of the H statistic from 1999 to 2005, which are generated by a series of rolling regressions of Models A and B, are also employed to assess the change of H statistic from 1999 to 2005. 3. To study how competitive pressures vary with bank size, Models E and F will be estimated to facilitate the analysis. Models E and F differ from Models A and B in that the formers include the interactions between the input-price variables and bank-scale dummies, Size, to examine whether the competitive condition among large banks is different from that of smaller banks. In a given period, a bank is considered as large (that is Size = 1) if its asset size is one of the seven largest. These model specifications can deliver a more in-depth analysis on how the competitive condition relates to bank size.

2.4 Data and estimation methods The dataset used in the estimation is a panel dataset of all retail banks in Hong Kong covering the period from 1991 Q1 to 2005 Q4. Retail banks are the locally incorporated banks plus a number of the larger foreign banks whose operations are similar to those of the locally incorporated banks in that they operate a branch network and are active

Wong, Wong, Fong and Choi 23 Table 2.2 Summary statistics on the sample (1991 Q1–2005 Q4)

Total revenue (HK$ mn) Unit price of labour Unit price of funds Unit price of capital Total assets (HK$ mn) Capital adequacy ratio (%) Deposit mix (%) Growth (%) Inflation (%)

Median

Mean

584 0.0015 0.0122 0.6995 32,352 19.7 83.1 1.200 0.250

1,169 0.0019 0.0115 3.6293 76,628 25.9 78.6 1.123 0.232

Notes: 1. Deposit mix is defined as the ratio of deposits from customers of a bank to its total funding. 2. The Growth series is the seasonally adjusted quarterly real GDP growth rate series published by the Census and Statistics Department. 3. The Inflation series is constructed by quarter-end figures from the seasonally adjusted monthly CPI(A) inflation series published by the Census and Statistics Department.

in retail banking. The banking data are obtained from the regulatory returns that the Authorized Institutions in Hong Kong must file with the Hong Kong Monetary Authority (HKMA). Since our purpose is to examine the banking competition in Hong Kong, the sample is restricted to incorporate only the data on the Hong Kong offices of retail banks. Table 2.2 presents summary statistics on the sample. The six models, Models A to F, are estimated by the panel dataset, and the first difference forms of equations (2.1) and (2.2) are estimated instead of the original series. This is for several reasons. First, differencing the equation removes the individual effects (which are time invariant and cross-section specific), reducing the number of parameters to be estimated. Secondly, removing the individual effects also avoids complications arising from the possibility that they may be correlated with the explanatory variables. Thirdly, differencing the equation avoids the omitted-variable bias stemming from the cross-sectional unobserved heterogeneities that are constant over time. In estimating the equation, we follow a feasible generalized leastsquares (FGLS) procedure instead of applying the method of ordinary least squares (OLS) because estimators of the former are more efficient with a large sample.11 In the FGLS procedure, we use the seemingly unrelated regression (SUR) weights to correct for both cross-section heteroskedasticity and contemporaneous correlation.12

24 The Banking Sector in Hong Kong

2.5 Estimation results Empirical results of the six models are presented in Tables 2.3 and 2.4. The adjusted R-squared statistics of the six models, which measure the goodness of fit, range from 0.613 to 0.792. This is considered as satisfactory, given that the dependent variables are in first difference form. The coefficients of all input-price variables are positive and significant at the 1 per cent level, except that of the unit price of capital in Models C and D which are significant at the 10 per cent level. The estimated coefficients of all input-price variables are in line with the theory and empirical findings of other developed banking systems. As for the estimated coefficients of other bank-specific factors, CAR and DM are significant at the 1 per cent level in all the six models. The variable CAR has the expected negative sign, indicating that the level of risk positively affects the level of revenue. The variable DM has a positive sign, suggesting that banks with a larger portion of their funding from customer deposits may generate larger revenue. As for the macroeconomic variables, all estimated coefficients are statistically significant at the 1 per cent level, except for the variable Growth which are only significant at the 10 per cent level in Models A and B and at the 5 per cent level in Model F. Overall, the estimation results appear robust and stable, as the signs, values and statistical significance of coefficient estimates are not sensitive to the model specifications across Models A to F. The empirical results from Models A and B (Table 2.3), which mainly attempt to provide insights on the overall competitive condition during 1991–2005, suggest that the market can be characterized as monopolistic competition during the period 1991–2005.13 The estimated H statistics are around 0.64 in the two models, broadly in line with results obtained in other studies.14 Both the hypothesis of H = 0 and H = 1 are rejected statistically at the 1 per cent level, indicating that the market can neither be classified as perfect competition nor monopoly. Nevertheless, while the market structure cannot be described as perfect competition, the degree of competition was fairly high. The estimation results in Models C and D (Table 2.3), which facilitate the study of evolution of the degree of competition during the sample period, show that the H statistic for the period 1991 Q1–2001 Q215 is slightly higher than the H statistic for the period 2001 Q3–2005 Q416 . To evaluate the statistical significance of the change in H statistic over the two periods, the hypothesis of H1 = H2 is tested. The hypothesis is not rejected at the 10 per cent level in both Models C and D. This suggests that the competitive condition was not statistically different between the two periods. Time series of rolling estimates of the H statistic from

25 Table 2.3 Empirical results of the Panzar–Rosse model for the Hong Kong banking sector Independent variables

Regression results Sample period: 1991 Q1 to 2005 Q4 Models A

B

C

D

Dependent variables

Constant Unit price of labour Unit price of fund Unit price of capital Unit price of labour*DUM Unit price of fund*DUM Unit price of capital*DUM CAR DM

Total revenue/ total assets

Total revenue

Total revenue/ total assets

Total revenue

−0.007*** (0.001) 0.156*** (0.008) 0.462*** (0.008) 0.022*** (0.004)

−0.008*** (0.001) 0.157*** (0.009) 0.464*** (0.008) 0.020*** (0.004)

−0.031*** (0.007) 0.238*** (0.027)

−0.026*** (0.007) 0.267*** (0.027) 1.051*** (0.011) 0.002* (0.001) 0.010*** (0.003) 0.641

−0.009*** (0.001) 0.186*** (0.011) 0.490*** (0.014) 0.007* (0.004) −0.043* (0.016) −0.051*** (0.017) 0.070*** (0.010) −0.025*** (0.006) 0.215*** (0.026)

−0.010*** (0.001) 0.185*** (0.011) 0.497*** (0.014) 0.007* (0.004) −0.046* (0.016) −0.054*** (0.017) 0.067*** (0.010) −0.021*** (0.006) 0.237*** (0.027) 1.049*** (0.011) 0.002*** (0.001) 0.011*** (0.002)

TA Growth Inflation H statistic (1991 Q1 to 2005 Q4) H statistic (1991 Q1 to 2001 Q2) (H1 ) H statistic (2001 Q3 to 2005 Q4) (H2 ) Number of banks F -statistic Adjusted R-squared DW statistics Number of observations

0.002* (0.001) 0.012*** (0.003) 0.640

30 205.437 0.617 1.972 1,394

30 417.879 0.782 1.967 1,394

0.002*** (0.001) 0.014*** (0.002)

0.683

0.690

0.659

0.656

30 169.722 0.629 1.978 1,394

30 353.726 0.792 1.974 1,394

Notes: 1. The regressions are estimated by the FGLS method with cross-section seemingly unrelated regression weights. Except for the variables Growth and Inflation, all variables used in the estimation are expressed in first difference form of the natural logarithm of the series. The residuals are specified as an AR(4) process. 2. Numbers in brackets are standard errors unless specified. 3. *, ** and *** denote statistical significance at the 10%, 5% and 1% levels respectively. Source: HKMA.

26 The Banking Sector in Hong Kong Table 2.4 Empirical results of the Panzar–Rosse model for the Hong Kong banking sector (analysis of bank size) Independent variables

Regression results Sample period: 1991 Q1 to 2005 Q4 Models E

F

Dependent variables

Constant Unit price of labour Unit price of fund Unit price of capital Unit price of labour*Size Unit price of fund*Size Unit price of capital*Size CAR DM TA Growth Inflation H statistic (large banks) (HL ) H statistic (non-large banks) (HNL ) Number of banks F-statistic Adjusted R-squared DW statistics Number of observations

Total revenue/ total assets

Total revenue

−0.032*** (0.008) 0.163*** (0.009) 0.467*** (0.008) 0.019*** (0.004) −0.015*** (0.005) 0.026*** (0.008) 0.014*** (0.004) −0.026*** (0.007) 0.223*** (0.026)

−0.032*** (0.008) 0.165*** (0.009) 0.468*** (0.008) 0.018*** (0.004) −0.017*** (0.005) 0.027*** (0.008) 0.015*** (0.004) −0.021*** (0.007) 0.256*** (0.026) 1.058*** (0.011) 0.002** (0.001) 0.010*** (0.003) 0.675 0.651

0.002*** (0.001) 0.013*** (0.002) 0.673 0.648 30 158.915 0.613 1.969 1,394

30 328.815 0.779 1.964 1,394

Notes: 1. The regressions are estimated by the FGLS method with cross-section seemingly unrelated regression weights. Except for the variables Growth and Inflation, all variables used in the estimation are expressed in first difference form of the natural logarithm of the series. The residuals are specified as an AR(4) process. 2. Numbers in brackets are standard errors unless specified. 3. *, ** and *** denote statistical significance at the 10%, 5% and 1% levels respectively. Source: HKMA.

1999 to 2005, which are generated by a series of rolling regressions of Models A and B, show similar results – as shown in Figures 2.2 and 2.3, the H statistic estimates move around 0.6 to 0.8 between 2001 and 2005 and do not have a persistent upward or downward trend. The results of Models C and D suggest that despite significant changes in the operating environment of the banking sector in recent years, competitive pressures have been maintained.

Wong, Wong, Fong and Choi 27 Perfect competition

Monopolistic competition

Monopoly Figure 2.2

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1999

2000

2001

2002

2003

2004

2005

2003

2004

2005

Rolling estimates of H statistic of Model A

Source: HKMA.

Perfect competition

Monopolistic competition

Monopoly Figure 2.3

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1999

2000

2001

2002

Rolling estimates of H statistic of Model B

Source: HKMA.

As for the relationship between competitive conditions and bank size, estimation results of Models E and F show that the H statistic among larger banks17 has a slightly higher value than that of smaller banks18 .19 Interestingly, the hypothesis that the H statistic among larger banks (HL ) equals to the H statistic of smaller banks (HNL ) is rejected at the 1 per cent level in both Models E and F, suggesting that competitive pressures among larger banks are higher than that among smaller banks. The result is consistent with other studies. For example, Bikker and Haaf (2002), based on a panel dataset of 23 industrialized countries, concluded that competitive pressures were statistically higher among larger banks and lower among smaller banks. A plausible explanation is that while

28 The Banking Sector in Hong Kong

larger banks compete keenly with smaller banks in local retail markets such as mortgages and credit cards, they compete even more fiercely with other competitors at regional or international levels in the corporate banking market, wealth management or other off-balance sheet activities where larger banks usually are relatively more heavily involved than smaller banks. This may lead to higher competitive pressures observed among larger banks.

2.6 Conclusion With both the effects of major market liberalization and consolidation now being more fully realized,20 this chapter re-visits the issue of competitive conditions of the banking industry in Hong Kong, which were first examined in Jiang et al. (2004), to see how the extent of competition has changed in the years subsequent to the last study. Facilitated by a panel dataset of banks and with longer time series of data up to the end of 2005, the chapter also aims to provide a more accurate assessment. The empirical analysis based on the Panzar–Rosse approach reconfirms the previous findings that the degree of competition was fairly high during the period 1992–2002, and suggests that competitive pressures have been maintained in the subsequent years, notwithstanding significant changes in the operating environment. The estimation results also find that competitive pressures were higher among larger banks and lower among smaller banks. This may suggest that while larger banks compete with smaller banks keenly in local retail markets on products such as mortgages and credit cards, they may be subject to even stronger pressures from other competitors at regional or international levels in the corporate banking market, wealth management and other off-balance sheet activities, where they are more heavily involved. While relaxation of regulations and advances in technology tend to enhance competition in the banking system, the effect of consolidation may depend on the prevailing market settings. To the extent that bank consolidation in recent years may have hampered competition, regulatory liberalization and technological progress appear to have largely offset the adverse effect. The emergence of a number of larger banks through mergers and acquisitions, which should have become more capable of competing with existing large banks, may have also contributed to the maintenance of competitive pressures in the sector. Nonetheless, with bank consolidation expected to continue, how market

Wong, Wong, Fong and Choi 29

concentration may impact on competition in the years to come needs to be closely monitored.

Notes 1. Following the banking sector consultancy study in 1998, the Hong Kong Monetary Authority (HKMA) has gradually removed several barriers to competition, including regulated interest rates, branching restrictions for foreign banks, limited access of restricted licence banks (RLBs) to the Real Time Gross Settlement (RTGS) system, and certain market entry criteria to the banking sector. Technological advancement also enhanced competition by eliminating geographical barriers and facilitating product innovations. Meanwhile, bank consolidation has resulted in increased market concentration. The effects of the Asian financial crisis, an ongoing process of consolidation of international banks and weak credit demand have created ongoing pressures for mergers and acquisitions in the Hong Kong banking sector. 2. The paper was published as a HKMA Research Memorandum, RM 04/2004. 3. See Panzar and Rosse (1987). 4. Panel data, by combining inter-individual differences with intra-individual dynamics, offer many advantages over cross-sectional or time series data. Panel data enlarge the number of observations for estimation, increasing the degree of freedom and reducing the collinearity among explanatory variables, hence improving the efficiency of estimates. A more detailed discussion on the advantages of panel data estimation can be found in Hsiao (1986). 5. The assumptions include (1) banks are profit maximizing, single product firms facing normally distributed revenue and cost functions; (2) banks produce revenue using labour, capital and intermediated funds (mainly deposits) as inputs; (3) higher input prices are not associated with higher quality services that generate higher revenue; and (4) banks are in long run equilibrium. The single product firm assumption is consistent with the ‘intermediation’ approach, where banks are viewed mainly as financial intermediaries, transforming inputs of labour, capital and deposits into outputs including loans and investments (De Bandt and Davis 2000). Nonetheless, product differentiation is allowed in the monopolistic competition model (Gelos and Roldos 2002). 6. Total revenue includes gross interest revenue and non-interest revenue. 7. This follows Bikker and Groeneveld (1998) and Gelos and Roldos (2002). Note that other measures of unit price of labour as the ratio of staff expense to the number of employees are also frequently used (see, for example, Molyneux et al. 1994 and Claessens and Laeven 2004). 8. The deregulation of interest rates in Hong Kong was undertaken in two phases. Phase 1 of the deregulation took place in July 2000 which removed the interest rate cap on time deposits with a maturity less than seven days and the prohibition on benefits for all deposits with the exception of Hong Kong dollar current and savings accounts. Phase 2 of the deregulation took place in July 2001 which removed all interest rate rules over current and savings accounts.

30 The Banking Sector in Hong Kong 9. A detailed summary of other regulatory liberalization measures can be found in Box 1 of Jiang et al. (2003). The forming of the Bank of China Group involved the consolidation of the ten member banks of the Bank of China Group into the Bank of China (Hong Kong); the forming of the DSB Bank (Hong Kong) involved the merger of DBS Kwong On Bank, Dao Heng Bank and Overseas Trust Bank. Details of the consolidations can be found at Table 1 of Jiang et al. (2004). 10. The HHI is the sum of the squared market shares of assets of all retail banks, ranging from zero to one. A large number of banks, each with a small share, produce an HHI close to zero. A monopolist bank with a 100 per cent share produces an HHI of one. 11. With a panel dataset, the number of observations is sufficiently large, and FGLS is considered more appropriate. Note that OLS may be more efficient than FGLS with a small sample, if the departure from classical assumptions is not too severe. 12. Alternatively, we have also made use of the fixed effect model by adding individual effects into the differenced equation, which requires us to follow the least-squares dummy variable (LSDV) estimation. Estimates obtained from our FGLS procedure and the fixed effect model suggest the same competitive structure of the banking industry. The random effect model is not attempted because the residuals are expected to follow an autoregressive process. 13. For the H statistic to be valid and interpretable, the market under study needs to be in long-run equilibrium for the sample period (Panzar and Rosse 1987). In long-run equilibrium, the rate of returns should not be correlated with input prices (De Bandt and Davis 2000). To conduct the equilibrium test, equation (2.1) is estimated by replacing the endogenous variable with the rate of return and the hypothesis of H = 0 is tested. The results found that H = 0 cannot be rejected at the 10 per cent level, indicating that the rate of return is not correlated with input-price variables, satisfying the long-run equilibrium condition. 14. The H statistics obtained by Claessens and Laeven (2004) for the different banking sectors of 50 economies range from 0.41 (USA) to 0.92 (Costa Rica). The paper estimated the H statistic for Hong Kong to be 0.7, which was quite similar to our estimate of 0.64. The study also showed that a number of other developed countries have similar H statistics as Hong Kong, such as Austria (0.66), Belgium (0.73), Canada (0.67), Denmark (0.50), France (0.69), Germany (0.58), Italy (0.60), Luxembourg (0.82), Norway (0.57), Spain (0.53), Switzerland (0.67), and UK (0.74). The H statistic for Japan was estimated at 0.47. 15. H1 = 0.683 and 0.690 in Models C and D respectively. 16. H2 = 0.659 and 0.656 in Models C and D respectively. 17. HL = 0.673 and 0.675 in Models E and F respectively. 18. HNL = 0.648 and 0.651 in Models E and F respectively. 19. The estimation results are robust to moderate changes on the assumed thresholds for classifying the large banks. 20. The interest rate deregulation was fully completed in July 2001 and a number of other significant liberalization moves and substantial bank consolidation took place around 2002.

Wong, Wong, Fong and Choi 31

References J. A. Bikker and J. M. Groenevald, ‘Competition and Concentration in the EU Banking Industry’, Kredit und Kapital, 33(1) (2000) 62–98. J. A. Bikker and K. Haaf, ‘Competition, Concentration and Their Relationship: An Empirical Analysis of the Banking Industry’, Journal of Banking and Finance, 26 (2002) 2191–214. S. Claessens and L. Laeven, ‘What Drives Bank Competition? Some International Evidence’, Journal of Money, Credit and Banking, 36 (2004) 564–83. O. De Bandt and E. P. Davis, ‘Competition, Contestability and Market Structure in European Banking Sectors on the Eve of EMU’, Journal of Banking and Finance, 24 (2000) 1045–66. R. G. Gelos and J. Roldos, ‘Consolidation and Market Structure in Emerging Market Banking Systems’, IMF Working Paper, no. 186 (Washington DC: IMF , 2002). H. Hempell, ‘Testing for Competition Among German Banks’, Discussion Paper, Economic Research Centre, Deutsche Bundesbank, (2002). C. Hsiao, Analysis of Panel Data (New York: Cambridge University Press, 1986). G. Jiang, N. Tang, E. Law and A. Sze, ‘Determinants of Bank Profitability in Hong Kong’, HKMA Research Memorandums, 14/2003. G. Jiang, J. Wong, N. Tang and A. Sze, ‘Banking Sector Competition in Hong Kong – Measurement and Evolution over Time’, HKMA Research Memorandums, 04/2004. P. Molyneux, D. M. Lloyd-Williams and J. Thornton, ‘Competitive Conditions in European Banking’, Journal of Banking and Finance, 18 (1994) 445–59. A. Nathan and E. Neave, ‘Competition and Contestability in Canada’s Financial System: Empirical Results’, Canadian Journal of Economics, 22 (1989) 576–94. J. C. Panzar and J. N. Rosse, ‘Testing for “Monopoly” Equilibrium’, Journal of Industrial Economics, 35 (1987) 443–56. S. Shaffer, ‘A Non-structural Test for Competition in Financial Market’, proceedings of a conference on Bank Structure and Competition, Federal Reserve Bank of Chicago (1982) 225–43.

3 Testing for Collusion in the Hong Kong Banking Sector Jim Wong, Eric Tak-Chuen Wong, Tom Pak-Wing Fong and Ka-Fai Choi1

3.1 Introduction The banking industry in Hong Kong is characterized by the existence of a few major banking groups and a relatively high degree of market concentration. Reflecting this, the Herfindahl–Hirschman index (HHI)2 of the banking sector in Hong Kong is around 0.14 in 2005, which is higher than some other developed banking centres, such as the US (0.02), the UK (0.06) and Japan (0.06).3 The three-bank concentration ratio4 of Hong Kong is also high at around 0.56 in 2005, compared with 0.15 in the US, 0.34 in the UK, and 0.39 in Japan.5 Such a structure could be conducive to the forming of oligopolistic coordination, as large banks may gain strong market power and could exercise leadership in pricing. Indeed, the existence of the interest rate rules (IRRs) prior to 2001 had long been a competition concern. When the IRRs were in place, deposit rates offered by banks under an administered rate structure were to an extent dictated by the large banks. At the same time, the best lending rate (BLR), the reference rate for most bank loans, was set by the large banks, which was followed by other banks. There also appeared to be similar feesetting trends among banks.6 Even after the full deregulation of the IRRs, for a considerable period of time banks still adopted the same BLR set by the large banks, although the effective interest rates could be different due to different mark-ups. It was not until April 2005 that smaller banks began to adjust their BLRs differently from large banks.7 However, the gap between different BLRs has so far never exceeded 25 basis points. Our previous tests for market structure using a Panzar–Rosse approach in Wong et al. (2006) have shown that the banking sector in Hong Kong was highly competitive during the period 1992–2005. Nevertheless, evidence of the co-movement of BLRs and fee setting among banks, 32

Wong, Wong, Fong and Choi 33

even after the removal of the IRRs, has caused some concerns about the existence of oligopolistic coordination among banks. Whether such a phenomenon reflects oligopolistic coordination or is simply the result of price competition thus needs to be examined. This is particularly important in view of recent market consolidations that have resulted in fewer banks and an even more concentrated market. Oligopolistic coordination may lead to higher profit for the colluding banks at the expense of customers and other competitors, and would adversely affect economic efficiency. The issue is therefore of interest to policy makers. This chapter, based on the conjectural variation approach derived from the oligopoly theory, focuses on evaluating the degree of oligopolistic coordination of the banking industry in Hong Kong. It forms part of our series of projects examining the market structure and competitive environment of the banking sector. The rest of the chapter is organized as follows. The conjectural variation approach will be discussed in the next section. Sections 3.3 and 3.4 describe the empirical specifications, and data and estimation methods respectively. Section 3.5 presents the estimation results. Finally, section 3.6 concludes.

3.2 The conjectural variation approach The conjectural variation approach involves identification8 and estimation of a conjectural variation parameter of the market being examined. In our context, the parameter is defined as the bank’s belief about its rivals’ pricing responses to changes in its own interest rates charged on loans (hereafter referred to as λ).9 The theoretical model employed in this study to estimate λ is based on Coccorese (2002, 2005)10 which specifies a price-setting game in a duopolistic market with heterogeneous products, where each bank faces a demand function for its loans, qi = q(pi , p−i , Zi ),

i = 1, . . . , N

(3.1)

where N is the number of banks in the market, qi is the quantity demanded. pi and p−i are the interest rates charged (that is prices) on loans by bank i and by all other competitors respectively. Zi is a vector of exogenous factors affecting demand. This demand function assumes that each bank faces a single competitor which is formed by all other banks, and hence the demand for loans for each bank depends on the

34 The Banking Sector in Hong Kong

interest rate charged by itself as well as the average interest rate charged by all other banks. The cost function of banks in the model is specified by Ci = C(qi , wi , Yi ),

i = 1, . . . , N

(3.2)

where costs depend on quantity and a vector of k factor prices, wi = (w1 , w2 , . . . , wk ), as well as a vector of exogenous cost factors affecting bank costs, Yi . Based on equations (3.1) and (3.2), the profit function of banks can be written as πi = q(pi , p−i , Zi )pi − C(qi , wi , Yi ),

i = 1, . . . , N

(3.3)

where πi is the profit earned by bank i. To maximize profit subject to the exogenous factors, p−i , Zi , wi and Yi , banks must satisfy the following condition:11 1 pi = MCi − ηi (3.4) η−i , i = 1, . . . , N +λ pi p−i i where MCi = ∂C is the marginal cost, ηi = ∂qi

∂ ln qi ∂ ln pi

=

∂qi pi ∂pi qi

< 0 is the own-price

= > 0 is the cross-price elasticity, and λ = ∂p∂p−ii elasticity, η−i = is the conjectural variation parameter of bank i. The derivative λ = ∂p∂p−ii , if identified, can be interpreted as the degree of oligopolistic coordination between banks on pricing loans. By estimating λ, the existence of collusive behaviour on loan pricing can be detected. Specifically, a positive λ implies that collusive pricing behaviour exists in the loan market (see Figure 3.1). Such a pricing behaviour can be revealed by changes in the market equilibrium price and quantity as a consequence of an initial increase in price by one of the banks. For illustration, suppose a bank raises its loan price and thereby reduces its loans made. If its rivals are expected to increase their prices (λ > 0) too, then their output levels are expected to move in the same direction as that of the bank which initiates the price increase. On the whole, the equilibrium quantity is reduced, the equilibrium price is raised and the joint profit of banks is increased. In other words, such evidence suggests that the bank expects its rivals to match its prices, and to co-operate with each other in order to hold revenues at a profitable level. In the limit, the joint profit of the banks is maximized by perfect coordination in prices where the bank expects its changes in price to be followed exactly by all other banks (that is λ = 1). ∂ ln qi ∂ ln p−i

∂qi p−i ∂p−i qi

Wong, Wong, Fong and Choi 35 Perfect collusion

1.0 0.8

Oligopolistic collusion exists

0.6 0.4 0.2

λpre

λpost

0.0 0.2 Oligopolistic collusion does not exist

0.4 0.6 0.8 1.0

Perfect competition Figure 3.1 changes

∞ Degree of oligopolistic coordination before and after structural

Notes: λpre = The estimated value of the conjectural variation parameter for the period 1991 Q1–2001 Q2. λpost = The estimated value of the conjectural variation parameter for the period 2001 Q3– 2005 Q4. Source: HKMA.

In contrast, non-positive values of λ imply that banks react in a competitive fashion to any increase in price by their counterparts. A zero value for the conjectural variation parameter (that is, λ = 0) indicates that each bank does not (or fails to) consider rivals’ choices when setting prices. In other words, banks are expected to keep their prices fixed despite an increase in prices of their counterparts. For the banks to maintain their prices unchanged, they must increase their loans to fill the loan supply gap arising from the upward price adjustments by the bank which initiates the price change. On balance, the total amount of loans made by the banking sector as well as prices should be little affected or even unchanged. A negative conjectural derivative indicates that a bank raising its prices expects its rivals to react in a competitive fashion by reducing their prices. In the extreme, λ = −∞ implying perfect competition. While the formulation of the theoretical model varies somewhat in the literature, the conjectural variation approach has been widely applied to assess the degree of oligopolistic coordination between banks in the banking systems of the US (Shaffer 1989) and Canada (Shaffer 1993) since

36 The Banking Sector in Hong Kong

the 1980s, with later work focusing on European countries (Berg and Kim 1998; Angelini and Cetorelli 2003; Coccorese 2002 and 2005). Most of these studies found no evidence of significant oligopolistic coordination in the banking systems.

3.3 The empirical specifications 3.3.1 The system of equations In our application of the conjectural variation approach, a system formed by equations (3.1), (3.2) and (3.4) is estimated simultaneously to infer the λ statistic from a panel dataset of banks in Hong Kong. The demand function corresponding to equation (3.1) is specified by the following log-linear equation: ln qi = φ0,i + φ1 ln pi + φ2 ln p−i + φ3 ln Y + φ4 ln Bi + εD ,

(3.5)

where the quantity demanded qi and the price pi are measured by total loans produced by individual banks (the sum of loans and advances to customers and amount due from banks) and the ratio of total gross interest incomes to total loans respectively. The competitor’s price p−i is calculated as the ratio of the sum of gross interest incomes to the sum of total loans of all other banks. The estimated coefficient of ln pi (that is, φ1 ) is interpreted as the own price elasticity and that of ln p−i (that is, φ2 ) is interpreted as the cross-price elasticity, and they are expected to be negative and positive respectively. The demand for loans is assumed to be affected by two exogenous factors: Y and Bi , the quarterly real GDP growth rate in Hong Kong and the number of bank branches respectively. Generally, demand for loans should be higher under good economic conditions and for banks with a large branch network. Therefore, the estimated coefficients of φ3 and φ4 are expected to be positive. With respect to cost equation (3.4), a multi-product translog cost function, which is adopted by many related banking studies,12 is specified. Two regularity conditions are imposed on the cost equation to ensure that the estimated cost function is well behaved.13 The cost equation can be written as ln Ci = α0,i + α1 ln qi + α2 ln oqi + β1 ln w1,i + β2 ln w2,i + (1 − β1 − β2 ) ln w3,i + 0.5σ11 ln qi ln qi

Wong, Wong, Fong and Choi 37

+ 0.5σ22 ln oqi ln oqi + σ12 ln qi ln oqi − 0.5(γ12 + γ13 ) ln w1,i ln w1,i − 0.5(γ12 + γ23 ) ln w2,i ln w2,i − 0.5(γ13 + γ23 ) ln w3,i ln w3,i + γ12 ln w1,i ln w2,i

(3.6)

+ γ13 ln w1,i ln w3,i + γ23 ln w2,i ln w3,i − (δ12 + δ13 ) ln qi ln w1,i + δ12 ln qi ln w2,i + δ13 ln qi ln w3,i − (δ22 + δ23 ) ln oqi ln w1,i + δ22 ln oqi ln w2,i + δ23 ln oqi ln w3,i + εC where Ci is total costs of bank i. While this study mainly assesses the existence of collusive behaviour in the loan market, off-balance sheet (OBS) outputs generated by banks, oqi , are incorporated into the cost function estimation to serve as a control variable to avoid understating bank outputs.14 In this study, banks are considered as employing three factor inputs: funds, labour and capital. The unit price of funds, w1,i , is proxied by the ratio of interest expense to total funding (the sum of deposits from customers, due to banks, amount payable under repos and negotiable debt instruments issued and outstanding). The unit price of labour, w2,i , is computed as the ratio of staff expense to total assets.15 Finally, the unit price of capital, w3,i , is derived as the ratio of expense other than staff and interest expenses to total assets. Based on the specification of equation (3.6), the marginal cost function of bank i for producing qi can be derived as MCi =

∂Ci ∂qi

=

Ci ∂ ln Ci qi ∂ ln qi

=

Ci [α1 + σ11 ln qi + σ12 ln oqi qi

(3.7)

− (δ12 + δ13 ) ln w1,i + δ12 ln w2,i + δ13 ln w3,i ]. With the specification of equations (3.5) and (3.7), equation (3.4) can be specified as pi =

Ci [α1 + σ11 ln qi + σ12 ln oqi qi

38 The Banking Sector in Hong Kong

− (δ12 + δ13 ) ln w1,i + δ12 ln w2,i + δ13 ln w3,i ] −

(3.8)

1 + εp φ2 φ1 +λ pi p−i

The conjectural variation parameter λ can be inferred by estimating the system of equations formed by equations (3.5), (3.6) and (3.8).

3.3.2 The models A total of three models are specified for estimation: 1. To provide insights on the overall degree of oligopolistic coordination between banks during 1991–2005, Model A is specified to estimate a constant λ statistic for the entire sample period based on equations (3.5), (3.6) and (3.8). 2. To study how the degree of oligopolistic coordination in the banking sector has evolved over time, Model B, a modification of Model A, will be estimated. By including the interaction between λ and two dummy variables which separate the whole sample period into two sub-periods – one from 1991 Q1 to 2001 Q2 and the other from after 2001 Q2 to 2005 – Model B attempts to examine the effect of the structural changes on the degree of oligopolistic coordination in the banking sector. The time point 2001 Q2 is so chosen to distinguish the two periods as structural changes including major bank consolidations and bank deregulations either completed or took place around the time.16,17 Theoretically, while bank consolidations, which lead to a more concentrated market, may favour the development of collusion,18,19 bank deregulations can constrain market power of individual banks, and hence lower the likelihood of establishing and maintaining collusive behaviour among banks.20 The results of Model B would shed light on the net impact of these structural changes on the industry conduct. 3. To study how the degree of oligopolistic coordination varies in different bank markets, such as the local retail market versus the corporate loan market, Model C is estimated with the interaction between λ and bank-scale dummies, Size, included. As large banks in general are more active in the corporate loan market than smaller banks, the difference in the degree of pricing coordination between the group of larger banks and the group of smaller banks can facilitate our analysis of price co-ordination in different markets. In the model, a bank is

Wong, Wong, Fong and Choi 39

considered as large if its asset size is one of the seven largest at the specific point of time.21

3.4 Data and estimation methods The dataset used in the estimation is a panel dataset of all retail banks in Hong Kong covering the period from 1991 Q1 to 2005 Q4. Retail banks are the locally incorporated banks plus a number of larger foreign banks whose operations are similar to those of the locally incorporated banks in that they operate a branch network and are active in retail banking. The banking data are obtained from the regulatory returns that Authorized Institutions in Hong Kong must file with the Hong Kong Monetary Authority (HKMA). Since our purpose is to examine the degree of oligopolistic coordination among banks in Hong Kong, the sample is restricted to incorporate only data of their Hong Kong offices.22 All nominal values of the variables are deflated by the composite consumer price index. The three models, Models A to C, are estimated with equations (3.5) and (3.6) specified in the first difference form. This is for several reasons. First, differencing the equations removes the individual effects (which are time invariant and cross-section specific), reducing the number of parameters to be estimated. Secondly, removing the individual effects also avoids complications arising from the possibility that they may be correlated with the explanatory variables. Third, differencing the equation avoids the omitted-variable bias stemming from the cross-sectional unobserved heterogeneities that are constant over time. In estimating the system of equations (3.5), (3.6) and (3.8), we follow a non-linear three-stage least squares method instead of applying the single-equation method such as ordinary least squares, limited information maximum likelihood or two-stage least squares because estimators from the former are statistically consistent and asymptotically more efficient than the other estimators.23

3.5 Estimation results Empirical results of the three models are presented in Table 3.1. The adjusted R-squared statistics of the three models, which measure the goodness of fit, are all over 0.9, indicating that the specification of equations is appropriate. The estimated own-price elasticity (φ1 ) and cross-price elasticity (φ2 ) are negative and positive respectively, with a statistical significance at the 1 per cent level. The former implies a

40 Table 3.1 Empirical results of the conjectural variation parameter for the Hong Kong banking sector Independent variables

Regression results Sample period: 1991 Q1 to 2005 Q4 Models A

B

C

Dependent variables Equation (3.5): demand equation φ1 φ2 φ3 φ4 R-squared Equation (3.6): cost equation α1 α2 β1 β2 σ11 σ22 σ12 γ12 γ13 γ23 δ12 δ13

ln qi −1.0350*** (0.0064) 0.5430*** (0.0488) 0.8294* (0.4373) 2.4701*** (0.0786)

−1.0344*** (0.0063) 0.5422*** (0.0489) 0.8448* (0.4379) 2.4668*** (0.0787)

−1.0476*** (0.0070) 0.5508*** (0.0488) 0.8202* (0.4367) 2.4858*** (0.0786)

0.9837

0.9837

0.9834

−0.0130 (0.0414) −0.1671** (0.0792) 0.0001 (0.0004) 0.4232*** (0.0766) 0.0159*** (0.0055) 0.0379*** (0.0081) −0.0122** (0.0053) −0.1027*** (0.0013) −0.1040*** (0.0012) −0.0361*** (0.0010) −0.0092* (0.0047) −0.0116** (0.0047)

−0.0803* (0.0459) −0.1297* (0.0751) 0.0002 (0.0004) 0.5129*** (0.0770) 0.0207*** (0.0057) 0.0279*** (0.0081) −0.0081 (0.0057) −0.1026*** (0.0013) −0.1044*** (0.0012) −0.0362*** (0.0010) −0.0145*** (0.0047) −0.0058 (0.0047)

ln Ci −0.0096 (0.0420) −0.1546** (0.0786) 0.0002 (0.0004) 0.4716*** (0.0765) 0.0148*** (0.0056) 0.0339*** (0.0080) −0.0104* (0.0053) −0.1027*** (0.0013) −0.1043*** (0.0012) −0.0361*** (0.0010) −0.0120** (0.0047) −0.0084* (0.0046)

(Continued)

Wong, Wong, Fong and Choi 41 Table 3.1 (Continued) Independent variables

Regression results Sample period: 1991 Q1 to 2005 Q4 Models A

B

C

Dependent variables δ22 δ23

0.0032*** (0.0008) −0.0041*** (0.0011)

0.0031*** (0.0008) −0.0035*** (0.0011)

0.0033*** (0.0008) −0.0043*** (0.0011)

0.9958 1,887

0.9958 1,887

0.9964 1,887

R-squared Number of observations Equation (3.8): first-order condition λ

Pi −0.0023 (0.0067) −0.0048 (0.0066) 0.0054 (0.0068)

λpre λpost

−0.0156* (0.0082) 0.0003 (0.0070)

λL λNL R-squared Number of observations

0.9998 1,887

0.9999 1,887

0.9996 1,887

Notes: 1. Numbers in brackets are standard errors unless specified. 2. *, ** and *** denote statistical significance at the 10%, 5% and 1% levels respectively. Source: HKMA.

downward sloping demand curve for loans for individual banks and the latter implies that loans offered by a bank are substitutes of loans offered by other banks; both results are in line with standard economic theories. The estimated own-price elasticity in absolute value is larger than the cross-price elasticity, suggesting that the demand for loans of customers are more sensitive to the variation of prices offered by the bank which they currently bank with than to price changes of other banks. The estimated coefficients of the income variable (φ3 ) have the expected positive sign, and are statistically significant at the 10 per cent level.24 The number of bank branches is also estimated to be positively related

42 The Banking Sector in Hong Kong

to the demand for loans (that is φ4 > 0 and statistically significant at the 1 per cent level). As for the estimation result of the cost function, since the specification involves cross-product terms and quadratic terms, it is difficult to visualize the reasonableness of the estimated coefficients based on themselves alone. Nevertheless, a check on the marginal cost values for all observations, derived based on equation (3.6) with the estimated coefficients, found that they are all positive as expected. Overall, the estimation results appear robust and stable, as the signs, values and statistical significance of the estimated coefficients do not vary significantly with different specifications across Models A to C. The empirical result from Model A, which attempts to provide insights on the overall degree of oligopolistic coordination between banks during 1991–2005, suggests no evidence of oligopolistic coordination between banks during the period. The estimated conjectural variation λ is −0.0023 and is not significantly different from zero at the 10 per cent level, indicating that banks react in a competitive fashion in response to any increase in price by their counterparts in the market. As the estimated value of λ is far smaller than the perfect collusive value of one and is significantly larger than the perfect competition value of negative infinity, the market can neither be classified as a monopoly (formed by all of the banks) nor be considered as perfect competition. These findings are in line with Wong et al. (2006), which concludes that the degree of competition in Hong Kong’s banking industry was fairly high, although the market structure cannot be described as perfect competition. The estimation result in Model B, which studies the evolution of the degree of oligopolistic coordination during the sample period, shows that the estimated values of the conjectural variation parameter for the period 1991 Q1–2001 Q225 is slightly lower than that for the period 2001 Q3–2005 Q426 . However, they are both statistically indistinguishable from zero at the 10 per cent significance level. The result suggests that despite major mergers and acquisitions of banks taking place around 2001, which have resulted in higher market concentration in recent years, no significant evidence is found of collusive behaviour of banks in either the period before or after the bank consolidations. As for the analysis of oligopolistic coordination by different markets, the empirical results of Model C show that the estimated conjectural variation parameter among larger banks has a negative value27 while that of smaller banks has a positive value28 , although both values are close to zero. The null hypothesis of a zero value conjectural variation of large banks can be rejected at the 5 per cent significant level.29 On the

Wong, Wong, Fong and Choi 43

other hand, the null hypothesis of zero value conjectural variation of smaller banks cannot be rejected at the 10 per cent significant level.30 As large banks are more heavily involved in corporate banking than smaller banks, these findings suggest that while banks in general do not have sufficient market power to exercise any collusive pricing in the markets, it is relatively less likely to have oligopolistic collusion in the corporate loan market than in the retail market. This is in line with findings in the literature on collusion that it appears in general more feasible to develop and maintain effective oligopolistic collusions among firms in markets with more standardized products, less asymmetry on sellers, particularly on their cost structures, and more small buyers.31,32 To the extent that these characteristics play an important role in developing collusive pricing behaviour, the corporate loan market, especially for large and multinational corporations, in which regional and international banks also actively participate, is less prone to developing and maintaining oligopolistic coordination than the local retail market.

3.6 Conclusion The empirical analysis, based on the conjectural variation approach and a panel dataset which covers all retail banks in Hong Kong for the period from 1991 Q1 to 2005 Q4, suggests that banks in Hong Kong operated in a competitive fashion in the loan market without any significant sign of collusion on pricing during the period 1991–2002, and market conduct was largely maintained in the subsequent years, notwithstanding significant changes in the operating conditions. While major bank consolidations taking place in 2001–02 have resulted in fewer banks, and thus a market more conducive to developing and maintaining collusions, interest rate deregulations implemented around the same time have promoted a more competitive environment. Empirically, the evidence indicates that banks do not exercise any collusive pricing in either the retail market or the corporate loan market. The estimation results also suggest that oligopolistic collusions are less likely to develop in the corporate loan market than in the local retail market. This is probably due to the fact that in the corporate loan market, where the products are usually highly customized and wider product scopes exist, effective collusions are more difficult to be developed. Moreover, there are more participating banks in the corporate loan market, which is not limited to local larger banks, but also larger banks at the regional and international levels.

44 The Banking Sector in Hong Kong

Notes 1. The authors are grateful to Hans Genberg for his suggestions and comments. 2. The HHI is the sum of the squared market shares of assets of all retail banks, ranging from zero to one. A large number of banks, each with a small share, produce an HHI close to zero. A monopolist bank with a 100 per cent share produces an HHI of one. 3. Bikker and Haaf (2002) estimated the HHI for the banking industries of 20 countries. The HHI are found to range from 0.02 (US) to 0.26 (Switzerland). The average HHI for the 20 selected countries is found to be 0.11, which is lower than the HHI in Hong Kong in 2005 (that is 0.14). 4. The three-bank concentration ratio is defined as the ratio of the sum of assets of the first three largest banks to the sum of assets of all banks. 5. Besides the HHI, Bikker and Haaf (2002) also estimated the three-bank concentration ratio of the banking industries for 20 countries. The values range from 0.15 (US) to 0.78 (Netherlands), and the average value is 0.47, which is lower than that of Hong Kong in 2005 (0.56). 6. One of the notable examples was the service charge/maintenance fees imposed on small depositors, which were first introduced by one of the larger banks during 2001 amid the removal of the remaining interest rate rules. This was followed by most of the smaller banks later. 7. All banks have the same BLRs from July 2001 to March 2005. Since April 2005, they started to have different BLRs in response to the recent tightening of US interest rates. Concerns over the impact of fewer and larger banks in a market on competition resulting from bank consolidations stem from the structure–conduct–performance paradigm, which asserts that the degree of competition is positively related to the number of banks in the market. Fewer banks and a more concentrated market are said to be conducive to oligopolistic coordination, as it reduces the coordination problem among the incumbents, and favours the development or maintenance of collusion agreement among banks. 8. The conjectural variation parameter may be difficult to estimate econometrically due to the identification problem. For detailed discussions, see Bresnahan (1982), Lau (1982) and Nevo (1998). 9. The concept of conjectural variation was introduced and defined by Bowley (1924) and Frisch (1951) as the firm’s belief about the rivals’ response to changes of its decision variables. Regarding the decision variables, most past studies formulate the model with only one decision variable by assuming firms choosing either the output level (that is the Cournot model) or the price level (that is the Bertrand model). While the Cournot model is extensively applied on banking studies such as Spiller and Favaro (1984), Shaffer (1989, 1993), Berg and Kim (1998), Angelini and Cetorelli (2003) and Bikker (2003), the Bertrand model that assumes banks compete with their rivals by using prices is also very common. See Coccorese (2002, 2005) and Haan and Sterken (2006), for example. 10. For a more complete explanation of the model, see Roller and Sickles (1995) and Neven and Roller (1996) which develop the model originally to examine the market structure of European airline industry.

Wong, Wong, Fong and Choi 45 11. This is derived from the first-order condition of the bank profit maximization problem. Mathematically, the problem can be expressed as Max πi = q(pi , p−i , Zi )pi − C(qi , wi , Yi ). Pi

12. See Gilligan et al. (1984), Mester (1987) and Berger et al. (1987), for example. 13. Homogeneity of degree one in factor prices and symmetry are imposed. 14. Past studies on the cost structure of banking industry generally suggested that omitting OBS activities in the cost estimation could seriously understate actual bank outputs. For example, in cost-efficiency studies, Rogers (1998) and Clark and Siems (2002), by comparing the results which included proxies for the OBS outputs in the estimation, such as non-interest incomes, with those without incorporating OBS outputs in the estimation, showed that omitting OBS activities in the cost efficiency estimation could seriously understate actual bank outputs and efficiency levels. 15. This follows Bikker and Groeneveld (2000) and Gelos and Roldos (2002). Note that other measures of unit price of labour as the ratio of staff expense to the number of employees are also frequently used (see, for example, Molyneux et al. 1994 and Claessens and Laeven 2004). 16. (1) The interest rate deregulation was fully completed by July 2001, with interest rate restrictions on current and savings accounts also removed; (2) the restriction on the number of branches and offices for foreign banks was completely removed in 2001; (3) the market entry criteria have been relaxed since 2002, and (4) most major bank consolidations took place in 2001 and 2002, including the forming of the Bank of China Group and DBS Bank (Hong Kong) through mergers and acquisitions. 17. An alternative way to analyse the evolution of the degree of oligopolistic coordination is by including a time trend variable. However, such specification implicitly assumes that the evolution of the degree of oligopolistic coordination is either increasing or decreasing continuously and linearly over time, which is unlikely to be true in reality. Given that major bank consolidations and deregulations were concentrated around 2001–02, the evolution of the degree of oligopolistic coordination may be more appropriate to be specified by a structural break around the period. 18. This argument is based on the structure–conduct–performance paradigm (Bain 1951) which asserts that the degree of competition is positively related to the number of banks in the market and negatively related to the market concentration. Theoretically, joint profit of banks is maximized if all banks tacitly collude to behave as a single monopolist in the loan market. To form such a collusion or cartel, it would be more possible with fewer banks in the market. 19. Early studies based on the conjectural variation approach (Spiller and Favaro 1984; Shaffer 1993; Angelini and Cetorelli 2003; Toolsema 2002; Coccorese 2005; Uchida and Tsutsui 2005) generally suggested that the degree of strategic interactions across banks is lower after bank deregulations, while the impact of bank consolidations is inconclusive empirically. 20. This argument is based on the implication from the contestability theory which follows the lead of Baumol (1982) in stressing that potential competitors, like currently active competitors, can effectively constrain market

46 The Banking Sector in Hong Kong

21.

22.

23.

24. 25. 26. 27. 28. 29. 30. 31.

power of incumbents, so that in a market with only few competitors, sufficiently low barriers to entry which make potential competition highly possible can serve to discipline the established firms to act in a competitive fashion. Regarding the classification of large and small banks, another way of classification is based on the ranking of average asset size of banks in the whole sample period. Under such classification method, each bank will be classified into only one specific group for the whole sample period regardless of changes in the asset size of the bank during the period. This classification method should be appropriate in a case that only a few mergers and acquisitions happen in the sample period and the asset size of banks has not changed substantially over time. Since there were major bank consolidations taking place during 2000–01, which changed the asset size of some banks dramatically, we choose to adopt the classification of banks according to the asset size of each bank at each point of time. Regarding the data for estimation, another common source is from banks’ annual reports. Such data source is subject to various limitations. First, the relatively small number of observations constrains the construction and testing of more complicated models and the estimation results may be subject to large statistical variances, given the large number of parameters estimated under the conjectural variation approach. Second, most of the data disclosed in annual reports are on a consolidated basis that contain the operation of banks’ overseas branches and their subsidiaries, which may not be appropriate for analysing the local banking market structure. This is in particular the case for some large banks which have substantial operations overseas. Using such data to examine the banking market structure in Hong Kong may also generate results that are affected unduly by large banks’ data as their market shares and assets are exaggerated. The three-stage least squares estimator takes account of the fact that the system of equations be disturbance-related and makes use of the covariance matrix of disturbances among the equations within the framework of the seemingly unrelated regression method. So, the estimator is asymptotically more efficient than other single equation estimators. With a panel data, the number of observations is sufficiently large and the three-stage least squares method is considered more appropriate. Note that the singleequation estimator may be more appropriate if the number of observations is small. This is in line with Coccorese (2005) in which the income variable has a positive sign but is statistically significant in only some of the cases. λpre = −0.0048 λpost = 0.0054 λL = −0.0156 λNL = 0.0003 The null hypothesis is tested against the alternative hypothesis of a negative value conjectural variation of larger banks. The null hypothesis is tested against the alternative hypothesis of a positive value conjectural variation of smaller banks. See Stigler (1964), Eckbo (1976), Baker and Faulkner (1993), Symeonidis (2003), and Suslow (2005).

Wong, Wong, Fong and Choi 47 32. In essence, markets with such characteristics are more able to facilitate colluding firms to reach some mutually agreed prices in a single market and easier for colluding firms to monitor each other’s behaviour in order to deter or prevent cheating, which are fundamental for successful collusions. For instance, loan arrangements for large multinational corporations usually involve more customized terms to fit for the unique needs of individual corporations. These loans are also very common to tie-in with other related products provided by the bank or its affiliates such as legal and financial consultancy services, leading to the loan arrangements being more differentiated and involving wider product scopes. The complexity of such loans prevents banks from reaching a mutually agreed collusive price in this market. Moreover, potential colluding banks in this market could be banks operated in the domestic, regional, or international levels, leading to higher monitoring costs for detecting if each colluding bank follows the collusive agreement. These may contribute to the less likelihood of oligopolistic coordination observed among larger banks than among smaller banks.

References P. Angelini and N. Cetorelli, ‘The Effect of Regulatory Reform on Competition in the Banking Industry’, Journal of Money, Credit and Banking, 35(5) (2003) 663–84. J. Bain, ‘Relation of the Profit Rate to Industry Concentration: American Manufacturing, 1936–1940’, Quarterly Journal of Economics, 65 (1951) 293–324. W. E. Baker and R. R. Faulkner, ‘The Social Organisation of Conspiracy: Illegal Networks in the Heavy Electrical Equipment Industry’, American Sociological Review, 58(9) (1993) 837–60. W. Baumol, ‘Contestable Markets: An Uprising in the Theory of Industry Structure’, American Economic Review, 72 (1982) 1–15. S. A. Berg and M. Kim, ‘Banks as Multioutput Oligopolies: An Empirical Evaluation of the Retail and Corporate Banking Markets’, Journal of Money, Credit, and Banking, 30(2) (1998) 135–53. A. N. Berger, G. A. Hanweck and D. B. Humphrey, ‘Competitive Viability in Banking: Scale, Scope, and Product Mix Economies’, Journal of Monetary Economics, 20 (1987) 501–20. J. A. Bikker and K. Haaf, ‘Competition, Concentration and their Relationship: An Empirical Analysis of the Banking Industry’, Journal of Banking and Finance, 26 (11) (2002) 2191–214. J. A. Bikker and J. M. Groeneveld, ‘Competition and Concentration in the EU Banking Industry’, Kredit und Kapital, 33(1) (2000) 62–98. J. A. Bikker, ‘Testing for Imperfect Competition on EU Deposit and Loan Markets with Bresnahan’s Market Power Model’, Research Series Supervision, 52 (2003), Netherlands Central Bank. A. L. Bowley, The Mathematical Groundwork of Economics (Oxford: Clarendon Press, 1924). T. F. Bresnahan, ‘The Oligopoly Solution Concept is Identified’, Economic Letters, 10 (1982) 87–92.

48 The Banking Sector in Hong Kong J. A. Clark and T. F. Siems, ‘X-efficiency in Banking: Looking beyond the Balance Sheet’, Journal of Money, Credit and Banking, 34 (2002) 987–1013. S. Claessens and L. Laeven, ‘What Drives Bank Competition? Some International Evidence’, Journal of Money, Credit and Banking, 36 (2004) 564–83. P. Coccorese, ‘Competition Among Dominant Firms in Concentrated Markets: Evidence from the Italian Banking Industry’, Centre for Studies in Economic and Finance Working paper, 89 (2002), University of Salerno. P. Coccorese, ‘Competition in Markets with Dominant Firms: A Note on the Evidence from the Italian Banking Industry’, Journal of Banking and Finance, 29 (2005) 1083–93. P. L. Eckbo, The Future of World Oil (Cambridge: Ballinger, 1976). R. Frisch, ‘Monopoly–Polypoly: The Concept of Force in the Economy’, International Economic Paper, 1 (1951) 23–36. R. G. Gelos and J. Roldos, ‘Consolidation and Market Structure in Emerging Market Banking Systems’, IMF Working Paper, No. 186 (2002), Washington DC. T. Gilligan, M. Smirlock and W. Marshall, ‘Scale and Scope Economies in the Multiproduct Banking Firm’, Journal of Monetary Economics, 13 (1984) 393–405. L. D. Haan and E. Sterken, ‘Price Leadership in the Dutch Mortgage Market’, Working Paper, 102 (2006), Netherlands Central Bank. G. Jiang, N. Tang, E. Law and A. Sze, ‘Determinants of Bank Profitability in Hong Kong’, HKMA Research Memorandums, 14/2003. G. Jiang, J. Wong, N. Tang and A. Sze, ‘Banking Sector Competition in Hong Kong – Measurement and Evolution over Time’, HKMA Research Memorandums, 04/2004. M. Kim and S. A. Berg, ‘Banks as Multioutput Oligopolies: An Empirical Evaluation of the Retail and Corporate Banking Markets’, Journal of Money, Credit and Banking, 30(2) (1998) 135–53. L. J. Lau, ‘On Identifying the Degree of Competitiveness from Industry Price and Output Data’, Economic Letters, 10 (1982) 93–9. J. L. Mester, ‘A Multiproduct Cost Study of Savings and Loans’, Journal of Finance, 42(2) (1987) 423–45. P. Molyneux, D. M. Lloyd-Williams and J. Thornton, ‘Competitive Conditions in European Banking’, Journal of Banking and Finance, 18 (1994) 445–59. D. J. Neven and L. H. Roller, ‘Rent Sharing in the European Airline Industry’, European Economic Review, 40 (1996) 933–40. A. Nevo, ‘Identification of the Oligopoly Solution Concept in a Differentiatedproducts Industry’, Economic Letters, 59 (1998) 391–5. K. E. Rogers, ‘Nontraditional Activities and the Efficiency of US Commercial Banks’ Journal of Banking and Finance, 22 (1998) 467–82. L. H. Roller and R. C. Sickles, ‘Competition, Market Niches, and Efficiency: A Structural Model of the European Airline Industry’, CEPR working paper, (1995), London. S. Shaffer, ‘Competition in the U.S. Banking Industry’, Economic Letters, 29 (1989) 321–3. S. Shaffer, ‘A Test of Competition in Canadian Banking’, Journal of Money, Credit and Banking, 25(1) (1993) 49–61. P. T. Spiller and E. Favaro, ‘The Effects of Entry Regulation on Oligopolistic Interaction: The Uruguayan Banking Sector’, The RAND Journal of Economics, 15(2) (1984) 244–54.

Wong, Wong, Fong and Choi 49 G. Stigler, ‘A Theory of Oligopoly’, Journal of Political Economy, 72(1) (1964) 44–61. V. Y. Suslow, ‘Cartel Contract Duration: Empirical Evidence from Inter-War International Cartels’, Industrial and Corporate Changes, 15(5) (2005) 705–44. G. Symeonidis, ‘In Which Industries is Collusion More Likely? Evidence from the UK’, Journal of Industrial Economics, 51(1) (2003) 45–74. L. A. Toolsema, ‘Competition in the Dutch Consumer Credit Market’, Journal of Banking and Finance, 26 (2002) 2215–29. H. Uchida and Y. Tsutsui, ‘Has Competition in the Japanese Banking sector improved?’, Journal of Banking and Finance, 29 (2005) 419–39. J. Wong, E. Wong, T. Fong, and K. F. Choi, ‘Competition in Hong Kong Banking Sector: A Panzar–Rosse Assessment’, HKMA Research Memorandum, 16/2006.

