Research in Finance, Volume 22

CONTENTS LIST OF CONTRIBUTORS vii INTRODUCTION Andrew H. Chen ix CORPORATE OWNERSHIP IS NOT ALWAYS THE BEST POLICY J...

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CONTENTS LIST OF CONTRIBUTORS

vii

INTRODUCTION Andrew H. Chen

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CORPORATE OWNERSHIP IS NOT ALWAYS THE BEST POLICY John W. Kensinger and Stephen L. Poe

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THE INFORMATION CONTENT OF CORPORATE INVESTMENT ANNOUNCEMENTS: THE CASE OF JOINT VENTURES Arthur J. Keown, Paul Laux and John D. Martin

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AN EXPANDED STUDY ON THE STOCK MARKET TEMPERATURE ANOMALY Melanie Cao and Jason Wei

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VALUE AND GROWTH INVESTING IN ASIAN STOCK MARKETS 1991–2002 Joseph Kang and David Ding

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AN ANALYSIS OF STOCK PARTICIPATION ACCRETING REDEMPTION QUARTERLY-PAY SECURITIES K. C. Chen, Friderica Widyasari Dewi and Lijie Zhu

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CONTENTS

INVESTMENT INCENTIVES IN PROJECT FINANCE IN THE PRESENCE OF PARTIAL LOAN GUARANTEES Van Son Lai and Issouf Soumare´

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PRICING OPTIONS WITH PRICE LIMITS AND MARKET ILLIQUIDITY Chuang-Chang Chang, Huimin Chung and Tin-I Wang

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THE INCREASING INTEGRATION AND COMPETITION OF FINANCIAL INSTITUTIONS AND OF FINANCIAL REGULATION James A. Wilcox

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A MODEL OF LIQUIDITY AND BANK RESERVES Stephen A. Kane and Mark L. Muzere

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AN INVESTIGATION OF THE MID-LOAN RELATIONSHIP BETWEEN BANK LENDERS AND BORROWERS Aron A. Gottesman and Gordon S. Roberts

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ZERO–NON-ZERO PATTERNED VECTOR ERROR CORRECTION MODELLING FOR I(2) COINTEGRATED TIME SERIES WITH APPLICATIONS IN TESTING PPP AND STOCK MARKET RELATIONSHIPS T. J. Brailsford, J. H. W. Penm and R. D. Terrell

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EXCHANGE RATE COINTEGRATION ACROSS CENTRAL BANK REGIME SHIFTS Jose A. Lopez

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LIST OF CONTRIBUTORS T.J. Brailsford

UQ Business School, The University of Queensland, Brisbane, Australia

Melanie Cao

Schulich School of Business, York University, Toronto, Ontario, Canada

Chuang-Chang Chang

Department of Finance, National Central University, Taiwan, Republic of China

K.C. Chen

Craig School of Business, California State University, Fresno, CA, USA

Huimin Chung

Graduate Institute of Finance, National Chiao Tung University, Taiwan, Republic of China

Friderica Widyasari Dewi

Jakarta Stock Exchange, Jakarta, Indonesia

David Ding

Nanyang Business School, Nanyang Technological University, Singapore

Aron A. Gottesman

Lubin School of Business, Pace University, NY, USA

Stephen A. Kane

Frank Sawyer School of Management, Suffolk University, MA, USA

Joseph Kang

Nanyang Business School, Nanyang Technological University, Singapore

John W. Kensinger

College of Business Administration, University of North Texas, TX, USA

Arthur J. Keown

R. B. Pamplin College of Business, VPI & SU, VA, USA vii

viii

Van Son Lai

LIST OF CONTRIBUTORS

Laval University, Quebec, Canada

Paul Laux

Alfred Lerner College of Business & Economics, University of Delaware, DE, USA

Jose A. Lopez

Economic Research Department, Federal Research Bank of San Francisco, CA, USA

John D. Martin

Hankamer School of Business, Baylor University, TX, USA

Mark L. Muzere

Frank Sawyer School of Management, Suffolk University, MA, USA

J.H.W. Penm

Faculty of Economics and Commerce, The Australian National University, Canberra, Australia

Stephen L. Poe

College of Business Administration, University of North Texas, TX, USA

Gordon S. Roberts

Schulich School of Business, York University, Toronto, Canada

Issouf Soumare´

Faculty of Business Administration, Laval University, Quebec, Canada

R.D. Terrell

National Graduate School of Management, The Australian National University, Canberra, Australia

Tin-I Wang

Department of Finance, National Central University, Taiwan, Republic of China

Jason Wei

Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario, Canada

James A. Wilcox

Haas School of Business, University of California, Berkeley, CA, USA

Lijie Zhu

Craig School of Business, California State University, Fresno, CA, USA

INTRODUCTION A total of 12 papers in this volume represent some current research on important topics in ﬁnance. The contributions include analyses of issues relating to the recent reforms on corporate governance, the behavior of stock returns, the option pricing models, the ﬁnancial regulation and banking theory, and the international ﬁnance. Kensinger and Poe argue that the legal status of corporations and the higher costs of Sarbanes-Oxley will accelerate further hollowing of public corporations. Using stock price reactions to the information in joint venture announcements, Keown, et al. ﬁnd that the market considers relevant information for valuing the ﬁrms apart from the joint venture itself. Based upon data from a large sample of global ﬁnancial markets, Cao and Wei ﬁnd empirical evidence strongly supporting the negative relationship between stock returns and temperature. Kang and Ding ﬁnd differential results of stock returns on the ﬁnancial signals in Asian ﬁnancial markets. Chen et al. develop a binomial-tree pricing model for Stock Participation Accreting Redemption Quarterly-pay Securities (SPARQS), and show the pricing performance of the model. Lai and Soumare analyze the investment incentives in project ﬁnance in the presence of government ﬁnancial guarantees. Chang et al. develop option-pricing models with price limits and market illiquidity and show that both of these market imperfections have significant impact on the option values. The contributions to this volume also examine important issues in the ﬁnancial competition and regulation and the banking theories on the required reserves and the impact of bank lending, and in the testing of Purchasing Power Parity and the foreign exchange rates. Wilcox discusses beneﬁts of increasing ﬁnancial competition and regulation. Kane and Muzere develop a theoretical bank model to examine certain economic impact of required reserves and show that the required reserves above a bank’s optimally determined levels represent deadweight losses. Gottesman and Roberts provide an empirical analysis of the mid-loan relationship between the bank lenders and borrowers. Brailsford, et al. provide a new framework for zero-non-zero (ZNZ) patterned vector error-correction models (VECM) technique to examine the Purchasing Power Parity and stock markets ix

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relationships. Finally, Lopez applies cointegration tests to examine foreign exchange rates over various time periods linked to regime shifts in the behavior of central banks. Andrew H. Chen Series Editor

CORPORATE OWNERSHIP IS NOT ALWAYS THE BEST POLICY John W. Kensinger and Stephen L. Poe ABSTRACT This paper explores the advantages (for large investors) of directly owning productive assets, compared with indirect ownership through stock in corporations. Significant factors are agency costs and recent changes in the tax and regulatory environment. Recent corporate scandals have led to legislative and regulatory responses that significantly increase the monitoring costs and other burdens of becoming or remaining a public corporation. As a result, there has been a substantial increase in goingprivate transactions, particularly among smaller public companies. However, the pressures to go private are not entirely new. We trace the legal concept that the corporation is an entity separate and apart from its owners, showing how the legal status of corporations hinders resolution of conflicts among the parties to the enterprise. Thus, there have long been fundamental flaws inherent in the corporation as the form of organization for certain activities. Direct ownership of major assets by investors prevents future expropriation of resources, and is preferable to corporate ownership whenever other alternatives for indemnification or liability limitation are available (such as insurance, limited partnerships, limited liability companies, etc.). Finally, the renewal of direct ownership is not a radical shift, but a return to long-established tradition in the organization of business activities.

Research in Finance, Volume 22, 1–31 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22001-4

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JOHN W. KENSINGER AND STEPHEN L. POE The stockholder is therefore left as a matter of law with little more than the loose expectation that a group of men, under a nominal duty to run the enterprise for his beneﬁt and that of others like him, will actually observe this obligation. In almost no particular is he in a position to demand that they do or refrain from doing any given thing y . The legal doctrine that the judgment of the directors must prevail as to the best interests of the enterprise, is in fact tantamount to saying that in any given instance the interests of the individual may be sacriﬁced to the economic exigencies of the enterprise as a whole. Adolph Berle and Gardner Means (1932)

1. INTRODUCTION Efforts to discover how conﬂicts of interest between managers and investors can be resolved have focused on reforms in corporate governance, or the search for improvements in executive or employee compensation.1 In just the last few years, several corporate scandals have led to substantial changes in legislation and accounting standards – all aimed at the hope of improving corporate governance and accountability for public corporations. We begin with the Sarbanes-Oxley Act of 2002 and its consequent substantial increase in the cost of becoming (or remaining) a public corporation. In the aftermath, going-private transactions have increased substantially, particularly among smaller public corporations. If this becomes a trend, the ‘‘new economy’’ companies will increasingly become private entities, while public corporations will increasingly reﬂect the ‘‘old economy’’ companies. Then, we consider the erosion of executive stock options that has accompanied the reforms of the Sarbanes-Oxley era, and the additional burdens that have been added by pension fund controversies. Yet, the incentives to go private are not really new. To a significant extent, conﬂicts of interest are intrinsically irresolvable due to the unique legal demands inherent in the corporate form of organization since its inception. Thus, institutional investors have long sought alternative arrangements that avoid corporate ownership of assets, leaving corporations increasingly hollow. Besides any obligations to stockholders, corporate executives are legally charged with ensuring that the ﬁrm satisﬁes contractual and social obligations to various third parties, such as the ﬁrm’s creditors, employees, and even the community at large. More than two dozen states have formalized this requirement by adopting ‘‘corporate constituency’’ statutes, which expressly allow directors to take into account the interests of these third party groups in making business decisions for the ﬁrm.2 With regard to this

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requirement, Easterbrook and Fischel (1991, p. 38) have observed that ‘‘a manager told to serve two masters (a little for the equity holders, a little for the community) has been freed of both and is answerable to neither. Faced with a demand from either group, the manager can appeal to the interests of the other.’’ Stock in a widely held corporation has evolved into a sort of property that conveys few enforceable rights to its owners. Although property typically derives its substance from the protection of the courts through the due process of law,3 the courts stand ready to defend the incorporated enterprise as a whole, even at the expense of the stockholders. This is not necessarily due to any ﬂagrant disregard for stockholders’ rights, but reﬂects a duty to another ‘‘person’’ – the corporation itself – that stands before the courts as an entity separate and apart from individual stockholders, employees, or any other specific group of associates in the enterprise. The corporation represents an amalgam of all their interests, along with those of the state that chartered it. (Separate entity status for corporations is a long-standing legal principal with roots in Roman law, and the principal of limited liability for stockholders evolved from this separateentity status). Indeed, by seeking limited liability within the corporate form of organization – thereby disclaiming personal responsibility for corporate acts – shareholders explicitly acknowledge a separate identity for the corporation. Thereafter, any shareholder who seeks to disregard the separate existence of his own creature is likely to meet resistance not only from management, but also from the courts.4 As Berle and Means observed, ‘‘The owners of passive property, by surrendering control and responsibility over the active property, have surrendered the right that the corporation should be operated in their sole interest – they have released the community from the obligation to protect them to the full extent implied in the doctrine of strict property rights.’’5 Unless stockholders can organize themselves to make effective use of their votes (a costly and unreliable recourse) they must depend upon market forces to protect their property rights. The logic here – that when enough dissatisﬁed shareholders sell their stock, the price will drop to the point that it becomes attractive for someone to take over control – is meager consolation for the dissatisﬁed shareholders who sold on the way down, without whose sacriﬁce the survivors presumably would not have been able to obtain the eventual premium. At best this process provides only a slow-working kind of justice for shareholders as an amorphous group, but no dependable protection at all for any specific individual shareholder. There is no other

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form of property that depends for its fundamental protection upon something other than the due process of law. Further, the courts have frequently intervened to protect corporations against the forces of the ﬁnancial marketplace.6 Some commentators have even suggested that corporations have a duty to support ‘‘community’’ causes. For example, Adolph Berle states, ‘‘For practical purposes, the state has authorized corporations to withhold from their shareholders a portion of their profits, channeling it to schools, colleges, hospitals, research, and other good causes.’’7 Later in the same passage, though, Berle speculates, ‘‘But in the not too distant future it may well appear that the men in the corporate world who y insist that community formation is for individuals and therefore compel distribution of profits to their shareholders, instead of conscripting part of them for education and charity, may be found to be the true saviors of a free, energetic, and competitive society.’’ (Accomplishing this reform, though, has been primarily the work of a group unknown to Berle – the trustees of pension funds and other institutional investors.) How can investors avoid the conﬂicts of interest that are inherent in the corporate form, and irresolvable through reforms in the compensation scheme? One solution is to avoid corporate ownership of assets whenever possible. The recent past has witnessed significant downsizing by many companies. This has been associated with trends toward paying higher dividends, spinning off divisions into independent status, repurchasing shares, arranging leveraged buy-outs, farming out new growth to partially owned subsidiaries, and other forms of corporate ‘‘hollowing’’ in which corporations sell their marketable assets and hold increasing proportions of their ‘‘wealth’’ in nonmarketable assets. Investors are quietly turning to direct ownership of productive assets. Increasingly, investors prefer to own airplanes instead of stock in airline companies, oil wells or small exploration/production companies instead of large integrated oil companies, timberlands instead of forest products companies, and real estate of their own instead of stock in corporations that hold real estate. Indeed, when asked at the beginning of the decade what changes the 1990s would bring, Robert Farrell (chief technical analyst for Merrill Lynch) replied: ‘‘I y get a sense that the sun is setting on the era of stocks and other ﬁnancial assets, and that the ‘Nineties will see a new game come to the fore. I’m not sure what the new game will be, but an educated guess might be factories and other productive assets as opposed to pieces of paper.’’8 Although the trend did indeed start in the 1990s, momentum has begun to build in the current decade.

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2. THE SARBANES-OXLEY ACT ACCELERATES PRIVATIZATION Reacting to major corporate scandals involving Enron, Worldcom, and Adelphia, Congress enacted the Sarbanes-Oxley Act of 2002 (‘‘Sarbanes-Oxley’’ or ‘‘SOA’’). Apparently, the lawmakers hoped to restore the investing public’s conﬁdence and trust in public companies through Sarbanes-Oxley. It remains to be seen whether or not SOA will lead to improved accountability and better corporate governance. Without dispute, though, SOA has added substantially to the burden of monitoring costs associated with becoming or remaining a public corporation. Further, SOA exposes corporate ofﬁcers to the danger of prosecution for inadvertent technical violations. These higher costs of public corporation status enhance the motivation for selling assets and business units into private entity status, and even eventually taking the whole company private. So, an unintended consequence of Sarbanes-Oxley may be to accelerate the ‘‘Eclipse of the Public Corporation’’ described by Michael Jensen (1989). Indeed, in the wake of Sarbanes-Oxley, privatization announcements increased 30% from August 2002 to November 2003 (compared with the 16-month period preceding the Act’s initiation from April 2001 to July 2002). Smaller public companies in particular have felt the cost pinch and many have responded by going private. Grant Thornton (2004) further reports, ‘‘Since the introduction of the Sarbanes-Oxley Act, the median size of going private transactions has almost halved (from $81 million to $39 million) and the number of proposed buyouts by the management team has increased approximately 80 percent.’’9 Overall, Sarbanes-Oxley mandates that public companies adopt measures to ensure (i) independence for their outside auditors, members of their audit committees and a majority of the board of directors, (ii) increased transparency for their ﬁnancial statements and other processes and procedures, and (iii) compliance with increased corporate controls and new disclosure requirements. SOA imposes strict penalties for failure to comply. Also, the Securities and Exchange Commission (SEC) as well as the major stock exchanges (NYSE, AMEX, and NASDAQ) have adopted significant regulations and rules to supplement the statutory provisions since the passage of SOA.10 Moreover, SOA may not, and some say cannot, address the basic problem that prompted its enactment and prevent future scandals. In fact, some question whether many of the scandals of the early 2000s would have been prevented even if SOA had been in effect during that period.11 One commentator has suggested that true improvements in corporate governance

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require more than a change in legal structure, but instead ‘‘a change of mindset among many directors, managers, and advisors that internalizes the value of shareholder protection.’’12 In other words, as Mark Stark, CFO for The Exploration Company, Inc. has expressed eloquently, ‘‘While [SOA is] a very worthy and noble undertaking, you can have all the policies and procedures and internal controls in place; but ultimately, dishonest people will ﬁnd ways to do dishonest things, and I’m not sure that you will ever have a way to keep that from happening.’’13 What is very clear about SOA is that the cost of compliance for public companies has been staggeringly large. In 2004, Korn/Ferry International conducted a study of Fortune 100 companies, ﬁnding that these companies paid an average of $5.1 million each in order to come into compliance with SOA.14 Another survey conducted by Financial Executives International (FEI) reports that the average cost of being a public company increased 45% from FY 2003 to FY 2004 – direct costs of monitoring averaged $14.3 million (for companies with annual revenue of $1 billion or more) an increase of $4.4 million over FY 2003. Large public ﬁrms must pay an average of $3.14 million just to achieve initial compliance with that part of the statute’s provisions mandating transparency in all documentation. In addition, lost productivity due to the increased regulatory burden continued to represent a major concern for all companies responding to the FEI’s 2005 survey, particularly for the smaller public companies. Average costs attributed to lost productivity increased more than 556% (to $1 million in FY 2004) for companies with annual revenues under $1 billion, compared with an 18% increase (to $2.9 million in FY 2004) for companies with annual revenue over $1 billion.15 The survey reports that average costs of lost productivity increased from $160,000 in FY 2003 to $1,050,000 in FY 2004. Further, the FEI study reports that it continues to be increasingly expensive for companies of all sizes to attract and retain qualiﬁed directors. In FY 2004, S&P Small-Cap, S&P Mid-Cap, and S&P 500 companies witnessed increases in average annual director fees of 17%, 14%, and 13%, respectively. Over the past four years, the impact of corporate governance reform on director fees has been significant, with increases of 46% for S&P Small-Cap, 45% for S&P Mid-Cap, and 43% for S&P 500 companies between FY 2001 and FY 2004.16

2.1. Is Sarbanes-Oxley Fighting the Last War? Because of the many specific provisions created in reaction to specific scandals, Sarbanes-Oxley has been criticized for the appearance that the

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legislation is like military leaders who make the mistake of ﬁghting the last war instead of adapting to new challenges in the present. More problematic are the substantial burden of new costs that SOA imposes upon public companies, and the exposure to inadvertent technical violations SOA places on corporate ofﬁcers. Such costs and risk exposures add new motivation for splitting off portions of public companies into private entity status. Welsh (2003) describes SOA as follows: ‘‘Sarbanes-Oxley represents a sweeping attempt by the Congress and the Commission [SEC] to provide ‘protection’ to investors against the consequences of corporate wrongdoing and fraud. The Act and the rules promulgated pursuant to the Act seek to improve corporate governance and the capital markets by three principal means: First, although the risk of inadvertent or technical violations of SEC rules may be increased, the ﬁnal rules evidently seek to make violations of the securities laws less likely to occur than in the past by tightening the rules with respect to certain key disclosures and by compelling ofﬁcers and directors to focus more intently on quality disclosure. For example, the rules include heightened disclosure requirements for off-balance sheet ﬁnancing as well as new rules governing the use of non-GAAP reporting. The rules also impose certiﬁcation and code of ethics disclosure requirements on senior ﬁnancial and executive ofﬁcers. Secondly, the ﬁnal rules evidently seek to make detection of material violations of the law more likely to occur. In that regard, the rules contain extensive requirements relating to auditor independence and the standards of professional conduct for attorneys, as well as a prohibition on improper attempts to inﬂuence the conduct of an audit. Thirdly, the Act – though not the rules – significantly increases criminal and civil penalties for certain violations of the law affecting the securities markets. The Act, for example, increases the maximum penalty for mail and wire fraud from ﬁve years to twenty years per violation.’’17

2.2. The Higher Cost of Being a Public Company Sarbanes-Oxley mandates a whole new layer of monitoring costs, launching the Public Company Accounting Oversight Board (PCAOB). Fees collected from the auditors subject to oversight under SOA provide the funding for the ‘‘self-supporting’’ PCAOB. The members of the ﬁve-person Board are appointed by the SEC with the idea that this Board will be ‘‘independent,’’

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and ‘‘will set clear standards to uphold the integrity of public audits, and have the authority to investigate abuses and discipline offenders.’’18 The PCAOB’s website includes the following mission statement: ‘‘The PCAOB is a private-sector, non-profit corporation, created by the SarbanesOxley Act of 2002, to oversee the auditors of public companies in order to protect the interests of investors and further the public interest in the preparation of informative, fair, and independent audit reports.’’ As part of its oversight of auditors, the PCAOB (1) registers public accounting ﬁrms that prepare audit reports for public companies, (2) establishes auditing, quality control, ethics, independence, and other standards related to the preparation of audit reports for public companies, (3) conducts inspections of registered ﬁrms,19 and (4) conducts investigations and disciplinary proceedings concerning alleged infractions by registered ﬁrms. Of course, the cost borne by auditors in maintaining qualiﬁed status will be reﬂected in higher audit fees for public companies. Indeed, fees paid to outside auditors have increased rapidly post-SOA, averaging 61% up from FY 2003 to FY 2004 (84% for S&P Small-Cap companies, 92% for S&P Mid-Cap companies, and 55% for S&P 500 companies).20 One critic has pointed out that the process for appointing the members of the PCAOB may be unconstitutional because it gives powers to the SEC that are reserved for the President and Congress. Erika Birg argues, ‘‘Congress’s desire to create an ‘independent’ Board under the auspices of the SEC actually may run afoul of the Appointments Clause, US Constitution Article II, y 2, cl. 2, rendering the Board unconstitutionally created.’’21 SOA also altered the way the Financial Accounting Standards Board (FASB) is funded. The FASB is now funded by the mechanism established by the Act that replaces voluntary contributions with a mandatory funding model for public companies. The combined impact from establishing the PCAOB and mandating the change in the funding model for FASB results in significantly higher costs for becoming or remaining a public corporation – and adds incentives for splitting off pieces of the ﬁrm into private entity status.

2.3. Track Record so Far Although it is possible that corporate governance in public companies may improve as a result of Sarbanes-Oxley, it is still too early to tell what the full impact of the statute will be. SOA expressly regulates certain relevant activities, such as prohibiting ﬁrms from making personal loans to

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their ofﬁcers and directors and requiring senior executives to surrender profits obtained through sales of ﬁrm securities where misconduct has occurred and an accounting restatement has been necessary. The statute is also expected to be extremely inﬂuential on courts deciding cases in areas in which it does not expressly regulate, such as the ﬁduciary duties of ofﬁcers and directors.22 Many of the provisions of SOA and the recent supplemental rules, however, are quite broad and as yet untested. In addition, the deadline for companies to comply with this statute, in Autumn 2004, has only recently passed. Accordingly, some commentators have noted that in order to gauge the true impact of SOA on corporate governance, many of these provisions will require interpretation, ﬁrst by the public companies themselves, and ultimately the courts. Only then will it be clear exactly what these new rules require and what corporate boards and ofﬁcers will have to do in order to be in compliance.23 Although it is still too soon to determine how effective SOA will be in improving corporate governance in public companies, many are already questioning whether it will make more than a minor difference in their operations, especially in the long run. For example, although the government may be able to bring action to enforce the statute, it is doubtful whether private litigants, such as shareholders, would be able to bring suit against an ofﬁcer or director in violation of the statute’s provisions. SOA itself does not provide such a right, and the courts, particularly the US Supreme Court, have been reluctant to imply such a right in the absence of express statutory language. Also, as some commentators have noted, the supplementary standards enacted by NYSE, AMEX, and NASDAQ are likely to be viewed by the courts as a private contract between the public company and the respective exchange, giving shareholders no rights to enforce them.24 Any shareholder suits would thus have to be brought under existing state law, and this paper will later address the procedural problems faced by shareholders in bringing such suits. Given this lack of accountability to shareholders, then, it is small wonder that many shareholder rights groups do not believe that SOA goes far enough to promote corporate governance reform. For example, some of the additional changes that these groups want to see implemented include ‘‘stricter definitions of independence for directors, the separation of the CEO and chairman functions, limitations on executive compensation, majority voting requirements for the election of directors, restrictions on the number of boards or audit committees on which directors may serve and the elimination of staggered boards and poison pills. These areas of focus

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involve both the internal management of the company and potential impediments to the maximization of shareholder value.’’25 Dalley (2003) concludesy . ‘‘The corporate governance provisions of the SOA and the rules adopted by the SEC, the NYSE, and the NASDAQ are extensive, but it is questionable whether they would have been able to prevent any of the alleged wrongdoing that generated them. Enron, for example, had a board consisting of 14 members – 11 of whom were independent. Many of the independent directors received substantial compensation in cash and stock options, which would continue to be permitted under the new rules. If many of the recent earnings restatements were necessitated by executives ‘managing’ earnings to protect the value of their stock options, then ‘independent’ directors who are also compensated with stock would feel similar pressures. Enron’s independent directors approved at least some of the conﬂict-of-interest transactions that later proved so devastating. In addition, Enron’s audit committee had an ambitious charter requiring it to oversee ﬁnancial reporting and auditing.’’26 Even the tough penalties imposed by SOA may not be enough to effectively improve corporate governance in the public company. For example, in 2003 Richard Scrushy, the CEO of Health South (a large health care conglomerate) was charged under SOA with more than 85 federal criminal counts, including conspiracy, securities fraud, mail fraud, wire fraud, and money laundering. Under this criminal prosecution, which centered on the government’s contention that Scrushy knowingly ﬁled false ﬁnancial statements, Scrushy faced a maximum possible penalty of 650 years in prison and $36 million in ﬁnes. Following a criminal trial, Scrushy, the ﬁrst CEO ever charged under SOA, was acquitted in June 2005, in what some commentators have called ‘‘a stunning setback for the US government crackdown on white-collar crime.’’27 Without a true sense of accountability, obviously, the rest of the reforms contained in the statute cannot be expected to be very effective. These accountability issues, together with the tremendous cost imposed on ﬁrms to comply with the statute, have led some to call for a review and perhaps a major overhaul of Sarbanes-Oxley and the supplementary rules.28

3. EXECUTIVE STOCK OPTIONS IN THE SARBANES-OXLEY ERA For years, many companies have used stock options as a means of recruiting and retaining top executives. Further, many investors have hoped that

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judicious use of executive stock options could reduce the agency problems between owners and managers. Recently, however, stock options have become a subject of intense criticism, due to their involvement in the climate of corporate scandal that led to Sarbanes-Oxley. Executive stock options became linked with increasingly large compensation packages for executives, even for those whose ﬁrms have performed poorly. The use of stock options has even been blamed for creating incentives for executives to engage in short-term strategies designed to artiﬁcially inﬂate stock prices, sometimes leading to fraud in a company’s ﬁnancial statements and accounting practices.29 As such, executive stock options have become a target for corporate reformers. This desire for reform has led to a regulatory response designed to reign in the use of these options. Spurred by the advance of H.R. 3574 ‘‘The Stock Option Accounting Reform Act’’ through the legislative process in the US House of Representatives, hoping to forestall Congressional action by taking action of its own; the FASB accelerated its efforts to promulgate new standards of accounting for stock-based compensation.30 FASB announced its revisions in December 2004, with new rules scheduled to take effect June 15, 2005 (applying to the ﬁrst reporting period beginning after that date).31 Prior to these revisions, the cost of granting stock options did not have to be charged as an expense on a company’s ﬁnancial statements until the date the option was exercised, making them a fairly inexpensive means of compensating executives. Under the new rules, public companies are required to determine the fair market value of all of its employee stock options as of the date they are granted and then treat this value as an expense on their ﬁnancial statements – just like salary, bonuses, and other types of compensation.32 With these rules in place, it becomes much more expensive for companies to offer options as executive compensation. Anticipation of these rules taking effect, and perhaps the prodding of corporate reformers, may have motivated ﬁrms to reduce the use of stock options over the past few years.33 Although prior to the public outcry over executive compensation, stock options once hit a high of more than 90% of CEO’s total compensation, the controversies surrounding the corporate scandals have led to a major readjustment in the way senior executives are paid. In 2004, stock options comprised only about 31% of the total compensation packages of top executives at Fortune 100 ﬁrms, compared with 50% just two years previously.34 As more and more companies have reduced the use of stock options to compensate executives, however, they have replaced them with grants of

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restricted stock.35 Almost half of Fortune 100 companies included restricted stock as part of their compensation package, up from 29% in 2002.36 Restricted shares are grants of full shares in the ﬁrm, but typically they do not vest until the executive has been with the ﬁrm for a certain period of time, or in a minority of cases, until the ﬁrm has realized certain performance goals (performance standards may include such factors as profitability, capital spending outcomes, cash ﬂow, and inventory management). Also, multiyear performance plans tied to company ﬁnancials and stock price have grown in popularity. In fact, 50% of companies now have performance share plans (compared to 42% in 2002).37 Proponents of restricted stock argue that since executives are getting shares of stock rather than options, the interests of executives are aligned more closely to those of the company’s investors; while the ‘‘perverse incentive’’ created by stock options, i.e., to boost stock prices in the short term rather than focus on long-term performance, is eliminated.38 Restricted shares, on the other hand, allow executives to focus more on long-term performance since these shares cannot be cashed in until they vest. Also, restricted shares work better as a retention tool than stock options, since they provide executives with an incentive to stay with the company as they vest over time. From the companies’ point of view, restricted shares grant the right to a full share, so fewer are needed to give the same value as options. Finally, executives may prefer restricted stock over options; since the options become worthless if the value of the stock falls below the exercise price, while restricted shares always have some value (barring complete failure of the ﬁrm). On the other hand, opponents of restricted shares argue that since these shares have some value regardless of the price of the stock, executives have less incentive to improve share performance than they would with options. Also, with stock options, executives must purchase the shares at the option price with their own cash, while restricted stock costs them nothing. Although options reward executives only if the ﬁrm’s stock price rises above the exercise price, restricted stock rewards them whether the stock price goes up or down.39 In addition, these critics complain that a grant of restricted shares is merely a reward for executive survival, noting that less than 20% of companies that offer restricted stock link the stock to a performance standard. As a result, restricted shares may lead to the same types of problems as stock options since they allow executives to focus solely on stock price. Another criticism of restricted shares is that even when linked to performance40 standards, many ﬁrms are unlikely to deny underachieving executives their

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shares, in light of the common practice of companies who reprice stock options in an effort to retain their top executives. They also note that while fewer restricted shares are needed to give the same value as options, in fact ‘‘the dollar value of the restricted stock is much higher than the estimated value of options.’’41 A ﬁnal problem with the use of restricted stock is that executives are allowed to collect dividends on them even before the shares have vested. When shares are tied to performance goals (or even just the goal of executive survival), it may seem inconsistent to allow executives to collect rewards when the goals have not yet been reached.42 Also, although the executive must surrender the shares upon departing before the vesting date, most ﬁrms have no requirement that the executive return these dividends in such an event. As a result, the executive again receives some reward even if required performance goals are not met or even in the absence of fulﬁlling the minimum amount of time necessary to receive the shares. In sum, although the use of stock options to compensate top executives may tend to alleviate agency problems between a ﬁrm’s top management and its shareholders; it does not appear that the substitute that most ﬁrms have employed to replace these options (restricted stock) is likely to heal these problems any time soon.

4. PENSION CONTROVERSIES The recent wave of reform also has included changes in the way pension obligations must be disclosed. Given the possibility of ﬁnancial failure that plagues several of the major airlines and automakers in the United States today, these changes are particularly timely. FASB released new rules in 2003, taking effect with ﬁscal years ending after December 15, 2003 (with certain limited requirements deferred until ﬁscal years ending after June 15, 2004). The new standards were established in response to concerns expressed by users of ﬁnancial statements about their need for more information about pension plan assets, obligations, beneﬁt payments, contributions, and net beneﬁt cost.43 New disclosure requirements include information describing the types of plan assets, investment strategy, measurement dates, plan obligations, cash ﬂows, and components of net periodic beneﬁt cost recognized during interim periods. The new rules include reduced disclosure requirements for nonpublic entities. Compliance further increases the monitoring costs associated

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with becoming or remaining a public corporation. Also, the disclosures may be controversial and could lead to labor unrest. Perhaps even more impactful than the new disclosure rules are the controversies over pension plan reorganizations or conversions. United Airlines, Delta Airlines, General Motors, and other large public corporations are struggling with heavy burdens of legacy costs arising from pension and health care costs for retired workers. United Airlines recently announced settlement losses of $602 million related to the Pension Beneﬁt Guarantee Corporation (PBGC) takeover of the company’s deﬁned beneﬁt pension plans for ground employees, ﬂight attendants, management, and contract employees;44 and the nation’s second-largest airline continues to experience labor unrest over actions regarding the pension plans.45 Those companies forced into bankruptcy will ﬁnd that the courts must assign clear priorities in these cases. Although the courts will protect employees over the company’s shareholders, this protection is more a function of federal bankruptcy law, federal labor law, and ERISA, than traditional corporate law per se. In order to address the controversy over pension conversion, let us use the AT&T case as an illustration. On October 7, 2004 plaintiffs ﬁled a class action lawsuit in the US District Court in New Jersey on behalf of 25,000 current and former employees of AT&T. Internal memos from AT&T show estimated savings of nearly $2 billion in future beneﬁt obligations. The briefs include claims that AT&T:46 (1) did not properly adopt the adverse features of the cash balance plan amendments, (2) did not disclose the beneﬁt reductions and disadvantages effected by cash balance as required, such as up to 13-year periods in which employees could experience no increases in their pension beneﬁts, (3) did not comply with beneﬁt accrual rules established under federal pension laws, (4) excessively reduced beneﬁts for early retirements before age 55, and (5) offered two new options for commencements of beneﬁts after 1998 that were ‘‘clearly less valuable’’ than the traditional annuity options without ever disclosing the lower values of the new options. A related suit was ﬁled on behalf of 20,000 current and former employees of CIGNA Corporation.47 The suits claim that AT&T and CIGNA employees have been ﬁnancially devastated by their company’s cash balance conversions, and seek relief on the grounds of age discrimination. The corporate action that triggered these suits was conversion of deﬁned-beneﬁt

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plans into cash balance plans. The arguments in the cases focus on the method for estimating the value of beneﬁts already accrued under the old plan. The claims of age discrimination are based on the allegation that the changes harm older workers ﬁnancially, while leaving younger workers as well off or better than before the conversion (as though the companies had revised the plans in order to continue to attract younger workers, while saving money on the costs of providing beneﬁts to the older workers). At the time of writing these cases are awaiting decisions in the courts. If the courts hold with precedent, they will likely tend to lean in favor of the older workers, while the interests of shareholders take a back seat.