4 Determinants of the Performance of Banks in Hong Kong Jim Wong, Tom Pak-Wing Fong, Eric Tak-Chuen Wong and Ka-Fai Choi1

4.1 Introduction What factors determine the performance of banks in general, and how banks’ profits and pricing behaviours are affected by market structure in particular, have been extensively studied. Amongst the various approaches, a number of studies have focused on the structure–performance relationship of banks, with the structure– conduct–performance (SCP) hypothesis and the efficient-structure (EFS) hypothesis widely tested.2 In general, banks’ profitability and pricing power are hypothesized to be determined by the market structure of the banking industry, such as the number of participating banks in the market and the market shares of banks, and bank-specific factors, such as cost efficiency, scale efficiency, and the risk attitude of banks. Macroeconomic factors, such as real GDP growth and unemployment, may also be important determinants. As for the structure–performance relationship of banks, empirical results have been mixed. In some studies, market structure of the banking sector was found to be one of the main determinants of banks’ performance. Specifically, banks’ profitability was found to be positively related to the level of market concentration. This was interpreted as profitability being enhanced by a higher degree of price coordination which was facilitated by fewer competitors. This suggests that concentration could have an adverse effect on the competitive environment of the industry. Likewise, some studies found that banks with larger market shares possessing strong market power could earn supernormal profits, which would hamper competition and could affect the health of other smaller banks. On the other hand, other studies found that the relationship between banks’ performance and concentration/market power is 50

Wong, Fong, Wong and Choi 51

spurious, with efficiency being the principal determinant of both profitability and market structure. Individual banks’ relative performance and the sector’s profitability were more dependent on the production efficiency of banks, in addition to other operating factors and macroeconomic conditions. Which of these hypotheses is valid thus points to different implications of increased concentration (and thus of mergers and acquisitions) for the banking industry. Understanding the crossrelationships among market structure, production efficiency and banks’ performance in Hong Kong is therefore useful to policy makers. This is particularly important given the recent market consolidations resulting in fewer banks and new larger banks, and the fact that larger banks appear to have generally performed better than smaller banks.3 Our previous studies using the Panzar–Rosse approach in Wong et al. (2006b) and the conjectural variation approach in Wong et al. (2007) have shown that the banking sector in Hong Kong operated with a high degree of competition with no significant sign of collusive pricing. As part of our series of projects examining the market structure and competitive environment of Hong Kong’s banking industry, this chapter further examines the issue through identifying the key determinants of banks’ relative performance. Based on the approach proposed by Berger and Hannan (1993) and with the aid of a panel dataset of retail banks covering the period 1991–2005, this chapter examines what factors determine the performance of banks, and tests whether market concentration and efficiency are among the main factors contributing to the profitability of banks in Hong Kong. It also evaluates possible policy implications of what effects these and other determinants may have on banks’ performance. The rest of the chapter is organized as follows. A literature review, particularly the Berger–Hannan approach, will be presented in the next section. Sections 4.3 and 4.4 describe the empirical specifications, and data and estimation methods respectively. Section 4.5 presents the estimation results. Section 4.6 concludes.

4.2 Literature review The structure–performance relationship of banks has been extensively studied in the case of the US banking industry.4 Earlier studies on the structure–performance relationship of the banking industry have usually been based on regression analyses in which indicators of bank performance, such as bank profitability and prices, were regressed on indicators of market structure such as the concentration index of the

52 The Banking Sector in Hong Kong

banking industry and market shares of individual banks. While a positive correlation between banks’ performance and market concentration (or market shares) was found frequently, the interpretation of this result, and hence the policy implication, varied among the studies: some authors interpreted it as support of the SCP hypothesis, which asserts that banks in a concentrated market are more likely to engage in some form of non-competitive behaviour such as collusions, consequently setting less favourable prices to customers and earning higher profits.5 Others viewed it as supporting the EFS hypothesis, which states that efficient firms increase in size and market share because of their abilities to generate higher profits, which usually leads to an increased concentration of markets and higher market shares for individual banks.6 The ambiguity in interpreting the result indicates the significant limitation of the approach. Berger and Hannan (1993) tackled the problem by explicitly incorporating two efficiency indicators, which measure the X-efficiency and scale efficiency of banks, as explanatory variables in the regression equations, together with two market structure indicators, which are proxied by market concentration and the market shares of banks. In Berger and Hannan (1993), profit rates and prices are employed as the dependent variables to proxy for banks’ performance. The X-efficiency variable, which is computed from an estimated efficient cost frontier from the data, aims to measure the closeness of cost of banks to the minimum that could be achieved on the efficient cost frontier which is defined by the best-practice banks in the sample. The scale–efficiency variable, which is derived from an estimated cost-function of banks from the data, aims to measure the closeness of cost for the bank’s actual output level to the cost of the bank’s minimum average cost output. Other factors such as the population of the state where the banks’ headquarters locate, branching restrictions of banks and the business failure rate were included in the estimation to control for the differences in market size, regulatory restrictions and business conditions respectively. Four important hypotheses that relate to the performance of the US banking industry were tested in Berger and Hannan (1993). In addition to the SCP, Berger and Hannan (1993) also tested the relative market power (RMP) hypothesis which asserts that banks with larger market shares are able to exercise market power to earn higher profits. Since the SCP and RMP hypotheses assert that higher profits are associated with anti-competitive pricing behaviours in the markets, prices should be positively related to market concentration and market shares of banks. The remaining two hypotheses tested by Berger and Hannan (1993) relate

Wong, Fong, Wong and Choi 53

to the EFS hypothesis: Under the X-efficient hypothesis (ESX), banks with superior management of costs for a given output level should attain higher profits. Under the scale efficient hypothesis (ESS), banks operating at optimal economies of scale should have the lowest average costs, resulting in higher profits. Both ESX and ESS imply that efficiency is positively related to banks’ profitability. It is also expected that efficient banks can offer more favorable prices to bank customers, leading to a negative relationship between efficiency and prices. Empirically, Berger and Hannan (1993) found that market concentration (that is the SCP hypothesis) better explains bank profits and prices than do efficiency (that is the ESX and ESS hypotheses) and market share (that is the RMP hypothesis). Goldberg and Rai (1996) later applied the Berger–Hannan approach on 11 European banking industries, but found that cost efficiency was the main determinant of banks’ performance in some low-market-concentration European countries, while scale efficiency and market structure only played a little role.

4.3 The empirical specification In this chapter, we employ the approach of Berger and Hannan (1993) to examine how banks’ performance is determined, by including direct measures of efficiency in the empirical analysis, along with variables representing market structures and other controlling factors. Two equations are specified as follows: it = β0 + β1 CONCt + β2 MSit + β3 DUMt + β4 CIEit + β5 SIEit + β6 z it + f (eit ),

(4.1)

and Pit = β7 + β8 CONCt + β9 MSit + β10 DUMt + β11 CIEit + β12 SIEit + β13 z it + f (eit ),

(4.2)

where i and t index bank and time respectively;  and P are the profitability and pricing ability of banks, which are adopted as the measures of banks’ performance; CONC is market concentration and MS is banks’ market shares, which represent the market structure of the banking sector; DUM is the dummy variable which is introduced to quantify the impact of regulatory liberalization; CIE and SIE denote cost inefficiency (that is X-inefficiency) and scale inefficiency of banks respectively.7 z is a

54 The Banking Sector in Hong Kong

vector of control variables and f (eit ) consists of autoregressive terms of a white noise process to capture autocorrelation in residuals. Profitability of banks, , is measured by the return on assets (ROA), which is defined as the ratio of post-tax profits (or losses) to total net assets.8 The pricing ability P is proxied by the interest rate spread (IRS) of banks, which is defined as the average price of interest-bearing assets minus the average cost of interest-bearing liabilities. The former is adjusted to exclude the portion of interest incomes and assets contributed by interbank placements, so as to reflect more closely the price of loans to non-bank customers. A higher IRS may suggest greater market power, as banks with greater market power could charge loans with a higher spread over their interest costs. CONC is proxied by the Herfindahl–Hirschman index (HHI), which is defined as the sum of the squared market shares of assets of individual banks, ranging from zero to one. A large number of banks, each with a small share, produce an HHI close to zero, while a single monopolist bank with a 100 per cent share produces an HHI of one. MS is measured as the ratio of individual banks’ total assets for each period to the sum of assets of all banks for that period. Regarding the sign of the estimated coefficients of CONC and MS, the SCP hypothesis suggests a positive sign for CONC in equations (4.1) and (4.2), while the RMP hypothesis predicts a positive sign for MS in the two equations.9 DUM is defined as one after 2001 Q2, and zero otherwise. DUM is so specified as to examine the effect of a series of regulatory liberalization measures in the banking sector taking place around 2001. The time point 2001 Q2 is so chosen to distinguish the two periods as major regulatory liberalization measures either completed or took place around this time: (a) The interest rate deregulation was fully completed by July 2001, with interest rate restrictions on current and savings accounts also removed;10 (b) the restriction on the number of branches and offices for foreign banks was completely removed in 2001; and (c) the market entry criteria have been relaxed since 2002. Note that since the regulatory liberalization was implemented almost at the same time when there was a sharp rise in CONS due to a number of mergers and acquisitions taking place, putting CONS and DUM in the same equations may subject the estimation to the problem of

Wong, Fong, Wong and Choi 55

multicollinearity. This issue will be further discussed in the following sections. The variable CIE, which is derived from a stochastic cost frontier, represents the cost inefficiency of banks. Cost inefficiency is an estimate of the percentage by which total production cost could have been reduced if the bank had operated on the stochastic cost frontier, holding the output levels and input prices constant. What cost inefficiency refers to is the situation in which the bank can reduce the production cost and still obtains the same quantities of outputs, given the input prices, but it has failed to do so. Theoretically, such a deviation occurs when the bank does not choose the right mix of inputs to produce the target output or employs excessive quantities of the factor inputs to produce the same amount of output. The estimate of CIE in this chapter is equivalent to the variable IE (that is inefficiency estimate) in Wong et al. (2006a). Under the ESX hypothesis, the sign of the estimate coefficient for CIE is negative in equation (4.1) when ROA is the dependent variable, and is positive in equation (4.2) when IRS is the dependent variable. Scale inefficiency SIE used in the regression analyses is computed from the parameters of the cost function estimated in Wong et al. (2006a), which is also adopted to calculate the CIE. SIE measures the absolute deviation of the bank’s actual output level from its optimal-scale output level that has the minimum average cost. By definition, SIE ranges from zero to one. The lower the value of SIE is, the closer the bank operates to its optimal scale. Detailed derivations of the CIE can be found in Wong et al. (2006b) and the definition of SIE is provided in Appendix 4A. The coefficient estimate for SIE is expected to be negative in equation (4.1) and positive in equation (4.2), if the ESS hypothesis holds. Some variables reflecting bank characteristics are incorporated to control for other heterogeneities in the samples. These include the ratio of loan loss provisions to total loans (LLoss), the ratio of total interestbearing funds11 to assets (DEPASS), and the capital adequacy ratio (CAR). LLoss is included in the estimation to capture differences in the quality of banks’ loan portfolios. A higher LLoss of banks indicate a loan portfolio of poorer credit quality, which may lead to lower profits due to higher operating costs relating to credit risk and loan loss management.12 It may also trigger banks to shift to other assets with lower risks, resulting in lower IRS. DEPASS is adopted as a proxy for the leverage of banks. A higher DEPASS indicates that a greater portion of the bank’s assets is funded by non-equity funds which could lead to higher funding costs, resulting in lower ROA and IRS. Such a relationship implies a negative estimated coefficient for DEPASS in regression equations (4.1) and (4.2).

56 The Banking Sector in Hong Kong

However, according to Goldberg and Rai (1996), a higher DEPASS may indicate that banks are more aggressive in asset-liability management which could lead to higher ROA and IRS. If this is the case, a positive sign for the coefficient estimate of DEPASS in equations (4.1) and (4.2) is expected. CAR is considered as a proxy for banks’ risk attitude. The coefficient estimate is expected to be negative, as a more aggressive portfolio (with a lower CAR value) should normally require a higher ROA or IRS for compensation. In addition to bank characteristics, we incorporate the real GDP growth rate (GDP) and the unemployment rate (UR) in Hong Kong into equations (4.1) and (4.2) to control for the influence of economic cycles. Generally, banks should generate higher profits and be able to charge higher prices under good economic conditions.

4.4 Data and estimation method In the estimation we employ a panel dataset that involves 38 retail banks in Hong Kong and covers the period from 1991 Q1 to 2005 Q4.13 Retail banks are the locally incorporated banks plus a number of the larger foreign banks whose operations are similar to those of the locally incorporated banks in that they operate a branch network and are active in retail banking. The banking data are obtained from the regulatory returns that the Authorized Institutions in Hong Kong must be filed with the Hong Kong Monetary Authority (HKMA). Since our purpose is to examine the profit–structure relationship in Hong Kong, the data used in the study cover only Hong Kong offices of the banks. After removing outliers and missing data, 1,418 observations are used for the study. Table 4.1 reports some descriptive statistics about the dataset. Figure 4.1 depicts the average ROAs of retail banks for the study period. It shows that prior to 1998 Q4 (before the full reflection of the effect of the Asian financial crisis), banks’ profitability was usually higher than 0.4 per cent. A sharp fall to the negative region of the ROA for the fourth quarter of 1998 indicates the lag effect of the Asian financial crisis. Although banks on average recovered from their quarterly loss after 1998 Q4, their ROAs were shown to have since stayed at a lower level of around 0.3 per cent. The IRS exhibited a mild downward trend in the study period, suggesting that the pricing ability of banks was generally lower in recent years than previously. The impact of industry consolidations on market concentration is apparent. As can be seen in Figure 4.2, the market concentration measured by the HHI increased sharply around the second half of 2001, reflecting merger and acquisition activities. As major regulatory

Wong, Fong, Wong and Choi 57 Table 4.1 General features of the data (sample period: 1991Q1–2005Q4; no. of observations: 1,418) Variable

Mean

Median

Std. dev.

ROAa IRSa CONC MS CIE SIE LLoss DEPASS CAR GDP growthb Unemployment rate

0.0036 0.0076 0.0973 0.0275 0.16 0.07 0.02 0.83 0.22 0.0110 0.0440

0.0035 0.0074 0.0869 0.0101 0.14 0.05 0.02 0.85 0.20 0.0120 0.0445

0.0030 0.0034 0.0211 0.0510 0.09 0.07 0.02 0.10 0.14 0.0158 0.0215

Minimum −0.0263 −0.0053 0.0790 0.0001 0.03 2.13e–05 0.00 0.19 0.09 −0.0390 0.0150

Maximum 0.0434 0.0377 0.1392 0.2860 0.79 0.45 0.21 0.92 1.10 0.0650 0.0860

Notes: (a) Quarterly figures, not annualized. (b) Seasonally adjusted Hong Kong real GDP growth rates, obtained from the Census and Statistics Department.

(%) 0.70

(%) 1.60

0.60

1.40

0.50

1.20

0.40

1.00

0.30

0.80 0.60

0.20 ROA (lhs) IRS (rhs)

0.10

0.40 0.20

0.10

0.00 1991Q3 1992Q1 1992Q3 1993Q1 1993Q3 1994Q1 1994Q3 1995Q1 1995Q3 1996Q1 1996Q3 1997Q1 1997Q3 1998Q1 1998Q3 1999Q1 1999Q3 2000Q1 2000Q3 2001Q1 2001Q3 2002Q1 2002Q3 2003Q1 2003Q3 2004Q1 2004Q3 2005Q1 2005Q3

0.00

Figure 4.1

Time series plots of average quarterly ROA and IRS

Source: HKMA.

liberalization took place at almost the same time as market consolidations, the variable DUM is shown to be very similar to the evolution of market concentration. Such a close resemblance of the time series pattern of CONS and DUM suggests there may exist a degree of multicollinearity. Equations (4.1) and (4.2) are estimated by the least squares method. A fixed cross-sectional effect is specified in the estimation so as to capture

58 The Banking Sector in Hong Kong DUM

HHI 0.15

1.2

0.14 DUM (rhs)

0.13

1.0 0.8

0.12 0.11

HHI (lhs)

0.10

0.6 0.4

0.09

0.2

0.08 0.0

0.07 1991/03 1991/09 1992/03 1992/09 1993/03 1993/09 1994/03 1994/09 1995/03 1995/09 1996/03 1996/09 1997/03 1997/09 1998/03 1998/09 1999/03 1999/09 2000/03 2000/09 2001/03 2001/09 2002/03 2002/09 2003/03 2003/09 2004/03 2004/09 2005/03 2005/09

0.06

Figure 4.2

0.2

Market concentration and regulatory liberalization

Notes: 1. The HHI is the sum of the squared market shares of assets of all retail banks in the market, ranging from zero to one. 2. DUM is defined as one after 2001 Q2 and zero otherwise to capture the effect of regulatory liberalization which took place around 2001. Source: HKMA.

unobserved idiosyncratic effects of different banks. To correct for the presence of cross-section heteroskedasticity, the cross-section weights are used in the estimation. The coefficient variances are derived by the White cross-section method so that the estimator is robust to cross equation correlation and different error variances in each bank.

4.5 Estimation results Estimation results are presented in Table 4.2 where Models A and B follow the specification in equations (4.1) and (4.2) respectively. The adjusted R-squared statistics of the two models, which measure the goodness of fit, are 0.46 and 0.41 in Models A and B respectively, indicating that the specifications are reasonably adequate. While not all variables included in Models A and B are statistically significant and obtain an expected sign, the F-statistics for both models reject the hypothesis that the set of selected variables do not give significant explanatory powers on ROA or IRS. Key findings are summarized as follows: 1. The estimated coefficients of CONC, MS, and DUM are found insignificant in the models (at the 5 per cent significance level). It was also

Wong, Fong, Wong and Choi 59

found that the sign and significance of the coefficient estimate for CONC change significantly when DUM is included in the estimation due to the problem of multicollinearity.14 Given this, the dummy variable is finally excluded in the specification of the equations (4.1) and (4.2). The estimated results for CONC and MS are therefore representing the net effect of increased market concentration in conjunction with the series of regulatory liberalization. This empirical evidence suggests that market structure, as measured by market concentration and market shares of banks, is either not a significant determinant of banks’ performance or, to the extent that market consolidations in recent years have hampered competition, thus enhancing banks’ profitability, its adverse effect has been largely offset by regulatory liberalization and technological progress during the same period. The emergence of a number of larger banks through mergers and acquisitions which should be more capable of competing with existing large banks may have also contributed. This is in line with the empirical results found in Wong et al. (2006b) and Wong et al. (2007) which showed that banks in Hong Kong operated in a competitive fashion in the loan market during the period 1991–2005 without any significant sign of collusion on pricing.15 2. For cost efficiency, the estimated coefficient of CIE is found to be negative in the ROA regression and positive in the IRS regression. CIE is statistically significant at the 5 per cent and 1 per cent level in the ROA and IRS regressions respectively. This suggests that banks with a higher level of cost efficiency are able to improve their profits through optimizing the input mix to produce a given level of outputs, and to offer more favourable prices to customers. This empirical result is consistent with the X-efficiency hypothesis. 3. Since larger banks have been found to be more cost efficient than smaller banks,16 the above finding suggests that for the same product in the loan market, larger banks can offer lower prices to customers than smaller banks, yet attaining a similar or even higher level of profits. Therefore, to the extent that price competition squeezes interest margins and profits of banks, smaller banks are more likely than larger banks to find themselves operating with loss. This suggests that smaller banks are more vulnerable to intense price competition in the loan market. 4. For scale efficiency, the coefficient of SIE is found to be negative in the ROA regression but positive in the IRS regression. However, it is statistically significant only in the IRS regression. This suggests that while banks can offer more favourable prices to customers by optimizing

60 The Banking Sector in Hong Kong Table 4.2 Estimation results of ROA and IRS Variable

ROA model (1)

IRS model (2)

Constant CONCt MSit CIEit SIEit LLossit DEPASSit CARit GDPt URt

0.0027 0.0046 0.0040 −0.0068** −0.0005 −0.0165* 0.0035 0.0015 0.0112** −0.0359**

−0.0004 −0.0346 −0.0088 0.0027* 0.0051* −0.0107 0.0127** −0.0025 0.0287* 0.0027

Adj. R-squared F-statistics

0.4573 33.2766

0.4143 24.8776

Note: * and ** denote significance at the 5% and 1% levels respectively.

their production scale, the effect of scale efficiency on profits is not significant. 5. Credit quality of loan portfolios, as expected, is found to be one of the determinants of banks’ profitability. Banks with higher loan loss provisions to assets appear to earn lower levels of profits. A higher level of loan provisions suggests poorer credit quality of loan portfolios, which may call for higher operation costs relating to credit risk and loan loss management, such as credit approval control, foreclosing bad loans, debt recovery expenses, and other loan-restructuring expenses, leading to lower profits. On the other hand, the ratio of loan loss provisions to assets does not appear to be a significant determinant of loan prices. 6. DEPASS and CAR, which measure the risk attitude of banks, appear to be not significant determinants of banks’ profitability. However, DEPASS is found to be positively correlated with the IRS. This indicates that aggressive banks may be more likely to participate in markets with higher risks, where higher prices are charged. 7. With regard to macroeconomic factors, the real GDP growth rate and unemployment rate are found to be positively and negatively related to banks’ profitability respectively, and the real GDP growth rate is found to be positively related to the IRS of banks. This indicates

Wong, Fong, Wong and Choi 61

that under good economic environments banks are more capable of charging higher prices in the loan markets and earn higher profits.

4.6 Conclusion Empirical evidence finds that market structure, as measured by market concentration and the market shares of banks, is either not a significant determinant of banks’ performance or, to the extent that market consolidations in recent years have hampered competition thus enhancing banks’ profitability, that its adverse effect has been largely offset by regulatory liberalization and technological progress during the same period. The emergence through mergers and acquisitions of a number of larger banks which should be more capable of competing with existing large banks may have also contributed. This finding is consistent with the empirical results of our previous studies17 which showed that the banking sector in Hong Kong operated with a high degree of competition without any significant sign of collusive pricing. Nonetheless, with bank consolidation expected to continue, how market concentration may impact on competition in the years to come needs to be closely monitored. On the other hand, cost efficiency is found to be positively correlated with banks’ profitability and negatively correlated with loan prices. Banks with a higher level of cost efficiency appear to be able to enhance their profitability and offer more attractive prices to customers. This suggests that bank with a lower production cost may earn higher profits through optimizing the input mix to produce outputs. Since larger banks are found to be more cost efficient in general, as shown in Wong et al. (2006a), larger banks can offer their services at lower prices to compete with smaller banks, yet attaining a similar or even higher level of profits. To the extent that price competition squeezes interest margins and profits of banks, smaller banks are more likely than larger banks to incur loss. Smaller banks may, therefore, be more vulnerable to intense price competition in the loan market, particularly under an operating environment of cut-throat price wars.18 Empirical results also indicate that banks with a loan portfolio of lower credit quality earn less profits, probably due to higher operational costs relating to credit risk and loan loss management. Loan prices are observed to be sensitive to banks’ risk attitude. Aggressive banks may be more likely to participate in markets with higher risks, where higher spreads are charged. In addition, banks’ profitability and loan spreads are in general positively correlated with macroeconomic environments.

62 The Banking Sector in Hong Kong

Appendix 4A Measures of scale inefficiency The measure of scale efficiencies indicates how the scale of banks with a particular level of production and management technology deviates from their optimal economies of scale.19 It is given by:

Si =

J  ∂ ln Ci j=1

=

J  j=1

∂ ln yji τj +

J J  

γjl log yli +

j=1 l=1

K 

ωjk log wki .

k=1

The variable Si is estimated for each of the banks at their respective output levels. Other notations can be referred to Wong et al. (2006a). Banks experience a constant return to scale when the estimate of Si is equal to one. If Si is less than one, banks are operating below their optimal scale levels and they could lower costs by increasing output further. On the other hand, while Si is greater than one, banks are required to downsize in order to achieve optimal input combinations. Both cases imply a degree of inefficiencies. A measure of scale inefficiency, SIE, is used in the actual regression:  SIEi

=Si − 1 =1 − Si

if Si > 1 if Si < 1

(4A.1)

In such form, the smaller the SIE is, the closer the banks’ scale is to the optimal level.

Wong, Fong, Wong and Choi 63

Notes 1. The authors are grateful to Hans Genberg for his suggestions and comments. 2. For a detailed summary of the studies published on or before 1983, see Gilbert (1984). For studies published after 1983, see Smirlock et al. (1984, 1986), Smirlock (1985), Allen and Hagin (1989), Timme and Yang (1991) and Berger (1995), for example. 3. Using the panel set of retail banks in Hong Kong covering the period 1991– 2005, a regression of banks’ return on assets on their asset sizes shows that the two variables are positively related. 4. See Note 1. 5. See Berger and Hannan (1989) and Hannan (1991). 6. For example, see Demsetz (1973, 1974) and Peltzman (1977). 7. For estimation convenience, for the study of how cost efficiency and scale efficiency affect the performance of banks, the actual explanatory variables used in the regression analyses are cost inefficiency and scale inefficiency instead. This approach follows the specifications of Berger and Hannan (1993) and Goldberg and Rai (1996). 8. The total net assets are the total assets less provisions. 9. The SCP hypothesis suggests a positive sign for CONC in equations (4.1) and (4.2), as it asserts that banks in a concentrated market are more likely to engage in some form of noncompetitive behaviour which allows banks to set less favourable prices to customers and earn higher profits. The RMP hypothesis suggests a positive sign for MS in the two equations as it asserts that banks with larger market shares are able to exercise market power to earn higher profits. 10. The deregulation of interest rates in Hong Kong was undertaken in two phases. Phase 1 of the deregulation, which took place in July 2000, removed the interest rate cap on time deposits with a maturity less than seven days and also the prohibition on benefits for all deposits with the exception of Hong Kong dollar current and savings accounts. Phase 2 of the deregulation took place in July 2001 which removed all interest rate rules over current and savings accounts. 11. Interest-bearing funds are defined as the sum of deposits from customers, interbank borrowings, and the amount payable under repos and negotiable debt instruments issued and outstanding. 12. This includes, for example, cost relating to credit approval control, foreclosing bad loans, debt recovery expenses, and other loan-restructuring expenses. 13. Initially, there were a total of 45 banks in various periods covered by the study. After removing samples with missing information, 38 retail banks remained in the estimation. Note that the number of banks covered by the study varied in different periods. After the major mergers and acquisitions, the number fell from 38 during 2001 Q2 to 28 during 2005 Q4. 14. The correlation coefficient between CONC and DUM is around 0.95. 15. Despite that market consolidations in recent years have resulted in an increase in market concentration, which favours the development of collusions among banks. 16. See Wong et al. (2006a).

64 The Banking Sector in Hong Kong 17. See Wong et al. (2006b) and Wong et al. (2007). 18. For illustration, we select three larger banks and three smaller banks to calculate the impact of cost efficiency on profits and IRS. Based on the dataset used in this study, the average X-inefficients (XIEs) of the three larger banks and three smaller banks in 2005 Q4 were 0.066 and 0.190 respectively. Using the estimated coefficients in Table 4.2, the difference in XIEs of larger banks and smaller banks has caused an annualized ROA gap of 0.34 per cent, while the resulting gap on IRS is −0.13 per cent. In other words, ROA of larger banks in general is larger than that of smaller banks by 0.34 per cent, while their IRS is lower than that of smaller banks by 0.13 per cent due to the difference in their cost efficiency. The differences are considered significant, given that the average values of annualized ROA and IRS of all banks in the dataset are 1.44 per cent and 3.04 per cent respectively. 19. Detailed discussions of scale economies can be found in Murray and White (1983).

References R. F. Allen and A. S. Hagin, ‘Scale-Related Efficiencies as a (Minor) Source of the Profits–Market Share Relationship’, Review of Economics and Statistics, 71 (1989) 523–6. A. N. Berger, ‘The Profit–Structure Relationship in Banking – Tests of Market-power and Efficient-structure Hypothesis’, Journal of Money, Credit and Banking, 27 (1995) 404–31. A. N. Berger and T. H. Hannan, ‘The Price–Concentration Relationship in Banking’, Review of Economics and Statistics, 71 (1989) 291–9. A. N. Berger and T. H. Hannan, ‘Using Efficiency Measures to Distinguish among Alternative Explanations of the Structure–Performance Relationship in Banking’, Federal Reserve Board Working Paper, (1993). H. Demsetz, ‘Industry Structure, Market Rivalry, and Public Policy’, Journal of Law and Economics, 16 (1973) 1–19. H. Demsetz, ‘Two Systems of Beliefs about Monopoly’, in H. Goldschmid (ed.), Industrial Concentration: The New Learning, (Boston: Little Brown, 1974). R. A. Gilbert, ‘Studies of Bank Market Structure and Competition: A Review and Evaluation’, Journal of Money, Credit, and Banking, 16 (1984) 617–44. L. G. Goldberg and A. Rai, ‘The Structure–Performance Relationship for European Banking’, Journal of Banking and Finance, 20 (1996) 745–71. T. H. Hannan, ‘Bank Commercial Loan Markets and the Role of Market Structure: Evidence form Surveys of Commercial Lending’, Journal of Banking and Finance, 15 (1991) 133–49. J. D. Murray and R. W. White, ‘Economies of Scale and Economies of Scope in Multiproduct Financial Institutions: A Study of British Columbia Credit Unions’, Journal of Finance, 38(3) (1983) 887–902. S. Peltzman, ‘The Gains and Losses from Industrial Concentration’, Journal of Law and Economics, 20 (1977) 229–63. M. Smirlock, ‘Evidence on the (Non) Relationship between Concentration and Profitability in Banking’, Journal of Money, Credit and Banking, 17 (1985) 69–83.

Wong, Fong, Wong and Choi 65 M. Smirlock, T. Gilligan and W. Marshall, ‘Tobin’s q and the Structure-Performance Relationship’, American Economic Review, 74 (1984) 1050–60. M. Smirlock, T. Gilligan and W. Marshall, ‘Tobin’s q and the Structure-Performance Relationship: Reply’, American Economic Review, 74 (1986) 1211–13. S. G. Timme and W. K. Yang, ‘On the Use of a Direct Measure of Efficiency in Testing Structure–Performance Relationships’, Working paper, (1991), Georgia State University. J. Wong, T. Fong, E. Wong and K. F. Choi, ‘The Cost Efficiency of Commercial Banks in Hong Kong’, HKMA Research Memorandum, 12/2006 (2006a). J. Wong, E. Wong, T. Fong and K. F. Choi, ‘Competition in Hong Kong’s Banking Sector: A Panzar-Rosse Assessment’, HKMA Research Memorandum, 16/2006 (2006b). J. Wong, E. Wong, T. Fong and K. F. Choi, ‘Testing for Collusion in the Hong Kong Banking Sector’, HKMA Research Memorandum, 03/2007.

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Part II Interest Rate and Default Risks in the Mortgage Market

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5 Interest Rate Risk in the Pricing of Banks’ Mortgage Lending1 Jim Wong, Laurence Kang-Por Fung, Tom Pak-Wing Fong and Cho-Hoi Hui

5.1 Introduction Intensive competition among banks in Hong Kong has driven the effective mortgage interest rates down to a historic low of around 2.75 per cent below best lending rate (BLR) with cash rebates of 1 per cent of loan amounts in general since early December 2004.2 This, together with falling interest rates, has brought the average mortgage rate down gradually from over 11 per cent in early 1998 to just over 2 per cent in December 2004 (see Figure 5.1). One key reason why banks can offer such low rates is their extraordinarily low funding cost. The spread of BLR over 3-month Hong Kong Interbank Offered Rate (HIBOR) has been maintained at around 460 basis points (bps) since September 2003, as a result of the abundance of liquidity in the banking sector. At the same time, customers’ deposit rates have also been at very low levels. On average, the spreads of BLR over the average time deposit rate (TDR) and the effective deposit rate (EDR) have been about 500 bps.3 The keen competition and high liquidity have benefited home mortgage borrowers. However, given the long repayment period of mortgages, for loans priced on the currently very low funding cost, there are risks of a reduction on the interest rate margin in the time ahead and over their mortgage life. These risks could arise from the following two sources: 1. Historically, the average BLR – HIBOR spread narrows during periods of increasing interest rates. Looking forward, therefore, as US interest rates continue to move upwards, spreads are expected to decline, other things being equal. 2. The currently very loose monetary conditions are not expected to be permanent. The HIBOR will eventually return to a level close 69

70 The Banking Sector in Hong Kong % p.a. 12

Weighted average mortgage rate Average BLR Average TDR

10 8 6 4 2 0 Jan-97 Figure 5.1

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Jan-04

Average mortgage rate and BLR

Sources: CEIC and HKMA staff estimates.

to US dollar interbank rates, from its current level of a substantial discount. When this happens, the BLR – HIBOR spread will revert back to the more normal level.4 It is even possible that the spread could become smaller than the normal level during the lifetime of the current mortgage pool. Banks are thus faced with interest rate risk, and in this case the basis risk in particular, which could affect banks’ net interest margin through changes in the spread between rates earned (the mortgage rate) and rates paid (the HIBOR or deposit rates).5 Given that mortgage lending represents a significant component of bank assets, how banks are affected by the interest rate risk is therefore an issue of interest.6 This study looks at the historical BLR – HIBOR spread and its behaviour during different phases of an interest rate cycle, as well as the movement of the risk premium of Hong Kong interest rates over US rates, and illustrates how the above risks may affect the interest rate margin of banks’ current mortgage portfolio. A distinction is made between mortgage loans that are funded on the interbank market and those that are funded by customers’ deposits. Using estimates of a cointegration and error correction model, the study also attempts to quantify the impact, by simulating different scenarios of interest rate upswing and risk premium reversal. It is found that loans priced on the basis of the current low funding cost could face a tangible reduction in their interest rate margin.

Wong, Fung, Fong and Hui 71 Spread (bps) 600

BLR (% p.a.) 12

500

10

400

8

300

6

200

4

100

2

0 100

0 BLR - HIBOR (LHS) BLR - EDR (LHS) BLR (RHS)

200 Jan-89 Jan-91 Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Figure 5.2

2 4

Interest spreads and BLR

Sources: CEIC and HKMA staff estimates.

The chapter is organized as follows. Section 5.1 examines the narrowing of interest margin during the tightening phase of an interest rate cycle. Section 5.2 discusses the possible shift in the risk premium. Section 5.3 assesses the potential reductions in the interest margin under different scenarios, based on the estimation results of an error correction model. Conclusions are provided in the final section.

5.2 Narrowing of spread during the tightening phase of interest rate cycle The average BLR – HIBOR spread in the past 16 years (January 1989 to December 2004) is 300 bps. For the easing phases of the interest rate cycles during the period, the average spread was 310 bps. In contrast, in the tightening phases of the cycles, the average spread was much tighter at 250 bps (Figure 5.2).7,8 One often-cited reason for the narrowing of spread during the rate tightening phase is that Hong Kong’s market rates tend to incorporate expected BLR increases ahead of actual BLR adjustments. This is because HIBOR is very responsive to changes in US market rates, while BLR normally only adjusts when there is a change in the US Federal funds target rate or when pressures from changes in cost of funds are built up to a certain level.9

72 The Banking Sector in Hong Kong % p.a. 14 HIBOR LIBOR

12 10 8 6 4 2 0 Jan-89

Jan-91

Figure 5.3

Jan-93

Jan-95

Jan-97

Jan-99

Jan-01

Jan-03

Movements of 3-month HIBOR and 3-month LIBOR

Source: CEIC.

To examine the hypothesis that Hong Kong’s market rates move ahead of BLR, joint tests of cross-correlations and Granger causality test are conducted. Details of the tests are presented and discussed in Annex 5B. The results confirm that the observed narrowing of spread during the tightening phase of the interest rate cycle was due partly to the lead-lag relationship between HIBOR and BLR in their response to US interest rate adjustments. A graphical illustration of the lead-lag relationship and the narrowing of the spread is given in Annex 5C.

5.3 Shift in risk premium Under the Currency Board system, interest rates in Hong Kong have to track their US counterparts closely. Short-term deviations in interest rates reflect the risk premium of Hong Kong dollar over the US dollar. Since June 2003, HIBOR has been at a consistent discount relative to LIBOR (Figure 5.3), averaging 94 bps from June 2003 to December 2004, and 200 bps in the past two months.10 However, the current difference is not expected to be permanent. HIBOR will eventually return to a level close to interbank rates of the US dollar. To illustrate the potential size of the HIBOR – LIBOR differential, a longterm mean level is established by taking the average of the differential

Wong, Fung, Fong and Hui 73 bps 700 (F)

600 500 400 300 200

95% confidence band

Historical mean

(C) (A) (B)

100

(D)

(E)

(G)

0 100 (H)

200 300 Jan-89 Figure 5.4

Jan-91

Jan-93

Jan-95

Jan-97

Jan-99

Jan-01

(I)

Jan-03

Risk premium

Notes: Historical mean and the confidence band are calculated by excluding observations during the Asian financial crisis and the ‘double-market play’ episode. Some of the fluctuations of the risk premium over the period appear to have roughly matched the following events: (A) June 4 event, 1989. (B) Interest rate hikes by a total of 100 bps in April 1990. (C) Closure of BCC (HK) in June 1991. (D) ERM turmoil in the fourth quarter of 1992. (E) Mexican currency crisis in January 1995. (F) The Asian financial crisis and the ’double-market play’ episode between July 1997 and September 1998. (G) Tension over the Taiwan Strait in 1999. (H) Strong demand for Hong Kong dollar assets in the second half of 2000, as the US economy began to show signs of slowing down. (I) Increased inflows of funds from the fourth quarter of 2003 onwards, triggered by US dollar weakness and increased pressures on a renminbi appreciation. Sources: CEIC and HKMA staff estimates.

over the past 16 years.11 This mean level is estimated to be near zero (negative 1.4 bps) with a standard deviation of 56 bps. At 95 per cent confidence level, the upper bound of the risk premium is at +109 bps and the lower bound is at −112 bps. This 95 per cent confidence band provides a simple illustration of the historical dispersion of the risk premium (Figure 5.4). The analysis shows that if the risk premium shifts to its historical mean level, HIBOR could rise significantly from its current level (by more than 200 bps), even if US market interest rates remain unchanged.

74 The Banking Sector in Hong Kong Reflects movements of US money market rates and expectations of changes in Federal funds target rate BLR

LIBOR



HIBOR

Risk premium (HIBOR – LIBOR)

TDR (or EDR)

Reflects the speculative pressure on the HK dollar, as well as liquidity and credit risk Decomposition Influence Explanations Figure 5.5

Flow of influence

5.4 Potential reduction in interest rate margins12 In order to assess the potential impact on interest margins of banks’ existing mortgage portfolio of: (i) the narrowing of spread during the current tightening phase of the US interest rate cycle; and (ii) a possible reversal of the risk premium, we make use of estimated error correction models.13 In the models, the two sources of influence are examined separately by decomposing the HIBOR as follows:14 HIBOR = LIBOR + risk premium The flow of the two sources of influence is illustrated in Figure 5.5. While these two influences will have one-to-one effects on changes in HIBOR through the above identity, the transmission of the effect to the BLR, the TDR and the EDR can be estimated by the models. In turn, the impact on the interest rate margin of banks’ current mortgage loan portfolio can be assessed by comparing the difference between the response of HIBOR and BLR to these two influences for HIBOR-financed loans, and between the response of TDR (or EDR) and BLR for loans financed by customers’ deposits.15,16

Wong, Fung, Fong and Hui 75

5.4.1 Model specification and estimation results Three models (A, B and C) are established for the assessment. Model A examines how BLR may move in response to changes in LIBOR (representing changes in US interest rates) and risk premium, while Models B and C capture the relationships between TDR or EDR, respectively, and changes in LIBOR and risk premium. The model specifications are given in Annex 5E. They are constructed so as to facilitate the identification of long-term co-movements and short-term deviations as well as their interactions.17 The models are estimated using data from January 1989 to January 2005. The estimation results are summarized and discussed in Annex 5E. The main findings are as follows: 1. A 100 bps increase in LIBOR would result in a 42 bps increase in BLR in the short run, while a 100 bps rise in risk premium would increase BLR by 29 bps. In the long run, a 100 bps rise in HIBOR, arising either from changes in LIBOR or risk premium, would increase BLR by 74 bps. 2. A 100 bps increase in LIBOR would result in a 59 bps increase in TDR (or a 52 bps increase in EDR) in the short run, while a 100 bps rise in risk premium would increase TDR by 61 bps (or by 49 bps in EDR). In the long run, a 100 bps increase in HIBOR (either from changes in LIBOR or in risk premium) would increase TDR by 91 bps and EDR by 81 bps. 3. The fact that (i) the responses of BLR to HIBOR, LIBOR and risk premium are less than unity (as against the unity response of HIBOR to LIBOR and risk premium); and (ii) the response of TDR and EDR to a rise in LIBOR and risk premium is greater than the response of BLR underlies the risk of a possible reduction in the interest rate margin of banks’ existing mortgage loan portfolio. As a result, the BLR – HIBOR, BLR – TDR and BLR – EDR margins will narrow on a rise in LIBOR and a risk premium reversal.18,19 4. The possible reduction on interest margin would be less severe for deposits-financed loans than HIBOR-financed loans, as the former’s funding cost would increase less than the latter’s, given that TDR and EDR would rise not as much as HIBOR.

5.4.2 How interest margins of banks may be affected To illustrate how the estimated response arising from a rise of US interest rates and shifts in risk premium may translate into possible effects on banks’ interest rate margins, we consider the following three scenarios where the LIBOR and Federal funds target rate increase by 120 bps over a

76 The Banking Sector in Hong Kong Table 5.1 Potential reduction of mortgage spreads (with an increase of 120 bps in US interest rates) Scenario of risk premium level (i) Current (ii) Historical (iii) Upper bound mean of two-standard deviations over mean (−197 bps) (−1 bps) (109 bps) Short-term effect (bps) BLR HIBOR TDR EDR

+51 +120 +71 +63

+119 +355 +213 +178

+158 +488 +293 +243

Long-term effect (bps) BLR HIBOR TDR EDR

+89 +120 +109 +97

+263 +355 +324 +288

+361 +488 +445 +396

Total cumulative effect in one year (bps) BLR +46 HIBOR +120 TDR +93 EDR +70

+148 +316 +240 +195

+205 +426 +322 +265

−74 −47 −24

−168 −92 −47

−221 −117 −60

Interest Margin (BLR – HIBOR) Interest Margin (BLR – TDR) Interest Margin (BLR – EDR)

Notes: For interpretation of the impact, please see Notes 22 and 24. ‘−ve’ numbers indicate decreases while ‘+ve’ numbers indicate increases. The short-term effect reflects the response of the dependent variable in the immediate month, while the long-term effect measures average changes in the dependent variable over the study period.

12-month period20 and the risk premium (i) stays at the current level (at −197 bps), (ii) moves to its historical mean level (at about −1 bps), and (iii) moves to two-standard deviations above its mean level (at 109 bps).21 The short-term and long-term impacts on the interest margin as well as the cumulative effect over a 12-month period are presented in Table 5.1.22 The simulations of the above three scenarios show that: 1. If we assume an adjustment of 120 bps in LIBOR and the Federal funds target rate, and no change in risk premium, the cumulative effect in a year’s time on the spread of BLR over HIBOR is estimated at −74 bps.23 The cumulative effect by the final month of the simulation period on

Wong, Fung, Fong and Hui 77

the spread of BLR over TDR will be −47 bps, while that for BLR over EDR will be milder at −24 bps.24 2. If the risk premium reverts to its historical mean level (from the current level of −197 bps to −1 bps), the combined impact of an increase of 120 bps in US interest rates and the risk premium reversal would be much larger. The spread of BLR over HIBOR would be reduced by a cumulative 168 bps in 12 months’ time, while the spreads of BLR over TDR, and of BLR over EDR, would narrow by 92 bps and 47 bps respectively. 3. In a drastic scenario that the risk premium shifts to the upper bound of the two-standard deviation level (from −197 bps to 109 bps), the spread would be under significant pressure.25 The spreads of BLR over HIBOR, and that of BLR over TDR and over EDR, are expected to narrow by a cumulative 221 bps, 117 bps and 60 bps respectively in 12 months’ time.

5.4.3 Impact on net interest margin of currently priced loans and banks’ overall mortgage portfolio Table 5.2 presents the simulation results of the impact on net interest margin of currently priced loans and the overall mortgage portfolio. With mortgage loans currently priced at about BLR −3 per cent,26 HIBOR, TDR and EDR at 0.70 per cent, 0.07 per cent and 0.03 per cent respectively, the gross interest margin for loans financed with interbank funds is about 1.30 per cent, while for loans financed with TDR and EDR, it is 1.63 per cent and 1.67 per cent respectively, including the acquiring cost of deposits. In this study, the gross mortgage margin is derived as the mortgage rate less the funding cost. The funding cost includes the interest cost and the acquiring cost. The interest cost for HIBOR-financed loans is HIBOR, while that for deposits-financed loans is correspondingly TDR or EDR. The acquiring cost is defined as the cost for acquiring deposits. This cost is small for HIBOR-financed loans but quite substantial for depositsfinanced loans, since maintaining a retail deposit base requires a bank to operate a large branch network. Specifically, the acquiring cost for HIBOR-financed loans is assumed to be zero, while for deposits-financed loans it is conservatively estimated to be 30 bps, as discussed in detail in Note 27. Taking into account the operating cost for mortgage lending and credit cost, the net interest margins for loans financed by HIBOR, TDR and EDR are estimated at 90 bps, 123 bps and 127 bps respectively.27,28 Under the scenario where US interest rates rise by 120 bps and the risk premium reverses back to its historical mean level, such mortgage loans

78 Table 5.2 Simulated impact on net interest margin of currently priced loans and banks’ overall mortgage portfolio (with an increase of 120 bps in US interest rates) Scenario of risk premium level (i) Current

(ii) Historical mean

(−197 bps)

(−1 bps)

(A) Impact on net interest margin of currently priced loans HIBOR-financed loans (bps) Mortgage Pricing 200 200 Funding Cost −70 −70 Current Gross Mortgage Margin 130 130 Operating Cost −30 −30 Credit Cost −10 −10 Current Net Mortgage Margin 90 90 Estimated Reduction of −74 −168 Mortgage Margin Simulated Net Mortgage Margin After Impact 16 −78 TDR-financed loans (bps) Mortgage Pricing − currently priced Funding Cost Current Gross Mortgage Margin Operating Cost Credit Cost Current Net Mortgage Margin Estimated Reduction of Mortgage Margin Simulated Net Mortgage Margin After Impact EDR-financed loans (bps) Mortgage Pricing Funding Cost Current Gross Mortgage Margin Operating Cost Credit Cost Current Net Mortgage Margin Estimated Reduction of Mortgage Margin Simulated Net Mortgage Margin After Impact

(iii) Upper bound of two-standard deviations over mean (109 bps)

200 −70 130 −30 −10 90 −221

−131

200

200

200

−37 163 −30 −10 123 −47

−37 163 −30 −10 123 −92

−37 163 −30 −10 123 −117

76

31

6

200 −33 167 −30 −10 127 −24

200 −33 167 −30 −10 127 −47

200 −33 167 −30 −10 127 −60

103

80

67 (Continued)

79 Table 5.2 (Continued) Scenario of risk premium level (i) Current

(ii) Historical mean

(−197 bps)

(−1 bps)

(iii) Upper bound of two-standard deviations over mean (109 bps)

(B) Impact on net interest margin of banks’ overall mortgage portfolio HIBOR-financed loans (bps) Mortgage Pricing 260 260 260 Current Gross Mortgage Margin 190 190 190 Current Net Mortgage Margin 150 150 150 Estimated Reduction of −74 −168 −221 Mortgage Margin Simulated Net Mortgage Margin After Impact 76 −18 −71 TDR-financed loans (bps) Mortgage Pricing Current Gross Mortgage Margin Current Net Mortgage Margin Estimated Reduction of Mortgage Margin Simulated Net Mortgage Margin After Impact EDR-financed loans (bps) Mortgage Pricing Current Gross Mortgage Margin Current Net Mortgage Margin Estimated Reduction of Mortgage Margin Simulated Net Mortgage Margin After Impact

260 223 183 −47

260 223 183 −92

260 223 183 −117

136

91

66

260 227 187 −24

260 227 187 −47

260 227 187 −60

163

140

127

Notes: The mortgage pricing conservatively estimated in this section includes cash rebates of around 1% of the loan amounts and assumed a full amortization period of three years. In this section the assessment covers only the first year but it is worth noting that by the fourth year the effective mortgage pricing will become BLR − 2.75% when the cash rebates are fully amortized. See section 5.4.3 for a discussion of the funding cost which consists of interest cost and acquiring cost, and notes 27 and 28 for the operating cost and the credit cost respectively. The same funding cost, operating cost and credit cost are applied to estimations of the net mortgage margin of currently priced loans as well as banks’ overall mortgage portfolios. For interpretation of the results, please see Notes 22 and 24.

80 The Banking Sector in Hong Kong

financed purely with interbank placements (and any new loans made with similar pricing) would become loss-making assets of banks. The simulation results show that net mortgage margin for these loans by the end of the simulation period (January 2006) could fall to −78 bps. The loss would be significant if the risk premium shifts towards its upper bound of historical two-standard deviations range – net mortgage margin would drop to −131 bps by January 2006. For loans financed by a mix of customers’ deposits, the impact would also be tangible, but the net mortgage margin should remain positive. It is noted that banks active in Hong Kong in the residential mortgage business generally have a sizeable customers’ deposit base. For the banks’ existing overall mortgage portfolio, the average mortgage pricing is estimated to be roughly BLR minus 2.4 per cent.29 As there remains in their books a large portion of loans made earlier with less aggressive pricing, banks would have a larger buffer to absorb the possible reduction in the mortgage margin. Taking into account the deposit-acquiring cost, operating cost and credit cost, the net mortgage margin of HIBOR-financed loans would be reduced to negative 18 bps in 12 months’ time, if US interest rates rise by 120 bps and the risk premium reverses back to its mean level. Under the drastic scenario that the risk premium shifts to the upper bound of two-standard deviations above its historical mean, when the effect filters through, the net mortgage margin would be reduced to negative 71 bps by January 2006. For depositsfinanced loans, their loan portfolios would remain profitable under the three scenarios, although their net mortgage margin would be materially curtailed. The impact would be less significant for EDR-financed loans than for TDR-financed loans. Note that the above analysis simulates the cases of entirely HIBOR and deposits-financed loans. How the margin of the mortgage portfolio of individual banks may be affected depends to a considerable extent on their funding compositions and their actual operating and credit costs, with banks more reliant on interbank fundings estimated to be more adversely impacted. Compared to large retail banks which have substantial demand and savings deposits in their customers’ deposit base, banks with a larger share of time deposits, which are more HIBOR related, could be more adversely affected.

5.5 Conclusion With US interest rates in the tightening phase of the interest rate cycle, and given the long repayment period of mortgages, there are risks of a

Wong, Fung, Fong and Hui 81

reduction on the interest rate margin for mortgage loans made under the prevailing monetary conditions, in the time ahead and over their mortgage life. Such risks could arise from an expected narrowing of BLR – HIBOR, BLR – TDR and BLR – EDR spreads and a reversal of the risk premium of Hong Kong dollar against the US dollar to a more neutral level. As suggested by simulation results derived under the assumption of a further rise in US interest rates and different scenarios of risk premium reversal, the mortgage portfolio of banks priced on the currently very low funding cost could face a reduction in their interest rate margin. Under the scenario that the risk premium reverses to its mean level, loans financed purely with interbank placements may become loss-making assets of banks. It is noted that banks active in Hong Kong in the residential mortgage business generally have a sizeable customers’ deposit base. Nevertheless, banks should take into account such interest rate risk in the pricing and management of their mortgage portfolios.30

82 The Banking Sector in Hong Kong

Annex 5A Effective mortgage rates A brief survey of selected retail banks on 15 January 2005 shows that they were offering cash rebate ranging from 0.7 per cent to 1.4 per cent of the mortgage amount. Taking into account this cash rebate and assuming a full amortization period of three years, the effective mortgage rate is conservatively estimated at around BLR – 3 per cent. Note that by the fourth year of the loans, when the cash rebates are fully amortized, the effective mortgage pricing will become BLR – 2.75 per cent. On 28 February 2005, the Hong Kong Monetary Authority (HKMA) issued a circular to all Authorized Institutions (AIs) reminding them of the need to monitor carefully the risks associated with residential mortgage lending including setting out the treatment of cash rebates and interest/repayment holidays within the context of the 70 per cent loan-to-value (LTV) ratio guideline. The term ‘cash rebates’ applies to lump sum payments, payments by instalments, and interest or repayment holidays offered to borrowers. The circular states that: • if a cash rebate is in excess of 1 per cent of the loan amount of a

residential mortgage, it should be treated as part of the loan amount for calculating the LTV ratio; • if a cash rebate is not in excess of 1 per cent of the residential mortgage, there is no need for it to be counted as part of the loan amount. However, disbursement of the cash rebate should be made only after completion of the purchase of the property in question; and • for residential mortgage schemes involving cash rebate subsidy offered by property developers, the lower of the discounted price or the valuation of the property should be used as the basis for calculating the LTV ratio. AIs should ensure that adequate disclosure regarding such schemes has been made to the borrowers in conformity with the spirit and objectives of the Code of Banking Practice.

Wong, Fung, Fong and Hui 83

Annex 5B Tests of lead-lag relationship between LIBOR and BLR To examine such a hypothesis that Hong Kong’s market rates move ahead of BLR, joint tests of cross-correlations and Granger causality test are conducted. In order to perform the assessment, HIBOR is decomposed into US market interest rates (LIBOR) and the spread of HIBOR over LIBOR, with the latter reflecting the risk premium of the Hong Kong dollar against the US dollar, which is determined by speculative pressures on the currency, as well as liquidity and credit risk. The influence of risk premium is controlled and the tests are conducted on BLR and LIBOR. As shown in Table 5B.1, the test result of cross-correlations shows that past adjustments of LIBOR has predictive ability for current changes in BLR, while that of Granger causality also accepts that changes in LIBOR Granger cause changes in BLR. These findings confirm that the observed narrowing of spread during the tightening phase of interest rate cycle has been partly due to the lead-lag relationship between HIBOR and BLR in their response to US interest rate adjustments.

Table 5B.1

Tests of lead-lag relationship between LIBOR and BLR

Joint test of cross-correlations1 Null hypothesis:  BLRt−k does not predict LIBORt  LIBORt−k does not predict BLRt

Test statistic 22.60 73.31*

Pairwise Granger Causality test2 Null hypothesis:  BLR does not Granger cause  LIBOR  LIBOR does not Granger cause  BLR

1.48 5.69*

Notes: 1. Joint tests with up to 12 lags of cross-correlations are considered. The test statistic follows asymptotically a χ2 distribution with 12 degrees of freedom. 2. Wald statistics for the joint hypothesis are reported. The test is based on the past 12 lags of observations. * Denotes significance at the 5% level.

84 The Banking Sector in Hong Kong

Annex 5C Graphical illustration of the narrowing of interest spread between BLR and HIBOR during the tightening phase of an interest rate cycle Figure 5C.1 illustrates the narrowing of interest spread between BLR and HIBOR during the tightening phase of an interest rate cycle. During the easing cycle of US interest rates (when interest rates move from point A to point B), the HIBOR falls ahead of BLR and the average interest spread between the two interest rates is represented by Area X. During the up cycle of US interest rates (when interest rates move from point B to point C), the average interest spread is represented by Area Y. Area Y is smaller than Area X.

% p.a.

C1

A1

A2

C2

Area X Area Y B1

BLR HIBOR

B2

A

B Easing phase

Time

C Tightening phase

US interest rate cycle Figure 5C.1

Illustration of interest spread narrowing

Wong, Fung, Fong and Hui 85

Annex 5D

Cointegration and error correction model

Consider a vector of n time series, Yt = (y1t , y2t , . . . , ynt )T , all of which are integrated of order one, such that their first differences (Yt , or Yt − Yt−1 ) are stationary. If there exists at least one linear combination of these time series such that the residuals exhibit a stationary pattern, they are said to be cointegrated. The error correction mechanism allows short-term deviations from the long-term equilibrium and measures the rate of correction. Thus, the whole model provides a more general form to describe the co-movement of several nonstationary time series. The general representation of the model is as follows: Yt = μ + αβYt−1 +

K 

φi Yt−i + εt .

(5D.1)

i=1

Equation (5D.1) is the error correction representation of the evolution of the variables in Y. The term βYt−1 captures the long-run relationship between them and α measures the speed with which deviations from long-run equilibrium are eliminated. The lags of Y are included to capture the short-run interactions between the variables. A full description of the cointegration and error correction framework can be found in Engle and Granger (1987) and Johansen (1991). Some recent empirical applications of the model to interest rates can be found in Scholnick (1996, 1999) which focus on bivariate variables of Yt in the error correction form.

86 The Banking Sector in Hong Kong

Annex 5E

Model specification and estimation results

In order to assess the potential impact on the interest margin of banks’ existing mortgage portfolio of (i) the narrowing of the spread during the current tightening phase of US interest rate cycle and (ii) a possible reversal of the risk premium, an error correction model is specified. Three models (A, B and C) are considered. Model A is specified with the BLR as the dependent variable, while Model B is specified with the TDR and Model C with the EDR as the dependent variable respectively. They both have LIBOR and risk premium as independent variables in the short-run and long-run equations. A restriction is imposed on the longrun equations to require the coefficients for the variables LIBOR and risk premium to be the same. This is because the long-run response of local retail interest rates to changes in market rates should be similar regardless of whether such changes are arising from movements in LIBOR or in risk premium.31 Past M lags of the changes in BLR, TDR and EDR are included in the models to control for serial correlations among observations.32 In addition, dummy variables are introduced to control for the effect of the Asian financial crisis. This model specification can facilitate the identification of short-term deviations and long-term co-movements as well as their interactions. Specifically, the error correction models for BLR (Model A), TDR (Model B) and EDR (Model C) are as follows:

Model A BLRt = α0 + α1 RAt−1 + φ1 LIBORt + φ2 premt + φ3 DSt +

M 

ϕj BLRt−j + et

j=1

(5E.1) with RAt = BLRt − β1 LIBORt − β1 premt

(5E.2)

Model B TDRt = α0 +α1 RBt−1 +φ1 LIBORt +φ2 premt +φ3 DSt +

M 

ϕk TDRt−k + et

k=1

(5E.3) with RBt = TDRt − β2 LIBORt − β2 premt

(5E.4)

Wong, Fung, Fong and Hui 87 Table 5E.1 ADF unit root test results Variable

BLR TDR EDR HIBOR 95% Critical values

Level No trend

Trend

−1.84 −1.13 −1.11 −1.61 −2.88

−2.04 −1.75 −1.62 −1.98 −3.43

First difference −7.03* −10.76* −10.35* −4.63* −2.88

Notes: * denotes significant at the 5% level. The unit root test is conducted with lags of up to 12.

Table 5E.2 ADF unit root test on long-run equilibrium Null hypothesis: Residuals have a unit root

Level No trend

Cointegrated variable BLR, HIBOR (LIBOR + prem) TDR, HIBOR (LIBOR + prem) EDR, HIBOR (LIBOR + prem) 95% Critical values

−4.01* −3.94* −4.92* −3.78

Notes: *denotes significance at the 5% level. Critical values are provided in Engle and Yoo (1987).

Model C EDRt = α0 +α1 RCt−1 +φ1 LIBORt + φ2 premt +φ3 DSt +

M 

ϕl EDRt−l + et

l=1

(5E.5) with RCt = EDRt − β3 LIBORt − β3 premt

(5E.6)

where premt is the risk premium at time t, DSt is a dummy variable controlling for the dramatic behaviour of interest rates during the Asian financial crisis, RAt , RBt and RCt are variables for the long-run equilibrium, and  is the difference operator.33 Monthly data from January 1989 to January 2005, taken from CEIC, are used for the empirical studies. Results of the tests of nonstationarity and cointegration support that the movements of BLR, TDR and EDR have equilibrium relationships with HIBOR (LIBOR + risk premium) in the long run. The test results are summarized in Tables 5E.1 and 5E.2.

88 Table 5E.3 Estimation results of Models A, B and C35 Variable

Coefficient

t-statistic

p-value

0.47* −0.11* 0.42* 0.29* 0.18 0.07*

4.54 −4.75 5.67 3.34 1.65 2.74

0.00 0.00 0.00 0.00 0.10 0.01

0.74* 0.74*

15.40 15.40

0.00 0.00

−0.06 −0.09* 0.59* 0.61* 0.14* 0.43*

−1.80 −3.30 7.14 7.29 2.15 8.24

0.07 0.00 0.00 0.00 0.03 0.00

0.91* 0.91*

14.22 14.22

0.00 0.00

−0.06* −0.08* 0.52* 0.49* 0.15* 0.34*

−2.02 −3.20 7.67 7.35 2.08 8.30

0.04 0.00 0.00 0.00 0.04 0.00

Model A: BLR Short run (1) Constant RAt−1 LIBORt premt BLRt−1 DSt Long run (2) LIBOR prem Adj. R-squared Q(6) Q(12) DW

0.50 6.89 11.41 2.17

Model B: TDR Short run (3) Constant RBt−1 LIBORt premt TDRt−1 DSt Long run (4) LIBOR prem Adj. R-squared Q(6) Q(12) DW Model C: EDR Short run (5) Constant RCt−1 LIBORt premt EDRt−1 DSt

0.71 11.90 14.88 2.34

(Continued)

Wong, Fung, Fong and Hui 89 Table 5E.3 (Continued) Variable

Coefficient

Long run (6) LIBOR prem Adj. R-squared Q(6) Q(12) DW

0.81* 0.81*

t-statistic

p-value

13.38 13.38

0.00 0.00

0.72 15.77* 18.07 2.37

Notes: *denotes significance at the 5% level. DW indicates the Durbin-Watson test statistic. Q(k) is the Ljung-Box test statistic up to lag k. It asymptotically follows the χ2 distribution with k degrees of freedom, which is denoted by χ2 (k). The critical values for χ2 (6) and χ2 (12) at the 5% level are 12.59 and 21.03 respectively. The short-run effect reflects the response of the dependent variable in the immediate month, while the long-run effect measures average changes in the dependent variable over the study period.

Estimation results of equations (5E.1) to (5E.6) are summarized in Table 5E.3, and discussed in section 5.4.1. All estimated coefficients, except the constant term in equation (5E.3) and the previous change of BLR in equation (5E.1), are statistically significant at the 5 per cent level and have an expected sign. The significance of the coefficients for RAt−1 , RBt−1 and RCt−1 implies that the cointegration and error correction models are appropriate to describe BLR, TDR and EDR.34 Diagnostic tests for all three models, including the Durbin-Watson test and the Ljung-Box test, suggest that they are adequately specified without significant serial correlations. Given that all estimated coefficients for LIBOR are less than unity in Model A and changes in LIBOR have one-to-one effects on changes in HIBOR, the interest rate margin between BLR and HIBOR will respond asymmetrically to a tightening and a easing of US interest rates (Note that the asymmetry discussed in this chapter refers to the difference between the responses of interest rate margin to an increase and a decline in US interest rates and does not refer to the difference in the estimated coefficients.) Based on the estimation results, an increase of 100 bps in LIBOR will increase BLR by 42 bps and HIBOR by 100 bps. The difference in the rates of change narrows the spread by 58 bps at the end of the projection period, that is, the interest rate margin will decrease. On the other hand, when LIBOR decreases by 100 bps, BLR and HIBOR will fall by 42 bps and 100 bps respectively. The change will widen the spread by 58 bps at the end of projection period. Thus, the slower response rate of BLR compared with that of HIBOR will give rise to an asymmetric

90 The Banking Sector in Hong Kong

performance in interest rate margins during the tightening and easing phases of an interest rate cycle. The asymmetric responses to different phases of an interest rate cycle are also observed in the interest rate margins of BLR – TDR and BLR – EDR. Since all estimated coefficients for LIBOR in Models B and C are larger than those in Model A, the response of BLR to LIBOR will be slower than that of TDR and EDR. Similar to the interest rate margin of BLR – HIBOR, the margins of BLR – TDR and BLR – EDR therefore behave asymmetrically to a easing or a tightening of US interest rates.

Wong, Fung, Fong and Hui 91

Notes 1. The analysis of this chapter covers the market situation up to January 2005, and uses data up to that month. Since then the market situation has changed, with banks raising their effective mortgage rates, along with the narrowing of risk premium of Hong Kong dollar over the US dollar to a more normal level. 2. In Hong Kong, mortgage rates are set by individual banks. The majority of mortgage loans are adjustable-rate mortgages and the rate is commonly referenced to BLR with a mark-up, which account for about 96 per cent of new loans approved. The average mortgage rate has come down from around BLR plus 1 per cent in mid-1998 to around BLR minus 2.75 per cent since early December 2004. Taking into account also the cash rebate and other benefits offered by banks, the mortgage rate is estimated conservatively at around BLR minus 3 per cent, assuming a full amortization period of three years for the cash rebates. Note that the effective mortgage pricing will become BLR – 2.75 per cent by the fourth year of the loans when the cash rebates are fully amortized (see Annex 5A). 3. This refers to interest rates that banks offer to non-bank customer deposits. The TDR is the average rate of time deposits weighted by different maturity composition. The EDR is the average interest rates on demand, savings and time deposits weighted by the deposit composition of the entire banking sector. 4. A normal level in this study refers to a BLR – HIBOR spread in a situation where HIBOR is close to the corresponding interbank interest rate of the US dollar. 5. The HIBOR, which is the wholesale money market rate, normally represents the interest cost for wholesale and foreign banks. On the other hand, for banks that have large retail deposit base, their interest cost is dominated by the interests paid on customers’ deposits. It should, however, be noted as far as total funding cost is concerned, while the interest rates of customers’ deposits are usually lower than HIBOR, a significant acquiring cost, as part of the funding cost, is required to obtain customers’ deposits. See Note 27 for a detailed discussion. 6. As at end-November 2004, mortgage loans accounted for 29 per cent of total loans and advances for use in Hong Kong. 7. The spreads discussed in this section exclude those occurred during the Asian financial crisis and the ‘double-market play’ episode (from October 1997 to September 1998). 8. The average spread of 250 bps during the tightening phases of the interest rate cycles is statistically smaller than the average spread of 310 bps during the easing phases at 5 per cent significance level. 9. Such as in the cases of October and November 1997. BLR was raised twice due to changes in cost of funds, in particular increases in HIBOR, when the US Federal funds rate was unchanged. 10. LIBOR stands for London Interbank Offered Rate, which is the interest rate on US dollar-denominated deposits (also known as the Eurodollars) traded between banks in London. LIBOR is widely used as a proxy for US market interest rates.

92 The Banking Sector in Hong Kong 11. The average is calculated by excluding the risk premium during the Asian financial crisis and the ‘double-market play’ episode. 12. In this study, the assessment focuses on the potential reduction in interest rate margins in the future period (that is when US interest rates continue to rise or there is a reversal of risk premium). The issue of intertemporal maximization (of the current period and the future period) is not examined. In addition, it is assumed that, given the highly competitive environment and consumer protection, banks will not be able to unilaterally change the current interest rate structure of fixing mortgage rates in relation to BLR or HIBOR for the existing loan portfolio, or to set BLR significantly different from market BLR rates. They will also refrain from charging different BLRs for new and existing loans. 13. See Annex 5D for a discussion of the cointegration and error correction model. 14. This follows the analysis of Peng et al. (2003) in which they examine how different sources of change in interbank interest rates impact on the banking sector’s profitability, as well as lending and deposit rates. 15. In this study, to simplify the analysis, we classify mortgage loans into three groups: HIBOR-financed loans, time deposits-financed loans, and loans financed by a mix of customers’ deposits weighted by their relative shares (the interest cost of which is proxied by EDR). We further assume that the former group of loans is entirely funded by interbank borrowings while the latter two groups by the respective types of customers’ deposits. 16. Savings deposit rate is generally adjusted along with the BLR by similar magnitudes. However, as time deposit rates are influenced by the movement of HIBOR, the spread of EDR over BLR varies overtime. 17. The short-run effect reflects the response of the dependent variable in the immediate month, while the long-run effect measures average changes in the dependent variable over the study period. 18. As discussed in section 5.1, the less than unity response of BLR to LIBOR and risk premium reflects the current practice of banks in setting BLR and deposit rates – BLR normally only adjusts when there is a change in the US Federal funds target rate or when pressures from changes in cost of funds are built up to a certain level. As a result, the transmission of changes in HIBOR (either arising from changes in LIBOR or from risk premium) to BLR is on average less than one. 19. The greater response of TDR and EDR to changes in LIBOR and risk premium (that is to HIBOR) than BLR reflects the fact that, while interest rates on savings deposits have a similar feedback as BLR to changes in LIBOR and risk premium, interest rates on time deposits are more sensitive than BLR to changes in HIBOR. 20. According to the Federal funds futures traded at the Chicago Board of Trade, the market has priced in a further rise of interest rates of 120 bps by December 2005. 21. See section 5.2 for a discussion on risk premium. 22. Note that by assuming that the rates of changes in LIBOR and risk premium are gradual and constant throughout the period, the cumulative impact presented in this study refers to the estimated changes between the projected situation in the final month of the forecast period (that is January 2006), and

Wong, Fung, Fong and Hui 93

23.

24.

25.

26. 27.

28.

29.

30.

31.

the current situation in January 2005 whence BLR is at 5 per cent, average HIBOR at 0.70 per cent, average TDR at 0.07 per cent, average EDR at 0.03 per cent and average risk premium at –197 bps. The less than unity transmission is due to the fact that market interest rates tend to price in expected BLR increases ahead of actual BLR adjustments. For a detailed discussion, see section 5.1. Since the savings rate moves largely in line with the BLR, the reduction on mortgage margin for loans financed entirely by savings deposits would be minimal, while the margin for loans financed purely by demand deposits would in fact widen. For mortgage loans which are funded by customers’ deposits which are mainly savings and demand deposits, the impact would be small. The selected high level of two-standard deviations upper bound represents the extreme risk at the high end. There is, nonetheless, a probability of 2.5 per cent that the mean of risk premium may happen to be even higher than this level under the normality assumption. See note 2. The average acquiring costs of deposits or the average operating costs for all banking activities (such as deposit taking, mortgage lending and other transactions) are assumed to be the same in this chapter. They include staff and other operating costs. Specifically, they are derived as the average ratio of operating expenses to the sum of total assets and total liabilities for the banking sector as a whole, and by assuming the same operating cost per dollar of transaction for all banking activities. Based on the annual survey from the Census and Statistics Department and HKMA staff estimates, the average operating cost of banks is around 50 bps which is in line with the operating cost estimated in a research note by Morgan Stanley Dean Witter of November 2000. In this study, for simulation purposes, such cost is assumed to be a conservative 30 bps. However, it should be noted that such cost varies greatly among different banks. The credit cost is estimated with information provided informally by a few banks. This is lower than the 30 bps estimated in a research note by Morgan Stanley Dean Witter of November 2000, and is in line with the fact that, based on recent performance of the property market and the low level of delinquency rate, the current provisions for mortgage loans should be smaller than in 2000. It should, however, be noted that in the case of a sharp reversal of risk premium, which could result in a significant increase in interest rates, the provision cost could increase materially. The average pricing is derived by averaging the interest margins for new loans from December 2001 to October 2004 collected by HKMA’s Residential Mortgage Survey. Detailed supervisory guidance on interest rate risk management is set out in the HKMA guidance note on ‘Interest Rate Risk Management’ (IR – 1) of the Supervisory Policy Manual. The imposition of such restriction is equivalent to estimating the longrun equation with HIBOR as the explanatory variable; where in Model A, the equation RAt = BLRt − β1 HIBORt , and HIBOR = LIBOR + prem. Similar restriction is imposed for Models B and C.

94 The Banking Sector in Hong Kong 32. The number of lags M included is chosen according to the Schwarz criterion (SC). Compared with the Akaike information criterion (AIC), SC imposes a greater penalty for the number of estimated model parameters, hence the use of minimum SC for model selection will always result in a chosen model which has a smaller (or at most equal) number of parameters than that chosen under AIC. 33. The value of Yt is the difference between Yt and Yt−1. 34. The magnitude of the estimated coefficients for RAt−1 , RBt−1 and RCt−1 describes the speed of adjustment for the disequilibrium. A larger coefficient would imply a faster adjustment to the equilibrium. The negative sign of the coefficients indicates that when the BLR, TDR or EDR are too high relative to the LIBOR and risk premium, the current BLR, TDR or EDR will be adjusted downward to restore the long-run equilibrium relationship. 35. Models A, B and C are estimated with the restriction that the estimated coefficients for the variables LIBOR and prem in the long-run equations are the same (see Annex 5E). Note that, consistently, if no such restriction is imposed, the estimated coefficients for the two variables in the long-run equations are not statistically different from each other.

References R. F. Engle and C. W. J. Granger, ‘Cointegration and Error Correction: Representation, Estimation and Testing’, Econometrica, 55 (1987) 251–76. R. F. Engle and B. S. Yoo, ‘Forecasting and Testing in Cointegrated Systems’, Journal of Econometrics, 35 (1987) 143–59. C. W. J. Granger, ‘Investigating Causal Relations by Econometric Methods and Cross-Spectral Methods’, Econometrica, 34 (1969) 424–38. S. Johansen, ‘Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models’, Econometrica, 59(6) (1991) 1551–80. P. Kennedy, A Guide to Econometrics, 3rd edn (Oxford: Blackwell, 1996). W. S. Peng, K. Lai, F. Leung and C. Shu, ‘The Impact of Interest Rate Shocks on the Performance of the Banking Sector’, HKMA Research Memorandum, 07/2003. B. Scholnick, ‘Asymmetric Adjustment of Commercial Bank Interest Rates: Evidence from Malaysia and Singapore’, Journal of International Money and Finance, 15(3) (1996) 485–96. B. Scholnick, ‘Interest Rate Asymmetries in Long-term Loan and Deposit Markets’, Journal of Financial Services Research, 16(1) (1999) 5–26. C. Sims, ‘Money, Income and Causality’, American Economic Review, 62 (1972) 540–52.

6 Hong Kong Mortgage Rate Setting – An Alternative Reference Rate?1 Jim Wong, Cho-Hoi Hui and Laurence Kang-Por Fung

6.1 Introduction Currently, the lending rates for most mortgage loans are set with reference to the best lending rate (BLR). Such a pricing method has been adopted by banks for many years, and it is well received by borrowers. While mortgage products with fixed rates or rates set with reference to Hong Kong Interbank Offered Rates (HIBORs) are also offered in the market, they have not been popular. It is, however, commonly accepted that the use of BLR as a reference rate for pricing mortgage is not necessarily conducive to banks’ management of interest rate risk, as the movement of BLR may in times deviate significantly from the cost of funds. This is particularly the case for those banks which do not have a sufficiently large BLR-related deposit base which is commensurate with their BLR-based lending.2 In times when HIBORs rise faster than BLR (typically during an interest rate hike cycle or when the risk premium of the Hong Kong dollar over the US dollar widens), the interest margin of these banks’ existing mortgage portfolios would be squeezed. Such basis risk is one of the major sources of risk underlying the interest rate risk exposures of banks that are active in mortgage activities. If the level of the basis risk in some banks is high due to the current interest rate environment, this may lead to a material decline in their earnings and may impact on banking and financial stability. The market conditions during late January to April 2005 demonstrate vividly such risk. Intense competition drove down the mark-ups of effective mortgage rates relative to the BLR to as low as around minus three percentage points by January 2005, which was made possible by the extraordinary low funding cost, with HIBOR being at an unusually deep 95

96 The Banking Sector in Hong Kong

discount to LIBOR of about 200 basis points (bps). However, with US interest rates rising and as funding cost increased faster than the BLR in subsequent months, the margin on loans priced on the previously very low funding cost came under pressure. Simulation results of our study show that such a squeeze of margin could be tangible. For instance, based on the market situation and data up to January 2005, under the scenario where US interest rates rise by 120 bps in the 12 months from February 2005 and the risk premium of Hong Kong dollar over the US dollar reverts back to its normal level (that is, HIBORs rise to close to the level of their US counterparts), the net mortgage margin for loans financed by a mix of customers’ deposits would be materially curtailed, while loans financed purely with interbank placements would become loss-making assets of banks.3 Indeed, the reduction of the interest rate margin has already been taking place since January 2005, with 3-month HIBOR (HIBOR3) rising by 190 bps, but BLR only by 45 to 70 bps.4 For the mortgage portfolios that banks acquired during January 2005, the margins for HIBOR-financed loans have been reduced by 125 bps. For those financed by customers’ time deposits or a mix of customers’ demand, savings and time deposits, their margins have also been reduced by 17 bps and 7 bps respectively. Further reductions may be expected if the above scenario continues to materialize. In addition, since the abolition of the Interest Rate Rules (IRR), banks are free to set their BLR-related deposit rates. To maximize profit, banks may make different adjustments to these deposit rates according to their different balance sheet positions. In the past, BLR set by the major banks which have a large retail deposit base was largely followed by other banks, even if the latter did not have the same retail deposit base.5 However, more recently some banks have changed their practice, and have raised their BLR independently of the major banks in order to preserve the interest margin of their existing portfolios amid rising interbank rates.6 With banks changing their previous practice of making concerted adjustments for their BLRs, there are concerns that the different BLRs among banks may cause confusion to mortgage borrowers. In view of the above, there have been calls to consider the merits of adopting an alternative reference rate (to the BLR) for the setting of the mortgage rate.7 By drawing on overseas experience and by examining the characteristics of the various local interest rates, this chapter investigates the possibilities, and the pros and cons, of the use of these rates as an alternative reference rate.

Wong, Hui and Fung 97

It should, however, be stressed that, given the widespread use of BLR as a reference rate for mortgage lending and other loan products, and its dominance in existing loan contracts, any change in the pricing method would have far-reaching impacts. Administratively, it could also be a complex process. Due to the absence of relevant data (such as the cost data), a complete assessment of the cost and benefit of a change is beyond the scope of this chapter.

6.2 Overseas experience The practice of setting mortgage rates varies among countries. The mortgage markets in different countries are characterized by different types of mortgage contracts, partly reflecting regulatory differences and partly contracts and conventions established in earlier periods. It should be noted that rather than converging towards a certain type of contracts or mortgage rates, the mortgage markets are characterized by different variations in the products. This has made the ‘typical’ products almost impossible to define. For example, in the US and Japan, fixed rate mortgage loans are more common, while in the UK, Switzerland and Australia variable rates are more popular. When the mortgage rates are adjustable, the reference rates chosen are commonly the interest rates which reflect banks’ cost of funds. They are either tied to the Treasury bond or a cost of funds index, like that in the US, or they are adjusted in line with the policy rates of the central banks, like that in the UK (the bank rate of the Bank of England) and Australia (the cash rate of the Reserve Bank of Australia). In Germany, mortgage loans are mostly fixed for at least one year and up to five years, or over five years to until maturity, before being renegotiated.8 A more detailed description of the use of some of these reference rates for the pricing of mortgage loans in respective countries is given in Annex 6A. In other EU countries, such as Belgium, Denmark and the Netherlands, mortgage rates are mostly fixed for more than five years to until final maturity. On the other hand, in countries like Greece, Luxembourg, Portugal and Finland, mortgage rates are variable and are renegotiable or tied to market rates after being fixed for less than one year.9

6.3 Possible alternative reference rates: an evaluation 6.3.1 Some suggested criteria Drawing on overseas experience, we examine a number of local interest rates as possible reference rates for mortgage rate setting,

98 The Banking Sector in Hong Kong

which can serve as alternatives to the BLR. Such possible alternatives include:10 3-month HIBOR (HIBOR3):

The rate of interest offered on Hong Kong dollar loans by banks in the interbank market for a 3-month period

Effective deposit rate (EDR):11

The average interest rate on demand, savings and time deposits offered by selected banks weighted by the deposit composition of the entire banking sector. EDR is currently calculated by the Hong Kong Monetary Authority (HKMA) for research purposes

Composite interest rate of HIBOR3 and EDR (Composite rate):11

The average interest rate of HIBOR3 and EDR weighted by the amount of interbank borrowings and the deposit composition of the entire banking sector.12 The composite rate is currently calculated by the HKMA for research purposes

Base rate of the HKMA (Base rate):

The interest rate the HKMA charges licensed banks when they approach the Discount Window for overnight liquidity

Yield of the 3-year Exchange Fund Note (EFN3):

The official mid-yield fixing of the 3-year benchmark Exchange Fund Note

Figure 6.1 shows the movements of these alternative reference rates and the BLR since 1997. In the evaluation of their appropriateness, several criteria are considered, some of which are highlighted by the drawbacks of using BLR as a reference rate. These criteria can be classified into two groups: criteria from consumers’ requirements and factors relevant to banks: (i) From borrowers’ point of view, they would prefer a reference rate that is stable and with a low level of volatility. This is important as borrowers normally have a steady monthly income and would like to limit fluctuations in their monthly mortgage payments. In addition, it

Wong, Hui and Fung 99 % p.a. 14 12

Base rate

BLR

10 8 EFN3 6 4 HIBOR3 2

EDR Composite rate

0 Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Jan-04

Jan-05

Figure 6.1 Alternative reference rates and BLR (January 1997 to April 2005, monthly average)

should be market-determined, simple, transparent and easy to understand. To avoid confusion, there should be only one such rate in the market and for all banks. (ii) From banks’ point of view, important criteria for a good reference rate are that it should closely represent (and move in line with) banks’ cost of funds, and there should exist efficient hedging instruments, so that on the whole the use of such reference rate helps banks in their interest rate risk management.13 In addition, the factors relevant to customers are also relevant to banks. Administrative simplicity is an important factor to be considered by banks. The criteria that the rate should be unique, simple and easy to understand would help banks in their daily operation, in particular in their dealing with customers. At the same time, a mortgage rate with lower volatility would help reduce repayment risk of customers. To the extent that the use of an alternative reference rate will benefit banks’ risk management, it would result in reductions in credit and management cost. Through competition, some of this gain would be passed through to customers in the form of lower mortgage rates.

100 The Banking Sector in Hong Kong

6.3.2 The evaluation Based on our econometric analysis and qualitative assessments, the relative features of the possible reference rates, in terms of the various criteria from customers’ requirements and banks’ considerations, are discussed in this section, and the merits and drawbacks of these rates are illustrated in Table 6.1. The discussions are summarized in Annex 6C.

6.3.2.1 Customers’ requirements All of the possible rates under study have a single rate, and they are either fully or largely market determined. HIBOR3 has the advantage of being completely market determined. It is widely quoted in the market and is relatively well known to borrowers. Unlike HIBOR3, which has a daily fixing provided by The Hong Kong Association of Banks (HKAB), the derivation of EDR and composite rate requires data collection and calculation. Nevertheless, as the HKMA is currently compiling EDR as a routine for research purposes, the additional work required would be moderate. The concepts of these rates are not difficult to understand but they are relatively more complex than the others. Some efforts would be required to explain the calculation of these rates to the borrowers. Both EFN3 and the base rate are quoted in the market but they have the disadvantage of not being well known to retail borrowers.14 However, in terms of volatility of the possible rates – the most important criterion as far as customers’ requirements are concerned – EDR, the composite rate and the base rate are clearly superior to HIBOR3 and EFN3. In this study, we assess their relative volatility by comparing the average monthly fluctuations of these rates during specific periods, which is presented in Table 6.2. It shows that the average monthly variations of HIBOR3 and EFN3, at 0.46 per cent and 0.40 per cent respectively, are significantly larger than that of EDR (0.21 per cent), the composite rate (0.27 per cent) and the base rate (0.11 per cent). This is particularly the case during the Asian financial crisis, when the monthly average of HIBOR3 and EFN3 surged to as high as 10 per cent and 8.5 per cent respectively in October 1997, while EDR, the composite rate and the base rate only rose to 6 per cent, 7.3 per cent and 7 per cent respectively. In Table 6.3, we compare the changes in the alternative reference rates during two particularly volatile periods, September/October 1997 and July/August 1998. We find that in terms of both changes in the monthly average rates and the differences between the highest and the lowest daily rates, HIBOR3 has the largest variations, followed by EFN3 or the composite rate, while EDR and the base rate have the smallest changes.

• It has a higher volatility, in terms of both the average monthly changes and the frequency of changes, as compared with most other reference rates.

• Data collection and calculation are required. Nevertheless, as the HKMA is currently compiling EDR for research purposes, only a small amount of additional work would be required. • The concept is not difficult to understand, but it is more complex than the others. • No direct hedging instruments are available. • It has the same drawbacks as EDR.

• There is only one single rate for all banks and it is relatively well known to the public. • The rate is completely market determined. • It is simple, transparent, and easy to understand. • HIBOR3 is a good measure of banks’ short-term cost of funds at the wholesale level. • The availability of exchange-traded and OTC derivative instruments also enhances its conduciveness to risk management.

• There is only one single rate for all banks, which is largely market determined, as its calculation includes retail savings and time deposit rates of selected banks. • It is a good measure of the short-term cost of funds at the retail level. However, in terms of desirability per interest rate risk management, it is not as good as the composite rate and HIBOR3. • Less volatile than the composite rate and HIBOR3.

• Similar to EDR, there is only a single rate for all banks and it is largely market determined. • It offers the best measure of banks’ cost of funds (better than HIBOR3 and EDR) as it represents the funding cost of an average bank with mixed funding sources.

HIBOR3

EDR

Composite rate

(Continued)

Drawbacks

Merits and drawbacks of alternative reference rates

Merits

Table 6.1

101

• Its movements mainly reflect changes in the US policy rate. As the liquidity condition in Hong Kong and the US may at times be different, it may not be a good measure of banks’ funding cost. • The rate is downwardly rigid, barred by the level of the US Federal funds target rate, but with no cap on upward adjustment. • Less well known to customers. • Similar to HIBOR3, it has a higher volatility. • It is not as good a measure of banks’ funding cost as HIBOR3, EDR or the composite rate. • Less well known to customers.

• Similar to HIBOR3, it is unique, market determined, and has direct hedging instruments available.

EFN3

Drawbacks

• A unique and transparent standard rate. • It has the lowest volatility among the alternative rates under study.

• The use of composite rate as a reference rate would reduce banks’ mortgage margin variability and help reduce banks’ exposure to interest rate risk. • Although no complete hedging instruments are available, partial hedging can be done for the HIBOR element of the rate. The close approximation to cost of funds also reduces the need for hedging. • Its volatility is less than HIBOR3, but larger than EDR.

Merits

(Continued)

Base rate

Table 6.1

102

Wong, Hui and Fung 103 Table 6.2 Volatility of monthly payment burden of possible reference rates January 1997 to April 2005 (The period including the Asian financial crisis) (%)

January 1999 to April 2005 (%)

Reference rate HIBOR3 EDR Composite rate Base rate EFN3

0.46 0.21 0.27 0.11 0.40

0.24 0.12 0.14 0.12 0.29

Memorandum item BLR

0.10

0.09

Note: Volatility (in %) is defined as the average monthly changes (in absolute term) in the reference rate over the specific period. The higher the figure, the higher is the volatility.

Table 6.3 Changes in monthly average rates and differences between daily high and low of reference rates during two particularly volatile periods Asian financial crisis

Government stock market operation

(October 1997/September 1997) (August 1998/July 1998) Increase in the monthly average rate (%)

Difference between high/low (%)

Increase in the Difference monthly between average rate high/low (%) (%)

Reference rate HIBOR3 EDR Composite rate Base rate EFN3

2.5 0.2 1.0 0.5 1.9

17.8 1.5 7.3 0.8 2.7

3.3 0.5 1.3 0.0 0.1

10.5 1.3 3.9 0.0 0.5

Memorandum item BLR

0.2

0.8

0.0

0.0

Figure 6.2a shows the movements of derived mortgage rates since February 1997 based on HIBOR3, EDR and the composite rate for loans priced in January 1997, and Figure 6.2b presents their relative monthly fluctuations. It is clear that both EDR and the composite rate are more stable than HIBOR3 and have lower monthly fluctuations.15

104 % p.a. 16 14 12 10

Mortgage rates set with reference to: EDR

8 6 4

Composite rate 2 Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

HIBOR3

Jan-03

Jan-04

Jan-05

Figure 6.2a Mortgage rates based on possible reference rates (for mortgage loans priced in January 1997 with constant mark-ups throughout the remaining contractual period) Note: The mark-ups of mortgage rate over the reference rates are as follows: HIBOR3 + 3.4%, EDR + 4.8% and composite rate + 4.3%.

% p.a. ± 3.5 3.0

HIBOR3 EDR Composite rate

2.5 2.0 1.5 1.0 0.5 0.0 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Figure 6.2b Relative monthly fluctuations of selected reference rates (February 1997 to April 2005, monthly average, in absolute terms) Note: The fluctuations are in terms of monthly absolute changes, which can be an increase or a decrease in the specific month.

Wong, Hui and Fung 105

6.3.2.2 Banks’ considerations This section focuses on the criteria regarding interest rate risk management.

(a) A good measure of cost of funds A reference rate which closely reflects the average funding cost of banks could offer a stable margin for the loan portfolio once the pricing is fixed. As a constant mark-up over such reference rate is guaranteed by the contracts and the movement of such reference rate resembles the cost of funds, such a pricing would be conducive to banks’ interest rate risk management. To test which reference rate has such a property, we examine how each of the rates might have been considered (as cost of funds) in the setting of the mortgage rate during the period from January 1999 to April 2005. Using monthly average interest rate data, the assessment is done by a single equation regression analysis which is specified with the average mortgage rate as the dependent variable, and each of these reference rates as the explanatory variable.16 The estimation results (presented in Table 6D.1 of Annex 6D) indicate that the composite rate, as a funding cost proxy, offers the best approximation to the actual mortgage rate, judging from the adjusted R-squared statistic of the regression and the fitted average mortgage rate. This is followed by HIBOR3 and EDR. EFN3 and the base rate have a lower goodness of fit and are poor approximations to the funding costs. These econometric results are largely expected. In the wholesale market, the interbank rate is certainly one of the best measures of cost of funds. It is most widely traded and reflects closely the short-term funding cost of banks – in particular, those who do not have a large retail deposit base. In the retail market, on the other hand, for banks which have a large retail deposit base, the most widely quoted funding costs are the savings deposit rates and time deposit rates. To measure the aggregate change in such cost of funds, the EDR is derived, which is defined as the average interest rate on demand, savings and time deposits weighted by the deposit composition of the entire banking sector. However, as most of the banks have a mix of funding sources, the composite rate, which is the weighted average of EDR and HIBOR3, is a better measure of cost of funds than HIBOR3 and EDR. The base rate is the interest rate that the HKMA charges licensed banks when they come to the Discount Window operated by the HKMA, with Exchange Fund paper, at the end of the day when they find themselves short of liquidity. The base rate is set mechanically through the use of a transparent formula, which is 150 bps above the prevailing US Federal

106 The Banking Sector in Hong Kong

funds target rate or the average of the five-day moving averages of the overnight and 1-month HIBOR, whichever is the higher. Hence, the base rate is automatically determined without any discretion from the HKMA or any banks.17 Given this, the base rate may at times be not a good measure of banks’ funding costs, when the liquidity condition in Hong Kong is different from that in the US.18 The base rate also has the characteristic of being downwardly rigid in particular situations. Specifically, when there is ample liquidity in the banking system which drives the interbank rates to a low level, banks will enjoy a widening of mortgage margin, as customers will be stuck with the same base rate, if there is no policy rate adjustment in the US. On the other hand, when there is a shortage of liquidity in the banking system and the short-term interbank rates rise to a high level, the base rate will adjust upward. There is no cap on upward adjustments.19,20 Similar to the base rate, EFN3 clearly does not offer as good a fit as the other three rates, suggesting that it probably plays a lesser role in banks’ decisions of setting the mortgage rate.

(b) Variability of interest rate margins

To assess how the various reference rates may perform under the criterion of offering a stable interest rate margin, we study possible changes in the margin variability of an actual mortgage portfolio acquired in January 1999, based on monthly average interest rates. Under the scenarios of adopting different reference rates, we examine how the variability of such portfolio’s margin may be affected based on the two identified best measures of average funding costs – the composite rate and HIBOR3. The results, as reported in Table 6.4 and Annex 6E, show that on the whole a mortgage rate that is set with reference to a composite rate or HIBOR3 offers lower margin variability, compared with those derived from using other reference rates. A lower margin variability is considered to be a desirable property in banks’ risk management, which can be demonstrated especially when there is a sudden change in interest rates that goes against the mortgage margin. Based on monthly average interest rates, Table 6.5 illustrates how the interest margin of banks’ mortgage portfolios may be squeezed when the mortgage rate is set with reference to BLR. By using the pricing data of loan portfolio acquired during January 2005 and the changes in cost of funds through April 2005, we show that the squeezes in the net mortgage margins were more severe when the mortgage rate was set with reference to BLR, than under the scenarios that the mortgage rates were set with reference to the composite rate or HIBOR3.21

107 Table 6.4 Variability of margin for banks’ mortgage portfolio of January 19991,2 (during the period January 1999 to April 2005) Average funding costs represented by Composite rate

HIBOR3

Reference rate HIBOR3 EDR Composite rate Base rate EFN3

0.42 0.14 0.00 0.47 0.64

0.00 0.55 0.42 0.64 0.74

Memorandum item BLR

0.36

0.72

Notes: 1. The margin is defined as the mortgage rate set with the reference rate plus a mark-up, less the cost of funds proxy. 2. Variability (in %) is defined as the standard deviation of margin during the period January 1999 to April 2005. It measures the average dispersion of margins from its mean level during the study period. The lower the figure, the lower is the variability.

Table 6.5 Estimated squeezes of interest margins resulting from the recent rise in cost of funds under different reference rates1,2 (for banks’ mortgage portfolio acquired during January 2005) The estimated squeeze compared with the margin in January 2005 (bps) 2005 March

April

(A) Cost of funds represented by the Composite rate Reference Rate (i) BLR −17 −33 (ii) HIBOR3 63 118 (iii) Composite rate 0 0

−40 110 0

February

(B) Cost of funds represented by HIBOR3 Reference Rate (i) BLR −80 (ii) HIBOR3 0 (iii) Composite rate −63

−151 0 −118

−150 0 −110

Notes: 1. The mortgage margin is defined as the mortgage pricing less funding cost, operating cost and credit cost. 2. Positive figures indicate a widening of margin.

108 The Banking Sector in Hong Kong

(c) Availability of hedging tools

Of the various local interest rates, only HIBOR3 and EFN3 have their derivative instruments traded in the Hong Kong Exchanges and Clearing Ltd., although the trading is not very active. As for other local interest rates, no hedging instruments are currently directly available in the market, but for the composite rate, partial hedging for its HIBOR element can be performed. Note that the need for hedging is less if a reference rate that reflects closely banks’ funding costs is adopted.

6.3.2.3 Overall assessment Each of the possible reference rates has its own merits and drawbacks. In the selection of an appropriate reference rate, these merits and drawbacks should be carefully assessed and weighted against each other. A balance will have to be struck between the requirements of customers and banks. The weights given to each of the criteria in the evaluation of the suitability of the alternative reference rates can be drawn from industry experience. To illustrate this idea, we focus our assessment based on two major criteria in this section: (i) the stability of the reference rates which is key to customers’ acceptance; and (ii) the conduciveness to interest rate risk management in terms of whether the rate is a good measure of banks’ cost of funds. The ranking of the reference rates based on these two criteria are given in Table 6.6. Using a two-dimensional chart, we illustrate the relative positions of the five alternative reference rates in terms of the two major criteria – their stability and conduciveness to interest rate risk management (Figure 6.3). Note that the scale (or unit) used to plot the chart is arbitrary as the relative weights of the criteria are not known. The chart shows that the ranking of the five rates is clear in terms of each of the two major criteria. However, their ranking based on the combined performance of the two criteria is not easy to determine, although some rough ideas can still be obtained from the chart. Moreover, in the complete analysis, other factors including the criteria of being simple, transparent and easy to understand, as well as administrative simplicity, should also be considered.

6.4 Conclusion Each of the possible reference rates discussed above has its own merits and drawbacks. In the selection of an appropriate reference rate, these merits and drawbacks should be carefully assessed and weighted against each other. A balance will have to be struck between the requirements

109 Table 6.6 Ranking of possible reference rates Ranking

Major criteria Stability of the rate1

Conduciveness to interest rate risk management2

High 1

With an average monthly change of 0.11%, Base rate has the lowest volatility among the reference rates.

Composite rate offers the best measure of cost of funds for an average bank which has a mix of wholesale and retail funding sources.

2

EDR has a slightly higher volatility than the Base rate. Its average monthly change is 0.21%.

HIBOR3 is a good measure of banks’ short-term cost of funds at the wholesale level.

3

The volatility of the Composite rate is slightly higher than EDR, but lower than EFN3 and HIBOR3. The average monthly change in the Composite rate during the study period is 0.27%

EDR is a good measure of banks’ short-term cost of funds at the retail level.

4

EFN3 is slightly less volatile than HIBOR3. But its average monthly change of 0.4% is higher than other reference rates.

EFN3 is not a good measure of banks’ funding costs.

Low 5

HIBOR3 has the highest volatility among the alternative rates under study. Its average monthly change over the study period is 0.46%.

Base rate’s movements mainly reflect changes in the policy rate of the US. It may be in times not a good measure of banks’ funding costs. In addition, the Base rate has the asymmetric characteristic that it is downwardly rigid but with no cap on upward adjustment.

Notes: 1. Stability is measured by the volatility of the reference rate, which is defined as the average monthly changes (in absolute term) in the reference rate from January 1997 to April 2005, including the Asian financial crisis period (as shown in Table 6.2). The lower the volatility (or the lower the average monthly change), the higher is the stability, and vice versa. 2. Conduciveness to interest rate risk management is measured by the goodness of fit of the regression using the specific rate to explain the actual mortgage rate (measured by the adjusted R-squared as presented in Annex 6D). The higher the R-squared, the higher is the conduciveness to interest rate risk management, because the reference rate would track the funding cost more closely.

110 The Banking Sector in Hong Kong Average monthly change (%) 0.0 Base rate

Stability of the rate

0.1

EDR

0.2

Composite rate

0.3 0.4

EFN3 HIBOR3

0.5 0.6 0.76

0.80

0.84

0.88

0.92

0.96

1.00 R-squared

Conduciveness to interest rate risk management

Figure 6.3 Ranking of the reference rate in terms of stability and conduciveness to interest rate risk management Notes: 1. Stability is measured by the volatility of the reference rate, which is defined as the average monthly changes (in absolute term) in the reference rate from January 1997 to April 2005, including the Asian financial crisis period (as shown in Table 6.2). The lower the volatility (or the lower the average monthly change), the higher is the stability, and vice versa. 2. Conduciveness to interest rate risk management is measured by the goodness of fit of the regression using the specific rate to explain the actual mortgage rate (measured by the adjusted R-squared as presented in Annex 6D). The higher the R-squared, the higher is the conduciveness to interest rate risks management, because the reference rate would track the funding cost more closely.

of customers and banks. The weights given to each of the criteria in the evaluation of the suitability of the alternative reference rates can be drawn from industry experience. It is noted that mortgage products with reference rates other than BLR (such as HIBOR) are currently being offered in the market. However, they are not as popular as BLR. This may be due to: (i) their high volatility in the past, (ii) the lack of standardization in terms of product features and price fixing, and (iii) the lack of promotion and low transparency of the products. If any of the above rates is chosen to be the alternative reference rate, smoothing methods may be employed to reduce its volatility.22 This is quite important for both the borrowers and the banks. Borrowers will be skeptical about the use of a reference rate that could fluctuate widely within a short period of time, such as during the Asian financial crisis. The ‘smoothed’ reference rate can be used as the standard reference

Wong, Hui and Fung 111 % p.a. 10 9 8 7 BLR

6 5

Mortgage rate (based on the monthly average Composite rate, excluding the mark-ups) Mortgage rate (based on the daily Composite rate, excluding the mark-ups)

4 3 2 1 0 Jan-01

Jul-01

Jan-02

Jul-02

Jan-03

Jul-03

Jan-04

Jul-04

Jan-05

Figure 6.4 Adjustments of the mortgage rate (based on a prescribed triggering rule) and BLR∗

Note: ∗ Prescribed adjustment rule: a change in the mortgage rate would be made only if the reference rate changes by more than 25 bps.

rate, which would be made public on a pre-determined regular basis (for example monthly or quarterly basis). If the 1-month average is used, the reference rate for the current month would be calculated based on the average of the daily rates of the previous month. The new reference rate would be announced on the first day of the current month and would be applicable for the pricing of new mortgage loans and the re-pricing of existing mortgage loans in banks’ mortgage portfolios throughout the month.23 To further reduce the frequency of mortgage rate adjustments so as to improve borrowers’ acceptance to the chosen reference rate, a rule may be adopted so that a change in the mortgage rate would be made only if the reference rate changes by more than a prescribed amount, for example, by more than 25 bps.24 As an illustration, if we use the composite rate as the mortgage reference rate and adopt the above rule, the number of instances that the mortgage rate would need to be changed from January 2001 to April 2005 would be 12 times based on the monthly average reference rate.25 This compares with 15 actual adjustments in the BLR during the same period (see Figure 6.4). On the other hand, it may be desirable to have contingency arrangements in place, under which the composite rate can be adjusted before

112 The Banking Sector in Hong Kong

the regular rate fixing date, if necessary, such as when interest rates move drastically. The conditions for activating such arrangements should be clearly specified,26 in addition to the normal rule governing how the rate is adjusted regularly on a monthly basis. To promote such a reference rate, its specific features should be carefully designed in order to increase borrowers’ acceptance. In addition, the calculation and fixing of such reference rate should be standardized. Promotion, such as educational campaigns, would need to be made to improve public understanding.27 The new reference rate can be introduced either as an alternative or as a replacement for BLR. Given the need for BLR to continue to be the reference rate for loans made prior to the introduction of a new reference rate, it would be desirable to have the new reference rate introduced to the market along with the BLR. Market forces will determine which rate is more acceptable. Given the widespread use of BLR as a reference rate for mortgage lending and other loan products, and its dominance in existing loan contracts, any change in the pricing method would have far-reaching impacts on the mortgage market. Administratively, it could also be a complex process.28 While the HKMA has a supervisory interest in the vulnerability of bank earnings to interest rate risk, it is up to the industry to decide which reference rate to use for mortgage lending. If it is agreed that any of the above rates can be considered as an alternative reference rate, a more complete analysis would be required to assess the cost and benefit for such a move. Such a complete study would require the active involvement of the banking industry. We would be happy to assist in the process, through participating in the discussion and by providing technical support. If a decision is made to introduce an alternative reference rate, the HKMA is prepared to help ensure its transparency through encouraging the use of a single rate and the standardization of its calculation and quotation. In particular, if the composite rate is adopted, the HKMA could help by taking up the task of the computation and announcement of the rate, if deemed desirable.

Wong, Hui and Fung 113

Annex 6A Reference rates for pricing mortgage loans in the US, UK and Australia In the US and Japan, fixed rates mortgage loans are more common, while in the UK, Switzerland and Australia variable rates are more popular. When the mortgage rates are adjustable, they are either tied to the Treasury bond or a cost of funds index, like that in the US, or they are adjusted in line with the policy rates of the central banks, like that in the UK (the base rate of the Bank of England [BOE]) and Australia (the cash rate of the Reserve Bank of Australia [RBA]). In the US, there are several cost of funds indices for pricing mortgage loans. The one that is most widely used by mortgage lenders (especially in the West Coast) to set the floating interest rate on adjustable rate mortgage loans is the Eleventh District Cost-of-Funds Index (COFI). The monthly weighted average COFI has been published by the Federal Home Loan Bank of San Francisco since August 1981. COFI is not an interest rate, but a ratio that reflects the interest expenses reported for a given month by the COFI reporting members. The COFI is computed from the book values of liabilities for all insured savings and loan institutions in the Eleventh District (institutions in California, Nevada, and Arizona). These liabilities include money on deposit at the institutions, loans obtained from a Federal Home Loan Bank and money borrowed from other financial institutions. The interest paid on these types of funds is the cost of these funds. The ratio of the dollar amount paid in interest during the month to the average dollar amount of the funds for that month is the weighted average COFI for that month.29 Mortgage lenders will periodically adjust the interest rate on adjustable rate mortgage loans based on this COFI. In countries like the UK and Australia with inflation targeting as one of the central banks’ core objectives, the instrument of monetary policy is a short-term interest rate that can be closely controlled by the central bank. The relevant interest rate for the UK is the ‘base rate’ and for Australia is the ‘cash rate’. They are also called the policy rates in the sense that they reflect the monetary policy stance of the central banks. In the UK, the BOE sets the base rate for its own dealing with the market and that rate then affects the whole pattern of rates set by the commercial banks for their savers and borrowers. For instance, two mortgage loan interest rates that are influenced by the movement of the base rate are the standard variable rate and the base rate tracker. For the standard variable rate mortgage, the lender’s variable interest rate charged

114 The Banking Sector in Hong Kong

to existing borrowers is set marginally higher than the base rate, and it usually varies in relation to the increase and decrease imposed by the BOE’s base rate. So if the base rate changes, the variable rate will change accordingly (although lenders can also choose not to pass rate changes on to their customers). The base rate tracker is a variable rate mortgage loan where the interest rate is a set amount above (or below) the BOE’s base rate for a fixed term period, and so its changes are always in line with (or ‘track’) changes in the BOE’s base rate. The base rate tracker thus removes part of the discretionary elements in the standard variable rate. In Australia, the cash rate is the market interest rate on overnight funds. The RBA exercises close control over the cash rate through its financial-market operations, so as to keep the cash rate at or near an operating target decided by the RBA. The cash rate is the rate charged on overnight loans between financial intermediaries. Movements in the cash rate are passed through quite quickly to the whole structure of deposit and lending rates. For example, mortgage and business loan rates tend to move broadly in line with movements in the cash rate. Thus, changes in monetary policy mean a change in the operating target for the cash rate, and hence a shift in the interest rate structure prevailing in the financial system.

Wong, Hui and Fung 115

Annex 6B A technical note on the construction of the effective deposit rate and the composite rate 30,31 Banks in Hong Kong obtain Hong Kong dollar funding from various sources. Broadly speaking, these sources can be categorized by funding from the retail market and from the wholesale market. Retail market funding consists of Hong Kong dollar deposits from non-bank customers,32 while wholesale market funding includes interbank borrowing from banks in Hong Kong and abroad.33 The funding costs incurred by banks can be assessed by the interest rates charged on the funding components from the retail and wholesale markets. Table 6B.1 presents the components which make up the average funding of banks and their associated interest rates. Figures 6B.1 and 6B.2 plot the interest rates associated with the different funding components from the retail and wholesale markets.

Table 6B.1

Major funding sources of banks and interest rates

Funding component1 Retail market Customers’ deposits Demand deposits Savings deposits Time deposits No more than 1 month Between 1 and 3 months Later than 3 months Wholesale market Interbank borrowing In Hong Kong On demand Within 3 months Later than 3 months From abroad On demand Within 3 months Later than 3 months

Interest rate2

Interest rate on demand deposits is assumed to be zero Average savings deposit rate Average rate for 1-week time deposits Average rate for 1-month and 3-month time deposits Average rate for 6-month and 12-month time deposits

Overnight HIBOR Average rate of 1-week, 1-month and 3-month HIBORs Average rate of 6-month, 9-month and 12-month HIBORs Overnight HIBOR Average rate of 1-week, 1-month and 3-month HIBORs Average rate of 6-month, 9-month and 12-month HIBORs

Notes: 1. The classification of funding components in customers’ deposits and interbank borrowing is based on ‘Return of Assets and Liabilities of an Authorized Institution’. 2. A detailed discussion of the various interest rates is given in sections 6B.1 and 6B.2.

116 % p.a. 10 Savings deposit rate 1-week time deposit rate average rate for 1 and 3 months deposits average rate for 6 and 12 months deposits

9 8 7 6 5 4 3 2 1 0 Jan-97

Jan-98

Figure 6B.1

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Jan-04

Jan-05

Interest rates of retail market funding

% p.a. 14 Overnight HIBOR Average of 1-week, 1-month and 3-month HIBORs Average of 6-month, 9-month and 12-month HIBORs

12 10 8 6 4 2 0 Jan-97

Jan-98

Figure 6B.2

Jan-99

Jan-00

Jan-01

Jan-02

Interest rates of wholesale market funding

Jan-03

Jan-04

Jan-05

Wong, Hui and Fung 117

The construction of the effective deposit rate (EDR) and the composite rate makes use of the above mentioned funding components and their corresponding interest rates.

Annex 6B.1

Effective deposit rate

The EDR is a measure of banks’ retail market funding costs. It is defined as the average interest rates on demand, savings and time deposits weighted by the Hong Kong dollar deposit composition of the entire banking sector. As shown in Table 6B.1, the deposit composition of the entire banking sector is as follows: 1. Demand deposits of licensed banks 2. Savings deposits of licensed banks 3. Time deposits of licensed banks, restricted licence banks and deposittaking companies, which are further classified into three groups based on their maturities: – No more than 1 month – Between 1 and 3 months – Later than 3 months. The interest rates on savings and time deposits of various maturities are the simple period average rates taken from Table 6.4.2 of the Monthly Statistical Bulletin (MSB). Currently, these average interest rates are calculated based on the daily quotations of eight selected banks.34 On a particular day, the interest rate on savings deposits is the simple average of the quoted savings deposit rates.35 The group of selected banks can be enlarged to include more banks to improve the representation. Criteria can be established and reviewed for the selection of these banks. For example, a group of banks, which have the largest market shares of deposits and as a whole represent the market, can be selected based on their average deposit sizes over the past 12 months. The group of selected banks can be reviewed annually. EDR is derived by summing the individual average interest rates on demand, savings and time deposits, weighted by their corresponding shares in the deposit composition as reported to the HKMA at monthend, based on the following equation:  EDR =

CCirm × IRrm i  CCirm

(6B.1)

118 The Banking Sector in Hong Kong Table 6B.2

Derivation of EDR (for April 2005) Average Deposit composition interest rate (month-end outstanding) of the month (% p.a.)1 (A) HK$ Share to million total (%) (B)

Demand deposits Savings deposits Time deposits No more than 1 month Between 1 and 3 months 1 month 3 months Later than 3 months 6 months 12 months

Weighted average rate (% p.a.) (A × B)

0.0002 0.098

240,117.7 953,412.6

0.12 0.48

0.0000 0.0470

0.1053⎫ 0.3014⎬ 0.260 ⎭ 0.342 ⎫ 0.6305⎬ 0.460 ⎭ 0.800

571,608.3

0.29

0.0305

148,776.4

0.07

0.0211

89,501.4

0.04

0.0252

EDR is

0.1238

Notes: 1. This is the period average interest rate on the deposits (less than HK$100,000) quoted by the eight selected banks. 2. The interest rate on demand deposits is assumed to be zero. 3. Since there is no breakdown on the deposit composition of less than 1-month time deposits, the interest rate taken is the average 1-week time deposit rate. 4. Since there is no breakdown on the deposit composition of 1-month and 3-month time deposits, the interest rate taken is the simple average rate of 1-month and 3-month time deposit rates. 5. Since there is no breakdown on the deposit composition of time deposits with maturity later than 3 months, the interest rate taken is the simple average rate of 6-month and 12-month time deposit rates.

where CCirm is the i funding component from the retail market, IRrm i represents the corresponding interest rate of the i funding component from the retail market (as shown in Table 6B.1 under the heading  ‘Retail market’) and CCirm is the sum of all funding components from the retail market. Table 6B.2 illustrates the derivation of EDR for a particular month. Note that the interest rates used in the derivation of EDR as reported in the main text of the chapter are slightly different from those presented in Table 6B.2. In the main text of the chapter, for simplicity, the 1-month time deposit rate is used to proxy the interest rate for deposits with maturity less than 1 month. The 3-month time deposit rate is used to proxy the rate for deposits with maturity between one month and three months. Figure 6B.3 presents the profile of EDR, as composed based on the calculation method illustrated in Table 6B.2.