5. AN ENTITY SEPARATE AND APART The incentives for going-private transactions are not all new – there have long been inherent weaknesses in the corporate form as a means for owning assets. Stock in a widely held corporation provides only modest recourse to the courts for protection of property rights. (Stockholders’ principal entitlements are the right to receive equal dividends as others in the same class, and the pre-emptive right to buy enough new shares to maintain their proportional ownership when more shares are issued.) Although a few bondholders can force a corporation into receivership if it is no longer capable of paying an adequate return on capital, stockholders cannot sue for liquidation. A highly leveraged corporation will be quickly terminated once it ceases to be economically viable, but there is little to keep a corporation with a conservative capital structure from wasting away to nothing when it becomes obsolete or overburdened by regulations. Management’s continuing allegiance to the corporate entity, rather than to stockholders, is all too clear in Gordon Donaldson’s detailed study of 12 large Fortune 500 ﬁrms. The managers he observed did not try to maximize shareholders’ wealth, but instead sought to maximize ‘‘corporate wealth,’’ deﬁned as ‘‘the aggregate purchasing power available to management for strategic purposes during any given planning period [emphasis in original] y this wealth consists of the stocks and ﬂows of cash and cash equivalents (primarily credit) that management can use at its discretion to implement decisions involving the control of goods and services y . In practical terms it is cash, credit, and other corporate purchasing power by which management commands goods and services.’’48 This orientation does not necessarily constitute an indictment of crass self-interest on the part of managers, who understandably feel commitments

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to many other corporate stakeholders besides the investors who contributed capital.49 Managers are typically far closer to the corporation’s employees, for example, than to the investors. Likewise, they feel closer ties to their host community than they do to a faceless and widely dispersed group of public investors. (In fairness it should be noted that host communities often contribute property as well as tax privileges to the corporation, while employees often contribute effort beyond that commanded by their wages, in the hope of gaining job security). Managers may even be convinced that building a strong, enduring corporate institution is best for the stockholders in the long run, even without conﬁrmation from the stock market. Several arguments have been advanced to explain why corporate law gives so much deference to the discretion of managers. First, such deference is felt to be necessary in order to allow managers to fully exercise their presumed expertise in running the ﬁrm,50 so as not to reduce managerial incentives to take business risks. Second, it has been observed that the law does not need to be as diligent in monitoring managers since their power and discretion are effectively restricted by the continuing need to raise capital and thus to periodically submit to the judgment of the market.51 Third, some contend that states purposefully compete to attract management by enacting laws favoring its interests at the expense of investors.52 The gulf between ownership and management is a long-standing issue. In 1918, Walther Rathenau commented about the great corporations: ‘‘No one is a permanent owner. The composition of the thousand-fold complex which functions as lord of the undertaking is in a state of ﬂux y . The depersonalization of ownership simultaneously implies the objectiﬁcation of the thing owned. The claims to ownership are subdivided in such a fashion, and are so mobile, that the enterprise assumes an independent life, as if it belonged to no one; it takes an objective existence, such as in earlier days was embodied only in state and church, in a municipal corporation, in the life of a guild or a religious order y . The depersonalization of ownership, the objectiﬁcation of enterprise, the detachment of property from the possessor, leads to a point where the enterprise becomes transformed into an institution which resembles the state in character.’’53 From this description, Adolph Berle and Gardner Means conclude, ‘‘The institution here envisaged calls for analysis, not in terms of business enterprise but in terms of social organization.’’54 It is precisely the removal of the right for investors to terminate the enterprise that marks the ﬁrst appearance of the modern publicly held corporation. The corporation as a large-scale, quasi-permanent property owner traces its roots to the impoundment of capital in the Dutch East India

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Company in 1612 – before that time any stockholder could redeem shares on demand at par value from the company treasury. This change in the corporate charter was enacted by the state, not by a vote of shareholders. Of course, it represented a significant increase in the power of the managing directors, who were chosen by the governing bodies of the major Dutch cities. This unprecedented action arose from the difﬁculty of liquidating assets such as ﬂeets at sea and warehouses half a world away – not to mention treaties negotiated with sovereign heads of state and paid for with company funds – leading to fears that a panic could ruin the company. The government enacted the new rules out of the belief that strengthening the company would beneﬁt the nation as a whole. Although shares in the company soon began trading on the merchants’ exchanges, the directors tried long and hard to regulate sales in the secondary market, and for many years a sale of stock could not be transacted ofﬁcially without their approval.

6. SEPARATE ENTITY STATUS BRINGS LOSS OF ACCOUNTABILITY Instead of making managers accountable to investors, the law exacerbates principal-agent conﬂicts by giving substantial deference to the discretion of managers, in several ways. First, corporate law is in many ways enabling rather than prescriptive, giving managers great freedom to determine the form of corporate ownership and the structure of corporate control as well as to make just about all decisions pertaining to the ﬁrm’s daily operations (including the compensation packages and incentives that managers receive).55 The problem was not always so severe. Under traditional corporate law (prior to the early nineteenth century) managers could not exercise corporate powers unless they had been expressly granted by the general incorporation statute or provided for in the ﬁrm’s charter. In the event that management exercised powers that were not expressly authorized, the transaction was ultra vires, and the directors would be liable for damages to the ﬁrm. When ﬁrst instituted, this ultra vires rule limited management discretion in handling the ﬁrm’s resources (and retained some control for investors, since shareholder approval was required for charter amendments granting management additional powers). Modern corporate law has evolved in such a way that it significantly hinders investors from successfully challenging management actions or decisions.

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Today, the ultra vires doctrine is essentially meaningless – the issue seldom arises anymore since nearly all states allow corporations, once chartered, to engage in virtually any lawful activity management chooses. Thus, unless express duties (such as the duty of care or the duty of loyalty) have been violated, investors today have very little recourse under the law against managers who make decisions that are not in the best interests of the investors. Even in these areas, however, the law generally protects management over investors.

6.1. Duty of Care is Difficult to Enforce Under the duty of care, managers must conduct corporate affairs with the same care that a prudent person would exercise in the management of his own affairs, and are theoretically liable for both active and passive negligence. In cases where managers are charged with violating this duty, however, the business judgment rule, an extremely deferential approach, is applied, with the result that managers are usually exonerated.56 Even in cases where a clear violation of this duty has been shown, managers may still be protected from the consequences of their action (or inaction) since most states allow them to be indemniﬁed by the ﬁrm for litigation expenses and for liability in such cases. Firms also may purchase insurance for directors where indemniﬁcation is prohibited. Hanks (1988) reports that in most states, statutes have been enacted that reduce or eliminate entirely director’s liability for duty of care violations.

6.2. Duty of Loyalty is Also Difficult to Enforce Under the duty of loyalty, managers must act with utmost loyalty and good faith in pursuing the interests of the investors (as opposed to their own personal interests). In these cases, it is still presumed that managers have made business decisions in good faith, unless fraud, bad faith, or self-dealing can be shown.57 When it can be shown that managers have engaged in self-dealing or other conﬂict of interest transactions, managers may still avoid liability by showing that the transaction was approved by a majority of disinterested directors or was ‘‘fair’’ (beneﬁcial) to the ﬁrm, meaning that the bargaining process was fair and that the transaction occurred at a fair price.58

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If the transaction was approved by a majority of ﬁnancially disinterested directors, then the burden shifts to the party bringing the action to show that the transaction was substantively unfair.59 Violations of the duty of loyalty thus receive slightly more judicial scrutiny than do those involving the duty of care, as courts perceive a greater need to protect investors in such cases. 6.3. Other Difficulties of Legal Challenge The primary tool that corporate law provides investors to control managers’ conduct is the right to elect directors and to approve fundamental corporate changes. In practice, however, voting gives investors very little leverage over managers – particularly in the case of public corporations with large numbers of shareholders – due to collective action problems, high information costs, and management’s power to set and control the agenda of shareholders’ meetings.60 Legal challenges are hampered by procedural requirements that often make it impractical to even bring such actions.61 These requirements are significant restrictions in that they effectively limit the ability of shareholders to bring derivative suits.62 Usually imposed by statute, such restrictions include the demand requirement, the contemporaneous stock ownership requirement, the veriﬁcation of pleadings requirement, and provisions that require the shareholders bringing the action to give security for the ﬁrm’s expenses in defending the suit.63 Perhaps the most significant impediment, however, is the power of directors to effectively terminate derivative suits once they have found that the litigation is not in the best interests of the ﬁrm.64 Such a decision, when made by a committee of independent directors to whom the ﬁrm’s authority to seek dismissal of a derivative suit has been delegated, is usually accorded the same deference by a court as any other business decision, and courts will accordingly grant the ﬁrm’s motion to dismiss. It may be presuming too much, as the law does, to suppose that directors will be impartial in deciding whether the ﬁrm should sue them. Whatever the reason, such committees almost always recommend dismissal of the suit.65 As a result of these procedural obstacles, shareholder derivative actions are seldom initiated today. 6.4. Legal Barriers to Challenge via Proxy Ballot As a result of these limitations, managers of public corporations have a significant advantage in a shareholder vote unless an organized challenge

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arises in the form of a proxy contest, where the opposition actively solicits proxies from shareholders to contest the proposals of management. Such a contest may occur, for example, when opposition arises to management’s slate of nominees for election to the board of directors, or to a fundamental corporate change proposed by management, such as a merger, the adoption of a charter amendment, or a recapitalization plan that impairs the rights of current shareholders. Corporate law creates difﬁculties for shareholders who wish to use the proxy contest as a means of opposing management. This observation is not new – in 1954 Adolph Berle wrote the following: ‘‘Change of management by contesting for stockholders’ votes is extremely rare, and increasingly difﬁcult and expensive to the point of impossibility. The legal presumption in favor of management, and the natural unwillingness of courts to control or reverse management action save in cases of the more elementary types of dishonesty or fraud, leaves management with substantially absolute power.’’66 Perhaps the greatest obstacle to management accountability, given the cost involved in waging a proxy contest in a public corporation, is that challengers in a proxy contest have no right under the law to obtain reimbursement for their expenses. Under corporate law in most states, whether or not the expenses of parties in a proxy contest will be reimbursed by the ﬁrm is generally a business decision to be made by the board of directors. In practice, therefore, the expenses of candidates nominated by management are fully reimbursed by the ﬁrm, whereas those of challengers are only reimbursed in the event they are successful and gain control of the board.67 Those who contest management and fail are virtually never reimbursed for their expenses (and the likelihood of failure is significant due to collective action problems that almost always lead uninformed shareholders to back management in these contests). For all these reasons, together with the fact that any gains realized from changes in management or corporate policy will be spread pro-rata among all shareholders in proportion to their equity interests, it makes far more sense for disgruntled shareholders to sell their shares rather than to wage a proxy ﬁght,68 and perhaps as a result proxy contests are a last resort.69

6.5. Legal Barriers to Contests for Control An alternative to the proxy contest, in terms of transferring control of a ﬁrm and replacing existing management, is the hostile tender offer or other contest for control. This is yet another area in which the law allows managers to

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promote their own interests at the expense of investors. Although contests for control are usually beneﬁcial for investors, managers are frequently (and legally) allowed to block such efforts in order to maintain their control of the ﬁrm, through the adoption of devices such as supermajority rules, litigation, greenmail, poison pills, or other strategies that delay or increase the cost of taking control. Many courts tend to give such defensive measures a more rigorous scrutiny than other types of business decisions, requiring that management show that the measure adopted is ‘‘reasonable in relation to the threat posed’’ by the challenge for control in order for the measure to be protected by the business judgment rule.70 This standard, or a variation of it, has been used by courts to invalidate many of these defensive measures. In response, large ﬁrms have undertaken massive lobbying efforts aimed at getting state legislatures to adopt anti-takeover statutes, in order to override this case law and thus make it easier for such devices to be legally employed.71 These statutes, which impose significant restrictions on tender offers, have been adopted in a majority of states.

7. INVESTORS PRIZE ACCOUNTABILITY Regardless of the rationale, corporate law has failed to adequately monitor conﬂicts of interest between managers and investors, to make management accountable to investors, and to help control agency costs. As a result, more and more spin-offs and other downsizing transactions are occurring, as investors seek to eliminate these conﬂicts, to obtain more accountability, and to reduce agency costs.72 The pendulum swinging far in the direction of separating stockholders from their property rights, institutional investors turned activist (one headline, for example, declared in no uncertain terms, ‘‘Mad as hell, institutional investors turn activist’’73). Investors have learned that they need not huddle in submission to the corporate entity; they can protect themselves. Increasingly, activist institutional investors are using their clout to inﬂuence the choice of key executives, change corporate strategies, resist the imposition of anti-takeover devices, and accomplish governance reforms. Even more significant, many are choosing a less conspicuous avenue – direct ownership of assets by investors. In the public criticism of leveraged buy-outs, hostile takeovers, and other forms of corporate restructuring, the emphasis has tended to focus upon ‘‘bust-up’’ liquidations of corporate assets. But these assets do not disappear

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from the face of the Earth! Instead, they often end up being directly owned by investors – frequently with no change in function. Overt restructurings, moreover, are just one highly visible aspect of the realignment of power that is being accomplished through direct ownership of specific productive assets by investors.74

8. DIRECT INVESTMENT AND ‘‘DOWNSIZING’’ OFFER SOLUTIONS As if these property-rights problems were not enough, the separate entity status of corporations is the legal principal upon which corporate income taxation is based.75 It is clearly undesirable for a tax-sheltered pension fund or a tax-exempt endowment fund to own real estate or capital equipment indirectly via stock in a tax-paying corporation – if it is possible to own the assets directly through an arrangement such as a trust or limited partnership that can pass income untaxed directly to its owners.

8.1. Tax Advantages of Direct Investment There are several income sources that are commonly understood to be passive for income tax purposes: interest, dividends, real property rents or capital gains, and gains from commodities trading for a partnership specializing in such trading (including futures, forward, and options). Also, under y 7704 of the Internal Revenue Code (enacted in the Revenue Act of 1987), the list of allowable passive income sources includes the following activities involving natural resources: exploration, development, mining or production, processing, reﬁning, and transportation (including gas or oil pipelines) or the marketing of any mineral, or natural resource (including fertilizer, timber, and geothermal energy).76 A potential concern for an institutional investor in arranging asset acquisition, moreover, is to avoid being considered an active participant in the business activity; which could expose it to taxation as a corporation. But the current rules offer wide latitude. A passive investor cannot run an airline, for example, but it can own airplanes for lease. If the investor is a pension fund, tax liabilities arising from the cash ﬂowing through the lease are deferred until the fund makes payments to its retirees,77 and double taxation at the corporate entity level is completely avoided. Stronger still, if the investor

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is tax-exempt (such as a college endowment fund), income tax is completely avoided. Also, an investor can earn passive interest income through a limited recourse leveraged lease arrangement in which a ﬁnancial entrepreneur takes the equity stake and borrows most of the cost of the equipment from the institution, with the cash ﬂows from the lease agreement providing credit support. Then the institutional lender’s risk/reward proﬁle is substantially the same as if it owned the asset directly, when the lender’s recourse is for practical purposes limited to the cash ﬂows from the lease and the lessee has substantial freedom of cancellation (American Airlines, for example, has entered into several aircraft leases which allow it substantial freedom to cancel). The downsizing trend among corporations has been facilitated by the growing practice of securitizing specialized pools of assets. For example, it is now commonplace for ﬁnancial institutions to sell insured mortgages in the form of securities. Credit card receivables, auto and truck loans are likewise packaged into high-denomination securities for resale. In addition, there are hundreds of limited partnerships that own oil and gas wells, hydro, geothermal and cogeneration78 power production facilities, oil reﬁneries, and even factories; as well as timberland properties, cable television systems, real estate, mortgages, restaurant services, and mortgage loan servicing. All sorts of income-producing operations that require little more than caretaker management have been organized as partnerships or other independent entities, and funded through limited-recourse project ﬁnancings.79 Even management-intensive operations such as R&D projects have been ﬁnanced as separate organizational entities.

8.2. Control Advantages of Direct Investment Direct ownership not only reduces risk by providing investors with moreenforceable property rights, but also reduces the tax burden. Astute corporate executives therefore can lower the cost of access to capital by ﬁnding new ways of working within the framework of direct investor ownership. Lower capital costs can be achieved by leasing equipment instead of owning it as well as buying inputs and components from investor-owned facilities. Lower capital costs in turn enhance American companies’ competitiveness in the global economy. Besides the tax advantages, there is an important additional effect as well, in the form of increased managerial accountability. The sale of a

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corporation’s real estate holdings to a trust or limited partnership, for example, or the decision to lease rather than buy equipment such as ships, aircraft, or factories, can be a particularly potent step in the process of returning resource allocation decisions to the marketplace. When it owned the property, the corporation might weather a bad year or two without having to confess that it was losing money. Without the necessity of writing rent checks, the management could ignore the fact that the company was not earning enough to justify the space it occupied. After the sale of the company’s real estate, though, management would have to give an accounting if the company could not pay its rent. Shared ownership of specific productive assets, moreover, predates the corporation by several hundred years. As early as the thirteenth century, one could buy shares in the royalties from a silver mine near Siena, and shares were available even earlier in royalties from salt mines, copper mines, and metal-works. The regular practice of shared ownership of galleys in the Mediterranean trade dates back before the ﬁfteenth century. ‘‘Kuxen’’ shares in the royalties from Central-European mines were widely traded in the sixteenth century. Shared ownership of mills, dams, and drainage systems was also prevalent in Europe during the Middle Ages.80 Such arrangements not only provided a means of risk-sharing, but also for practical purposes a full measure of limited liability. They were all-equity arrangements and the worst that could happen was for the ship to be lost, or the mine play out – in which case each shareholder stood to lose the amount invested, but no more. The renewal of direct investment, then, is not a radical step into a new order; but rather a return to long-established tradition in the conduct of commerce and industry.

9. CONCLUSION This paper addresses the issue of reforming corporate governance in a unique way. Instead of seeking to discover ways of resolving conﬂicts of interest between owners and managers of corporations, we recognize the inherent inability to resolve these conﬂicts arising from the body of corporate law that has evolved over several centuries. Rather than being frustrated by this difﬁculty, institutional investors have found alternative arrangements that provide for direct ownership of assets by investors. Direct ownership of assets by investors avoids the conﬂicts that would be inherent with corporate ownership, plus providing significant

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tax advantages. Additionally, direct ownership of assets provides the investor with full control over reinvestment of cash ﬂows derived from them. As the trend toward direct ownership progresses, the result would be further hollowing of corporations and a greater array of investment opportunities for institutional and individual investors.

NOTES 1. See Jensen and Meckling (1976). Under this theory, the smaller the ﬁnancial stake that management has in the ﬁrm’s profits, the greater this divergence may be expected to become. 2. See Orts (1992). 3. Most people conceive of property in terms of traditional – one might even say ancient – legal classiﬁcations. Tangible property is either ‘‘real’’ property (in the form of land or rights derived from land) or ‘‘personal’’ property (something capable of being consumed or used, yet mobile and so capable of being moved by its owners or taken away from them). In both instances, the courts and their agents stand ready to enforce the owner’s rights to exclusive use of the property, and to protect it from unlawful taking. Intangible property is a claim on others that is capable of being enforced in the courts, such as a debt contract. 4. The National Carbide Co. opinion is often cited in determining whether a principal-agency relationship exists between shareholders and management. Source: Bittker and Eustice (2005, Chapter 2, Paragraph 2.10). The Delaware high court, moreover, was upholding the principle that a corporation has a separate existence from stockholders in its controversial August 1989 decision concerning the Time-Warner merger. 5. Berle and Means (1932, pp. 311–312). 6. In addition many states, including New York, Illinois, Pennsylvania, New Jersey, Ohio, Michigan, Connecticut, Massachusetts, Maryland, Indiana, Minnesota, and Kentucky have enacted anti-takeover laws. The Federal Reserve Board, furthermore, imposed restrictions (in 1986) on borrowing for purposes of taking over control of a corporation. 7. Adolph Berle (1954, pp. 168–169, 185). 8. Quoted in Barron’s, October 16, 1989, p. 8. 9. See Grant Thornton LLP (2004, p. 1). 10. Concerning the rules and regulations promulgated by the stock exchanges, the courts likely would view these as private contractual arrangements enforceable in state civil courts at the behest of the exchanges (rather than in response to shareholder initiative). See Johnson and Sides (2004). 11. See Dalley (2003). 12. See Dalley (2003). Quote is from p. 209. 13. Quoted in Analisa Nazareno, ‘‘Corporate governance: Compliance proves costly,’’ San Antonio Express-News, December 4, 2004, H6. The Exploration Company (Nasdaq: TXCO) is a San Antonio-based independent exploration and production

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company with producing oil and gas properties in the Maverick Basin (South Texas) and the Williston Basin (Dakotas and Montana). 14. See Korn/Ferry (2004). 15. See Hartman (2005). 16. See Hartman (2005). 17. Quoted from Welsh (2003). 18. Quotes are from a July 30, 2002 speech by U.S. President George W. Bush. 19. The inspection of registered ﬁrms involves detailed examination of selected audit and review engagements for public companies, including conformity with auditing and independence standards, and the auditors’ evaluation of the public companies’ compliance with accounting standards. 20. See Hartman (2005). 21. See Birg (2005). 22. See Tonsick (2004, p. 42), see also Johnson and Sides (2004). 23. See Johnson and Sides (2004, p. 1149). 24. See Johnson and Sides (2004, p. 1209). 25. Quoted from Shapiro and Skolnick (2005, p. 37). 26. Quoted from Dalley (2003, p. 209). 27. Associated Press, ‘‘Scrushy acquittal a setback for US corporate crimes clampdown,’’ Wednesday, June 29, 2005. 28. See Fricklas and Matthews (2005). 29. David S. Hilzenrath, ‘‘A popular reward: Restricted stock; job performance link is debatable,’’ Washington Post, June 27, 2005, p. D12. 30. FASB News Release, ‘‘Financial Accounting Foundation chairman responds to House Subcommittee’s action on ‘The Stock Option Accounting Reform Act,’’’ May 17, 2004. 31. FASB News Release, ‘‘FASB issues ﬁnal statement on accounting for sharebased payment,’’ December 16, 2004. 32. FASB Statement No. 123, ‘‘Share-based payment,’’ (revised 2004). 33. Carrie Johnson, ‘‘SEC grants latitude on options; agency may extend deadline for changing accounting methods,’’ Washington Post, March 30, 2005, p. E03. 34. Hewitt Associates, ‘‘Fewer stock options for executives in 2004,’’ December 15, 2004. 35. Ross Kerber, ‘‘Meet the new stock option,’’ Boston Globe, April 17, 2005, p. E1. 36. Sandra Guy, ‘‘New rule expected to limit executives’ options,’’ Chicago SunTimes, December 16, 2004, p. 61. 37. ‘‘SEC must update restricted stock plan rules,’’ Investment News, March 27, 2005, p. 10. 38. Laura Smitherman, ‘‘Once-hot stock option programs losing some luster,’’ Baltimore Sun, May 15, 2005, p. 1D. 39. Hilzenrath (op. cit.). 40. Hilzenrath (op. cit.). 41. Pradnya Joshi, ‘‘Top 100 executive compensation,’’ Newsday, June 27, 2005, p. D2. 42. Phyllis Plitch, ‘‘Executives ﬁnd restricted stock pays dividends from the getgo,’’ Wall Street Journal, February 28, 2005, p. C3.

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43. FASB Statement No. 132, ‘‘Employers’ disclosures about pensions and other postretirement beneﬁts – an amendment of FASB statements no. 87, 88, and 106’’ (Issued 2003). 44. UAL Press Release, ‘‘UAL Corporation reports second-quarter 2005 results,’’ July 28, 2005. 45. UAL Press Release, ‘‘Statement from United Airlines,’’ July 28, 2005. 46. Engers v. AT&T Managment Pension Plan, C.A. 98-3660 (D.N.J.). 47. Amara et al. v. CIGNA Corp., 01-2361 (D. Conn). 48. Gordon Donaldson (1984, pp. 3, 22). 49. See Cornell and Shapiro (1987). 50. See, e.g., Smith v. Van Gorkom, 488 A.2d 858, 872 (Del. 1985) (citations omitted). A corollary to this argument is that courts and legislative bodies do not have the competence or expertise to evaluate managers’ decisions, and thus are hesitant to substitute their judgment for that of the board in the ﬁrm’s business matters. See Auerbach v. Bennett, N.E.2d 994, 1000 (1979) (noting that these rules are based ‘‘on the prudent recognition that courts are ill equipped and infrequently called on to evaluate what are and must be essentially business judgments’’). 51. See Easterbrook and Fischel (1991, pp. 1–39). Yet, as they observe on p. 161, ‘‘ﬁrms and their lawyers [have] become increasingly creative in altering the riskreturn attributes of investment through methods that do not require the managers to raise new capital and submit to the judgment of the market.’’ 52. See, e.g., Cary (1974). Such competition, if it exists, might best explain why so many states in the past few years have been so quick to adopt anti-takeover laws, statutes that limit or eliminate director liability in duty of care cases, and corporate constituency statutes. 53. Walther Rathenau (1918, pp. 120–121). Quoted in Berle and Means (1932, p. 309). 54. Berle and Means (1932, p. 309). 55. For a general discussion of the mandatory/enabling nature of corporate law, see Coffee (1989). 56. Under the business judgment rule, the fact that a business decision has turned out poorly for the ﬁrm or its investors will not lead the court to infer that the managers have breached their duty of care. Instead, this rule presumes that in making corporate decisions, managers have ‘‘acted on an informed basis, in good faith, and in the honest belief that the decision in question was in the best interest of the company.’’ Smith v. Van Gorkom, 488 A.2d 858, 872 (Del. 1985). In order to hold managers liable for breach of the duty of care, the burden is on the party bringing the action to demonstrate that some aspect of this presumption is not true in the instant case. Id. 57. See, e.g., Smith v. Van Gorkom, 488 A.2d 858, 873 (Del. 1985) (citations omitted). 58. See Model Business Corp. Act, yy 8.60-8.63 (1991). 59. Id. As Easterbrook and Fischel (1991, p. 104) have observed, although directors may have no direct ﬁnancial interest in the proposed transaction, they nevertheless ‘‘are quite interested in maintaining the managers’ esteem and places on the board,’’ and thus may gain some personal beneﬁt from approving the transaction.

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60. These problems and the resulting apathy of shareholders in large public corporations have been much discussed. See Easterbrook and Fischel (1991, pp. 63–72), Clark (1986, pp. 357–400), Bebchuk (1989, pp. 1820, 1837–1838), and Coffee (1989, p. 1675, n. 234). 61. Shareholder derivative suits are the principal if not sole means for individual shareholders to obtain compensation for injuries inﬂicted by management on the ﬁrm. In fact, as the American Law Institute (ALI) has noted, ‘‘the derivative action may offer the only effective remedy in those circumstances where a control group has the ability to engage in self-dealing transactions with the corporation.’’ ALI, Principles of Corporate Governance: Analysis and Recommendations, 7.03 Comment E, at 588 (Proposed Final Draft, March 31, 1992). The empirical data on the effectiveness of this remedy, however, is not conclusive. Id., Reporter’s Note at 596. 62. The purpose of these restrictions is ostensibly to discourage the bringing of meritless actions by those who would seek to use the remedy as a means of extorting money from the ﬁrm. 63. See Roger J. Magnuson, Shareholder Litigation 8.02 (1981 & Supp. 1992). 64. Under the Model Business Corporation Act, for example, courts are directed to dismiss a derivative suit on the ﬁrm’s motion if a committee of disinterested directors ‘‘determined in good faith after conducting a reasonable inquiry on which its conclusions are based that the maintenance of the derivative proceeding is not in the best interests of the corporation.’’ Model Business Corp. Act, y 7.44(a) (1991). Interestingly, the fact that a director is named as a defendant in the derivative suit does not disqualify the director from serving on the committee. Id. at y 7.44(c)(2). 65. See Solovy et al. (1990). 66. Adolph Berle (1954, p. 180). 67. Although there are some nominal limitations on the right of incumbents to receive compensation, they are largely insignificant and seldom prevent reimbursement (see Bebchuk & Kahan, 1990). They conclude that ‘‘whatever restraints incumbents may feel, in practice they are reimbursed for all their proxy contest expenses.’’ Professors Bebchuk and Kahan argue in this article that the current law in this area is seriously ﬂawed in that it allows management too much of an advantage in most proxy contests (pp. 1134–1135). 68. Easterbrook and Fischel (1991, p. 83). 69. Until quite recently, major proxy contests occurred only about 25–30 times per year in the United States (Bebchuk & Kahan, 1990, pp. 1074–1075). 70. Unocal Corp. v. Mesa Petroleum Co., 493 A.2d 946, 955-56 (Del. 1985). Interestingly, the Delaware Supreme Court stated in this case that such an analysis could take into account not only threats to shareholder interests, which were ‘‘not a controlling factor,’’ but also ‘‘the impact on ‘constituencies’ other than shareholders (i.e., creditors, customers, employees, and perhaps even the community generally).’’ This line of reasoning was conﬁrmed in a subsequent case, Paramount Communications, Inc. v. Time, Inc., 571 A.2d 1140, 1152 (Del. 1990), where the court ruled that ‘‘Time’s culture’’ (i.e., Time’s ‘‘perceived editorial integrity in journalism’’) was one of the ‘‘constituencies’’ that management could protect from threats posed by a takeover attempt of Time, Inc. 71. See Coffee (1989, p. 1685). 72. See Jensen (1989).

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73. Barron’s, February 12, 1990, p. 28. 74. For example, more than 27% of the 143 companies that disappeared from the Fortune 500 from 1985 to 1989 did so because downsizing left them too small to be included (23 companies) or shifted the focus of their activities so much that they were reclassiﬁed from an industrial company to a service company (another 16 companies, for a total of 39 out of 143). 75. In Keller v. CIR, the Tax Court observed, ‘‘The [legislative] policy favoring the recognition of corporations as entities independent of their shareholders requires that we not ignore the corporate form so long as the corporation actually conducts business.’’ Source: Bittker and Eustice (2005, Chapter 2, Paragraph 2.07, Footnote 154). 76. Because the choice of organizational form used for securitizing assets is sensitive to the tax environment, the mechanisms change in accordance with it. The 1987 tax act, for example, levied the requirement that publicly traded partnerships be taxed as corporations; and in the absence of favored tax treatment for publicly traded partnerships, other organizational forms rose into favor as repositories for the assets (e.g., a trust or nontraded partnership). This continual give and take between innovative ﬁnancial engineers and the taxing authorities reﬂects the ‘‘regulatory dialectic’’ at work – as fast as the authorities close one avenue, innovators ﬁnd new ways to carry on. 77. This tax deferral occurs when the lessee deducts lease payments, but the pension fund is exempt from taxation of its earnings. 78. Cogeneration is the simultaneous production of electricity and high-temperature steam for use in a production process such as a chemical plant, reﬁnery, or enhanced oil recovery site. 79. For more information about project ﬁnancing, see Kensinger and Martin (1988). 80. See Braudel (1992, pp. 439–440).

ACKNOWLEDGMENT An earlier version was presented at the European Conference of the Financial Management Association International, May 2000.

REFERENCES Bebchuk, L. A. (1989). Limiting contractual freedom in corporate law: The desirable constraints on charter amendments. Harvard Law Review, 102, 1820, 1837–1838. Bebchuk, L. A., & Kahan, M. (1990). A framework for analyzing legal policy towards proxy contests. California Law Review, 78, 1073–1108. Berle, A. (1954). The twentieth century capitalist revolution. New York: Harcourt, Brace & Company. Berle, A., & Means, G. (1932). The modern corporation and private property. New York: Macmillan. Page references are for the Revised Edition (New York: Harcourt, Brace & World, Inc., 1967)

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Birg, E. C. (2005). Is the public company accounting oversight board constitutional? The Federalist Society for Law and Public Policy Studies February 2, 2005. Quote is from page 2. The paper is available at www.fed-soc.org. Bittker, B. I., & Eustice, J. S. (2005). Federal income taxation of corporations and shareholders (7th ed.). Boston: Warren, Gorham & Lamont, Inc. Braudel, F. (1992). The wheels of commerce (civilization and capitalism: 15th through 18th centuries (Vol. II). Berkeley: University of California Press. Cary, W. L. (1974). Federalism and corporate law: Reﬂections upon Delaware. Yale Law Journal, 83, 663. Clark, R. C. (1986). Corporate law. New York: Little Brown. Coffee, J. C., Jr. (1989). The mandatory/enabling balance in corporate law: An essay on the judicial role. Columbia Law Review, 89, 1618. Cornell, B., & Shapiro, A. (1987). Corporate stakeholders and corporate ﬁnance. Financial Management, 16(Spring), 5–14. Dalley, P. J. (2003). Public company corporate governance under the Sarbanes-Oxley Act of 2002. Oklahoma City University Law Review, 28, 185. Donaldson, G. (1984). Managing corporate wealth. New York: Praeger. Easterbrook, F. H., & Fischel, D. R. (1991). The economic structure of corporate law. Cambridge, MA: Harvard University Press. Fricklas, M. D., & Matthews, C. W., Jr. (2005). Project: Corporate counsel part II (unintended consequences and compliance readiness) factors accelerating flight from the civil justice system. The Metropolitan Corporate Counsel, August. Grant Thornton LLP. (2004). More small to mid-size public companies contemplating going private, February 4, 2004. Hanks, J. J., Jr. (1988). Evaluating recent state legislation on director and ofﬁcer liability limitation and indemniﬁcation. Business Law, 43, 1207, 1243. Hartman, T. E. (Foley & Lardner LLP). (2005). The cost of being public in the era of SarbanesOxley. Financial Executives International, June 16, 2005. Jensen, M. C. (1989). Eclipse of the public corporation. Harvard Business Review, 67(September–October), 61–74. Jensen, M. C., & Meckling, W. H. (1976). Theory of the ﬁrm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics, 3(4), 305–360. Johnson, L. P. Q., & Sides, M. A. (2004). Corporate governance and the Sarbanes-Oxley Act: The Sarbanes Oxley Act and ﬁduciary duties. William Mitchell Law Review, 30, 1149, 1153, 1210. Kensinger, J. W., & Martin, J. D. (1988). Project ﬁnancing: Raising money the old-fashioned way. Journal of Applied Corporate Finance, 1(3), 69–81. Korn/Ferry International. (2004). 31st Annual Board of Directors Study. Orts, E. W. (1992). Beyond shareholders: Interpreting corporate constituency statutes. George Washington Law Review, 61, 14f. Rathenau, W. (1918). In: E. Paul, & C. Paul (Trans.), Von Kommenden Dingen (Berlin, 1918). [Days to come] (London, 1921). London: G. Allen and Unwin Ltd. Shapiro, J. M., & Skolnick, S. M. (2005). Project: Corporate counsel (compliance readiness) part II; corporate governance does not end with Sarbanes-Oxley. The Metropolitan Corporate Counsel, June. Solovy, J. S., Levenstam, B., & Goldman, D. S. (1990). The role of special litigation committees in shareholder derivative litigation. Tort and Insurance Law Journal, 25, 864f.

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Tonsick, J. (2004). Project: Corporate counsel: Financial statement fraud, Sarbanes-Oxley and corporate governance. The Metropolitan Corporate Counsel, January. Welsh, P. L. (2003). Recent rulemaking activity by the securities and exchange commission under the Sarbanes-Oxley Act of 2002. The Federalist Society for Law and Public Policy Studies. February 4, 2003. Quote is from page 1. The paper is available at www.fed-soc.org.

THE INFORMATION CONTENT OF CORPORATE INVESTMENT ANNOUNCEMENTS: THE CASE OF JOINT VENTURES Arthur J. Keown, Paul Laux and John D. Martin ABSTRACT Partner firms to the same joint venture experience sharply different stock price reactions. These differences cannot be explained by mechanical factors related to differences in firm size and ownership share in the project, nor are they attributable to different partner roles in the project or differences in investor anticipation of the announcement. We conclude that the stock price reactions reflect a revaluation of non-project assets that is different for each partner. Additionally, we find evidence indicating that investors infer information about agency problems (in the sense of Jensen, 1986) from the joint venture announcements and subsequently, revalue the whole firm – not just the marginal project being announced. Finally, we find that free cash flow is value-enhancing for one type of partner firm after we control for the extent of agency problems.