Wong, Hui and Fung 119 % p.a. 7 6 5 4 3 2 1 0 Jan-97

Jan-98

Figure 6B.3

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Jan-04

Jan-05

EDR

Annex 6B.2

The composite rate

The composite rate is a measure of banks’ wholesale and retail funding costs. It is the average interest rates of HIBOR and EDR weighted by the amount of Hong Kong dollar interbank borrowing from the wholesale market and the Hong Kong dollar deposits obtained from the retail market.36 As shown in Table 6B.1, interbank borrowing includes the following items:37 1. Amount due to Authorized Institutions in Hong Kong (MSB Table 4.2), which can be further categorized into: – payable on demand and money at call – repayable or callable within 3 months – repayable or callable later than 3 months 2. Amount due to banks abroad (MSB Table 3.9.1). While the MSB table only shows the total amount, the ‘Return of Assets and Liabilities of an Authorized Institution’ has breakdowns with categories similar to that of the amount due to Authorized Institutions in Hong Kong. The interest rates used for the derivation of EDR are discussed in the previous section. The interest rates for various categories of interbank borrowing are the period average of HIBORs taken from the MSB Table 6.3.2. Similar to the derivation of EDR, the average HIBORs quoted

120 The Banking Sector in Hong Kong

by a group of selected banks can be used in the calculation. Alternatively, Hong Kong Dollar Interest Settlement Rates, which are fixed by the HKAB, can be used for the calculation of the composite rate. The composite rate is derived by summing the individual average interest rates on HIBORs, demand, savings and time deposits, weighted by their corresponding shares in the combined interbank borrowing and customers’ deposits as reported to the HKMA at the end of each month, based on the following equation:38  Composite rate =

Table 6B.3

CCi × IRi  CCi

(6B.2)

Derivation of the composite rate1 (for April 2005)

Funding components

Retail Market EDR2 Wholesale Market Interbank borrowing In Hong Kong (total) On demand3 Within 3 months4 Later than 3 months5 From abroad (total)6 On demand Within 3 months Later than 3 months Total funding (retail + wholesale)

Amount (HK$ mn)

Share to total (%) (A)

Interest rate (% p.a.) (B)

Weighted average rate (% p.a.) (A) × (B)

2,003,416

0.81

0.12

0.0972

311,205 33,791 240,168 37,246 146,241

0.13 0.01 0.10 0.02 0.06

1.36 1.98 2.61 2.25

0.0136 0.1980 0.0522 0.1350

2,460,862 The Composite rate is

0.4960

Notes: 1. This table provides an illustration of the derivation of the composite rate which is slightly different from the one composed in the main text of the chapter. 2. The EDR is the derived figure in Table 6B.2. 3. The interest rate for interbank borrowing callable on demand is the overnight HIBOR. 4. Since there is no breakdown on interbank borrowing callable within three months, the interest rate taken is the simple average rate of 1-week, 1-month and 3-month HIBORs. 5. Since there is no breakdown on interbank borrowing callable later than three months, the interest rate taken is the simple average rate of 6-month, 9-month and 12-month HIBORs. 6. The amount of Hong Kong dollar interbank borrowing from abroad is from MSB Table 3.9.1, which is the total amount and no breakdown is available. For illustration, the interest rate is assumed to be the 3-month HIBOR. If breakdowns of interbank borrowing from abroad are available, the specific interest rates should apply to these breakdowns as indicated in Table 6B.1.

Wong, Hui and Fung 121

where CCi is the i funding component from the retail or wholesale markets, IRi represents the corresponding interest rate of the i funding  component (as shown in Table 6B.1) and CCi is the sum of all components from the two markets. Table 6B.3 presents the derived composite rate for a particular month. From Table 6B.3, it is shown that the shares of customers’ deposits, interbank borrowing in Hong Kong and from abroad used for the calculation of the composite rate are 81 per cent, 13 per cent and 6 per cent respectively. Figure 6B.4 illustrates the profile of the composite rate. % p.a. 10 9 8 7 6 5 4 3 2 1 0 Jan-97

Jan-98

Figure 6B.4

Jan-99

Jan-00

The composite rate

Jan-01

Jan-02

Jan-03

Jan-04

Jan-05

Yes

Yes

Base rate

EFN3

Yes

Yes

Yes The concept is not difficult to understand, but it is complex than the others Same as EDR

Yes

Simple and transparent

Simple

Simple

Simple Requires compilation by the HKMA, but only a small amount of additional work would be needed Same as EDR

Simple

Administrative simplicity

A weighted average of HIBOR3 and retail deposit rates, which are largely market determined Rule-based, not entirely market determined Market determined

Market determined A weighted average of retail deposit rates which are largely market determined

Largely market determined

Rate setting: market determined or rule-based

0.40

0.11

6

5

2

1 3

0.463 0.21

0.27

4

Desirability per risk management purposes2

0.10

Volatility of monthly payment burden1

Notes: 1. Volatility (in %) is defined as the average monthly changes (in absolute term) in the reference rate over the specific period from January 1997 to April 2005. The higher the figure, the higher is the volatility. 2. The ranking is based on the assessments in section 6.3.2.2. The lower the ranking, the higher is the desirability. 3. If the Asian financial crisis period is excluded, the volatility of HIBOR3 (for the period from January 1999 to April 2005) reduces to 0.23, which is compatible to that of other possible reference rates ranging from 0.12 to 0.29 under the same period.

Yes, compiled by the HKMA

Used to be a single rate, but recently banks have started to quote different BLRs Yes Yes, compiled by the HKMA

A single rate in the market and for all banks

Relative features of alternative reference rates

Composite rate

HIBOR3 EDR

BLR

Annex 6C 122

Wong, Hui and Fung 123

Annex 6D A quantitative assessment of the approximation of alternative reference rates as a measure of average cost of funds With monthly average interest rate data, a simple linear regression model is used to assess the property of the alternative reference rates as a good measure of the average cost of funds in the banking sector. In the analysis, the changes in pricing due to competition and changes in operating costs are assumed to be the same under the various scenarios of using different reference rates. To avoid the wide fluctuation in reference rates during the Asian financial crisis period, which is rare and extraordinary, the Table 6D.1 Estimation results (from January 1999 to April 2005) (Specification: Mortgage Ratet = Constant + Alternative reference ratet ) Alternative reference rate

Adjusted R-squared

Composite rate HIBOR3 EDR BLR EFN3 Base rate

0.93 0.92 0.91 0.86 0.85 0.84

Actual and fitted mortgage rates % p.a. 10 9 8 7 Fitted mortgage rate

6 5 4 3

Actual mortgage rate

2 1 0 Jan-99 Figure 6D.1

Jan-00

Jan-01

Jan-02

Based on the composite rate

Jan-03

Jan-04

Jan-05

124 The Banking Sector in Hong Kong

regression estimation starts from January 1999 to April 2005. Only the adjusted R-squared statistics are reported. Figures 6D.1 to 6D.6 show the actual and fitted mortgage rates, based on the above model specification. % p.a. 10 9 8 7 Fitted mortgage rate

6 5 4 3

Actual mortgage rate

2 1 0 Jan-99 Figure 6D.2

Jan-00

Jan-01

Jan-02

Jan-03

Jan-04

Jan-05

Based on HIBOR3

% p.a. 10 9 8 7 6 Fitted mortgage rate

5 4 3

Actual mortgage rate

2 1 0 Jan-99 Figure 6D.3

Jan-00

Jan-01

Based on EDR

Jan-02

Jan-03

Jan-04

Jan-05

125 % p.a. 10 9 8 7 6 Fitted mortgage rate 5 4 3 2 1 0 Jan-99 Figure 6D.4

Actual mortgage rate

Jan-00

Jan-01

Jan-02

Jan-03

Jan-04

Jan-05

Based on BLR

% p.a. 10 9 8 7 Fitted mortgage rate

6 5 4 3 2 1 0 Jan-99 Figure 6D.5

Actual mortgage rate

Jan-00

Jan-01

Based on EFN3

Jan-02

Jan-03

Jan-04

Jan-05

126 % p.a. 10 9 8 7 6 Fitted mortgage rate 5 4 3 2 1 0 Jan-99 Figure 6D.6

Actual mortgage rate

Jan-00

Jan-01

Based on the base rate

Jan-02

Jan-03

Jan-04

Jan-05

Wong, Hui and Fung 127

Annex 6E Simulation of interest margin for the loan portfolio acquired in January 1999 under the scenario of different reference rates Interest rate margin (in per cent) 7 BLR

Base rate

EDR

6 5 4 3 Composite rate 2 EFN3

HIBOR3

1 0 Jan-99 Figure 6E.1

Jan-00

Jan-01

Jan-02

Jan-03

Jan-04

Jan-05

Cost of funds represented by the composite rate

Interest rate margin (in per cent) 7 6 5

BLR Base rate

HIBOR3

4 3 Composite rate

2

EDR EFN3

1 0 Jan-99 Figure 6E.2

Jan-00

Jan-01

Jan-02

Jan-03

Cost of funds represented by HIBOR3

Jan-04

Jan-05

128 The Banking Sector in Hong Kong

Notes 1. The analysis of this chapter covers the market situation up to May 2005, and uses data up to that month. 2. In this chapter, BLR-related deposits refer to retail deposits (such as savings deposit rates) of which the interest rates move largely in tandem with the BLR. 3. See Chapter 5. 4. The interest rates are monthly average rates, covering data up to May 2005. Using daily data, the 3-month HIBOR was in fact at par with LIBOR by the end of May 2005. 5. Although the BLR was not part of the IRR, it was in most cases adjusted along with changes in retail deposit rates. When differences in the movements of BLR and HIBORs emerged, in the trade-off between variability of interest margins and the maintenance of market shares, the smaller banks usually chose to accept a degree of margin variability (sometimes a squeeze in the margin of the existing mortgage portfolios), in order to maintain market shares. 6. A few small and medium-sized banks raised their BLR by 25 bps in early April amid rising interbank rates, while the three big banks with large retail customers’ deposits did not adjust their BLR. Instead, they raised their effective mortgage rates to a level compatible to these small and medium-sized banks by increasing the mark-ups slightly and eliminating cash rebates to mortgage borrowers. 7. Some banks proposed alternative reference rates which are either based on HIBORs or the base rate of the Hong Kong Monetary Authority (HKMA). However, some other banks still consider that the BLRs should be used as the reference rate. 8. See D. B. Diamond, Jr. and M. J. Lea, ‘Housing Finance in Developed Countries: An International Comparison of Efficiency’, Journal of Housing Research, 3(1) (1992) 1–271 and European Central Bank, ‘Structural Factors in EU Housing Markets’, March (2003). 9. See European Central Bank, ‘Structural Factors in EU Housing Markets’, March (2003). 10. The use of similar interest rates of different maturities as reference rates can also be examined. For simplicity, only these rates with the specific maturity as listed are assessed in this chapter. 11. A detailed discussion of the construction of EDR and the composite rate is given as a technical note in Annex 6B. 12. The amount of interbank borrowings is taken from the Monthly Statistical Bulletin and refers to the Hong Kong dollar borrowings by Authorized Institutions in the local interbank market and abroad regardless of maturity. 13. Another way of calculating banks’ cost of funds is the one adopted by the Federal Home Loan Bank of San Francisco in the US for the calculation of the Eleventh District Cost-of-Funds Index. For details of its calculation, as well as the advantages and drawbacks of the use of such an index, please refer to Annex 6A and Note 29. 14. This may change over time as Exchange Fund Notes are now being issued specifically for retail investors.

Wong, Hui and Fung 129 15. The patterns of derived mortgage rates based on EFN3 and the base rate are not shown here. Their relative performances as compared with HIBOR3, EDR and the composite rate are similar to those represented by the figures in Table 6.2. 16. In the analysis, the changes in pricing due to competition and changes in operating costs are assumed to be the same under the various scenarios of using different reference rates. 17. It should be noted that the use of the base rate of the HKMA is different from the policy rates of other central banks, such as the base rate of the Bank of England or the cash rate of the Reserve Bank of Australia. In the UK and Australia, their policy rates are used as a monetary policy instrument to influence the short-term interest rates, and thus the interest rate structures in the respective financial markets (see Annex 6A for a discussion of these policy rates). On the other hand, under the Currency Board system in Hong Kong, the base rate of the HKMA mainly follows the interest rate movement in the US. 18. For example, the base rate was raised eight times from June 2004, but the short-term interbank rates fell to their low levels up to early January this year, before rising in the subsequent months. 19. Under extraordinary situations, the base rate could rise to a level as high as HIBOR3. This makes mortgage loans using the base rate as the reference rate suffer from the same interest rate risk as using HIBOR3 as the reference rate. 20. This asymmetry works clearly against borrowers. Note also that if the base rate is used as a reference rate, any revision of the formula of setting the base rate in the future would need to consider the reaction from the mortgage market. 21. For a detailed study regarding the derivation of the estimated squeezes in interest margins, please refer to Chapter 5. 22. Such as using the monthly or quarterly average of the daily rates. 23. For example, the monthly average rate in March announced on the first day of April can be used for the pricing of new mortgage loans and the re-pricing of existing loans throughout April. 24. The change will be assessed on a cumulative basis. For example, if the reference rate increases from 3 per cent in the previous month to 3.24 per cent in the current month, no change will be made on the mortgage rate. However, the mortgage rate will be adjusted when the composite rate increases by cumulatively more than 25 bps, say to 3.3 per cent in the following month. Using a mark-up of two percentage points as an illustration, the mortgage rate would be at 5 per cent in the previous month. The rate would not be changed in the current month, but will be raised by 30 bps to 5.3 per cent in the following month. 25. The mortgage rate would need to be changed by 16 times if the adjustments are made based on the changes in the daily composite rate. 26. Detailed arrangements should be worked out by the industry, if an alternative reference rate is to be adopted. 27. To avoid imposing additional administrative burden on banks, the standard reference rate can be calculated and announced through specific arrangements. Similar to their current practice, banks just need to set a mark-up over this standard reference rate when pricing their mortgage products. This

130 The Banking Sector in Hong Kong

28.

29.

30.

31.

32. 33.

34.

35.

36.

37.

arrangement also facilitates banks in their management of interest rate risk because a standard reference rate is provided and instruments for hedging purpose, such as deposits with interest rates based on the reference rate, can be developed. There would also be costs for system changes, documentation, public relations, calculation and dissemination of the new reference rate. The cost could be significant if customers are allowed to make a choice to switch their existing contracts (mostly set against BLR) to contracts based on the new reference rate. One of the advantages of using the actual dollar amount paid in interest during the month when calculating the COFI is that it reflects more accurately the average funding costs incurred by the reporting institutions. However, it would involve additional information from the reporting institutions and it may further widen the time gap between data collection and the release of the COFI. This technical note provides a detailed description on the construction of the effective deposit rate (EDR) and the composite rate. Note that while the actual derivation of the EDR and the composite rate used in the main text of the chapter is a simplified version of the methodology described in this annex, the underlying concepts are the same. Another way of calculating banks’ cost of funds is the one adopted by the Federal Home Loan Bank of San Francisco in the US for the calculation of the Eleventh District Cost-of-Funds Index. For details of its calculation, as well as the advantages and drawbacks of using such index, please refer to Annex 6A and Note 29. In this chapter, all non-bank customers’ deposits, regardless of their size, are classified as retail market funding. Other funding sources such as the negotiable debt instruments issued by banks and amounts payable under repo are not being considered in the analysis. The eight selected banks are HSBC, Hang Seng Bank, Standard Chartered Bank, Bank of China (Hong Kong), Bank of East Asia, DBS Bank, Citibank and Nanyang Commercial Bank. Note that in this chapter, the average interest rates for the groups of banks are the simple averages of their quoted rates. Alternatively, weighted rates can be calculated based on the actual shares of individual banks’ deposit base. Note also that for some banks, the quoted interest rates and the interest rates actually offered to clients may differ. When possible, the actual rates should be used in the calculation. On the calculation of the composite rate, some banks suggested that other Hong Kong dollar funding should be included such as those Hong Kong dollar funds obtained through Hong Kong dollar/US dollar swaps and, therefore, the weights of HIBORs in the formula should be upward adjusted. They also suggested that, if the average rate is to be calculated as a weighted average rate by the shares of individual banks’ deposit base, there should be an upper bound for the weights assigned to individual banks, in order to avoid the dominance of the rates quoted by a few banks. The classification of interbank borrowing is based on ‘Return of Assets and Liabilities of an Authorized Institution’.

Wong, Hui and Fung 131 38. Note that the components and interest rates used in the derivation of the composite rate as illustrated in Table 6B.1 and equation (6B.2) are slightly different from the composite rate reported in the main text of the chapter. In the main text of the chapter, for simplicity, the 1-month time deposit rate is used to proxy the interest rates for deposits with maturity less than one month. The 3-month time deposit rate is used to proxy the rate for deposits with maturity between one month and three months. In addition, 3-month HIBOR is the interest rate for interbank borrowing, regardless of the repayable periods. Nevertheless, the difference does not affect the analysis in the main text of the chapter.

7 Residential Mortgage Default Risk in Hong Kong Jim Wong, Laurence Kang-Por Fung, Tom Pak-Wing Fong and Angela Sze

7.1 Introduction The sharp fall in property prices following the Asian financial crisis has led many residential mortgage holders in Hong Kong to experience negative equity. At the end of September 2004, there were about 25,400 loans with a market value lower than the outstanding loan amount. The total value of these loans was HK$43 billion. The mortgage delinquency ratio reached a peak of 1.43 per cent in April 2001. While it has improved since the second half of 2001, the delinquency rate in September 2004, at 0.47 per cent, is still higher than 0.29 per cent in June 1998 when data were first collected.1 Given that residential mortgage lending represents a significant component of bank assets, how borrowers’ decisions to default are affected by the negative equity position of their mortgages is of interest to policy makers.2 This study utilizes micro-level mortgage loan data to examine the determinants of residential mortgage default risk in Hong Kong, and the effect of changes in these determinants, in particular the current loanto-value (CLTV) ratio, on default probabilities. A preliminary attempt is also made to assess the impact of macroeconomic variables on default probability. Overall, the results suggest that the CLTV ratio is central to mortgage default decisions. The study finds that default probability is positively correlated with the CLTV ratio, as well as with interest rates and the unemployment rate, and negatively correlated with changes in stock prices. The remainder of the chapter is organized as follows. Section 7.2 provides a brief review of the theoretical framework in explaining mortgage default behaviour. Section 7.3 discusses the specification of the logit model and the data for empirical estimations. The estimation results 132

Wong, Fung, Fong and Sze 133

are summarized in section 7.4. Simulations to estimate the impact of the variation in CLTV ratio on default probabilities are given in section 7.5. Section 7.6 introduces two macroeconomic variables, the unemployment rate and changes in stock prices, into the model. Section 7.7 simulates how a relaxation of the maximum 70 per cent loan-to-value (LTV) ratio guideline on mortgage lending may affect banks’ asset quality. Concluding remarks are provided in the final section.

7.2 Theoretical background and literature review There are two main views relating to home mortgage default behaviour ( Jackson and Kasserman 1980). The equity theory of default holds that borrowers base their default decisions on a rational comparison of financial costs and returns involved in continuing or terminating mortgage payments.3 An alternative is the ability-to-pay theory of default (the cash flow approach), according to which mortgagors refrain from loan default as long as income flows are sufficient to meet the periodic payment without undue financial burden. Under the equity theory, the CLTV ratio, which measures the equity position of the borrower, is considered to be the most important factor impacting on default decisions. By contrast, under the ability-to-pay model, the current debt servicing ratio (CDSR), defined as the monthly repayment obligations as a percentage of current monthly income, which captures the repayment capability of the borrower, plays a critical role in accounting for defaults. More recently, research has attempted to incorporate trigger events, such as divorce, loss of a job, and accident or sudden death, in influencing default behaviour (Riddiough 1991). In the simple model, some defaults may be driven by a sudden drop or loss of income caused by unemployment, job shift or a sudden increase in expenses such as medical fees. Furthermore, there was also empirical evidence that transaction costs were present in default decisions (Vandell 1990, 1992; Riddiough and Vandell 1993). For instance, borrowers may consider the value of their reputation and credit rating when deciding on whether to default or not. A final issue relates to the lender’s influence on default decisions. Workout plans helping borrowers who are faced with financial hardships to overcome payment difficulties have long provided an alternative to default. Upon consideration of the financial health of the borrower, the lender may respond in different ways to the threat of a possible default, such as loan restructuring, mortgage recourse, and the adoption of extended repayment plan or refinancing.4 In Hong Kong’s case, post-foreclosure debt collections and possible initiation of a bankruptcy

134 The Banking Sector in Hong Kong

petition by creditors are believed to be the major deterrent to default. Transaction costs and lender’s influence are clearly part of the reasons why a borrower does not default when the value of the property falls below the outstanding amount of the mortgage loan. Earlier empirical work has not come to firm conclusions regarding the relative importance of equity and affordability in mortgage default behaviour. While most of the literature finds the equity position to be the primary determinant in mortgage default decisions, some studies argue that non-equity effects, such as the source of income, are more significant. The importance of the LTV ratio can be overstated if other variables are excluded from the empirical specification. In general, there are two approaches taken in the empirical literature on mortgage defaults. One approach is to relate individual mortgage defaults to loan and borrower characteristics as well as macroeconomic variables. The alternative is to relate aggregate measures of default incidence to macroeconomic variables. While most previous studies apply individual mortgage data for empirical investigations of mortgage defaults, there exists a limited literature on empirical analysis using aggregate data. There are several studies that look into the residential mortgage market in Hong Kong. However, these studies concentrate mainly on explaining the characteristics of the mortgage terms such as mortgage tenors and variable payments, fixed versus floating rate loans and mortgage rates.5 Few have focused on the default risk of mortgage loans.

7.3 Methodology and data 7.3.1 Model specification Research on mortgage default or prepayment behaviour using microlevel data is typically based on techniques for survival analyses and duration modelling. An alternative approach, where survival time is less an issue, is to estimate binary choice models for a particular study period. Following many previous studies, this chapter applies the logit model to explain mortgage defaults, which is a binary (0/1) dependent variable.6

(a) The logistic function In general, if the default probability (P(Y)) is a linear function f of a vector of explanatory variables x, where x includes loan-related and

Wong, Fung, Fong and Sze 135

non-loan-related variables, under the logistic distribution, the default probability can be specified as: P(Y = default) =

ef (x) 1 + ef (x)

(7.1)

and f (x) = c + β1 X1 + β2 X2 + · · · + βn Xn where c is the constant term, Xi is the explanatory variable and βi is the coefficient.

(b) Dependent variable The dependent variable is the default status of a loan. A mortgage loan is defined as a default case in this study if it is overdue for more than 90 days.7 The Hong Kong Monetary Authority (HKMA) defines delinquency to be loans overdue for more than three months, and the Hong Kong Mortgage Corporation (HKMC) uses 90 days as the benchmark. Based on this definition of default, the dependent variable used in the logit model is equal to one if the loan becomes overdue for more than 90 days in the study period and zero otherwise.

(c) Explanatory variables Both loan-related and non-loan-related factors are used as explanatory variables.8 Reflecting the structure of Hong Kong’s mortgage market and data availability, the following explanatory variables are included in the model (see Table 7.1).9 As for loan-related factors, the inclusion of the CLTV ratio and CDSR has been discussed in the preceding section. Other loan-related factors include the LTV ratio and the debt servicing ratio at origination (ODSR). One view is that as banks only offer loans with a high LTV ratio and ODSR to mortgagors with good credit standing and payment ability (such as having a stable job), such loans should correspond to lower default risks. The alternative view is that as less wealthy mortgagors tend to borrow a larger amount of loan and at a higher ODSR, a higher LTV ratio or ODSR should point to higher default risks. The signs of these two variables are thus ambiguous. Non-loan-related factors include seasoning variables and propertyrelated variables such as the property area, current unit property price and the age of the property.10 The seasoning of the mortgage is expected to have a negative sign, as the longer one has served the mortgage, the

136 The Banking Sector in Hong Kong Table 7.1 Explanatory variables for the logit model Abbreviation

Expected sign4

OLTV CLTV CLTVSQ ODSR CDSR Mortgage

+/− + − +/− + +

Seasoning – Expected seasoning at origination (months) – Seasoning up to the study period (months)

Oseason Season

+/− −

Property – Property area (sq. ft.) – Current unit property price (HK$)3 – Age of property (months) – Age of property squared

Garea Price Oage Oagesq

+/− +/− +/− +/−

Loan-related factors – Loan-to-value ratio at origination (%) – Current loan-to-value ratio (%) – Current loan-to-value ratio squared – Debt servicing ratio at origination (%) – Current debt servicing ratio (%)1 – Mortgage rate (%)2 Non-loan-related factors

Notes: 1. CDSR is derived as the payment in the current month divided by the estimated income in the current month. Monthly income at origination is estimated by mortgage payment for the first month divided by the ODSR. Income in the current month is derived by adjusting the estimated monthly income at origination by the nominal wage index. 2. The mortgage rate variable is given by best lending rate (BLR) plus mortgage rate spreads. 3. Defined as the current price of the property per sq ft. 4. Expected signs indicated are based on theoretical deliberations and previous empirical findings.

less likely one will default. The signs of the other property-related variables could be positive or negative. Two explanatory variables, the CLTV ratio and the age of the property, are included in the model in squared terms as well to capture the potential non-linearity effect of these variables on default probabilities. They have negative signs in most previous studies (in contrast to the signs of the original variables), suggesting the existence of non-linearity.

7.3.2 Sources of data and data characteristics Micro-level loan data are obtained from the HKMC. The HKMC purchased a total of 19,176 mortgage loans from Authorized Institutions (AIs) during the period between its incorporation in March 1997 and September 2003. As at the end of 2003, the loan portfolio of HKMC totalled HK$9.8 billion, equivalent to 1.9 per cent of all mortgages extended by AIs in Hong Kong. There exist two types of data for each

Wong, Fung, Fong and Sze 137 (%) 2.0 Industry (delinquency ratio, including rescheduled loan ratio) Industry (delinquency ratio) 1.6 HKMC (delinquency ratio) 1.2

0.8

0.4

0.0 Jun-98 Figure 7.1

Jun-99

Jun-00

Jun-01

Jun-02

Jun-03

Mortgage delinquency rate in Hong Kong

Note: Information of rescheduled loans of HKMC’s portfolio is not available. Sources: HKMA and HKMC Monthly Mortgage Portfolio Statistics.

loan: information at origination and the dynamic record. Information at origination includes those loan- and property-related data listed in Table 7.1. The dynamic record includes data of payment history, CLTV ratio over time, mortgage rate spreads over time and the delinquency status. It should be noted that HKMC’s mortgage portfolio appears to be of better quality compared with the industry average, which is reflected by the fact the delinquency rate has consistently been lower than that of the industry (see Figure 7.1). As the current study utilizes only loan data from the HKMC, inference regarding the overall market drawn from findings of this study should be made with caution. In particular, the default probabilities estimated in this chapter are likely to be lower than the industry average.

7.3.3 Sample periods The study covers the period from July 2000 to September 2003. As the HKMC acquired loans from different AIs throughout the period and market conditions have been changing all the time, in order to capture more comprehensively information in the portfolio, ‘snapshots’ are taken in January and July of each year to examine loan delinquencies. Data in a

138 The Banking Sector in Hong Kong Table 7.2 Number of loan cases No. of loans

July 2000

Jan. 2001

July 2001

Jan. 2002

July 2002

Jan. 2003

July 2003

Sep. 2003

Total

6,622

8,199

7,256

6,320

5,698

8,861

9,317

9,087

selected month by themselves are utilized to examine the determinants of default in that particular month. A loan is considered as a default case if it is overdue for more than 90 days during that month. Table 7.2 shows the total number of loan cases in each of the samples.

7.4 The model and estimation results 7.4.1 The model In the initial process, models specified to have various combinations of the explanatory variables listed in Table 7.1 are examined. We start with models focusing on the CLTV ratio and CDSR. The inclusion of the CLTV ratio is based on the equity theory while the CDSR is used to test the ‘ability-to-pay’ hypothesis. All other variables, in different combinations, are also included in the model specification. Contrary to expectation, the models with CDSR as one of the explanatory variables are unsatisfactory (see Annex 7A). Specifically, the estimated coefficients of CDSR are either statistically insignificant in some snapshot months, or are sometimes unexpectedly negative. This could be due to the data quality of the derived CDSR.11 Moreover, as some of the mortgagors may have other debt obligations, such as car loans and other consumer loans, the data of CDSR derived from the mortgage records may not reflect their complete payment burden. Furthermore, possible reductions in salaries, changes of job, or layoff of the borrower since the origination of the loan may also affect the accuracy of the data significantly.12 The regression findings in Annex 7A should thus not be interpreted as suggesting that CDSR is not a factor determining default risk. In view of this, mortgage rates are used to proxy CDSR. These current mortgage rates differ quite significantly among customers even for the same snapshot, as different spreads are charged on customers of different credit worthiness. For example, the mortgage spreads charged on July 2003 ranged from five percentage points to −2.65 percentage points and have a median of −1.75 percentage points. As shown in Annex 7B, this modification leads to improved results. The estimated coefficients for the

Wong, Fung, Fong and Sze 139

CLTV ratio and the mortgage rate are both statistically significant and have an expected positive sign. On the other hand, most non-loan factors (seasoning and property variables) are statistically insignificant, and they are therefore dropped from the subsequent statistical analysis. Note that the variables of squared property age and squared CLTV are statistically insignificant, suggesting that in Hong Kong’s case non-linearity in these two variables is not an issue.

7.4.2 Estimation results Logistic regressions are then performed on models with the CLTV ratio and the mortgage rate as core variables together with different combinations of other variables. The model specifications which yield the best results are adopted and further analysed. The estimation results of the standard model are given in Table 7.3. As can be seen from the table, the estimated coefficients for CLTV ratio and the mortgage rates are both statistically significant and have an expected positive sign in all the eight snapshot months. The results suggest the higher the CLTV ratio of a loan, the greater is the default probability, and the higher the mortgage rate, which implies a relatively heavier payment burden for the borrower, the greater is the likelihood of default. This lends support to both the ‘equity theory’ and the ‘ability-to-pay’ approaches of explaining default decisions. The estimated coefficients of current unit property price variable are negative in most of the snapshot periods. This suggests that mortgage loans on properties at the luxury end of the market are less likely to experience default. The estimated parameters are not easily interpretable, and, in particular, cannot be used in the same way as the parameters in linear regression. As shown in equation (7.1), the default probability is a non-linear function of the independent variables and there is no simple way to express the effect on the default probability of changing the independent variables. One way to express the effect is to derive the relationship of default probability and the level of CLTV ratio by holding the other variables at their mean levels. This is discussed in greater detail in section 7.5.

7.4.3 Diagnostic checks The Wald test statistics test the null hypothesis that all the coefficients in the model are zero are highly significant, indicating that all estimated coefficients are statistically different from zero. The Pseudo R2 statistics range from 0.16 to 0.26, which are low but common in micro-level

–

−20.96 (0.00) 68.78 (0.00) 0.26 −128.00

8,074 (0.00)

–

−23.93 (0.00) 28.78 (0.00) 0.23 −88.80

12,658 (0.00)

Percentage Change of Hang Seng Index Constant

3,246 (1.00)

−16.53 (0.00) 109.67 (0.00) 0.25 −155.30

–

0.06 (0.82) 0.04 (0.00) 1.02 (0.00) –

3,310 (1.00)

−11.78 (0.00) 109.38 (0.00) 0.21 −177.40

–

−0.10 (0.51) 0.02 (0.00) 0.90 (0.00) –

3,454 (1.00)

−9.35 (0.00) 93.28 (0.00) 0.17 −203.90

–

−0.28 (0.10) 0.02 (0.00) 0.73 (0.00) –

3,531 (1.00)

−10.32 (0.00) 162.66 (0.00) 0.24 −219.20

–

−0.39 (0.02) 0.02 (0.00) 0.89 (0.00) –

5,643 (1.00)

−8.64 (0.00) 152.46 (0.00) 0.20 −281.60

–

−0.48 (0.00) 0.01 (0.00) 0.77 (0.00) –

6,071 (1.00)

−8.61 (0.00) 159.75 (0.00) 0.16 −325.60

–

−0.22 (0.05) 0.01 (0.00) 0.63 (0.00) –

50,754 (1.00)

−12.75 (0.00) 708.45 (0.00) 0.18 −1,646.20

−0.24 (0.00) 0.02 (0.00) 0.37 (0.00) 0.49 (0.00) −0.15 (0.00)

50,754 (1.00)

−12.75 (0.00) 330.63 (0.00) 0.18 −1,646.20

−0.24 (0.08) 0.02 (0.00) 0.37 (0.00) 0.49 (0.00) −0.15 (0.00)

July 2000 to Sep. 2003B

N.A.

−13.70 (0.00) 676.58 (0.00) 0.18 −1,598.10

−0.30 (0.00) 0.02 (0.00) 0.39 (0.00) 0.66 (0.00) −0.13 (0.00)

July 2000 to Sep. 2003C

Notes: 1. For a discussion of the models with macroeconomic variables, please see Section 7.6. The estimation result A refers to the regression using data without adjustment. The estimation results B and C refer to the regressions using variance-adjusted and weight-adjusted methods respectively. For the weight-adjusted method, the goodness-of-fit test statistic is not available. 2. Numbers in parentheses are p-values.

Pseudo R2 Log- Pseudo Likelihood Goodness-of-fit Test

Wald Test

0.21 (0.24) 0.04 (0.00) 1.13 (0.00) –

July 2000 Jan. 2001 July 2001 Jan. 2002 July 2002 Jan. 2003 July 2003 Sep. 2003 July 2000 to Sep. 2003A

Estimation results

0.28 (0.20) CLTV 0.05 (0.00) Mortgage 1.23 (0.00) Unemployment –

Price

Variables

Table 7.3

Wong, Fung, Fong and Sze 141

analyses.13,14 The Pearson chi-squared (χ2 ) goodness-of-fit tests indicate that the selected model does not differ from the theoretical distribution for most of the selected months. Results for the goodness-of-fit test are satisfactory in general. There are concerns about the multicollinearity between the variables CLTV ratio and mortgage rate. As the correlation coefficient of the two variables is estimated to be −0.05, the issue of multicollinearity between the two variables does not appear to be a problem.

7.5 Default probability and the level of CLTV With the estimated results, the relationship between default probability and the level of CLTV ratio, holding other explanatory variables at their mean levels, can be derived based on equation (7.2).15,16 ⎛

ˆ P(Y = default)

X2 =X 2 , X3 =X 3 , ... , Xn =X n

⎜ ln⎝

=

e

1−P ⎛

⎜ ln⎝

1+e

⎞

P

⎟ ˆ ⎠+β1 (X1 −X 1 )

P 1−P

⎞

(7.2)

⎟ ˆ ⎠+β1 (X1 −X 1 )

where P is the average default probability, X 1 is the mean level of the CLTV ratio and βˆ 1 is the estimated coefficient for the ratio. By holding all other variables at their mean levels for all months, the default probability of loans at different levels of CLTV (up to the upper end of the actual CLTV level) for respective months is derived and presented in Figure 7.2. An enlarged graphical exhibition of simulations up to the CLTV level of 150 per cent is given in Figure 7.3 for detailed inter-period comparison.17 The estimated default probabilities at selected CLTV levels are listed in Table 7.4. It is found that they differ significantly at the same level of CLTV for different months. For instance, when the level of CLTV is 150 per cent, the expected probability of default ranges from 0.48 per cent (for January 2003) to 0.99 per cent (for September 2003). The diversity in results may be due to the variations of macroeconomic conditions in different months.

7.6 Estimated default probability and macro variables In some studies, data on residential mortgages in different regions were matched with economic variables in the corresponding regions to assess

142 Default prob. (%) 20 Jul-00 Jan-01 Jul-01 Jan-02 Jul-02 Jan-03 Jul-03 Sep-03

16

12

8

4

0 0

50

100

150

200

250

300

CLTV (%) Figure 7.2 Default probability and CLTV ratio by snapshot month (with other explanatory variables held at mean levels)

Default prob. (%) 1.0 Jul-00 Jan-01 Jul-01 Jan-02 Jul-02 Jan-03 Jul-03 Sep-03

0.8

0.6

0.4

0.2

0.0 0

30

60

90

120

150

CLTV (%) Figure 7.3 Default probability and CLTV ratio (an enlarged graphical exhibition of Figure 7.2)

Wong, Fung, Fong and Sze 143 Table 7.4 Estimated default probability at different CLTV levels Default probability (%) CLTV Level (%)

July 2000

Jan. 2001

July 2001

Jan. 2002

July 2002

Jan. 2003

July 2003

Sep. 2003

50 75 100 125 150 175 200

0.00 0.02 0.05 0.18 0.59 1.96 6.29

0.01 0.03 0.08 0.21 0.56 1.47 3.80

0.02 0.06 0.14 0.37 0.94 2.38 5.91

0.08 0.14 0.25 0.44 0.78 1.38 2.42

0.17 0.26 0.40 0.61 0.93 1.41 2.15

0.08 0.13 0.20 0.31 0.48 0.74 1.14

0.15 0.21 0.28 0.38 0.51 0.69 0.93

0.24 0.34 0.48 0.69 0.99 1.42 2.03

the role of macroeconomic conditions.18 This approach is not feasible in the present case since there is no ‘regional’ variation in macroeconomic conditions in Hong Kong. While not resorting to more complex models, in order to capture the effect of changes in economic conditions on default probability, a preliminary attempt is made by pooling all loan data of the eight time-series observations to form one cross-sectional dataset. Data of each loan in a specific month are then matched with the prevailing macroeconomic conditions in that month.19 It should be noted that by so doing, the same loan, as far as it continues to be in HKMC’s portfolio, is treated as different observations in the various months. Given that major characteristics of the loan – the CLTV ratio and mortgage rate – would have changed tangibly in the six-month intervals, pooling the data together may be in general acceptable (see Loh and Tan 2002). However, the results should be interpreted with caution. To the extent that some characteristics specific to an individual loan may have remained the same throughout the period, pooling the loan data together may result in using repeated observations in the sample and could cause biases in the statistical analysis. For instance, the true variance would be underestimated, so it may wrongly reject the null hypothesis (Type I errors) in parameter testing (see Neuhaus 1992; Williams 2000; Cho and Kim 2002). A conventional method to deal with repeated observations is to consider an unbiased variance estimation which adjusts the variance for the intra-cluster correlation. This method avoids Type I errors in hypothesis testing. Another method is to introduce sampling weights – weights are given to specific loans in order to make adjustments for the relative frequencies that these loans are

144 The Banking Sector in Hong Kong

included due to the sampling design.20 In this study, logistic regressions are performed using both methods to assess the possible biases. In addition to the interest rate variable, which is already included in the model, the unemployment rate and the change in the Hang Seng Index (HSI) are selected as proxies for macroeconomic conditions. The former is intended to reflect the stress in the labour market, and the latter is chosen to represent the general financial market sentiment.21 The estimation results for regressions using unadjusted, varianceadjusted, and weight-adjusted methods are given in the last three columns of Table 7.3. All estimated coefficients are statistically significant and are with expected signs. All specification tests, including the Wald test, the Pearson χ2 goodness-of-fit test and the Pseudo R2 statistic, are satisfactory. The positive sign for the estimated coefficient of unemployment rate is in line with the expectation that the higher the unemployment rate, the greater the default probability. The negative sign for the percentage change in HSI is also consistent with general belief that when market conditions are buoyant, there is less incentive to default. As expected, Models A and B have the same estimated coefficients but different standard errors because Model A uses the traditional variance estimators with full scores but Model B calculates the variance estimators by using grouped scores.22 Empirical results show that there is no change in the significance of the coefficients between Models A and B. At the same time, the estimated coefficients of Model C are similar in magnitude to that of Models A and B. All these imply that the assumption of independence among repeated observations may not be too strong.23 For simplicity, the analysis in the following sections is based on the set of estimated coefficients in Model B, which is estimated by using the variance-adjusted method. Equation (7.2) computes the effects of changes in the CLTV on the default probability, under the assumption that all other explanatory variables are at their mean levels. Such effects are derived and summarized in Figure 7.4. To illustrate how labour market conditions may affect default probability, Figure 7.5 shows the simulated default probability in relation to the CLTV ratio when the unemployment rate is set at 8.5 per cent and 4.5 per cent, as well as its mean level (6.5 per cent). The estimated default probability would be 2 per cent at the CLTV level of 200 per cent, when the unemployment rate is at its mean level (6.5 per cent). With a higher unemployment rate, the default probability curve is higher. When unemployment rates are at 8.5 per cent and 4.5 per cent, the estimated default probabilities are 5.3 per cent and 0.8 per cent respectively. Similar comparisons, holding other variables at their mean levels, with regard

Wong, Fung, Fong and Sze 145 Default prob. (%) 6 5 4 3 2 1 0 0

50

100

150

200

250

CLTV (%)

Figure 7.4

Default probability and CLTV ratio (all other variables at mean levels)

Default prob. (%) 14 Unemployment rate  8.5% 12 Unemployment rate  6.5% Unemployment rate  4.5%

10 8 6 4 2 0 0

50

100

150

200

250

CLTV (%) Figure 7.5

Default probability and CLTV ratio at different unemployment rates

to the relationship between default probability and the CLTV ratio at different levels of mortgage rate or percentage change of HSI are given in Figures 7.6 and 7.7 respectively. In general, a higher mortgage rate or a lower percentage change of HSI tends to raise the default probability at a given CLTV level. Illustrations showing how estimated default probability changes at selected CLTV levels with varying macroeconomic conditions are given in Table 7.5.

146 The Banking Sector in Hong Kong Default prob. (%) 8 Mortgage rate  6.3% 7 Mortgage rate  5.3% 6 Mortgage rate  4.3% 5 4 3 2 1 0 0

50

100

150

200

250

CLTV (%) Figure 7.6

Default probability and CLTV ratio at different mortgage rates

Default prob. (%) 10 Change of Hang Seng Index  4% Change of Hang Seng Index  1.8%

8

Change of Hang Seng Index  2% 6 4 2 0 0

50

100

150

200

250

CLTV (%) Figure 7.7 Index

Default probability and CLTV ratio at different changes of Hang Seng

7.7 The 70 per cent LTV ratio and asset quality The quarterly survey on residential mortgage loans in negative equity provides statistics on the average CLTV level since March 2002 for residential mortgages which are in negative equity. As of September 2004, the average CLTV level is estimated at 121 per cent. To assess how a

Wong, Fung, Fong and Sze 147 Table 7.5 Estimated default probability (%) at different CLTV levels under varying macroeconomic conditions All other explanatory variables at mean levels CLTV level (%) Unemployment rate Mortgage rate (%) (%)

50 75 100 125 150 175 200 225 250

8.5

6.5∗

4.5

6.3

5.3∗

4.3

0.24 0.41 0.69 1.15 1.92 3.20 5.27 8.58 13.65

0.09 0.15 0.26 0.43 0.73 1.22 2.03 3.38 5.57

0.03 0.06 0.10 0.16 0.27 0.46 0.77 1.29 2.15

0.13 0.22 0.37 0.62 1.05 1.75 2.91 4.80 7.80

0.09 0.15 0.26 0.43 0.73 1.22 2.03 3.38 5.57

0.06 0.11 0.18 0.30 0.50 0.84 1.41 2.36 3.91

Change of HSI (%) −4.0 0.17 0.28 0.47 0.79 1.32 2.20 3.66 6.01 9.73

−1.8∗ 0.09 0.15 0.26 0.43 0.73 1.22 2.03 3.38 5.57

2.0 0.07 0.11 0.19 0.32 0.54 0.90 1.51 2.52 4.18

Note: * The mean level of the variable in question.

relaxation of the maximum 70 per cent LTV ratio guideline on property lending may affect banks’ asset quality, we consider a hypothetical scenario under which the guideline was relaxed to 90 per cent some time before 1997. We further assume that all banks would aggressively exploit this relaxation to expand their business by extending mortgage loans to cover 90 per cent of the property values.24 We then compare the estimated potential amount of defaulted loans based on the actual average CLTV level and the simulated CLTV level under the hypothetical scenario. The difference will measure the impact of a relaxation of the guideline. Using the negative equity loan position in September 2004 as an example, the impact is simulated and presented in Table 7.6. With the sharp fall in property prices since late 1997, the average CLTV of negative equity loans under the hypothetical scenario would be about 163 per cent, significantly higher than the actual CLTV level reported by the mortgage survey. At this level of CLTV ratio, the default probability of these negative equity loans, as derived from our model developed in section 7.6 based on the pooled data of July 2000 to September 2003, would have been 0.95 per cent, which is twice the actual level of 0.45 per cent. Correspondingly, the potential amount of loans in default is estimated to have risen from HK$0.2 billion to HK$0.4 billion, an increase of HK$0.2 billion. These are conservative estimates as the delinquency

148 The Banking Sector in Hong Kong Table 7.6 Estimated loan defaults with and without a relaxation of the maximum LTV ratio guideline

Maximum LTV ratio guideline (%) Average CLTV level (%) Default probability (%) Estimated amount of default loans (HKD billion)

Actual policy of maximum LTV

Hypothetical maximum LTV

70 127 0.45 0.2

90 163 0.95 0.4

Note: Mortgage loans in negative equity amounted to HK$43 billion as of September 2004.

rate of HKMC’s loan portfolio is only two-fifths that of the industry. If the estimated probability of default is adjusted proportionally according to the ratio of actual delinquency rate of the industry to that of HKMC, the estimated increase in the potential amount of defaulted loans would be more than twice this amount.25

7.8 Conclusion The above analysis of mortgage default probability in Hong Kong confirms the importance of the CLTV ratio as a determinant of mortgage default decisions, with default probability of a mortgage loan positively correlated with its CLTV level. While this relation holds consistently well for the study period, its precise shape is found to vary over time with the prevailing market conditions. The mortgage rate, which serves as a proxy for the payment burden of borrowers, is also positively correlated with mortgage default risks. These results provide support for both the ‘equity theory’ and the ‘ability-to-pay’ approaches of explaining mortgage default. A preliminary attempt to introduce macroeconomic variables into the model by pooling data of different months into one single crosssectional dataset reveals that, in addition to interest rates, both labour and stock market conditions have a significant impact on default probability. While default probability is positively correlated with the unemployment rate, it is negatively correlated with changes in the HSI. With the CLTV level found to be central to mortgage default decisions, this study lends strong support to the prudential policy of encouraging the adoption of a maximum 70 per cent LTV ratio in residential mortgage lending.

−0.01 (0.37) 0.04 (0.12) −0.00 (0.80) 0.00 (1.00) 0.01 (0.90) −0.00 (0.68) 0.02 (0.20) −0.00 (0.35) 0.11 (0.64) −0.01 (0.23) 0.00 (0.11) −9.21 (0.00) 108.70 (0.00) 0.11 −160.70 6,597 (1.00)

−0.03 (0.47) 0.02 (0.61) 0.00 (0.33) 0.14 (0.00) −0.14 (0.00) −0.01 (0.40) 0.03 (0.01) −0.00 (0.96) −0.05 (0.88) 0.01 (0.40) −0.00 (0.88) −8.73 (0.00) 88.36 (0.00) 0.19 −93.60 5,037 (1.00)

OLTV

Note: Numbers in parentheses are p-values.

Pseudo R2 Log- Pseudo Likelihood Goodness-of-fit Test

Wald Test

Constant

Oagesq

Oage

Price

Garea

Season

Oseason

CDSR

ODSR

CLTVSQ

CLTV

Jan. 2001

July 2000 0.01 (0.45) 0.15 (0.10) −0.00 (0.22) −0.14 (0.00) 0.13 (0.00) 0.00 (0.97) 0.01 (0.60) −0.00 (0.54) −0.02 (0.96) −0.01 (0.07) 0.00 (0.24) −14.32 (0.01) 79.42 (0.00) 0.22 −149.70 58,876 (0.00)

July 2001 −0.02 (0.28) 0.19 (0.00) −0.00 (0.01) −0.12 (0.00) 0.14 (0.00) −0.00 (0.81) 0.01 (0.59) 0.00 (0.55) 0.11 (0.64) 0.00 (0.75) −0.00 (0.87) −17.42 (0.00) 110.42 (0.00) 0.22 −172.40 4,997 (1.00)

Jan. 2002 −0.03 (0.05) 0.15 (0.00) −0.00 (0.01) −0.07 (0.00) 0.10 (0.00) 0.00 (0.31) 0.02 (0.28) −0.00 (0.81) −0.03 (0.91) 0.00 (0.58) −0.00 (0.99) −14.77 (0.00) 109.92 (0.00) 0.18 −196.40 4,786 (1.00)

July 2002 −0.03 (0.01) 0.09 (0.00) −0.00 (0.01) −0.02 (0.25) −0.03 (0.18) −0.00 (0.71) 0.01 (0.16) 0.00 (0.49) −0.15 (0.47) 0.00 (0.59) −0.00 (0.68) −9.76 (0.00) 103.98 (0.00) 0.20 −224.70 5,629 (1.00)

Jan. 2003 −0.03 (0.01) 0.06 (0.00) −0.00 (0.03) 0.01 (0.47) −0.05 (0.00) 0.00 (0.95) 0.01 (0.58) −0.00 (0.76) −0.24 (0.18) 0.01 (0.38) −0.00 (0.74) −7.36 (0.00) 104.98 (0.00) 0.17 −286.50 8,444 (0.93)

July 2003 −0.01 (0.33) 0.04 (0.01) −0.00 (0.24) 0.02 (0.35) −0.04 (0.01) 0.00 (0.68) −0.01 (0.55) −0.00 (0.29) −0.07 (0.64) 0.01 (0.15) −0.00 (0.49) −7.29 (0.00) 124.50 (0.00) 0.14 −326.40 7,030 (1.00)

Sep. 2003

Estimation results for initial model specification with the CLTV ratio and CDSR as core

Variables

Annex 7A variables

−0.01 (0.26) 0.07 (0.01) −0.00 (0.32) 0.04 (0.12) 1.28 (0.00) −0.00 (0.31) 0.03 (0.00) −0.00 (0.12) 0.28 (0.07) −0.01 (0.24) 0.00 (0.07) −24.60 (0.00) 94.89 (0.00) 0.29 −122.00 7,816 (0.00)

−0.05 (0.27) 0.06 (0.27) 0.00 (0.90) 0.02 (0.54) 1.48 (0.00) 0.00 (0.93) 0.05 (0.00) −0.00 (0.41) 0.25 (0.25) 0.01 (0.54) 0.00 (0.94) −27.00 (0.00) 91.66 (0.00) 0.32 −79.20 5,829 (0.17)

OLTV

Note: Numbers in parentheses are p-values.

Pseudo R2 Log- Pseudo Likelihood Goodness-of-fit Test

Wald Test

Constant

Oagesq

Oage

Price

Garea

Season

Oseason

Mortgage

ODSR

CLTVSQ

CLTV

Jan. 2001

July 2000

Variables 0.02 (0.13) 0.12 (0.08) −0.00 (0.23) −0.02 (0.46) 1.08 (0.00) −0.00 (0.25) 0.01 (0.54) −0.00 (0.30) 0.09 (0.81) −0.01 (0.42) 0.00 (0.92) −20.80 (0.00) 122.21 (0.00) 0.28 −150.20 3,912 (1.00)

July 2001 −0.01 (0.52) 0.13 (0.00) −0.00 (0.03) −0.01 (0.72) 0.91 (0.00) −0.01 (0.23) 0.00 (0.91) 0.00 (0.48) 0.03 (0.88) 0.00 (0.93) −0.00 (0.95) −17.06 (0.00) 121.53 (0.00) 0.23 −172.20 3,445 (1.00)

Jan. 2002 −0.03 (0.07) 0.13 (0.00) −0.00 (0.02) 0.01 (0.68) 0.67 (0.00) 0.00 (0.89) 0.00 (0.75) −0.00 (0.80) −0.02 (0.92) 0.00 (0.60) −0.00 (0.98) −15.53 (0.00) 141.42 (0.00) 0.20 −195.60 4,655 (1.00)

July 2002 −0.02 (0.08) 0.07 (0.00) −0.00 (0.03) −0.03 (0.04) 0.84 (0.00) −0.00 (0.86) 0.02 (0.13) 0.00 (0.18) −0.17 (0.38) 0.00 (0.73) −0.00 (0.91) −13.29 (0.00) 157.70 (0.00) 0.27 −211.80 4,047 (1.00)

Jan. 2003 −0.01 (0.22) 0.04 (0.03) −0.00 (0.18) −0.02 (0.08) 0.71 (0.00) 0.00 (0.84) 0.01 (0.55) 0.00 (0.84) −0.03 (0.06) 0.01 (0.32) −0.00 (0.62) −9.85 (0.00) 161.76 (0.00) 0.21 −277.20 6,699 (1.00)

July 2003 0.01 (0.66) 0.02 (0.29) −0.00 (0.92) −0.01 (0.33) 0.61 (0.00) 0.00 (0.44) −0.01 (0.49) −0.00 (0.34) −0.13 (0.35) 0.01 (0.11) −0.00 (0.38) −9.34 (0.00) 203.23 (0.00) 0.18 −320.50 6,002 (1.00)

Sep. 2003

Annex 7B Estimation results for initial model specification with the CLTV ratio and mortgage rate (as a proxy for CDSR) as core variables

Wong, Fung, Fong and Sze 151

Annex 7C The derivation of the relationship between default probability and the CLTV level This annex presents the steps, based on the estimated logit model, for deriving the relationship between a particular variable X1 (that is, CLTV ratio in this chapter) and the default probability, by holding other independent variables at their mean levels. Consider a logit model with three independent variables: ec+β1 X1 +β2 X2 +β3 X3 1 + ec+β1 X1 +β2 X2 +β3 X3

P= The fitted model is: Pˆ =

ˆ

ˆ

ˆ

ecˆ +β1 X1 +β2 X2 +β3 X3 1+

ecˆ +βˆ 1 X1 +βˆ 2 X2 +βˆ 3 X3

As ˆ

P= So

 cˆ = ln

Pˆ =

=

=

ˆ

ˆ

ecˆ +β1 X1 +β2 X2 +β3 X3 1 + ecˆ +βˆ 1 X1 +βˆ 2 X2 +βˆ 3 X3 P

1−P ˆ

ˆ

 − βˆ 1 X 1 − βˆ 2 X 2 − βˆ 3 X 3

ˆ

ecˆ +β1 X1 +β2 X2 +β3 X3 1+ e

ecˆ +βˆ 1 X1 +βˆ 2 X2 +βˆ 3 X3

 ln

1+e e

 ln

 ln

1+e

P 1−P

P 1−P

P 1−P

 ln

 −βˆ 1 X 1 −βˆ 2 X 2 −βˆ 3 X 3 +βˆ 1 X1 +βˆ 2 X2 +βˆ 3 X3  −βˆ 1 X 1 −βˆ 2 X 2 −βˆ 3 X 3 +βˆ 1 X1 +βˆ 2 X2 +βˆ 3 X3

 +βˆ 1 (X1 −X 1 )+βˆ 2 (X2 −X 2 )+βˆ 3 (X3 −X 3 )

P 1−P

 +βˆ 1 (X1 −X 1 )+βˆ 2 (X2 −X 2 )+βˆ 3 (X3 −X 3 )

By holding other independent variables at their mean levels, that is X2 = X 2 and X3 = X 3 , the above equation is reduced to: ˆ P(Y = default)

X2 =X 2 ,X3 =X 3

=

e

 ln

1+e

P 1−P

 ln



+βˆ 1 (X1 −X 1 )

P 1−P



+βˆ 1 (X1 −X 1 )

152 The Banking Sector in Hong Kong

The model can be extended to include n independent variables. By holding all other independent variables at their mean levels, that is X2 = X 2 , X3 = X 3 , . . . , Xn = X n , the default/CLTV probability formula becomes: 

ˆ P(Y = default)

X2 =X 2 , X3 =X 3 , ... , Xn =X n

=

e

ln

P 1−P



1+e

ln



+βˆ 1 (X1 −X 1 )

P 1−P



+βˆ 1 (X1 −X 1 )

Furthermore, to consider different scenarios, one may alter the level of any of the other variables from their means. For example, when X2 − X 2 = 2 (the unemployment rate is set at 2 percentage points higher than its mean level to see how unemployment rate changes may shift the default/CLTV probability curve), X3 = X 3 , the above equation becomes: ˆ P(Y = default)

X2 −X 2 =2,X3 =X 3

=

e

 ln

1+e

P 1−P

 ln



+βˆ 1 (X1 −X 1 )+2βˆ 2

P 1−P



+βˆ 1 (X1 −X 1 )+2βˆ 2

Based on the above equation, the CLTV ratio/default probability relationship, with X2 − X 2 = 2 and other independent variables (except X1 ) at their mean levels, can be derived. The formula can be extended for the model with n independent variables.

Wong, Fung, Fong and Sze 153

Notes 1. The improvement is smaller if rescheduled loans are taken into account. 2. ‘Decision to default’ is a widely used term in literature. In practice, however, such defaults are best seen as arising from the financial hardship of borrowers. 3. If borrowers attempt to maximize the equity position in the mortgaged property at each point of time, they will cease to continue payments when and if the market value of the mortgaged property at time t declines sufficiently to equal the outstanding mortgage loan balance at time t. 4. Loan restructuring has helped keep the mortgage delinquency rate in Hong Kong at a relatively low level in more recent years (see Figure 7.1 in section 7.3.2). 5. See He and Liu (2002), Chiang et al. (2002) and Chow and Liu (2003). 6. See Campbell and Dietrich (1983), Vandell and Thibodeau (1985), Gardner and Mills (1989), Capozza et al. (1997), Goldberg and Capone (1998) and Archer et al. (2002). Other studies use the logit model to predict mortgage prepayment risk, for instance, LaCour-Little (1999). For a review of logit model, see Horowitz and Savin (2001). 7. Loans which are overdue for more than 90 days are more likely to be finally defaulted than those that are overdue for a shorter duration. This is because the third missed payment is unlikely to be due to negligence and may thus reflect severe financial stresses of the borrower. Furthermore, with three missed payments and a fourth payment due, it becomes more difficult for the borrower to raise enough funds to settle the overdue amount. According to data from HKMC, among the 214 loans which were overdue for more than 90 days during the period from February 1999 to September 2003, 99 were written off, 23 were fully prepaid, while 92 loans were still in the HKMC’s portfolio at the end of the period. Assuming about half of the loans which were still outstanding would be written off at the end, the write-off ratio would be as high as 60–70 per cent. In some states of the US, state property laws permit initiation of foreclosure processes after a delinquency of 90 days. 8. The unemployment rate and changes in the Hang Seng Index (HSI) are introduced in section 7.6 to capture the effect of macroeconomic conditions. 9. To address the effect of trigger events, transaction costs and lenders’ influence, a micro-behavioural mortgage payment database is required to gather detailed information when mortgage termination occurs. Due to the absence of these data, the effects of these factors have not been examined in this study. 10. Seasoning variables measure how long the mortgage is expected to be served or has been served. The current unit property price is defined as the current price of the property in question per square foot. 11. Due to the absence of actual current income data, income data are all proxies derived by the debt servicing ratio at origination with adjustments made by changes in the nominal wage index (see Note 1 of Table 7.1). 12. These trigger events have not been examined in the study due to the absence of relevant micro-level data. 13. The Pseudo R2 is McFadden’s (1974) likelihood ratio index. It equals to 1 − (LUR /L0 ), where LUR is the log-likelihood function for the estimated model

154 The Banking Sector in Hong Kong with all coefficients present, the L0 is the log-likelihood function with an intercept only (under the null hypothesis that all coefficients are zero in the restricted model). If all coefficients are zero, then the Pseudo R2 equals to zero. 14. For the case of a dischotomous dependent variable the upper limit for Pseudo R2 is likely to be substantially less than one, see Christensen (1997). 15. See the derivation of the equation in Annex 7C. 16. Another common way to see the relationship is to derive the marginal effect of the jth explanatory variable on the default probabilities by the following equation: ∂P(Y = default) = Z βˆ j ∂Xj

ˆ

where

Z=

ˆ

ˆ

ecˆ +β1 X1 +β2 X2 +···+βn Xn (1 + ecˆ +βˆ 1 X1 +βˆ 2 X2 +···+βˆ n Xn )2

17. The CLTV ratios are mostly below 150 per cent. 18. For instance, see Campbell and Dietrich (1983), Cunningham and Capone (1990), Lawrence and Smith (1992). 19. The unemployment rates used in the analysis are given below. Based on the definition of default, the unemployment rate used in the estimation should lead the dependent variable by three months. For example, for the snapshot month of July 2000, the unemployment rate of April 2000 is used.

%

April 2000

Oct. 2000

April 2001

Oct. 2001

April 2002

Oct. 2002

April 2003

June 2003

5.4

4.8

4.5

5.7

7.1

7.4

7.8

8.5

Source: CEIC. 20. The weight attached is the inverse of the frequency that a particular loan appears in the sample. This is particularly applicable for cases that the attributes of repeated observations are constant. 21. Based on the definition of default, the percentage change in HSI used in the estimation should lead the dependent variable by three months. 22. Scores are the first partial derivatives of the log-likelihood function with respect to the model parameters. Full scores include all individual observations (regardless of whether they are repeated observations) in the computation, while for grouped scores, repeated observations are grouped as specific independent observations in the calculation. 23. Various studies have shown that the estimated variances of coefficients are biased because of the correlation of repeated observations, but the values of estimated coefficients remain unbiased (see Cirillo et al. 1996; Cho and Kim 2002). The estimated results of this study are in line with these studies. 24. This assumption is made to assess the maximum effect. However, in reality, this is unlikely to happen, as banks will decide on the maximum loan amount based on their assessment on the credit worthiness of the borrowers and the debt servicing ratio. This is evidenced by the fact that the actual LTV ratio for new loans made around 1997 was on average below 60 per cent, far lower than the maximum ratio of 70 per cent permitted under the guideline.

Wong, Fung, Fong and Sze 155 25. There are also other caveats. On the one hand, the impact can be underestimated as loans which were originally in positive equity region could have fallen into negative equity region if the loans were initially originated at a CLTV level of 90 per cent under the hypothetical scenario. On the other hand, as pointed out in note 24, in reality, it is unlikely that banks would be so aggressive to fully exploit the hypothetical relaxation.

References W. R. Archer, P. J. Elmer, D. M. Harrison and D. C. Ling, ‘Determinants of Multifamily Mortgage Default’, Real Estate Economics, 30(3) (2002) 445–73. T. Campbell and J. Dietrich, ‘The Determinants of Default on Conventional Residential Mortgages’, Journal of Finance, 38(5) (1983) 1569–81. D. R. Capozza, D. Kazarian and T. A. Thomson, ‘Mortgage Default in Local Markets’, Real Estate Economics, 25(4) (1997) 631–55. R. C. Chiang, Y. F. Chow and M. Liu, ‘Residential Mortgage Lending and Borrower Risk: The Relationship between Mortgage rates and Individual Characteristics’, Journal of Real Estate Finance and Economics, 25(1) (2002) 5–32. H. J. Cho and K. S. Kim, ‘Analysis of Heteroscedasticity and Correlation of Repeated Observations in Stated Preference (SP) Data’, KSCE Journal of Civil Engineering, 6(2) (2002) 161–9. Y. F. Chow and M. Liu, ‘The Value of the Variable Tenor Mortgage Feature in Hong Kong’, Pacific-Basin Finance Journal, 11 (2003) 61–80. R. Christensen, Log-linear Models and Logistic Regression, 2nd edn (New York: Springer-Verlag, 1997). C. Cirillo, A. Daly and K. Lindveld, ‘Eliminating Bias due to the Repeated Measurements Problem in SP Data’, Proceedings of the 24th European Transport Forum (PTRC), Association for European Transport, Brunel University, England, (1996). D. F. Cunningham and C. A. Capone, ‘The Relative Termination Experience of Adjustable to Fixed-Rate Mortgages’, Journal of Finance, 45(5) (1990) 1687–703. M. J. Gardner and D. L. Mills, ‘Evaluating the Likelihood of Default on Delinquent Loans’, Financial Management, (Winter) (1989) 55–63. L. Goldberg and C. A. Capone, Jr., ‘Multifamily Mortgage Credit Risk: Lessons From Recent History’, Journal of Policy Development and Research, 4(1) (1998) 93–113. J. He and M. Liu, ‘Swapping Default Risk for Interest Rate Risk: The Rise of Fixed Rate Mortgage Loans in Hong Kong’, Research in Banking and Finance, 2 (2002) 167–78. J. L. Horowitz and N. E. Savin, ‘Binary Response Models: Logits, Probits and Semiparametrics’, Journal of Economic Perspectives, 15(4) (2001) 43–56. J. Jackson and D. Kasserman, ‘Default Risk on Home Mortgage Loans: A Test of Competing Hypotheses’, Journal of Risk and Insurance, 3 (1980) 678–90. M. LaCour-Little, ‘Another Look at the Role of Borrower Characteristics in Predicting Mortgage Prepayments’, Journal of Housing Research, 10(1) (1999) 45–60.

156 The Banking Sector in Hong Kong E. C. Lawrence and L. D. Smith, ‘An Analysis of Default Risk in Mobile Home Credit’, Journal of Banking and Finance, 16 (1992) 299–312. L. C. Loh and T. H. Tan, ‘Asset Write-Offs – Managerial Incentives and Macroeconomic Factors’, ABACUS, 38 (1) (2002) 134–51. D. McFadden, ‘The Measurement of Urban Travel Demand’, Journal of Public Economics, 3 (1974) 303–28. J. M. Neuhaus, ‘Statistical Methods for Longitudinal and Clustered Designs with Binary Responses’, Statistical Methods in Medical Research, 1 (1992) 249–73. T. J. Riddiough, ‘Equilibrium Mortgage Default Pricing with Non-Optimal Borrower Behavior’, University of Wisconsin PhD diss., (1991). T. J. Riddiough and K. Vandell, ‘Implied Foreclosure Probability and Loss Recoveries in the Application of the Contingent-Claims Approach to Pricing Risky Commercial Mortgage Debt: A Comment’, University of Cincinnati Working Paper Series, (1993). K. Vandell, ‘Predicting Commercial Mortgage Foreclosure Experience’, Salomon Brothers, Bond Market Research, (1990). K. Vandell, ‘Predicting Commercial Mortgage Foreclosure Experience’, Journal of the American Real Estate and Urban Economic Association, 20(1) (1992) 55–88. K. Vandell and T. Thibodeau, ‘Estimation of Mortgage Defaults Using Disaggregate Loan History Data’, AREUEA Journal, 13(3) (1985) 292–316. R. L. Williams, ‘A Note on Robust Variance Estimation for Cluster-Correlated Data’, Biometrics, 56 (2000) 645–6.

Part III Quantifying Risks, Capital Adequacy and Stress-Testing Framework of Systemic Risk

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8 Determinants of the Capital Level of Banks in Hong Kong Jim Wong, Ka-Fai Choi and Tom Pak-Wing Fong

8.1 Introduction Banks incorporated in Hong Kong generally maintain a capital adequacy ratio (CAR) well above the regulatory requirement.1 For example, the average CAR of licensed banks was 28.3 per cent in the second quarter of 2004, against an average required minimum of just 10.3 per cent.2 This phenomenon is also common in other economies.3 It raises the question of what factors determine the actual amount of capital held by banks and, specifically, whether changes in regulatory requirements can affect the level of bank capital.4 Following the approach of Alfon et al. (2004), we examine the behaviour of licensed banks in Hong Kong towards their decisions regarding capital adequacy. A qualitative analysis is carried out and an econometric model is constructed to assess the relevance of hypotheses made in various studies.5 The qualitative analysis is based on the results of a survey on banks’ opinions of what govern the decisions on desired capital (that is, the amount or a range of capital that banks would like to hold) and the level of actual capital. In the quantitative analysis, we estimate an empirical model which relates CAR to a number of possible determinants using a panel dataset on licensed banks incorporated in Hong Kong. The rest of this chapter is organized as follows. Section 8.2 examines the hypotheses on the possible determinants of bank capital that the literature has emphasized, and evaluates their relevance to Hong Kong. Section 8.3 concludes.

159

160 The Banking Sector in Hong Kong

8.2 Possible determinants of capital holdings of banks In this section, we evaluate the relevance to Hong Kong’s banking sector of the possible determinants suggested by the previous studies. The assessments are based on the results of our quantitative analysis and survey,6 details of which are presented in Annexes 8A and 8B respectively. Following Alfon et al. (2004), we classify the possible determinants into three categories: banks’ internal considerations, market discipline and the regulatory framework. They correspond to the three parties involved in determining banks’ capital structure: the bank itself, the market and the regulator.

8.2.1 Banks’ internal considerations These internal factors include the risk level of the banks, the effects of economic cycles, the agency problem, banks’ business strategies and the opportunity cost of capital.

8.2.1.1 The risk level of banks It is widely recognized that capital can serve as a buffer to absorb unexpected losses, reducing the probability of insolvency and, therefore, the expected bankruptcy cost. However, the level of minimum CAR set by the regulator may not fully capture banks’ risks. There could also be risks that do not concern the regulator, but affect banks’ capital holding decisions, including financial distress caused by a loss of franchise value.7 As such, banks’ views on the appropriate level of capital may differ from the minimum level set by the regulator. Our evidence on the relevance of banks’ own risk assessment for capital decisions seems to support the view that risk is a determinant of the level of CAR held by banks. All respondents to the survey (24 banks) said the cushion effect against unexpected losses arising from material risks was an important determinant in their desired capital ratio. The majority of banks (14 out of 24) formed their views by first assessing how much capital was needed to run the business and then verifying whether it met the regulatory requirement. An important consideration in setting the desired capital for three quarters of the banks was that the regulatory capital underestimated the risks it was intended to capture. 19 banks even said that assets attracting zero risk weight in the calculation of the risk-weighted assets (RWA) also needed capital. These results indicate that banks have their own assessments of risk that may be different from the assessment embedded in the calculation of RWA under the current Basel Capital Accord. Their view that regulatory

Wong, Choi and Fong 161

capital is inadequate for insuring against risks possibly causes them to hold a capital buffer. The fact that the actual CARs maintained by large banks are, in general, lower than those of smaller banks seems to support the hypothesis that risk is a relevant criterion. The general view is that larger banks tend to face a lower risk than smaller banks. First, a given amount of investment constitutes a smaller portion of the overall portfolio of a large bank than of a smaller one, so the portfolios of large banks can be better diversified. Second, large banks tend to have better risk management and controls than smaller banks, because scale economies exist in screening borrowers and monitoring loans. If this is the case, other things being equal, the amount of capital needed for covering the risks of an asset portfolio will be larger for small banks than for large banks.8 To examine the validity of this claim, Figure 8.1 plots the combinations of CARs and banks’ total assets observed in the sample covering the period from the first quarter of 1992 to the third quarter of 2004.

Log of CAR 2.8

(398%) 2.6 2.4 2.2

(100%) 2.0 1.8 1.6 1.4 1.2

(10%) 1.0 0.8 8 (HK$0.01bn)

9

10 (HK$1bn)

11

Log of total assets Figure 8.1

CAR and bank size

Notes: (a) Quarterly data are used. (b) The logarithms are to the base 10. Source: HKMA.

12 (HK$100bn)

13

162 The Banking Sector in Hong Kong

A clear negative relationship is observed, suggesting that large banks tend to maintain a lower level of CAR. It should be pointed out that this observation alone is not sufficient for concluding that large banks maintain a lower CAR due to their lower risk based on their own assessment. This is because the negative relationship displayed in Figure 8.1 may stem from the fact that larger banks may hold riskier assets with the same amount of capital than smaller banks, which could also result in a lower CAR. In our econometric estimation, to test how the risk perceived by banks affects CAR, we include in our regression a bank asset size variable, which is used to represent indirectly each bank’s perceived risk level. To control for the factor that large banks may hold riskier assets, we also incorporate a variable measuring the relative riskiness of the assets held by different banks: the ratio of risky assets to total assets.9 The estimation results show there is a statistically significant negative relationship between CAR and bank size. However, the estimated coefficient of the risky asset ratio is statistically insignificant. This may reflect that the risky assets ratio is not a good proxy to represent the risk level of banks, and the variable is removed finally by our model selection procedure.10 Our quantitative analysis cannot, therefore, distinguish the contributions of the two hypotheses. The negative relationship between CAR and bank size is consistent with the hypothesis that CARs are positively correlated with the risk level perceived by banks. Alternatively, it is also in line with the hypothesis that larger banks may tend to be more aggressive in risk taking.11,12 Nevertheless, both hypotheses support that banks’ risk is a relevant factor. The estimated coefficient of bank size implies that a 10 per cent higher asset value will result in a 0.35 per cent decline in CAR in the short run, and a 2.58 per cent reduction in the long run.13

8.2.1.2 Economic cycles Economic cycles may affect the level of CAR, as capital holdings may change over time to accommodate fluctuations in risk arising from variations in the economic environment that are not captured by the fixed risk weights attached by the regulator to the assets. In an economic downturn, the likelihood of a fall in capital increases as a result of possible increases in the write-offs and provisions. Banks may therefore take precautionary measures by holding more capital, and those relying on credit rating to gain access to capital markets may also need to raise their capital holdings to maintain their ratings during a downturn. In an upturn, risks are less likely to materialize and banks can safely hold less capital.

Wong, Choi and Fong 163 GDP Growth (%)

CAR (%)

8

25 CAR Real GDP growth rate

6

20 4 15

2 0

10

2 5 4 6

Figure 8.2

2004/03

2003/06

2002/09

2001/12

2001/03

2000/06

1999/09

1998/12

1998/03

1997/06

1996/09

1995/12

1995/03

1994/06

1993/09

1992/12

1992/03

0

CAR and economic cycles

Notes: (a) Quarterly data are used. (b) CAR is the median of CARs of all licensed banks. (c) Real GDP growth rate is the seasonally adjusted quarter to quarter growth rate. Sources: HKMA and Census and Statistics Department.

One could then expect that during a downturn banks would hold higher CARs than during an upturn. Figure 8.2 depicts the time series of the median of the CARs of licensed banks in Hong Kong, together with Hong Kong’s real GDP growth rates.14 As shown by the chart, the median of the CARs remained fairly stable around 16 per cent before the third quarter of 1997. But it started to climb during the Asian financial crisis which caused a sharp decline in Hong Kong’s real GDP growth. The median of the CARs decreased gradually in the latter sample period as the economy recovered. The chart suggests that the level of CAR chosen by banks may be related fairly closely to Hong Kong’s macroeconomic performance.15 Evidence from our survey indicates that the level of CAR indeed relates to economic cycles. All 24 banks regarded insuring against the impact of economic downturn as either an important or a very important consideration in deciding their desired capital. 20 of them thought that

164 The Banking Sector in Hong Kong

actual capital could fall below the desired level as a result of unexpected events in the economy that adversely affected the banking sector. To prevent this, banks may maintain a higher level of CAR during downturns. Quantitative evidence supports this. We found that CAR and the real GDP growth rate are negatively correlated, suggesting that the capital ratio could have a pro-cyclical effect on the economy. In other words, the CAR would have an amplifying effect on economic cycles. For example, in difficult times, the increase in CAR may be achieved through a tightening of lending, which could further depress the economy.16 The estimates show that a 100 per cent decline in real GDP growth from, say, 2 per cent to 0 per cent would cause the CAR to increase by 1.8 per cent (from, say, 12 per cent to 12.22 per cent) in the short term and by 13.3 per cent in the long term. In addition, CARs of small banks were found to be more responsive than large banks to economic cycles.17 This may reflect that assets of larger banks are better diversified into other sectors that are affected differently by macroeconomic performance, and into a range of economies to be less susceptible to the condition of the local economy.

8.2.1.3 Agency problem Jensen and Meckling (1976) pioneered the study of the agency problem stemming from the separation of ownership and control in modern organizational structures. This problem arises when the agent, who is hired by the principal, does not work in a way to achieve the principal’s objective. In the context of this chapter, the bank management can be viewed as the agent of the shareholders whose objective is to maximize the bank’s value. However, the former may not want to pursue as high a leverage as desired by the shareholders because of the greater difficulty in managing the risk of a bank that is more leveraged.18 As a result, excess capital may be held by bank management’s pursuit of a ‘quiet life’ at the sacrifice of the shareholders.19 Our survey result seems to suggest the existence of such a problem. Of the 24 banks, 17 said that their actual capital was usually higher than the desired level. 16 attributed maintaining a higher-than-desired level of capital to ‘conventional practice’. Only seven said they would reduce their actual capital to meet the desired level as quickly as possible even if they found the excess was not due to transitory factors. It should, however, be pointed out that such practice may not be caused entirely by the agency problem. It may also reflect the downward rigidity of CAR arising from strategic reasons, which will be discussed in the following subsection.

Wong, Choi and Fong 165

Hong Kong banks may not have a severe agency problem. First, competition in the banking sector has been intense, making it difficult for bank management to adequately remunerate a higher ratio of capital simply by charging more for its services. Secondly, there are a number of banks with concentrated ownership and participation of major shareholders in management.20 Thirdly, banks with dispersed ownership are mostly listed on the stock market. Their greater susceptibility to hostile takeovers forces them not to be excessively capitalized.

8.2.1.4 Business strategy Banks may hold more capital for strategic reasons. Three reasons identified by the literature – financing growth, adjustment cost and downward rigidity of capital – are examined in this section.

(a) Financing business growth Capital may be held to finance future business growth and exploit future business opportunities, such as mergers and acquisitions. Accumulating excess capital by retaining earnings could be a bank’s business strategy, giving rise to the persistence of a capital buffer. Our survey found that excess capital may arise from the bank’s need to finance its long-term strategy. All banks replied that this is either an important or very important determinant of desired capital. They regarded this as the second most important factor among the 13 possible determinants of desired capital given in the survey.21 Evidence found in the quantitative analysis of a negative correlation between capital ratio and size can support the hypothesis that small banks need to maintain excess capital to finance their long-term strategies.22 (b) Adjustment cost Adjusting the levels of capital to accommodate unexpected changes in market conditions could be costly to banks because of the time lag between the decisions to adjust the capital level and the completion of the transactions for such adjustments. Among the factors making banks susceptible to a time lag are the possible need for legal, regulatory and procedural work. Transaction costs, including fees to investment banks and lawyers, will also be incurred. Information asymmetries between bank management and investors could give rise to indirect costs. An issuance of new capital or a disposal of existing capital may be seen by investors as a signal the bank considers the market price to be above (or below) its intrinsic value. The share price may move unduly, thus raising the cost of adjustment.

166 The Banking Sector in Hong Kong

Our empirical findings provide some support to the hypothesis that adjustment costs are a determinant of the observed capital buffers. Half of the respondents in our sample considered the cost of raising extra capital was an important reason for banks to stay with a lower-than-desired capital. (Given that banks generally maintain a higher-than-desired capital level, the existence of adjustment cost implies that this may be a factor for holding such a capital buffer.) Our econometric analysis investigates the existence of adjustment costs by examining the effect of the lagged CAR. Its coefficient was found to be positive and significant, indicating that the full adjustment in CAR does not occur instantaneously. This is consistent with the existence of adjustment costs.23 An excess, or a deficiency, of capital can arise as a result of the difficulties in capital adjustment. However, the consequence of falling short of capital is probably more serious, so banks are more likely to be ‘over-capitalized’ than ‘under-capitalized’. In other words, a part of the observed capital buffer may be held for precautionary purposes, due partly to frictions in adjusting capital level.

(c) Downward rigidity of capital Another possible strategic reason for holding excess capital, even in the absence of profitable opportunities, is that banks may refrain from returning surplus capital to shareholders in case the action generates undesirable market signals to the banks’ earning abilities. This consideration would lead management to simply follow the past practice of choosing the level of CAR, resulting in a downward rigidity of the capital ratio. In our qualitative analysis, we found that most banks considered high actual capital reflected conventional or market practice. This is in line with another survey result of the actual capital usually exceeding the desired capital for most banks.24 The econometric result that the current CAR depends positively on the past CAR also supports the hypothesis of the existence of downward stickiness of capital. 8.2.1.5 Cost of capital When the return on equity is high, it is costly to hold excess capital. In this case, a profit-maximizing bank may maintain a lower CAR (probably through taking more risk) when the opportunity cost of capital is high. In our econometric study, we use the inflation-adjusted return on equity to approximate the opportunity cost of capital. The estimation obtains a negative correlation between CAR and the return on equity, suggesting that banks would reduce capital holding when the cost of capital is high.25 The estimate shows that a 10 per cent rise in return on

Wong, Choi and Fong 167

equity would result in an immediate decline in CAR by 0.87 per cent. The decrease would be 6.41 per cent in the long term.

8.2.2 Market discipline This section reviews the role that market discipline can play in the determination of capital holdings. In other studies, the main focus is on the relevance of the role of market discipline exerted through credit rating, uninsured funding and peer group pressure. However, instead of studying uninsured deposits, as Hong Kong’s deposit insurance scheme is not yet in place, we consider whether market discipline arises from the wholesale funding market and how this may affect banks’ capital level.26

8.2.2.1 Credit rating and wholesale funding Creditors and depositors will demand higher interest rates or withdraw funds when they perceive a bank is risky. Their assessment of a bank’s risk may differ from the regulator’s, as they do not have the same access to its information. Therefore, they may force the bank to hold capital different from that required by the regulator. In response, the bank may choose to hold a higher level of capital. Rated banks are probably disciplined by the market to a larger extent, with rating agencies acting as intermediaries in the disclosure process. Banks may also hold higher levels of capital to get a rating that facilitates their access to specific capital markets (for example, subordinated debt). Thus, a dependency between capital levels and ratings may be expected. In our qualitative analysis, we explore the role that market discipline and ratings can play in determining capital. All respondents to our survey considered banks’ risks as perceived by the market to be an important or very important determinant of desired capital. And all rated banks said that maintaining or improving their credit ratings by external credit rating agencies was an important or very important factor. These two factors were ranked respectively as the third and fifth most important determinants (among the 13 factors) by banks. The qualitative analysis also found that securing wholesale funding – wholesale deposits or access to money markets or both – was regarded as an important determinant of desired capital. Of the 24 banks in the sample, 18 regarded wholesale deposits as either important or very important, while 19 considered interbank access as important or very important. Our econometric analysis examines the market disciplinary role of the wholesale funding market by incorporating a variable representing the

168 The Banking Sector in Hong Kong

proportion of wholesale funding to total funding. Due to data limitations, the ratio of interbank deposits to total deposits is used as a proxy in the analysis.27 A positive and statistically significant coefficient is obtained. So banks relying more heavily on the interbank market as a funding source choose to appear to be better capitalized. The estimates imply that a 10 per cent rise in this variable would increase CAR by 1.9 per cent and 13.9 per cent in the short and long terms respectively. We found that all rated banks in the sample regarded the market’s most likely reaction to an unexpected drop in capital as being a review of their rating (with a possible increase in funding costs), and 12 out of the 13 rated banks considered their shares would trade at a lower multiple of earnings as a likely outcome. A tightening of the terms of loans in the interbank market was considered likely by 19 out of the 24 banks, and a withdrawal of wholesale deposits was seen as a likely reaction by 13 banks. As such, banks appear to perceive there is a certain degree of market discipline exerted through credit rating and the wholesale markets. In gathering further evidence on the ratings’ role, we also asked banks to rank the likelihood of various reactions to a rating downgrade. We focus on the likelihood in the short to medium term of changes in desired capital, actual capital, and RWA (as a proxy to changes in the business). While seven out of the 16 rated banks would raise the desired capital, ten of them would raise the actual capital and 13 said they would reduce the actual RWA. These findings suggest that market discipline exerted through ratings plays a significant role in capital decisions.

8.2.2.2 Peer pressure Peer group pressure in capital holding could also result from incomplete information. In appraising the financial strength of a bank, the market and rating agencies may assess how its CAR stands in relation to others. Banks may use capital as a signalling device by holding a higher level of CAR to differentiate themselves from their peers. Our survey results show that 15 out of 24 banks regarded peer pressure to be an important factor in capital decisions. In our quantitative analysis, we include in our regression the average CAR of all other banks of similar size to the bank concerned to represent peer group pressure. The CAR was found to be positively correlated with the peer group pressure variable.28 The result suggests that banks are using their capital as a signal for competition with similar banks in the market to appear well-capitalized in relation to their peers.

Wong, Choi and Fong 169

8.2.3 The regulatory framework This section reviews the regulatory environment’s role in determining capital holding. In particular, decisions on capital may be affected by how capital requirements are set by the regulator and perceived by banks, and by the supervisory approach on regulatory breaches.

8.2.3.1 Capital requirement as a minimum In Hong Kong, the regulator sets individual capital requirements as minima with the expectation that banks’ CARs will always exceed them. Our qualitative analysis reveals that two thirds of the banks form their views on desired capital by first assessing how much capital is needed to run the business and then verifying whether it meets the regulatory requirement. The rest assess how much additional capital is needed on top of the regulatory capital requirements. Holding capital above the minimum is thus in line with the regulator’s supervisory approach. Banks’ responses to our question about their potential reaction to changes in their own individual capital requirements show that even when their CARs are above the adjusted requirements, some would still react to the changes. More than half of the banks answered that they would change the amount of desired capital in the short to medium term, while ten banks would change their actual capital. Only six banks indicated they would change their business (as represented by actual RWA), but more than half of them would change the portfolio composition to reduce the risk level. Our econometric results indicate that individual capital requirements are a significant factor in capital decisions. We obtain a positive and significant correlation between actual CARs and regulatory requirements, indicating that the higher the required CAR, the higher the actual CAR. In addition, we found the response to a regulatory change is significantly larger when a bank’s actual CAR is close to the regulatory minimum.29 The estimates suggest that on average about 12 per cent of changes in individual capital requirements is translated into a change in the actual capital in the immediate period, and the translation is 89 per cent in the long term. In other words, the buffer only partially absorbs changes in individual capital requirements.

8.2.3.2 Regulatory rules and supervisory behaviour In addition to adjusting the minimum capital ratio, the regulator may affect banks’ capital level in other ways. For example, depending on the regulatory rules and the supervisor’s reaction to a breach of the capital requirement, and how serious the regulatory interventions may be,

170 The Banking Sector in Hong Kong

banks may choose to hold a CAR higher than required to reduce the risk of an accidental breach.30 The survey results found that avoiding the consequences of a potential breach of regulatory capital was regarded as very important by all banks. It is also ranked top of the most important determinants for capital decisions. This suggests the supervisory approach regarding a breach of regulatory capital is stringent, as perceived by banks, and may have induced them to hold a higher level of CAR.

8.3 Conclusion In line with the experience in other economies and consistent with findings in banking literature, the CAR levels of banks in Hong Kong are determined by a number of factors, in addition to the regulatory requirements. While banks generally hold a CAR well above the regulatory requirement, the buffers are, in most cases, deliberately maintained and reflect banks’ internal considerations, their responses to market discipline and the regulatory framework. Among banks’ internal factors, risk appears to be highly relevant. It was found that banks’ own assessments of risk, which may be different from that of the regulator, could have resulted in banks’ holding a high level of capital. This could be partly due to the fact that the capital requirements under the current Capital Accord do not fully capture all risks that are being taken into account by banks or the variations in the risks arising from changes in prevailing macroeconomic conditions. In addition, banks’ strategic considerations in relation to the existence of adjustment costs, the market’s perceived preference of financing growth by capital, and the trade-off between holding excess capital and the sending of undesirable signals to the market by returning surplus capital to shareholders, may have contributed to the high capital ratio. The presence of the agency problem could also lead to banks holding a higher CAR than required. However, given the competitive environment of the banking sector, the impact of this problem is likely to be modest. Our analysis also indicates that banks perceive a degree of market discipline, in addition to regulatory discipline, exerted through the wholesale funding markets, credit rating agencies and peer group pressure, to be contributing factors. These disciplinary forces stem largely from imperfect information and the need for banks to compete for funding resources, and could be partly responsible for banks maintaining the capital buffer.

Wong, Choi and Fong 171

While the holding of excess capital may be largely in line with the regulator’s expectations, banks appear to be very concerned about the adverse implication of a breach of the regulatory minimum. How this may have led to banks’ holding a large capital buffer is difficult to quantify. Notwithstanding the presence of excess capital, we found that banks still respond to changes in capital requirements, and the capital buffer will only partially absorb a change in the regulatory requirement. The minimum capital requirement, therefore, remains an effective policy instrument. Action could be taken to improve the use of capital to the extent that part of the high capital buffer is due to the agency problem, information asymmetries or a mismatch between expectation of the regulator and banks regarding the approach to maintaining a capital buffer to prevent a breach of capital requirements. In this connection, the initiative under Basel II is expected to help address some of these issues. Our analysis also confirms that banks tend to hold a higher CAR in economic downturns, but a lower capital ratio in upturns. The implications of such a procyclical nature of the capital ratio on the economy, and how it may be affected by the forthcoming changes in the more risk-sensitive approach under Basel II, are worth exploring.

172 The Banking Sector in Hong Kong

Annex 8A A quantitative analysis of determinants of bank capital in Hong Kong Annex 8A.1 Model specifications The general form of the panel data model adopted to examine the relevance of the various possible factors governing capital decisions in Hong Kong is defined in equation (8A.1): CARit = α0 + α1 REGit + α2 RISKit + α3 SIZEit + α4 GROWTHit + α5 ROEit + α6 PEERit + α7 WFit + α8 CARi,t−1 + α9 AFCt

(8A.1)

+ ηi + εit , where subscripts i and t denote bank and time respectively.31 The variables in equation (8A.1) are specified in natural logarithm. The coefficient vector α = (α0 , α1 , . . . , α8 ) is fixed across banks and over time by assumption.32 ηi are the individual effects capturing the unobserved idiosyncratic features of different banks. They are assumed to remain Table 8A.1

Description of the explanatory variables

Variable

Description

REG

The specific regulatory capital requirement (that is, the minimum ratio of capital base to total risk-weighted assets) assigned to the bank.

RISK

The ratio of the bank’s assets with 100% risk weight to its total assets.

SIZE

The inflation-adjusted value of total assets of the bank.

GROWTH

Hong Kong real GDP growth rate.

–

ROE

The real return on equity (that is, inflation adjusted).

–

PEER

The average CAR of other banks in the same peer group as classified by asset sizes. The ratio of the interbank borrowing to the total borrowing which comprises ‘due to other banks’, ‘due to the Exchange Fund’, ‘deposits from customers’, ‘amount payable under repos’ and ‘negotiable debt instruments issued and outstanding’.

+

The one-period lagged CAR. Dummy for the Asian financial crisis.

+ +

WF

CARt−1 AFC

Expected effect +

+/− –

+

Wong, Choi and Fong 173

the same over time. εit are the disturbances. The estimated α reflects influences stemming from both differences across banks and temporal changes that they experienced. The dependent variable CAR is the capital adequacy ratio. The explanatory variables and the expected signs of their coefficients are described in Table 8A.1. The adjustments for inflation (or deflation) in the SIZE and ROE variables are based on the GDP deflator. For the PEER variable, sampled banks are divided into three groups: large, medium and small according to their asset sizes in 2001 Q3.33 Large banks refer to banks with total assets exceeding HK$130 billion in the quarter. Those having total assets below HK$10 billion are classified as small banks. Others are classified as medium banks.

Annex 8A.2 Data and estimation results (a) The data Licensed banks incorporated in Hong Kong are the set of banks considered. The periodic returns submitted by them are the sources of banking data for the econometric analysis. Figures from the banking returns are on a combined basis. The data are on a quarterly basis, covering the period from 1992 Q1–2004 Q3 and involving 31 banks. However, the three smallest banks are removed because their CARs were abnormally high and may potentially distort the estimation results. Due to activities like mergers and acquisitions, changes in the location of incorporation, and so on, the number of locally incorporated banks considered in the study varies over the sample period, from 22 to 28. The dataset is thus an unbalanced panel. Moreover, some observations with dramatic fluctuations are excluded to avoid possible biases. Table 8A.2 reports some descriptive statistics about the dataset, which includes 1221 observations. Note that the required capital ratio does not change much over time. For most of the banks, it stayed at 8 per cent before 1998 Q4 and remained at 10 per cent thereafter. Only three banks experienced changes in their required ratios more than once. On the other hand, cross sectional differences in capital requirements exist in each of the periods.

(b) Estimation results and interpretations Equation (8A.1) is estimated by the generalized method of moments (GMM) because it involves variables that may be endogenous. ROE, WF

174 The Banking Sector in Hong Kong Table 8A.2 General features of the data (sample period: 1992 Q1–2004 Q3; No. of banks: 28; No. of observations: 1,221)1 Variable

Mean

Median

Std. Dev.

Minimum

Maximum

CAR (%) REG (%) RISK SIZE (in HK$ bn) PEER (%) ROE WF GROWTH (%)2

19.28 9.31 0.30 91 19.28 0.15 0.09 1.00

18.48 10.00 0.31 31 18.62 0.13 0.05 1.20

6.27 1.20 0.12 206 3.21 0.11 0.12 1.65

9.23 8.00 0.01 1 11.90 −0.55 0.00 −3.60

45.31 12.00 0.84 1590 33.14 0.88 0.95 6.80

Notes: 1. Outlier observations are removed from the sample. 2. Seasonally adjusted Hong Kong real GDP growth rates, obtained from the Census and Statistics Department.

and CARt−1 are instrumented by their one-period lags, whereas other variables serve as their own instruments.34 In the estimation, we apply the orthogonal deviation technique which transforms equation (8A.1) into first differences with GLS transformation applied to remove moving average serial correlations.35 The estimates are presented in Table 8A.3. Two regression results are reported. Model A refers to the model stated in equation (8A.1). Model B extends Model A by incorporating two more variables to study the interaction between REG and the closeness of CAR to REG (that is, the variable CLOSE) and the interaction between the size of the bank (that is, the variable BIG) and economic growth.36 All variables are included in the initial estimation. The final results reported in the table are arrived at through the backward elimination procedure. The application of orthogonal deviation transformation requires that the error term is not second-order serially correlated. As shown by the test statistics, m2 , this condition is met. Table 8A.4 summarizes the estimated effects on CAR of changes in the exogenous variables. There are short-run changes and long-run changes because the full response of CAR to an exogenous change is found to be not instantaneous. The short-term change reflects the response of CAR in the contemporaneous quarter, whereas the long-term change measures the response that will be reached ultimately when no more exogenous change occurs.

175 Table 8A.3

Determinants of banks’ capital level: GMM estimates

Variable

Model A

REG SIZE GROWTH ROE PEER WF CARt−1 RISK AFC Interactions REG × CLOSE GROWTH × BIG m2 No. of banks No. of obs.

Model B

Coeff.

t-statistic

Coeff.

t-statistic

.1205*** −.0350*** −.0180** −.0866** .0586* .1892** .8643*** (removed) (removed)

2.7363 −3.3550 −2.3527 −2.4490 1.8692 2.1809 39.8726 – –

.1149*** −.0529*** −.0231*** −.1151*** .0575* .1781** .8838*** (removed) (removed)

2.6122 −4.7470 −2.8686 −3.2297 1.8511 1.9968 30.2558 – –

– –

– –

.0160** .0233***

2.1200 3.2606

1.5633 28 1,221

1.6485 28 1,221

Notes: 1. RISK, ROE, WF and CARt−1 are instrumented by their one-period lags. 2. t−statistics are based on robust standard errors. 3. ***, ** and * denote significance at the 1%, 5% and 10% levels respectively. 4. All variables are considered initially. Those with insignificant coefficients are removed during the model selection procedure. 5. m2 is the test statistic for second-order serial correlation based on residuals from the first-difference equation with orthogonal deviation transformation. Asymptotically, it follows the standard normal distribution. The critical values for the 1%, 5% and 10% levels of significance are 1.65, 1.96 and 2.57 respectively.

Table 8A.4

A summary of the estimated effects of exogenous changes

Explanatory variable

Model A % change

increases by 10%

REG SIZE GROWTH ROE PEER WF

Model B % change

Short-term

Long-term

Short-term

Long-term

+1.2 −0.4 −0.2 −0.9 +0.6 +1.9

+8.9 −2.6 −1.3 −6.4 +4.4 +13.9

+1.1 −0.5 −0.2 −1.2 +0.6 +1.8

+8.4 −3.9 −1.7 −8.5 +4.3 +13.1

176 The Banking Sector in Hong Kong

Annex 8B Details of the survey results Annex 8B.1 Background The ‘Survey on Capital Holding Decisions’ was sent to all locally incorporated licensed banks on 20 December 2004. Table 8B.1 gives the response rate. Survey questions and banks’ answers are presented in the rest of this Annex. In the survey, regulatory capital requirement refers to the minimum capital adequacy ratio set by the Hong Kong Monetary Authority (HKMA) on individual banks (that is, it may be higher than the Basel 8 per cent minimum) and desired capital means a range within which the bank wishes its actual capital to stay.

Annex 8B.2 Questions and replies This section states the survey questions and presents the statistics of banks’ responses. The questionnaire is adapted from that of Alfon et al. (2004), with slight modifications.

Table 8B.1 Response rate of the survey Population No. of surveys completed Rate of response

24 24 100%

1.

How is desired capital specified?

A. B.

A ratio (of capital base to risk-weighted assets). A level of capital base (that is in terms of amount).

2.

If your AI’s actual capital is above desired capital due to non-transitory factors, you will reduce the actual capital as quickly as possible.

A. B. C. D.

Very likely. Likely. Unlikely. Very unlikely.

3.

If your AI’s actual capital is below desired capital due to non-transitory factors, you will increase the actual capital as quickly as possible.

% ————— 87.50 12.50 —————

% ————— 8.33 20.83 54.17 16.67 —————

% —————

Wong, Choi and Fong 177

A. B. C. D.

Very likely. Likely. Unlikely. Very unlikely.

4.

Suppose your AI’s actual capital deviates from desired capital due to non-transitory reasons.

A.

B.

C.

Actual capital will be adjusted to meet desired capital more quickly if actual capital exceeds desired capital than if the opposite is the case. Actual capital will be adjusted to meet desired capital more quickly if desired capital exceeds actual capital than if the opposite is the case. The pace of adjustments in both cases will be the same.

58.33 33.33 8.33 0 ————— % —————

0

79.17 20.83 —————

5.

A.

B.

C. 6. 6.1.

How does regulatory capital requirement enter into your decision in setting desired capital? Given the regulatory capital requirement, we assess how much additional capital we should hold. We assess how much capital is needed to run the business and then verify whether it meets the regulatory requirement. Others (please specify). What are the determinants of your AI’s desired capital? To avoid the consequences of breaching regulatory capital requirement.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.2.

To maintain/improve your AI’s credit rating by external credit rating agencies.

A. B. C.

Very important. Important. Not important.

% ————— 29.17

58.33 12.5037 —————

% ————— 93.94 6.06 0 0 ————— % ————— 16.67 58.33 0

178 The Banking Sector in Hong Kong

D. E.

Not relevant. Not applicable, because my AI is not rated.

6.3.

Capital held by your AI’s peers.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.4.

Your AI’s risks as perceived by the markets (which may differ from your own assessment).

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.5.

Financing your AI’s long-term business strategy.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.6.

Securing access to inter-bank money markets.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.7.

Securing wholesale deposits.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.8.

Securing retail deposits.

A. B. C. D.

Very important. Important. Not important. Not relevant.

0 25.00 ————— % ————— 0 62.5 29.17 8.33 ————— % ————— 25.00 75.00 0 0 ————— % ————— 58.33 41.67 0 0 ————— % ————— 29.17 50.00 16.67 4.17 ————— % ————— 12.50 62.50 16.67 8.33 ————— % ————— 37.50 41.67 20.83 0 —————

Wong, Choi and Fong 179

6.9.

Complement to risk management and internal systems and controls.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.10.

Cushion against the effect of economic downturn.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.11

Cushion against unexpected losses arising from material risks faced by your AI.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.12.

Regulatory capital underestimates the risks that it captures.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.13.

Activities attracting no capital requirements yet requiring capital.

A. B. C. D.

Very important. Important. Not important. Not relevant.

6.14. Other considerations. Note: One bank said that the large exposure limit and other regulatory limits were relevant.

% ————— 29.17 66.67 4.17 0 ————— % ————— 33.33 66.67 0 0 ————— % ————— 41.67 58.33 0 0 ————— % ————— 4.17 70.83 16.67 8.33 ————— % ————— 4.17 75.00 8.33 12.50 —————

180 The Banking Sector in Hong Kong

6.15.

Please select the top five determinants of desired capital from factors 6.1 to 6.14 and rank them according to their degree of importance in determining your AI’s desired capital by 1, 2, 3, 4 and 5, with 1 being assigned to the most important factor, 2 to the second most important factor, . . . .

Table 8B.2

Banks’ replies to question 6.15

6.1 6.2 6.3 1 91.7 0 0 2 4.2 16.7 0 3 4.2 4.2 4.2 4 0 8.3 8.3 5 0 4.2 4.2 S2 95.8 16.7 0 S3 100.0 20.8 4.2 S4 100.0 29.2 12.5 S5 100.0 33.3 16.7

6.4 0 12.5 12.5 16.7 8.3 12.0 25.0 41.7 50.0

6.5 8.3 33.3 16.7 12.5 16.7 41.7 58.3 70.8 87.5

6.6 0 0 4.2 8.3 16.7 0 4.2 12.5 29.2

6.7 0 0 0 12.5 4.2 0 0 12.5 16.7

6.8 0 8.3 8.3 4.2 8.3 8.3 16.7 20.8 29.2

6.9 0 4.2 16.7 8.3 8.3 4.2 20.8 29.2 37.5

6.10 0 4.2 8.3 8.3 8.3 4.2 12.5 20.8 29.2

6.11 0 12.5 16.7 8.3 12.5 12.5 29.2 37.5 50.0

6.12 0 0 4.2 0 0 0 4.2 4.2 4.2

6.13 0 0 0 0 8.3 0 0 0 8.3

Note: For example, 91.7% of respondents ranked 6.1 as the most important factor and 8.3% of the respondents ranked 6.5 as the most important factor, so forth.38 S2 to S5 are cumulative figures. For example, given a particular factor, the numbers on row S3 show the percentage of respondents who assigned the ranking of 1, 2, or 3 to that factor. By comparing these cumulative figures, the following suggestive ordering is obtained (the degree of importance diminishes from left to right): 1  5  4 () 11 () 2, where () is less conclusive than .

7. A. B. C. D.

How does desired capital differ from actual capital? Actual capital usually exceeds desired capital. Desired capital usually exceeds actual capital. Desired capital is usually very close to actual capital. Actual capital may exceed or fall below desired capital.

8.

Why is actual capital persistently higher or persistently lower than desired capital?

8.1.

This is your AI’s conventional practice.

A. B. C.

Very important. Important. Not important.

% ————— 70.83 12.50 4.17 12.50 —————

% ————— 4.17 62.50 12.50

Wong, Choi and Fong 181

D. E.

Not relevant. Not applicable, because my answer to 7 is C/D.

8.2.

Other reasons (please specify). Note: Some banks said that this was a market practice.

9.

Why would actual capital be lower than desired capital?

9.1.

Unexpected developments within the AI.

A. B. C. D.

Very important. Important. Not important. Not relevant.

9.2.

Unexpected events in the economy affecting adversely the banking sector.

A. B. C. D.

Very important. Important. Not important. Not relevant.

9.3.

Cost of raising extra capital.

A. B. C. D.

Very important. Important. Not important. Not relevant.

9.4.

Other factors (please specify).

10.

What would be the markets’ reaction to an unexpected reduction in your AI’s actual capital arising from, say, a significant reduction in profits?

10.1

Shares would be traded at a lower multiple of earnings.

A. B. C. D. E.

Very likely. Likely. Unlikely. Not relevant. Not applicable, because my AI is not listed.

4.17 16.67 —————

% ————— 16.67 41.67 8.33 33.33 ————— % ————— 29.17 54.17 0 16.67 ————— % ————— 20.83 29.17 16.67 33.33 —————

% ————— 25.00 25.00 4.17 4.17 41.67 —————

182 The Banking Sector in Hong Kong

10.2 A. B. C. D. E.

Credit rating would be reviewed. Very likely. Likely. Unlikely. Not relevant. Not applicable, because my AI is not rated.

10.3

The interbank market would tighten the terms of loans to your AI.

A. B. C. D.

Very likely. Likely. Unlikely. Not relevant.

10.4.

Wholesale depositors would withdraw funds.

A. B. C D.

Very likely. Likely. Unlikely. Not relevant.

10.5.

Retail depositors would withdraw funds.

A. B. C. D.

Very likely. Likely. Unlikely. Not relevant.

10.6.

Other reactions (please specify).

11.

Suppose your AI had experienced a downgrade in its credit rating as a result of an event such as a significant deterioration in credit quality, how would you react to the downgrade?

11.1.

To change the desired capital (as defined by your answer to question 1).

A. B.

The desired capital would not be changed in the short or medium term. The desired capital would be increased in the short and medium term.

% 33.33 45.83 0 0 20.83 ————— % ————— 16.67 62.50 12.50 8.33 ————— % ————— 4.17 50.00 37.50 8.33 ————— % ————— 0 45.83 54.17 0 —————

% ————— 37.50 16.67

Wong, Choi and Fong 183

C.

F.

The desired capital would be increased in the medium term only. The desired capital would be increased in the short term only. The desired capital would be reduced in the short or medium term. Not applicable, because my AI is not rated.

11.2.

To change the actual capital base.

A.

The actual capital would not be changed in the short or medium term. The actual capital would be increased in the short and medium term. The actual capital would be increased in the medium term only. The actual capital would be increased in the short term only. The actual capital would be reduced in the short or medium term. Not applicable, because my AI is not rated.

D. E.

B. C. D. E. F. 11.3.

A. B. C. D. E. F. 11.4.

To change the actual risk-weighted assets (RWA). The actual RWA would not be changed in the short or medium term. The actual RWA would be reduced in the short and medium term. The actual RWA would be reduced in the medium term only. The actual RWA would be reduced in the short term only. The actual RWA would be increased in the short or medium term. Not applicable, because my AI is not rated. To change the risk level by changing the composition of the actual RWA (that is the size of the actual RWA may or may not be changed as a result).

8.33 4.17 0 33.33 ————— % ————— 25.00 29.17 12.50 0 0 33.33 ————— % ————— 12.50 41.67 8.33 4.17 0 33.33 —————

% —————

184 The Banking Sector in Hong Kong

A.

F.

The composition will not be changed in the short or medium term. The composition will be changed to reduce the risk level in the short and medium term. The composition will be changed to reduce the risk level in the medium term only. The composition will be changed to reduce the risk level in the short term only. The composition will be changed to increase the risk level in the short or medium term. Not applicable, because my AI is not rated.

11.5.

Other reactions (please specify).

12.

If your AI’s regulatory capital requirement is increased but its current capital adequacy ratio is still above the new requirement, how would you react to it? To change the desired capital (as defined by your answer to question 1).

B. C. D. E.

12.1. A. B. C. D. E.

The desired capital would not be changed in the short or medium term. The desired capital would be increased in the short and medium term. The desired capital would be increased in the medium term only. The desired capital would be increased in the short term only. The desired capital would be reduced in the short or medium term.

12.2.

To change the actual capital base.

A.

The actual capital would not be changed in the short or medium term. The actual capital would be increased in the short and medium term. The actual capital would be increased in the medium term only. The actual capital would be increased in the short term only.

B. C. D.

8.33 45.83 8.33 4.17 0 33.33 —————

% ————— 45.83 20.83 33.33 0 0 ————— % ————— 58.33 16.67 25.00 0

Wong, Choi and Fong 185

E.

The actual capital would be reduced in the short or medium term.

12.3.

To change the actual RWA.

A.

The actual RWA would not be changed in the short or medium term. The actual RWA would be reduced in the short and medium term. The actual RWA would be reduced in the medium term only. The actual RWA would be reduced in the short term only. The actual RWA would be increased in the short or medium term.

B. C. D. E. 12.4.

A. B. C. D. E.

To change the risk level by changing the composition of the actual RWA (that is the size of the actual RWA may or may not be changed as a result). The composition will not be changed in the short or medium term. The composition will be changed to reduce the risk level in the short and medium term. The composition will be changed to reduce the risk level in the medium term only. The composition will be changed to reduce the risk level in the short term only. The composition will be changed to increase the risk level in the short or medium term.

12.5.

Other reactions (please specify).

13.

Do you make use of any financial or economic capital model for determining desired capital?

A. B. C. D.

Yes. No. No, but there is a plan to develop such model in the near future. Others (please specify).

0 ————— % ————— 83.33 8.33 8.33 0 0 —————

% ————— 45.83 20.83 33.33 0 0 —————

% ————— 25.00 41.67 33.33 0 —————

186 The Banking Sector in Hong Kong

14. A. B. C.

D. 15.

A. B. C. D. E.

Do stress tests play a role in setting desired capital? Yes. No. No, but there is a plan to make more use of stresstesting for assessing capital level in the near future. Others (please specify). To what extent are your decisions on desired capital influenced or determined by group capital allocation policies? To a great extent. To a limited extent. Not at all. Others (please specify). Not applicable, because my AI is not a subsidiary of a foreign banking group.

% ————— 45.83 20.83

33.33 0 —————

% ————— 33.33 16.67 4.17 8.3339 37.5 —————

Wong, Choi and Fong 187

Notes 1. The method and components used in the calculation are specified in the Third Schedule to the Banking Ordinance. 2. According to the Banking Ordinance, all Authorized Institutions (AIs) incorporated in Hong Kong are required to adhere to the minimum 8 per cent CAR. This is in accordance with the 1988 Basel Capital Accord. However, the HKMA may increase it to not more than 12 per cent for a licensed bank (raised to 16 per cent pursuant to the Banking (Amendment) Ordinance 2005); or not more than 16 per cent for a restricted licence bank or deposit-taking company. In other words, regulatory capital requirement can be bank-specific. 3. In the UK, the assets-weighted average CAR of banks was 14.16 per cent for the period from 1997 to 2002, while the assets-weighted average required minimum was only 9.42 per cent (see Alfon et al. 2004). 4. A number of studies have addressed this question, although not for the case of Hong Kong. See, for example, Ediz et al. (1998). 5. See, for example, Marcus (1983), Lindquist (2004), Ayuso et al. (2004) and Alfon et al. (2004). 6. The survey is basically a replication of the survey adopted in Alfon et al. (2004), with appropriate modifications to reflect the environment of Hong Kong’s banking industry. 7. Demsetz et al. (1996) found that banks having a lower franchise value behave more aggressively. 8. Another possible reason that could generate a negative correlation between CAR and bank size is that larger banks may be more aggressive and tend to take more risk with a specific amount of capital. 9. This variable is the ratio of the amount of assets having 100 per cent risk weight to the total assets. Using alternatively the ratio of RWA to the total assets gives a similar result. However, the fact that RWA is the denominator of CAR, the dependent variable in our regression analysis, makes the use of such a ratio less desirable. 10. Alternatively the insignificance of the coefficient may suggest that, given a particular value of total assets, the change in capital base and the change in RWA are at a similar rate. This could be because the bank’s assessment of how much the capital base should be increased to buffer against the heightened risk as a result of a change in the portfolio composition, is similar to that as implied by the associated change in RWA. In other words, the assessments of the banks and the regulator on the relative riskiness between different assets are similar. 11. Note that as mentioned later in this chapter this could support the hypothesis that small banks have larger adjustment costs and thus choose to hold more capital. The finding is also consistent with the hypothesis that small banks need to maintain excess capital to finance their long-term strategies and to rely more on excess capital in signalling financial strength. Our quantitative analysis cannot distinguish the contributions of these hypotheses. 12. We have also assessed directly the impact of risk on banks’ capital decisions by studying how the simple ratio of capital base to total assets is affected by the relative amount of risky assets held (the proportion of the bank’s total

188 The Banking Sector in Hong Kong

13.

14. 15.

16. 17.

18.

19. 20.

21.

22. 23.

24. 25.

26.