Research in Finance, Volume 22, 33–71 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22002-6

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1. INTRODUCTION This paper investigates the divergent stock price reactions of ﬁrms that announce similar real investments. Researchers have usually interpreted cross-sectional variation in the market’s reactions to corporate investments as differences in prospective project values.1 This is less plausible when the companies share an identical project, such as a joint venture. We provide evidence of economic differences in partners’ stock price reactions to the same joint venture and investigate several explanations. The results show that the announcement of a corporate investment can affect the value of entire ﬁrm, including seemingly unrelated assets. Our evidence suggests that the stock price reactions to corporate investments should be interpreted broadly. Intentionally or unintentionally, the announcement reveals information that the market considers relevant for valuing the ﬁrm overall. Our results imply that the common interpretation of event-study cumulative abnormal returns as the unanticipated net present value of the activity is too narrow. Moreover, theoretical explanations for stock price reactions are then directly tied to the value of the whole ﬁrm. For example, evidence substantiating Jensen’s (1986) free-cash ﬂow theory would then indicate not just that some managers sometimes take on what the market believes to be a negative net present value project, but additionally that the market revises its assessment of the value-effects of those managers’ propensities to do so in the future. The possibility of extra-project information in corporate announcements has often been recognized, but seldom directly studied. Referring to takeover situations, Roll (1986) emphasizes that ‘‘(b)idders are activists y, and their announcements may convey as much information about their own prospects as about the takeover.’’2 The possibility of extra-project information is also recognized in the caveats that accompany the standard project-value interpretation of event study results. For example, McConnell and Nantell (1985) say about joint venture announcements: ‘‘It is possible that joint venture announcements convey additional implicit information to the market about the ﬁrm’s past or future earnings or investment opportunities.’’ Our experiment provides statistically and economically signiﬁcant evidence that support these statements. The idea behind our experiment is straightforward. Cross-partner differences in partners’ stock price reactions to joint venture announcements, adjusted for each partner’s ownership share and equity value, effectively ‘‘net out’’ the net present value of the joint venture-investment project.3 Any remaining cross-partner differences reﬂect inﬂuences on the

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values of the partner ﬁrms apart from the value of the project itself. After ruling out explanations based on differential expectations and roles of the partners, any systematic differences indicate that extra-project information is revealed for at least one partner. Interpreted as differences in project value, our results would imply that the smaller partner’s shareholders value the average project at almost $140 million more than do the larger partner’s shareholders, or almost 10% of the equity value of the average smaller partner. This establishes the presumption, which we then investigate further, that extra-project information is revealed. Because larger ﬁrms are often thought to be more subject to shareholder– manager agency problems than are smaller ﬁrms, we investigate whether indicators of the extent of such problems can explain the differences in stock price reactions. The average difference is statistically explained by taking into account which partner has the larger values of ownership by insiders, the greater leverage, and the higher Tobin’s q.4 Additionally, the extent of internal cash for smaller partners is positively correlated with the extraproject information revealed for those partners, once these indicators have been accounted for. This is consistent with the idea that, once the effects of agency problems have been controlled, internal cash ﬂows are valueenhancing because they allow the ﬁrm to accept proﬁtable projects without incurring the extra costs involved in securing external funds (Myers & Majluf, 1984; Fazzari, Hubbard, & Petersen, 1988). Our evidence supports the view that ﬁnancial markets condition their reaction to managers’ decisions on what they know of the manager’s tendency to pursue non-shareholder goals. Moreover, because the evidence centers on extra-project information and its relation to managerial goals, it implies that stock price reactions to investments (at least joint venture investments) include a substantial component that reﬂects the market’s assessment of how much ﬁrm value, independent of the project, must be revised to reﬂect what the market has learned from the fact that management undertook this joint venture. Some of our indicators of the extent of agency problems are also related to the efﬁcacy of intentional signaling of a ﬁrm’s unobservable opportunities. Brennan (1990) advances the recognition of extra-project information in corporate announcements through his suggestion that managers attempt to reveal extra-project information when it is positive and to conceal it when it is not. Thus, there are ‘‘y dangers of making inferences from stock price reactions to the announcement of corporate decisions without giving due attention to the objective of management.’’ We address this issue of intentional signaling, and some of our evidences support the hypothesis that

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partners vary in their ability to signal ﬁrm quality via the investment decision. In the next section, we present a framework for assessing differences in partner’s stock price reactions and develop testable hypotheses. Our investigation then proceeds in three steps: First, we establish that there are statistically and economically signiﬁcant cross-partner differences in the stock price reactions to joint ventures, even after accounting for partners’ ownership shares and for the mechanical inﬂuence of ﬁrm size on abnormal returns. Second, we examine project-speciﬁc explanations for differences in partners’ reactions. Finally, we examine the possibility of extra-project information and investigate its nature.

2. ASSESSING THE INFORMATION IN JOINT VENTURE ANNOUNCEMENTS Fundamentally, a joint venture announcement reveals a mix of information about the shared project, the partner ﬁrms, their managers, and their industries, and typically results in a stock price reaction. Because the project is common to the partners, its inﬂuence can be partly or completely isolated by differencing the partners’ stock price reactions. Using this idea, we develop a framework for studying extra-project effects and develop testable hypotheses within this framework. We begin with a measure of the aggregate value revealed by the announcement. Malatesta (1983) points out that the total value change resulting from a multi-ﬁrm event is measured by a value-weighted average of stock price reactions, which avoids artiﬁcially over-emphasizing the returns of smaller ﬁrms.5 He also notes that the portion of the portfolio return due to each ﬁrm is given by its dollar-denominated wealth change, because percentage returns are sensitive to the ﬁrm’s size. We follow Malatesta’s suggestions. To enhance cross-sectional comparability, we normalize dollarvalue reactions by the total equity value of the two partners.6 The total stock price reaction to a joint venture announcement is thus up, the abnormal return to a value-weighted portfolio of the partners: up ¼

u1 E 1 u2 E 2 þ E1 þ E2 E1 þ E2

(1)

where uj ðj ¼ 1; 2Þ refers to the abnormal return for partner j and Ej to its equity value.

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Letting Sj represent the proportion of the joint venture owned by the jth partner, and deﬁning the share-adjusted contribution of a partner to portfolio abnormal return as Cj

uj E j S j ðE 1 þ E 2 Þ

(2)

we can alternatively write Eq. (1) as up ¼ S 1 C 1 þ S 2 C 2

(3)

Each partner’s share-adjusted contribution measures the (normalized) wealth gain that accrues to that partner per unit of ownership share. The reason we adjust for ownership share is that partners may not own equal shares of the joint venture, and stock price reactions related to the net present value of the project would differ accordingly. The share-adjusted contribution is the primary measure of stock price reaction used in this paper. Because it normalizes for cross-partner differences in terms of size and ownership share, this measure facilitates meaningful cross-partner comparisons. A standard interpretation of stock price reactions around joint venture announcements is that, on average, they reﬂect the unanticipated value created by the project undertaken (see, for example, McConnell & Nantell, 1985). Sufﬁcient conditions for this interpretation are as follows: A1. There is no extra-project information revealed by the announcement. B1. The project is equally unanticipated for each partner. C1. The announcement does not change the market’s valuation of assets invested in the joint venture. D1. Each partner invests and beneﬁts in proportion to its ownership share.7 If all these assumptions hold, then the total dollar-value wealth gain to both partners equals the unanticipated net present value of the project. Moreover, the dollar-valued wealth gain to a single partner is simply that partner’s ownership share times the unanticipated value of the project: uj E j ¼ S j Pð1 pÞ

(4)

where P is the market’s assessment of the total net present value of the project to both partners, including any synergies, and p is the market’s prior probability of the event. Thus, the wealth gain per unit ownership share is identical for all partners, and share-adjusted contributions are equal (as seen

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ARTHUR J. KEOWN ET AL.

by substituting Eq. (4) into Eq. (2)):8 C1 ¼ C2 ¼

Pð1 pÞ E1 þ E2

(5)

If Assumptions A1–A4 do not hold, then the economic interpretation of share-adjusted contributions to the portfolio abnormal return is more involved. Allowing for violations, the dollar-value abnormal returns to each partner can be expressed as a u1 E 1 ¼ S 1 P 1 p1 þ o1 þ X1 S1 and a u2 E 2 ¼ S 2 P 1 p2 þ o2 þ þ X2 S2

(6)

where pj ðj ¼ 1; 2Þ is the market’s prior probability that partner j announces this joint venture, oj is the effect of revaluation of assets contributed to the joint venture by that partner (expressed as a proportion of that partner’s share of the project value), a is a (possibly negative) proportion of the total value of the joint venture that is shifted from the ﬁrst partner to the second, and Xj is the value of extra-project information implied by the announcement. If A1 is violated, then either X 1 a0 or X 2 a0: If A2 is violated, then p1 ap2 : If A3 is violated, then o1 a0 or o2 a0: Effects of violations of A4 are represented by a non-zero a parameter. To see this, suppose that the joint venture agreement confers more ownership beneﬁts on the second partner than it pays for via its share of the investment. This is in effect a transfer of beneﬁts from the ﬁrst partner, and a would be positive. This outcome could occur if the second partner is in a stronger bargaining position than the ﬁrst, for example, or due to synergies that accrue to one partner independent of its ownership share. From an empirical point of view, the most important point about a is that it corresponds to effects speciﬁc to the joint venture announcement that could cause partners to experience stock price reactions out of proportion to ownership share even if no extra-project information is revealed. Since aeffects are project-speciﬁc, we should be able to control for them using information about the joint ventures themselves. Similarly, based on information in the announcements and the partner’s prior activities,

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39

controls for the effects of p1, p2, o1, and o2 can be devised. Speciﬁc controls are discussed in the empirical section. Substituting from Eq. (6) into Eq. (2) for each partner results in a more general interpretation of partners’ share-adjusted contributions: P 1 p1 þ o1 a=S 1 þ X 1 =S 1 C1 ¼ E1 þ E2 and

P 1 p2 þ o2 þ a=S 2 þ X 2 =S 2 C2 ¼ E1 þ E2

(7)

Comparing the expressions for share-adjusted contributions from Eq. (4) with the more general interpretation in Eq. (7) shows how project-speciﬁc and extra-project informations can affect each partner’s contribution to the value-weighted portfolio return. Working from this comparison, we list several propositions that guide our later empirical work. The propositions focus on cross-partner differences in share-adjusted contributions to portfolio return, denoted D. Proposition 1. If A1, A2, A3, and A4 hold, then D C 1 2C 2 ¼ 0: Alternatively, if A2, A3, and A4 hold, but A1 is violated (i.e., there is extra-project information), then D C1 C2 ¼

X 1 =S1 X 2 =S 2 E1 þ E2

The ﬁrst statement follows directly from Eq. (4) and implies that each partner’s share-adjusted contribution is an unbiased estimate of the total unanticipated value of the project. The second statement follows from Eq. (7) with p1 2p2 ¼ o1 ¼ o2 ¼ a ¼ 0: Under the assumptions, a non-zero D is direct evidence of extra-project value. Note that effective tests of this proposition may require a sample in which ownership shares are equal, to avoid the randomness they would otherwise impart. Maintaining A1 while relaxing the other assumptions, A2 through A4, yields: Proposition 2. If A1 holds, then ln|u1| ¼ ln|u2|ln E1+ln E2+ln E2+ln S1ln S2+v, where n ¼ ln(1p1+o1a/S1)—ln(1p2+o2a/S2). If p1p2 ¼ 0, o1o2 ¼ 0, and a ¼ 0, then n ¼ 0. This statement is obtained by setting the deﬁnition of share-adjusted contribution in Eq. (2) equal to the interpretation in Eq. (7) for each

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partner, while maintaining X 1 ¼ X 2 ¼ 0: We then solve each partner’s expression for the total project value for each partner, setting the results equal to one another, and manipulating the equation yields the proposition. The reason for taking absolute values is to state the result as a linear expression, which facilitates later testing. To state the result this way requires log returns to be used, and some abnormal returns are negative. Relative to Proposition 1, Proposition 2 implies a less restrictive test of the assumption of no extra-project information because it does not require the other assumptions. Further, it suggests a test of those additional assumptions: if n ¼ 0; they cannot be rejected. As a practical matter, n depends on project-speciﬁc information, so tests of this proposition can be implemented provided that appropriate project-speciﬁc variables can be identiﬁed. We discuss the available variables in Section 4. Finally, if we maintain A2, A3, and A4, or can control for the effects of their being violated, then we can test hypotheses about extra-project information: Proposition 3. D C 1 C 2 ¼ ½X 1 =S 1 X 2 =S 2 =E 1 þ E 2 þ Z; where Z ¼ P=E 1 þ E 2 p2 p1 þ o1 o2 þ a=S 2 a=S 1 is a residual. If p1 p2 ¼ 0; o1 o2 ¼ 0; and a ¼ 0 (or S 1 ¼ S2 ), then Z ¼ 0: If the term in square brackets can be approximated as a linear function of data z, then D ¼ zT b þ þ Z; where b is a coefﬁcient vector and e is a regression error. Proposition 3 is obtained by taking the difference of the partner’s contributions in Eq. (7). Even if Z is not zero for a particular joint venture, it represents only noise unless there is a systematic tendency for p1p2, o1o2, S1S2 to be positive or negative.9 In subsequent sections, we present tests of these propositions. Our tests establish the extent to which extra-project information is present in the stock price reactions to joint ventures. In addition, we statistically explain extra-project information using partner characteristics indicative of the extent of agency problems and asymmetric information costs. In the remainder of the paper, we test these propositions to learn about the information content of joint venture announcements.

3. EVENT STUDY DATA, METHODS, AND RESULTS 3.1. Data For our purposes, it is important that the partners to a joint venture invest in the same project in such a way that the project is isolated from the rest of

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the company. Thus, we are careful to distinguish joint ventures from other types of cooperative agreements among ﬁrms. For our purposes, a joint venture involves two or more independent companies that create a shared entity, the risks and returns of which are shared according to a contract, and which utilizes only a fraction of the partners’ assets. The risk and return sharing in combination with the formation of a separate business entity distinguishes a joint venture from all other forms of alliances (e.g., licensing contracts, marketing agreements, distribution agreements, etc.), even where these cooperative arrangements involve equity stakes in the alliance partners. Further, the independence of partner ﬁrms and the involvement of only a fraction of each company’s assets distinguishes a joint venture from a merger, acquisition, or a minority equity investment. We require a sample of joint ventures for which share-adjusted contributions (to the abnormal return of a value-weighted portfolio of joint venture partners), C1 and C2, and their difference, D, can be measured. Thus, a joint venture announcement must meet two criteria to be included in the sample: it must have two publicly traded domestic partners with daily stock price data available surrounding the announcement, and the announcement must disclose partners’ ownership shares. The ﬁrst criterion allows stock returns data to be obtained from CRSP ﬁles. The second criterion allows us to account for differential ownership across partners. We identify a total of 85 joint venture announcements during the period 1972–1990 that meet both criteria. If a joint venture has more than two partners with data available, we select the ﬁrst two usable partners in the order of their inclusion in the press release. Joint ventures announced during 1972–1978 come from the McConnell and Nantell (1985) study. Their sample contains 136 announcements identiﬁed from The Wall Street Journal Index, of which 16 report partners’ ownership shares. Announcements during 1979–1990 are identiﬁed using both the ‘‘Joint Venture Roster’’ (published in Mergers and Acquisitions) and the Dow Jones News Retrieval Service.10 A total of 69 joint ventures from the latter period meet our data requirements. The announcement date corresponds to the ﬁrst public announcement in the Dow Jones News Retrieval Service, or, for the McConnell and Nantell announcements, the day prior to The Wall Street Journal story. A typical announcement in our sample provides information about the nature of the joint venture’s business and the terms of the agreement: Endotronics Inc. said it signed an agreement with Summa Medical Corp., Albuquerque, N.M. to form a joint venture to produce biologicals on a contract basis. Endotronics said the venture will be equally owned by both companies. It said the joint venture

42

ARTHUR J. KEOWN ET AL. facility is to be located in Albuquerque, it is to be managed by staff from both companies, and it will begin producing biologicals in May 1985. (The Wall Street Journal, 1985, March 20)

Ownership share in the joint venture is clearly stated in 76 of the 85 announcements.11 In the remaining nine instances we establish the ownership shares based on the fraction of the total investment made by each partner, as stated in the announcement.12 In 61 of the 85 joint ventures the ownership shares are equal, and there are only two cases where the split is more disparate than 75–25. Table 1 describes the broad characteristics of the sample. It shows some industry concentration. Also, there are more announcements late in the sample period, possibly due to more extensive data being available for the more recent period, and/or the US antitrust regulatory environment being more conducive to joint ventures during this period. Finally, the sample shows more home-industry focus for the most recent joint ventures in that the percentage of joint ventures in the same industry as both parents has increased. This is consistent with the evidence of Comment and Jarrell (1995) that corporate focus has increased over the late 1980s. Eighteen ﬁrms engaged in two sample joint ventures each, and seven engaged in more than two each. A careful reading of the announcements reveals no evidence that multiple joint ventures by a single ﬁrm are part of pre-announced programs. In only one case do two joint ventures involving the same ﬁrm appear to be related at all. Furthermore, the mean time between announcements for ﬁrms with more than one joint venture is more than three years, with only one pair coming less than 100 days apart. Thus, we treat each joint venture as an independent event.

3.2. Event Study Empirical Methods We perform an event study to obtain cumulative abnormal returns that are the statistical basis for our analysis. The event study is also of interest for its own sake as an update of the McConnell and Nantell (1985) event study of joint venture announcements. As suggested in Eq. (1), we calculate abnormal returns to each partner ﬁrm, then for a value-weighted portfolio of the partners to each joint venture. We use the market model, the CRSP equal-weighted index, and Scholes-Williams betas. We have obtained similar event-study results with market-adjusted returns and CRSP-style excess returns using portfolio betas.

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Sample Characteristics.

Table 1.

Panel A: Industry representation of partner ﬁrms SIC Codes and Representative Industries

Number of Partner Firms

100 1000s 2000s 3000s 4000s 5000s 6000s 7000s 8000s Total

1 21 (SIC 49 (SIC 45 28 (SIC 3 8 12 (SIC 3 170

Mining Food, chemical, petroleum Machinery, transportation Utilities Retail Banking and ﬁnance

1040: 9 ﬁrms) 2911: 15 ﬁrms) 4011: 7 ﬁrms)

7812: 8 ﬁrms)

Panel B: Announcement year representation Year

Number of Events

Year

Number of Events

Year

Number of Events

1972 1973 1974 1975 1976 1977 1978

3 2 1 3 3 0 4

1979 1980 1981 1982 1983 1984 1985

4 7 6 4 7 5 3

1986 1987 1988 1989 1990 Total

6 6 10 8 3 85

Panel C: Number of joint ventures per ﬁrm Number of Joint Ventures

Number of Firms

5 4 3 2 1 Total

1 (General Electric) 2 (Dow and Texas Eastern) 4 (Gulf, GTE, W.R. Grace, and Warner Comm.) 18 145 170

Panel D: Percentage of sample joint ventures involving partners in the same industry, by time period Period 1971–1975 1976–1980 1981–1985 1986–1990

Same 4-Digit SIC Industry

Same 2-Digit SIC Industry

0 11 08 24

0 22 12 33

Note: The table summarizes characteristics of 85 joint venture announcements by 170 partner ﬁrms between 1972 and 1990. To be included, both partners to the joint venture must be listed in the CRSP daily returns ﬁle, and the announcement must report the ownership shares of each partner.

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For our tests to be valid, it is important that stock prices completely impound the market’s assessment of the information content of the announcement. We have reasons to be concerned about the time period required for the information to become fully impounded in the stock prices of the smaller partner ﬁrms. For example, the trading volume around the announcements for the group of smaller partner ﬁrms to each joint venture is quite small and is only about half that of the larger partners, on average. Volume data for smaller partners around the dates of these joint ventures suggest that many of them trade only a few times each day. Further, the number of analysts that follow the smaller partner ﬁrms is dramatically smaller than the number of analysts that follow the larger ﬁrms.13 Additionally, investors possibly continue to collect and evaluate information for at least a short time after the announcement.14 As a consequence, we ultimately focus on a seven-day event window (–3, +3), from three days before the event day until three days after.15 We prefer to use an event period longer than the standard two-day window in order to be conﬁdent that the full valuation effect of the announcement has been impounded in stock prices. Because this seven-day window is non-standard we also report abnormal returns based on a standard two-day event window for comparison. Some, but not all, of our analyses require that partners be a priori separated into economically meaningful groups (rather than merely designated as, say, partners 1 and 2). We group partners based on market value of equity. That is, we separate the group of larger partners to each joint venture from the group of smaller partners. This split is interesting for several reasons. First, McConnell and Nantell (1985) have found a relative size effect in abnormal returns, suggestive of different extra-project information across these partners. Moreover, splitting the sample into groups by relative partner size is useful in investigating explanations for differences in stock price reactions based on shareholder–manager agency problems. Previous literature stretching back as far as Berle and Means (1932) suggests that such problems may be more important for larger ﬁrms.16 To assess the signiﬁcance of abnormal returns, i.e., u1 and u2 in Eq. (1), around joint venture announcements we use standard statistical tests. The Patell (1976) standardized residual test statistic is reported, as is the crosssectional standardized residual test statistic suggested by Boehmer, Musumecci, and Poulsen (1991). The latter statistic is robust to eventinduced changes in variance, which is a possible explanation, a priori, for cross-partner differences in stock price reactions. We also present a standard binomial test statistic, the form of which is in Boehmer et al.

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For statistical tests on share-adjusted contributions by speciﬁc groups of partners, C1 and C2, we adapt the method used by Malatesta (1983) for testing dollar-valued effects. For tests on the contribution difference between partners to the same joint venture, D, we additionally allow for cross-partner correlations by extending Malatesta’s approach using results in Collins and Dent (1984) for event studies in which ﬁrms’ reactions are not independent. These approaches yield z-statistics appropriate for testing C and D, which are described in the appendix.

3.3. Event Study Results The event study results reported in Table 2 provide the raw material for our tests concerning share-adjusted contributions. Panel A of the table reports mean cumulative abnormal returns for the full sample over a seven-day window around joint venture announcements. Smaller partners experience an average 2.1% abnormal return, which is highly statistically signiﬁcant. In contrast, larger partners experience scarcely any average abnormal return at all. The mean abnormal return for larger partners is 0.00006%, which is not statistically signiﬁcant at any reasonable level. Thus, as in McConnell and Nantell’s (1985) results, there appears to be a size effect.17 For comparison to the full sample results over the seven-day window, Panel B of Table 2 contains abnormal returns calculated for uncontaminated subsamples over two-day and seven-day event windows as well as for the complete sample over a two-day window.18 The uncontaminated subsamples are free of earnings and dividend announcements during the event window. The seven-day results for uncontaminated subsamples are similar to those for the full sample except that the smaller partners’ mean abnormal return is even stronger at about 2.5%. Note that the presence of randomness induced by contaminating announcements in the full sample increases the difﬁculty of explaining cross-partner differences in stock price reactions, but induces no biases. Two-day cumulative abnormal returns for both the full and uncontaminated samples tend to be nearer to zero than those in Panel A. The apparently larger reactions for smaller partners could point to the economic differences in extra-project information that we have hypothesized. Alternatively, they could be at least partially induced by size differences across partners to the same joint venture. Intuitively, a joint venture with a $10 million net present value would have very little effect, in percentage terms, on the value of a $10 billion ﬁrm, but would be more

46

Table 2.

ARTHUR J. KEOWN ET AL.

Summary of Event Study Results for 170 partners in 85 Joint Ventures (1972–1990).

Statistics

Larger Partners

Smaller Partners

Panel A: Abnormal stock price reactions, full sample, seven-day event window Mean abnormal return (Patell z) [BMP z] {N} Percent positive (Binomial z)

0.00006% (0.35) [0.37] {85} 48.235 (0.32)

2.104% (3.09) [2.72] {85} 61.176 (2.06)

Panel B: Abnormal stock price reactions, various subsamples and event windows Clean Sample, Seven-Day Event Window Mean abnormal return (Patell z) {N}

0.364% (1.11) {73}

2.486% (3.11) {73}

Full sample, two-day event window Mean abnormal return (Patell z) {N}

0.514% (0.812) {85}

0.983% (1.14) {85}

Clean sample, two-day event window Mean abnormal return (Patell z) {N}

0.53% (0.81) {80}

1.39% (1.96) {78}

Cross-sectional sample, seven-day event window Mean abnormal return (Patell z) {N}

0.238% (0.20) {61}

2.08% (2.49) {61}

Note: The table shows mean abnormal returns and test statistics for portfolios of both joint venture partners and for the larger and smaller partner separately. The Patell z-statistics is calculated as in Patell (1976). The BMP z-statistics is robust to event-induced changes in variance, and is calculated as in Boehmer et al. (1991). N is the number of observations. The binomial z-statistic tests the null hypothesis that the percentage of positive reactions is 50%. Inferences drawn from BMP and binomial z-statistics are identical to those from Patell z-statistics. Signiﬁcant at the 5% level in a two-tailed test. Signiﬁcant at the 1% level in a two-tailed test.

important for a $100 million ﬁrm. Others have also noted how ﬁrm size can affect event study results (e.g., Roll, 1986). The difference between the equity values of the larger and smaller partners in our sample of 85 joint ventures is more than $7 billion, suggestive of this mechanical explanation.19

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On the other hand, the conditional probability of one partner having a positive (negative) abnormal return, given that the other partner has a positive (negative) abnormal return over the seven-day window is only 31.1% (36.4%). Thus, partners to a joint venture tend to experience stock price reactions in opposite directions. Since size scaling affects only the magnitude of abnormal returns, not the sign, this suggests that economic differences exist. Further investigation thus seems warranted. As a ﬁrst step in investigating the possible economic signiﬁcance of crosspartner differences in stock price reaction, we convert partner’s abnormal returns to share-adjusted contributions using Eq. (2). Recall that a partner’s contribution is deﬁned as its dollar-value abnormal return scaled by its ownership share in the joint venture and the total equity value of both partners. Equity value is computed as the product of shares outstanding (from Compustat for the year prior to the announcement) and share price (from CRSP for 10 days before the announcement). Because the contribution is normalized using the total size of both partners, it does not mechanically depend on ﬁrm size. Panel A of Table 3 reports contributions separately for larger and smaller partners. As with the abnormal returns, larger partners’ contributions are, on average, slightly negative and statistically insigniﬁcant. Smaller partners contributions average 0.99% of the total equity value of both partners and reliably different from zero. Assuming that there is no extra-project information and also that simplifying assumptions A2, A3, and A4 hold, then the cross-partner difference in contributions should be zero (Proposition 1). The proposition serves as the null hypothesis for two tests of the signiﬁcance of the apparent differences in Panel B. In the ﬁrst test, we avoid imposing our a priori impression that differences reﬂect a relative size effect. To perform a test on unordered differences, we work from the intuition that unsigned differences should tend to be close to zero in the absence of extra-project information. Accordingly, we form a weighted sum of squared cross-partner differences to each joint venture. This statistic, developed in the appendix, is distributed as a w2 random variable if there is no systematic tendency for partners’ contributions to diverge. In the second test, we ask whether the larger partner’s contribution tends to be different from the smaller partner’s contribution using a z-test. Panel B of Table 3 presents the results of applying these tests to both the full sample of joint ventures and to a sample that includes only joint ventures where partners have equal ownership shares. The latter sample is used because tests could otherwise fail to reject simply because differential

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ARTHUR J. KEOWN ET AL.

Table 3. Contributions of Joint Venture Partners to Value-Weighted Portfolio Abnormal Return, per Unit of Ownership Share, for 170 Partners in 85 Joint Ventures (1972–1990). Panel A: Contributions of larger and smaller partner groups Statistics

Larger Partners

Smaller Partners

0.407% (0.31) {85} 48.235 (0.32)

0.991% (2.23) {85} 61.176 (2.06)

Unordered Differences

Larger Partner Less Smaller Partner

Full sample Mean difference measure (Test statistics) {N} Percent positive (Binomial z)

|D| ¼ 7.077% (w2 ¼ 106.8) {85} —

D ¼ 1.398 (z ¼ 1.01) {85} 51.765 (0.33)

Equal shares sample Mean difference measure (Test statistics) {N} Percent positive (Binomial z)

|D| ¼ 7.327% (w2 ¼ 81.71) {61} —

D ¼ 2.362 (z ¼ 1.90) {61} 31.765 (3.36)

Mean contribution (C) (z-statistics) {N} Percent positive (Binomial z) Panel B: Cross-partner differences in contribution

Note: This table reports contributions and cross-partner differences in contributions calculated for a seven-day event window around joint venture announcements. A partner’s contribution is deﬁned as its dollar-value abnormal stock price reaction scaled by its ownership share in the joint venture and by the total equity value of both partners, as given in Eq. (2) of the text. The table also presents test statistics against the null hypothesis that the mean contribution (in Panel A) or the mean cross-partner difference (in Panel B) is zero. The z and w2 statistics are developed in the appendix, and the binomial z is standard. Signiﬁcant at the 10% level in a two-tailed test. Signiﬁcant at the 5% level in a two-tailed test. Signiﬁcant at the 1% level in a two-tailed test.

ownership shares add too much randomness. To give an informal sense of the size of the unsigned differences, the table reports the mean absolute difference. This absolute difference is more than 7% of the total equity value of the partners for the both samples, (i.e., the root mean square cross-partner

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difference in contributions is more than 7% of total partner value). The w2 tests on unordered differences indicate that cross-partner differences in contributions are reliably different from zero at about the 5% level for both samples.20 Either there is extra-project information, or one of the simplifying assumptions of Proposition 1 is violated. The z-tests on ordered differences (larger less smaller partner) indicate that, although the null hypothesis of no difference cannot be rejected for the full sample, it is rejected for the equalshares sample (mean DE–2.4%, z ¼ –1.90).21 This ﬁnding is consistent with that of the unordered test, and also suggests that controls for differences in ownership share should be included in subsequent tests. The mean value of the D (ordered as larger less smaller partner contribution) is reported in the second column of Panel B. The mean D is about –1.4% of the total value of the partners for the full sample and –2.4% for the equal-shares sample. For the full sample, total value of the partners averages 10.2 billion dollars, so the dollar-valued difference amounts to about 140 million dollars. If the difference is instead measured relative to the size of the smaller partners ($1.5 billion), it amounts to 9.3%. As a preliminary indication that this large difference reﬂects more than project effects, we note that for the 26 joint ventures with available data, the total dollar investment by both partners in the joint venture has a median level of only $75 million.22 For this subsample, the mean dollar-valued difference, calculated as above, is about $155 million. Moreover, about two-thirds of the differences are larger than the corresponding investments. Finally, when both differences in stock price reactions and investments are measured as a proportion of both partners’ equity value, differences are about twice as large as investments on average. The overall impression is that the total investment in the project is small relative to the difference between partners’ reactions. Consequently, even if project values are allocated out of proportion to investments, these projects do not seem large enough to account for such large differences in stock price reaction. The large differences thus seem to point to the presence of extra-project information.

4. EXPLANATIONS OF CROSS-PARTNER DIFFERENCES IN STOCK PRICE REACTIONS USING JOINT VENTURE CHARACTERISTICS In this section, we substantiate our preliminary conclusion that stockprice reaction differences are a reﬂection of extra-project information by

50

ARTHUR J. KEOWN ET AL.

investigating the extent to which the differences we observe might be due to project-speciﬁc inﬂuences. We have discussed how cross-partner differences in the prior probability that a partner would participate in the joint venture, bargaining power, synergies, or the revaluation of contributed assets could lead to cross-partner differences in contributions even if there is no extraproject information. Proposition 2, which holds in the absence of extraproject information, provides the null hypothesis for our investigation of these project-speciﬁc inﬂuences. Written as a linear regression equation, the proposition states that lnju1 j ¼ a0 þ a1 lnju2 j þ a2 ln E 1 þ a3 ln E 2 þ a4 ln S 1 þ a5 ln S2 þ xT f þ

ð8Þ

where a0 ¼ 0, a1 ¼ –a2 ¼ a3 ¼ a4 ¼ –a5 ¼ 1, x is a vector of data that accounts for the project-speciﬁc inﬂuences discussed above, f is a vector of coefﬁcients, and e is an error term. In estimating these regressions, we designate larger partner’s abnormal return as the dependent variable because the larger partners’ reactions are measured with greater error. Our earlier discussion points to two types of variables that belong in the vector of project-speciﬁc inﬂuences denoted by x. One type consists of indicators of different prior probabilities of entering the joint venture. Another type consists of indicators of possible transfers of wealth from one partner to the other via partners receiving value out of proportion to their ownership share. By carefully re-reading the announcements, we identify indicator variables reﬂecting cross-partner differences that could lead to such transfers. Each variable is one for a joint venture for which the response is ‘yes,’ and zero otherwise.23 In the list below, the proportion of times the response is ‘yes’ is in parentheses. Does this joint venture represent a new activity for both partners? (61.18%) Does operating control reside with one partner? (23.53%) Is one partner the major source of funding? (25.88%) Does one partner contribute disproportionate real assets? (27.06%) Does one partner contribute disproportionate intangible assets? (2.35%) The ﬁrst question indicates which joint ventures likely involve partners for which the market assesses different prior probabilities of participating in this joint venture. We hypothesize that the probabilities are more likely equal across partners when the joint venture is a truly new activity for both

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of them. If it involves an existing activity for one of the partners, the market is likely to have more information about that partner’s plans. The remaining four questions tend to be answered afﬁrmatively in situations where one partner’s role in the joint venture is substantially different from the other. If one partner provides the funding and the other contributes real or intangible assets, we might expect to see stock price reactions out of proportion to ownership share. For example, the presence of disproportionate funding by one partner might certify, and thus enhance, the value of the assets contributed by the other, similar to the way bank lending appears to certify the value of industrial ﬁrms (Fama, 1985; James, 1987). Alternatively, the market might learn about the value of the contributed assets by observing the ownership share that was obtained for them. In either case, the project-based reaction in partners’ share prices would not be in proportion to their ownership shares. Regression results are reported in Table 4.24 The ﬁrst column reports estimates for the full sample of 85 joint ventures without the indicator variables. This regression provides a benchmark by showing the extent to which the larger partner’s abnormal return is explained by that of the smaller partner. The results indicate that the absolute magnitude of the smaller partner’s abnormal return is statistically signiﬁcant in explaining the larger partner’s abnormal return. However, the coefﬁcient is small (about 0.23, which is reliably smaller than 1.0 – t ¼ 8.02, not reported in the table). Moreover, while most of the slope coefﬁcients are statistically non-zero and all are of the correct sign as speciﬁed in Eq. (7), they are not equal to 71 as predicted by Proposition 2. A Wald w2 test at the foot of the column indicates that this joint hypothesis is soundly rejected.25 We conclude that the smaller partner’s abnormal return is a biased predictor of the larger partner’s abnormal return even after controlling for ﬁrm size and ownership share. This ﬁnding is consistent with either extra-project information or with unaccounted-for project-speciﬁc variables. The unrestricted regression reported in the second column of Table 4 shows that the project-speciﬁc variables in the vector x are not the reason that smaller partners’ reactions are biased predictors. The slope coefﬁcients from the benchmark regression are little affected when these additional regressors are included. Moreover, the adjusted R2 rises only from 15.2% to 17.6% on the addition of the new variables, indicating a very modest increase in explanatory power. Finally, a w2 test reported at the foot of the table does not reject the joint hypothesis that the coefﬁcients on all projectspeciﬁc regressors are zero. Thus, we conclude that project-speciﬁc variables are unable to explain the differences we observe.

52

Table 4.

ARTHUR J. KEOWN ET AL.

Results of Regressions on Abnormal Returns for 170 Partners to 85 Joint Ventures (1972–1990).

Regressor

N ¼ 85 Coefﬁcient

N ¼ 85 Coefﬁcient

N ¼ 61 Coefﬁcient

N ¼ 61 Coefﬁcient

Constant

1.982 (1.56) 0.228 (2.36) 0.274 (3.39) 0.132 (1.72) 0.546 (1.89) 0.461 (1.33) —

2.089 (1.58) 0.206 (2.09) 0.241 (3.05) 0.117 (1.52) 0.378 (1.19) 0.331 (0.95) 0.057 (0.21)

1.990 (1.57) 0.253 (1.89) 0.309 (2.64) 0.168 (1.57) 0.704 (1.91) 0.615 (1.26) —

2.20 (1.79) 0.263 (1.97) 0.255 (2.33) 0.149 (1.44) 0.625 (1.58) 0.580 (1.21) 0.254 (0.75)

—

0.0007 (0.002) 0.682 (2.26) 0.808 (2.08) 0.367 (0.69)

—

0.044 (0.14) 0.652 (1.89) 0.766 (1.84) 0.350 (0.61)

Absolute abnormal return of smaller

partner

Equity value of larger partner Equity value of smaller partner Ownership share of larger partner Ownership share of smaller partner y

Indicator: Does this joint venture represent a new activity for both partners? y Indicator: Does operating control reside with one partner? y Indicator: Is one partner the major source of ﬁnancing? y Indicator: Does one partner contribute disproportionate real assets? y Indicator: Does one partner contribute disproportionate intangible assets? Joint hypothesis tests w2 test with 5 d.f., Ho: all starred (*) coefﬁcients are 1 [sig. level] w2 test with 5 d.f., Ho: all daggered (y) coefﬁcients are zero [sig. level] R2 (Adj. R2)

— — —

163.28 [0.00] — 0.203 (0.152)

174.18 [0.00] 5.93 [0.31] 0.274 (0.176)

— — —

110.51 [0.00] — 0.211 (0.139)

96.08 [0.00] 5.36 [0.37] 0.290 (0.148)

Note: The table reports the results of the log-linear regression speciﬁed in Eq. (8). Dependent variable is the absolute value of larger partners abnormal return, where abnormal returns are calculated for a seven-day event window. The ﬁrst two columns use the full sample and the ﬁnal two columns use a smaller sample for which addition cross-sectional variables used in subsequent analyses are available. For each regressor, the OLS regression coefﬁcient and a tstatistics (in parentheses) are reported. The results of several joint hypothesis tests are reported at the foot of the table. All test statistics are calculated using a heteroskedasticity-consistent covariance matrix. Signiﬁcant at the 10% level in a two-tailed test. Signiﬁcant at the 5% level in a two-tailed test. Signiﬁcant at the 1% level in a two-tailed test.