27.

assets that attracts a risk weight of 100 per cent). Such analytical method is also adopted by Ediz et al. (1998). A positive and significant coefficient is obtained, suggesting a positive correlation between the amount of capital and risk level. However, the way the CAR ratio may respond to any change in risk perceived by banks cannot be derived simply by such a relationship. Short-term changes refer to the response of the endogenous variable in the immediate period, whereas long term changes refer to its cumulative response when the adjustment process is complete. As shown in Figure 8.1, there are outlier observations in the sample, so median, instead of mean, is depicted in Figure 8.2. Similar patterns appear for the time series of the capital buffer as measured by the ratio of the difference between the actual CAR and minimum CAR to minimum CAR. This suggests that the relationship conveyed by the chart is not greatly altered even if the variations of regulatory minimum are taken into account. Similar results are obtained by Ayuso et al. (2004) and Alfon et al. (2004) for Spain and the UK respectively. The coefficient of the interaction between the size of banks (that is the variable BIG) and the economic growth (that is the variable GROWTH) is found to be positive and significant in Model A. Details of the estimation can be seen in Annex 8A. Bris and Cantale (2004) emphasize that this agency problem should be taken into consideration in bank capital regulation because it would lead to banks taking too little risk (or creating too little credit). Poor cost efficiency is another manifestation of the agency problem (see Berger and Hannan 1998). If there is no separation between ownership and control, the cost of holding more capital is entirely borne by the owner, and the agency problem becomes irrelevant. The importance may stem from the fact that financing the extra capital needed for business growth by retained earnings is generally perceived to be preferred by the market. Financing long-term strategy by capital could also improve operational flexibility, and the banks may wish to pre-fund future acquisitions. Note that this could also support other hypotheses, see Note 11. In our survey, the banks are asked whether the cost of adjusting capital might induce them to keep their CARs lower than the desired level. Opinions are somewhat diverse, with half of the respondents giving a firm ‘yes’ reply. This could be due to the fact that the banks generally maintain a CAR that is above the desired level and, therefore, have not experienced capital deficiency. As indicated in a previous part of this chapter, the evidence also supports the agency–problem hypothesis. The possible endogeneity of the return on equity (ROE) due to the effect on leverage (and hence ROE) of changes in CAR is handled by an instrumentvariable technique in the quantitative analysis. We hypothesize that interbank lenders and wholesale depositors are more sophisticated in their assessment of banks’ credit risk compared with their retail counterparts. No wholesale deposits data are readily available.

Wong, Choi and Fong 189 28. The estimated coefficient is small, suggesting that the peer pressure in capital holding is moderate. 29. The interaction between the regulatory requirement (that is the variable REG) and the closeness of CAR to regulatory requirement (that is the variable CLOSE) is found to be significantly positive in Model B. Details of the estimation are in Annex 8A. 30. Milne (2002) suggests that capital requirements act as an incentive mechanism in which a breach gives rise to a penalty. It is then shown that banks would want to hold more capital than the regulatory minimum. 31. The model can be generalized to test if CAR responds asymmetrically to positive and negative changes in the explanatory variables. This approach has been attempted, but no significant asymmetries were found. Thus, the model stated in equation (8A.1) suffices. 32. A more general empirical model which allows α to differ across banks may be used. But this would increase the number of coefficients to be estimated by as many times as the number of banks in the sample. Given that our sample has only 51 time points but 31 cross sectional units, such procedure is inappropriate. For similar reasons, we do not assume a time-varying α. 33. This quarter is used because all sampled banks existed. 34. Anderson and Hsiao (1981), Arellano and Bond (1991) and Arellano and Bover (1995) suggested alternative instrumental variable estimation methods that lead to consistent estimators. In this chapter, we apply the procedure proposed by Arellano and Bover (1995). 35. See Maeshiro and Vali (1988) for details about how orthogonal deviations offer efficiency gains over first differences. 36. CLOSE is a dummy variable that equals one (zero) if the bank’s CAR is higher (lower) than REG by less than one standard deviation of its CAR. BIG is another dummy variable. It equals one (zero) if the bank’s real value of total assets is above the upper quartile of the data on SIZE. 37. A combination of A and B. 38. Table 8B.2 does not incorporate 6.14 because only one reply to question 6.14 was received. 39. One bank said that both group and own policies were important. Another bank said that it has no such group policy.

References K. Alexander and W. Wagner, ‘Excess Capital: A New Market Failure?’, Financial Regulator, 9 (2004) 58–63. I. Alfon, I. Argimon and P. Bascunana-Ambros, ‘What Determines How Much Capital is held by UK Banks and Building Societies?’, FSA Occasional Paper, Financial Services Authority, (2004). T. W. Anderson and C. Hsiao, ‘Estimation of Dynamic Models with Error Component’, Journal of the American Statistical Association, 76(375) (1981) 598–606. M. Arellano and S. Bond, ‘Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations’, Review of Economic Studies, 58 (1991) 277–97.

190 The Banking Sector in Hong Kong M. Arellano and O. Bover, ‘Another Look at the Instrumental Variables Estimation of Error Components Models’, Journal of Econometrics, 68 (1995) 29–52. J. Ayuso, D. Perez and J. Saurina, ‘Are Capital Buffers Pro-cyclical? Evidence from Spanish Panel Data’, Journal of Financial Intermediation, 13 (2004) 249–64. BCBS, International Convergence of Capital Measurement and Capital Standards: A Revised Framework, Basel Committee on Banking Supervision (www.bis.org, 2004). A. N. Berger, ‘The Relationship between Capital and Earnings in Banking’, Journal of Money, Credit and Banking, 27 (1995) 432–56. A. N. Berger and T. H. Hannan, ‘The Efficiency Cost of Market Power in the Banking Industry: A Test of the “Quiet Life” and Related Hypotheses’, Review of Economics and Statistics, 80 (1998) 454–65. A. N. Berger, R. J. Herring and G. P. Szego, ‘The Role of Capital in Financial Institutions’, Journal of Banking and Finance, 19 (1995) 393–430. C. Borio and P. Lowe, ‘To Provision or Not to Provision’, BIS Quarterly Review, (2001) 36–48. A. Bris and S. Cantale, ‘Bank Capital Requirements and Managerial Self-interest’, Quarterly Review of Economics and Finance, 44 (2004) 77–101. R. S. Demsetz, M. R. Saidenberg and P. E. Strahan, ‘Banks with Something to Lose: the Disciplinary Role of Franchise Value’, Economic Policy Review, Federal Reserve Bank of New York, 2(2) (1996), 1–14. D. W. Diamond and R. G. Rajan, ‘A Theory of Bank Capital’, Journal of Finance, 55 (2000) 2431–65. T. Ediz, I. Michael and W. Perraudin, ‘The Impact of Capital Requirements on U.K. Bank Behaviour’, FRBNY Economic Policy Review, Federal Reserve Bank of New York, (1998). M. Flannery and K. Rangan, ‘Market Forces at Work in the Banking Industry: Evidence from the Capital Buildup of the 1990s’, AFA 2003 Washington, DC Meetings; EFA 2002 Berlin Meetings Presented Paper, (2002). M. Jensen and W. Meckling, ‘Theory of the Firm: Managerial Behaviour, Agency Costs, and Ownership Structure’, Journal of Financial Economics, 3 (1976) 305–60. K. Lindquist, ‘Banks’ Buffer Capital: How Important is Risk’, Journal of International Money and Finance, 23 (2004) 493–513. A. Maeshiro and S. Vali, ‘Pitfalls in the Estimation of a Differenced Model’, Journal of Business & Economic Statistics, 6 (1988) 511–15. A. Marcus, ‘The Bank Capital Decision: A Time Series-Cross Section Analysis’, Journal of Finance, 38 (1983) 1217–32. A. Milne, ‘Bank Capital Regulation as an Incentive Mechanism: Implications for Portfolio Choice’, Journal of Banking and Finance, 26 (2002) 1–23. F. Modigliani and M. Miller, ‘The Cost of Capital, Corporation Finance, and the Theory of Investment’, American Economic Review, 48 (1958) 261–97. M. O’Hara and W. Shaw, ‘Deposit Insurance and Wealth Effects: The Value of Being “Too Big to Fail”’, Journal of Finance, 45 (1990) 1550–600. R. Repullo, ‘Capital Requirements, Market Power, and Risk-taking in Banking’, Journal of Financial Intermediation, 13 (2004) 156–82. J. Richardson and M. Stepheson, ‘Some Aspects of Regulatory Capital’, FSA Occasional Paper, Financial Service Authority, (2000). J. A. Santos, ‘Bank Capital Regulation in Contemporary Banking Theory: A Review of the Literature’, BIS Working Papers, no. 90 (2000).

9 Benchmarking Model of Default Probabilities of Listed Companies1 Cho-Hoi Hui, Eric Tak-Chuen Wong, Chi-Fai Lo and Ming-Xi Huang

9.1 Introduction The Basel Committee on Banking Supervision is responsible for proposing capital requirements for internationally active banks. The Committee first proposed the Basel New Capital Accord, also known as Basel II, in 1999, with the final version (Basel Committee on Banking Supervision 2004) in June 2004. By year-end 2006, Basel II is expected to replace the original Basel Accord, which was implemented in 1988. Basel II allows banks to choose among several approaches to determine their capital requirements to cover credit risk. The standardized approach allows less sophisticated banks to use external credit ratings to classify their assets into different risk classes. Over time, banks are expected to evolve to the internal ratings-based (IRB) approaches (foundation and advanced), which rely on their own experience in determining the risk characteristics of various asset classes according to their internal rating systems. For example, the foundation IRB approach for corporate, sovereign, and bank exposures allows banks to provide estimates of probability of default (PD) but requires banks to use supervisory estimates of loss given default (LGD), exposure at default (EAD), and maturity. The advanced IRB approach for such exposures allows banks to provide estimates of all these risk characteristics. As credit risk measures are estimated by banks, systematic underestimation of such measures and the corresponding regulatory capital in a bank (or a number of banks) will increase the bank’s vulnerability to adverse changes in market conditions, in particular during a financial or banking crisis. The safety and stability of the banking system would thus be affected by whether credit risk measures are estimated in a sound and prudent manner. Therefore, the validation methodologies of IRB systems 191

192 The Banking Sector in Hong Kong

have emerged as one of the important issues of the implementation of Basel II. Validation comprises an assessment of the validity of the risk components EAD, PD, and LGD, and the underlying rating system itself. For the validation of PDs, there are in general two stages: validation of the discriminatory power of a rating system and validation of the accuracy of the PD quantification. Compared with the evaluation of the discriminatory power, methods for validating the accuracy of the PD quantification are at a much earlier stage. While one of the methods is back-testing, a major obstacle to back-testing of PDs is the scarcity of data, caused by the infrequency of default events and the impact of default correlation.2 Even if the five-year requirement of Basel II for the length of time series for PDs is met, the explanatory power of statistical tests will still be limited. Statistical tests alone will be insufficient to establish supervisory acceptance of an internal rating system. Nevertheless, banks should be expected to use various quantitative validation techniques to detect weaknesses in a rating system. Due to the limitations of using statistical tests to verify the accuracy of the PD quantification, benchmarking can be a complementary tool for the validation and calibration of PD estimates. Benchmarking involves the comparison of a bank’s PD estimates to results from alternative sources. It is quite flexible in the sense that it gives banks and supervisors latitude to select an appropriate benchmark. An important technical issue is the design of the mapping from an individual bank’s estimates to the benchmark. Benchmarking seems to be promising and would allow supervisors to make inferences about the characteristics of an internal rating system. It also appears to be part of the whole process of producing internally generated estimates at banks’ IRB systems. For example, banks frequently use external and independent references to calibrate their own IRB systems in terms of PDs. Benchmarking internal PD estimates with external and independent PD estimates is implicitly given a special credibility, and deviations from this benchmark provide a reason to review the internal estimates. This chapter proposes a benchmarking model for the purpose of IRB validation of listed companies, which is developed upon using a credit risk model and a simple mapping process. The credit risk model is based on the recent studies of the predictive capability of structural models. Black and Scholes (1973) and Merton (1974) have been the pioneers in the developments of the structural models for credit risk of corporates using a contingent-claim framework.3 They treat default risk equivalent to a European put option on a firm’s asset value and the firm’s liability is the option strike. To extend the Merton model, the structural models

Hui, Wong, Lo and Huang 193

with more complex and dynamic liability structures have been considered by Black and Cox (1976), Longstaff and Schwartz (1995), Briys and de Varenne (1997), Collin-Dufresne and Goldstein (2001) and Hui et al. (2003).4 Delianedis and Geske (1999) show that PDs produced by the simple structural models of Merton (1974) and Geske (1977) possess significant and very early information about credit rating migrations. While the sample of companies that actually default is small, changes in the shape of the term structures of PDs appears to detect impending migrations to default. Leland (2004) finds that PDs generated from the Longstaff and Schwartz model fit actual default rates provided by Moody’s (1998) for longer time horizons quite well for reasonable parameters with proper calibrations.5 However, the default boundary in the Longstaff and Schwartz model should be specified as a certain fraction of the principal bond value. This specification imposes a constraint to some of the calibrations for the model (for example the asset volatility), that may not be empirically reasonable, in order to obtain consistent results. Hui et al. (2006) propose a structural model where the underlying stochastic variable is the leverage ratio of a firm, which is mean-reverting to a time-dependent target leverage ratio. They show that unlike the Merton model and other variants mentioned above, the model is capable of generating term structures of PDs which are consistent with the term structures of actual default rates of credit ratings of BBB and below reported by Standard & Poor’s (S&P’s) (2002), in particular at longer time horizons. In a special case of the structural model where the liability is assumed to be not mean-reverting, the model converges into a simplified model in which the two main input parameters are the leverage ratio of a firm and its associated volatility. These input parameters can be obtained from market data. The calibrations of the time-dependence and levels of target leverage ratios are not necessary for the simplified model. The use of this simplified model for benchmarking purposes can thus avoid the calibration problem found in Leland (2004). The following section demonstrates that model PDs generated from this simplified structural model based on market data are consistent with the actual default rates of credit ratings of BBB and below. In view of the capability of the structural model for capturing actual default rates without any specific calibration, credit risk measures of listed companies (with market information about their leverage ratios and associated volatilities) can be obtained from the structural model. Regarding the mapping process of the benchmarking model, the idea is to associate a company with an external credit rating by mapping the

194 The Banking Sector in Hong Kong

term structure of PDs of the company generated by the structural model to the term structures of default rates reported by a rating agency (for example S&P’s). According to the actual default rates reported by credit rating agents such as S&P’s, different ratings give different term structures of default rates in terms of values and shapes. Such term structures reflect the characteristics of default risk of companies with different ratings. The term structures of PDs and default rates could be interesting for examining the changing credit structure of either individual companies, industries, or the whole economy. The term structure of PDs could contain information about the business cycle. The use of the entire term structure (that is up to the cumulative default rate of 15 years) for mapping purposes could also avoid the issue of choosing which particular time horizon (say one-year or five-year) of the default rates as the appropriate basis. After mapping the company to an external credit rating (say S&P’s BBB), the corresponding one-year default rate of the BBB rating is assigned as the benchmark one-year PD of the company. Such benchmark PD can be considered as the average one-year PD estimate based on a pool of companies which have been covered by S&P’s rating assessment. The use of such mapping method could avoid the problem of downward-biased PDs at short maturities produced directly by credit risk models. The remainder of the chapter is organized as follows. In the following section we present the structural model of Hui et al. (2006) used for the benchmarking model. In section 9.3, we illustrate how the benchmarking model is developed from the structural model and the mapping process. The empirical results of the benchmarking model based on data in the US are presented in section 9.4. The final section summarizes the findings.

9.2 Structural model of term structures of PDs The structural model employed for generating term structures of PDs follows the model proposed by Hui et al. (2006). In the original model, a firm’s liability is assumed to be governed by a time-dependent meanreverting stochastic process whilst the firm value (that is defined as market-value capitalization) follows a simple lognormal process. To simplify the model specification, it is assumed that the dynamic process of the liability is not mean-reverting. It is therefore unnecessary for the calibration of the time-dependent mean-reverting process in this context. The liability in fact plays no direct role in the simplified model. The key feature is the risk-adjusted probability of the leverage ratio, which

Hui, Wong, Lo and Huang 195

is defined as the ratio of a firm’s liability to its market-value capitalization, hitting a certain value. A firm’s leverage ratio and the risk-free interest rate are the stochastic variables in the model. The leverage ratio is assumed to follow a lognormal diffusion process and the dynamics of the interest rate is drawn from the term structure model of Vasicek (1977), that is the Ornstein–Uhlenbeck process. The risk-adjusted dynamic of the leverage ratio L is modelled by the following stochastic differential equation: dL = α(t)Ldt + σL (t)LdZL ,

(9.1)

where α(t) and σL (t) are the drift and the volatility of L respectively and are time dependent. The drift α(t) is effectively taken as zero in the chapter.6 The continuous stochastic movement of the interest rate r follows: dr = κ(t)[θ(t) − r]dt + σr (t)dZr ,

(9.2)

where σr (t) is the instantaneous volatility. The short-term interest rate r is mean-reverting to long-run mean θ(t) at speed κ(t). The Wiener processes dZL and dZr are correlated with dZL dZr = ρ(t)dt. Applying the Ito’s lemma, the partial differential equation governing the price P(L, r, t) of a corporate discount bond with time-to-maturity of t based on the model is ∂P 1 1 ∂2 P ∂2 P ∂2 P = σL2 (t)L2 2 + σr2 (t) 2 + ρ(t)σL (t)σr (t)L ∂t 2 ∂L 2 ∂r ∂L∂r ∂P ∂P + κ(t)[θ(t) − r] − rP. + α(t)L ∂L ∂r

(9.3)

The bond value is obtained by solving equation (9.3) subject to the final payoff condition and the boundary condition. When the firm’s leverage ratio is above a predefined level L0 , bankruptcy occurs before bond maturity at t = 0. This is consistent with the event of bankruptcy being associated with a high level of the leverage ratio. On the other hand, if the leverage ratio has never breached the predefined level L0 , the payoff to bondholders at bond maturity is the face value of the bond.

196 The Banking Sector in Hong Kong

As shown in the appendix of Hui et al. (2006), the corresponding default probability, Pdef (L, t), of a corporate discount bond over a period of time t based on equation (9.3) can be approximated by

Pdef (L, t) = 1 −

⎧ ⎨

⎡ N⎣

 ln

⎩

L0 L



− b2 (t)

 2b1 (t)

⎤ ⎦

      L + b2 (t) + 16β2 b1 (t) − exp 4β ln L0 ⎡ × N⎣

 ln

L L0



⎤⎫ + b2 (t) + 8βb1 (t) ⎬ ⎦ ,  ⎭ 2b1 (t)

(9.4)

where N(.) is the cumulative normal distribution function, β is a real number parameter, and b1 (t) and b2 (t) are defined as follows:

b1 (t) =



1 2

t 0



t

b2 (t) =

σL2 (t  )dt  ,

γ(t  )dt  ,

0

γ(t) = α(t) + ρ(t)σL (t)σr (t)a2 (t) exp [a1 (t)] − 

t

a1 (t) = −

1 2 σ (t), 2 L

κ(t  )dt  ,

0



t

a2 (t) = −

exp [−a1 (t  )]dt  .

0

The parameter β is adjusted such that the approximate solution in equation (9.4) provides the best approximation to the exact results by using a simple method developed by Lo et al. (2003) for solving barrier option values with time-dependent model parameters. The computed PDs within a period of 15 years based on equation (9.4) for companies with ratings CCC, B, BB and BBB are presented in Figure 9.1. The leverage ratios used for individual ratings are based on the

Hui, Wong, Lo and Huang 197 Default Probabilities (%)

Model

S&P's data

70 65

CCC

60 55 50 45

B

40 35 30 BB

25 20 15 10

BBB

5 0 1

2

3

4

5

6

7 8 9 Tenor (Year)

10

11

12

13

14

15

Figure 9.1 PD term structures generated from the structural model and actual cumulative default rates reported by S&P’s (2002) of ratings of CCC, B, BB and BBB Notes: The leverage ratios of ratings CCC, B, BB and BBB are 0.732, 0.538, 0.495 and 0.315 respectively. The leverage volatilities σL of ratings CCC, B, BB and BBB are 0.299, 0.27, 0.241 and 0.213 respectively.

industry median reported by S&P’s (2001). The values of σL fall close to the asset volatilities of firms with individual ratings estimated by Delianedis and Geske (1999).7 Other common parameters used in calculations are L0 = 1.0, α = 0, κ = 1, θ = 5%, σr = 0.03162 and ρ = 0. The model term structures of PDs are compared with the term structures of cumulative default rates of the corresponding ratings based on 9769 companies’ assigned long-term ratings from 1981 to 2001 reported by S&P’s (2002). The results in Figure 9.1 show that the model gives the basic shapes and values of the term structures of PDs for ratings of BBB and below, which broadly match with the actual default rates. However, Hui et al. (2006) report that the PDs generated by the model for credit ratings A and above are all much lower than S&P’s default rates.8 This means that the structural model is not capable of differentiating default risks among credit ratings of A− and above. In the benchmarking process, the ratings of A− and above are treated as one single rating whose term structure of PDs is the average of those of ratings of A− and above.

198 The Banking Sector in Hong Kong

9.3 Benchmarking process According to the requirements under Basel II, PD estimates should be a long-run average of one-year default rates for borrowers. In the benchmarking model, instead of using the structural model presented in the above section to obtain the one-year PD for benchmarking purposes directly, a corresponding rating of a listed company is obtained by mapping its model term structure of PDs generated by the structural model to the term structure of actual default rates of an external credit rating. The one-year PD of the listed company is thus assigned as the actual oneyear average default rates of the corresponding credit rating. According to S&P’s (2002), the one-year default rate of a rating is the average default rate over the period 1981–2001. Such mapping process can therefore satisfy the requirement of a long run average. The benchmarking process involves the structural model and mapping. A mapping is a process of establishing a correspondence between the risk assessment or measurement of a company and the reference data from external sources such as rating agencies. The process can be thought of as characterizing each company as if it were part of the reference data. The characterizing factor used in this chapter is the term structures of PDs determined by the structural model and the term structures of cumulative default rates of different ratings reported by S&P’s (2002). Each company is mapped to the reference data based on this characterizing factor. Figure 9.2 illustrates the benchmarking process. Based on the structural model described in section 9.2, a company’s leverage ratio and its volatility are the input parameters used to generate the model term structure of PDs of the company. Using the least square fit, the model term structure of PDs is mapped to the ‘closest’ term structure of default rates of a S&P’s rating. Such rating is assigned to the company as a benchmark rating ranging from CCC to A− and above. The actual one-year average default rate of the benchmark rating gives the corresponding one-year benchmark PD of the company. This benchmarking process can avoid the problem of downward-biased PDs at short maturities, that is common to many credit risk models in particular contingent-claims models which assume continuous dynamics. The one-year benchmark PD could be compared with a bank’s one-year PD estimate of a company according to its IRB system. The comparison may show whether the PD estimated by the bank is higher or lower than the benchmark PD. Based on comparisons for a number of companies, the results would indicate any inconsistencies or systematic

Hui, Wong, Lo and Huang 199 Input market parameter: Leverage ratio and its volatility of a listed company

Model Engine Generate the PD term structure of the company

Mapping with S&P’s default rates Map the model PD term structure of the company to S&P’s default-rate term structures of different ratings (static pools cumulative average default rates)

Assigning benchmark ‘S&P’s’ rating Based on the mapping result, a rating is assigned to the company

Implied one-year benchmark PD of the company It is based on the actual one-year average default rate of the benchmark rating

Compare the one-year benchmark PD with the bank’s oneyear PD of the company based on its IRB system. Based on comparisons for a number of companies, the results will indicate any inconsistencies/systematic underestimation in the bank’s PD estimates Figure 9.2

Benchmarking process of benchmark PD estimation

underestimation in the bank’s PD estimates relative to the benchmark PDs. Another important application of the benchmarking model is as a means to rank credits on a relative basis. Such benchmark ranking could be compared with the ranking of credits conducted by a bank’s internal rating system.

200 The Banking Sector in Hong Kong

9.4 Data and empirical results 9.4.1 Leverage ratios and their volatilities The performance of the benchmarking model in ranking credits is studied in this section. The data used for the analysis consist of 3943 samples from 193 listed industrial companies in the US with S&P’s ratings from March 1990 to July 2004. Table 9.1 presents the numbers of companies in the respective S&P’s ratings (from CCC to A− and above) and assigned ordinal numbers. The two input variables (that is the leverage ratio and its volatility) of each sample company in the benchmarking model are computed based on the data of its consolidated financial statements and stock prices. A sample company’s liability D includes the principal value of all financial debts, short-term and long-term borrowings and convertible bonds which participate in the financial leverage of the company. It also includes quasi-financial debts such as capital leases, underfunded pension liabilities or preferred shares. Non-financial liabilities such as accounts payable, deferred taxes and reserves are not included. The details of the calculation of the company’s liability are given in Appendix 9A. As the company’s market-value capitalization can be obtained from its equity values, its leverage ratio can be obtained as the ratio of the liability to market-value capitalization. In order to obtain the term structures of PDs specified in equation (9.4), it is necessary to link the leverage volatility σL to the equity volatility σS . The values of σL are assumed to fall close to the asset volatilities Table 9.1 Assignment of ordinal numbers to S&P’s ratings and numbers of sample companies with S&P’s ratings S&P’s ratings

Ordinal numbers

Numbers of sample companies

A− and above BBB+ BBB BBB− BB+ BB BB− B+ B B− CCC

1 2 3 4 5 6 7 8 9 10 11

942 422 618 430 338 368 457 207 91 46 24

Source: Bloomberg.

Hui, Wong, Lo and Huang 201

of companies. This means that the volatility of a company’s liability is assumed to be immaterial. The daily standard deviation of equity returns (t) σS is calculated based on a window of 1000 days, where t is the obser(t) vation date. The estimate of the daily asset volatility σL at time t is (t) obtained by applying a gearing ratio to σS as: (t)

(t)

σL = σS

S , S+D

(9.5)

where S denotes the company’s equity price at time t. The gearing ratio (t) is derived in Appendix 9B. The annualized leverage volatility σL at time t is constructed as the square root of 250 times the corresponding daily leverage volatility.

9.4.2 Relative credit risk assessment On each sample company, we compare its ratings derived from: 1. the benchmarking process described in section 9.3 above (referred to as a benchmark rating); and 2. the S&P’s ratings (referred to as a market rating). The ordinal numbers are assigned to individual S&P’s ratings as in Table 9.1. The differences between the market and benchmark ratings based on the ordinal numbers of the sample companies are presented in Table 9.2. A positive figure refers to a situation of an underestimation of a rating (that is overestimation of credit risk) of a company by the benchmarking process. For example, the market rating is BBB+, while the benchmark rating is BBB−. The histograms of the mismatch distribution of the market and model rating are presented in Figure 9.3. Table 9.2 Mismatch statistics of benchmark ratings versus S&P’s ratings of 3,943 sample companies Mismatch statistics Differences 0 ±1 ±2 ±3 ±4 ±5 ±6

Sample companies (%)

Cumulative figures (%)

21.7 25.9 21.2 12.8 8.8 5.7 2.2

21.7 47.6 68.8 81.7 90.5 96.1 98.4

202 The Banking Sector in Hong Kong

21.7

Percentage of the sample (%) 25

16.6

16.5

20

10 9 8 7 6 5 4 3 2 1 0 1 Mismatches

2

9.3

10.1

15

0.2

0.6

0.1

2.1

0.8

1.4

0.8

0.2

0.0

0.0

0.0

0.0

5

2.7

4.7

4.9

7.4

10

8

9

10

0 3

4

5

6

7

Figure 9.3 Mismatch distribution of benchmark ratings versus S&P’s ratings of 3,943 sample companies

The results presented in Table 9.2 show that the benchmark ratings of 22 per cent of the sample companies exactly match with the market ratings. Regarding the difference of −1 and +1, the coverage is about 26 per cent of the sample companies. As the exact matching and the differences of ±1 broadly cover one major rating (for example BBB−, BBB and BBB+ are the sub-ratings of the major BBB rating), 48 per cent of the sample companies match between the benchmark ratings and the market ratings in terms of major grades. The results show that the benchmark ratings could broadly track the market ratings. Figure 9.2 shows that most of the sample companies have differences between −2 and +2, though there are some large discrepancies. Such differences mean deviations of two sub-grades or less in the S&P’s rating scale. According to the matching statistics presented in Table 9.2, the differences between ±2 cover about 69 per cent of the sample companies. The most significant outliers tend to be the cases where the benchmarking model imputes a high PD to a company that is on the other hand rated much better by S&P’s. Figure 9.2 also shows that the distribution of mismatches is negatively skewed. This reflects that the benchmarking model tends to assign lower ratings to companies relative to the market ratings assigned by S&P’s. This observation could be explained by the finding by Delianedis and Geske (1999) who find that both rating migrations (mostly rating downgrades) and defaults are detected by the structural models (that is

Hui, Wong, Lo and Huang 203

the Merton and Geske models) months before the actual events. This means that the structural models would probably give higher credit risk with early information about rating downgrades and default incorporated, compared with the actual ratings at a given time. However, the use of different lag time for the matching process does not provide better results of the mismatch statistics. It is because the lag time between early information and actual rating downgrades is not uniform in the sample companies and the lag time also gives ‘inconsistent’ ratings for those sample companies without any risk of rating downgrades and default.

9.4.3 Discriminatory power One method to examine the benchmarking model’s ability to accurately rank credit risks is through a receiver operating characteristic (ROC) which is a visual tool. The ROC can be constructed as two representative groups of S&P’s ratings for investment rated (that is BBB− and above) and non-investment rated (that is BB+ and below) companies which are available in the sample companies. Benchmark ratings are assigned to individual sample companies according to the mapping process discussed in section 9.3 above. The construction of the ROC does not require the sample composition to reflect the true proportion of investment rated and non-investment rated companies. Concavity of the ROC is equivalent to the conditional PDs being a decreasing function of the underlying ratings and non-concavity indicates sub-optimal use of information in the specification of the rating function. The ROC curve is constructed as follows. Someone has to find out from the benchmark PDs that which sample companies will be categorized as investment rated or non-investment rated companies. A ranking of the companies is established in line with the assessment of their risk according to their benchmark PDs, starting with the riskiest company and ending with the company classified as being the least risky. Each company will be checked whether its benchmark PD correctly assigns it as an investment rated or non-investment rated company by comparing with its S&P’s rating. The hit rate HR(PD) is defined as HR(PD) =

H(PD) , NNI

(9.6)

where H(PD) is the number of companies assigned correctly as noninvestment rated companies based on the benchmarking model, and NNI is the total number of non-investment rated companies in the samples. This means that the hit rate is the fraction of non-investment rated

204 The Banking Sector in Hong Kong Hit rate (%) 100 Accuracy ratio  0.7104 90 80 70 Benchmarking model 60 50 40 30 Random model

20 10 0 0

10

20

30

40

50

60

70

80

90

100

False alarm rate (%) Figure 9.4 Receiver operating characteristic curve and accuracy ratio of the benchmarking model

companies which are classified correctly. The false alarm rate FAR(PD) is defined as FAR(PD) =

F(PD) , NI

(9.7)

where F(PD) is the number of false alarms, that is the number of investment rated companies that are classified incorrectly as non-investment rated companies based on the benchmarking model. The total number of investment rated companies in the samples is denoted by NI . The ROC curve is a plot of HR(PD) versus FAR(PD), which is illustrated in Figure 9.4. A model’s performance is the better the steeper the ROC curve is at the left end and the closer the ROC curve’s position is to the point (0,1). This means that the model is the better, the larger the area under the ROC curve is. The quality of the benchmarking model is measured by the accuracy ratio (AR). Engelmann et al. (2003) prove a relation between the AR and the area under the ROC curve. The AR is defined as  AR = 2 0

1

HR(FAR)d(FAR) − 1.

(9.8)

Hui, Wong, Lo and Huang 205

The AR is 0 for a random model without discriminatory power and it is one for a perfect model. As the AR of the benchmarking model in Figure 9.4 is 0.71, the benchmarking model has adequate discriminatory power of ranking credit risks of the sample companies and is a reasonable model in practice.

9.4.4 Measures of association Measures of the association between the market and benchmark ratings are studied in this subsection. One standard measure is a simple correlation statistic. However, correlation can be overly influenced by outlier data. The correlation statistic is likely to be dominated by the companies with the highest credit risk, and high credit quality companies are likely to be given little weight. To address these concerns, rank correlation statistics: Kendall’s tau, Stuart’s tau and gamma, are examined. Such rank order statistics measure the degree of co-monotonic dependence of two random variables. The notion of co-monotonic dependence generalizes linear dependence that is expressed via (linear) correlation. In particular, any pair of random variables with correlation one (that is any linearly dependent pair of random variables) is co-monotonically dependent. But in addition, as soon as one of the variables can be expressed as any kind of increasing transformation of the other, the two variables are co-monotonic. Given a pair of random variables (X, Y), Kendall’s tau is defined as τb = P(X1 < X2 , Y1 < Y2 ) + P(X1 > X2 , Y1 > Y2 ) − P(X1 < X2 , Y1 > Y2 ) − P(X1 > X2 , Y1 < Y2 ),

(9.9)

where (X1 , Y1 ) and (X2 , Y2 ) are independent copies of (X, Y). Hence, τb can be seen as the difference between two probabilities, namely the probability that the larger of the two X-values is associated with the larger of the two Y-values and the probability that the larger X-value is associated with the smaller Y-value. Two series that are identical will have a statistic of one while a statistic of zero will indicate no association. The detailed definitions of the rank order statistics (that is Kendall’s tau, Stuart’s tau and gamma) are illustrated in Appendix 9C. The measures of association for the benchmark ratings with the market ratings are presented in Table 9.3. The calculations of the statistics are based on the method in Brown and Benedetti (1977). The rank correlation statistics of Kendall’s tau, Stuart’s tau and gamma are 0.5241, 0.5070 and 0.5873 respectively. The asymptotic standard errors of the statistics,

206 The Banking Sector in Hong Kong Table 9.3 Degree of association between benchmark ratings versus S&P’s ratings of 3,943 sample companies Degree of association Type of statistics

Estimates

Asymptotic standard error

p-value of no association

Kendall’s tau (τb ) Stuart’s tau (τc ) Gamma ()

0.5241 0.5070 0.5873

0.0090 0.0088 0.0101

0.0000 0.0000 0.0000

which are obtained by assuming the null hypothesis of no association (that is τb = 0, τc = 0 and  = 0) between the variables, are equal to or less than 1 per cent. The p-values of no association of the statistics are zero. The results show that the benchmark ratings could broadly track the market ratings and the association between them is adequately significant. This indicates that the likelihood where the rating agencies (for example, S&P’s) and benchmarking model would rank companies in the same order is reasonably high.

9.5 Summary This chapter presents a benchmarking model for the purpose of IRB validation of PD estimates of publicly listed companies. In view of the capability of the structural credit risk models for capturing term structures of actual default rates, credit risk measures of listed companies can be obtained from the chosen model without any specific calibration in this chapter. The model inputs of leverage ratios and associated volatilities are available in market data. The benchmarking model assigns benchmark ratings and one-year PDs to companies by mapping the term structures of PDs of the companies generated by a chosen structural model to the term structures of default rates reported by S&P’s. The empirical results show that the benchmark ratings could broadly track the S&P’s ratings of the US sample companies. The association between them is statistically significant. The results demonstrate that the benchmarking model has adequate discriminatory power of ranking credit risk of the sample companies in terms of differentiating investment rated and non-investment rated companies. Benchmark PDs obtained from the model could thus be used as external and independent PD estimates for comparisons with banks’ internal PD estimates of listed companies. Significant deviations from this benchmark provide a reason to review the banks’ internal estimates and their credit rating processes.

Hui, Wong, Lo and Huang 207

Appendix 9A A company’s leverage ratio is defined as the ratio of its liability to marketvalue capitalization. The liability D is determined from financial data in consolidated statements. Using Bloomberg’s data, the financial debt of the company is the sum of the short-term and long-term interest-bearing financial obligations (for example loans and bonds) and 50 per cent of other non-interest bearing obligations (see Pan 2001). The 50 per cent weight is assumed because some of these obligations (for example pension liabilities) are similar to the nature of financial liabilities while some of them (for example provisions) are not. The financial data in the consolidated financial statement contain 100 per cent of the financial liabilities of subsidiaries even though the parent company does not fully own the subsidiaries. This may therefore exaggerate the liabilities of the company. To adjust for this, a portion of the liabilities of its subsidiaries that are not owned by the company should be subtracted from the financial debt. The liability of the company is equal to its financial debt less the minority interest which represents the portion of interest that the parent company does not own in the subsidiaries. In the calculation, the amount of the minority interest is limited to no more than half of the financial debt. Therefore, the liability D is D = financial debt − Min (minority interest, financial debt/2)

208 The Banking Sector in Hong Kong

Appendix 9B The derivation of the gearing ratio in equation (9.5) follows the methodology used in Pan (2001). Let S and σS denote a company’s equity price and its equity volatility respectively. The volatility σL of the company is assumed to fall close to the volatility σV of the company’s asset value. This means that the volatility of the company’s liability is assumed to be immaterial. In general, σS and σV are related through σS = σV

V ∂S . S ∂V

(9B.1)

The distance to default measure η is defined as the number of annualized standard deviations separating the company’s current equity value from the default threshold such that     1 V ∂S V V η= = log , (9B.2) log σV D σS S ∂V D where V and D are the company’s asset value and liability respectively. To obtain the gearing ratio, the boundary conditions of equations (9B.1) and (9B.2) are examined. The first boundary condition is the behaviour of V near D that is the default threshold. As default approaches, S approaches zero. Thus, V |S=0 = D,

(9B.3)

at the boundary and V ≈D+

∂V S, ∂S

(9B.4)

near the boundary. By substituting equation (9B.4) into equation (9B.2), we have η ≈ 1/σS ,

(9B.5)

near the boundary. The second boundary condition is far from the default barrier (that is S  D). Here, we have S/V → 1.

(9B.6)

This leads to an approximation for η under equation (9B.2) as: η

1 log σS



 S . D

(9B.7)

Hui, Wong, Lo and Huang 209

The simplest expressions for V and η that simultaneously satisfy the near default boundary conditions (9B.3) and (9B.5) and the far from default conditions (9B.6) and (9B.7) are V = S + D and η=

S+D log σS S



 S+D . D

(9B.8)

Thus, equations (9B.2) and (9B.8) give σL = σS

S , S+D

(9B.9)

by assuming σL ≈ σV . Equation (9B.9) relates the leverage volatility to the observable equity volatility.

210 The Banking Sector in Hong Kong

Appendix 9C In the following illustration, all measures are defined by their sample analogs. Let aij denote the observed frequency in cell (i, j) in an I × J   contingency table. Let ri = i aij be the ith row total, ci = j aij the jth  column total and N = i j aij the total frequency. Let Aij =



akt +

k
Dij =





akt ,

(9C.1)

akt ,

(9C.2)

k>i t>j

akt +

k>i t
 kj

and P = Q =

 i

j

i

j



aij Aij

(9C.3)

aij Dij .

(9C.4)

Aij is the total frequency of the cells whose indices are either both greater or both less than (i, j). Dij is the total frequency of the cells that have one index greater and one index less than (i, j). Thus P is twice the number of agreements, and Q is twice the number of disagreements in the ordering of the cell indices when all pairs of observations are compared. In this context, an interpretation of P is the probability that for a randomly chosen pair of companies, both the market and benchmarking models will rank the firms in the same order. Q represents the probability that the market and benchmarking models disagree on the ranking. The definitions of P and Q exclude ties, where ties are defined as pairs of observations sharing at least one common index. As given in Kendall (1955), Kendall’s tau τb is estimated by ⎡ τb = (P − Q)/ ⎣ N 2 −



⎞⎤ 21 ⎛  ri2 ⎝N 2 − cj2 ⎠⎦

i

(9C.5)

j

and Stuart’s tau τc is estimated by τc = (P − Q)/[N 2 (m − 1)/m],

(9C.6)

Hui, Wong, Lo and Huang 211

where m = min (I, J). Goodman and Kruskal (1954) propose the measure of association gamma which is estimated by  = (P − Q)/(P + Q).

(9C.7)

These three measures have the same numerator but differ in the manner by which they are normalized. It is noted that |τc | ≤ |τb | ≤ || (see Brown and Benedetti 1977).

212 The Banking Sector in Hong Kong

Notes 1. A revised and edited version has been published in Journal of Fixed Income, vol. 15 (2006). 2. Due to correlation between defaults in a portfolio, observed default rates can systematically exceed the critical PD values if these are determined under the assumption of independence of the default events. 3. The second approach is the reduced-form models in which time of default is assumed to follow a stochastic process governed by its own distribution that is characterized by an intensity or hazard rate process. This approach has been considered by Jarrow and Turnbull (1995), Jarrow et al. (1997), Madan and Unal (1998), and Duffie and Singleton (1999). Their models in general focus on more sophisticated characterization of the hazard process. The derived pricing formulas can be calibrated to market credit spreads. Some extensions explore assumptions surrounding recovery rate, risk-free interest rate processes, and contract boundary conditions. 4. See also the survey of Bohn (2000). 5. The predicted PDs are too low for short maturities. The problem of downwardbiased PDs at short maturities is however common to all contingent-claims credit risk models which assume continuous dynamics. 6. If a firm’s market-value capitalization and liability are assets that some agent is willing to hold, their risk-adjusted drift will be equal to the instantaneous interest rate. The drift of their ratio L is therefore zero. 7. The volatility of a company’s liability is assumed to be immaterial. 8. The reason is that the problem of downward-biased default risk of companies with good credit quality is common to models which assume continuous dynamics of the underlying variables.

References Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards: a Revised Framework (2004). F. Black and J. C. Cox, ‘Valuing Corporate Securities: Some Effects of Bond Indenture Provisions’, Journal of Finance, 31(2) (1976) 351–67. F. Black and M. Scholes, ‘The Pricing of Options and Corporate Liability’, Journal of Political Economics, 81 (1973) 637–54. J. R. Bohn, ‘A Survey of Contingent-claims Approaches to Risky Debt Valuation’, Journal of Risk Finance, Spring (2000) 53–69. E. Briys and F. de Varenne, ‘Valuing Risky Fixed Rate Debt: An Extension’, Journal of Financial and Quantitative Analysis, 32 (1997) 230–48. M. B. Brown and J. K. Benedetti, ‘Sampling Behavior of Test for Correlation in Two-way Contingency Tables’, Journal of the American Statistical Association, 72 (1977) 309–15. P. Collin-Dufresne and R. S. Goldstein, ‘Do Credit Spreads Reflect Stationary Leverage Ratio?’, Journal of Finance, 56(5) (2001) 1929–57. G. Delianedis and R. Geske, ‘Credit Risk and Risk Neutral Default Probabilities: Information about Rating Migrations and Defaults’, Unpublished working paper, University of California, Los Angeles, (1999).

Hui, Wong, Lo and Huang 213 D. Duffie and K. Singleton, ‘Modeling Term Structures of Defaultable Bonds’, Review of Financial Studies, 12 (1999) 687–720. B. Engelmann, E. Hayden and D. Tasche, ‘Testing for Rating Accuracy’, Risk, 16( January) (2003) 82–6. R. Geske, ‘The Valuation of Corporate Liabilities as Compound Options’, Journal of Financial and Quantitative Analysis, 12 (1977) 541–52. L. A. Goodman and W. H. Kruskal, ‘Measures of Association for Cross Classifications’, Journal of the American Statistical Association, 49 (1954) 732–64. C. H. Hui, C. F. Lo and S. W. Tsang, ‘Pricing Corporate Bonds with Dynamic Default Barriers’, Journal of Risk, 5(3) (2003) 17–37. C. H. Hui, C. F. Lo and M. X. Huang, ‘Are Corporates’ Target Leverage Ratios Time-dependent?’, International Review of Financial Analysis, 15 (2006) 220–36. R. Jarrow, A. Lando and S. Turnbull, ‘A Markov Model for the Term Structure of Credit Spreads’, Review of Financial Studies, 10 (1997) 481–523. R. Jarrow and S. Turnbull, ‘Pricing Options on Financial Securities subject to Default Risk’, Journal of Finance, 50 (1995) 53–86. M. G. Kendall, Rank Correlation Methods, 2nd edn (London: Charles Griffin and Co, 1955). H. E. Leland, ‘Predictions of Expected Default Frequencies in Structural Models of Debt’, Journal of Investment Management, 2(2) (2004) 5–21. C. F. Lo, H. C. Lee and C. H. Hui, ‘A Simple Approach for Pricing Black–Scholes Barrier Options with Time-dependent Parameters’, Quantitative Finance, 3 (2003) 98–107. F. A. Longstaff and E. S. Schwartz, ‘A Simple Approach to Valuing Risky Fixed and Floating Rate Debt’, Journal of Finance, 50(3) (1995) 789–819. D. Madan and H. Unal, ‘Pricing the Risks of Default’, Review of Derivatives Research, 2 (1998) 121–60. R. C. Merton, ‘On the Pricing of Corporate Debt: the Risk Structure of Interest Rates’, Journal of Finance, 29 (1974) 449–70. Moody’s Investors Services, Historical Default Rates of Corporate Bond Issuers, 1920– 97 (New York: Moody’s Investors Services, 1998). G. Pan, ‘Equity to Credit Pricing’, Risk, 14(November) (2001) 99–102. Standard & Poor’s, Adjusted Key U.S. Industrial Financial Ratios (New York: Standard & Poor’s, 2001). Standard & Poor’s, Rating Performance 2001 (New York: Standard & Poor’s, 2002). O. A. Vasicek, ‘An Equilibrium Characterisation of the Term Structure’, Journal of Financial Economics, 5 (1977) 177–88.

10 Measuring Provisions for Collateralized Retail Lending1 Cho-Hoi Hui, Chi-Fai Lo, Eric Tak-Chuen Wong and Po-Kong Man

10.1 Introduction While banks have faced difficulties over the years for a multitude of reasons, the major cause of serious banking problems continues to be related directly to lax credit standards for borrowers, poor portfolio risk management, or a lack of attention to changes in economic or other circumstances that can lead to a deterioration in the credit standing of a bank’s counterparties. In view of this experience, the Basel Committee on Banking Supervision (2000) sets out the sound practices which specifically address establishing an appropriate credit risk environment and maintaining an appropriate credit administration, measurement and monitoring process. These practices should also be applied in conjunction with a system in place for determining the adequacy of provisions. In some countries, bank supervisors require banks’ provisioning systems to be forward looking such that future changes in economic conditions that could have unfavourable effects on the banks’ credit exposures should be taken into account.2 The level of provisions will be based on the banks’ forecasts of collateral value and other macroeconomic conditions, regardless of the current losses, defaults and restructurings in their loans. On the other hand, in other countries, banks are required to determine provisions with reference to the losses, defaults and restructurings that have already occurred in their loans, according to detailed regulations on loan classification with minimum provisioning requirements.3 The rationale behind issuing detailed regulatory parameters could be to level the playing field or make bank regulations more easily enforceable. Under this approach, collateral is taken into account when classifying a loan, for example, to a more favourable category 214

Hui, Lo, Wong and Man 215

than that reflecting its own risk and determining the level of provisions accordingly. While a central feature of provisioning systems is typically to refer to losses that have already been incurred or are anticipated with a high degree of confidence, provisioning requirements may differ significantly for several reasons. One is whether provisioning requirements aim at addressing only losses that follow from visible and identifiable events, or at establishing provisions for expected losses. Another issue is how banks are expected to factor in the value of collateral. In many countries, the value of collateral is subtracted from the required provisions to determine the level of the actual provisions to be established. Specific provisioning requirements are often designed for certain portfolio segments, such as retail loans including residential mortgage loans and credit card lending. Several countries (for example Australia, France, Korea, the Netherlands, Saudi Arabia and Singapore) do not require retail loans to be classified and provisioned on an individual basis but allow them to be assessed on a pooled basis. In Australia, for example, management is allowed to deal with small consumer loans on a portfolio basis. The Basel Committee is responsible for proposing regulatory requirements, including capital and provisioning requirements, for internationally active banks. Typically, bank supervisors around the world adopt the guidelines put forth by the Basel Committee. The Basel Committee first proposed the Basel New Capital Framework, also known as Basel II, in June 1999, with revisions in January 2001 and June 2004 (Basel Committee on Banking Supervision 2004). By year-end 2006, Basel II is expected to replace the current Basel Accord. Both the current and new capital adequacy frameworks are based on the concept of a capital ratio where the numerator represents the amount of capital of the bank available and the denominator is a measure of the risks faced by the bank and is referred to as risk-weighted assets. The resulting capital ratio must be no less than 8 per cent. According to the proposals in Basel II, banks will be allowed to calculate regulatory capital charges for their credit exposures, including those in their retail portfolios, using the standardized approach or the internal ratings-based (IRB) approach. The standardized approach allows less sophisticated banks to use external credit ratings to classify their corporate, bank and sovereign assets into risk classes and to apply different defined risk weights to other assets, including retail exposures. Over time, banks are expected to evolve to the IRB approach, which rely on the bank’s own experience in determining the risk components of various asset classes.

216 The Banking Sector in Hong Kong

The IRB calculation of risk-weighted assets for credit exposures relies on four basic risk components: (i) probability of default (PD), which measures the likelihood that the borrower will default over a given time horizon; (ii) loss given default (LGD), which measures the proportion of the exposure (after taking the presence and type of collateral into account) that will be lost if a default occurs; (iii) exposure at default, which measures the bank’s exposure at the time of default; and (iv) effective maturity. Different risk-weight functions based on the risk components are used by the IRB bank for calculating the corresponding risk-weighted assets of different types of credit exposures. There are three distinct IRB risk-weight functions for different classes of retail exposures: (i) residential mortgages; (ii) revolving credit, and (iii) other retail loans. Under the framework of Basel II, the IRB banks will also be required to compare their actual provisions with expected losses (see Basel Committee on Banking Supervision 2004). Any shortfall (that is the expected loss amount exceeds the provision amount) should be deducted from Tier 1 and Tier 2 capital of the bank and any excess (that is the provision amount exceeds the expected loss amount) will be eligible for inclusion in Tier 2 capital subject to a cap set by individual bank supervisors. It is therefore important to ensure adequate provisions being provided by banks against expected losses. Basel II defines expected loss as PD times LGD times exposure at default (see Basel Committee on Banking Supervision 2004). This makes the assumption that the PD and LGD are independent variables, that is uncorrelated. The time horizon of the PD and LGD estimates is defined to be one year. It is however noted that defaults are likely to be clustered during times of economic distress and LGD may be correlated with default rates. For example, an increase in defaults in residential mortgage loans leads to an increase in the supply of properties associated with those defaulted loans, and correspondingly to a reduction in their prices and to larger losses for banks. The effects of the correlation between PD and LGD (including collateral value) on credit risk measures have been considered in the context of corporate loans in recent years. In Frye’s (2000a) structural model which draws from the conditional approach suggested by Finger (1999) and Gordy (2000b), collateral and asset values of firms (that is borrowers) are modelled using a single index based on a systematic (the state of the economy) and an idiosyncratic risk factor. Correlations between PD and LGD result from joint dependence of borrowers’ asset value and of collateral value on the systematic risk factor (that is the economic cycle). Frye’s (2000b) empirical analysis shows a strong positive correlation between default rates and LGD for corporate bonds. The results allow

Hui, Lo, Wong and Man 217

him to conclude that the economic cycle can produce a double misfortune involving greater-than-average default rate and poorer-thanaverage recoveries. By incorporating collateral value uncertainty to LGD, Jokivuolle and Peura (2003) propose a model of risky debt in which collateral value is correlated with the PD of a borrower. The borrower’s PD is based on the default mechanism proposed by Merton (1974) where the borrower defaults its debt if its asset value is less than its outstanding liability at the maturity of the debt. Their numerical studies demonstrate the importance of factors such as collateral value volatility and correlation between collateral value and the borrower’s asset value for the estimation of credit risk quantity. On a portfolio basis, Altman et al. (2002) use a US corporate bond database covering the period 1982–2000 and find strong evidence of a positive relationship between PD and LGD. They explore through simulation analysis what effect incorporating the positive correlation between PD and LGD has on the value-at-risk for a broadly representative commercial loan portfolio. For their particular simulations they find that setting the correlation between the PD and LGD to zero (as is usual practice), rather than to its estimated value, leads to a reduction in the value-at-risk of at least one quarter. Although several models and studies exist to examine the effects of the relationship between PD and LGD on credit losses of corporate loans, the body of research on retail credit risk measurement is quite sparse according to the studies conducted by Allen et al. (2004). In view of this observation, Allen et al. suggest that techniques of credit risk measurement (such as KMV’s Portfolio Manager4 and Credit Suisse Financial Products’ Credit Risk Plus5 ) for corporate loans could be applied to retail loans. As PD is also assumed to be independent from LGD in these two techniques, the corresponding expected losses remain simply measured as PD times LGD. Apart from correlation between PD and LGD, the time horizon of the expected-loss measure, which is defined in Basel II as one year, also raises a concern with underestimating provisioning requirements. In order to ensuring adequate level of provisions being provided by banks for expected losses, it is necessary for banks to measure expected losses of retail loans for different time horizons, particularly for long-term secured lending such as residential mortgage loans. While losses on any single retail loan will not cause a bank to become insolvent, Gross and Souleles (2002) find that retail borrowers were increasingly willing to default on their debt, in large part because of the falling social and legal costs of default. This implies that the provisioning requirements of expected losses for individual banks which are active

218 The Banking Sector in Hong Kong

in retail lending could increase due to higher default rates of the banks’ retail loans. The Basel Committee on Banking Supervision (2001) realizes that the longer-term viability of the IRB framework would be enhanced by further international agreement on standards for provisioning of expected loss, as capital adequacy critically depends on accurate valuation of banks’ assets and liabilities. This would make it easier to revisit the IRB framework should future efforts to consider changes in the definition of regulatory capital and/or more harmonized provisioning rules be undertaken. In view of the above developments, the measurement of provisions against expected losses of retail lending secured by collateral would be important for improving the capital adequacy framework for banks. The purpose of this chapter is to develop a model for measuring provisions of a pool of collateralized retail loans which have the same collateral type (for example residential properties) and broadly the same loan-tovalue ratio. The model follows the contingent-claim approach of pricing options developed by Black and Scholes (1973) and Merton (1973). Merton (1974) has also been the pioneer in the pricing of corporate bonds using the contingent-claim framework. He treats default risk equivalent to a European put option on a firm’s asset value and the firm’s liability is the option strike. To extend the Merton model, structural models with more complex and dynamic liability structures have been considered by Black and Cox (1976), Longstaff and Schwartz (1995), Briys and de Varenne (1997), Collin-Dufresne and Goldstein (2001) and Hui et al. (2003). These models are able to explain empirical term structures of credit spreads of corporate bonds with different credit ratings to some extent. Regarding the proposed model in this chapter, the pool of collateralized retail loans is equivalent to a put option written by a bank to its borrowers, where the borrowers could walk away by letting the bank reprocess the collateral upon default. The strike of the put option is the outstanding amount of the loans. When the borrowers default their loans, the loss incurred in the bank is the amount of the loans less the value recovered from the sales of the collateral securing the loans. The loss is the same as a standard payoff of a put option. The provision is therefore equivalent to the option premium multiplied by the PD of borrowers in the pool. The model thus takes account of the stochasticity of the collateral value. The PD of borrowers in the pool over a given time horizon is another stochastic variable in the model. This means that there is a probability that each loan in the pool will default within a time period. The effects of the correlation between PD and the collateral value on the provisioning measures are considered in the model.

Hui, Lo, Wong and Man 219

It is recognized that the collateral value in a pool of loans will affect its associated PD, in particular when the loans are in negative equity. In general, the collateral value (such as property value) is closely correlated with movements in personal income over time. Additionally, changes in local unemployment rates are strongly correlated with changes in personal income growth. Both are good measures of the state of the local economy. Therefore, changes in local unemployment rates can be expected to do a good job of explaining changes in default rates. They could also reflect changes in the prevalence of a trigger event such that some borrowers will have reason to examine their financial situations. Empirically, Campbell and Dietrich (1983) find that during the 1960s and 1970s default for insured residential mortgages has been significantly influenced by changes in regional rates of unemployment in the US. Similarly, Agarwal and Liu (2003) find that unemployment is a significant determinant of a household’s delinquency and bankruptcy decision by focusing on the credit card market in the US. As changes in unemployment rates reflect the states of an economic cycle, these empirical findings support that the PD of residential mortgage loans could be affected by an economic cycle. The dynamics of the PD of retail loans could thus be assumed to follow a mean-reverting random process, which is more general than a pure-random process and captures the characteristics of an economic cycle.6 The PD and the parameters governing its dynamics can be obtained from a bank’s historical default data of their retail portfolios. We derive a closed-form formula from the model as a function of the collateral value and PD to measure the provision of a pool of collateralized retail loans. The two stochastic variables are explicitly correlated in the model. The model allows the PD to follow a meanreverting process. The model parameters such as the volatility, correlation and drift of PD are time dependent in the derivation. The model structure, which fits well with the data typically available for banks, can be applied to measuring provisions of retail lending secured by collateral. More accurate measurement of provisioning requirements would enhance banks’ capabilities of managing credit risk of such lending. The scheme of this chapter is as follows. In the following section, we develop the model of measuring provisions based on the proposed dynamics of the PD and collateral value. The corresponding closed-form formula is derived. In section 10.3, we present some empirical findings of the dynamics of the PD of residential mortgage loans and property values based on the residential mortgage market in Hong Kong. The impact of

220 The Banking Sector in Hong Kong

the model parameters on required provisions is studied in section 10.4. In the final section we shall summarize our investigation.