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Considered individually, two of the new regressors are statistically signiﬁcant. Both regressors are related to the possibility of a certiﬁcation effect due to one partner providing funding. When one partner is the primary source of ﬁnancing, the larger partner’s abnormal return is greater in absolute value. When one partner contributes more real assets than the other, the larger partner’s abnormal return tends to be less in absolute value. Further examination of the announcements indicates, when partners differ along these dimensions, the larger partner usually supplies disproportionate funding and the smaller partner supplies disproportionate real assets. These two signiﬁcant coefﬁcients are about equal in absolute magnitude. The coefﬁcients and the tendency for the larger partner to provide disproportionate funding while the smaller partner provides disproportionate assets together mean that the effects offset for most joint ventures. We conclude that there is only limited evidence of a certiﬁcation effect, since it is observed only in cases where one partner contributes funding and both partners contribute assets.26 Our empirical work below requires more extensive data on each joint venture partner. The extra data requirements restrict the number of sample points with complete data from 85 joint ventures to 61. To demonstrate that the smaller sample has properties similar to the full sample, the ﬁnal two columns of Table 4 replicate the regressions in the ﬁrst two columns for the sample of 61 joint ventures. The results are very similar. Overall, we interpret these regressions as rejecting Proposition 2. That is, differences in stock price reactions across partners are not substantially due to project-speciﬁc factors. This suggests that focusing on differences in stock price reactions largely nets-out the effects of project value, leaving us to concentrate on extra-project information. However, the data do not completely rule out the inﬂuence of project characteristics related to a certiﬁcation effect, and so we allow for their possible inﬂuence in subsequent tests.

5. EXPLANATIONS FOR CROSS-PARTNER DIFFERENCES IN STOCK PRICE REACTIONS USING PARTNER CHARACTERISTICS In this section, we report evidence on the cross-sectional determinants of D, the cross-partner difference in contributions to portfolio return, based on the characteristics of the partners. Having established that project-speciﬁc

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ARTHUR J. KEOWN ET AL.

variables are not the major source of the differences, we now work from Proposition 3, which emphasizes extra-project information as the source of the differences. We assess whether variables describing the partner ﬁrms are correlated with this difference. The results establish that the relative size effect, in which larger partners’ share-adjusted contributions are systematically smaller than smaller partners’ contributions, is explained by ﬁrmspeciﬁc characteristics. A substantial portion of the cross-sectional variation in D is also explained. We initially focus on ﬁrm characteristics that indicate of the extent of shareholder–manager agency problems. Our results support the idea that the market evaluates managers’ investment decisions differently based on what it knows of the managers’ tendencies to follow goals other than shareholder-wealth maximization. Moreover, these effects extend beyond the market’s evaluation of the net present value of the marginal project to involve its evaluation of the value of the rest of the ﬁrm’s assets.

5.1. An Explanation for the Relative Size Effect We have hypothesized that smaller and larger partners might differ in the degree to which the separation of management and control allows managers to pursue goals that are not in the interest of shareholder wealth maximization. The difference in equity value between the two groups is substantial: $8.7 billion versus $1.5 billion for the sample of all 85 joint ventures, and $10.81 billion versus $1.98 billion for the regression sample of 61 joint ventures we use below. Moreover, size is negatively correlated with other variables known to correspond to the severity of shareholder–manager agency problems such as the proportion of shares owned by insiders (Morck, Shleifer, & Vishny, 1988) and Tobin’s q (Lang & Litzenberger, 1989) Another possible explanation for extra-project information is that larger and smaller partners differ in their potential for signaling otherwise unobservable information via investment activities. Such variables include insider ownership and Tobin’s q (see, for example, Leland & Pyle, 1977; John & Mishra, 1990). Although the average cross-group difference in insider ownership is small, Tobin’s q differs appreciably.27 We directly investigate this alternative interpretation in the next section. To see if differences in the extent of agency problems are the source of the relative size effect, we enact tests of Proposition 3. In our ﬁrst test, we regress D, the cross-partner contribution difference, on a set of indicator

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variables. The indicators effectively split the sample into groups according to which partner is more likely subject to agency problems. We base the split on variables that others have found to be correlated with the severity of such problems. The bases for these indicators are the extent of insider shareholdings in each partner ﬁrm, their levels of ﬁnancial leverage, their levels of Tobin’s q, and whether they invest in their home industries. Our ﬁrst indicator variable is set to one if the larger partner’s level of insider holdings is greater than the smaller partner’s level. Many previous studies have observed that shareholder and manager goals should be more compatible when managers hold a larger stake in the ﬁrm’s equity.28 This idea has empirical support as well (Morck et al., 1988). A code of ‘‘1’’ thus means the larger ﬁrm is less likely subject to agency problems, according to the values of the underlying variables. We measure insider holdings as the proportion of shares owned by managers, directors, and beneﬁcial owners on the most recent date for which data is available prior to the joint venture. These data are obtained from Spectrum 6 and ValueLine when possible, and from proxy statements or from the ﬁrm via telephone in the remaining cases.29 Our second indicator variable is set to one if the larger partner’s debt-toequity ratio is greater than the smaller partner’s. It has often been argued that high levels of debt obligations discipline managers, forcing them to avoid negative net present value projects. Analogous to the insider holdings indicator above, a code of ‘‘1’’ means that the larger partner is less likely subject to shareholder–manager goal incompatibilities than the other partner, according to the values of the underlying variables. We measure debt-to-equity ratios using the market value of equity as calculated earlier and Compustat data on debt for the year just prior to the announcement. Our next indicators are based on the level of Tobin’s q for the partners. The idea here is that lower levels of q correspond to fewer proﬁtable growth opportunities for the ﬁrm, and thus, if managers are reluctant to rebate excess funds directly to shareholders, to an increased possibility of managers using those funds for other purposes. Alternatively, following Lang et al. (1989), q can be thought of as an index of management quality. Consistent with previous studies, we form one indicator for each partner that is set to one if the partner’s q is greater than one (see, for example, Lang & Litzenberger, 1989). Thus, if the larger ﬁrm’s indicator is ‘‘1’’ and the smaller ﬁrm’s indicator is ‘‘0,’’ this criterion implies that the larger ﬁrm is less likely subject to agency problems, according to the values of the underlying variables. We measure Tobin’s q using a variant of the Lindenberg and Ross (1981) procedure.30

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Our ﬁnal indicators are based on the similarity between the joint venture and each partner’s main business. Jensen (1986) has proposed that ﬁrm size and scope is one goal pursued by managers that may not be in keeping with shareholder wealth maximization. Comment and Jarrell (1995) provide consistent evidence that industry focus is value-increasing. For each partner, we assign a value of ‘‘1’’ if the joint venture is in the ﬁrm’s home 2-digit SIC industry. Thus, if the larger partner’s indicator is ‘‘1’’ and the smaller partners is ‘‘0,’’ this criterion suggests that the larger partner is less likely involved in ‘‘empire-building.’’ We obtain partners’ SIC industries from Compustat, and assess the joint venture’s industry by reading the announcements. The results of regressing cross-partner differences in share-adjusted contributions (larger partner minus smaller partner) on these indicators are presented in the ﬁrst column of Table 5. The intercept is signiﬁcantly negative (–5.2% of the total equity value of the partners). This means that if all indicators are zero, the larger partner’s contribution tends to be less than the smaller partner’s contribution, consistent with the relative size effect found earlier. However, if the larger ﬁrm is the one less likely subject to agency problems by all the criteria above, the negative intercept is more than offset: that is, the relative size effect is fully explained by differences in exposure to agency problems, as we describe below. In Table 5, we place an asterisk by indicator variables that, when set to ‘‘1,’’ signiﬁes less severe agency problems for the larger partner. The sum of the starred coefﬁcients is signiﬁcantly positive for the regression in the ﬁrst column, as shown by a w2 test reported at the foot of the table. When this positive sum is added to the negative intercept, the w2 test at the foot of the table indicates that the sum is signiﬁcantly positive. This result is evidence that the relative size effect is due to the market’s perception that larger and smaller partners tend to differ in the degree to which they are subject to manager–shareholder agency problems. When explicit indicators as to which ﬁrm is more subject to agency problems are taken into account, then the relative size effect is offset. In fact, it seems that if the larger ﬁrm is less subject to agency problems by all three measures, its contribution is predicted to be greater than that of the smaller partner. Because equity value and ownership share in the joint venture are mechanically involved in the calculation of contributions, we report an extended version of this regression in which they are included as control variables in the second column of Table 5. Thus, we can be assured that apparent correlations involving the three indicator variables are not the spurious result of correlations involving ﬁrm size or ownership share. Such

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Table 5. Regression Analysis of the Determinants of the Relative Size Effect in Contributions to Value-Weighted Portfolio Abnormal Return for 122 Partners to 61 Joint Venture Announcements (1972–1990). Regressor Constant Indicator variable: one if larger partner has

greater percentage of insider holdings

Indicator variable: one if larger partner has

greater debt-to-equity ratio

Indicator variable: one if larger partner has

Tobin’s q41 Indicator variable: one if smaller partner has Tobin’s q41 Indicator variable: one if the joint venture is in the larger partner’s industry Indicator variable: one if the joint venture is in the smaller partner’s industry Ownership share of larger partner

Coefﬁcient 0.052 (1.92) 0.029 (1.36) 0.023 (1.19) 0.008 (0.44) 0.008 (0.39) 0.056 (3.01) 0.008 (1.91) —

Ownership share of smaller partner

—

Equity value of larger partner

—

Equity value of smaller partner

—

Hypothesis tests on sums of coefficients Sum of coefﬁcients on starred (*) indicator variables [w2 test p-value] Sum of coefﬁcients on starred (*) indicator variables plus intercept [w2 test p-value]

0.116 [0.0004] 0.064 [0.008]

R2 Adjusted R2

0.187 0.097

Coefﬁcient 0.195 (3.19) 0.046 (2.09) 0.022 (1.13) 0.012 (0.68) 0.004 (0.22) 0.045 (2.59) 0.017 (0.93) 0.072 (0.88) 0.213 (2.31) 0.0000007 (1.18) 0.000002 (1.16) 0.125 [0.0002] 0.07 [0.246] 0.300 0.160

Coefﬁcient 0.184 (2.92) 0.050 (2.15) 0.025 (1.29) 0.023 (1.27) 0.009 (0.45) — — 0.053 (0.56) 0.25 (2.57) 0.0000004 (0.84) 0.000003 (0.21) 0.098 [0.007] 0.08 [0.208] 0.205 [0.083]

Note:The table reports the results of regressions based on Proposition 3. The dependent variable in each regression is the difference between the larger partner’s and smaller partner’s contribution to the portfolio abnormal return, i.e., DC1C2. Coefﬁcients and t-statistics (in parentheses) are presented for each regression model. At the foot of the table are tests of several relevant sums of coefﬁcients with signiﬁcance levels [in brackets] from Wald w2 test against the null hypothesis that the sum is zero. All test statistics are calculated using a heteroskedasticityconsistent covariance matrix. Signiﬁcant at the 10% level. Signiﬁcant at the 5% level. Signiﬁcant at the 1% level.

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correlations could be important, a priori, because we know that insider holdings and q, in particular, are correlated with ﬁrm size. Our conclusions about the source of the relative size effect are unchanged by the inclusion of the control variables. The extended regression results show a signiﬁcantly negative intercept, as before. Also as before, the sum of the intercept and the slopes on the three indicator variables is not signiﬁcantly negative. In this regression, the sum is not reliably different from zero. Thus, in the presence of the control variables, it appears that the relative size effect is fully accounted for by, but not more than offset by, the indicators of the likelihood of agency problems.31 Finally, the regression in the third column of Table 5 shows that the same results obtain if the indicator variables specifying whether the joint venture is in a partner’s home industry are excluded. Thus, even when only a priori observable indicators are allowed in the regression, the conclusion stands.

5.2. Free Cash Flow and Extra Project Information Recent literature on shareholder–manager agency problems has emphasized the role of free cash ﬂow in allowing managers to pursue their own goals. The idea is that, for ﬁrms subject to agency problems, management actions that use cash in inefﬁcient ways are more likely when there is more cash. In our language, low or negative project values are more likely for ﬁrms with high levels of free cash ﬂow. Alternatively, for ﬁrms that are not subject to such serious agency problems, cash may represent ﬁnancial slack in the sense of Myers and Majluf (1984). Financial slack allows the ﬁrm to undertake proﬁtable projects without having to visit capital markets and incur the higher cost of external funds (see also Fazzari et al., 1988). If our indicator variables have truly controlled for differences in the level of agency problems for the larger and smaller partners, then this second role for free cash ﬂow should be evident in the data. To see, we amend the regression test of Proposition 3 to include a measure of free cash ﬂow. Free cash ﬂow is measured using the Lehn–Poulsen deﬁnition and Compustat data from the year prior to the announcement (Lehn & Poulsen, 1989). For cross-sectional comparability, we follow other researchers and scale cash ﬂow by the book value of total assets. Following Lang and Litzenberger (1989), who argue that agency-cost effects should be most evident for ﬁrms with Tobin’s qo1, we construct a regressor that is the product of a partner’s free cash ﬂow and an indicator variable for low Tobin’s q (i.e., qo1). Thus, if our indicator variables incompletely discriminate between partners based

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on agency problems, the agency effect of free cash ﬂow should be clearly evident in our results. Table 6 reports the results of the extended regression. The ﬁrst column shows results for the regression using the full cross-sectional sample of 61 joint ventures. Coefﬁcients on previously included variables are similar to those reported in Table 5, and the statistical reliability of coefﬁcients on the agency-problem indicators is often higher. The coefﬁcients on the newly included free cash ﬂow regressors are reported near the foot of the table. For the larger partner, more free cash ﬂow has a positive but statistically insigniﬁcant effect on extra-project information revealed (relative to that for the smaller partner). This suggests that, while larger partners may not beneﬁt from more ﬁnancial slack, perhaps because liquidity constraints are not binding on such large ﬁrms, neither is free cash ﬂow perceived by investors as being connected with negative extra-project information. Thus, we conclude that, when a larger partner invests in a joint venture, even when the partner has a low q, the market does not infer a greater chance of the management wasting shareholders’ funds than it previously did. For the smaller partner, the coefﬁcient on free cash ﬂow is large and reliably negative. Since the smaller partner’s contribution is subtracted in forming D, this means that the smaller partner’s extra-project reaction tends to increase (relative to the other partner) when it has more free cash ﬂow. This is consistent with the idea that free cash ﬂow indicates the presence of value-enhancing ﬁnancial slack, and that the joint venture is regarded by investors as an indication that management is now more likely to ﬁnd good uses for such slack. Note that the inclusion of the free cash ﬂow regressors leads to a signiﬁcant increase in the ﬁt of the regression: the adjusted R2 is 0.224 in this regression versus 0.160 for the corresponding regression in Table 5. Thus, free cash ﬂow is an important variable in the market’s set of conditioning information. Moreover, the fact that this simple regression equation can explain about 38% of the cross-sectional variation in D, our measure of differences in extra-project information, is additional strong evidence that these differences do not represent noise in stock market prices, but rather rationally determined differences in the market’s assessment of the partners’ investment choices. Earlier in the paper, we report evidence that there might be disproportionate differences in the value of the project to each partner if one partner contributes most of the ﬁnancing or real assets needed for the joint venture to proceed. In view of this, the second column of Table 6 replicates the

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Table 6. Extended Regression Analysis of the Determinants of the Relative Size Effect in Contributions to Value-Weighted Portfolio Abnormal Return for 122 Partners to 61 Joint Venture Announcements (1972–1990). Regressor

N ¼ 61 Coefﬁcient

N ¼ 36 Coefﬁcient

Constant

0.167 (2.93) 0.046 (2.33) 0.035 (1.071) 0.028 (1.23) 0.070 (2.68) 0.056 (3.16) 0.017 (0.98) 0.116 (1.65) 0.187 (2.62) 0.000001 (1.05) 0.000002 (0.88) 0.249 (0.86) 1.129 (2.57)

0.243 (3.87) 0.084 (2.97) 0.061 (1.99) 0.030 (0.55) 0.085 (1.90) 0.065 (2.64) 0.043 (1.91) 0.128 (1.80) 0.265 (2.62) 0.000001 (1.58) 0.000003 (1.15) 0.199 (0.33) 1.172 (2.18)

0.379 0.224

0.524 0.277

Indicator variable: one if larger partner has greater percentage of insider holdings Indicator variable: one if larger partner has greater debt-toequity ratio Indicator variable: one if larger partner has Tobin’s q41 Indicator variable: one if smaller partner has Tobin’s q41 Indicator variable: one if the joint venture is in the larger partner’s industry Indicator variable: one if the joint venture is in the smaller partner’s industry Ownership share of larger partner Ownership share of smaller partner Equity value of larger partner Equity value of smaller partner Cash ﬂow-to-assets ratio of larger partner indicator variable: one if larger partner has qo1 Cash ﬂow-to-assets ratio of smaller partner indicator variable: One if smaller partner has qo R2 Adjusted R2

Note: The table reports the results of regressions based on Proposition 3. The dependent variable in each regression is the difference between the larger partner’s and smaller partner’s contribution to the portfolio abnormal return, that is, DC1C2. The regression in the ﬁrst column uses the full cross-sectional sample of 61 joint venture announcements. The regression in the second column uses a restricted sample containing only those announcements where neither partner is clearly identiﬁed in the announcement as supplying a disproportionate amount of the ﬁnancing or real assets to the joint venture. Coefﬁcients and t-statistics (in parentheses) are presented for each regression model. All test statistics are calculated using a heteroskedasticity-consistent covariance matrix. Signiﬁcant at the 10% level in a two-tailed test. Signiﬁcant at the 5% level in a two-tailed test. Signiﬁcant at the 1% level in a two-tailed test.

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current analysis for a restricted sample. According to Proposition 3, such project-value effects are incorporated in the error term of our regression and could lead to biased coefﬁcient estimates.32 Thus, we have performed the same analysis for a subsample of joint ventures in which no partner contributes disproportionate ﬁnancing or real assets. With no crosssectional variation on this count, induced biases on other coefﬁcients (except the intercept) are prevented. The results of this regression are very similar to the one reported above, indicating that no important biases have been induced. We have also estimated a version of this regression (not reported in the table) that includes indicator variables for disproportionate contributions of ﬁnancing and real assets. The corresponding regression coefﬁcients are very small, statistically insigniﬁcant, and the other coefﬁcients are unchanged.

5.3. Could Partners’ Stock-Price Reaction Differences be Due to Signaling The previous section presents evidence that the large differences in jointventure partners’ stock price reactions can be statistically explained by characteristics indicative of the extent of shareholder–manager agency problems. Two of the explanatory variables, Tobin’s q and insider holdings, are also associated with signaling explanations for stock price reactions to corporate announcements. Recall that the Tobin’s q regressor is not inﬂuential, but that the insider holding indicator is signiﬁcant. The insider holdings coefﬁcient is consistent with the idea that a difference in the efﬁcacy of signaling via investments explains part of the cross-partner difference in contributions.33 The cash ﬂow signaling hypothesis holds that managers may optimally announce costly deviations from actions that would be optimal in a fullinformation equilibrium in order to convincingly signal valuable but otherwise-unobservable information to the market. In this section, we investigate signaling as an alternative interpretation of our results. In the context of joint ventures, signaling has several possible meanings: The investment in the joint venture functions as a signal of quality that is common to both partners. The investment in the joint venture by one partner functions as a signal of quality for the other. The investment in the joint venture by each partner functions as a separate signal of quality for that partner.

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Additionally, signaling could refer to mixtures of these ideas. The ﬁrst rendition of the signaling hypothesis is not a plausible explanation for large differences in partners’ stock price reactions to the same joint venture announcement. If the joint venture is a common signal for both partners, then it should induce similar changes in each partner’s value. We have already investigated on aspect of the second rendition of the signaling hypothesis, and found it to have limited explanatory power. When one partner provides disproportionate funding for the joint venture, the difference in partners’ stock price reactions is greater. This seems to be evidence of a certiﬁcation effect. However, when the other partner contributes disproportionate real assets, as is frequently the case, there is an offsetting negative effect. This pattern does not seem in keeping with the idea that a larger partner, acting essentially as a ‘‘banker,’’ certiﬁes the value of the smaller partner’s contributed assets. However, these prior results do not show that the second rendition of the signaling hypothesis is without empirical content. It may be that the very presence of investment by a larger partner is taken as a signal of that partner’s conﬁdence in the smaller partner. If the market views the larger partner as specially qualiﬁed to judge the smaller partner’s value, then we might expect a larger reaction for the smaller partner. If we assume that the market considers the larger partner to be a better judge of the value of smaller partner’s assets when the larger and smaller partners are in the same industry, then this notion is testable. Under this assumption, partners in the same industry should experience more disparate stock price reactions under the certiﬁcation hypothesis. To check this possibility, we replicate our earlier regression analyses of differences in partners’ contribution measures with the addition of another explanatory variable. This variable is equal to one if both joint venture partners are in the same four-digit SIC industry, and zero otherwise. The results are categorical and hold for all speciﬁcations: the difference in partners’ stock price reactions is completely unrelated to the new regressor. Thus, we are unable to generate further support for this second form of the signaling hypothesis. For the third rendition of the signaling hypothesis, in which partners’ investments signal only that partner’s value, we can obtain predictions from standard models of signaling via corporate investments (e.g., Trueman, 1986; Ambarish, John, & Williams, 1987; John & Mishra, 1990). The earliest models in this vein predict that the stock price reaction to unexpected corporate investment should be positive, as over-investment serves as an unambiguous signal of ﬁrm quality. However, these models do not predict

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large signaling-based differences in stock price reactions, for both partners are undertaking the same investment. Later ‘‘efﬁcient’’ signaling models, such as John and Mishra (1990), indicate that different types of ﬁrms optimally signal differently. In particular, growth ﬁrms effectively signal quality by over-investing relative to the full-information equilibrium, whereas declining ﬁrms signal quality by under-investing. Since both partners to a joint venture announce a largerthan-expected investment, we might expect differences in stock price reaction if only one of the partners is a growth ﬁrm. John and Mishra suggest using Tobin’s q as an indicator of growth versus declining ﬁrms. To check on the efﬁcacy of this form of the signaling hypothesis, we again replicate our earlier regression analyses. This time we added two indicator variables. The ﬁrst indicator is equal to one if the larger partner has q greater than one and the smaller partner has q less than one. The second indicator is analogous: it equals one when the larger partner has q less than one and the smaller partner has q greater than one. The indicators are set to zero if the respective condition does not hold. The signaling hypothesis predicts that the coefﬁcient on the ﬁrst indicator should be positive and the coefﬁcient on the second regressor should be negative. That is, when the larger partner has a high q, it is hypothesized to gain from the investment announcement whereas a low-q smaller partner is not. The difference in their stock price reactions should be large in this circumstance. Similar reasoning leads to the prediction of a negative inﬂuence for the other indicator. The results of this test indicate that for cases in which the larger ﬁrm has a high q and the smaller ﬁrm has a low q, the difference in their stock price reactions is in fact signiﬁcantly larger. This indicator variable is able to account for about 1/3 of the average difference between larger and smaller partner reactions. This conclusion holds for all speciﬁcations tested. However, the second indicator variable, which should be accorded a negative inﬂuence, is never inﬂuential in any speciﬁcation. Thus the results on this third rendition of the signaling hypothesis are mixed.

6. CONCLUSION We provide evidence that the stock price reactions to joint venture announcements deviate substantially from the unanticipated net present value of the project. Partners to the same joint venture experience sharply different stock price reactions even after adjusting for differences in ﬁrm size and ownership share in the project. Furthermore, these differences in

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partner reactions cannot be explained by differences in the partner roles in the project or differences in expectations regarding the joint venture announcement. That is, the announcement reveals information that the market considers relevant for valuing the ﬁrm apart from the joint venture itself. Systematic cross-partner differences in the stock price reactions to joint-venture announcements suggest that event studies of corporate investment announcements should be interpreted broadly as reﬂecting both project and extra-project information. We ﬁnd evidence that ﬁrm characteristics, indicative of the extent of shareholder–manager agency problems, can explain a signiﬁcant portion of the observed differences in joint venture partners’ stock price reactions. Thus, investors learn about the importance of agency problems for the value of the whole ﬁrm (not just the value of the marginal project being announced) via the announcement of these joint investments. Finally, after controlling for the extent of agency problems, free cash ﬂow is found to be value-enhancing for some partner ﬁrms rather than an indication of the potential for agency problems in the way that others have used it. Our evidence supports the view that investors condition their reaction to managers’ decisions on what they know of the manager’s tendency to pursue non-shareholder goals. Moreover, because the evidence centers on extraproject information, it implies that a substantial component of the stock price reactions to joint ventures reﬂects the market’s assessment of how much ﬁrm value, independent of the project, must be revised to reﬂect what the market has learned from management’s decision to undertake this joint venture. By differencing the size- and share-adjusted price reactions of partners to the same joint venture, we effectively net out the project value effects and are left with differences in the revaluation of the partner ﬁrms due to extraproject information. Differencing could fail to eliminate important sources of project-related differences if the project is not equally unanticipated for all partners or if the project investment/beneﬁt is not shared among partners in proportion to their ownership shares. Although we include control variables in our analysis designed to register the effects of these possibilities, some of their effects may have ﬁltered through. However, it appears implausible that project-value inﬂuences could explain differences of the magnitude we observe.

NOTES 1. For example, McConnell and Muscarella (1985) state that ‘‘(t)he positive revaluation associated with unexpected capital expenditure increases comes about

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because the market immediately capitalizes the incremental positive net present value associated with the unexpected projects to be undertaken by the ﬁrm.’’ Similarly, with respect to joint venture announcements, McConnell and Nantell (1985) comment that ‘‘we have attributed the entire market reaction to joint venture announcements to the joint venture per se.’’ 2. Bhagat and Hirshleifer (1993) is another paper in the takeover literature with relevance to our work. They use a pair of stock price reactions to separate the valueenhancing effects of takeover announcements from their information effects, analogous to our use of a pair of stock price reactions to separate project and extra-project effects. 3. We also allow for the possibility that the benﬁt of the joint venture project is not split among the partners according to ownership share, though we can uncover little evidence of this. 4. The substantial explanatory power of simple cross-sectional regressions is also evidence that cross-partner differences are not simply the result of ‘‘noise’’ in stock prices. However, substantial cross-sectional variation is also unexplained, leaving room for other explantions. 5. Other authors also focus on the value-weighted portfolio return for similar reasons, e.g., Lang, Stulz, and Walkling (1989). 6. Malatesta (1983) focuses directly on the dollar-valued abnormal returns rather than a percentage version. We focus on percentage reactions because our data contains a diversity of partner and joint venture sizes. Thus, the scaled reactions can more appropriately be summarized as cross-sectional averages. With dollar value reactions, given a wide range of sample ﬁrm sizes, a few observations for very large ﬁrms could dominate, leading to erroneous inferences. Also, for our sample, the distribution of scaled reactions is closer to the normal distribution. Bradley, Desai, and Kim (1983) also discuss statistical difﬁculties in making inferences about dollar value reactions to corporate events. By focusing on value-weighted returns (i.e., total dollar reaction divided by total ﬁrm size), we are able to use a sensible measure of the value of the reaction that has well-known statistical properties. A cost to our approach is a greater chance that a meaningful reaction is lost in background noise. 7. In A4, a partner’s investment in a joint venture project is taken to include all value contributed, including real assets, patents, technologies, etc. Beneﬁts include all synergies. Investing and beneﬁting in proportion to ownership share precludes any reallocations of wealth between the partners. Such reallocations would be present if the beneﬁts of synergies accrue independently of ownership share, or if there are differences in bargaining power, which allow one partner to obtain an ownership share that is more than proportional to its investment. 8. The reason Eq. (4) holds under the assumptions is this: the weighted sum of measured contributions, found in Eq. (3), is equal to the unanticipated project value (as a proportion of the partners’ total value) only if Eq. (4) describes the component contributions C1 and C2. 9. In this case, the methodology must allow for the fact that the error term depends on PCðE 1 þ E 2 Þ: 10. One sample observation for 1979 is also in McConnell and Nantell’s sample. 11. This is illustrated by the following example: ‘‘Endotronics Inc. said it signed an agreement with Summa Medical Corp, Albuquerque, N.M. to form a joint

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venture to produce biologicals on a contract basis. Endotronics said the venture will be equally owned by both companies.’’ (WSJ, 1985, March 20). 12. For example, in the case of the Conrail and OHM joint venture, we determine that each partner owns half of the joint venture since each contributes equally to the total investment: ‘‘The joint venture will be funded with $10 million of equity, with contributions of $5 million each to be made by Conrail and OHM.’’ (WSJ, 1989, April 11). 13. Fifty-four of the joint ventures in our sample are recent enough to be listed on the I/BE/S tapes. While the larger partners clearly generate an analyst following (about 9.5 analysts per ﬁrm on average, with the largest ﬁrms having nearly 30 analysts following them), the smaller partners are much less closely followed. The average smaller partner has less than 4.5 analysts following it, and the 75th percentile observation is only 6. Most strikingly, the analyst following of the smaller partner is zero in almost half of the cases. 14. Long-event windows have been used for similar reasons in other settings, notably, the division of takeover gains, a situation that is in some ways similar to a joint venture. See McConnell and Nantell (1985) for discussion on this point. 15. We investigate the sensitivity of our regression results (presented later) to the choice of a seven-day event window by using two-day abnormal returns for the group of larger partners and seven-day abnormal returns for the smaller partners. The results are very similar to those presented, and all economic conclusions are identical. 16. In a previous version of this paper, we reported a parallel investigation of cross-partner differences grouped by the shareholdings of corporate insiders and by Tobin’s q, characteristics also thought to be correlated with the severity of agency problems. This investigation leads to the same conclusions as when differences are grouped by equity value. 17. Though not directly relevant to our arguments, we note for completeness that the mean abnormal return to an equally weighted portfolio, 1.00%, is statistically signiﬁcant at conventional levels. The mean abnormal return to a value-weighted portfolio, 0.35%, which is dominated by the very small mean abnormal reaction of larger partners, is not statistically signiﬁcant. 18. We attribute abnormal returns to the joint venture announcement. Since a joint venture could be the ﬁrst step in a merger between the two parents, it is possible that the abnormal returns should actually be interpreted as takeover premia. Cusatis, Miles, and Woolridge (1993) provide evidence that this explains part of the stock price reaction to spinoffs. This is not the case in this sample. None of the ﬁrms in our sample merge with each other (or any other company) during the ﬁve years following their venture. Only two ﬁrms in the sample, Pegasus and Merck, were involved in any takeover-related news at all during that ﬁve-year period. 19. Differences would also result if the degree to which the joint venture is anticipated differs across ﬁrms. We have addressed this concern with additional analysis. First, as we noted earlier, there was no indication in the announcements that any of the sample joint ventures was a part of a pre-announced program. Additionally, we have examined reports of all joint venture activity within ﬁve years by ﬁrms in our sample in the Wall Street Journal Index, whether or not that activity results in an observation in our sample. We ﬁnd that 82 of 170 partners were

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involved in some previous joint venture activity, with the median (mean) time between the most recent previous activity and the sample announcement being 419 (528) days. The cumulative abnormal return for partners that had engaged in a previous joint venture (0.4%) is actually larger than, although insigniﬁcantly different from, those who had not (0.2%). A few ﬁrms show activity in the very recent past (less than 75 days), and we have checked that the corresponding sample points are not the source of the differences documented below. Overall, the assumption that prior announcement probabilities are equal across partners seems justiﬁed. 20. The exact signiﬁcance level for the full sample is 0.0551. 21. In tests not reported in the table, we ﬁnd that the difference of larger and smaller partners’ abnormal returns is also signiﬁcantly non-zero. 22. The average investment for this subsample is larger due to one outlier of 1.36 billion dollars. With this exception, all observations involve less than $400 million in investment. Seventeen of the twenty-seven involve less than $100 million. 23. While there are certainly other relevant questions that could be posed, we do not believe there would be any cross-sectional variation in the responses. The joint venture announcements do not often provide extensive detail about the projects. We have posed as many relevant questions as the data will answer. 24. All regression test statistics are calculated with a heteroskedasticity-consistent covariance matrix. 25. Interestingly, the hypothesis that all slopes are equal in absolute value and of the sign predicted by the proposition cannot be rejected at conventional signiﬁcance levels. 26. This is consistent with the idea that a smaller company with an attractive opportunity might have difﬁculty obtaining sufﬁcient ﬁnancing. In this situation, a larger partner to 1/4 with excess funds who understands the value of the project would be an attractive partner. 27. Speciﬁcally, the percentage of insider ownership, free cash ﬂow as a percentage of assets, and Tobin’s q for the smaller partners average 19.3 and 1.48, respectively. The corresponding ﬁgures for larger partners are 19.4 and 1.15. 28. Morck et al. (1988) ﬁnd evidence that levels of insider ownership beyond a cutoff point lead to entrenched managements that can pursue their own goals. We have experimented to see if the nature of the results we report changes if we allow for such a possibility. We have been unable to reverse the results reported here. 29. When we rely on Spectrum 6 data, we are careful to correct for the doublecounting, which is known to occur in data from this source. 30. Speciﬁcally, we use a shorter time series of Compustat data in calculating replacement value and the market value of debt, which allows more ﬁrms to be included in the analysis, and is particularly useful in retaining small companies. In about one-third of the cases for which all other variables were available, we did not have sufﬁcient historical data to compute the q’s. We retained these ﬁrms nonetheless, provided that a book-value proxy for q could be computed from Compustat and CRSP data. From ﬁrms where both q’s are available, we know that the two measures are highly correlated (r40.9), but that Compustat q’s tend to be somewhat larger (by about 0.2). To enable comparisons between the Compustat q’s and the Lindenberg-Ross q’s, we compute a proxy for the Lindenberg-Ross q as a

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ARTHUR J. KEOWN ET AL.

ﬁtted value based on a linear regression of available Lindenberg-Ross q’s on book q’s from ﬁrms where both q’s are available. The fact that q is used only as the basis for indicator variables reduces concerns about measurement inaccuracies. 31. Using log equity value rather than its level does not affect results in any important way. 32. Proposition 3 also indicates that the error may depend on partners’ ownership shares, but this inﬂuence is only important when shares differ across partners, which is seldom the case in our sample. 33. Even so, the importance of regressors motivated by the agency explanation, but which do not have strong motivation as variables related to signalling, indicates that the agency explanation has independent explanatory power.

ACKNOWLEDGMENTS We thank Stephen Brown, Diane Denis, Martin Gruber, Robert Hansen, John Kensinger, Wayne Mikkelson, Robert Parrino, Richard Roll, A.J. Senchack, Seha Tinic, Michael Vetsuypens, and Michael Weisbach. We thank John McConnell and Timothy Nantell for sharing their sample of joint venture announcements. This paper is based on one that was presented at the American Finance Association Meetings.

REFERENCES Ambarish, R., John, K., & Williams, J. (1987). Efﬁcient signaling with dividends and investment. The Journal of Finance, 42(2), 321–343. Berle, A., & Means, G. (1932). The modern corporation and private property. New York: Harcourt, Brace, and World. Bhagat, S., & Hirshleifer, D. (1993). Market based estimates of value gains from takeovers: An intervention approach. Working paper, Anderson School of Business. Boehmer, E., Musumecci, J., & Poulsen, A. (1991). Event study methodology under conditions of event-induced variance. Journal of Financial Economics, 30(2), 231–252. Bradley, M., Deseai, A., & Kim, E. H. (1983). The rationale behind interﬁrm tender offers. Journal of Financial Economics, 11(1), 183–206. Brennan, M. (1990). Latent assets. The Journal of Finance, 45(3), 709–730. Collins, D., & Dent, W. (1984). A comparison of alternative testing methodologies used in capital market research. Journal of Accounting Research, 22(1), 48–84. Comment, R., & Jarrell, G. (1995). Corporate focus and stock returns. Journal of Financial Economics, 37, 67–87. Fama, E. (1985). What’s different about banks? Journal of Monetary Economics, 15(1), 29–39. Fazzari, S., Hubbard, R. G., & Petersen, B. (1988). Financing constraints and corporate investments. Brookings Papers on Economic Activity, 1, 141–206. James, C. (1987). Some Evidence on the Uniqueness of Bank Loans. Journal of Financial Economics, 19(2), 217–236.