10.2 Model for measuring provisions In the model for measuring provisions of a pool of retail loans, the provision is equivalent to the option premium capturing the expected loss of the loans in negative equity multiplied by the PD of borrowers in the pool. The collateral value is therefore one of the two variables. It is reasonable to assume that the loans in the pool will default subject to the following conditions: (1) trigger events happen drawing borrowers’ attention to the financial options to default their obligations in the pool; and (2) the collateral value falls substantially below outstanding loan balance. Such conditions give a PD that each loan in the pool would default within a time period. The PD is thus the second variable in the model. The PD is defined as an average PD of borrowers in a pool of retail loans over a time horizon of t. The pool is composed of loans with the same collateral type and broadly the same loan-to-value ratio. Its continuous stochastic movement, which is denoted by D, is governed by a mean-reverting lognormal diffusion process. It follows the stochastic differential equation: dD = κD (t)[ln θD (t) − ln D]dt + σD (t)dzD D

(10.1)

The parameter κD (t) determines the speed of adjustment toward a mean PD of θD (t). σD (t) is the volatility of D and dzD is a standard Wiener process. The model parameters are time dependent. Equation (10.1) implies that D drifts towards θD (t) when the level of D is different from the mean PD. When κD (t) is set equal to zero, the dynamics of D is a lognormal diffusion process without any drift. Let V denotes the collateral value securing the loans in the pool. V is assumed to follow a lognormal diffusion process and governed by dV = μV (t)dt + σV (t)dzV V

(10.2)

where σV (t) and μV (t) are the volatility and the rate of return respectively of V. This process is considered to be valid for financial collateral such as equities and physical collateral such as real estate collateral (see for example Kau et al. 1992). The differentials of the Wiener processes dzD

Hui, Lo, Wong and Man 221

and dzV in equations (10.1) and (10.2) are correlated with dzD dzV = ρ(t)dt

(10.3)

By applying Ito’s lemma for equations (10.1), (10.2) and (10.3), the partial differential equation governing the value P (D, V , t) of the provision of the pool of retail loans is ∂P ∂2 P 1 1 ∂2 P ∂2 P = σD2 (t)D2 2 + σV2 (t)V 2 2 + ρ(t)σD (t)σV (t)DV ∂t 2 ∂D 2 ∂V ∂D∂V ∂P ∂P + (r − s)V − rP (10.4) + [κD (t)(ln θD (t) − ln D)]D ∂D ∂V where r is the risk-free interest rate and s is dividend if the collateral is equities. It is noted that physical collateral (for example, residential real estate) could be analogous to a stock providing a known dividend yield. The owner of the collateral may receive a yield (for example, a rental yield) equivalent to a ‘dividend yield’. The solution of equation (10.4) is subject to the final condition that represents the loss incurred in a bank over a time horizon of t. The amount of the loss depends on the outstanding loan value L of the loans in the pool and the collateral value after time t. The value L is the bank’s actual exposure after taking repayments for the loan principals over time t into account. As the loans in the pool have broadly the same loan-to-value ratio, the pool can be viewed as an aggregated loan. The final condition of the provision is thus specified as P(D, V , t = 0) = D max (L − V , 0)

(10.5)

where max (L − V, 0) is the standard payoff of a put option.7 The solution of equation (10.4) subject to the final condition (10.5) is P(D, V, t) = Dη(t) exp



t

0

 − V exp 

t

    z0 α(t  )dt  − rt × LN − √ 2c1 ρ(t  )σD (t  )σV (t  )η(t  )dt  − (s − r)t

0

z0 + 2c1 ×N − √ 2c1



 (10.6)

222 The Banking Sector in Hong Kong

where

  σ 2 (t) 1 η(t) + σD2 (t)η2 (t), α(t) = κD (t) ln θD (t) − D 2 2    t κD (t  )dt  , η(t) = exp −

(10.7)

(10.8)

0

z0 (V, t) = ln (V/L) + (r − s)t − c1 (t)  t dt  ρ(t  )σD (t  )σV (t  )η(t  ), +

(10.9)

0

 c1 (t) = 0

t

dt 

σV2 (t  ) , 2

(10.10)

and N is the cumulative normal distribution function. The detailed derivation of the solution in equation (10.6) is given in Appendix 10A. When the model parameters are constant or timedependent functions which can be integrated, z0 (t) and c1 (t) can be integrated analytically and equation (10.6) is thus in a closed form. The closed-form solution in equation (10.6) involves nothing more complex than the standard normal distribution function in terms of D and V. It has an intuitive structure. It is composed of a put-option solution as a function of V multiplied by a factor as a function of D. The put-option part is a decreasing function of the collateral value V and depends on V and L only through their loan-to-value ratio (L/V ). The ratio therefore provides a summary measure of facility risk (that is LGD) and can be used by banks for categorizing internal facility ratings of retail loans. Similar to a put option, the provision is an increasing function of σV (t). The value of D affects the provision of the pool as a multiplication factor with a scale factor of η(t) in the solution. The dynamics of D affects the provision indirectly through its correlation ρ with V . A large and negative ρ reduces the value of the second minus term of the solution t through exp [ 0 dt  ρ(t  )σD (t  )σV (t  )η(t  )] and thus increases P(D, V , t). This is consistent with the intuition regarding some retail lending such as residential mortgage loans where the decrease in property prices will increase the default rate of the loans (that is −ρ), that increases the required provision. Equation (10.6) also shows that the provision is an increasing function of θD (t). This means that an increase in the mean level of D

Hui, Lo, Wong and Man 223

implies a higher provision of a retail loan portfolio. When the current D is lower (higher) than θD (t), κD (t) drifts D higher (lower) towards θD (t). A corresponding increase in κD (t) will increase (decrease) the provision. If κD (t) is sufficiently large, D would stick to θD (t) with very small random movement and becomes stationary.

10.3 Empirical analysis In this section, we present some empirical findings of the dynamics of the PD of residential mortgage loans and property values based on the data of the residential mortgage market in Hong Kong. The data sample is the monthly private domestic price index in Hong Kong8 , and the monthly problem-loan ratio which is defined as the sum of the delinquency ratio (that is overdue more than three months) and the rescheduled loan ratio of residential mortgage loans in banks. The problem-loan ratio can be viewed as a proxy of the default rate of the loans. It is however noted that a one-year default rate is expected to be higher than the problemloans ratio as the default rate is a cumulative figure while the number of problem loans will be reduced after writing off the loans. The data consists of residential mortgage loans with different loan-to-value ratios. The sample does not differentiate between loans in positive value and in negative value. The problem-loan ratio and the private domestic price index represent the dynamical variables of the PD (D) and the collateral value (V) specified in equations (10.1) and (10.2) respectively. The samples, which cover the periods from June 1998 to February 2004 for D and from January 1993 to February 2004 for V , are published by the Hong Kong Monetary Authority and the Rating and Valuation Department of the Hong Kong SAR Government respectively.9 They provide with 69 observations for D and 134 observations for V . The data series and their descriptive statistics are presented in Figure 10.1 and Table 10.1 respectively. Using the augmented Dickey–Fuller (ADF) test and the maximum-likelihood technique on the available monthly data, the problem-loan ratio of residential mortgage loans is shown to follow a mean-reverting process. We also describe the econometric approach used for estimating the model parameters relating to D and V . Applying Ito’s Lemma and defining X = ln D and Y = ln V, equations (10.1) and (10.2) are respectively rewritten as:   1 dX = κD (t) ln θD (t) − σD2 (t) − X dt + σD (t)dzD 2

(10.11)

224 The Banking Sector in Hong Kong Private domestic price index (1999  100) 200

Problem-loan ratio 1.8

180

1.6 Private domestic price index

160

1.4

140

1.2

120

1.0

100

0.8 Problem-loan ratio

80

0.6

1 January 2004

1 January 2003

1 January 2002

1 January 2001

1 January 2000

1 January 1999

1 January 1998

1 January 1997

1 January 1996

1 January 1995

0.2 1 January 1994

0.4

40 1 January 1993

60

Figure 10.1 Private domestic price index (V ) and problem-loan ratio (D) of residential mortgage loans

Table 10.1 Statistics of the data series of V and D Variables

Number of Data samples coverage

Sample Standard Minimum Maximum mean derivation

V Private domestic price index (1999 = 100)

134

Jan-1993 to 100.6 Feb-2004

Monthly price change #

133

D Problemloan ratio

69

27.8

58.4

172.9

Feb-1993 to −0.0012 0.0314 Feb-2004

−0.1259

0.0930

Jun-1998 to 0.0129 Feb-2004

0.0029

0.0165

0.0031

Note: # The monthly price change is defined as ln(PPI(t )) − ln(PPI(t − 1)), where PPI is the private domestic price index.

  1 dY = μV (t) − σV2 (t) dt + σV (t)dzV 2

(10.12)

The log values can be characterized by an Ornstein–Uhlenbeck process. Following Brennan and Schwartz (1982), Marsh and Rosenfeld (1983) and Dietrich-Campbell and Schwartz (1986), we can estimate the parameters of the continuous-time model in equations (10.11) and (10.12) using the following discrete-time econometric specification: Zt+1 − Zt = αZ + βZ Zt + εZ,t+1

(10.13)

Hui, Lo, Wong and Man 225

E[εZ,t+1 ] = 0,

E[ε2Z,t+1 ] = σZ2

(10.14)

where Z refers to X or Y. It is worth mentioning that the econometric specification in equations (10.13) and (10.14) assumes that the model parameters are independent of time. This specification is therefore regarded as a time-independent case of the model described in section 10.2. The corresponding model parameters in equations (10.1) and (10.2) can be found by κD = −βX

(10.15)

! σX2

(10.16)

σD =

 θD = exp

2αX + σX2 −2βX

μV = αY +

1 2 σ 2 Y

σV =

! σY2

 (10.17)

(10.18)

(10.19)

Our econometric approach is to estimate equations (10.13) and (10.14) for X (that is, ln D) and Y (that is, ln V ) using the maximum-likelihood method. The maximum-likelihood technique has been used in empirical tests of continuous-time models of interest rates by Marsh and Rosenfeld (1983), De Munnik and Schotman (1994) and Bali (1999). In regard of X and Y respectively, we begin by estimating models specified in equations (10.13) and (10.14), and assuming βY = 0. These specifications assume that the dynamics of X and Y follow the model description in section 10.2. Further to this estimation, we consider other model specifications. For X, we consider another specification by restricting the parameters in equation (10.13) to αX = βX = 0, that is no mean-reverting process for X. For Y, we consider a restriction of αY = 0 in equation (10.13), that is μY = σY2 /2. The appropriateness of the model restrictions for X and Y is evaluated using the likelihood ratio test. Table 10.2 presents the parameter estimates, asymptotic t-statistics, coefficient of determination (R2 ) and log-likelihood statistics (LL) for the unrestricted model and the restricted model of X and Y. The likelihood ratio (LR) test statistics of the restricted models are computed to evaluate

–

–

−0.0012 (−0.4560)

–

βY

αY

0.0314 (16.2946)

0.0313 (16.2909)

σY

0.0668 (11.7126)

0.0370 (11.6261)

σX

394.177 394.074

−0.0016

LL

149.784

190.315

LL

0.0000

R2

–0.1215

0.6595

R2

0.2060 (0.6499)

–

LR (p-value)

81.0620 (0.0000)

–

LR (p-value)

3.8415

–

χ2(0.05)

5.9918

–

χ2(0.05)

1

–

df

2

–

df

where Z refers to X or Y .

E[εZ,t+1 ] = 0,

E[ε2Z,t+1 ] = σZ2

Zt+1 − Zt = αZ + βZ Zt + εZ,t+1

Table 10.2 displays the maximum likelihood estimates of alternative models of X (ln D) and Y( ln V). The parameter estimates with asymptotic t -statistics in parentheses are presented for each model. For each variable, the maximized log-likelihood statistics (LL) for the unrestricted model and the restricted model are shown to compare the explanatory power of the unrestricted model and the restricted model. Likelihood ratio (LR) tests evaluate the restriction imposed by the restricted model against the unrestricted model. The LR test statistics with the associated p-value, degrees of 2 ) at the 5 per cent level of significance are reported. The parameters are estimated from the freedom (df) and Chi-squared critical values (χ(0.05) following discrete time system of equations:

Restricted Model of Y (αY = 0)

Unrestricted Model of Y

–

–

−0.1499 (−11.4593)

−0.6368 (−11.0417)

Unrestricted Model of X

Restricted Model of X (αX = βX = 0)

βX

αX

Estimation results of alternative models of X (ln D) and Y (ln V )

Model (Restriction)

Table 10.2

226

Hui, Lo, Wong and Man 227

the appropriateness of the model restriction. For X, the LR test statistic is 81.0620 and the null hypothesis of the test is αX = βX = 0. As the test involves two restrictions on the parameters, the test statistic has a Chi-squared distribution with two degrees of freedom (χ22 ). As the probability of the χ22 variable being larger than 5.9918 is 5 per cent and the LR test statistic is 81.0620 (>5.9918), the null hypothesis of αX = βX = 0 is rejected at the 5 per cent level of significance. The test result suggests that the unrestricted model for X is preferred and X follows a meanreverting process. The parameter βX is negative and implies that κD is positive. This finding is consistent with the model description of the PD in section 10.2. Further investigation is conducted to determine whether the dynamical process of X is mean-reverting. A unit root test provides a simple method of testing for mean reversion. The unit root test adopted here is the ADF test of Said and Dickey (1984). Applying the test for X, it requires estimating the following ordinary least squares (OLS) regression equation: Xt+1 − Xt = αX + βX Xt +

N 

ϕi (Xt+1−i − Xt−i ) + εX,t+1

(10.20)

i=1

The ADF test consists of testing the negativity of βX in equation (10.20). To accommodate any serial correlation in the residuals, equation (10.20) is augmented with N lagged difference terms. The null hypothesis of the ADF test is βX = 0 (κD = 0), that is X contains a unit root. Rejection of the null hypothesis in favour of the alternative: βX < 0 (κD > 0) implies that X is stationary. Stationarity of X implies that the mean and the variance of X are both constant over time. In order to test the null hypothesis of the ADF test, it is necessary to know the distribution of the statistic used for the test. In this case, it is the distribution of the Dickey–Fuller statistic of βX , which is derived by the ratio of the OLS estimate of βX to its OLS standard error. Under the null hypothesis where X contains a unit root, the Dickey–Fuller statistic of βX does not however have a limiting normal distribution. Dickey and Fuller (1981) show that the distributions of Dickey–Fuller statistics are complicated and, in general, do not have any known analytical forms. It is therefore difficult to find exact critical values for the tests. In practice, critical values are usually approximated through simulation. For example, Cheung and Lai (1995) compute critical values for any sample size and for any number of lagged difference terms using simulation and response surface analysis. The test adopted here is augmented with a drift

228 The Banking Sector in Hong Kong

term (αX ) to use −3.5201 which is given by Cheung and Lai (1995) as the critical values at the 99 per cent confidence level. The ADF test statistic for X is −6.0470 with one lagged difference term.10 The result rejects the null of βX = 0 (that is κD = 0) at the 1 per cent level of significance and thus suggests that X follows a mean-reverting process. The relative performance of the unrestricted model and the restricted model (that is αY = 0) of Y is evaluated by the LR test statistic. As shown in Table 10.2, the LR test statistic is 0.2060. The null hypothesis under consideration is αY = 0. The test here involves a single restriction, and thus the test statistic has a Chi-squared distribution with one degree of freedom (χ12 ). As the probability of the χ12 variable being larger than 3.8415 is 0.05 and the test statistic is 0.2060 (<3.8415), we accept the null hypothesis of αY = 0 at the 5 per cent level of significance. The result indicates that the restricted model is preferred and Y follows an Ornstein– Uhlenbeck process with no mean reversion.11 The model parameters relating to D and V can be obtained from the estimates presented in Table 10.2. Based on the estimation result of the unrestricted model of X and substituting βX of −0.1499 into equation (10.15), the parameter κD in equation (10.1) is estimated to be 0.1499. Since the estimation of X is based on the monthly time series, the annualized κD is 0.1499 × 12 = 1.7988. The long-run value θD of D can be calculated by substituting the estimates of αX , βX and σX from the unrestricted model of X into equation (10.17). The value of θD is found to be 0.0144.12 It is however noted that the long-run PD of residential mortgage loans in negative equity (that is loans with loan-to-value ratios >1) would be much higher than the estimated value of 0.0144. The volatility σD of D is obtained by substituting the estimate of σX into equation √ (10.16) and σD is 0.037. The annualized volatility of D is 0.037 × 12 = 0.1282.13 The drift μV and volatility σV of V in equation (10.2) can be estimated by substituting the estimate of σY from the restricted model of Y into equations (10.18) and (10.19) respectively. The values of μV and σV are estimated to be 0.0005 and 0.0314 respectively. The annualized μV √ and σV are found to be 0.0005 × 12 = 0.006 and 0.0314 × 12 = 0.1087 respectively.14 The value of ρ in equation (10.3) can be approximated by the sample correlation coefficient between the estimated series of εX,t and εY,t in equation (10.13). The value of the estimated ρ is −0.2603. The t−statistic for testing the significance of the estimate is −2.1901.15 It is noted that the test statistic has a t-distribution with 66 degrees of freedom (because of the 69 observations for D) and the 5 per cent critical value for a two-tail

Hui, Lo, Wong and Man 229

test is ±1.9966. Since the test statistic of −2.1901 is less than −1.9966, the null hypothesis of no correlation between εX,t and εY,t is rejected at the 5 per cent level of significance.

10.4 Numerical results The detailed effects of the model parameters on the model provisions required for pools of retail loans are illustrated in the following numerical examples. The current collateral value V of the pool of loans is one. The time horizon is three years. The average three-year PD of the pool is assumed to be D = 5% and the mean level θD of D is set at 8 per cent. As the delinquency ratio of residential mortgage loans in negative equity in Hong Kong was 2.92 per cent in September 2002, the use of the mean level of the three-year PD at 8 per cent is reasonable.16 The interest rate r and ‘dividend’ yield s are both 2.5 per cent per annum. Different values of L are used to illustrate the model provisions for different loan-to-value ratios. In order to eliminate the effect of the dynamics of D on provisions in Figure 10.2, that will be studied in Figure 10.4, κD and ρ are set to be zero. Figure 10.2 shows that the increases in provisions depend on the loan-to-value ratio (L/V ) and the volatility of the collateral value (σV ). For σ V = 0.1, the provisions are material when the L/V is larger than 0.8. When σ V increases to 0.2 and 0.3, the threshold of materiality lowers to about L/V = 0.6. The results reflect that provisions are still necessary for loans in positive equity (that is L/V < 1), in particular where the collateral value is volatile. The increases in provisions with different σV are significant when L/V is around one. Because the model adopts the option-pricing approach, this observation is similar to vega risk of a European option (that is sensitivity to the change in volatility of the underlying asset of the option), which is at the maximum when the underlying asset value is equal to the strike price. When L/V is larger than 1.6, the impact of the changes in σV is immaterial.17 This means that the volatility of collateral value does not affect the provisioning requirements for loans which are deep in negative equity. The change in the provision with respect to the change in the loanto-value ratio is studied in Figure 10.3, using the same model parameters in Figure 10.2. Such change is defined as:

δ=

P(D, V , t) 1 · , (L/V ) D

230 The Banking Sector in Hong Kong Provisions (%) 6 5 4 3 σV  0.3 2 σV  0.2

σV  0.1

1 0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Loan-to-value ratios Figure 10.2 Provisions of pools of loans with different loan-to-value ratios and volatilities of collateral value for a three-year time horizon Notes: The volatilities of the collateral value are σV = 0.1, 0.2 and 0.3. The average threeyear PD of the pool is 5 per cent with no mean-reverting movement (that is κD = 0) and is uncorrelated with the collateral value (that is ρ = 0). Other parameters are r = 2.5%, s = 2.5% and σD = 0.11.

which is normalized by D such that δ is just associated with the loanto-value ratio. The measure δ is the elasticity of provisions with respect to the loan-to-value ratio and is similar to the delta risk of a European option (that is sensitivity to the change in the value of the underlying asset of the option). The results demonstrate that δ increases with L/V and is at the maximum of 90 per cent when L/V is larger than 1.5. This means that the provisioning requirements for loans in negative equity with L/V > 1.5 increase almost linearly with a decline in the collateral value. Figure 10.3 also shows that δ increases significantly when the loanto-value ratios range from 0.8 to 1. The required provision will change quite rapidly for such a range of the loan-to-value ratios. The result is similar to that in an at-the-money European option of which the delta changes significantly when the underlying asset value is close to the strike price. Figure 10.4 illustrates the impact of the mean-reverting process of D and the correlation ρ between D and V on provisions. The impact is measured as the percentage changes in provisions compared with the

Hui, Lo, Wong and Man 231 δ (%) 100

80

60

40

σV  0.3

20

σV  0.2 σV  0.1

0 0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

Loan-to-value ratios Figure 10.3 Changes in provisions with respect to changes in loan-to-value ratios (that is δ) under different loan-to-value ratios and volatilities of collateral value for a three-year time horizon Notes: The volatilities of the collateral value are σV = 0.1, 0.2 and 0.3. The average threeyear PD of the pool is 5 per cent with no mean-reverting movement (that is κD = 0) and is uncorrelated with the collateral value (that is ρ = 0). Other parameters are r = 2.5%, s = 2.5% and σD = 0.11.

provisions with zero correlation. Figure 10.4 considers three cases: (i) κD = 0 and σD = 0.22; (ii) κD = 0 and σD = 0.11; and (iii) κD = 0.5 and σD = 0.11. The volatility σV of V is 0.3 per annum. The provision associated a pool with ρ = 0 and κD = 0 is 1.1 per cent. The numerical results show that the percentage changes in provisions increase with the decrease (more negative) in the correlation. The negative ρ implies that the PD increases when the collateral value drops. The amount of loss due to default risk and the corresponding provision thus increases. The changes in provisions may be up to 30 per cent in the case of negative ρ, κD = 0 and σD = 0.22. This means that the effect of correlation between PD and the collateral value is material on measuring provisions. Figure 10.4 shows that the increase in κD reduces the changes in provisions with ρ. The positive κD implies a stationary movement of D and the effect on changes in provisions due to the correlation is reduced. The result is consistent with the property of the function z0 (V , t) in the solution of equation (10.6), which shows that the positive κD gives a discounting effect on the covariance term ρ(t)σD (t)σV (t). The numerical results

232 The Banking Sector in Hong Kong Percentage changes (%) 40 30 20

kD  0 σD  0.22 kD  0 σD  0.11

10 0 10

kD  0.5 0.9

0.7

0.5

0.3

0.1

0.1

0.3

0.5

0.7

0.9

20 30 40

Correlation

Figure 10.4 Percentage changes in provisions of pools of loans with different correlation between collateral value and PD compared with the provisions with zero correlation under different dynamics of PD Notes: The loan-to-value ratio (L/V ) is one and the time horizon is three years. The volatility of the collateral value is σV = 0.3. The dynamics of PD is defined as: (i) κD = 0 and σD = 0.22; (ii) κD = 0 and σD = 0.11; and (iii) κD = 0.5 and σD = 0.11. The average three-year PD of the pool is 5 per cent with the mean level θD of D at 8 per cent. Other parameters are r = 2.5% and s = 2.5%. The provision associated with ρ = 0 and κD = 0 is 1.1%.

demonstrate that the effect of an economic cycle (that is the present of a mean-reverting process) on the PD could reduce the impact of the correlation on provisions. Figure 10.4 also shows that the increase in σD increases the changes in provisions with ρ, by comparing the results of the cases with σD = 0.22 and 0.11. This observation illustrates that the volatility of the PD may affect provisions through its correlation with the collateral value. The required provision-given-default is defined as P(D, V, t)/D and is a measure similar to loss given default (LGD). Its properties are illustrated in Figure 10.5 based on four cases: (i) ρ = −0.75 and κD = 0; (ii) ρ = 0 and κD = 0; (iii) ρ = 0.75 and κD = 0; and (iv) ρ = 0 and κD = 0.5. The volatility σV and σD of V and D are 0.3 and 0.11 per annum respectively. The loanto-value ratio equal to one is used for the calculations. The results show that the provision-given-default increases with time horizons. This property is consistent with the intuition that the uncertainty of the collateral coverage (that is LGD) increases with time. The rate of the increments of the provision-given-default with time in case (i) is higher than those in

Hui, Lo, Wong and Man 233 Provision-given-default (%) 60 50 40

kD  0.5 ρ  0.75

30

ρ0 ρ  0.75

20 10 0 1

2

3

4

5

6

7

Time (years) Figure 10.5 Provision-given-default of pools of loans with different time horizons and correlation between collateral value and PD Notes: The loan-to-value ratio (L/V ) is 1 and the volatility of the collateral value is σV = 0.3. The four lines represent (i) ρ = − 0.75 and κD = 0; (ii) ρ = 0 and κD = 0; and (iii) ρ = 0.75 and κD = 0. and (iv) ρ = 0 and κD = 0.5. The mean level θD of D is at 8 per cent. Other parameters are r = 2.5%, s = 2.5% and σD = 0.11.

cases (ii) and (iii) with higher ρ. This reflects that the negative correlation between the PD and collateral value increases the uncertainty of the collateral coverage (that is LGD) for loans over time. For case (iv) with ρ = 0 and κD = 0.5, as the mean-reverting drift of D would pull the current D = 5% to the mean level of θD = 8% over time, the mean-reverting process causes the highest rate of the increments of the provision-givendefault with time in case (iv). The results in Figure 10.5 demonstrate that collateralized retail loans (in particular long-term lending) require different amounts of provisions for different time horizons.

10.5 Summary This chapter develops a simple model for measuring the provision for a pool of collateralized retail loans with homogenous characteristics (that is the same type of collateral and broadly the same loan-to-value ratio), where the collateral coverage is treated as a put option with the strike

234 The Banking Sector in Hong Kong

price equal to the outstanding loan amount of the pool. The collateral value and the PD of borrowers in the pool are the two correlated stochastic variables in the model. A closed-form formula of the model is derived and used to calculate the required provision for a pool of loans over a given time horizon. Empirical findings based on the data of the residential mortgage market in Hong Kong are consistent with the proposed mean-reverting dynamics of the PD of residential mortgage loans. The numerical results show that the loan-to-value ratio, correlation between the collateral value and the PD, volatility of the collateral value, mean-reverting process of the PD and time horizon are the important factors for measuring provisions and what their effects are. As the information associated with these factors is in general available in banks’ retail portfolios, the model can be readily incorporated into their internal risk management systems as a useful quantitative tool for measuring provisions.

Hui, Lo, Wong and Man 235

Appendix 10A Without loss of generality, the solution P(D, V , t) is rewritten in the form:   t P(D, V , t) = Dη(t) F(V , t) exp (10A.1) α(t  )dt  , 0

where α(t) and η(t) are defined in equations (10.7) and (10.8) respectively. F(V, t) satisfies the following partial differential equation: ∂2 F 1 ∂F ∂F = σV2 (t)V 2 2 + [r − s + ρ(t)σD (t)σV (t)]V − rF ∂t 2 ∂V ∂V

(10A.2)

and the corresponding final condition is given by F(V , t = 0) = L max (1 − V /L, 0).

(10A.3)

It is then not difficult to show that F(V, t) is given by (Lo and Hui 2001) as  F(V, t) =

∞

−∞



=L

dyK(V , t; y, 0)F(y, 0)

0

−∞

dyK(V , t; y, 0)[1 − exp (y)],

(10A.4)

where  " exp (−rt) [y − z0 (V , t)]2 exp − K(V , t; y, 0) =  4c1 (t) 4πc1 (t)

(10A.5)

is the kernel of equation (10A.2), and z0 (V , t) and c1 (t) are defined in equations (10.9) and (10.10) respectively. The integral in equation (10A.4) can be evaluated analytically to yield a closed-form solution of      z0 z0 + 2c1 F(V, t) = L exp (−rt) × N − √ − exp (z0 + c1 )N − √ 2c1 2c1 (10A.6) After substituting equation (10A.6) into equation (10A.1), the solution of equation (10.6) is obtained.

236 The Banking Sector in Hong Kong

Notes 1. Reprinted with permission from Elsevier Limited; C. H. Hui, C. F. Lo, T. C. Wong and P. K. Man, ‘Measuring Provisions for Collateralised Retail Lending’, Journal of Economics and Business, vol. 58 (2006). 2. The European Union provides principle-based rules, with only general guidance on how to determine adequate provisioning. 3. Most emerging markets adopt this approach (see World Bank 2002). 4. A comparative analysis of these techniques can be found in Crouhy et al. (2000) and Gordy (2000a). KMV’s Portfolio Manager is based on the work of Black and Scholes (1973) and Merton (1974) in the pricing of corporate bonds using a contingent-claim framework. In Black–Scholes–Merton’s structural framework, a firm’s market value of total assets is observable in principle. Furthermore default happens if the total asset value is lower than the value of liabilities. Default risk is therefore equivalent to a European put option on the firm’s asset value. 5. Credit Risk Plus is on the other hand based on the theoretical underpinnings of reduced-form models in which default time is a stopping time of some given hazard rate process and the payoff upon default is specified exogenously. These models have been considered by Jarrow and Turnbull (1995), Jarrow et al. (1997), and Duffie and Singleton (1997). 6. The mean-reverting process has also been adopted for modelling the dynamics of risk-free interest rates with cyclical characteristics. Interest rates appear to be pulled back to some long-run mean level over time (see Vasicek 1977) according to different states of an economic cycle. When interest rates are high, the economy tends to slow down and there is less requirement for funds on the part of borrowers. As a result, rates decline. When rates are low, there tends to be a high demand for funds on the part of borrowers. As a result, rates tend to rise. 7. Regarding residential mortgage loans with a mortgage-insurance scheme, if an insurance coverage of I due to default is in place, the final condition is modified as max(L – V – I, 0). 8. Private domestic premises refer to residential properties which are developed and managed by private developers. 9. The data can be obtained at http://www.info.gov.hk/hkma/eng/ statistics/msb/attach/T0307.xls and http://www.info.gov.hk/rvd/property/ content.htm. 10. The lag length is chosen using the Akaike information criteria and the maximum number of lags is set to be ten. 11. An ADF test shows that Y does not follow a mean-reverting process. The ADF statistic is –2.1110 with a drift and seven lagged difference terms. Since the critical value at the 90 per cent confidence interval is –2.5471 and the ADF test statistic is larger than the critical value, the null hypothesis cannot be rejected at the 10 per cent level of significance. 12. The data of the problem–loans ratio (instead of the actual default rate) are used in the estimation. As the number of problem loans will be reduced after writing off the loans, the long-run one-year default rate is expected to be higher than the estimated figure here.

Hui, Lo, Wong and Man 237 13. Based on the data of the property price index during the period from December 1995 to December 1998, its annualized volatility was up to 16.4 per cent. 14. The low mean rate of 0.6 per cent of appreciation of V per year is also reflected from the price changes in Table 10.1, where the simple mean of changes is even smaller at –0.01 per cent per year. These low values are due to the continuous decline in the property price index in Hong Kong since 1997 (see Figure 10.1). ! 15. The t-statistic is calculated by t = ρ

n−2 1 − ρ2

. This t-statistic has a student-

t distribution with (n − 2) degrees of freedom where n is the number of samples. 16. The delinquency ratios of residential mortgage loans in negative equity in Hong Kong have been collected by the Hong Kong Monetary Authority since September 2002. The figure of 2.92 per cent can be found at http://www.info.gov.hk/hkma/eng/press/index.htm. The maximum of the data series of D is 1.65 per cent in July 2003. A three-year default rate is expected to be higher than the delinquency ratio as the default rate is a cumulative figure while the number of problem loans will be reduced after writing off the loans. 17. Because the property price index in Hong Kong declined 66 per cent from 173 in 1997 to 58 in 2003 (see Table 10.1), some residential mortgage loans might have loan-to-value ratios of 160 per cent or even above.

References S. Agarwal and C. Liu, ‘Determinants of Credit Card Delinquency and Bankruptcy: Macroeconomic Factors’, Journal of Economics and Finance, 27 (2003) 75–84. L. Allen, G. DeLong and A. Saunders, ‘Issues in the Credit Risk Modeling of Retail Markets’, Journal of Banking and Finance, 28 (2004) 727–52. E. Altman, A. Resti and A. Sironi, ‘The Link between Default and Recovery Rates: Effects on the Procyclicality of Regulatory Capital Ratios’, BIS Working Papers, no. 113 (2002). T. G. Bali, ‘An Empirical Comparison of Continuous Time Models of the Short Term Interest Rate’, Journal of Futures Markets, 19(7) (1999) 777–97. Basel Committee on Banking Supervision, Principles for the Management of Credit Risk (Basel: BIS, 2000). Basel Committee on Banking Supervision, The IRB Treatment of Expected Losses and Future Margin Income, Working Paper (Basel: BIS, 2001). Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards: a Revised Framework (Basel: BIS, 2004). F. Black and J. C. Cox, ‘Valuing Corporate Securities: Some Effects of Bond Indenture Provisions’, Journal of Finance, 31(2) (1976) 351–67. F. Black and M. Scholes, ‘The Pricing of Options and Corporate Liability’, Journal of Political Economics, 81 (1973) 637–54.

238 The Banking Sector in Hong Kong M. J. Brennan and E. S. Schwartz, ‘An Equilibrium Model of Bond Pricing and a Test of Market Efficiency’, Journal of Financial and Quantitative Analysis, 17 (1982) 75–100. E. Briys and F. de Varenne, ‘Valuing Risky Fixed Rate Debt: an Extension’, Journal of Financial and Quantitative Analysis, 32 (1997) 230–48. T. S. Campbell and J. K. Dietrich, ‘The Determinants of Default on Insured Conventional Residential Mortgage Loans’, Journal of Finance, 38 (1983) 1569–81. Y. W. Cheung and K. S. Lai, ‘Lag Order and Critical Values of the Augmented Dickey-Fuller Test’, Journal of Business and Economic Statistics, 13 (1995) 277–80. P. Collin-Dufresne and R. S. Goldstein, ‘Do Credit Spreads Reflect Stationary Leverage Ratio?’, Journal of Finance, 56(5) (2001) 1929–57. M. Crouhy, D. Galai and R. Mark, ‘A Comparative Analysis of Current Credit Risk Models’, Journal of Banking and Finance, 24 (2000) 57–117. J. De Munnik and P. Schotman, ‘Cross Sectional versus Time Series Estimation of Term Structure Models: Empirical Results for the Dutch Bond Market’, Journal of Banking and Finance, 18 (1994) 997–1025. D. A. Dickey and W. A. Fuller, ‘Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root’, Econometrica, 49 (1981) 1057–72. B. Dietrich-Campbell and E. S. Schwartz, ‘Valuing Debt Options: Empirical Evidence’, Journal of Financial Economics, 16 (1986) 321–43. D. Duffie and K. J. Singleton, ‘An Econometric Model of the Term Structure of Interest-Rate Swap Yields’, Journal of Finance, 52 (1997) 1287–322. C. Finger, ‘Conditional Approaches for CreditMetrics Portfolio Distributions’, CreditMetrics Monitor, April (1999). J. Frye, ‘Collateral Damage Detected’, Federal Reserve Bank of Chicago, Working Paper, Emerging Issues Series, October (2000a) 1–14. J. Frye, ‘Depressing Recoveries’, Risk, 91(4) (2000b). M. B. Gordy, ‘A Comparative Anatomy of Credit Risk Models’, Journal of Banking and Finance, 24 (2000a) 119–49. M. B. Gordy, ‘Credit VaR models and Risk-Bucket Capital Rules: A Reconciliation’, Federal Reserve Board, Working Paper, March (2000b). D. B. Gross and N. S. Souleles, ‘An Empirical Analysis of Personal Bankruptcy and Delinquency’, Review of Financial Studies, 15 (2002) 319–47. C. H. Hui, C. F. Lo and S. W. Tsang, ‘Pricing Corporate Bonds with Dynamic Default Barriers’, Journal of Risk, 5(3) (2003) 17–37. R. A. Jarrow, ‘Default Parameter Estimation using Market Prices’, Financial Analysts Journal, 57(5) (2001) 75–92. R. Jarrow and S. Turnbull, ‘Pricing Options on Financial Securities Subject to Default Risk’, Journal of Finance, 50 (1995) 53–86. R. Jarrow, A. Lando, and S. Turnbull, ‘A Markov Model for the Term Structure of Credit Spreads’, Review of Financial Studies, 10 (1997) 481–523. E. Jokivuolle and S. Peura, ‘Incorporating Collateral Value Uncertainty in Loss Given Default Estimates and Loan-to-Value Ratios’, European Financial Management, 9 (2003) 299–314. J. B. Kau, D. C. Keenan, W. J. Muller and J. F. Epperson, ‘A Generalised Valuation Model for Fixed-Rate Residential Mortgages’, Journal of Money, Credit and Banking, 24 (1992) 279–99.

Hui, Lo, Wong and Man 239 C. F. Lo, and C. H. Hui, ‘Valuation of Financial Derivatives with Time-Dependent Parameters – Lie Algebraic Approach’, Quantitative Finance, 1 (2001) 73–8. F. A. Longstaff and E. S. Schwartz, ‘A Simple Approach to Valuing Risky Fixed and Floating Rate Debt’, Journal of Finance, 50(3) (1995) 789–819. T. A. Marsh and E. R. Rosenfeld, ‘Stochastic Processes for Interest Rates and Equilibrium Bond Prices’, Journal of Finance, 38 (1983) 635–46. R. C. Merton, ‘Theory of Rational Option Pricing’, Bell Journal of Economics and Management Science, 4 (1973) 141–83. R. C. Merton, ‘On the Pricing of Corporate Debt: the Risk Structure of Interest Rates’, Journal of Finance, 29 (1974) 449–70. S. E. Said and D. A. Dickey, ‘Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order’, Biometrika, 71 (1984) 599–607. O. A. Vasicek, ‘An Equilibrium Characterisation of the Term Structure’, Journal of Financial Economics, 5 (1977) 177–88. World Bank, Bank Loan Classification and Provisioning Practices in Selected Developed and Emerging Countries, eds A. Laurin and G. Majnoni (2002).

11 A Framework for Stress Testing Banks’ Credit Risk1 Jim Wong, Ka-Fai Choi and Tom Pak-Wing Fong

11.1 Introduction Macro stress testing refers to a range of techniques used to assess the vulnerability of a financial system to ‘exceptional but plausible’ macroeconomic shocks.2 Increasingly, macro stress testing plays an important role in the macro-prudential analysis of public authorities. The main objective is to identify structural vulnerability and overall risk exposures in a financial system that could lead to systemic problems. In conjunction with stress testing to assess the vulnerability of the portfolios of individual institutions, macro stress testing forms the main part of system-wide analysis, which measures the risk exposure of a group of financial institutions to a specific stress scenario. It can also serve as a tool for cross-checking results obtained by financial institutions’ internal models. In this chapter, a macro stress-testing framework is developed for testing the loan portfolios of retail banks in Hong Kong. It involves the construction of macroeconomic credit risk models, each consisting of a multiple regression model and a set of autoregressive models (for examining the relationship between the default rate of bank loans and different macroeconomic values based on historical data) estimated by the method of seemingly unrelated regression (SUR). Two macroeconomic credit risk models are built. One model is specified for the overall loan portfolios of banks and, to illustrate how the same framework can be applied for stress testing loans to different economic sectors, the other model is for the banks’ mortgage exposures only. Macro stress testing is then performed to assess the vulnerability and risk exposures of banks’ overall loan portfolios and mortgage exposures. Adverse macroeconomic scenarios are taken and, using the 240

Wong, Choi and Fong 241

framework, the possible combinations of stressed macroeconomic values are obtained from a Monte Carlo simulation. Based on this, distributions of possible default rates of bank loans under a specific shock can be generated. Value-at-Risk (VaR) is computed to evaluate how the stressed macroeconomic environment may affect the default probability of banks’ loan portfolios.3

11.2 Elements of stress test and the common methodology Macroeconomic stress tests involve two major elements. First, scenarios of extreme but plausible adverse macroeconomic conditions need to be devised.4 Secondly, the adverse macroeconomic scenarios need to be mapped onto the impact on banks’ balance sheets. Through this, the robustness of banks can be evaluated. For the first element, given that since an adverse macroeconomic scenario refers to a combination of adverse developments in several macroeconomic variables, it is important to ensure its internal consistency and that the specified values of the macroeconomic variables constitute a realistic mix. The conventional approach, as adopted by Froyland and Larsen (2002), Hoggarth and Whitley (2003), Mawdsley et al. (2004) and Bunn et al. (2005), is to devise scenarios that imitate historical episodes of tail events or to generate scenarios with the aid of a macro-econometric model. After devising the scenarios, the impact on banks will be estimated. This usually requires first estimating an empirical model that relates a certain financial soundness indicator y to a number of macroeconomic variables x1 ,…, xM that the scenarios encompass: y = f (x1 , . . . , xM ) + ε, where ε is an error term capturing determinants of the indicator other than x1 , . . . , xM. The values of x1 , . . . , xM given by the scenarios will then be substituted into the estimated equation and the predicted values of y are computed under the assumption that ε = 0. These predicted values are (point) estimates of the expected values of y conditional on the occurrence of the scenarios. Changes in the predicted values of y as a result of the imposition of the scenarios are usually regarded as the estimated impacts. This approach suffers from two problems: first, once a scenario is chosen, how likely it is to occur is no longer an issue in the stress test;5 secondly, even if the predicted value of the soundness indicator is not significantly affected by the realization of the adverse scenario, it is

242 The Banking Sector in Hong Kong

hard to conclude that the risk is low because a large deviation from the average may occur with a ‘tangible’ probability. By taking into account the possibility that ε is non-zero in the y equation and there is randomness in the behaviour of the macroeconomic variables with the various stochastic components being correlated, Wilson (1997a, 1997b) and Boss (2002) developed a stress-testing framework that examines default risk and the development of macroeconomic conditions. Their framework has several advantages over the conventional approach since it takes into account the probabilistic elements and explicitly considers the variation of ε and its correlation with the macroeconomic variables x1 , . . . , xM . Boss (2002) and Virolainen (2004) applied this framework to conduct credit-risk stress tests for the corporate loan portfolio of Austrian and Finnish banks respectively.

11.3 The framework A framework for stress testing the credit exposure of Hong Kong’s retail banks to macroeconomic shocks is developed based on Wilson (1997a, 1997b), Boss (2002) and Virolainen (2004). In essence, our framework comprises: (i) an empirical model with a system of equations on credit risk and macroeconomic dynamics, and (ii) a Monte Carlo simulation for generating distribution of possible default rates (or credit losses).

11.3.1 The system of empirical equations Suppose there are J economic sectors to which banks lend.6 Let pj,t be the average default rate in sector j observed in period t, where j = 1, . . . , J. As pj,t is bound between zero and one, we use its logit-transformed value yj,t as the regressand. That is,  yj,t = ln

1 − pj,t pj,t



is applied to transform pj,t to yj,t , hence −∞ < yj,t <+∞.7 Obviously, pj,t and yj,t are negatively related; a higher yj,t is associated with a better credit-risk status.

Wong, Choi and Fong 243

Let yt = ( y1,t , . . . , yJ,t ) . We model it as depending linearly on its lags and on the current and lagged values of M macroeconomic variables: yt = m + A1 xt + · · · + A1+s xt−s + 1 yt−1 + · · · + k yt−k + vt ,

(11.1)

where xt is an M × 1 vector of macroeconomic variables; m is a J × 1 vector of intercepts; A1 , . . .,A1+s are J × M and 1 , . . . , k are J × J coefficient matrices; and vt is a J × 1 vector of disturbances. The characterization of equation (11.1) explicitly links the default behaviours in the J economic sectors to the macroeconomic conditions. In Wilson (1997a, 1997b), yt is assumed to depend only on xt . Similar to Virolainen (2004), our specification is more general, allowing the impact of a macroeconomic shock to be prolonged and defaults in different economic sectors to be correlated.8 Another part of the equation system in Wilson’s framework is on the dynamics of the M macroeconomic variables. In his original specification, each of them follows an autoregressive (AR) process. We generalize it by adopting the following specification: xt = n + B1 xt−1 + · · · + Bp xt−p + 1 yt−1 + · · · + q yt−q + εt ,

(11.2)

where n is an M × 1 vector of intercepts; B1 , . . . , Bp are M × M and 1 , . . . , q are M × J coefficient matrices; and εt is an M × 1 vector of disturbances. Our specification is similar to Virolainen (2004) and has two advantages over Wilson’s. First, equation (11.2) embodies a more realistic dynamic process in which the macroeconomic variables are mutually dependent. Secondly, equation (11.2) explicitly models the feedback effects of bank performances on the economy by letting xt depend on yt−1 , . . . , yt−q .9 Equations (11.1) and (11.2) together define a system of equations governing the joint evolution of the economic performance, the associated default rates, and their error terms. In this system, we assume that vt and εt are serially uncorrelated and normally distributed with variance–covariance matrices v and ε respectively; vt and εt are correlated, with variance–covariance matrix v,ε . In sum, the structure of the disturbances is as follows: et =

  vt ∼ N(0, ), εt

 =

v v,ε

 v,ε . ε

(11.3)

Allowing the off-diagonal elements of v , ε and v,ε to be non-zero is desirable. First, influences stemming from factors affecting the dependent variables but not explicitly incorporated in equations (11.1) and

244 The Banking Sector in Hong Kong

(11.2) will not be omitted altogether. Secondly, the contemporaneous correlation between the two disturbances in equations (11.1) and (11.2) can be captured and the feedback effects of bank performances on the economy can be more accurately assessed.10

11.3.2 Monte Carlo simulations and stress tests In our framework, stress tests are conducted by comparing the estimated frequency or probability distribution of credit losses of the stressed scenario, where an artificial adverse macroeconomic development is introduced, with that of the baseline scenario, where no artificial adverse shock takes place. Estimated frequency distributions of the horizonend default rates for each sector corresponding to stressed and baseline scenarios are obtained separately from simulating a large number of future joint sector-specific default rates by applying a Monte Carlo method. Let us first discuss the estimation of the baseline distribution. To simulate a vector of one-period-ahead values of joint sector-specific default rates, we first draw a vector of random variables r from the multivariate normal distribution with mean being zero and variance-covariance matrix being the estimated . The vector so drawn represents a realization of the vector of disturbances e. Given the current and past values of the M macroeconomic variables, the J default rates and the realization r, the associated one-period-ahead values yj,t+1 and xi,t+1 can be calculated based on the estimated equations (11.1) and (11.2). Similarly, the two-period-ahead values can be calculated with another independently drawn r and the one-period-ahead values previously obtained. Repeating the same procedure yields a future path of the joint sector-specific default rates, given the time horizon. By simulating a large number of such paths, a frequency distribution of the horizonend default rates (of the baseline scenario) for each of the J sectors can be constructed. These paths stem from different future evolutions of the macroeconomic environment and the innovations vt in equation (11.1). With specific assumptions or actual data on the loss given default (LGD), the associated distribution of possible credit losses can be estimated. In constructing the distribution of possible credit losses for a stressed scenario, we introduce an artificial adverse macroeconomic development subject to which another set of paths of future joint sector-specific default rates is simulated. Consider first the simulation of the one-periodahead default rates of a particular path. We introduce in the vector of innovations an artificial shock over a macroeconomic variable through

Wong, Choi and Fong 245

replacing the corresponding element in r by the assumed shock (normalized by the respective standard deviation), so r becomes pseudo random. Nevertheless, the other macroeconomic variables would be accordingly affected, since the off-diagonal elements of ε need not be zero. In other words, the artificially shocked macroeconomic variable would not be the only variable that is affected adversely in the simulation because the shock would be transmitted to other variables through the impact on its disturbance to other disturbances. The simulation of the two-period-ahead default rates requires drawing another r. If the adverse development of the previously shocked macroeconomic variable is assumed to last, we continue to make the r pseudo random. Otherwise, we simply let the r to be random, as in the baseline simulations. The farther-ahead default rates can be simulated in the same manner. Based on this procedure, a path of future joint sector-specific default rates can be constructed, given the duration of the artificial shock. With a sufficiently large number of simulated paths, the distribution of credit losses for a stressed scenario can be estimated. Note that our equation system stated in section 11.3.1 characterizes both the dynamics of sector-specific default rates and the macroeconomic variables. In both baseline and stressed scenarios, a simulated future path of joint sectorspecific default rates is partly governed by the simulated future paths of the macroeconomic variables. The reasonableness of the simulated mixes of macroeconomic variables is supported by the estimated relationships based on historical data. Intuitively, the baseline simulations produce an estimated unconditional probability distribution of possible credit losses, without the information about the occurrence of a particular shock. In some simulations, a serious credit loss occurs because there can be adverse macroeconomic developments in the baseline simulations due to randomness. On the other hand, in stressed simulations, as the different future evolutions of the macroeconomic environment and the innovations vt that the simulated paths involved share the same artificial economic shocks, the estimated distribution is conditional on the occurrence of such shocks.11 Hence, comparing the conditional loss distribution of the stressed scenario with the unconditional distribution of the baseline scenario provides information on the possible impact of adverse macroeconomic conditions triggered by the shock that we introduce. A better understanding on the adopted stress-testing approach can be gained by comparing it to the conventional approach as described in section 11.2. Consider for simplicity the aggregate case where borrowers of different sectors are not distinguished. Given a particular pre-selected

246 The Banking Sector in Hong Kong

macroeconomic scenario, in the conventional stress-testing approach, the impact is mapped out by substituting into equation (11.1) the values of the M macroeconomic variables given by the scenario. In constructing the scenario, with the aid of a macro-econometric model, a shock can be artificially introduced over a particular macroeconomic variable, which is the stress origin, and the responses of the other variables in the model can be computed assuming that all disturbances are zero – the scenario is the combination of the obtained numerical values of the macroeconomic variables. Conceptually, the values so computed are, on average, what the responses would be. However, in our approach the responses of the other macroeconomic variables to the shock of the stress origin are probabilistic because the disturbances are not assumed to be zero in our Monte Carlo exercise. The effect of this probabilistic treatment is represented in the numerous simulated paths which associate with different rs .12 With this, the framework allows us to assess banks’ vulnerability through the use of VaR statistics. The above illustrates an essential feature of our stress-testing approach: the probabilistic components of the default rates and the macroeconomic variables are not ignored, but are used to produce information on responses that deviate from the average. This feature is important because in stress testing public authorities are concerned with ‘exceptional but plausible’ shocks, which are usually accompanied by rather abnormal behaviour of the macroeconomic variables.

11.4 The model and estimation results The equation system on default probability and macroeconomic dynamics is estimated by using retail banks’ data covering the period from 1994 Q4 to 2006 Q1. The default rates for the overall loan portfolios and mortgage exposures of banks are chosen in this study.13,14 In particular, the default rate is specified to depend on the following macroeconomic variables: (i) (ii) (iii) (iv)

real GDP growth of Hong Kong ( g HK ) real GDP growth of Mainland China ( g CN ) real interest rates in Hong Kong (r)15 real property prices in Hong Kong ( prop).16

• The default rate is measured as a ratio of the amount of loans which

have been overdue for more than three months to the total amount of loans. The data series on default rate is transformed by the logit

Wong, Choi and Fong 247

•

• •

•

formula to produce the yt series. Results obtained from an augmented Dickey–Fuller test suggest that yt is an I(1) process. Thus, we opt to model its first difference yt . GDP governs the ability of agents in the economy to service their debt. For loans used to finance economic activities in the domestic market, the GDP of Hong Kong should be an important factor influencing the ability to repay. We also incorporate the GDP of Mainland China because the Hong Kong and Chinese economies are closely integrated. The reason for incorporating interest rates as an explanatory variable is obvious: they directly affect the burden of the debt. We use the three-month Hong Kong Interbank Offered Rate (HIBOR) to represent nominal interest rates. We consider property prices relevant because real estate is the major item of collateral. If the collateral value declines, the incentive to continue servicing the debt will weaken. The property price index compiled by the Rating and Valuation Department is used to calculate the variations in property prices in Hong Kong.

The equation system, which consists of equations (11.1) to (11.3), is estimated by the SUR method. The four macroeconomic series stated above are I(0), as suggested by the results of an augmented Dickey–Fuller test, so we do not use their first differences in the regression. The SUR estimation results are presented in Table 11.1. For the yt equation, the results shown in the table are obtained by removing the insignifiHK cant variables from the more general specification in which gtHK , gt−1 , CN CN gt , gt−1 , rt , rt−1 , propt , propt−1 , yt−1 and yt−2 are incorporated as explanatory variables. Similarly, the results from the equations of the macroeconomic variables are also obtained by removing the insignificant variables from a more general specification. As shown in Table 11.1, the signs of the coefficients of the macroeconomic variables in the yt equation are all as expected. The results suggest that the default rate would become higher if real GDP growth in Hong Kong and the Mainland deteriorated, property prices in Hong Kong declined, and interest rates rose, and vice versa. The coefficient of the lagged default rate yt−2 is positive and significant, so there is positive autocorrelation in default rates, suggesting that a macroeconomic shock can produce a prolonged impact on the default rate. This leads us to analyse the development of the default rate over a time horizon that is longer than the duration of the artificial shock in order to reflect the long-term impact of the stress.

248 The Banking Sector in Hong Kong Table 11.1 SUR estimates for the equation system (sample period: 1994 Q4 to 2006 Q1) Variable

Dependent variable

yt

Intercept HK gt−1

gtCN

−0.087** (0.037) 0.034*** (0.008) 0.032** (0.016)

gtHK 0.510** (0.220) 0.475*** (0.117)

CN gt−1

rt rt−1 propt−1 yt−2 Adj. R2 DW statistic No. of obs.

gtCN 1.858*** (0.267)

rt −0.051 (0.080)

propt 0.180 (0.731)

0.198* (0.108) −0.024** (0.011) 0.005** (0.002) 0.512*** (0.089) 0.631 1.756 43

−0.173** (0.071)

0.191 1.94 64

0.113 2.129 64

0.682 1.689 56

0.629*** (0.104)

0.336 1.978 51

Notes: 1. In the estimation, dummy variables are added respectively in the g HK , g CN and r equations to control for the effects of structural breaks. 2. Standard errors are in parentheses. 3. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively. Data Sources: CEIC, Census & Statistics Department of Hong Kong, HKMA.

11.5 The simulation of future credit losses and stress testing We now proceed to simulate paths of future default rates based on the SUR estimates and to construct the accompanying distributions of credit losses.17 The time horizon of a path is one year. As most of the shocks last four quarters, taking the macroeconomic conditions in 2006 Q1 as the current environment, a simulated future path has the eight time points covering a two-year period from 2006 Q2 to 2008 Q1. As mentioned earlier, in constructing the loss distribution for the baseline scenario, no artificial adverse shock is introduced. For the four stressed scenarios, different shocks arising from four different stress origins are considered: (i) reductions in Hong Kong’s real GDP by 1.7 per cent, 3.9 per cent, 0.8 per cent and 1.1 per cent respectively in each of the four consecutive quarters starting from 2006 Q2;

Wong, Choi and Fong 249

(ii) a fall in Mainland China’s real GDP by 3 per cent in only the first quarter (that is 2006 Q2); (iii) a rise of real interest rates by 300 basis points in the first quarter, followed by no change in the second and third quarters and another rise of 300 basis points in the fourth quarter; and (iv) reductions in real property prices by 4.4 per cent, 14.5 per cent, 10.8 per cent and 16.9 per cent respectively in each of the four consecutive quarters starting from 2006 Q2. These are quarter-to-quarter changes and are supposed to change separately from 2006 Q2 to 2007 Q1. Their magnitudes are in general similar to those during the Asian financial crisis.18 No further artificial shock is introduced for the subsequent quarters. For each of the baseline scenario and stressed scenarios, we simulate 10,000 future paths and use the simulated 10,000 default rates in 2008 Q1 to construct a frequency distribution of credit loss percentages.19 If no formal statistics are available for the LGD, some studies assign a rough constant ratio based on market information to obtain the estimated credit loss. If no market information is available, a ratio of 0.5 may be assumed for the calculation of loss figures. In this chapter, we assume the LGD will vary with property prices as properties are by far the most important collateral for lending. Property prices should therefore have an impact on how much banks can recover from their losses. For simplicity, we assume the LGD in 2006 Q1 to be 0.5 and the LGD in 2008 Q1 to be inversely proportional to the percentage change in the property price index (PI) around the initial level 0.5, as follows:20 LGD2008Q1 = 0.5 − 0.5 ×

PI2008Q1 − PI2006Q1 . PI2006Q1

The simulated frequency distributions of the baseline and stressed scenarios are depicted in Figure 11.1. Introducing a shock shifts the loss distribution to the right, representing an increase in the frequency of the higher credit loss percentages at the expense of the lower ones. Salient statistics are presented in Table 11.2 to provide highlights of the distributions of credit losses for the baseline scenario and for the four stressed scenarios with different macroeconomic variables as the stress origin. In the baseline scenario, the percentage of credit loss that is expected to prevail in 2008 Q1 (or the mean of the credit loss distribution) is 0.34 per cent. Introducing the artificial shocks substantially increases the expected percentage of credit loss. For example, it becomes

250 Frequency 2500 Normal

Stressed Hong Kong’s Real GDP

2000

1500

1000

500

0 0

1

2

3

4 5 6 Credit Loss (%)

7

8

9

10

Figure 11.1a A GDP shock: simulated frequency distributions of credit loss under baseline and stressed scenarios Note: Each distribution is constructed with 10,000 simulated future paths of default rates.