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Jensen, M. (1986). Agency costs of free cash ﬂow, corporate ﬁnance, and takeovers. American Economic Review, 76(2), 323–329. John, K., & Mishra, B. (1990). Information content of insider trading around corporate announcements: The case of capital expenditures. The Journal of Finance, 45(3), 119–136. Judge, G., Grifﬁths, W. E., Hill, R. C., Lu¨tkepohl, H., & Lee, T.-C. (1985). The theory and practice of econometrics (2nd ed.). New York: John Wiley and Sons. Lang, L., & Litzenberger, R. (1989). Dividend announcements: Free cash ﬂow or signalling? Journal of Financial Economics, 24, 181–191. Lang, L., Stulz, R., & Walkling, R. (1989). Managerial performance, Tobin’s q, and the gain from successful tender offers. Journal of Financial Economics, 24(1), 137–154. Lehn, K., & Poulsen, A. (1989). Free cash ﬂow and stockholder gains in going private transactions. The Journal of Finance, 44, 771–789. Leland, H., & Pyle, D. (1977). Information asymmetrics, ﬁnancial structure and ﬁnancial intermediation. The Journal of Finance, 32(2), 371–387. Lindenberg, E., & Ross, S. (1981). Tobin’s q ratio and industrial organization. The Journal of Business, 54(1), 1–32. Malatesta, P. (1983). The wealth effect of merger activity and the objective function of merging ﬁrms. Journal of Financial Economics, 11(1–4), 155–182. McConnell, J., & Muscarella, C. (1985). Corporate capital expenditure decisions and the market value of the ﬁrm. Journal of Financial Economics, 14, 399–442. McConnell, J., & Nantell, T. (1985). Corporate combinations and common stock returns: The case of joint ventures. The Journal of Finance, 40(2), 519–536. Morck, R., Shleifer, A., & Vishny, R. (1988). Management ownership and market valuation: An empirical analysis. Journal of Financial Economics, 20(1–2), 293–316. Myers, S., & Majluf, N. (1984). Corporate ﬁnancing and investing decisions when ﬁrms have information that investors do not have. Journal of Financial Economics, 13(2), 197–221. Patell, J. (1976). Corporate forecasts of earnings per share and stock price behavior. Journal of Accounting Research, 14, 246–276. Roll, R. (1986). The hubris hypothesis of corporate takeovers. The Journal of Business, 59(2)(Part 1), 197–216. Trueman, B. (1986). The relationship between the level of capital expenditures and ﬁrm value. Journal of Financial and Qunatitative Analysis, 21(2), 115–129.

APPENDIX Z-Statistics for Testing Hypotheses about Contributions Referring to the contribution of the partner in group jðj ¼ 1; 2Þ for the kth sample joint venture as Cj,k and subscripting other data items analogously, it follows from Eq. (2) that an unbiased estimator of the mean contribution of group-j partners is ¯j ¼ C

N X k¼1

S j;k

uj;k E j;k =N E 1;k þ E 2;k

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ARTHUR J. KEOWN ET AL.

where N is the number of sample joint ventures. We measure equity value as the product of the stock price just before the event period and the number of shares outstanding at the end of the previous calendar year from Compustat. Assuming cross-sectional independence of the uj,k, an unbiased estimate of the standard error of the mean contribution is vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ !2 u N uX E j;k t =N sðC¯ j Þ ¼ s2 ðuj;k Þ S j;k E 1;k þ E 2;k k¼1 where s2(uj,k) is an unbiased estimate of an abnormal return’s standard deviation computed in the manner of Patell (1976). We use the results to form z-statistics to test hypotheses about the contribution of a speciﬁc group of partners. An unbiased estimator of the difference in contributions between two groups is given by the difference of the mean contributions for each group D ¼ C1 C2 Then the standard error of the difference is N X E 1;k E 2;k ¯ ¼ s 2 ðC ¯ 1 Þ þ s 2 ðC ¯ 2Þ 2 s 2 ðDÞ s ðu1;k ; u2;k Þ N k¼1 S 1;k S2;k E 1;k þ E 2;k

where s(u1,k,u2,k) is an unbiased estimator of the covariance between the contributions of the two partners to a particular joint venture k. Collins and Dent show how to compute this covariance using the market-model residuals in the pre-event period.

A w2 Test Statistic for Unordered Differences in Partner’s Contributions Let N represent the number of joint venture announcements, and let C be the (1 2N) vector of all partners’ contributions, arranged so that partners to the same joint venture are adjacent. To evaluate the validity of the restriction that the contributions of both partners to the same joint venture

Information Content of Corporate Investment Announcements

are equal, also reﬁne the 2 1 1 60 0 6 6 0 0 R¼6 6 .. 6 .. 4. . 0 0

71

(N 2N) matrix R as 0 1

0 1

0 0

0 0

... ...

0 0 0 0

0 0

0 .. . 0

0 .. . 0

1 .. . 0

1 .. . 0

... .. . 0

0 0 .. .. . . 0 0

0 .. . 1

3 0 0 7 7 7 0 7 7 .. 7 . 5 1

Also let S represent the (2N 2N) covariance matrix of the elements of C, computed using the approach of Collins and Dent (1984) and the assumption that only contributions to the same joint venture have nonzero correlations. Then, assuming the joint normality of the elements of C, the statistic CTRT(RTSR)1RC is distributed as a w2 random variable with N degrees of freedom under the null hypothesis that both elements of C corresponding to each particular joint venture are equal (see, for example, Judge, Hill, Grifﬁths, Lu¨tkepohl, & Lee, 1985, p. 185).

AN EXPANDED STUDY ON THE STOCK MARKET TEMPERATURE ANOMALY Melanie Cao and Jason Wei ABSTRACT This is a companion paper to our previous study in Cao and Wei (2005) on stock market temperature anomaly for eight international stock markets. The temperature anomaly is characterized by a negative relationship between stock market returns and temperature. This line of work relies on the impact of environmental variables, such as temperature, on mood and behavior changes. In this paper, we expand the sample in Cao and Wei (2005) to include 19 additional financial markets. Our evidence confirms the identified negative relationship for the expanded sample. More importantly, our nonparametric tests, as opposite to the parametric or semiparametric approaches used by previous related studies, demonstrate that this negative relationship is robust to distributional assumptions. Based on the sub-sample analysis, we find that this negative relationship is stable over time. Furthermore, we consider temperature deviation and demonstrate that this negative relationship is not just a level effect.

Recently, there are four main studies linking the stock market return anomaly to nature-related variables such as the amount of sunshine, the length of Research in Finance, Volume 22, 73–112 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22003-8

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daylight and temperature.1 In particular, Saunders (1993) is the ﬁrst study which examines the relationship between stock market returns and the amount of sunshine. Focusing on the city of New York for the period of 1927–1989, Saunders (1993) demonstrates that less cloud cover is associated with higher returns for the DJIA index, the NYSE/AMEX value-weighted index, and the NYSE/AMEX equal-weighted index, and the returns on most cloudy days are significantly different from the returns on the least cloudy days. Hirshleifer and Shumway (2003, hereafter HS) conﬁrm these results for 26 international stock markets for the period of 1982–1997. The common conjecture made by these three authors is that investors’ mood is upbeat or optimistic on sunny (or least cloudy) days, which uplifts the stock market returns, and that their pessimistic mood on cloudy days depresses the stock returns. Kamstra, Kramer, and Levi (2003, hereafter KKL) draw a link between stock market returns and the length of daylight. By examining the stock returns in the US, Canada, UK and Germany and a few other countries, they ﬁnd that lower returns are associated with longer nights. Their explanation rests on the impact of seasonal affective disorder (SAD) on human behavior. Based on the psychological and clinical evidence, the authors conjecture that lower returns are caused by investors who are depressed because of longer nights. In a recent study in Cao and Wei (2005, hereafter CW), we examine the linkage between temperature and stock returns for the US, Canada, Britain, Germany, Sweden, Australia, Japan and Taiwan. We ﬁnd that stock returns are negatively correlated with temperature. That is, the lower the temperature, the higher the return, and vice versa. This negative correlation is statistically significant. Such a negative relationship still remains even after controlling for the above-mentioned sunshine and SAD effects. Similar to Saunders (1993), HS (2003) and KKL (2003), we conjecture that this relationship is attributed to temperature impacts on human behavior. In particular, the psychological literature indicates that very high or very low temperatures cause aggression and very high temperature can also induce hysteria and apathy.2 Given this psychological ﬁnding, we hypothesize that lower temperature is associated with higher stock returns due to aggressive risk taking while high temperature can lead to either higher or lower stock returns since both aggression (associated with risk taking) and apathy (associated with risk averting) are possible consequences. The net impact on investors’ risk taking depends on the trade off between the two. Apparently, the common feature shared by these studies is this chain of thinking: environmental variables, such as sunshine, length of daylight and temperature, affect people’s mood which in turn inﬂuences people’s behavior.

An Expanded Study on the Stock Market Temperature Anomaly

75

Such thinking is motivated and supported by literature on mood and decision-making. For example, Schwarz (1990), and Loewenstein, Weber, Hsee, and Welch (2001) provided theories linking mood and feelings to general decision-making, while Etzioni (1988), Romer (2000) and Hanock (2002) established the importance of emotions in economic decision-making. Mehra and Sah (2002) showed theoretically that the emotional state of investors would inﬂuence equity prices when investors’ subjective parameters such as risk-aversion change in response to mood ﬂuctuations. This line of research has taken its roots in mainstream ﬁnancial research. As a result, in order to better understand these nature-related stock market anomalies, more studies are needed. The current paper, a sequel study to our previous work (CW, 2005), is intended to fulﬁll this objective. We propose alternative tests and provide additional evidence to support the uncovered stock market temperature anomaly. In particular, we perform the bin test and regression analysis used in CW (2005) for an expanded sample which includes 27 international markets. Moreover, we use alternative tests (including nonparametric methods) to further examine the relationship between temperature and stock returns. Our additional tests and results (using either CW’s original sample or an expanded data set) conﬁrm the uncovered stock market temperature anomaly documented in CW (2005). The rest of the paper is organized as follows. Section 1 briefly describes the expanded data set and reports summary statistics of returns and temperatures for the 27 international stock markets and locations. Section 2 applies the bin test and regression analysis developed by CW (2005) to the expanded data set, and demonstrates that the uncovered negative relationship between temperature and stock returns remains for a much wider range of ﬁnancial markets. Section 3 proposes alternative testing methods to further examine the temperature anomaly. Our new evidence shows that the uncovered temperature anomaly is robust to distributional assumptions and is not just a level effect. Section 4 concludes the paper.

1. DATA As stated earlier, the current paper is a companion work to CW (2005). To be consistent, we utilize the original data, which includes nine international stock indices, covering eight ﬁnancial markets in the United States, Canada, Britain, Germany, Sweden, Australia, Japan and Taiwan. In addition, we expand the data set to include 19 other nonoverlapping ﬁnancial markets studied by either HS (2003) or KKL (2003). As noted in CW (2005), the

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stock index data are retrieved from Datastream while the temperature data are purchased from the Earth Satellite Corporation (EarthSat).3 Following HS (2003), the temperature data for the additional 19 locations are obtained from the national climate data center (NCDC). The corresponding stock markets are either represented by the Datastream Global Indices, or by local market indices which cover a longer sample period. The temperature variable is the average of the daily maximum and minimum temperatures, which we simply refer to as ‘‘daily temperature.’’ For a given sample period, there are always more observations for temperature than for returns since the latter can only be observed for trading days. To perform empirical analysis, the return and temperature series have to be matched. That is, temperature observations for holidays and weekends need to be removed. After matching for the eight ﬁnancial markets in CW (2005), Sweden has the smallest sample size of 3,129 while the US has the largest sample size of 9,442. This data set is called ‘‘the full sample’’ set in CW (2005) since they cover each market’s longest possible period. To facilitate seemingly unrelated regressions and to ensure comparability of results, an ‘‘equal-sized sample’’ is also created in CW (2005) by matching all indices and temperatures across markets within the common sample period of January 2, 1989–December 31, 1999. The equal-sized sample has 2,252 observations from each market. As for the 19 additional locations, temperature data from the NCDC are limited to the sample period of 1982–1997. Also, some indices have starting dates later than 1982. In contrast to the temperature data obtained from EarthSat, the temperature data from the NCDC are typically incomplete (i.e., with many missing observations) and sometimes contain errors (e.g., some temperatures are higher than 3001C). After deleting the obvious erroneous observations for each location, we end up with the number of observations as shown in Table 1. The corresponding ‘‘equal-sized sample’’ for the 27 international markets overlaps from 1989 to 1997 with total observations of 1,509 for each location. Table 1 presents city locations, countries/state, sample periods and summary statistics of daily returns and daily temperatures. For daily returns, the mean ranges from 0.005% for Japan to 0.662% for Brazil. The standard deviation varies across indices, with Argentina being the most volatile market at 3.775% and the CRSP equal-weighted index the least volatile at 0.68%. The largest single-day loss was 28.71%, experienced in Australia during the October 1987 crash. The largest single-day gain was 26.182%, experienced in Argentina. Most of the index returns exhibit negative skewness and strong kurtosis.4

City, Country/State

Latitude

Summary Statistics.

Sample Period

Daily Return (%) No. of obs.

Panel A: Daily Returns

Mean

Std. dev.

Min

Skew

Kurt

New York, U.S.A (CRSP-EW) New York, U.S.A (CRSP-VW) Toronto, Canada London, Britain Frankfurt, Germany Stockholm, Sweden Sydney, Australia Tokyo, Japan Taipei, Taiwan

Financial 411460 N 411460 N 431410 N 511290 N 501030 N 501210 N 331570 S 351410 N 251020 N

6.944 8.669 8.650 7.597 8.862 13.142 5.739 12.430 7.581

1.110 1.120 1.130 0.990 0.480 0.320 6.160 0.120 0.270

16.980 26.220 16.470 13.900 8.050 6.200 162.380 9.170 2.810

and KKL (2003) 11.032 7.936 14.632 15.311 12.788 9.153 19.612 26.182 8.929 6.009 15.485 8.700 12.540 8.742 12.220 13.165 14.528 7.915 17.067 11.666 9.734 6.939 15.786 15.657 8.435 8.402

0.645 0.070 0.248 1.363 0.577 1.277 0.532 0.097 1.392 1.080 0.387 0.052 0.185

13.120 10.334 14.118 8.133 8.045 23.335 11.759 2.324 15.836 19.328 7.885 10.369 4.363

Markets and Locations Examined in CW (2005) 62–99 9,442 0.0075 0.068 10.484 62–99 9,442 0.051 0.821 17.173 77–01 6,099 0.036 0.850 12.010 84–01 4,285 0.038 0.985 13.029 70–01 7,901 0.028 1.124 13.706 89–01 3,129 0.054 1.426 7.491 84–00 4,145 0.036 1.012 28.713 84–01 4,314 0.005 1.364 16.135 77–01 6,777 0.037 1.675 9.710

Additional Financial Markets and Locations Examined in HS (2003) 82–97 4,173 0.056 0.887 Amsterdam, Netherlands 521180 N Athens, Greece 371540 N 88–97 2,607 0.082 1.756 Auckland, New Zealand 371010 N 88–97 2,608 0.024 1.181 Buenos Aires, Argentina 341490 S 88–97 2,605 0.418 3.775 82–97 4,173 0.054 0.869 Copenhagen, Demark 551380 N Dublin, Ireland 531260 N 82–97 4,173 0.063 1.043 Helsinki, Finland 601190 N 87–97 2,869 0.041 1.104 88–97 2,607 0.241 2.606 Istanbul, Turkey 401580 N Johannesburg, South Africa 261080 N 82–97 4,173 0.067 1.236 Kuala Lumpur, Malaysia 031070 N 82–97 4,174 0.011 1.403 Madrid, Spain 401270 N 82–97 4,174 0.058 1.015 86–97 3,130 0.085 1.878 Manila, Philippines 141310 N Milan, Italy 451260 N 82–97 4,173 0.043 1.221

77

Max

a

An Expanded Study on the Stock Market Temperature Anomaly

Table 1.

78

Table 1. (Continued ) City, Country/State

Oslo, Norway Paris, France Rio de Janeiro, Brazil Santiago, Chile Vienna, Austria Zurich, Switzerland

Latitude

0

60112 N 491010 N 221540 S 331230 S 481070 N 471230 N

Sample Period 82–97 82–97 86–97 87–97 83–97 82–97

Daily Return (%) No. of obs.

Mean

Std. dev.

Min

Max

Skew

Kurt

4,173 4,173 3,107 2,869 3,911 4,173

0.059 0.053 0.662 0.101 0.049 0.056

1.366 1.005 3.709 0.987 0.920 0.826

21.087 9.895 17.714 12.304 9.250 12.310

10.321 7.967 22.813 6.471 7.703 6.620

1.029 0.642 0.188 0.432 0.183 2.193

20.879 8.878 2.299 12.771 14.877 31.223

34.44 30.35 27.40 29.30 26.70 32.00 33.40 34.00

0.19 0.23 0.02 0.11 0.08 0.11 0.06 0.32

0.89 0.82 0.60 0.65 0.65 0.65 1.15 0.85

and KL (2003) 11.80 25.50 0.60 35.00 2.00 33.00 1.70 32.65 17.00 25.90 3.60 22.00 34.25 24.85 4.00 29.30

0.21 0.05 0.21 0.15 0.09 0.02 0.31 0.05

0.21 1.14 0.03 0.78 0.62 0.68 0.05 1.18

Panel B: Daily Temperature (Celsius)b

Amsterdam, Netherlands Athens, Greece Auckland, New Zealand Buenos Aires, Argentina Copenhangen, Demark Dublin, Ireland Helsinki, Finland Istanbul, Turkey

Financial 411460 N 431410 N 511290 N 501030 N 501210 N 331570 S 351410 N 251020 N

Markets and Locations 62–99 13,696 77–01 8,835 84–01 6,189 70–01 11,508 89–01 4,558 84–00 5,992 84–01 6,396 77–01 8,373

Examined in CW (2005) 12.71 9.62 16.39 7.61 10.59 24.70 11.23 5.67 7.55 10.08 7.41 14.20 6.97 7.78 20.95 18.30 4.10 8.15 16.34 7.91 0.90 22.81 5.50 1.55

Additional Financial Markets and Locations Examined in HS (2003) 82–97 5,778 9.74 6.08 521180 N 371540 N 88–97 3,604 18.01 7.11 371010 N 88–97 3,648 15.12 4.11 88–97 3,536 17.00 5.99 341490 S 551380 N 82–97 5,844 8.20 6.80 531260 N 82–97 5,796 9.79 4.39 87–97 3,955 4.94 8.80 601190 N 401580 N 88–97 3,264 14.53 7.49

MELANIE CAO AND JASON WEI

New York, U.S.A Toronto, Canada London, Britain Frankfurt, Germany Stockholm, Sweden Sydney, Australia Tokyo, Japan Taipei, Taiwan

a

261080 031070 401270 141310 451260 601120 491010 221540 331230 481070 471230

N N N N N N N S S N N

82–97 82–97 82–97 86–97 82–97 82–97 82–97 86–97 87–97 83–97 82–97

5,467 5,830 5,816 4,375 5,806 5,460 5,387 4,242 3,983 5,478 5,692

16.19 27.79 14.37 27.69 13.21 4.24 11.27 21.89 7.32 5.67 6.33

4.33 1.01 7.38 1.76 8.19 8.85 6.58 2.84 4.38 7.57 6.65

0.45 21.50 3.50 14.50 10.05 27.95 13.50 11.00 6.00 22.00 20.20

27.00 33.60 31.60 32.50 29.60 23.50 30.70 33.00 22.00 23.00 22.00

0.45 0.38 0.18 1.19 0.07 0.34 0.14 0.07 0.46 0.35 0.22

0.38 1.22 0.99 6.49 1.1 0.31 0.41 0.44 0.51 0.42 0.51

Daily returns are in percentage forms. For example, the mean return for Amsterdam is 0.056%. For daily temperature, due to missing observations, the number of observations across cities can be quite different even within the same sample period.

b

An Expanded Study on the Stock Market Temperature Anomaly

Johannesburg, South Africa Kuala Lumpur, Malaysia Madrid, Spain Manila, Philippines Milan, Italy Oslo, Norway Paris, France Rio de Janeiro, Brazil Santiago, Chile Vienna, Austria Zurich, Switzerland

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The average temperature ranges from 4.241C in Oslo, Norway to 27.791C in Kuala Lumpur, Malaysia. The standard deviation of daily temperature varies from 2.841C in Rio de Janeiro, Brazil to 10.591C in Toronto, Canada. The lowest temperature was 34.251C in Helsinki, Finland while the highest temperature was 35.001C in Athens, Greece. For most cities, the temperature series reﬂects a negative skewness, indicating that it is more common to have extremely cold days than extremely hot days. To illustrate the temperature progressions throughout the calendar year, we plot the historical average daily temperature for the four cities in Fig. 1: New York, London, Sydney and Tokyo.5 For cities on the Northern Hemisphere, seasonal temperature changes are similar, though the range of variations can be quite different. Naturally, an opposite pattern is observed for Sydney which is on the Southern Hemisphere. It is clear from Fig. 1 that Sydney has the smallest seasonal variation in temperature.

2. EMPIRICAL RESULTS OF BIN TESTS AND REGRESSION ANALYSIS In this section, we ﬁrst briefly recapitulate the two types of tests used in CW (2005). Then we perform these tests (with variations) for the original and the Tokyo

Sydney

London

New York

35.00

Historical Daily Average Temperature

30.00 25.00 20.00 15.00 10.00 5.00 0.00

0

30

60

90

120

150

180

210

240

270

300

Day of theYear

-5.00

Fig. 1.

Historical Daily Average Temperature.

330

360

An Expanded Study on the Stock Market Temperature Anomaly

81

expanded sample to ascertain the relationship between temperature and stock market returns uncovered in CW (2005). 2.1. Bin Tests In our previous study (CW, 2005), we use two main tests: the ‘‘Bin Test’’ and the ‘‘Regression Analysis.’’ The ‘‘Bin Test’’ is implemented by grouping returns according to temperature ordering and calculating a z-score to assess the statistical difference between return-groups. This test is semi-parametric in nature because of the ordering procedure. In particular, we sort the matched return and temperature data by temperature in ascending order, and then divide the sorted series into sub-groups or bins. For each temperature bin, we compute the mean return and the frequency or percentage of positive returns, then compare the mean returns associated with the lowest bin (i.e., the bin covering the lower spectrum of the temperature range) and the highest bin (i.e., the bin covering the higher spectrum of the temperature range) and determine whether the difference in mean returns is significant. Similar comparisons and tests are done for the percentage of positive returns of the two extreme bins. The purpose of examining the frequency of positive returns is to see if the return difference between bins is driven by outliers. If, for example, lower temperature is indeed associated with higher stock returns and vice versa, then we would expect that the higher returns in the low-temperature bin are broadly based. In other words, we would expect the percentage of positive returns to be high in the low-temperature bin. The precise testing procedure is as follows: First, we compute the difference between the maximum and minimum of the temperature series. Then, we divide the difference by the number of bins, k to obtain the temperature range of each bin. That is, D ¼ (TempmaxTempmin)/k. The ﬁrst bin contains temperatures in the range [Tempmin, Tempmin+D); the second bin contains temperatures in the range [Tempmin+D, Tempmin+2D); ... and so on. For example, if the maximum and minimum temperatures are 24 and 3, respectively, and the number of bins is 3, then the ﬁrst bin will contain temperatures ranging from 3 to 6, the second bin ranging from 6 to 15, and the third ranging from 15 to 24. To determine whether the mean returns associated with the highest temperature bin (i.e., bin k) and the lowest temperature bin (i.e., bin 1) are significantly different, we compute the following z statistic: mk m1 z_scoremean k;1 ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ s2k =nk þ s21 =n1

82

MELANIE CAO AND JASON WEI

where mi, si and ni stand for the mean return, the standard deviation of return and the number of observations in bin i(i ¼ 1 or k). A similar z statistic is calculated to determine whether the frequencies of positive returns are significantly different between the two extreme bins: pk p1 ﬃ z_scorefrequence ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ k;1 pk ð1 pk Þ=nk þ p1 ð1 p1 Þ=n1 where pi stands for the percentage of positive returns in bin i (i ¼ 1 or k). It can be argued that the potential heteroscedasticity in the variance estimators used to construct the z statistic should be largely absent for two reasons. First, the heteroscedasticity in the variance for the frequency of positive daily returns is ruled out because the variable measures a binomial outcome. Second, it is unlikely that the variance for daily percentage returns is heteroscedastic because the observations are grouped by temperature, a random exogenous factor. In daily or monthly return time series, heteroscedasticity is often present, as documented by French, Schwert, and Stambaugh (1987) and Schwert (1989). In CW (2005), we have only presented the ‘‘Bin Test’’ results for the 4-bin case with the ‘‘full sample’’ as well as the ‘‘equal-sized sample.’’ The 4-bin case divides temperature into four ranges. The test results show that there exists a strong negative correlation between temperature and return. That is, for all stock markets, the lower the temperature, the higher the returns, this relationship is generally monotonic. Recently, Keller et al. (2005) study the effects of temperature on mood and cognition. They conﬁrm that people tend to have aggression when temperature is either very high or very low. However, when temperature is in the middle range, say during spring, this aggression disappears and people tend to have clear minds. Their results seem to suggest that people’s mood is regulated by three different temperature ranges. Based on these ﬁndings, it is natural to conjecture that a test based on 3-bin division for temperature should exhibit a stronger negative relationship between temperature and returns. To conﬁrm this, we ﬁrst perform a 3-bin test for the ‘‘full sample’’ and the ‘‘equal-sized sample’’ (as opposite to the 4-bin case in CW, 2005), and then we use the expanded sample to conduct 3- and 4-bin tests. The 3-bin test results are presented in Table 2. Panel A of Table 2 is for the ‘‘full sample’’ while Panel B for the ‘‘equal-sized sample.’’ The results are stronger than the 4-bin tests in CW (2005), conﬁrming our conjecture made earlier. In particular, most z-scores are bigger than those for the 4-bin case. For example, for Britain, the z-score for the mean return of the full sample has increased from no significance for the 4-bin case to a 5% significance

bin 1 U.S. CRSP-EW

U.S. CRSP-VW

Canada

Britain

Germany

Sweden

Australia

Japan

0.0020 0.0064 0.6780 0.0009 0.0071 0.5855 0.0007 0.0082 0.5737 0.0016 0.0091 0.5702 0.0011 0.0108 0.5385 0.0022 0.0129 0.5613 0.0007 0.0080 0.5306 0.0006 0.0128 0.5380

Panel A: Full-Sized Sample

Panel B: Equal-Sized Sample

No. of bins ¼ 3

No. of bins ¼ 3

bin 2

bin 3

z-score

3,1

bin 1

0.0008 0.0003 7.4261 0.0018 0.0072 0.0063 0.0048 0.6079 0.5868 5.5041 0.7312 0.0006 0.0003 2.3042 0.0010 0.0087 0.0078 0.0067 0.5432 0.5428 2.4684 0.6022 0.0003 0.0002 1.4287 0.0009 0.0092 0.0077 0.0064 0.5414 0.5304 2.1973 0.5817 0.0002 0.0004 2.3702 0.0012 0.0103 0.0089 0.0088 0.5187 0.5375 1.1737 0.5201 0.0002 0.0002 2.0186 0.0006 0.0116 0.0106 0.0140 0.5135 0.5167 1.0454 0.5427 0.0008 0.0001 2.1230 0.0023 0.0153 0.0126 0.0128 0.5256 0.5206 0.9566 0.5714 0.0003 0.0006 2.2800 0.0006 0.0114 0.0088 0.0078 0.5284 0.5018 0.8844 0.5208 0.0002 0.0002 1.7398 0.0003 0.0147 0.0130 0.0151 0.4983 0.5066 1.5900 0.5048

bin 2

bin 3

0.0012 0.0055 0.6444 0.0007 0.0079 0.5459 0.0004 0.0072 0.5499 0.0001 0.0089 0.5109 0.0003 0.0125 0.5266 0.0009 0.0140 0.5240 0.0001 0.0088 0.5222 0.0001 0.0145 0.4956

0.0006 0.0060 0.6406 0.0003 0.0080 0.5599 0.0002 0.0070 0.5257 0.0003 0.0087 0.5399 0.0001 0.0116 0.5180 0.0000 0.0117 0.5331 0.0002 0.0094 0.5179 0.0007 0.0148 0.4845

z-score

3,1

2.9372 2.4926 1.2758 1.0655 2.4993 1.6166 1.3803 0.5744 0.6123 0.7586 1.7096 0.7234 1.1299 0.0724 0.4569 0.7422

83

Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns

Bin Tests.

An Expanded Study on the Stock Market Temperature Anomaly

Table 2.

84

Table 2. (Continued ) Panel A: Full-Sized Sample

Panel B: Equal-Sized Sample

No. of bins ¼ 3

No. of bins ¼ 3

bin 1

bin 2

bin 3

z-score

3,1

bin 1

bin 2

bin 3

z-score

3,1

Taiwan

Return mean Std. dev. of return % of positive returns

0.0024 0.0128 0.6923

0.0008 0.0167 0.5309

0.0000 1.3377 0.0168 0.5130 2.7795

0.0033 0.0215 0.5388

0.0003 0.0189 0.5048

0.0012 3.0655 0.0202 0.4806 1.6800

U.S. CRSP-EW with Other Indices

Return mean Std. dev. of return % of positive returns Return mean Std. dev. of return % of positive returns

0.0014 0.0088 0.6028 0.0011 0.0090 0.5777

0.0005 0.0109 0.5419 0.0004 0.0111 0.5277

0.0003 0.0122 0.5363 0.0002 0.0124 0.5272

5.3787

0.0015 0.0086 0.5968 0.0013 0.0088 0.5794

0.0005 0.0119 0.5366 0.0005 0.0121 0.5256

0.0000 0.0149 0.5204 0.0001 0.0150 0.5126

U.S. CRSP-VW with Other Indices

5.7902 3.9778 4.3666

4.0728 3.8067 3.7565 3.3064

MELANIE CAO AND JASON WEI

Note: 1. Bin-test results for the full sample and the equal-size sample. The length of the full sample varies across markets; that of the equal-size sample covers the period of 1989–1999 with 2,252 observations. We report the mean return and the percentage of positive returns for each of the three bins and the z-scores. qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ frequence 2 2 2. z_scoremean ¼ ðpk p1 Þ= pk ð1 pk Þ=nk þ p1 ð1 p1 Þ=n1 ; where mi and si are the return k;1 ¼ ðmk m1 Þ= sk =nk þ s1 =n1 and z_scorek;1 mean and standard deviation for bin i; pi the percentage of positive returns in bin i; and ni the number of observations in bin i for each statistic. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

An Expanded Study on the Stock Market Temperature Anomaly

85

level for the 3-bin case. As for Taiwan, the improvements are even stronger. The z-score for the percentage positive returns of the full sample has increased from no significance to 1% significance while the z-score for the mean return of the equal sample has increased from 5% significance to 1% significance. Now we briefly discuss the general results for the 3-bin case. For the ‘‘full sample,’’ the z statistics of mean return comparisons for all markets other than Canada and Taiwan are significant at the 10% level, with some being significant at the 5% and 1% levels.6 For Canada and Taiwan, the z statistics for frequencies of positive returns are both significant at the 5%. In general, the lower the temperature, the more likely that stocks will experience a positive price change. When we combine all the indices, the relationship remains. For both combinations involving the CRSP equalweighted and value-weighted indices, the z-scores are all significant at the 1% level. This conﬁrms that there is universal negative correlation between temperature and stock returns. For Australia, the z-score is significant at the 5% level and the ranking of mean returns and frequencies of positive returns is strictly monotonic for the 3-bin case. This is a very important observation in that the same season actually covers different calendar months on the Northern and Southern Hemispheres. It is seen in Fig. 1 that temperatures progress in opposite directions on the two hemispheres. The observations for Australia convincingly imply that temperature is a common factor to the stock market returns. Another observation relates to equal-weighted vs. value-weighted indices. Panel A of Table 2 conﬁrms that the temperature impact is much stronger on the CRSP equal-weighted index. As stated in CW (2005), prices of smallcap stocks respond to investors’ mood change in a much more pronounced fashion. Nonetheless, it is comforting to realize that what we have uncovered is not driven by a few small-cap stocks. Panel B of Table 2 contains the 3-bin test results for the ‘‘equal-sized sample.’’ This test is aimed at making valid comparisons between markets since the equal-sized sample not only covers the same time period, but also has the same number of observations for all markets. With only a few exceptions, the z-scores are lower than those for the full sample due to fewer observations. As in the 4-bin case in CW (2005), the z-score is significant at the 5% level for three markets (US, Canada and Taiwan), and significant at the 10% level for one market (Sweden). The significance level for Canada and Taiwan is actually higher than that for the full sample. The z-score for the CRSP value-weighted index is no longer significant, which reﬂects the

86

MELANIE CAO AND JASON WEI

dominance of small-cap stocks in mood impacts. Evidently, even with a shorter sample period and fewer observations, the general monotonic patterns remain in mean returns and frequencies of positive returns for the 3-bin case, conﬁrming similar ﬁnding for the 4-bin case in CW (2005). In addition, when all indices are combined the z-scores are all significant at the 1% level. To provide further supporting evidence, we perform 3- and 4-bin tests on the expanded sample. To save space, we only report the results with the ‘‘equal-sized’’ expanded sample. Table 3 contains the results for the 3- and 4-bin cases. Several observations are in order. First, comparing the top portion of Table 3 with Panel B of Table 2 for the ‘‘equal-sized sample,’’ we see a drop in significance for the eight locations we previously examined. This is mainly due to the lower testing power associated with a smaller sample (1,509 vs. 2,252). Nevertheless, with the exception of Japan (3-bin), the z-score for the bin return comparison is negative for all locations, conﬁrming the previously observed negative correlation between temperature and returns. Second, for the additional markets, seven (out of 19) have a negative and significant z-score under the 3-bin test and ﬁve under the 4-bin test. Most of the z-scores are negative, conﬁrming a negative correlation between temperature and returns. Remarkably, the z-score for Auckland is negative and significant for both the 3- and 4-bin tests. The 3-bin z-score is also significant for Australia. The results for the two markets residing on the South Hemisphere once again conﬁrm the universal negative association between temperature and returns. Third, the negative correlation is also observed for the combined sample. For return comparisons, the 4-bin z-scores are significant at the 5% level for both combinations involving either the CRSP-EW index or the CRSP-VW index, while the 3-bin z-score are nearly significant at the 10% level. For comparisons of percentages of positive returns, the 3- and 4-bin z-scores are all significant at the 1% level for both combinations. To summarize, the bin test results in Tables 2 and 3 provide strong evidence in support of the conclusion presented in CW (2005). That is, there exists an overall negative correlation between temperatures and returns.

2.2. Regression Analysis – Controlling for Known Anomalies As we have reasoned in CW (2005), the bin tests can only establish an association between temperature and returns. They cannot measure the precise correlation; nor can they control for some of the known anomalies in

No. of bins ¼ 3 bin 1

New York, U.S. CRSP-EW New York, U.S. CRSP-VW Toronto, Canada London, Britain Frankfurt, Germany Stockholm, Sweden Sydney, Australia Tokyo, Japan Taipei, Taiwan

Amsterdam, Netherlands Athens, Greece Auckland, New Zealand Buenos Aires, Argentina

Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive

returns returns returns returns returns returns returns returns

returns returns returns returns

bin 3

z-score (3,1)

bin 1

0.1268 0.6622 0.0885 0.5856 0.0724 0.5837 0.0972 0.5455 0.1028 0.5602 0.2622 0.5833 0.0752 0.5292 0.0446 0.5094 0.2711 0.5571

0.0874 0.6339 0.0540 0.5283 0.0287 0.5350 0.0048 0.5006 0.0097 0.5195 0.0907 0.5211 0.0055 0.5175 0.0007 0.4943 0.0680 0.5146

0.0763 0.6553 0.0179 0.5577 0.0259 0.5456 0.0876 0.5606 0.0003 0.5180 0.0069 0.5314 0.0943 0.4700 0.0364 0.4751 0.1403 0.4846

1.3275 0.1789 0.1855 0.7115 1.4013 0.1373 0.7208 0.6346 1.1179 0.1130 1.0271 0.6231 0.1654 0.1454 0.3992 0.5667 1.1537 0.1612 1.0335 0.5354 1.6775 0.3783 0.7761 0.6667 0.0816 1.8595 1.0959 0.5380 0.0809 0.0025 1.0287 0.5224 2.6217 0.6887 1.8574 0.6531

0.1369 0.5972 0.1137 0.5000 0.1167 0.5628 0.3132 0.5188

0.0330 0.5414 0.1164 0.4719 0.0503 0.5216 0.2972 0.5184

0.0193 0.5593 0.0761 0.4911 0.0525 0.4797 0.3336 0.5408

1.8617 0.8048 0.4001 0.2711 2.4341 2.0585 0.0829 0.5742

0.0954 0.6250 0.1216 0.5000 0.1076 0.5505 0.1967 0.5336

bin 2

bin 3

bin 4

z-score (4,1)

0.0879 0.6326 0.0585 0.5348 0.0424 0.5237 0.0235 0.5167 0.0547 0.5409 0.1476 0.5342 0.0317 0.5105 0.0460 0.4876 0.0462 0.5013

0.0677 0.6399 0.0278 0.5329 0.0042 0.5405 0.0463 0.5205 0.0228 0.5160 0.0191 0.5051 0.0164 0.5173 0.0000 0.4937 0.0894 0.5032

0.0912 0.6536 0.0266 0.5599 0.0378 0.5593 0.0054 0.5149 0.0064 0.5090 0.0059 0.5539 0.0887 0.4839 0.0541 0.4714 0.1767 0.4861

1.6597 1.1666 1.5613 1.4203 1.2844 1.3005 1.6132 0.9395 1.4486 0.4505 1.4589 1.1285 1.1495 0.5797 0.3995 1.2409 4.0181 3.1695

0.1200 0.5743 0.1526 0.5010 0.0887 0.5408 0.3349 0.5233

0.0293 0.5227 0.0429 0.4758 0.0074 0.5000 0.3753 0.5189

0.0373 0.5690 0.0737 0.4676 0.0626 0.4730 0.0320 0.5192

0.5389 0.7739 0.3872 0.7740 1.8219 1.3302 0.5334 0.2450

87

Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive

returns

bin 2

No. of bins ¼ 4

An Expanded Study on the Stock Market Temperature Anomaly

Table 3. Bin Test for Expanded Sample with Equal Size.

88

Table 3. (Continued ) No. of bins ¼ 3

Copenhagen, Demark Dublin, Ireland Helsinki, Finland Istanbul, Turkey Johannesburg, South Africa Kuala Lumpur, Malaysia Madrid, Spain

Milan, Italy Oslo, Norway Paris, France Rio de Janeiro, Brazil Santiago, Chile Vienna, Austria

returns returns returns returns returns returns returns returns returns returns returns returns returns returns

bin 1

bin 2

bin 3

z-score (3,1)

0.0720 0.5619 0.1338 0.5469 0.1732 0.5492 0.3240 0.5239 0.0605 0.5608 0.0468 0.4021 0.0766 0.5303 0.0931 0.5000 0.1552 0.5521 0.1156 0.6040 0.1691 0.5870 0.7981 0.5526 0.0489 0.5000 0.2813 0.5714

0.0310 0.5319 0.0375 0.5076 0.0293 0.4964 0.2926 0.5222 0.0194 0.5086 0.0701 0.5277 0.0414 0.4937 0.0638 0.5000 0.0411 0.5024 0.0881 0.5194 0.0102 0.5042 0.6335 0.5667 0.0889 0.5139 0.0326 0.5327

0.0124 0.5053 0.0220 0.4939 0.0292 0.5046 0.2805 0.5405 0.1113 0.5656 0.0759 0.4600 0.0584 0.4720 0.0270 0.4970 0.0511 0.4753 0.0339 0.5315 0.0325 0.4829 0.7728 0.5679 0.0720 0.4756 0.0140 0.5052

1.4337 1.4057 1.4811 1.3180 1.2562 0.8934 0.2375 0.4902 0.5936 0.1023 0.2172 0.9011 1.9528 1.6408 0.1707 0.0170 2.3793 2.2202 0.7420 1.3781 2.9653 2.7032 0.0789 0.3559 0.4207 0.6546 2.4524 1.0650

bin 1

bin 2

0.1122 0.5373 0.0564 0.5055 0.2669 0.5763 0.6252 0.5556 0.0149 0.5370 0.0262 0.3714 0.0722 0.5160 0.1668 0.5714 0.2489 0.5886 0.1467 0.6222 0.2396 0.6619 0.6247 0.5106 0.0627 0.5128 0.5796 0.6800

0.0423 0.5535 0.0919 0.5268 0.0423 0.4991 0.1414 0.5151 0.0027 0.5246 0.0198 0.5163 0.0865 0.5090 0.4531 0.6364 0.0132 0.4979 0.1365 0.5319 0.0445 0.5208 0.7723 0.5551 0.0795 0.5252 0.1330 0.5683

bin 3

bin 4

z-score (4,1)

0.0138 0.4981 0.0141 0.4890 0.0091 0.4906 0.3551 0.5378 0.0777 0.5206 0.0761 0.5201 0.0497 0.4746 0.0157 0.4924 0.0265 0.4989 0.0456 0.5251 0.0404 0.4861 0.6212 0.5841 0.0925 0.5000 0.0057 0.5110

0.0288 0.5241 0.0319 0.5323 0.0545 0.5208 0.2600 0.5253 0.0849 0.5989 0.2846 0.3846 0.0384 0.4915 0.0328 0.5026 0.0365 0.4767 0.0221 0.5260 0.0306 0.4807 0.7795 0.5400 0.0465 0.4588 0.0285 0.4834

0.8483 0.1949 0.2198 0.4252 1.4126 0.7935 1.4567 0.6812 0.5151 0.8066 1.0746 0.1050 1.3048 0.5238 0.3037 0.3654 2.5343 2.5045 0.8029 1.2655 2.7641 3.3143 0.2181 0.3696 0.2434 1.1182 2.6995 2.0342

MELANIE CAO AND JASON WEI

Manila, Philippines

Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive Return mean % of positive

No. of bins ¼ 4

Return mean % of positive returns

0.1880 0.6517

0.0472 0.5450

0.0111 2.9456 0.5301 2.9333

0.1974 0.5974

0.0991 0.5899

0.0208 0.5306

0.0027 1.9647 0.5280 1.1169

U.S. CRSP-EW with Other Indices U.S. CRSP-VW with Other Indices

Return mean % of positive returns Return mean % of positive returns

0.1336 0.5700 0.1287 0.5644

0.0717 0.5280 0.0707 0.5249

0.0931 0.5175 0.0908 0.5133

0.2233 0.6311 0.2274 0.6311

0.1010 0.5477 0.0985 0.5428

0.0555 0.5175 0.0545 0.5145

0.1173 0.5175 0.1149 0.5134

1.4335 3.6197 1.3336 3.5118

2.0767 4.4281 2.2012 4.5891

Note: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ frequence 2 2 1. z_scoremean ¼ ðpk p1 Þ= pk ð1 pk Þ=nk þ p1 ð1 p1 Þ=n1 ; where mi and si are the return k;1 ¼ ðmk m1 Þ= sk =nk þ s1 =n1 and z_scorek;1 mean and standard deviation for bin i; pi the percentage of positive returns in bin i; and ni the number of observations in bin i for each statistic. 2. The common sample period is from 1988 to 1997 and the matched number of observations is 1,509. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

An Expanded Study on the Stock Market Temperature Anomaly

Zurich, Switzerland

89

90

MELANIE CAO AND JASON WEI

stock returns. The second type of test is the ‘‘Regression Analysis’’ which is used to gain further insights into the relationship between temperatures and returns while controlling for some known anomalies such as the Monday effect and tax-loss selling effect. The ﬁrst regression is speciﬁed as follows: rt ¼ a1 þ a2 rt1 þ a3 DMon þ a4 DTax þ a5 Tempt þ t t t Mon

(1)

where rt is the daily return at time t for a given index; Dt a dummy variable which equals 1 for Mondays and 0 otherwise, DtMon a dummy variable which equals 1 for the ﬁrst 10 days of the taxation year and 0 otherwise, Tempt the daily temperature at time t, and et is the residual term. The tax year starts on July 1 in Australia, April 6 in Britain and Ireland, April 1 in New Zealand, March 1 in South Africa, and January 1 in all other jurisdictions. In our previous study (CW, 2005), we ﬁrst run individual OLS regressions for the ‘‘full sample’’ as a preliminary check. Subsequently, we also run a seemingly unrelated regression (SUR) by combining the CRSP valueweighted index with all other indices. It is clear that the full sample results can only be preliminary for several reasons. First, the sample periods are different among markets, making valid comparisons difﬁcult; second, the returns and temperatures are correlated among markets, casting doubt on the validity of the OLS regressions; third, it is impossible to perform joint tests of the temperature variable’s significance across markets. The SUR can address these concerns. It takes into account the inter-market correlations and, at the same time, allows for joint tests on the temperature coefﬁcients. The ﬁrst test is designed to determine if all the coefﬁcients are jointly different from zero. It helps establish whether the negative correlations (between temperature and stock returns) observed for individual markets are jointly significant after controlling for inter-market correlations. The second test is aimed at determining whether all coefﬁcients are equal. It helps to ascertain if investors in different markets react to the same temperature change to the same degree. To provide complementary evidence, this paper presents the SUR results for the CRSP equal-weighted index together with all other indices. For comparison purposes, we replicate the individual OLS results for the ‘‘full sample’’ from CW (2005) and present them in Panel A of Table 4. The SUR results are reported in Panel B of Table 4. In addition, we also perform individual OLS regressions for the ‘‘equal-sized sample.’’ For brevity, we only report the temperature variable’s coefﬁcient estimate, its t-value, and the R2 from the individual regressions. For the seemingly unrelated regressions, we report the system-wide R2.

An Expanded Study on the Stock Market Temperature Anomaly

91

Let us briefly summarize the results for Panel A of Table 4. To begin with, returns on Mondays are lower for all markets with the exception of Sweden and Australia. This Monday effect is significant at the 1% level for US, Canada, Britain and Germany, and it is significant at the 5% for Japan and Taiwan. In contrast, the tax-loss effect is significant for only US and Australia, and it has the right sign for all markets with the exception of Canada and Japan. As for the temperature variable, with the exception of Canada and Australia, all markets have a negative coefﬁcient that is significant at the 10% level. Some are significant at the 5% and 1% levels. The significant, negative coefﬁcient for most markets is consistent with the bin test results. The temperature coefﬁcient for Canada is negative and the t-value is nearly significant at the 10% level. For Australia, the coefﬁcient is positive but close to zero in significance. The R2 is relatively higher for the US and Canada. In terms of pattern and magnitude, the R2 across markets is very similar to that in KKL (2003). The temperature coefﬁcient from OLS regressions is negative for all markets, and significant at the 5% level or higher for US, Canada, Germany, Sweden and Taiwan. The t-value for Britain is nearly significant at the 10% level. Unlike in the full sample, Australia now has a negative coefﬁcient, albeit not a significant one. The SUR results in Panel B of Table 4 for the CRSP equal-weighted index are stronger than the SUR results in CW (2005) for the CRSP value-weighted index, as we expect. However, the t-values are generally lower than those from the individual OLS regressions. There are several cases (e.g., Germany) where the t-value is significant in the OLS regression but not in the SUR. This is to be expected due to the positive inter-market correlations. Only US (CRSP equal-weighted index), Sweden and Taiwan have a t-value significant at the 10% level or higher. However, the w2 statistic for the ﬁrst test is significant at the 1% level. This means that the negative correlation between temperature and stock returns is jointly significant across all markets. The w2 statistic for the second test is significant at the 5% level. These results are consistent with the SUR results presented in CW (2005). This regression analysis establishes a strong negative correlation between temperature and stock returns after controlling for auto-correlation in returns, the Monday effect and the tax-loss effect. The second regression used in our previous study (CW, 2005) is to further control some known naturerelated anomalies associated with the amount of sunshine in Saunders (1993) and HS (2003) and the seasonal affective disorder (SAD) in KKL

92

Table 4.

Regression Analysis with Monday Dummy, Tax-Dummy and Temperature.

Panel A: Individual Regression with Full-Sized Sample

Panel B: SUR Test of Equal-Sized Sample with CRSP-EW

rt ¼ a1+a2rt1+a3DtMon+a4DtTax+a5Tempt+et a2 0.3809 40.0903 U.S. CRSP-VW 0.1713 16.9216 Canada 0.1900 15.1222 Britain 0.0725 4.7544 Germany 0.0418 3.7201 Sweden 0.0615 3.4503 Australia 0.0849 5.4867

a4

a5

R2

0.3054 18.7260 0.1471 6.9822 0.1327 4.8211 0.1080 2.8099 0.1408 4.4329 0.0380 0.5928 0.0491 1.2330

0.1798 5.1848 0.0350 0.7822 0.0165 0.2894 0.0086 0.1081 0.0575 0.8647 0.0462 0.3409 0.1755 2.1635

0.0021 3.0669 0.0016 1.7319 0.0014 1.3369 0.0051 1.9127 0.0037 2.1243 0.0077 2.2936 0.0011 0.2700

0.1723

a2

a3

0.1821 0.2180 11.5868 6.9750

a4

a5

0.0793 0.0019 1.3290 1.7113

a0 5

R2

0.0030 2.3795

0.0914

0.0030 2.1041 0.0048 1.4676 0.0072 1.9836 0.0081 2.2252 0.0043 0.9532

0.0353

0.0344 0.0394 0.0079 0.0050 0.0060 0.0089

0.1169 6.9112 0.0022 0.1294 0.0175 1.0568 0.0101 0.6064 0.0254 1.3576

0.0296 0.7475 0.0831 1.6321 0.0269 0.3749 0.0477 0.6318 0.0449 0.9203

0.0272 0.3450 0.0345 0.4846 0.1104 0.9041 0.0903 0.6802 0.0412 0.5009

0.0017 1.2564 0.0024 0.8244 0.0038 1.2001 0.0071 2.2073 0.0051 1.2224

0.0060 0.0033 0.0079 0.0024

MELANIE CAO AND JASON WEI

U.S. CRSP-EW

a3

Taiwan System-wide R2 w2(8) w2(7)

0.0039 0.2537 0.1003 8.1519

0.1195 2.2788 0.1263 2.2780

0.0906 0.7475 0.0075 0.0655

0.0047 1.7409 0.0074 1.9177

0.0019 0.0029 0.1508 0.0114 0.0083 0.4005

0.2719 3.2035 0.0122 0.1073

0.0051 0.0009 0.0033 0.0306 0.2295 0.7821 0.3169 0.0276 0.0292 1.3270 3.4631 3.6295

0.0052 0.0062

0.0140 22.0509^^^ 15.4249^^

Note: 1. This table reports regression analysis of both the full sample OLS regression and the equal-size sample SUR. We control for ﬁrst-order auto-correlation (rt1), the Monday effect (DtMon), and the tax-loss effect (DtTax). The tax dummy (DtTax) covers the ﬁrst 10 trading days of the taxation year. The taxation year starts on April 6 in Britain, July in Australia and January 1 in all other jurisdictions. 2. For each market, the ﬁrst row contains the parameter estimates, the second contains the t-values. For brevity and clarity, we omit the intercept estimate and only indicate the significance for explanatory variables DtMon, DtTax, and Tempt. The last column of each panel contains the R2 of individual OLS regressions. The system-wide R2 is for SUR. 3. The column with heading a0 contains the coefﬁcients and t-values of the temperature variables Temp from individual regressions using the equal-size sample. 4. The w2 statistic with 8 degrees of freedom is for testing if all coefﬁcients for each explanatory variable are equal to zero. The second w2 statistic with 7 degrees of freedom is for testing if all coefﬁcients are equal. The carets ^, ^^ and ^^^ indicate statistical significance at the 10%, 5% and 1% levels, respectively. 5. The common sample period is from 1989 to 1999 and the number of observations is 2,252. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

An Expanded Study on the Stock Market Temperature Anomaly

Japan

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(2003). The augmented regression takes the following form: rt ¼ a1 þ a2 rt1 þ a3 DMon þ a4 DTax t t þ a5 Tempt þ a6 Cloud t þ a7 SADt þ t

ð2Þ

where Cloudt is the cloud cover and SADt the number of night hours minus 12 for the period from September 21 to March 20, and zero otherwise. As stated earlier, to correct for inter-market correlations and to ensure comparability, the SUR is used for this augmented regression. To provide further evidence, we present the results with the expanded data set. As in HS (2003), the ‘‘total sky cover’’ from the NCDC is used to measure cloud cover, which is the hourly average from 6:00 a.m. to 4:00 p.m. The variable ‘‘total sky cover’’ ranges in value from 0 (clear) to 8 (overcast). Canada, Brazil, Germany and Japan are eliminated from the sample since the sky cover observations are not complete for Toronto, Rio de Janeiro, Frankfurt and Tokyo. Since the cloud cover data are available for the period from 1982 to 1997, for the remaining 23 markets, we match the ‘‘equal-sized sample’’ of temperature (with 1,509 observations) with the cloud data. The ﬁnal sample size is reduced to 1,013 with a common sample period ranging from 1989 to 1997. Table 5 reports the mean and standard deviation of cloud cover for each market, and the regression results. First and foremost, the temperature coefﬁcient for the SUR test is negative for 21 of the 23 markets, and the t-values for ﬁve coefﬁcients are significant at the 10% level or higher. The two w2 statistics are significant at the 5% and 10% levels, respectively. For individual regressions, the temperature coefﬁcient is positive for only one market (Malaysia). It is evident that, the negative correlation between temperature and returns is prevalent across markets even after controlling for other known anomalies. The SAD effect also appears strong in the expanded sample, although none of the w2 statistics is significant. The SAD coefﬁcient is negative for most of the cities. This negative association between returns and the length of the night conﬁrms the general ﬁndings of KKL (2003) who examine nine markets. As for the sunshine effect, the cloud cover coefﬁcient is negative for many cities, consistent with the ﬁndings of HS (2003). However, the coefﬁcient is positive and statistically significant for three cities under either the individual or SUR tests. Therefore, after controlling for temperature and SAD effects, the sunshine effect is no longer uniform across all locations. Up to now, we have presented more evidence in support of the conclusion drawn in our previous study (CW, 2005). That is, there is indeed a

SUR and Related Tests for Expanded Sample with Equal Size. rt ¼ a1+a2rt1+a3DtMon+a4DtTax+a5Tempt+a6Cloudt+a7SADt+et

Panel A: Cloud Clover

Panel B: SUR with CRSP-VW

Mean

Std. dev.

Tempt

0.0015 0.6120 0.0021 0.4810 0.0026 0.5021 0.0219 3.1561 0.0429 3.0882

New York, U.S. CRSPVW London, Britain

4.749

2.734

5.832

1.889

Stockholm, Sweden

5.309

1.955

Sydney, Australia

3.812

2.320

Taipei, Taiwan

5.432

1.918

Amsterdam, Netherlands

5.434

2.239

Athens, Greece

3.431

2.592

Auckland, New Zealand

4.685

2.272

Buenos Aires, Argentina

4.152

2.774

Copenhagen, Demark

5.362

2.199

Panel C: Individual Test

SADt

0.0016 0.2063 0.0049 0.4714 0.0028 0.1662 0.0084 0.9234 0.0005 0.0124

0.0331 0.5286 0.0391 0.5183 0.0750 0.6667 0.1465 1.6381 0.0863 0.4518

0.0024 0.9344 0.0034 0.6311 0.0069 1.1014 0.0279 3.0909 0.0439 3.0859

0.1025 1.5935 0.2388 1.3328 0.1468 1.1892 0.1977 0.4401 0.1266 1.8034

0.0136 2.8576 0.0075 0.7511 0.0352 2.7920 0.0077 0.2909 0.0017 0.3635

0.0086 0.0024 0.3593 2.4431 0.0029 0.0339 0.3026 1.4059 0.0286 0.0085 2.7955 0.6818 0.0147 0.1112 0.5650 2.3893 0.0014 0.0189 0.3446 1.8282

Tempt

SADt

R2

0.0080 0.9415 0.0094 0.6591 0.0019 0.0848 0.0035 0.2947 0.0092 0.2387

0.0148 0.2312 0.0267 0.3360 0.0015 0.0118 0.2435 2.2378 0.0909 0.4692

0.0108

0.0104 0.9146 0.0417 1.6463 0.0157 1.0070 0.1093 2.2956 0.0240 1.9171

0.1570 2.1878 0.2754 1.5059 0.2907 2.0269 0.1122 0.2454 0.0836 1.0762

Cloudt

0.0085 0.0073 0.0137 0.0151 0.0120 0.0233 0.0142 0.0231 0.0244

95

Cloudt

An Expanded Study on the Stock Market Temperature Anomaly

Table 5.

96

Table 5. (Continued ) rt ¼ a1+a2rt1+a3DtMon+a4DtTax+a5Tempt+a6Cloudt+a7SADt+et Panel B: SUR with CRSP-VW

Mean

Std. dev.

Tempt

Dublin, Ireland

5.904

1.829

Helsinki, Finnland

5.533

2.330

Istanbul, Turkey

3.921

2.576

Johannesburg, South Africa Kuala Lumpur, Malaysia

3.061

2.420

6.866

0.352

Madrid, Spain

3.597

2.621

Manila, Philippines

5.312

2.055

Milan, Italy

4.102

2.792

Oslo, Norway

5.439

2.256

Paris, France

5.294

2.298

Santiago, Chile

3.099

3.065

0.0070 1.0716 0.0026 0.5868 0.0011 0.0924 0.0022 0.2571 0.0066 0.1704 0.0023 0.6054 0.0043 0.1575 0.0032 0.6560 0.0035 0.6937 0.0073 1.8226 0.0029 0.4460

Panel C: Individual Test

Cloudt

SADt

Tempt

Cloudt

SADt

R2

0.0033 0.2430 0.0104 0.7846 0.0086 0.2736 0.0124 0.9386 0.0684 0.7752 0.0188 2.0446 0.0149 0.6418 0.0128 1.1162 0.0033 0.2151 0.0097 1.1849 0.0049 0.6366

0.0119 0.1460 0.1450 1.4812 0.0332 0.1465 0.2245 1.9471 0.0437 0.4049 0.0938 1.1016 0.0061 0.0436 0.0573 0.5342 0.1348 1.1523 0.0032 0.0390 0.1974 2.2846

0.0119 1.5559 0.0046 0.9374 0.0014 0.1237 0.0060 0.6185 0.0103 0.2349 0.0058 1.1929 0.0140 0.4873 0.0058 1.0670 0.0063 1.0545 0.0133 2.5643 0.0019 0.2754

0.0148 0.8954 0.0162 1.0501 0.0052 0.1599 0.0010 0.0650 0.0825 0.8202 0.0213 1.6365 0.0072 0.2960 0.0235 1.7909 0.0137 0.7098 0.0261 2.0224 0.0042 0.5327

0.0437 0.4918 0.1138 1.0837 0.0092 0.0401 0.3176 2.5351 0.0236 0.2040 0.0444 0.4677 0.0239 0.1649 0.0166 0.1452 0.1928 1.5059 0.0581 0.6641 0.2099 2.3655

0.0126 0.0317 0.0201 0.0194 0.0190 0.0116 0.0465 0.0231 0.0178 0.0141 0.0863

MELANIE CAO AND JASON WEI

Panel A: Cloud Clover

5.076

2.459

Zurich, Switzerland

5.283

2.465

System-wide R2 w2(23) w2(22)

0.0023 0.5084 0.0052 1.5076

0.0137 1.2007 0.0077 1.1072

35.8773^^ 35.5255^

25.3794 32.8806^

0.0345 0.3723 0.0145 0.2034

0.0084 1.6223 0.0098 2.1207

0.0094 0.6803 0.0088 0.7984

0.0448 0.4473 0.0326 0.4141

0.0600 0.0116

0.0251 31.7398 30.2556

Note: 1. Cloudt measures the cloud cover, and SADt is the number of night hours minus 12 for the period from September 21 to March 20, and zero otherwise; The number of night hours is calculated as 7.72 arcos[-tan (2pd/360) tan (lt)] for the Southern Hemisphere, and 24 minus this quantity for the Northern Hemisphere. In the above, d is the latitude of the market location, and lt ¼ 0.4102 sin [(2p/ 365)(julian-80.25)] where ‘‘julian’’ represents the day of the year, i.e., julian ¼ 1 for January 1, 2 for January 2, and so on. The equal-size sample is from 1989 to 1997 with the matched number of observations is 1,013. 2. For brevity and clarity, we only report the coefﬁcients and t-values for Tempt, Clouldt and SADt. 3. The tax dummy, DtTax covers the ﬁrst 10 trading days of the taxation year. The taxation year starts on April 6 in Britain, July 1 in Australia and January 1 in all other jurisdictions. 4. The w2 statistic with 23 degrees of freedom is for testing if all coefﬁcients for each explanatory variable are equal to zero. The second w2 statistic with 22 degrees of freedom is for testing if all coefﬁcients are equal. The carets ^, ^^ and ^^^ indicate statistical significance at the 10%, 5% and 1% levels, respectively. 5. The common sample period is from 1989 to 1997 and the number of observations is 1,013. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

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Vienna, Austria

97

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MELANIE CAO AND JASON WEI

‘‘temperature anomaly’’ in stock markets around the globe. Specifically, a statistically significant, negative correlation exists between temperature and stock returns, after controlling for the ﬁrst order auto-correlation in returns, the Monday effect, the tax-loss effect, the cloud cover effect, and the lengthof-the-night effect. The statistical significance is obtained in both the individual OLS regressions and the seemingly unrelated regressions which control for inter-market correlations. In the next section, we propose some additional empirical tests to see whether this negative relationship continues to remain under different speciﬁcations.

3. ALTERNATIVE TESTS AND ROBUSTNESS CHECK Given that the expanded data have a much shorter sample period and the quality of the temperature data from NCDC for this sample is inferior to that of the ‘‘full sample,’’ we will use the ‘‘full sample’’ to perform alternative tests in this section.

3.1. Nonparametric Tests The two main tests used in CW (2005) are either semi-parametric (bin tests) or completely parametric (regression tests). It is helpful to know whether those types of analyses are robust to distributional assumptions. To this end, we propose two nonparametric tests, with one testing the general correlation between temperature and stock returns, and the other testing whether investors react to the same temperature change to the same extent. The ﬁrst, Spearman’s rank correlation test, is roughly a nonparametric counterpart of the bin test, but is stronger and more precise; the second, Friedman’s twoway analysis of variance, is the nonparametric counterpart of the w2 test in SUR that tests if all the temperature coefﬁcients are equal. Unlike the usual Pearson’s correlation which requires the data series to be normally distributed, the Spearman’s correlation is based on the ranks of the two data series in question and is therefore distribution-free. The precise formula is rs ¼ 1 ½6Sni¼1 d 2i =½nðn2 1Þ where rs is the Spearman’s rank correlation, n the number of observations and di the rank difference for the ith observation. When the number of observations is larger than 10, rs has a t-distribution with n2 degrees of freedom, and the test statistic is given pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ by t ¼ r2s ðn 2Þ=ð1 r2s Þ:

An Expanded Study on the Stock Market Temperature Anomaly

99

To avoid spurious correlations, we calculate Spearman’s correlation based on temperature bins. Table 1 reveals that the maximum temperature range for the full sample is about 501. We therefore put temperatures into 50 bins and calculate the mean temperature and return for each bin. A rank correlation is then calculated using the mean temperatures and returns. For robustness check, we also use 30, 40, 60, 70 and 100 bins. The rank correlation is calculated for each individual market and all the markets combined. Panel A of Table 6 reports the results. When the number of bins is 40, 50 or 60, correlations for all the markets (except Australia) are significant at the 10% level or higher. Although not significant, the correlation for Australia is negative. With a bin size of 50, the correlation for all markets combined is significant at the 1% level (twotailed test) when the CRSP equal-weighted index is used, and significant at the 5% level when the CRSP value-weighted index is used. Although the size of the correlations decreases as the number of bins increases (which is a common feature of most time series), the significance remains more or less unchanged. We now turn to the second nonparametric test. The regression analyses indicate that investors in different temperature domiciles react to temperature changes to different extents. We would like to ascertain if this result holds up to nonparametric tests. We design the test in the following way. We ﬁrst create temperature bins common to all markets; we then test if returns are equal across markets within each temperature bin or range. This joint test essentially allows us to determine if investors react to the absolute levels of temperature, or to the levels relative to the local norm. In other words, it helps to answer the following question: Does a temperature range of, say 51C–81C induce the same reaction among investors around the globe? Intuition would suggest a negative answer since a cool temperature in one place may be perceived as a warm temperature in another, depending on the local year-round average temperature. The Friedman’s two-way analysis of variance is an ideal choice for our test. Let k be the number of markets and n be number temperature bins. The Friedman’s test statistic is then calculated as ½12=knðk þ 1ÞSkj¼1 S 2j 3nðk þ 1Þ; where Sj is the sum of ranks received by the jth market. This statistic has a w2 distribution with (k1) degrees of freedom. Since this is a joint test, we again have two versions of the combination, depending on whether we use the CRSP equal-weighted index or the CRSP value-weighted index for US In addition, we must choose a common temperature range applicable to all markets. Table 1 indicates that, for the full sample, the lowest maximum temperature among all the markets is 26.701C (Sweden),

100

Table 6.

MELANIE CAO AND JASON WEI

Nonparametric Tests for Correlation and Temperature Level Effect. Number of Temperature Bins 30

40

50

60

70

100

0.5512 0.3201 0.2933 0.1910 0.2370 0.2698 0.0781 0.2932 0.2876

0.5343 0.2216 0.2044 0.1585 0.2474 0.2012 0.0683 0.2019 0.2602

Panel A: Spearman’s Rank Correlation between Temperature and Returns U.S. CRSP-EW U.S. CRSP-VW Canada Britain Germany Sweden Australia Japan Taiwan

0.6329 0.4679 0.4492 0.2801 0.3811 0.3366 0.1417 0.3531 0.4723

CRSP-EW & all others 0.4616 CRSP-VW & all others 0.2627

0.6583 0.3878 0.3302 0.2750 0.2790 0.3771 0.1064 0.2949 0.3792

0.6268 0.3817 0.2976 0.2905 0.3047 0.2547 0.0805 0.2887 0.3484

0.5763 0.3429 0.2545 0.2636 0.2326 0.3138 0.0736 0.2442 0.3268

0.4443 0.4138 0.3982 0.3160 0.2950 0.3004 0.2791 0.2362 0.2377 0.2235

Panel B: w2 Statistics for Friedman’s Test No. of Temperature Bins 2 3 4 5

CRSP-EW and all Other Indices ^^

5.5000 6.1111^^ 8.5833^^ 9.6000^^

CRSP-VW and all Other Indices 5.6667^^ 5.2222^ 9.1667^^ 7.9333^

Note: 1. Spearman’s rank correlation is calculated based on the average temperature and return of each temperature bin. Please see the text for details. 2. Friedman’s two-way analysis of variance is used to test the temperature level effect. The test helps to determine if investors around the globe exhibit a uniform investment behavior within the same temperature range. The carets ^, ^^ and ^^^ indicate statistical significance of the w2 statistics at the 10%, 5% and 1% levels, respectively. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

and the highest minimum temperature is 8.151C (Australia). We therefore set 8.151C as the lower bound and 26.701C as the upper bound. Temperature bins are created within this range. The w2 statistics and their significance are reported in Panel B of Table 6. With up to ﬁve temperature bins, the w2 statistic is significant at the 5% or 10% level, indicating that investors around the globe do not react to the

An Expanded Study on the Stock Market Temperature Anomaly

101

same temperature level to the same extent. In other words, a universal temperature-level effect does not exist across markets. This is consistent with the w2 test on the temperature coefﬁcients from SUR. When the number of temperature bins is greater than ﬁve, the w2 statistics are no longer significant. With a large number of bins, the temperature range within each bin is too narrow (e.g., it is only [26.78.15]/6 ¼ 3.091C with six bins) to pick up return differences. Overall, our nonparametric tests indicate that, regardless of distributional assumptions and inter-market correlations, a negative correlation between temperature and stock returns exists for individual markets and for all markets combined. Our bin tests and regression analyses are therefore quite robust.

3.2. Tests Based on Temperature Deviations All tests done here or in CW (2005) show a very strong negative relation between returns and temperature. It is of interest to see whether a similar relation exists between returns and temperature deviations, the latter being the difference between daily temperature and the historical average daily temperature. A positive deviation means a warmer-than-normal day and a negative deviation means the opposite. The absolute level of temperature may capture its overall seasonal impacts on returns, while the temperature deviations can capture the impact of daily temperature shocks. Since deviations reﬂect whether a particular day is warmer or colder than normal, and since very cold days are in the winter and very hot days are in the summer, we combine positive deviations for the summer and negative deviations for the winter to perform joint analyses. This approach has three advantages: (1) it uses both positive and negative deviations, (2) it covers the whole year and (3) it emphasizes the impact of temperature deviations most relevant for the season. Again, we use the equal-size sample for comparability. As evident in Fig. 1, the plot of historical average daily temperatures is not very smooth, due to the relatively short sample period. (Keep in mind that even for the longest sample (US), there are only 37 observations for each day of the year.) To smoothen the historical average daily temperatures, we calculate moving averages of the historical averages using window sizes of 3, 7, 15 and 31 days. We create two versions of the daily moving average, depending on whether the current day is placed in the middle or at the end of the moving window. As shown in Fig. 2 (using New York as an example), including more days in the moving window leads to a smoother

MELANIE CAO AND JASON WEI 35.00

20.00 15.00 10.00 5.00 0.00

0

60

120 180 240 300 Day of the Year

360

30.00 25.00 20.00 15.00 10.00 5.00 -5.00

0

60

120 180 240 300 Day of the Year

30.00 25.00 20.00 15.00 10.00 5.00 0.00 -5.00

35.00

0.00

Moving Average of Historical Daily Temperature

25.00

-5.00

Moving Average of Historical Daily Temperature

35.00

30.00

360

Moving Average of Historical Daily Temperature

Moving Average of Historical Daily Temperature

102

0

60

120 180 240 300 Day of the Year

360

0

60

120

360

35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 -5.00

180

240

300

Day of the Year

Fig. 2. Moving Average of Historical Daily Average Temperature for New York. Note: (1) The Plots are for the Moving Average of the Historical Daily Average Temperatures presented in Fig. 1. The Moving Window symmetrically straddles the Current day. For example, in the case of a 3-day Moving Window, we use the Temperatures for the Previous day, the Current day and the Next day to calculate the Moving Average. (2) To obtain the Moving Average for Days at the Beginning and End of the Year, we simply stack the Historical Daily Average Temperatures. To continue the above example, the Moving Average for January 1, is calculated using the Historical Daily Average Temperatures for December 31, January 1 and 2.

curve, as one would expect. With various versions of the daily average, we calculate daily temperature deviations and use them to perform bin tests as in Table 2 and regressions as in (1). For brevity, we only report the temperature coefﬁcient and its t-value from OLS regressions in Table 7. The temperature coefﬁcient is negative for all markets and all sizes of moving windows. The only exception is Japan where the moving window is 15 days. The negative coefﬁcient is significant at the 10% level for U.S. (CRSP equal-weighted index), and significant at the 1% level for Taiwan. The results do not seem to be sensitive to the smoothing of daily average temperatures, and the R2 is largely comparable to that in Table 4 for each

Temperature Deviation Test with the Equal-Size Sample. rt ¼ a1+a2rt1+a3DtMon+a4DtTax+a5(k-day MW Temp Devt)+et

U.S. CSRP-EW U.S. CSRP-VW Canada Britain Germany Sweden Australia Japan Taiwan

0-day MW Temp Devt

R2

3-day MW Temp Devt

R2

7-day MW Temp Devt

R2

15-day MW Temp Devt

R2

31-day MW Temp Devt

R2

0.00044 1.88048 0.00048 1.42707 0.00036 1.26418 0.00052 1.00194 0.00052 0.82440 0.00031 0.48429 0.00002 0.15059 0.00044 0.40343 0.00526 3.59446

0.0950

0.00041 1.76797 0.00045 1.32952 0.00032 1.13381 0.00054 1.06361 0.00052 0.82889 0.00044 0.69038 0.00002 0.16027 0.00066 0.60249 0.00491 3.41922

0.0994

0.00041 1.75766 0.00046 1.36794 0.00031 1.12833 0.00054 1.06048 0.00053 0.84209 0.00063 0.99010 0.00003 0.19735 0.00064 0.60567 0.00470 3.27036

0.1035

0.00042 1.89810 0.00056 1.77095 0.00032 1.24374 0.00053 1.11128 0.00031 0.52593 0.00034 0.55604 0.00002 0.13186 0.00014 0.15232 0.00406 2.97286

0.0880

0.00039 1.76232 0.00047 1.44533 0.00033 1.22541 0.00053 1.04470 0.00052 0.84773 0.00061 0.97066 0.00002 0.17065 0.00068 0.65273 0.00475 3.35219

0.0909

0.0089 0.0295 0.0068 0.0043 0.0030 0.0014 0.0057 0.0123

0.0092 0.0306 0.0098 0.0047 0.0051 0.0014 0.0061 0.0104

0.0107 0.0371 0.0087 0.0049 0.0065 0.0014 0.0057 0.0094

0.0083 0.0465 0.0059 0.0050 0.0055 0.0010 0.0064 0.0102

0.0076 0.0407 0.0082 0.0064 0.0046 0.0015 0.0055 0.0102

103

Note: 1. For brevity, we only report the coefﬁcients and the t-values for temperature deviations together with R2 of the regressions. 2. The explanatory variable ‘‘k-day MW Temp Devt’’ (k ¼ 0; 3, 7, 15 and 31) is the deviation of daily temperature from a moving window average of historical daily temperatures. The moving window symmetrically straddles the current day and k is the number of days used to calculate the moving average. 3. The tax dummy covers the ﬁrst 10 trading days of the taxation year. The taxation year starts on April 6 in Britain, July 1 in Australia and January 1 in all other jurisdictions. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

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Table 7.