Frequency 2500 Normal

Stressed China’s Real GDP

2000

1500

1000

500

0 0

1

2

3

4 5 6 Credit Loss (%)

7

8

9

10

Figure 11.1b A China GDP shock: simulated frequency distributions of credit loss under baseline and stressed scenarios Note: Each distribution is constructed with 10,000 simulated future paths of default rates.

251 Frequency 2500 Normal

Stressed Real interest rates

2000

1500

1000

500

0 0

1

2

3

4 5 6 Credit Loss (%)

7

8

9

10

Figure 11.1c An interest rate shock: simulated frequency distributions of credit loss under baseline and stressed scenarios Note: Each distribution is constructed with 10,000 simulated future paths of default rates.

Frequency 2500 Normal

Stressed Real Property Price

2000

1500

1000

500

0 0

1

2

3

4 5 6 Credit Loss (%)

7

8

9

10

Figure 11.1d A property price shock: simulated frequency distributions of credit loss under baseline and stressed scenarios Note: Each distribution is constructed with 10,000 simulated future paths of default rates.

252 The Banking Sector in Hong Kong Table 11.2 The mean and VaR statistics of simulated credit loss distributions Credit loss (%)

Mean VaR at 90% CLe VaR at 95% CL VaR at 99% CL VaR at 99.9% CL VaR at 99.99% CL

Baseline Stressed scenarios scenario GDP Property Interest rate Mainland China GDP shockd shocka price shockb shockc 0.34 0.76 1.05 1.91 3.13 4.38

1.59 2.99 3.77 5.56 8.95 12.56

1.21 2.30 2.88 4.54 8.29 10.92

0.71 1.48 1.94 3.22 6.08 9.15

0.73 1.56 2.12 3.73 6.66 9.38

Notes: (a) Reductions in Hong Kong’s real GDP by 1.7%, 3.9%, 0.8% and 1.1% respectively in each of the four consecutive quarters starting from 2006 Q2. (b) Reductions in real property prices by 4.4%, 14.5%, 10.8% and 16.9% respectively in each of the four consecutive quarters starting from 2006 Q2. (c) A rise of real interest rates by 300 bps in the first quarter, followed by no change in the second and third quarters and another rise of 300 bps in the fourth quarter. (d) A fall in Mainland China’s real GDP by 3.0% in only the first quarter (that is 2006 Q2). (e) CL denotes the confidence level

1.59 per cent in the stressed scenario where Hong Kong’s real GDP growth rate is shocked from 2006 Q2 to 2007 Q1. However, our focus is on the more-than-average adverse responses of the other macroeconomic variables and the default behaviour. In particular, we are more interested in the tails of the credit loss distributions. Table 11.2 shows that even for the VaR at the confidence level of 90 per cent, banks would continue to make a profit in most of the stressed scenarios, suggesting that the current credit risk of the banking sector is moderate. However, under the extreme case for the VaR at the confidence level of 99 per cent, banks’ credit loss with shocks from different origins would range from a maximum of 3.22 per cent to a maximum of 5.56 per cent of the portfolios, and if a confidence level of 99.9 per cent is taken, it could range from a maximum of 6.08 per cent to a maximum of 8.95 per cent. The estimated maximum losses are very similar to what the market experienced one year after the Asian financial shock.21 However, the probability of such losses and beyond is very low. We can also map out the impact of credit losses on banks’ profitability. For a given bank or the entire banking sector, the amount of credit losses is simply the product of the percentage of credit loss and the amount of loans and advances. Suppose the future level of operating profit before provisions was the same as the current level, if no default were to take place. After realizing defaults, the level of operating profit

Wong, Choi and Fong 253 Table 11.3 Post-default operating profit of a hypothetical local bank1,2 (in HK$ million) Profit (HK$ mn)

Mean VaR at 90% CLe VaR at 95% CL VaR at 99% CL VaR at 99.9% CL VaR at 99.99% CL

Baseline scenario

2,554 2,013 1,636 517 −1,066 −2,690

Stressed scenarios GDP shocka

Property price shockb

Interest rate shockc

927 −882 −1,900 −4,226 −8,629 −13,332

1,427 5 −746 −2,903 −7,774 −11,193

2,078 1,075 477 −1,182 −4,905 −8,900

Mainland China GDP shockd 2,051 970 242 −1,844 −5,661 −9,195

Notes: 1. The operating profit before provisions and the amount of loans and advances are assumed to be HK$3 billion and HK$130 billion respectively. 2. A positive figure indicates a profit while a negative figure indicates a loss. 3. For (a) to (e), see Table 11.2.

before provisions falls by the amount of credit losses. Table 11.3 shows post-default levels of operating profit before provisions of a hypothetical bank corresponding to the credit loss percentages given in Table 11.2. The operating profit before provisions and the amount of loans and advances of the hypothetical bank are assumed to be HK$3 billion and HK$130 billion respectively. We can see that for the more extreme situations, the bank may incur a loss as a result of the materialization of credit risk alone. Under the VaR at the 90 per cent confidence level with the GDP shock, banks could incur a loss of HK$882 million. The bank may also suffer a loss under shocks from other origins under the VaR at the 99 per cent confidence level. However, the occurrence of such extreme scenarios resulting in the estimated maximum loss and beyond would have a very small probability of only 1 per cent.

11.6 A stress test for banks’ mortgage portfolio The same framework can be applied for stress testing loans to different economic sectors. In this section, we apply the framework to analyse the default behaviour of residential mortgage loans (RMLs). This is of particular interest because banks in Hong Kong generally have a substantial exposure to this type of loan. For this exercise, the first difference of the logit-transformed default rate for RMLs ytRML is modelled as dependent on five macroeconomic variables: real GDP growth of Hong Kong (g HK ), the best lending rate in real terms (BLR), real property prices in

254 The Banking Sector in Hong Kong

Hong Kong ( prop), real GDP growth of Mainland China and Hong Kong’s unemployment rate. Table 11.4 presents the SUR estimates for the equation system for RMLs. Similar to the treatment in Table 11.1, results in Table 11.4 are derived by removing the insignificant variables (including Mainland China’s real GDP growth and Hong Kong’s unemployment rate) from a more general specification. As expected, the performance of the RMLs depends negatively on the BLR and positively on Hong Kong’s real GDP growth rate and changes in real property prices.22 Similar to the model for overall loans, the coefficient of the lagged dependent variable in the ytRML equation is positive and significant, so the impact of an economic shock on the credit risk associated with RMLs is likely to be prolonged. The credit loss is simulated over a one-year horizon after the three different shocks, originating separately from (1) real Hong Kong GDP, (2) real property prices, and (3) real interest rates, the magnitudes of which are similar to those during the Asian financial crisis. As in Figure 11.1, Figure 11.2 shows that the distribution of losses of the stressed scenarios shifts towards the right compared with the baseline scenarios, suggesting Table 11.4 SUR estimates for the equation system for RMLs (sample period: 1998 Q2 to 2006 Q1) Variable

Intercept gtHK

Dependent variable

ytRML

gtHK

blrt

propt

0.014 (0.014) 0.011* (0.006)

0.530** (0.228)

−0.025 (0.065)

0.127 (0.728)

HK gt−1

blrt−1 propt−1 RML yt−1

Adj. R2 DW statistic No. of obs.

0.452*** (0.124) −0.029** (0.014) 0.008*** (0.008) 0.562*** (0.072) 0.842 2.191 30

0.189* (0.104) 0.541*** (0.106)

0.190 1.892 64

0.363 2.051 56

0.336 1.819 51

Notes: 1. In the estimation, dummy variables are added respectively in the g HK and r equations to control for the effects of structural breaks. 2. Standard errors are in parentheses. 3. *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively. Data Sources: CEIC, Census & Statistics Department of Hong Kong, HKMA.

255 Frequency 1200 Normal

Stressed Hong Kong’s Real GDP

1000 800 600 400 200 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Credit Loss (%) Figure 11.2a A GDP shock: simulated frequency distributions of credit loss for RMLs under baseline and stressed scenarios Note: Each distribution is constructed with 10,000 simulated future paths of default rates.

Frequency 1200 Normal

Stressed Real Property Price

1000 800 600 400 200 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Credit Loss (%) Figure 11.2b A property price shock: simulated frequency distributions of credit loss for RMLs under baseline and stressed scenarios Note: Each distribution is constructed with 10,000 simulated future paths of default rates.

256 The Banking Sector in Hong Kong Frequency 1200 Normal

Stressed Real Interest Rates

1000 800 600 400 200 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Credit Loss (%) Figure 11.2c An interest rate shock: simulated frequency distributions of credit loss for RMLs under baseline and stressed scenarios Note: Each distribution is constructed with 10,000 simulated future paths of default rates.

that the shocks have resulted in increases in the expected percentage of credit losses. The simulation results also show that the impact on banks’ profit would be moderate. For all the three shocks of different origins, even with a high confidence level of VaR measure, banks would continue to make a profit. As shown in Table 11.5, the expected credit losses (under the mean credit losses) for the given severe shock are moderate, ranging from 0.08 per cent to 0.34 per cent of the bank’s total RMLs. Such credit loss may rise to a maximum of 1.12 per cent at the 99.9 per cent confidence level, which suggests that there is a probability of 0.1 per cent for banks to suffer from a credit loss of 1.12 per cent or more. Assuming that the hypothetical bank’s outstanding loans for RMLs in 2006 Q1 is HK$ 39 billion, the cut in profit is found to be at most HK$436.8 million at the 99.9 per cent confidence level, which amounts to 14.6 per cent of total operating profit before provisions (see Table 11.6).23 However, the occurrence of such adverse market conditions has a very low probability.

11.7 Conclusion This chapter studied a macro stress-testing framework for loan portfolios of banks in Hong Kong. Two macroeconomic credit risk models,

Wong, Choi and Fong 257 Table 11.5 The mean and VaR statistics of the simulated credit loss distributions for RMLs Credit loss (%)

Mean VaR at 90% CLd VaR at 95% CL VaR at 99% CL VaR at 99.9% CL VaR at 99.99% CL

Baseline scenario

0.08 0.16 0.21 0.35 0.53 0.69

Stressed scenarios GDP shocka

Property price shockb

Interest rate shockc

0.15 0.29 0.38 0.58 0.91 1.07

0.34 0.55 0.64 0.83 1.12 1.41

0.13 0.25 0.32 0.50 0.84 1.33

Notes: (a) Reductions in Hong Kong’s real GDP by 1.7%, 3.9%, 0.8% and 1.1% respectively in each of the four consecutive quarters starting from 2006 Q2. (b) Reductions in real property prices by 4.4%, 14.5%, 10.8% and 16.9% respectively in each of the four consecutive quarters starting from 2006 Q2. (c) A rise of real interest rates by 300bps in the first quarter, followed by no change in the second and third quarters and another rise of 300 bps in the fourth quarter. (d) CL denotes the confidence level.

Table 11.6 Post-default operating profit of a hypothetical local bank for RML1,2 (in HK$ million) Profit (HK$ mn)

Mean VaR at 90% CLd VaR at 95% CL VaR at 99% CL VaR at 99.9% CL VaR at 99.99% CL

Baseline scenario

2,970 2,937 2,916 2,865 2,793 2,731

Stressed scenarios GDP shocka

Property price shockb

Interest rate shockc

2,941 2,885 2,853 2,774 2,644 2,582

2,866 2,787 2,751 2,677 2,564 2,449

2,951 2,901 2,875 2,803 2,674 2,481

Notes: 1. The operating profit before provisions and the amount of loans for RML are assumed to be HK$3 billion and HK$39 billion respectively. 2. A positive figure indicates a profit while a negative figure indicates a loss. 3. For (a) to (d), see Table 11.5.

each comprising a multiple regression model explaining the default probability and a set of autoregressive models describing the macroeconomic environment, were constructed for the overall loan portfolios and mortgage exposures of banks respectively. The analysis suggests a significant relationship between the default rates of bank loans and key

258 The Banking Sector in Hong Kong

macroeconomic factors, including Hong Kong’s real GDP, real interest rates, real property prices and Mainland China’s real GDP. Macro stress testing is then performed to assess the vulnerability and risk exposures of banks’ overall loan portfolios and mortgage exposures. By using the framework, a Monte Carlo method is applied to estimate the distribution of possible credit losses conditional on an artificially introduced shock. Different shocks, the magnitude of which are specified according to those occurring during the Asian financial crisis, are individually introduced into the framework for the stress tests. The results show that even for the VaR at the confidence level of 90 per cent, banks would continue to make a profit in most of the stressed scenarios, suggesting that the current credit risk of the banking sector is moderate. Under extreme cases for the VaR at the confidence level of 99 per cent, banks could incur material losses. However, the probability of the occurrence of such events is extremely low. Using a hypothetical bank as an example, this chapter illustrates how estimates obtained from aggregate default rate data can be applied to stress test individual banks. The framework can also be applied in a more comprehensive manner to assess the vulnerability of individual (or groups of) banks by using bank level (or group level) data to obtain bank-specific (or group-specific) estimates for the macro credit risk model and VaR statistics.

Notes 1. Reprinted with permission from Incisive Media; J. Wong, K. F. Choi and T. Fong, ‘A Framework for Stress Testing Banks’ Credit Risk’, Journal of Risk Model Validation, 2(1) 2008. 2. This follows the IMF definition. See Blaschke et al. (2001) and Sorge (2004). 3. VaR refers to the maximum amount of money that may be lost over a certain period at a specific confidence level. 4. The importance of the first element lies in the fact that relying on an improperly specified scenario would render the stress test useless as a way to uncover systemic risk. For example, if the specified scenarios have a negligible probability of occurring, the exercise will be irrelevant. On the other hand, if they are too mild to pose a challenge, the exercise will be unable to reveal the downside risk to which the financial system is exposed. 5. This treatment is criticized by Berkowitz (1999). 6. Boss (2002) and Virolainen (2004) analyse loans to different sub-sectors of the corporate sector. However, there is no impediment in the framework to covering loans to the household sector as well. 7. This treatment represents a common practice (see, for example, Pain 2003, Boss 2002 and Virolainen 2004). Alternative ways of transformation, such as the probit, have also been attempted, and similar results are obtained.

Wong, Choi and Fong 259 8. As pointed out by Sorge (2004), the impact of a macroeconomic shock may persist for a number of years. Therefore, a dynamic specification like equation (11.1) is more desirable. 9. See Hoggarth et al. (2005). 10. In other words, the two disturbances in equations (11.1) and (11.2) of the same time period are allowed to correlate. 11. As mentioned earlier, the artificial shocks can be specified to last for one period or longer. 12. This means that, even in the baseline credit loss distribution, there could be certain simulated paths of default rates that accompany extreme movements in the macroeconomic variables. 13. The framework can also be applied for stress testing loans to other economic sectors. 14. The time series of classified loans of retail banks can be an alternative measure of default rates. However, such data only became available from 1997 Q1, which is too short for the estimation. 15. Real interest rates are calculated as [(1 + rt )/(1 + πt+1 )] − 1 , where rt and πt+1 are the nominal interest rate in period t and the inflation rate in period t + 1 respectively. We use the seasonally adjusted CPI to calculate the inflation rate. 16. The real rate of change of property prices is calculated as [(1 + propt )/(1 + πt )] − 1, where propt is the change of nominal property prices in period t. 17. A random vector of multivariate normal distribution can be obtained by first computing the Cholesky decomposition C of the variance–covariance matrix , where C is defined by = CC . Pre-multiplying a random vector z whose entries are independently drawn from the standardized normal distribution N(0,1) by C gives r. 18. Note that during the Asian financial crisis (from 1997 Q4 to 1998 Q3), real interest rates rose by 306 bps in the first quarter (that is 1997 Q4), but dropped by 90 bps and 86 bps in the second and third quarters respectively before rising again by 314 bps in the final quarter. Also, China’s GDP in all quarters recorded positive growth. Our assumed shocks are therefore more severe than the actual situation. 19. The percentage of credit loss is simply the product of the default rate and the LGD. 20. This is indeed a very crude assumption. 21. In the event, the credit loss of banks is estimated to have risen from 1.4 per cent before the Asian financial crisis to 6 per cent one year after the shock. These rough estimates are based on an assumed LGD of 70 per cent, and the actual default rates of overall loans at 2.01 per cent in 1997 Q3 and 8.58 per cent in 1998 Q4. 22. The estimated coefficient for real GDP growth of Mainland China is insignificantly different from zero. This may reflect that, unlike the part of business credit of overall loan exposures, mortgage loans are more affected by domestic factors and are less directly affected by the China factor. 23. It is assumed that the share of mortgage loans to the bank’s total loans for use in Hong Kong is 30 per cent, which is about the industry average. Note that this loss figure arises from only the bank’s RML portfolio.

260 The Banking Sector in Hong Kong

References J. Berkowitz, ‘A Coherent Framework for Stress-testing’, Finance and Economics Discussion Series, Federal Reserve Board (1999). W. Blaschke, M. T. Jones, G. Majnoni and S. M. Peria, ‘Stress Testing of Financial Systems: An Overview of Issues, Methodologies, and FSAP Experiences’, International Monetary Fund, (2001). M. Boss, ‘A Macroeconomic Credit Risk Model for Stress Testing the Austrian Credit Portfolio’, Financial Stability Report, 4 (2002), Oesterreichische Nationalbank. P. Bunn, A. Cunningham and M. Drehmann, ‘Stress Testing As a Tool for Assessing Systemic Risks’, Financial Stability Review, June 2005, Bank of England. E. Froyland and K. Larsen, ‘How Vulnerable are Financial Institutions to Macroeconomic Changes? An Analysis Based on Stress Testing’, Economic Bulletin, October 2002, Norges Bank. G. Hoggarth and J. Whitley, ‘Assessing the Strength of UK Banks through Macroeconomic Stress Tests’, Financial Stability Review, June 2003, Bank of England. G. Hoggarth, S. Sorenen and L. Zicchino, ‘Stress Tests of UK Banks Using a VAR Approach’, Bank of England Working Paper, no. 282 (2005). A. Mawdsley, M. McGuire and N. O’Donnell, ‘The Stress Testing of Irish Credit Institutions’, Financial Stability Report, 2004, Central Bank and Financial Services Authority of Ireland. D. Pain, ‘The Provisioning Behaviour Experience of the Major UK Banks: A Small Panel Investigation’, Bank of England Working Paper, no. 117 (2003). M. Sorge, ‘Stress-testing Financial Systems: An Overview of Current Methodologies’, BIS Working Papers, no. 165 (2004). K. Virolainen, ‘Macro Stress-testing with a Macroeconomic Credit Risk Model for Finland’, Bank of Finland Discussion Paper, no. 18/2004. T. C. Wilson, ‘Portfolio Credit Risk (I)’, Risk, 10(9) (1997a) 111–17. T. C. Wilson, ‘Portfolio Credit Risk (II)’, Risk, 10(10) (1997b) 56–61.

12 Assessing the Risk of Multiple Defaults in the Banking System Ip-Wing Yu, Laurence Kang-Por Fung and Chi-Sang Tam

12.1 Introduction Banks face different kinds of risks when conducting their business, such as interest rate risk, operational risk, payments and settlement risk, and credit risk. Among these risks, the assessment of credit risk of the banking system has long been one of the focuses of central banks from a financial stability perspective. For instance, since late 2004, both the Bank of England (BOE) and the European Central Bank (ECB) have published their estimated indicators based on the Merton-type model as part of the measures of banking system vulnerability in their regular Financial Stability Review (BOE 2004; ECB 2004).1 The International Monetary Fund (IMF) also reports similar indicators in its Global Financial Stability Report (IMF 2004, 2005). In addition to an aggregate measure of individual banks’ default probabilities, central banks also use an indicator based on an assessment of the likelihood for at least one bank to default within a short time period (rather than the probability of an individual default) in monitoring the systemic risk of the banking system. In this regard, the IMF (2005) modifies its credit risk indicators (CRIs) to reflect the probability of multiple defaults within a portfolio of banks.2 By taking into account the correlation among a group of banks, the US Federal Reserve Board (FRB) simulates the probability of multiple defaults such that more than one large financial institution among a group of about 40 large financial institutions may default within a period of one year and use this as one of the financial indicators to monitor the risks in the US financial market regularly (Nelson and Perli 2005). The methodology adopted by Nelson and Perli (2005) requires the simulation of the market value of assets of each bank in the portfolio,

261

262 The Banking Sector in Hong Kong

which is computationally intensive. It is also hard to verify whether the simulated pattern of asset values is realistic. An alternative approach by Cathcart and El-Jahel (2004) calculates the probability of multiple defaults based on probability theory. The advantage of this approach is that it provides the joint probabilities for default of at least one bank in a closed and tractable form. This study applies Cathcart and El-Jahel’s approach to estimate the multiple default risk (expressed as an index) of a portfolio of publiclylisted banks in Hong Kong.3 By incorporating asset correlations between two banks, we are able to capture the possible spillover and contagion effects of a bank’s default on the others in the risk assessment. The purpose of this analysis is to illustrate how we can extend the Merton model, originally designed for the estimations of individual banks’ default probabilities, to the case of multiple defaults and how the results can be used to assess the systemic risk of the banking system for surveillance purposes. The chapter is organized as follows. Section 12.2 discusses the methodology of the extended Merton model, the implementation of the probability theory to the model and the data. Section 12.3 presents the results of the estimation and examines the behavior of the indicator. Section 12.4 concludes.

12.2 Methodology and data 12.2.1 The model The structural approach proposed by Merton (1974) assumes that the default process is related to the capital structure of a company. When the value of the company’s asset (VA ) is less than the book value of its debt (X), the company is considered to be in default. Technical details on how the default probability of a single company is computed based on the Merton model are given in Appendix 12A. Using market data of equity values and accounting data, the default probability at the end of a period of time t (PDt ) is, according to the Merton model, given by: PDt = φ(−DD(Xt , VA , σA2 ))

(12.1)

where φ is the standard cumulative normal distribution, ln DD is the ‘default distance’ and is equal to

VA Xt

 + μ− √ σA t

σA2 2

 t , (12.2)

Yu, Fung and Tam 263

VA is the current market value of the company’s assets, μ and σA are the drift rate and volatility of VA respectively, and Xt is the book value of its debt due at time t. In a multiple company setting, the asset value (VAi ) of an individual company follows a stochastic process with drift μi and volatility σAi : dVAi = μi VAi dt + σAi VAi dzi

(12.3)

dzi is a Wiener process. For any two companies i and j, i = 1, . . . , N and j = 1, . . . , N, dzi and dzj are their respective Wiener processes such that dzi dzj = ρij dt. ρij is defined as the asset correlation of the two companies i and j. Given the estimated default probability of individual company (PDit ), and the asset correlation ρij , we can apply the probability theory to calculate multiple default probabilities of a portfolio of two to N companies.

12.2.2 Probability theory In the case of two companies (N = 2), the probability of joint default at the end of a period of time t, denoted as PD(1 ∩ 2)t , is given by:4 PD(1 ∩ 2)t = φ2 {−DD1 (Xt1 , VA1 , σ12 ), −DD2 (Xt2 , VA2 , σ22 ), ρ12 }

(12.4)

where φ2 is the bivariate standard cumulative normal distribution function, DDi (Xti , VAi , σi2 ) for i = 1,2 is the default distance of company i given by equation (12.2), and ρ12 is the asset correlation between companies 1 and 2. The probability of at least one company may default (PD(1 ∪ 2)t ) at the end of a period of time t is:5 PD(1 ∪ 2)t = PDt1 + PDt2 − PD(1 ∩ 2)t

(12.5)

When N > 2, the joint default probability will involve the multivariate cumulative normal distribution function and pairwise asset correlations between the companies and is given as: PD(1 ∩ 2 ∩ . . . ∩ N)t = φN {−DD1 (Xt1 , VA1 , σ12 ), . . . , −DDN (XtN , VAN , σN2 ), ρ12 , . . . , ρ1N , ρ23 , . . . , ρ2N , . . . , ρN−1N }

(12.6)

where φN is the N-th variate standard cumulative normal, DDi and ρij are specified as before.

264 The Banking Sector in Hong Kong

For N companies, one can derive the probability of at least one default (PD(1 ∪ 2 ∪ 3 ∪ . . . ∪ N)) as follows:6 PD(1 ∪ 2 ∪ 3 ∪ . . . ∪ N) = S1 − S2 + S3 − S4 + . . . ± SN

(12.7)

where  S1 = PD(i) with PD(i), i = 1, . . . , N, as individual company’s default probability,  S2 = PD(i ∩ j), i = j, with PD(i ∩ j), i = 1, . . . , N, j = 1, . . . , N, as the joint default probability of two companies,  S3 = PD(i ∩ j ∩ k), i = j  = k, with PD(i ∩ j ∩ k), i = 1, . . . , N, j = 1, . . . , N and k = 1, . . . , N, as the joint default probability of three companies, .. .. . . SN = PD(1 ∩ 2 ∩ 3 ∩ 4 ∩ . . . ∩ N), which is the joint probability of N defaults, and each Sm has N Cm combination of terms, where N Cm = N!/m!(N − m)!, which represents the number of different bivariate combination of size m ≤ N. As an illustration, when N = 3, the probability of at least one default, as given by equation (12.7), is: PD(1 ∪ 2 ∪ 3) = {PD(1) + PD(2) + PD(3)} − {PD(1 ∩ 2) + PD(1 ∩ 3) + PD(2 ∩ 3)} + PD(1 ∩ 2 ∩ 3) which can be represented graphically as:

PD(1 艚 2)

PD(1 艚 2 艚 3) PD(1) PD(1 艚 3)

PD(2)

PD(3)

PD(2 艚 3)

In the following analysis, we apply equations (12.6) and (12.7) to calculate the probability of at least one default in a portfolio of listed banks

Yu, Fung and Tam 265

in Hong Kong. This probability is then expressed as a multiple default risk index to show the relative vulnerability of the banking system to a reference period.

12.2.3 Asset correlation An essential component in the derivation of the joint default probability is the measure of asset correlation between companies (ρij ). There are various ways to estimate pairwise correlations, including sample correlation using rolling windows or correlations based on a factor model. In this study, we adopt the approach used by Nelson and Perli (2005) and Lehar (2005), which estimate the asset correlation with a simple exponentially-weighted moving average (EWMA) model. For each company, we estimate its individual default probability and market value of asset (VA ) according to the model in section 12.2.1. To measure the correlations and volatilities of a portfolio of companies, for each month in the sample period we estimate a variance-covariance matrix of asset returns using the EWMA model with a decay factor λ of 0.94.7 The variance of asset return is given by 2 2 = (1 − λ)R2i,t + λσi,t−1 σi,t

(12.8)

2 where Ri,t is the monthly asset return of company i. The covariance σij,t between the asset returns of companies i and j is estimated by 2 2 = (1 − λ)Ri,t Rj,t + λσij,t−1 σij,t

(12.9)

Once the variance–covariance matrix is estimated, the time-varying pairwise asset correlation can be determined as follows: ρij,t =

2 σij,t

σi,t σj,t

(12.10)

12.2.4 Data Next we illustrate the use of the model, using data of a portfolio of the publicly-listed banks in Hong Kong from January 1997 to January 2006.8 For each bank, its one-year PD is estimated on a monthly basis. The data needed for the estimation include the market value of equity (VE ), the volatility of equity (σE ), the debt level (X) and the one-year risk-free interest rate (r). The market value of equity is equal to the product of the outstanding number of shares and stock price.9 The volatility of equity prices is estimated by the EWMA method.10

266 The Banking Sector in Hong Kong (%) 30

Asian financial crisis

Internet bubble

25 20

Third quartile

15 Median First quartile

10

9/11 attack

SARS

5 0 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06

Figure 12.1

One-year default probability of listed banks

Note: Shaded areas represent major events or crises. Source: HKMA staff estimates.

To calculate the debt level of a bank, ‘short-term loans’, ‘due to creditors’, ‘long-term loans’ and ‘other long-term liabilities’ in the balance sheet are considered.11 The face value of debt is equal to (short-term loans + due to creditors) plus half of (long-term loans + other long-term liabilities).12 As audited balance sheet data are available on an annual basis, monthly figures are estimated by using a cubic interpolation routine.13 For simplicity, the expected drift rate of asset is assumed to be zero, given the short estimation horizon. Once the PDs of individual banks and ρij of pairwise asset correlations are estimated, the probability of at least one default in the portfolio of banks can be established using equations (12.6) and (12.7).

12.3 Empirical results Figure 12.1 presents the median one-year PDs of the listed banks as well as their first and third quartiles over the sample period. Figure 12.2 shows the aggregate one-year PD weighted by the market capitalizations of the listed banks in the portfolio. It is shown in Figure 12.1 that the median PDs rose sharply during the Asian financial crisis period, from 1 per cent in September 1997 to as high as 17 per cent in August 1998. The PDs of the banks in the third quartile reached over 20 per cent in August 1998, signaling high

Yu, Fung and Tam 267 (%) 5

Asian financial crisis

4

3

Internet bubble

2

1 SARS 0 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06

Figure 12.2

Aggregate one-year default probability of listed banks

Note: Shaded areas represent major events or crises. Source: HKMA staff estimates.

vulnerability among this group of the banks, while those under the first quartile were about 5 per cent. Interestingly, the PDs were not affected in other events. The aggregate one-year PD in Figure 12.2 depicts a similar trend. The biggest threat to the banking system was during the Asian financial crisis period when the aggregate PD started to climb in October 1997 and rose to 4.6 per cent in August 1998. The aggregate PD declined steadily after the Asian financial crisis, and it was not affected by other events over the rest of the study period. It is however noted that the aggregate PD may be distorted by one or two very large banks in the sample. In order to complement the aggregate PD for a better measure of the systemic risk in the banking system as a whole, and to capture the contagion effect among the banks in the banking sector, the probability of multiple defaults within a period of time is estimated and this probability is expressed as a multiple default risk index to show the relative vulnerability of the banking system to a reference period. To do so, we first need to derive the asset correlations between banks. Figure 12.3 shows the time-varying asset correlations between banks (as calculated by equation (12.10)) over the sample period. The estimated asset correlations in Figure 12.3 are positive and timevarying. The notable sharp increase in the correlations occurred during the Asian financial crisis, when the median correlation jumped from 0.53 in September 1997 to 0.78 in October 1997. The correlations among these banks remained at such a high level over the crisis period, with

268 The Banking Sector in Hong Kong 1.0 0.9

Asian financial crisis

Internet bubble 9/11 attack

0.8 SARS

Third quartile

0.7 0.6 0.5 Median 0.4 0.3

First quartile

0.2 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Figure 12.3

Monthly asset correlation between banks

Note: Shaded areas represent major events or crises. Source: HKMA staff estimates.

the first quartile around the 0.70 level and the third quartile over 0.85. Such a high level of asset correlation may contribute to systemic risk among banks during crises and would increase the vulnerability of the banking system. The correlations declined after the Asian financial crisis but picked up again after the SARS episode. Since mid-2003, the asset correlation has resumed its declining trend. Based on the default probabilities of individual banks and their pairwise asset correlations, we can use the results from equations (12.6) and (12.7), which estimate the probability of at least one default within the portfolio of listed banks, to derive the multiple default risk index for the banking system. Figure 12.4 presents the multiple default risk index for the banking system with the base period in January 1998. Similar to the aggregate one-year PD shown in Figure 12.2, the multiple default risk index indicates that the most stressful period for the banking system was the Asian financial crisis from October 1997 to September 1998. Given the severity of the financial crisis in 1997–98, the multiple default risk index can be used in addition to the aggregate PD in Figure 12.2 for the monitoring of systemic risk and trend in the banking sector. Furthermore, it is shown that the multiple default risk index jumped in advance of the financial crisis. It reached a reading of 23.7 in June 1997, from just 2.6 in April 1997, and continued to climb throughout

Yu, Fung and Tam 269 Index (Jan. 1998  100) 120 Asian financial crisis 100 80

Internet bubble

60 9/11 attack 40 20

SARS

0 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Figure 12.4 Multiple default risk index (based on one-year probability of at least one default of listed banks) Note: Shaded areas represent major events or crises. Source: HKMA staff estimates.

the year. The early-warning capability of this index on the systemic risk of the banking system is as informative as the aggregate PD.14 Systemic risk in the banking system remained high after the Asian financial crisis, but it has declined steadily throughout the years since 1999. The risk of multiple defaults during the internet bubble period did not stand out as prominently as in the US.15 The threat of the global liquidity and settlement crisis during and after the 9/11 attack in the US was not perceived as a substantial threat to the banking system in Hong Kong. The outbreak of the SARS epidemic in 2003 had little impact on the vulnerability of the banking system too. From mid-2004 onwards, the index has fallen below a reading of two, indicating that the risk of multiple defaults in the banking system as compared to the period in January 1998 has eased substantially. It takes over five years for the indicator to return back to its pre-Asian financial crisis level, partly due to the prolonged economic recession in Hong Kong following the Asian financial crisis and the ‘negative equity’ problem in some banks’ loan portfolios.16,17 As noted by Nelson and Perli (2005), it would be more informative to compare the relative levels of default indicator at different points in time. For instance, while the multiple default risk index was estimated at a level of 28 in September 2001 (the 9/11 attack), it is also of interest to

270 The Banking Sector in Hong Kong

note that the risk of at least one bank may default within one year was over three times less than that during the Asian financial crisis. Mainly due to the scarcity of data caused by the lack of actual default events in Hong Kong, the accuracy of PDs of individual banks estimated in this study has not been tested empirically. Nonetheless, these PDs, in association with asset correlations, help to derive the multiple default risk index which is a useful measure of the systemic vulnerability of the banking system, in addition to the aggregate PDs.

12.4 Conclusion The assessment of vulnerability of the banking system is an important challenge to regulators responsible for banking and financial stability. One of the credit risk models that has been widely used by central banks is the Merton model. This chapter extends the Merton model and applies it to assess the multiple default risk of a portfolio of publicly-listed banks in Hong Kong during the period of January 1997 to January 2006. In our estimation, the derived multiple default risk index indicates that the most stressful period of the banking system was during the Asian financial crisis. Since 1999, the systemic risk of the banks has declined steadily due to the economic recovery in Hong Kong and consolidation in the banking sector. The extended Merton model, by incorporating asset correlations between banks, has the advantage of providing high frequency information that can be used to assess the systemic risk in the banking system. This study has shown that, from a financial stability perspective, the multiple default risk index is as informative a measure of the systemic risk of the banking system as the weighted aggregate default probability. The multiple default risk index derived from this approach, when used together with aggregate and individual banks’ default probabilities as well as market intelligence, can be considered as an effective monitoring tool to aid the ongoing surveillance work of regulators.

Yu, Fung and Tam 271

Appendix 12A Technical details for deriving the default probability based on the structural approach To derive the default probability using the Merton approach, the market value of the company’s underlying assets is assumed to follow the stochastic process: dVA = μVA dt + σA VA dz

(12A.1)

where VA , dVA are the company’s asset value and change in asset value, μ, σA are the company’s asset value drift rate and volatility, and dz is a Wiener process. The probability of a company default is given by the likelihood that the market value of the company’s assets will be less than the book value of the company’s liabilities by the time when the debt matures, that is: PDt = Prob[VAt ≤ Xt VA0 = VA ] = Prob[ ln VAt ≤ ln Xt VA0 = VA ] (12A.2) where PDt is the probability of default by time t, VAt is the market value of assets at time t, and Xt is the book value of debt due at time t. Given equation (12A.1), the value of the company’s assets at time t, VAt , is:   √ σ2 (12A.3) ln VAt = ln VA + μ − A t + σA tε 2 where VA the company’s current asset value, μ is the expected return on the company’s assets, and ε is the random component of the company’s return. Combining equations (12A.2) and (12A.3) gives the PD as 



σ2 PDt = Prob ln VA + μ − A 2





√

t + σA tε ≤ ln Xt

or, alternatively ⎡ ⎢ PDt = Prob⎣−

ln

VA Xt

 + μ− √ σA t

σA2 2

⎤

 t

⎥ ≥ ε⎦

(12A.4)

The Black–Scholes model assumes that the random component of the asset return is normally distributed, ε ∼ N(0,1) and as a result the probability of default can be defined in terms of the cumulative normal

272 The Banking Sector in Hong Kong Market value of assets or debts

Possible path of asset value

5 4

1 3

2

Default probability 0

t

Figure 12A.1

Default barrier (Xt)

Time

Asset value, default barrier and default probability

Notes: 1. The current market value of assets (VA ). 2. The level of default barrier, the book value of debts due at time t (Xt ). 3. The expected rate of growth in the asset value (μ). 4. The volatility of asset (σA ). 5. The distribution of asset value (N (0.1)).

distribution as:

⎡ ⎢ PDt = N ⎣−

ln

VA Xt

 + μ− √ σA t

σA2 2

 ⎤ t ⎥ ⎦

(12A.5)

See Figure 12A.1 for an illustration. There are two unknowns, VA and σA , in equation (12A.5) for the estimation of the default probability. These can be obtained by simultaneously solving equations (12A.6) and (12A.7). VE = VA N(d1) − e−rt Xt N(d2) where r is the risk-free interest rate, ln (VA /Xt ) + (r + σA2 /2)t , √ σA t √ d2 = d1 − σA t, d1 =

N(·) is the standard cumulative normal distribution.

(12A.6)

Yu, Fung and Tam 273

and σE = ηE,A σA = (VA /VE )σA

(12A.7)

where ηE,A = (VA /VE )(∂VE /∂VA ) is the elasticity of equity value to asset value,18 σE is the volatility of the company’s equity value, and  is the hedge ratio, N(d1), from equation (12A.6). Equation (12A.6) is the Black–Scholes pricing formula, which relates the market value of equity (VE ) to the market value and volatility of the company’s underlying assets (VA and σA ), given that the company’s capital structure is only composed of equity and debt, and given Xt the book value of the debt which is due at time t. Equation (12A.7) links the volatility of equity value with that of the company’s assets value which is assumed to follow the stochastic process shown in equation (12A.1).

274 The Banking Sector in Hong Kong

Notes 1. The structural approach proposed by Merton (1974) is a standard framework frequently used by market participants, as well as central banks and international organizations, to help assess the default risk of banks. See Yu and Fung (2005) for a review of the Merton model. 2. The IMF (2004) develops the CRIs that measure the default probabilities associated with first-to-default swaps of a portfolio of banks. The idea is to examine how the market perceives the credit risk of a portfolio of banks through the swap spreads. 3. The portfolio of publicly-listed banks includes holdings companies which have overseas assets and / or may engage in businesses other than banking. 4. The symbol ∩ stands for ‘and’. 5. The symbol ∪ stands for ‘or’. 6. For the proof of this probability result, see Feller (1950). 7. We recognize that there are others ways to estimate volatility. Nevertheless, we use the EWMA model in this study as it is a standard model for market risk management. A comparison of different volatility estimation methods can be found in J.P. Morgan and Co. (1995). In the study, it is shown that a decay factor of 0.94 in the EWMA model gives the best forecast of volatility as compared to other methods such as GARCH-type models. 8. The banks in the portfolio represent about 80 per cent of assets in the locallyincorporated authorized institutions as of the end of 2004. The number of institutions in this study ranges from ten to 12 during the study period. 9. Outstanding number of shares and stock prices are obtained from Bloomberg and Datastream. 2 10. Equity volatility is given by σt2 = (1 − λ)R2t + λσt−1 , where Rt is the monthly return of equity price and λ is the decay factor which is set to be 0.94. The initial σt2 is estimated from the average of the first 12 observations of the data series. 11. The data are from Bloomberg. 12. The reason to use short-term loans and due to creditors is that debt due within one year is more likely to cause default. The reasons for including long-term liabilities in the calculation are two-fold, (i) companies need to service their long-term debt, and these interest payments are part of their short-term liabilities; and (ii) the size of the long-term debt may affect the ability of a company to roll over its short-term debt. Similar to other studies, a factor of 0.5 is used for the long-term debt because the default point is found to lie generally somewhere between total liabilities and short-term liabilities (Crosbie and Bohn 2002). 13. The same cubic smoothing method is also applied to extrapolate the debt levels of a bank for recent months when the current balance sheet data are not available. 14. Before the aggregate PD surged to about 3.8 per cent in October 1997 when the Asian financial crisis first broke out, it remained at a very subdue level of 0.6 per cent or below. Policy makers focusing only on this measure would find it difficult to extract any early warning to the potential systemic risk of the banking system.

Yu, Fung and Tam 275 15. In the US, the probabilities of multiple defaults in the spring of 2000 were as high as that in the fall of 1998. 16. Compared to the simulated indicator derived by the FRB (Nelson and Perli 2005) with about 40 large financial institutions, the decline in the probability of at least one default of financial institutions in the US during the post-crisis period is more rapid. 17. Factors that may contribute to the rise and fall of the aggregate PDs and the multiple default risk index will be examined in a separated research paper. 18. See Bensoussan et al. (1994).

References Bank of England, Financial Stability Review, June (2004). A. Bensoussan, M. Crouhy and D. Galai, ‘Stochastic Equity Volatility Related to the Leverage Effect’, Applied Mathematical Finance, 1 (1994) 63–85. L. Cathcart and L. El-Jahel, ‘Multiple Defaults and Merton’s Model’, Journal of Fixed Income, 14 (2004) 60–9. P. J. Crosbie and J. R. Bohn, ‘Modeling Default Risk’, KMV Working Paper, (2002). Available from http://www.moodyskmv.com. European Central Bank, Financial Stability Review, December (2004). W. Feller, An Introduction to Probability Theory and Its Applications (New York: John Wiley, 1950). International Monetary Fund (IMF), Global Financial Stability Report, September (Washington, DC: IMF, 2004). International Monetary Fund (IMF), Global Financial Stability Report, April (Washington, DC: IMF, 2005). J.P. Morgan & Co., RiskMetrics – Technical Document, 3rd edn, May 26 (New York; J.P. Morgan, 1995). A. Lehar, ‘Measuring Systemic Risk: A Risk Management Approach’, Journal of Banking and Finance, 29(10) (2005) 2577–603. R. C. Merton, ‘On the Pricing of Corporate Debt: the Risk Structure of Interest Rates’, Journal of Finance, 29(2) (1974) 449–70. W. R. Nelson and R. Perli, ‘Selected Indicators of Financial Stability’, Irving Fisher Committee’s Bulletin on Central Bank Statistics, 23 (2005) 92–105. I. W. Yu and L. Fung, ‘A Structural Approach to Assessing the Credit Risk of Hong Kong’s Corporate Sector’, HKMA Research Memorandum, 24/2005.

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Index 9/11 Attack

266, 268, 269

acquisitions, see mergers and acquisitions agency problem 160, 164–5, 170, 171, 188 Asian financial crisis 4, 8, 12, 29, 56, 73, 86, 87, 91, 92, 100, 103, 109, 110, 122, 123, 132, 163, 172, 249, 254, 258, 259, 266, 267, 268, 269, 270, 274 asset correlation 262, 263, 265, 266, 267, 268, 270 Authorized Institutions (AI) 6, 23, 39, 56, 82, 115, 119, 128, 130, 136, 137, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 274 bank deregulation 38, 45 banks, see also Authorized Institutions; interest rates; loans; locally incorporated banks; mortgages; retail banks acquiring cost 77, 79, 80, 91, 93 balance sheet 96, 241, 266, 274 Capital Adequacy ratio (CAR) 15, 20, 23, 24, 25, 26, 55, 56, 57, 60, 159, 160, 161, 162, 163, 164, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 184, 187, 188, 189 deposit mix (DM) 20, 23, 24, 25, 26 deposits 6, 10, 11, 12, 20, 23, 24, 29, 37, 63, 70, 74, 77, 80, 81, 91, 92, 93, 95, 96, 98, 105, 113, 115, 116, 117, 118, 119, 120, 121, 128, 130, 131, 167, 168, 172, 178, 188 funding cost 55, 69, 70, 75, 77, 78, 79, 81, 91, 95, 96, 101, 102, 105, 106, 107, 108, 109, 110, 115, 117, 119, 130, 168 interest cost 54, 77, 79, 91, 92 interest margin 59, 61, 71, 74, 75–7, 86, 93, 95, 96, 106, 107, 127, 128, 129

277

net interest margin 70, 77–80 return on assets (ROA) 54, 55, 56, 57, 58, 59, 60, 63, 64 Tier 1 capital 216 Tier 2 capital 216 Banking Ordinance 187 bankruptcy cost 160 Basel Capital Accord 160, 187 Basel Committee 191, 214, 215, 216, 218 Basel II 171, 191, 192, 198, 215, 216, 217 Basel New Capital Framework 215 benchmarking 191, 192, 193, 194, 197, 198–9, 200, 201, 202, 203, 204, 205, 206, 210 Berger–Hannan approach 51, 53 bonds bondholder 195 convertible bonds 200 corporate bonds 216, 217, 218, 236 corporate discount bond 195, 196 maturity 195 value 193, 195 capital buffer 161, 165, 166, 170, 171, 188 collusion 32, 35, 38, 43, 44, 45, 47, 52, 59, 63 collusive pricing 34, 43, 51, 61 competitive pressures 17, 18, 22, 26, 27, 28 conjectural variation 33–6, 38, 40, 42, 43, 44, 45, 46, 51 consolidation 12, 17, 18, 21, 28, 29, 30, 33, 38, 42, 43, 44, 45, 46, 51, 56, 57, 59, 61, 63, 270 contagion effects 262, 267 corporate loan market 38, 43 cost efficiency 3, 4, 6, 8, 10, 12, 13, 14, 15, 45, 50, 53, 59, 61, 63, 64, 188 cost inefficiency 5, 12, 53, 55, 63

278 Index credit exposures 214, 215, 216, 242 losses 217, 242, 244, 245–53, 254, 255, 256, 257, 258, 259 ratings 133, 162, 167–8, 177, 182, 191, 193, 194, 197, 198, 206, 215, 218 risk 12, 13, 15, 55, 60, 61, 74, 83, 188, 191, 192, 193, 194, 198, 201–3, 205, 206, 212, 214, 216, 217, 219, 240, 242, 252, 253, 254, 256, 258, 261, 270, 274 Currency Board system 72, 129 current debt servicing ratio (CDSR) 133, 135, 136, 138, 149, 150 current loan-to-value ratio (CLTV) 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151–2, 154, 155 Data Envelopment Approach (DEA) 4 debt servicing ratio (DSR) 154 default distance 208, 262, 263 default risk 192, 194, 197, 212, 218, 231, 236, 242, 274 deposit mix (DM), see banks, deposit mix (DM) deposits-financed loans, see loans, deposits-financed loans derivatives market barrier option values 196 option premium 218, 220 option-pricing 229 option strike 192, 218 OTC derivative instruments 101 put option 192, 218, 221, 222, 233, 236 discount window 98, 105 double-market play 73, 91, 92 efficient-structure (EFS) hypothesis 50, 52, 53 Exchange Fund note/paper 98, 105, 128 exposure at default (EAD) 191, 192, 216 financial distress 160 financial stability 95, 261, 270

Herfindahl–Hirschman index (HHI) 21, 22, 30, 32, 44, 54, 56, 58 idiosyncratic risk factor 216 inefficiency (IE) estimates 5, 8–10, 11, 15, 55 inflation 21, 23, 25, 26, 113, 166, 172, 173, 259 insolvency 160 interbank market 70, 98, 128, 168, 182 interest rates base rate of the HKMA (Base Rate) 98, 99, 100, 102, 103, 105, 106, 107, 109, 110, 122, 123, 126, 127, 128, 129 best lending rate (BLR) 32, 44, 69, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 103, 106, 107, 110, 111, 112, 122, 123, 125, 127, 128, 130, 136, 253, 254 BLR – HIBOR spread 69, 70, 71, 75, 76, 81, 90, 91 cap 29, 63 composite rate 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 115–7, 119–21, 123, 127, 128, 129, 130, 131 credit card lending 215 deregulation 18, 21, 29, 30, 32, 43, 45, 54, 63 effective deposit rate (EDR) 69, 71, 74, 75, 76, 77, 78, 79, 80, 81, 86, 87, 88, 89, 90, 91, 92, 93, 94, 98, 99, 100, 101, 102, 103, 104, 105, 107, 109, 110, 115, 117–19, 120, 122, 123, 124, 127, 128, 129, 130 effective mortgage rate, see mortgages, effective mortgage rate Hong Kong Interbank Offered Rates (HIBOR) 69, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 83, 84, 87, 89, 91, 92, 93, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 115, 116, 119, 120, 122, 123, 124, 127, 128, 129, 130, 131, 247 interest rate cycle 70, 71, 72, 74, 80, 83, 84, 86, 90, 91

Index 279 interest rate margin 69, 70, 74, 75, 81, 89, 90, 92, 96, 106, 127 interest rate risk 69, 70, 81, 95, 102, 112, 129, 130, 261 interest rate risk management 93, 99, 101, 105, 108, 109, 110 interest rate rules (IRRs) 29, 32, 33, 44, 63, 96, 128 interest rate spread (IRS) 54, 55, 56, 57, 58, 59, 60, 64 London Interbank Offered Rate (LIBOR) 72, 74, 75, 76, 83, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 128 nominal interest rates 247, 259 real interest rates 246, 249, 251, 252, 254, 256, 257, 258, 259 restriction 21, 45, 54 risk-free interest rate 195, 212, 221, 236, 265, 272 US Federal funds target rate 71, 74, 75, 76, 91, 92, 102, 105 internal ratings-based (IRB) approach 191, 192, 198, 199, 206, 215, 216, 218 leverage ratio 193, 194, 195, 196, 197, 198, 199, 200–1, 206, 207 liquidity 69, 74, 83, 98, 102, 105, 106, 269 loans, see also credit card lending collateralized retail loans 218, 219, 233 deposits-financed loans 75, 77, 80, 92 HIBOR-financed loans 74, 75, 77, 78, 79, 80, 92, 96 loss management 12, 13, 15, 55, 60, 61 loss provisions for banks 10, 11, 12, 13, 15, 55, 60 portfolios 11, 55, 60, 61, 74, 75, 80, 92, 105, 106, 127, 136, 148, 217, 223, 240, 241, 242, 246, 256, 257, 258, 269 prices 34, 60, 61 restructuring 133, 153, 214 residential mortgage loans, see mortgages, residential mortgage loans (RMLs)

retail loans 215, 216, 217, 218, 219, 220, 221, 222, 223, 229 loan-to-value (LTV) ratio 82, 133, 134, 135, 146-8, 154, 220, 221, 222, 223, 228, 229, 230, 231, 232, 233, 234, 237 locally incorporated banks 6, 22, 39, 56, 173 loss given default (LGD) 191, 192, 216, 217, 222, 232, 233, 244, 249, 259 macro stress testing 240, 256, 258 macroeconomic shock 240, 242, 243, 247, 259 market concentration 21, 22, 29, 32, 42, 45, 50, 51, 52, 53, 56, 57, 58, 59, 61, 63 market concentration index, see Herfindahl–Hirschman index market-value capitalization 194, 195, 200, 207, 212 mergers, see mergers and acquisitions mergers and acquisitions 12, 14, 21, 28, 29, 42, 45, 46, 51, 54, 56, 59, 61, 63, 165, 173, 188 Merton model 192, 193, 218, 262, 270, 274 monopolistic competition 19, 24, 27, 29 mortgages adjustable rate mortgage 91, 113, 114 amortization 79, 82, 91 default decision 132, 133, 134, 139, 148 default risk 132, 134, 135, 138, 148 delinquency rate 93, 132, 137, 148, 153 effective mortgage rate 82, 91, 95, 128 fixed rate mortgage 97 portfolio 70, 74, 77–80, 81, 86, 95, 96, 106, 107, 111, 128, 137, 253–6 mortgage rate 69, 70, 77, 91, 92, 96, 97, 99, 103, 104, 105, 106, 107, 109, 110, 111, 113, 123, 124, 125, 126, 129, 134, 136, 137, 138, 139, 141, 143, 145, 146, 147, 148, 150

280 Index mortgages – continued mortgage spread 76, 138 negative equity 132, 146, 147, 148, 155, 219, 220, 228, 229, 230, 237, 269 net mortgage margin 78, 79, 80, 96, 106 prepayment risk 153 rescheduled loan ratio 137, 223 residential mortgage default risk 132 residential mortgage loans (RMLs) 146, 215, 216, 217, 219, 222, 223, 224, 228, 229, 234, 236, 237, 253, 254, 255, 256, 257, 259 variable rate mortgage, see mortgages, adjustable rate mortgage multiple default risk 262, 265, 267, 268, 269, 270, 275 off-balance sheet (OBS) 3, 4, 13, 14, 20, 28, 37 oligopolistic coordination 32, 33, 34, 35, 36, 38, 39, 42, 43, 44, 45, 47 Panzar–Rosse approach 17, 18–19, 25, 26, 28, 32, 51 peer group pressure 167,168,170,189 perfect competition 19, 24, 27, 35, 42 private domestic price index 223, 224 probability of default (PD) 132, 134, 135, 139, 141–6, 147, 148, 151–2, 191, 192, 193, 194, 196, 197, 198, 199, 200, 202, 203, 204, 206, 212, 216, 217, 218, 219, 220, 223, 227, 228, 229, 230, 231, 232, 233, 234, 241, 246, 257, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271–3, 274, 275 production efficiency 51 provisioning requirements 214, 215, 217, 219, 229, 230 provisioning systems 214, 215 real GDP growth rate 10, 20, 23, 36, 50, 56, 57, 60, 163, 164, 172, 174, 246, 247, 248, 249, 250, 252, 253, 254, 255, 257, 258, 259 receiver operating characteristic (ROC) 203, 204

relative market power (RMP) hypothesis 52, 53, 54, 63 retail banks 4, 6, 7, 8, 9, 12, 14, 17, 22, 23, 30, 39, 43, 44, 51, 56, 58, 63, 80, 82, 240, 242, 246, 259 retail loans, see loans, retail loans revolving credit 216 risk-weighted assets (RWA) 160, 168, 169, 172, 176, 183, 185, 187, 215, 216 risk assessment 160, 198, 201, 262 risk exposures 95, 240, 258 risk premium 70, 71, 72–4, 75, 76, 77, 78, 79, 80, 81, 83, 86, 87, 91, 92, 93, 94, 95, 96 SARS 8, 12, 266, 267, 268, 269 scale efficient hypothesis (ESS) 53, 55 scale efficiency 50, 52, 53, 59–60, 63 scale inefficiency (SIE) 53, 55, 57, 59, 60, 62, 63 size efficiency 4, 12, 14 spillover 262 Standard & Poor’s (S&P’s) 193, 194, 197, 198, 199, 200, 201, 202, 203, 206 standardized approach 191, 215 stochastic frontier approach (SFA) 4, 12, 13 structure performance relationship 50, 51 structure–conduct–performance (SCP) hypothesis 50, 52, 53, 54, 63 subordinated debt 167 systematic risk 216 theory of default ability to pay 133, 139, 148 equity 133, 138, 139, 148 three-bank concentration ratio 32,44 Treasury bond 97, 113 US Federal Reserve Board

261

value-at-risk (VaR) 217, 241, 246, 252, 253, 256, 257, 258 X-efficiency 3, 14, 52 X-efficiency hypothesis

59