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regression. Overall, the correlation is understandably weaker in terms of statistical significance since we have removed the level effect. Nonetheless, the consistent sign across markets does imply a negative relation between temperature deviations and stock returns. The above results conﬁrm that the relationship between temperature and stock market returns is a manifestation of the day-to-day impacts of temperature shocks, as opposed to a reﬂection of purely seasonal effects. Subtracting the historical average from the realized temperatures amounts to removing any seasonal effects; what remains belongs to the realm of daily impacts. This is a significant point in that, just like the impact of sunshine, the temperature can exert psychological impacts on investors on a daily basis. The correlation between market returns and daily, season-adjusted temperature variations is the ultimate conﬁrmation of temperature impact on investors’ behavior.

3.3. Aggregating Temperature Impacts Across Regions We recognize that trades of a particular stock need not be always executed on the ﬂoor of the exchange. Stock price movements are due to trading actions of both local brokers/investors and market participants elsewhere. For instance, the trading registered on the NYSE is driven by investors in the city of New York and elsewhere. Conceivably, investors in other parts of the United States may be subject to quite a different weather condition. Therefore, as with the sunshine study of HS (2003), our study so far is subject to the question of investor concentration in the city which houses the stock exchange. Thankfully, unlike cloud cover or the amount of sunshine, temperatures tend to be highly correlated across regions. An indirect way to measure the aggregate temperature impact on market returns is to calculate the correlation between the average temperature across different regions and the national stock market index. This is the route we take. We identify seven major cities in the U.S. which represent the key regions of the country: Atlanta, Chicago, Dallas, Los Angeles, New York, Philadelphia and Seattle. The daily temperature data for all cities other than New York come from NCDC, which cover the period from January 1, 1982 to December 31, 1997. Two aggregate temperature indices are constructed, with the ﬁrst being a simple, equally weighted average of the seven temperature series, and the second being a population-weighted average. Bin tests and regression analyses are then performed using the CRSP indices and the aggregate temperature indices. Table 8 reports the results.

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It is seen that the general results for New York city alone from Table 2 (Panel A) and Table 4 (Panel A) also apply here, albeit the statistical significance for most estimates is now lower. It should be realized that the reduction in significance is not simply due to the use of a temperature index. A shorter sample period is undoubtedly another contributing factor, as is evident in Table 2. Nonetheless, a statistically significant, negative correlation between temperature and returns is largely preserved. For instance, three of the z-scores for mean return comparisons under three bins are significant at the 1% level, and one at the 5%. The t-value for the temperature coefﬁcient from regression analyses is significant at the 5% level for the CRSP equal-weighted index, and is far from zero for the CRSP valueweighted index. The above observations imply that our empirical ﬁndings are not subject to the criticism that the city housing the stock exchange may not represent the entire population of investors. While investors are scattered around the country, they are subject to very similar temperature variations because of the high correlations among regional temperatures.

3.4. Sub-Sample Results To provide some evidence on the intertemporal stability of the relationship between temperature and returns, we repeat the analyses for sub-samples. As in the previous sub-section, we focus on the U.S. market since the time series have the longest sample period. As shown in Table 1, the sample starts in 1962. To utilize all observations and to ensure rough equality between sub-samples, we cut the entire sample into three sub-periods corresponding to 1962–1974, 1975–1987 and 1988–1999, with the last sub-period approximately matching the equal-size sample period. Bin tests and OLS regression analyses are performed for each sub-sample and index. By and large, the qualitative relationship between temperature and market returns is quite stable. Quantitatively, the estimated coefﬁcients do not necessarily stay constant over time. To demonstrate this point, we report the regression results in Table 9. It is seen that, for both indices, the coefﬁcient for the temperature variable seems to be on the rise. This is just by chance since subsample analyses for other markets failed to produce similar results. Also, as evident in the t-values and the R2, the Monday effect, the tax effect and the temperature effect are all stronger in the equal-weighted index than in the value-weighted index for all sub-samples, consistent with the observations from previous tables.

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Table 8.

Aggregate Bin Test and Regression Analysis for the US CRSP Index.

Panel A: Bin Test No. of bins ¼ 3 bin 1 CRSP-EW TEMP-EW CRSP-EW TEMP-PW

CRSP-VW TEMP-PW

0.2273 0.5928 0.7103 0.2552 0.5719 0.7429 0.1517 0.8288 0.6012 0.1774 0.8105 0.6190

0.0982 0.7038 0.6289 0.0930 0.7037 0.6229 0.0625 0.9418 0.5433 0.0583 0.9373 0.5408

bin 3

z-score (3,1)

bin 1

bin 2

bin 3

bin 4

z-score (4,1)

0.0613 0.5020 0.6163 0.0617 0.5015 0.6169 0.0512 0.7463 0.5492 0.0512 0.7516 0.5490

4.7369

0.2030 0.5779 0.7265 0.2058 0.5806 0.7049 0.0884 0.9138 0.5812 0.1040 0.9029 0.6066

0.1490 0.5696 0.6432 0.1497 0.5533 0.6515 0.1014 0.7689 0.5555 0.0997 0.7524 0.5499

0.0669 0.7291 0.6241 0.0676 0.7306 0.6207 0.0422 0.9890 0.5468 0.0383 0.9895 0.5448

0.0579 0.5099 0.6155 0.0570 0.5153 0.6137 0.0530 0.7524 0.5479 0.0578 0.7586 0.5522

2.6317

3.3941 5.6465 4.6493 2.0368 1.7549 2.5804 2.3575

2.5704 2.7380 2.1061 0.4082 0.7015 0.5491 1.1766

Panel B: Regressions rt ¼ a1+a2rt1+a3DtMon+a4DtTax+a5Tempt+et

CRSP-EW, TEMP-EW

a1

a2

a3

a4

a5

R2

0.1017 9.4363

0.3265 22.0490

0.2911 12.7452

0.1480 3.0545

0.0252 2.2129

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CRSP-VW TEMP-EW

Return mean Std. Dev. of return % of positive returns Return mean Std. Dev. of return % of positive returns Return mean Std. Dev. of return % of positive returns Return mean Std. Dev. of return % of positive returns

bin 2

No. of bins ¼ 4

CRSP-VW, TEMP-EW CRSP-VW, TEMP-PW

0.1008 9.1853 0.0638 3.9890 0.0629 3.8695

0.3266 22.0515 0.1206 7.7299 0.1206 7.7300

0.2911 12.7460 0.0757 2.2471 0.0757 2.2476

0.1489 3.0761 0.0096 0.1340 0.0098 0.1373

0.0211 2.1829 0.0180 1.0661 0.0154 1.0727

0.1375 0.0162 0.0162

Note: 1. This table presents bin test and regression results for the US CRSP index (equal- or value-weighted) and the aggregate temperature which is either equal-weighted (TEMP-EW) or population-weighted (TEMP-PW) average of temperatures in the following cities: Atlanta, Chicago, Dallas, Los Angeles, New York, Philadelphia and Seattle. The sample period is from January 1, 1982 to December 31, 1997. qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ frequence 2 2 2. z_scoremean ¼ ðpk p1 Þ= pk ð1 pk Þ=nk þ p1 ð1 p1 Þ=n1 ; where mi and si are the return k;1 ¼ ðmk m1 Þ= sk =nk þ s1 =n1 and z_scorek;1 mean and standard deviation for bin i; pi the percentage of positive returns in bin i; and ni the number of observations in bin i for each statistic. 3. For the regression test, we only indicate the significance for explanatory variables DtMon, DtTax and Tempt. 4. The tax dummy covers the ﬁrst 10 trading days of the taxation year which starts on January 1. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

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CRSP-EW, TEMP-PW

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Table 9. Regression for the Sub-Sample Periods of the US CRSP Index. rt ¼ a1+a2rt1+a3DtMon+a4DtTax+a5Tempt+et a1

a2

a3

CRSP equal-weighted index 1962–1974 0.0650 4.2846 1975–1987 0.0966 6.8638 1988–1999 0.1033 8.5317

0.4262 26.3470 0.3722 23.0726 0.3015 17.4744

0.3249 10.7572 0.3453 12.1044 0.2380 9.4430

CRSP value-weighted index 1962–1974 0.0596 3.7487 1975–1987 0.0797 4.0913 1988–1999 0.0483 2.6737

0.2861 16.7847 0.1727 10.0770 0.0699 3.8628

0.2622 8.3144 0.1926 4.9176 0.0111 0.2968

a4

0.2439 3.7389 0.1978 3.2673 0.0534 1.0055

0.0632 0.9310 0.0958 1.1518 0.1347 1.7010

a5

R2

0.0009 0.7004 0.0025 2.0579 0.0036 3.2776

0.2087

0.0007 0.5088 0.0008 0.4751 0.0038 2.3486

0.1706 0.1162

0.0993 0.0368 0.0075

Note: 1. For each regression, the ﬁrst row contains the parameter estimates, and the second row contains the t-values. The R2 for each regression is reported in the last column. 2. For clarity, we only indicate the significance for explanatory variables DtMon, DtTax and Tempt. 3. The tax dummy covers the ﬁrst 10 trading days of the taxation year. The taxation year starts on January 1, in the US. 10% statistical significance level for two-sided test; 5% statistical significance level for two-sided test; 1% statistical significance level for two-sided test.

4. CONCLUSION This is a companion paper to our previous study in Cao and Wei (2005) where we have identiﬁed a stock market temperature anomaly. This line of work is parallel to studies which relate stock market returns to naturerelated variables such as the amount of sunshine in Sanders (1993) and HS (2003), the length of daylight in KKL (2003). The common feature shared by these studies is the same chain of reasoning: environmental variables, such as sunshine, length of daylight and temperature, affect the mood of the people which in turn inﬂuences people’s behavior. Such thinking is motivated and supported by literature on mood and decision-making. For example, Mehra and Sah (2002) show theoretically that the emotional state of investors will inﬂuence equity prices when investors’ subjective parameters such as risk-aversion change in response to mood ﬂuctuations.

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Saunders (1993) and HS (2003) demonstrate that less cloud cover is associated with higher returns and the returns on most cloudy days are significantly different from the returns on the least cloudy days. Their argument is that investors’ mood is upbeat or optimistic on sunny days, which uplifts the stock market returns, and that their pessimistic mood on cloudy days depresses the stock returns. KKL (2003) ﬁnd that lower returns are associated with longer nights. Their explanation rests on the impact of SAD on human behavior. They conjecture that lower returns are caused by investors who are depressed because of longer nights. Our study on temperature anomaly relies on a body of psychological literature concerning the impact of temperature on people’s mood and behaviors. The evidence shows that low temperature tends to cause aggression and high temperature tends to cause aggression, hysteria and apathy. We therefore hypothesize that lower temperature leads to higher stock returns due to investors’ aggressive risk-taking, and higher temperature can lead to higher or lower stock returns since aggression and apathy have competing effects on risk-taking. A statistically significant negative relationship between temperature and stock returns is found for eight international markets in CW (2005). In this companion paper, we expand our previous sample to include 19 additional ﬁnancial markets studied by either HS (2003) or KKL (2003). We provide strong evidence in support of the uncovered negative relationship between temperature and stock returns. This relationship prevails even after controlling for the Monday effect, the tax-loss effect, the sunshine effect and the SAD effect. More importantly, our nonparametric tests, as opposite to the parametric or semi-parametric approaches used in previous studies, demonstrate that this negative relationship is robust to distributional assumptions. Based on the sub-sample analysis, we ﬁnd that this negative relationship is stable over time. Furthermore, we consider temperature deviation and demonstrate that this negative relationship is not just a level effect.

NOTES 1. Other authors, such as Dichev and Janes (2003), Yuan, Zheng, and Zhu (2001), link stock market returns to lunar cycle. While Dichev and Janes (2003) focused on the US market only, Yuan et al. (2001) examined 48 international markets in depth. After removing the usual anomalies such as the January effect and the dayof-the-week effect, they showed that stock returns are much lower on days around a full moon than on days around a new moon.

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2. For comprehensive studies regarding temperature impacts on human behaviors, refer to Allen and Fisher (1978), Anderson (2001), Baron and Ransberger (1978), Bell (1981), Bell and Baron (1976), Cunningham (1979), Howarth and Hoffman (1984), Keller et al. (2005), Palamerek and Rule (1980), Parsons (2001), Persinger (1980), Pilcher, Nadler, and Busch (2002), Rind (1996), Rotton and Cohn (2000), Sanders and Brizzolara (1982), Schneider, Lesko, and Garrett (1980), Watson (2000) and Wyndham (1969). 3. EarthSat’s home page: http://www.earthsat.com. This is the company which provides quality temperature data for the settlement of weather derivative contracts traded at the Chicago Mercantile Exchange. 4. Returns and standard deviations are always expressed in percentage forms throughout the paper. 5. ‘‘Historical average daily temperature’’ refers to the average of daily temperature for each calendar day in the sample period. There are 366 such averages, including February 29 in leap years. 6. Following our study (CW, 2005), we only report two-tail tests throughout the paper. We use two-tail tests for conservative reasons, although we have a strong prior that an overall negative correlation exists between temperature and stock returns. Please note that, for one-tail tests at the 10% significance level, the critical z-score or t-value for a large enough sample is 1.282.

ACKNOWLEDGMENTS Both authors are grateful to the Social Sciences and Humanities Research Council of Canada for ﬁnancial support. They would like to thank conference participants at the 2002 Financial Management Association meeting, the 2002 Northern Finance Association meeting and the 2003 Western Finance Association meeting for helpful discussions and comments.

REFERENCES Allen, A. M., & Fisher, G. J. (1978). Ambient temperature effects on paired associate learning. Ergonomics, 21(2), 95–101. Anderson, C. A. (2001). Heat and violence, current directions in psychological science. Current Directions in Psychological Science, 10, 33–38. Baron, R. A., & Ransberger, V. M. (1978). Ambient temperature and the occurrence of collective violence: The long, hot summer revisited. Journal of Personality and Social Psychology, 36, 351–360. Bell, P. A. (1981). Physiological comfort, performance and social effects of heat stress. Journal of Social Issues, 37, 71–94. Bell, P. A., & Baron, R. A. (1976). Aggression and heat: The mediating role of negative affect. Journal of Applied Social Psychology, 6, 18–30.

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Cao, M., & Wei, J. (2005). Stock market returns: A note on temperature anomaly. Journal of Banking and Finance, 29, 1559–1573. Cunningham, M. R. (1979). Weather, mood and helping behavior: Quasi-experiment with the sunshine samaritan. Journal of Personality and Social Psychology, 37, 1947–1956. Dichev, I. D., & Janes, T. D. (2003). Lunar cycle effects in stock returns. Journal of Private Equity, 6(4), 8–29. Etzioni, A. (1988). Normative-affective factors: Towards a new decision-making model. Journal of Economic Psychology, 9(2), 125–150. French, K. R., Schwert, G. W., & Stambaugh, R. F. (1987). Expected stock returns and volatility. Journal of Financial Economics, 19, 3–29. Hanock, Y. (2002). ‘‘Neither an angel nor an ant’’: Emotion as an aid to bounded rationality. Journal of Economic Psychology, 23(1), 1–25. Hirshleifer, D., & Shumway, T. (2003). Good day sunshine: Stock returns and the weather. Journal of Finance, 58(3), 1009–1032. Howarth, E., & Hoffman, M. S. (1984). A multidimensional approach to the relationship between mood and weather. British Journal of Psychology, 75, 15–23. Kamstra, M. J., Kramer, L. A., & Levi, M. D. (2003). Winter blues: A SAD stock market cycle. American Economic Review, 93(1), 324–333. Keller, M. C., Fredrickson, B. L., Ybarra, O., Coˆte´, S., Johnson, K., Mikels, J., Conway, A., & Wager, T. (2005). A warm heart and a clear head: The contingent effects of weather on mood and cognition. Psychological Science, forthcoming. Loewenstein, G. F., Weber, E. U., Hsee, C. K., & Welch, N. (2001). Risk as feelings. Psychological Bulletin, 127(2), 267–286. Mehra, R., & Sah, R. (2002). Mood ﬂuctuations, projection bias and volatility of equity prices. Journal of Economic Dynamics and Control, 26, 869–887. Palamerek, D. L., & Rule, B. G. (1980). The effects of ambient temperature and insult on the motivation to retaliate or escape. Motivation and Emotion, 3, 83–92. Parsons, A. G. (2001). The association between daily weather and daily shopping patterns. Australasian Marketing Journal, 9(2), 78–84. Persinger, M. A. (1980). The weather matrix and human behavior. New York: Praeger Press. Pilcher, J. J., Nadler, E., & Busch, C. (2002). Effects of hot and cold temperature exposure on performance: A meta-analytic review. Ergonomics, 45(10), 682–698. Rind, B. (1996). Effects of beliefs about weather conditions on tipping. Journal of Applied Social Psychology, 26, 137–147. Romer, P. M. (2000). Thinking and feeling. American Economic Review, 90(2), 439–443. Rotton, J., & Cohn, E. G. (2000). Violence is a curvilinear function of temperature in Dallas: A replication. Journal of Personality & Social Psychology, 78, 1074–1081. Sanders, J. L., & Brizzolara, M. S. (1982). Relationship between mood and weather. Journal of General Psychology, 107, 157–158. Saunders, E. M. J. (1993). Stock prices and wall street weather. American Economic Review, 83, 1337–1345. Schneider, F. W., Lesko, W. A., & Garrett, W. A. (1980). Helping behavior in hot, comfortable and cold temperature: A ﬁeld study. Environment and Behavior, 2, 231–241. Schwarz, N. (1990). Feelings as information: Informational and motivational functions of affective states. In: E. T. Higgins & R. M. Sorrentino (Eds), Handbook of motivation and cognition (Vol. 2, pp. 527–561). New York: Guilford Press.

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Schwert, G. W. (1989). Why does stock market volatility change over time? Journal of Finance, 44, 1115–1153. Watson, D. (2000). Mood and temperament. Situational and environmental influence on mood. New York: Guilford Press (Chapter 3). Wyndham, H. C. (1969). Adaptation to heat and cold. Environmental Research, 2, 442–469. Yuan, K., Zheng, L., & Zhu, Q. (2001). Are investors moonstruck? Lunar phases and stock returns. Journal of Empirical Finance, forthcoming.

VALUE AND GROWTH INVESTING IN ASIAN STOCK MARKETS 1991–2002 Joseph Kang and David Ding ABSTRACT The study discussed in this article examines two empirical questions: (1) Can multiple financial signals enhance the intermediate-horizon returns of value and glamour investments on Asian stock markets? and (2) Do the return enhancements, if any, differ by value and growth firm types and vary across different markets? The results of this study show that financial signals affect return enhancements, and these enhancements differ by firm types and vary across markets. These differences can be explained by non-positive value premiums and relatively poor information quality documented on Asian markets.

1. INTRODUCTION Value and growth investing are now widely recognized investment strategies, especially for hedge funds, and a large amount of research has been conducted to investigate issues related to this type of investing. Recent studies on the US equity market ﬁnd that substantial enhancements in the intermediate-horizon returns of value and growth stock portfolios can be Research in Finance, Volume 22, 113–139 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22004-X

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obtained by using multiple ﬁnancial signals extracted from a simple ﬁnancial statement analysis.1 As a result of these ﬁndings and the implications for asset pricing in as well as value and glamour investing on emerging equity markets, the study discussed in this article examines the effect of ﬁnancial signals on the intermediate-horizon returns of value and glamour investments on Asian stock markets and whether return enhancements, if any, differ by value and growth ﬁrm types and vary across markets. The present study examines stocks traded from January 1991 to December 2002 on six relatively liquid Asian markets: Hong Kong, Korea, Malaysia, Singapore, Taiwan, and Thailand. These six Asian markets attract disproportionately large asset pricing studies and attention from emerging-market investors because, as with the Japanese market, these markets have experienced rapid market deregulation and liberalization since the late 1980s. The second half of the sample period included events such as the Asian ﬁnancial crisis (1997–1998), the dot.com collapse (1999), the Enron scandal (2000), the terrorist attack on the U.S. (2001), and severe economic recessions (2000–2002). Since good and bad market conditions prevailed in the pre-1997 and post-1996 periods, the results of this study should be of particular interest to both academicians and market practitioners. The remainder of this article is organized as follows: Section 2 is a review of the literature; Section 3 describes the aim of the study; Section 4 discusses the data and methodology; Section 5 discusses the study results; Section 6 tests whether the present study’s ﬁndings are robust for ﬁrm size, bookto-market (BTM) ratio, market conditions, and other intervening effects; and Section 7 summarizes the results and concludes the article.

2. REVIEW OF THE LITERATURE On US markets and markets in other developed countries, the 1- and 2-year returns of high BTM, or value, stocks tend to be larger than those of low BTM (growth or glamour) stocks. This empirical irregularity has resulted in the popularity of value investing. Fama and French (1992) claim that the positive, medium-term, valuegrowth spread (value premium or BTM effect) is consistent with rational equity pricing because a higher BTM ratio reﬂects the higher common risk of value stocks. Lakonishok, Shleifer, and Vishny (1994) use a behavioral perspective and claim that the value-growth spread is a result of investors’ irrational upward-biased (downward-biased) expectations on future returns

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for glamour (value) stocks, which are reversed only in intermediate horizons. The conclusions of Fama and French and Lakonishok et al. led many researchers to investigate the profitability of value investing.2 Growth investing is also a popular strategy, and it occurs when professional investors herd on glamour stocks, especially in shorter-term horizons. This herding leads to return continuations for glamour stocks: namely, glamour stocks with a strong appreciation in the prior period (i.e., those with low-BTM ratios) continue to outperform value stocks with a weak appreciation in the prior period (i.e., those with high-BTM ratios). The results of studies by Fama and French (1998) and many others show non-positive value-growth spreads (i.e., non-positive value premiums or non-positive BTM effects) in most emerging markets.3 These results suggest that growth investing may be a profitable strategy on emerging markets. Although it appears that positive (negative) value premiums have led to the profitability of value (growth) investing, Fama (1998) suggests that the value premium might be a time-specific irregularity that has no systematic explanation. Chan and Lakonishok (2004) examine the possibility that the value-growth spread has a time-specific nature. Their study ﬁnds that the superior returns from value investments are not time-specific. Recent studies on value or glamour investing have examined whether multiple ﬁnancial signals extracted from a simple ﬁnancial statement analysis help identify those value- or growth-style investments with the potential for enhanced returns. Piotroski (2000) focuses on value-style investments and measures ﬁnancial signals using nine proxies: six binary proxies for profitability and operating efﬁciency (return on asset and its change, cashﬂow ratio, cash ﬂow ratio minus return on asset, change in profit margin, and change in asset turnover ratio) and three binary proxies for ﬁnancial risk (change in leverage, change in current ratio, and equity offering). He aggregates the binary values of nine proxies into a composite index for ﬁnancial signals (F-SCORE), in which 9 (0) stands for a value ﬁrm with exceptionally strong (weak) ﬁnancial signals. Partitioning value ﬁrms according to the F-SCORE, he ﬁnds that from 1976 to 1996 value stocks with strong ﬁnancial signals (i.e., value stocks in the highest two F-SCORE deciles) earned a market-adjusted return of 13.4% (28.7%) in the ﬁrst (second) year after portfolio formation, which was 7.5% (16%) above the return of value stocks as a whole.4 According to Piotroski (2000), return enhancements for value stocks can be expected because few analysts follow these stocks, their price is based mainly on ﬁnancial statement information, and they do not trade in rapid information dissemination environments. Implicit in his explanation is that

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return enhancements for glamour stocks would be substantially smaller because they are followed by many stock analysts. However, the presence of large return enhancements for glamour stocks strongly supports the idea of a ﬁnancial signals effect. Motivated by the need for a stronger test, Mohanram (2003) examines the ﬁnancial signals effect for glamour stocks using the F-SCORE index as well as the FG-SCORE index. The FG-SCORE index is an expanded F-SCORE index that contains additional binary proxies related to glamour stocks. He found that from 1979 to 1999, glamour stocks with strong ﬁnancial signals earned 2.1% (0.9%) for the ﬁrst (second) year after portfolio formation, which is 8.1% (5.1%) above the return for growth stocks as a whole.5 These results strongly support the idea that multiple ﬁnancial signals can also be used to enhance market-adjusted returns for glamour stocks. Such return enhancements may be possible because the inclusion of more ﬁnancial signals may reveal a stock’s future return potential that is not fully captured by the BTM ratio. The ﬁnancial signals effect may be more important than the value-growth spread because the popularity of value and growth investing could have led investors to arbitrage away the abnormal returns obtained by ﬁltering stocks according to the BTM ratio.6 The results on glamour stocks are consistent with Piotroski’s (2000) explanation that glamour (value) ﬁrms face relatively fast (slow) information dissemination environments. Implicit in the explanation is that a larger (smaller) number and higher (lower) quality of analysts covering a glamour (value) ﬁrm would lead to investors’ good (bad) perceptions of the quality of the ﬁrm’s ﬁnancial statement information, and, as a result, the glamour (value) stock price will adjust to ﬁnancial statement information relatively fast (slow). The different speed of price adjustments to ﬁnancial statement information suggests that the return-enhancing effect of ﬁnancial signals will be relatively small (large) for glamour (value) ﬁrms. The results in Piotroski (2000) and Mohanram (2003) are also supportive of the prediction that the ﬁnancial signals effect differs by ﬁrm type. What are the non-US market implications of the explanation and evidence of the ﬁnancial signals effect? As compared to developed markets, the perceived quality of ﬁnancial statement information in less-developed markets is much lower, and, as a result, the stock price adjustment to ﬁnancial statement information may be either quite slow or inconsequential. There are also much fewer quality ﬁrms available for reputable analysts to follow. For example, reputable analysts follow mostly large and glamour ﬁrms in emerging markets because only

Value and Growth Investing in Asian Stock Markets 1991–2002

117

these ﬁrms attract much attention from (global) institutional investors whose utmost concerns are equity ownership restrictions and market liquidity (ﬂoat). The perceived quality difference between such and other ﬁrms’ ﬁnancial statement information would be much larger in these markets than in developed markets. These considerations suggest that the ﬁnancial signals effect on these markets would be quite different from that on the US and other developed markets.

3. AIM OF THE STUDY The present study is motivated by the empirical evidence of a ﬁnancial signals effect on the US equity market and its implications on asset pricing as well as value and glamour investing on emerging markets. The study in this article addresses two specific empirical questions: (1) Can ﬁnancial signals extracted from a simple ﬁnancial statement analysis enhance the intermediate-horizon returns of value and glamour investments on Asian stock markets? and (2) Do the return enhancements, if any, differ by value and growth ﬁrm types and vary across different markets? Addressing the ﬁrst question in the present study may constitute an even stronger test of the ﬁnancial signals effect particularly because investigating the effect of ﬁnancial signals on Asian markets would be difﬁcult for at least three reasons. First, because U.S and Asian markets are not highly integrated, Asian markets may not experience the empirical irregularity observed on the United States. Second, because the quality of ﬁnancial statement information for Asian companies is considered to be relatively poor, the ﬁnancial signals effect may not be as large as the effect on the United States. Third, because Asian markets tend to exhibit nonpositive value premiums, the ﬁnancial signals effect may be relatively small for value stocks when compared to US value stocks and Asian glamour stocks. The present study also examines whether the ﬁnancial signals effect differs by ﬁrm types and across markets. The results obtained from addressing the second question may be helpful in identifying additional explanations of the ﬁnancial signals effect: e.g., the investors’ perceptions on the quality of ﬁnancial statement information, which would differ by ﬁrm type and across markets. The results of this study can also beneﬁt professional investors on emerging markets for at least three ways. First, if the ﬁnancial signals effect is not present on Asian markets, then investors should be aware that the

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profitability of value and glamour investing is limited on these markets. Second, if the ﬁnancial signals effect is present on Asian markets, then a simple fundamental analysis of Asian corporations can be useful for valuation and portfolio investment purposes, especially because investors know that ﬁrm size and BTM ratio are unimportant pricing factors on these markets. Third, if the ﬁnancial signals effect differs according to ﬁrm type and across markets, then professional investors will be able to tailor their investment strategies to accommodate different ﬁrm type and market.

4. DATA AND METHODOLOGY 4.1. Data The present study tests the ﬁnancial signals effect for stocks traded from January 1991 to December 2002 on six relatively liquid Asian stock markets that attract global investors: Hong Kong, Korea, Malaysia, Singapore, Taiwan, and Thailand. There are at least three reasons why these markets attract global investors. First, they are relatively liquid as the stocks traded on these markets have less-severe restrictions on foreign ownership and foreign exchange compared to China and other emerging Asian markets. Second, over the past two decades, these markets have had the fastest-growing high-tech industries in Asia. Third, according to the Asian Corporate Governance Association (http://www.acga-asia.org), these markets score relatively high in terms of corporate governance quality. The sample in the present study consists of all non-ﬁnancial ﬁrms listed on the main boards that have the ﬁnancial data needed to measure a ﬁrm’s F-SCORE. Using stocks listed on the main boards avoids the stale price problem facing young, small, and non-liquid stocks, which could impair the measurement of ﬁnancial signals. Data on month-end stock prices and annual ﬁnancial statements are collected mainly from four databases: PACAP, BLOOMBERG, COMPUSTAT, and COMPANY ANALYSIS. The total number of ﬁrm-year observations is 14,797, while the ﬁrm-year observations for value and glamour stocks are 7,264 and 7,534, respectively. Table 1 provides a summary of the main ﬁnancial characteristics of highand low-BTM portfolios. The average size of glamour ﬁrms is larger than that of value ﬁrms in all markets, while the ratio between the two averages ranges from 2.27

Hong Kong High (n ¼ 1587)

Low (n ¼ 1675)

Korea High (n ¼ 1379)

Low (n ¼ 1424)

Malaysia High (n ¼ 1199)

Low (n ¼ 1216)

Singapore High (n ¼ 1112)

MVE

BTM

ROA

DROA

CFO

ACR

DLEV

DLIQ

EQ%

DP

DTURN

AVG SD %+ AVG SD %+

3.4 (10.9) n/a 27.8 (68.0) n/a

1.7 (0.5) n/a 0.4 (0.3) n/a

6.9 (20.8) 88.5 9.3 (16.2) 82.8

0.0 (0.3) 41.2 0.1 (0.2) 33.5

4.7 (13.7) 77.4 10.1 (15.3) 81.6

2.0 (21.6) 49.0 1.0 (16.0) 56.0

0.0 (0.1) 32.1 0.0 (0.1) 27.6

1.0 (20.3) 42.8 0.1 (1.6) 50.6

54.3 13.4 n/a 79.5 19.5 n/a

0.1 (2.3) 48.1 0.0 (2.1) 40.6

0.1 (0.6) 37.0 0.2 (0.6) 33.5

AVG SD %+ AVG SD %+

2.7 (15.2) n/a 20.4 (62.0) n/a

5.0 (3.9) n/a 1.5 (2.2) n/a

0.6 (7.0) 69.2 8.2 (25.7) 54.1

0.0 (1.0) 40.7 0.0 (0.3) 45.9

3.3 (10.0) 67.1 4.9 (13.6) 68.0

2.0 (11.0) 69.0 13.0 (24.8) 82.0

0.0 (0.1) 48.5 0.0 (0.2) 41.6

0.0 (0.6) 58.4 0.2 (1.2) 58.0

49.3 17.5 n/a 71.8 21.7 n/a

0.0 (0.2) 42.5 0.1 (1.8) 46.3

0.1 (0.8) 33.2 0.1 (0.5) 41.1

AVG SD %+ AVG SD %+

0.6 (0.8) n/a 5.8 (13.9) n/a

2.8 (1.7) n/a 0.3 (0.2) n/a

5.8 (16.6) 90.3 7.9 (11.7) 86.1

0.0 (0.2) 37.2 0.0 (0.1) 42.2

2.3 (20.9) 64.8 9.5 (20.7) 78.9

4.0 (30.2) 50.0 2.0 (20.4) 66.0

0.0 (0.1) 47.9 0.0 (0.1) 28.3

0.1 (2.3) 52.0 0.1 (1.3) 49.4

62.7 17.7 n/a 73.5 19.9 n/a

2.8 (39.6) 44.4 0.3 (3.1) 44.6

0.1 (1.4) 39.8 0.1 (0.7) 41.6

AVG SD %+

0.9 (1.7) n/a

2.6 (2.0) n/a

4.0 (6.6) 85.1

0.0 (0.1) 38.7

2.8 (14.5) 69.4

1.0 (14.4) 55.0

0.0 (0.1) 48.3

0.1 (1.6) 53.2

59.9 21.2 n/a

0.0 (0.1) 41.9

0.2 (0.9) 38.7

Value and Growth Investing in Asian Stock Markets 1991–2002

Table 1. Financial Characteristics of High and Low BTM Firms by Markets: 1991–2002.

119

120

Table 1. (Continued )

Low (n ¼ 1169)

Taiwan High (n ¼ 1074)

Low (n ¼ 1098)

Thailand High (n ¼ 912)

BTM

ROA

DROA

CFO

ACR

DLEV

DLIQ

EQ%

DP

DTURN

AVG SD %+

9.0 (28.9) n/a

0.4 (0.2) n/a

2.6 (41.8) 50.4

0.1 (0.4) 32.8

7.0 (26.4) 33.6

4.0 (24.0) 66.0

0.0 (0.1) 46.0

0.5 (5.5) 53.0

76.7 23.2 n/a

0.1 (0.3) 37.2

0.0 (0.6) 37.0

AVG SD %+ AVG SD %+

0.6 (0.5) n/a 18.9 (1.3) n/a

4.3 (3.9) n/a 1.2 (0.6) n/a

0.6 (8.2) 69.4 24.4 (267.7) 89.1

0.0 (0.1) 33.8 0.4 (6.5) 31.8

0.8 (11.1) 64.4 13.0 (121.6) 72.3

0.2 (13.5) 58.0 11.0 (147.7) 51.0

0.0 (0.1) 48.0 0.0 (0.1) 28.6

0.1 (1.6) 55.9 0.1 (1.2) 51.8

36.7 13.4 n/a 51.2 24.2 n/a

0.3 (4.2) 37.7 0.1 (0.7) 35.5

0.0 (0.2) 40.9 0.1 (20.5) 44.1

AVG SD %+ AVG SD %+

1.5 (2.8) n/a 3.4 (10.7) n/a

6.8 (5.4) n/a 0.5 (0.4) n/a

3.4 (5.4) 86.1 40.0 (510.7) 84.8

0.0 (0.1) 27.5 0.0 (6.5) 35.2

1.4 (13.8) 58.6 2.9 (170.2) 75.2

2.0 (13.2) 49.6 43.0 (680.3) 67.0

0.0 (0.1) 49.7 0.0 (0.1) 25.7

0.1 (0.8) 52.0 0.0 (1.7) 56.1

69.8 20.6 n/a 82.7 14.8 n/a

0.0 (0.3) 32.8 0.0 (0.3) 42.2

0.1 (0.4) 38.5 0.1 (1.4) 37.4

Abbreviation: n, ﬁrm-year observations; n/a, not applicable; %+, the fraction of ﬁrm-year observations that are positive in the variable; MVE, market value of equity at the beginning of a ﬁscal year (in 10 US$ Million); BTM, book value of equity at the beginning of a ﬁscal year, scaled by MVE; ROA, net income at the beginning of ﬁscal year, scaled by total assets; DROA, change in ROA; CFO, CFO ratio (the cash ﬂow from operations, scaled by total assets); ACR, accrual (CFO ratio minus ROA); DLEV, change in the debt-to-total asset ratio; DLIQ, change in the current ratio (the ratio between current assets and current liabilities); EQ%, the proportion of ﬁrms that make equity offerings; DP, change in the margin (the net sales minus the cost of goods sold, scaled by net sales), DTURN, change in the asset turnover ratio (the ratio between total asset and net sales).

JOSEPH KANG AND DAVID DING

Low (n ¼ 952)

MVE

Value and Growth Investing in Asian Stock Markets 1991–2002

121

(Thailand) to 31.71 (Taiwan). Value portfolios in this sample consist of relatively small ﬁrms (especially in Taiwan), a ﬁnding similar to that for the United States (e.g., Fama & French, 1995). The mean sizes of these value and glamour ﬁrms are, however, substantially smaller than the US ﬁrms reported in Piotroski (2000) and Mohanram (2003). The average BTM ratio for value ﬁrms ranges from 1.72 (Hong Kong) to 6.76 (Thailand), while the average BTM ratio for glamour ﬁrms ranges from 0.31 (Malaysia) to 1.45 (Korea). These BTM ratios are several times larger than the ratios found in US studies (see Piotroski, 2000; Mohanram, 2003). Although the BTM ratios for the glamour ﬁrms in the present study are not much different from those reported in earlier studies on Asian markets (e.g., Chui & Wei, 1998; Barry, Glarier, Lockwood, & Rodriguez, 1999), the BTM ratios are larger for value ﬁrms. For example, Chui and Wei (1998) report that the BTM ratios for medium-size value portfolios range from 0.81 (Thailand) to 2.93 (Korea). The statistics for the profitability of value ﬁrms are similar to those in Piotroski’s (2000) study, while the statistics for glamour ﬁrms are different from those in Mohanram’s (2003) study. These statistics indicate that value ﬁrms in Hong Kong, Korea, Singapore, and Taiwan had slightly stronger ﬁnancial signals for corporate profitability. The statistics for ﬁnancial risk and operating efﬁciency indicate that glamour ﬁrms in Hong Kong and Thailand had stronger ﬁnancial signals for ﬁnancial risk, while value ﬁrms in Hong Kong and Singapore had stronger ﬁnancial signals for operating efﬁciency. Altogether, these statistics suggest that although their stock prices were temporarily distressed, value ﬁrms in Asia were not ﬁnancially weak.7

4.2. Methodology The method used in the present study is based on Piotroski’s (2000) methodology. To construct BTM portfolios for each ﬁscal year, each ﬁrm’s BTM ratio is computed by dividing the book value of equity by the market value of equity at the beginning of a ﬁscal year. Stocks are ranked according to BTM ratios and then grouped into a tercile portfolio. In the present study, stocks in the highest BTM tercile are labeled high-BTM stocks, and stocks in the lowest tercile are labeled low-BTM stocks. The analysis in this study employs the F-SCORE index (Piotroski, 2000) that aggregates the binary ﬁnancial signals extracted from four proxies for profitability, three proxies for ﬁnancial risk, and two proxies for operating

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JOSEPH KANG AND DAVID DING

efﬁciency. Specifically, the F-SCORE index is computed as F_SCORE ¼ F_ROA þ F_DROAþF_CFO þ F _ACR þ F _DLEV þ F_DLIQþF_EQ þ F _DP þ F_DTURN

ð1Þ

Each binary proxy equals 1 (0) if realization for the ﬁscal year is good (bad). In the case of binary proxies for profitability (F_ROA, F_DROA, F_CFO, and F_ACR) and operating efﬁciency (F_DP and F_DTURN), each variable equals 1 if the underlying variable is positive and 0 if otherwise. For example, F_ACR equals 1 if the CFO ratio4ROA and 0 if otherwise. Similarly, F_DLEV (F_DLIQ) equals 1 if its underlying variable is negative (positive), and F_EQ equals 1 if there is no equity offering for the ﬁscal year. Therefore, the F-SCORE can range from 0 (the worst) to 9 (the best). For more details, see Table 1. High- and low-BTM stocks are then ranked according to the F-SCORE and grouped into an F-SCORE decile portfolio. Like the U.S. stocks in Piotroski (2000) and Mohanram’s (2003) studies, very few stocks in the present sample had an F-SCORE of 0 or 1 (especially in Taiwan), and very few stocks had an F-SCORE of 9 (especially in Thailand). In this study, high F-SCORE stocks (stocks with strong ﬁnancial signals) are the stocks in the top two F-SCORE deciles (stocks with an F-SCORE of 8 or 9), and low F-SCORE stocks are the stocks in the bottom three deciles (stocks with an F-SCORE of 0, 1, or 2). High F-SCORE ﬁrms in Piotroski (Mohanram) have 8 or 9 (7, 8, or 9) scores, and low F-SCORE ﬁrms in Piotroski (Mohanram) have 0 or 1 (0, 1, 2, or 3) scores. Future returns are measured for both 1- and 2-year market-adjusted returns, where market-adjusted returns are computed as unadjusted buyand-hold returns minus value-weighted market returns for a holding period. The equal-weighted market returns are not used in the present study because they give more weight to returns of value ﬁrms and yield quantitatively stronger results more susceptible to outliers. Firms are delisted for many reasons, including mergers, takeovers, and bankruptcies, and the stocks that are delisted during a holding period are excluded from the analysis because exclusion or assigning zero returns did not yield significantly different results.8 For each stock, the holding period starts 6 months after the end of its ﬁscal year, which is the end of the calendar year for nearly half of the sample ﬁrms. As Piotroski (2000) and Mohanram (2003) note, parametric tests of the differences among returns of high- and low-F-SCORE portfolios and value and glamour portfolios can be problematic due to low-frequency data.

Value and Growth Investing in Asian Stock Markets 1991–2002

123

Therefore, the test statistics obtained from a bootstrapping technique similar to that in Piotroski (2000) are provided.9

5. EMPIRICAL FINDINGS The F-SCORE index for ﬁnancial signals (Piotroski, 2000) is used to test for the effect of ﬁnancial signals on enhanced returns. The results show that the ﬁnancial signals effect exists on most markets, varies over time, and differs by ﬁrm type. These ﬁnancial signals effects are not, however, as large as those in the United States. Also, unlike U.S. market, return enhancements on Asian markets are relatively smaller for value stocks when compared to glamour stocks. The distribution statistics for 1-year, market-adjusted returns for value and glamour portfolios are reported in Table 2. The results reported are not significantly different from those for 2-year returns. The proportions of value stocks with positive returns range from 11% (Taiwan) to 32% (Thailand), which are smaller than the proportion (44%) Piotroski (2000) ﬁnds on the US market. On the other hand, the proportions of glamour stocks with positive returns range from 39% (Singapore and Thailand) to 51.1% (Korea), which are also smaller than the proportion (65%) Mohanram (2003) ﬁnds on the U.S. market. On all the markets examined in this study, except Malaysia, value stocks underperformed glamour stocks in both median and mean returns. This negative BTM effect on Asian markets contrasts with the positive BTM effect documented on U.S. and other developed markets. On markets other than Singapore and Taiwan, value stocks in the left 10th (25th) percentile of return distribution performed better (did not perform worse) than glamour stocks in the corresponding percentile. This ﬁnding that the distributions of value (glamour) stock returns have a relatively short negative (long positive) tail on most markets is consistent with earlier ﬁndings discussed in Chui and Wei (1998) and Barry et al. (1999), but it is not consistent with the U.S. ﬁndings discussed in Fama and French (1995), Piotroski (2000), and Mohanram (2003). To examine return enhancements and zero-investment returns, both 1- and 2-year market-adjusted returns of the portfolios constructed according to tercile BTM and high/low F-SCORE partitions are computed. The results show that 1- and 2-year returns are not qualitatively different from each other. Therefore, Table 3 reports only the 1-year returns of four portfolios:

124

Table 2.

MEAN

High–Low (t stat)

10th Percentile

25th Percentile

Median

High-Low (p-value)

0.284 0.143

0.141 (2.155)

0.599 0.628

0.417 0.403

0.217 0.124

0.093 (0.05)

0.291 0.060

0.351 (5.291)

1.121 1.231

0.538 0.535

0.236 0.005

0.242 (0.01)

0.295 0.139

0.434 (1.354)

0.376 0.381

0.306 0.275

0.207 0.050

0.157 (0.10)

0.218 0.095

0.123 (4.315)

0.443‘ 0.383

0.327 0.259

0.183 0.060

0.382 0.120

0.262 (7.558)

0.705 0.444

0.436 0.280

0.241 0.154

0.087 (1.936)

0.431 0.488

0.324 0.312

Indicates a statistical significance at the 5% level.

75th Percentile

90th Percentile

Percent Positive

0.051 0.227

0.535 0.640

0.282 0.397

0.001 0.568

0.318 1.509

0.251 0.511

0.019 0.350

0.345 0.889

0.260 0.452

0.123 (0.01)

0.052 0.141

0.167 0.433

0.203 0.387

0.285 0.045

0.240 (0.05)

0.143 0.182

0.007 0.453

0.107 0.429

0.194 0.104

0.090 (0.05)

0.073 0.139

0.330 0.403

0.316 0.387

JOSEPH KANG AND DAVID DING

Hong Kong High (1587) Low (1675) Korea High (1379) Low (1424) Malaysia High (1199) Low (1216) Singapore High (1112) Low (1169) Taiwan High (1074) Low (1098) Thailand High (912) Low (952)

Distribution of One-Year Market-adjusted returns of High and Low BTM Firms: 1991–2002.

Distribution of One-year Market- adjusted Returns for portfolios portioned by BTM and F_SCORE. High BTM

n Hong Kong All Low F High F High–low (bootstrap) Korea All Low F High F High–low (bootstrap) Malaysia All Low F High F High–low (bootstrap) Singapore All Low F High F High–low (bootstrap)

Mean

0.10

0.25

Median

Low BTM 0.75

0.90

%Posi

0.05 0.16 0.22 0.06 (0.05)

0.53 0.60 0.63 0.03 (0.05)

0.28 0.28 0.55 n/a (n/a)

1675 0.14 0.63 0.40 91 0.17 0.63 0.43 182 0.07 0.48 0.29 n/a 0.10 0.15 0.14 (n/a) (0.05) (0.05) (0.05)

1379 0.29 1.12 0.54 0.24 0.00 0.32 45 0.37 0.87 0.46 0.29 0.26 0.05 124 0.21 0.80 0.38 0.09 0.13 0.40 n/a 0.16 0.08 0.08 0.20 0.39 0.44 (n/a) (0.05) (0.05) (0.05) (0.05) (0.05) (0.05)

0.25 0.09 0.37 n/a (n/a)

1424 73 177 n/a (n/a)

1199 0.30 61 0.36 128 0.35 n/a 0.01 (n/a) (0.15)

0.35 0.05 0.05 0.00 (0.15)

0.26 0.25 0.19 n/a (n/a)

1216 0.14 51 0.19 190 0.13 n/a 0.07 (n/a) (0.15)

0.38 0.28 0.32 0.27 0.31 0.24 0.00 0.03 (0.15) (0.15)

1112 0.22 0.44 0.33 0.18 0.05 0.17 70 0.34 0.45 0.34 0.24 0.14 0.04 95 0.15 0.38 0.26 0.09 0.07 0.21 n/a 0.19 0.07 0.09 0.16 0.21 0.25 (n/a) (0.05) (0.05) (0.05) (0.05) (0.05) (0.05)

0.20 0.98 0.37 n/a (n/a)

1169 0.10 60 0.22 145 0.05 n/a 0.27 (n/a) (0.05)

0.38 0.26 0.39 0.38 0.31 0.19 0.08 0.19 (0.05) (0.05)

1587 0.28 0.60 0.42 0.22 72 0.31 0.65 0.43 0.25 106 0.23 0.47 0.33 0.15 n/a 0.08 0.18 0.10 0.10 (n/a) (0.05) (0.05) (0.05) (0.05)

0.38 0.37 0.40 0.03 (0.15)

0.31 0.21 0.33 0.31 0.35 0.28 0.02 0.03 (0.15) (0.15)

0.02 0.01 0.02 0.01 (0.15)

n

Mean

0.10

0.25

0.66 1.23 0.54 0.02 0.64 0.39 0.11 0.59 0.33 0.09 0.05 0.06 (0.05) (0.05) (0.05)

Median

0.75

0.90

%Posi

0.12 0.14 0.05 0.09 (0.05)

0.23 0.05 0.01 0.04 (0.05)

0.64 0.51 0.67 0.16 (0.05)

0.40 0.25 0.23 n/a (n/a)

0.57 0.48 0.67 0.19 (0.05)

1.51 1.45 1.52 0.07 (0.05)

0.51 0.57 0.63 n/a (n/a)

0.05 0.11 0.12 0.01 (0.15)

0.35 0.09 0.13 0.22 (0.15)

0.89 0.00 0.41 0.41 (0.15)

0.45 0.10 0.27 n/a (n/a)

0.06 0.23 0.01 0.24 (0.05)

0.14 0.13 0.23 0.10 (0.05)

0.43 0.39 0.42 0.03 (0.05)

0.39 0.25 0.71 n/a (n/a)

0.01 0.01 0.08 0.07 (0.05)

Value and Growth Investing in Asian Stock Markets 1991–2002

Table 3.

125

126

Table 3. (Continued ) High BTM n

Mean

Taiwan All 1074 0.38 Low F 46 0.40 High F 73 0.33 High–low n/a 0.07 (bootstrap) (n/a) (0.05) Thailand All 912 0.24 Low F 49 0.29 High F 49 0.20 High–low n/a 0.09 (bootstrap) (n/a) (0.10)

0.10

0.25

Median

Low BTM 0.75

0.90

0.70 0.44 0.29 0.14 0.01 0.85 0.53 0.30 0.15 0.01 0.59 0.40 0.25 0.09 0.00 0.26 0.13 0.05 0.06 0.01 (0.05) (0.05) (0.05) (0.05) (0.05) 0.43 0.32 0.19 0.40 0.26 0.24 0.35 0.21 0.17 0.05 0.05 0.07 (0.10) (0.10) (0.10)

0.07 0.07 0.18 0.11 (0.10)

0.33 0.13 0.35 0.22 (0.10)

%Posi

n

Mean

0.10

0.25

Median

0.75

0.90

%Posi

0.11 0.08 0.10 n/a (n/a)

1098 0.12 0.44 0.28 0.05 49 0.41 0.95 0.77 0.34 34 0.10 0.38 0.23 0.09 n/a 0.31 0.57 0.54 0.25 (n/a) (0.05) (0.05) (0.05) (0.05)

0.18 0.17 0.02 0.19 (0.05)

0.45 0.07 0.33 0.26 (0.05)

0.43 0.19 39.00 n/a (n/a)

0.32 0.33 0.54 n/a (n/a)

952 0.15 0.49 0.31 41 0.18 0.49 0.23 120 0.03 0.47 0.11 n/a 0.21 0.02 0.13 (n/a) (0.05) (0.05) (0.05)

0.14 0.40 0.13 0.12 0.18 0.49 0.31 0.61 (0.05) (0.05)

0.39 0.00 0.55 n/a (n/a)

0.10 0.15 0.02 0.17 (0.05)

JOSEPH KANG AND DAVID DING

Note: All sample ﬁrms are grouped into a tercile BTM portfolio. Both high and low BTM portfolios portioned into a F_SCORE decile portfolio. Table 3 reports on the portfolios partitioned by both BTM ratio and F_SCORE. The high F_SCORE ﬁrms (ﬁrms with strong ﬁnancial signals) are the ﬁrms with F_SCORE of 8 or 9, whereas low F_SCORE ﬁrms are the ﬁrms with F_SCORE of 0, 1, or 2. The p-value for return difference is based on the test statistics obtained from the bootstrapping technique and is provided in the parenthesis below the return difference. Denotes 5% statistical significance for mean return difference.

Value and Growth Investing in Asian Stock Markets 1991–2002

127

Value portfolios with strong or weak ﬁnancial signals and glamour portfolios with strong or weak ﬁnancial signals. On all the markets examined in this study, except Malaysia, return enhancements for both value and glamour stocks are positive. The median zero-investment return on value stocks (i.e., the median return difference between strong and weak ﬁnancial signals) ranges from 5% (Taiwan) to 20% (Korea), with 16% (Singapore) being the median. In glamour stocks, the median return difference ranges from 7% (Korea) to 25% (Taiwan), with 17% (Thailand) being the median. These results indicate that stocks with strong ﬁnancial signals outperform stocks with weak ﬁnancial signals, regardless of their BTM partitions, on all the markets examined in this study, except Malaysia. This ﬁnding suggests that even in less-developed markets multiple ﬁnancial signals extracted from ﬁnancial statement information can contain pricing information that the BTM ratio fails to capture. Comparing the value premium (BTM effects), return enhancement (net F-SCORE effect), and zero-investment return (ﬁnancial signals effect or gross F-SCORE effect) across the markets examined in this study is a complex exercise. A careful differentiation among the three types of effects is provided in the present study because it enables a precise comparison among these markets and US markets. In Fig. 1, the BTM effects are measured as the difference between median returns of high- and low-BTM stocks. The (net) F-SCORE effect reﬂects the return-enhancing effect of ﬁnancial signals, and it is measured as the difference between median returns of the value (glamour) stocks with strong ﬁnancial signals and value (glamour) stocks as a whole. The ﬁnancial signals effect (i.e., gross F-SCORE effect) is measured as the difference between median returns of high- and low-F-SCORE stocks in respective BTM partitions, and therefore, it reﬂects a return from the zero-investment, winner– loser strategy. The median negative BTM effect ranges from 9.0% (Thailand) to 25% (Korea), with 12% (Singapore) being the median. The value premium reported in the present study is more negative than that reported in earlier studies on Asian markets, mainly because the period examined in the present study (i.e., 1997–2002) contains events that affected value ﬁrms more than glamour ﬁrms. The median return enhancement (i.e., net F-SCORE effect) for value stocks ranges from 2% (Thailand) to 15% (Korea), while the median return enhancement for glamour stocks ranges from 5% (Thailand) to 7% (Korea, Singapore, and Hong Kong). The return enhancements for

128

Korea

Singapore F-SCORE Effects (Net)

-24%

-9% (n=124) High F

(n=1379)

-15%

15%

==>

-(-5%) -5%

==>

20%

1%

8%

(n=1424)

(n=3425)

-6%

1%

7%

(n=73) Low F

0%

7%

L BTM

H BTM L BTM

7% -(-17%) ==>

-17%

24%

-6%

-9% -18%

-18%

H BTM

H BTM

H BTM

High F

L BTM

High F

Fig. 1.

H BTM L BTM

24%

15%

0

0

Difference in Gross F-Score Effects = (20%) - (7%) =+13%

-24%

7%

H BTM's Return Increase = High F - H BTM = (-9%) - (-18%) = +9%

BTM Effect =H BTM - L BTM = (18%) - (6%) = -12% 0

7%

-9%

H BTM

==>

15%

BTM & F-Score Effects

0

Difference in Gross F-Score Effects = (15%) - (24%) = -9%

JOSEPH KANG AND DAVID DING

20%

0

-24%

-6%

(3rd )

H BTM's Return Increase = High F - H BTM = (-9%) - (-24%) = +15%

1% 0

(n=145) High F

-23% (n=60) Low F

(2nd )

BTM Effect = H BTM - L BTM = (-24%) - (1%) = -25%

==>

(1st )

Low BTM

-( 0%) ==>

1%

(n=1169)

(1st )

Low BTM

- (-6%)

(4th )

7%

==>

9%

==>

9%

-24% (n=70) Low F

All Firms

(n=177) High F

(Gross)

(2nd )

High BTM

-15%

(4th )

All Firms

-9% (n=95) High F

(n=1112) 15%

-29% (n=45) Low F

(n=4209)

(Net) -18%

(3rd )

High BTM

F-SCORE Effects

(Gross)

0

-29%

High F

-29%

-25%

H BTM

0

H BTM's Return Increase = High F - H BTM = (-25%) - (-29%) = +4%

(4th )

==>

0

H BTM L BTM

5%

25%

25%

0

-22%

Low BTM

(n=1675)

-12%

High BTM

L BTM

H BTM

-12%

-22% (n=1587)

BTM Effect H BTM - L BTM = (-22%) - (-12%) = -10%

All Firms

(n=4862)

-17%

Fig. 1. Continued

Difference in Gross F-Score Effects = (5%) - (25%) =-20%

-29%

-(-29%)

5%

- (-1%)

4%

-34% (n=49) Low F

-4%

-1%

4%

-4%

==>

==>

==>

(Gross)

F-SCORE Effects (Net)

(1st )

L BTM

Low BTM

-9% (n=34) High F

(3rd )

-30% (n=46) Low F

(2nd )

-25% (n=73) High F

H BTM

-5%

-5%

(n=1098)

BTM Effect H BTM -L BTM = (-29%) - (-5%) = -25%

All Firms

(n=3264)

-20%

High BTM

(n=1074)

-29%

Taiwan

0

-22%

==>

==>

==>

==>

High F

H BTM

-15%

H BTM's Return Increase = High F - H BTM = (-15%) - (-22%) = +7%

(2nd )

-14% (n=91) Low F

(1st )

-5% (n=182) High F

(4th )

-25% (n=72) Low F

(3rd )

-15% (n=106) High F

Hong Kong

0

10%

7%

9%

H BTM L BTM

9%

- (-2%)

7%

10%

- (-3%)

Difference in Gross F-Score Effects = (10%) - (9%) =+1%

-2%

7%

-3%

7%

(Gross)

F-SCORE Effects (Net)

Value and Growth Investing in Asian Stock Markets 1991–2002 129

130

Thailand

Malaysia F-SCORE Effects

F-SCORE Effects (Net) -19%

(Net)

-17% (n=49)

(n=912)

High F

High BTM

(2nd )

-15%

(Gross)

2%

==>

Low F

-5%

==>

- (-5%)

-12%

7%

(n=3625)

(3rd )

All Firms -10%

-28% (n=128)

(n=1199)

High F

High BTM

(3rd )

2%

-24% (n=49)

(n=2801)

-21%

Low BTM

(1st )

==>

-5%

-12% (n=190)

(n=1216)

High F

Low BTM

(2nd )

12%

Low F

- (-5%) -5%

==>

==>

-7%

3%

-7% - (-6%)

Low F

17%

-6%

==>

-1%

(1st )

H BTM L BTM

BTM Effect H BTM - L BTM = (-21%) - (-12%) = -9%

17%

0

0

H BTM's Return Increase = High F - H BTM = (-28%) - (-21%) = -7%

7%

3%

H BTM L BTM

0

-5% -1% 0

-10% -19%

-19%

-17%

H BTM

H BTM

L BTM

High F

Difference in Gross F-Score Effects = (7%) - (17%) =-10%

-21% -21%

Fig. 1. Continued

-28% H BTM

H BTM

L BTM

High F

Difference in Gross F-Score Effects = (3%) - (-1%) =+4%

JOSEPH KANG AND DAVID DING

H BTM's Return Increase = High F - H BTM = (-5%) - (-19%) = +14% 0

0

-10%

-11% (n=51)

(4th )

BTM Effect H BTM - L BTM = (-19%) - (-10%) = -9%

==>

(4th )

12%

-15% (n=41)

-7% - (-10%)

-31% (n=61)

All Firms

High F

-7%

==>

Low F

(n=120)

2%

(n=952)

(Gross)

Value and Growth Investing in Asian Stock Markets 1991–2002

131

value ﬁrms were slightly better than those for glamour ﬁrms in only a few markets. The median zero-investment return (i.e., ﬁnancial signals or gross F-SCORE effect) for value stocks ranges from 5% (Taiwan) to 20% (Korea), with 16% (Singapore) being the median, and the zero-investment return for glamour stocks ranges from 7% (Korea) to 25% (Taiwan), with 17% (Thailand) being the median. The ﬁnancial signals effect (i.e., the zero-investment return) for value stocks is much smaller than the effect Piotroski (2000) ﬁnds on U.S. markets (23% for 1-year and 43.2% for 2-year horizons), and the ﬁnancial signals effect for glamour stocks is slightly smaller than the effect Mohanram (2003) ﬁnds on US markets (20.3% for 1-year and 13.2% for 2-year horizons). These results suggest that investors on Asian markets may not trust the quality of ﬁnancial statement information (i.e., ﬁnancial signals) about Asian companies. Unlike the ﬁndings of U.S. studies, the results of the present study show that the ﬁnancial signals effect is relatively smaller for value stocks than for glamour stocks. This ﬁnding suggests that investors on Asian markets may not trust the positive value-growth spread (i.e., value premium or BTM effect), especially during events such as the Asian ﬁnancial crisis or severe economic recessions or during times when investors are concerned about terrorist attacks. The significant F-SCORE effects obtained from a simple ﬁnancial statement analysis are not expected to be larger than the benchmark-adjusted returns of sophisticated investment funds, such as hedge funds and emerging market funds. For emerging equity market funds, Fung, Xu, and Yau (2002) found that the average return for 10 emerging market funds from 1994 to 2000 was 11.3%. For Asian hedge funds, Koh, Koh, and Teo (2003) document the management characteristics of Asian hedge funds but do not report the statistics for mean and median market-adjusted returns. Using information available in their article (i.e., Table 4: Pre-fee Excess Monthly Returns), the present study approximates the median return of Asian hedge fund as 12%.10 The zero-investment returns in the present study (i.e., 16% for value stocks and 17% for glamour stocks) are larger than the returns for Asian hedge funds (12%) and emerging equity market funds (11.3%), although the extra returns are not as large as those reported in Piotroski (2000) and Mohanram (2003). This ﬁnding suggests that the use of multiple ﬁnancial signals can also lead to substantial return enhancements on Asian markets.

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JOSEPH KANG AND DAVID DING

6. ROBUSTNESS TO FIRM SIZE, BTM RATIO, MARKET CONDITIONS, AND OTHER EFFECTS F-SCORE effects are sensitive to alternative measures and selections of multiple ﬁnancial signals (e.g., ranked F-SCORE and FG-SCORE; combinations of other or more proxies) and corporate performance (e.g., earnings performance). Return enhancements and zero-investment returns may be also inﬂuenced by other pricing or risk factors (e.g., ﬁnancial distress proxied by Altman’s Z-score or Ohlson’s O-score, the number or quality of analysts following, market liquidity proxied by trading volume, and industry effect). In order to determine if these factors affected the ﬁnancial signals variables used in the present study, the variables are tested for robustness. Although the details are not reported here, the results of the present study are robust for all these factors. Many researchers and analysts recognize both ﬁrm size and BTM ratio as pricing factors, but they do not consider ﬁnancial signals as such. Therefore, it is important to also test the robustness of the ﬁnancial signals effect with respect to ﬁrm size and BTM factors. To determine the relative importance of ﬁnancial signals as a pricing factor, the present study provides a detailed analysis of the correlations between market-adjusted returns and ﬁrm size, BTM ratio, and the ﬁnancial signals effect (see Table 4) and the results from pooled cross-sectional regressions of market-adjusted returns against various combinations of these three factors (see Table 5). As shown in Table 4, the statistically significant correlations between market-adjusted returns and BTM ratio are positive for value stocks in Korea and glamour stocks in Taiwan, but negative for value stocks in Singapore, Taiwan, and Thailand. This ﬁnding shows that the BTM effect is weakest in Korea, and this suggests the performance of value stocks is strongest in Korea. The statistically significant correlations between returns and F-SCORE are positive for value stocks in Korea and Singapore and glamour stocks in Korea and Thailand. This ﬁnding indicates that the return-enhancing effect of value stocks’ ﬁnancial signals is strong in Korea and Singapore. The correlations between F-SCORE and 1-year (2-year) returns of highBTM stocks are 0.188 for Korea and 0.233 for Singapore (0.342 for Korea and 0.214 for Thailand). These correlations are larger than those reported in Piotroski (2000) (i.e., 0.121 and 0.130 for 1- and 2-year returns, respectively). Although statistically significant, the positive correlations with ﬁrm size suggest that the performance of value ﬁrms in Korea and Singapore might

Correlations between Market-Adjusted Returns, BTM Ratio, F_SCORE, and Firm Size: 1991–2002. Hong Kong

Korea

Malaysia

Singapore

Taiwan

Thailand

H_BTM L_BTM H_BTM L_BTM H_BTM L_BTM H_BTM L_BTM H_BTM L_BTM H_BTM L_BTM Corr (R, BTM ratio) R_1 0.005 0.149 (p-value) (0.932) (0.021) R_2 0.114 0.108 (p-value) (0.056) (0.096)

0.211 0.400 0.035 0.129 0.125 0.043 0.196 (0.000) (0.541) (0.627) (0.098) (0.063) (0.616) (0.001) 0.316 0.133 0.214 0.119 0.151 0.176 0.142 (0.000) (0.053) (0.004) (0.131) (0.027) (0.041) (0.032)

Corr (R, F_SCORE) R_1 (p-value) R_2 (p-value)

0.064 0.053 (0.286) (0.413) 0.095 0.030 (0.110) (0.646)

0.188 (0.001) 0.342 (0.000)

0.189 0.046 (0.004) (0.523) 0.212 0.030 (0.002) (0.686)

0.119 (0.128) 0.254 (0.001)

0.244 (0.000) 0.235 (0.000)

0.198 0.117 0.032 (0.020) (0.050) 0.633 0.132 0.025 0.014 (0.127) (0.710) (0.862)

Corr (R, In(MVE)) R_1 (p-value) R_2 (p-value)

0.106 (0.075) 0.120 (0.044)

0.144 0.211 (0.079) (0.000) 0.181 0.316 (0.005) (0.000)

0.089 0.030 (0.179) (0.677) 0.007 0.224 (0.920) (0.002)

0.043 (0.586) 0.272 (0.000)

0.184 (0.006) 0.142 (0.037)

0.122 (0.154) 0.200 (0.021)

0.158 (0.008) 0.105 (0.144)

0.189 0.137 0.076 (0.005) (0.032) (0.249) 0.272 0.235 0.012 (0.001) (0.000) (0.856)

0.062 (0.353) 0.183 (0.020)

0.090 0.147 (0.162) (0.026) 0.124 0.173 (0.001) (0.010) 0.077 (0.234) 0.106 (0.103)

0.127 (0.054) 0.157 (0.019)

Value and Growth Investing in Asian Stock Markets 1991–2002

Table 4.

Denotes a statistical significance at the 5% level.

133

134

JOSEPH KANG AND DAVID DING

contain a ﬁrm-size effect. The following analysis shows, however, that it is not the case. As shown in Table 5, regressions using 2-year returns are not significantly different from 1-year returns, so Table 5 reports only the results of six regressions using 1-year returns by markets and ﬁrm type. In the regression for BTM ratios, the coefﬁcient estimates are statistically significant for value stocks in Korea, glamour stocks in Malaysia, and both value and glamour stocks in Taiwan. The coefﬁcient estimates for BTM ratios for these stocks are all negative, however, suggesting a negative BTM effect. When the F-SCORE is added to the regression, the coefﬁcient becomes statistically significant for value stocks (but not for glamour stocks) in Korea, Singapore, and Taiwan. These results suggest that the ﬁnancial signals effect is stronger for value stocks than for glamour stocks. In the regression for ﬁrm size, the coefﬁcient estimates are only significant for value stocks in Korea, Malaysia, and Taiwan. This regression has a higher explanatory power than the regression for BTM ratios only for value stocks in Malaysia, where the correlation between return and ﬁrm size is negative. This result suggests that the ﬁnancial signals effect dominates the ﬁrm size effect in both Korea and Taiwan. When the F-SCORE is added to the regression, the F-SCORE has a statistically significant positive (negative) effect on the returns of value stocks in Korea and Taiwan (glamour stocks in Hong Kong and Malaysia). These results suggest that the return-enhancing effect of value stocks’ ﬁnancial signals is strongest in Korea and Taiwan. As compared to the regression for BTM ratios and F-SCORE, the regression for BTM ratios and ﬁrm size has a lower explanatory power for all stocks, except value stocks in Malaysia. This result suggests that the ﬁnancial signals effect is stronger than the ﬁrm size effect. As compared to the regression for BTM ratios and ﬁrm size, the regression for BTM ratio, ﬁrm size, and F-SCORE has a higher explanatory power for all stocks. For value stocks in Malaysia, however, the ﬁrm-size coefﬁcient remains the dominant explanatory variable. These results suggest that even after controlling for ﬁrm size and BTM ratio the ﬁnancial signals effect is significantly positive on most of the markets examined in the present study. In short, this study’s results reported in Tables 4 and 5 indicate that the ﬁnancial signals effect does not capture the effects of ﬁrm size or BTM ratio. The data in the present study are not controlled for the survivorship bias in the present study. The bias would not, however, affect the results of the present study because the bias is disproportionately large in value stocks,

Value and Growth Investing in Asian Stock Markets 1991–2002

135

Table 5. Regression of Market-Adjusted Returns: 1991-2002. Eqs.

a

1n(BTM)

1n(MVE)

F-SCORE

a

1n(BTM)

(High BTM) Hong Kong 1 0.22 2 0.08 3 1.52 4 1.52 5 2.40 6 2.31 Korea 1 0.13 2 0.34 3 1.79 4 1.71 5 1.26 6 1.13 Malaysia 1 0.08 2 0.05 3 1.13 4 1.12 5 1.23 6 1.24 Singapore 1 0.04 2 0.28 3 0.17 4 0.33 5 0.13 6 0.05 Taiwan 1 0.12 2 0.20 3 1.45 4 1.45 5 0.24 6 0.33 Thailand 1 0.04 2 0.07 3 0.75 4 0.76 5 0.74 6 0.80

0.22 0.01 n/a n/a 0.12 0.11 0.10 0.10 n/a n/a 0.06 0.07

n/a n/a 0.07 0.08 0.10 0.11 n/a n/a 0.06 0.05 0.04 0.03

0.01 0.03 n/a n/a 0.04 0.05

n/a n/a 0.07 0.06 0.07 0.07

0.10 0.09 n/a n/a 0.11 0.11

n/a n/a 0.00 0.00 0.01 0.01

1n(MVE)

F-SCORE

(Low BTM)

n/a 0.02 n/a 0.04 n/a 0.03

0.02 1.15 1.19 1.39 1.85 2.00

0.19 0.22 n/a n/a 0.29 0.27

n/a n/a 0.04 0.00 0.09 0.04

0.35 0.08 0.26 0.27 1.22 1.23

0.15 0.17 n/a n/a 0.25 0.25

n/a n/a 0.02 0.01 0.06 0.05

n/a 0.06 n/a 0.05 n/a 0.05

0.08 0.24 1.05 1.07 1.22 1.24

0.17 0.17 n/a n/a 0.21 0.21

n/a n/a 0.05 0.03 0.07 0.06

n/a 0.06 n/a 0.05 n/a 0.04

n/a 0.05 n/a 0.05 n/a 0.05

0.05 0.20 0.19 0.25 0.12 0.18

0.04 0.05 n/a n/a 0.04 0.05

n/a n/a 0.03 0.03 0.01 0.01

n/a 0.03 n/a 0.03 n/a 0.03

n/a n/a 0.01 0.01 0.00 0.00

n/a 0.03 n/a 0.03 n/a 0.03

n/a n/a 0.00 0.00 0.02 0.03

n/a 0.09 n/a 0.09 n/a 0.09

n/a 0.04 n/a 0.04 n/a 0.04 n/a 0.02 n/a 0.01 n/a 0.02

0.10 0.09 n/a n/a 0.09 0.09

n/a n/a 0.06 0.05 0.01 0.01

n/a 0.02 n/a 0.02 n/a 0.02

0.12 0.26 0.73 0.89 0.13 0.04

0.13 0.13 n/a n/a 0.14 0.13

0.03 0.03 n/a n/a 0.00 0.00

n/a n/a 0.03 0.03 0.03 0.03

n/a 0.00 n/a 0.01 n/a 0.01

0.13 0.65 0.16 0.57 0.27 0.13

0.06 0.05 n/a n/a 0.07 0.07

n/a 0.22 n/a 0.22 n/a 0.21

Note: The coefﬁcient estimates are obtained from the pooled cross-sectional regressions: (1) Ri ¼ aI+b1i1n(BTMi); (2) Ri ¼ ai+b1i1n(BTMi) + b2iF0 SCOREi; (3) Ri ¼ ai + b1i1n(MVEi); (4) Ri ¼ ai+b1i1n(MVEi) + b2iF0 SCOREi; (5) Ri ¼ ai+b1i1n(BTMi) + b2i1n(MVEi); (6) Ri ¼ ai + b1i1n(BTMi)+b2i1n(MVEi) + b3iF0 SCOREi Denotes a statistical significance at a 5% level.

136

JOSEPH KANG AND DAVID DING

and its correction could result in even lower returns for value ﬁrms, which would strengthen the ﬁnancial signals effect. This study also examines whether BTM ratios and the ﬁnancial signals effect were sensitive to market conditions. Although the details are not reported here, the value-growth spreads in these markets during times of crisis (1997–2002) were smaller than those during times without crisis (1991–1996). The decline in spreads from pre-1997 to post-1997 ranges from 3.2% (Thailand) to 0.9% (Singapore), with 1.6% (Korea) being the median. In other words, the non-positive value premiums on these markets became more distinct during times of trouble. The ﬁnancial signals effect on these markets during the post-1997 period was also smaller compared to the pre-1997 period. To be consistent with the decline in value premiums in the post-1997 period, the disparity between the ﬁnancial signals effects on growth and value stocks widened during the same period. The increase in the disparity ranges from 1.5% (Taiwan) to 0.6% (Singapore), with 1.2% (Korea) being the median. This ﬁnding indicates that the main ﬁndings of the present study are robust to different market conditions prevailed during the sample period.

7. SUMMARY AND CONCLUSIONS The results of the study discussed in this article show that the returnenhancing effect of ﬁnancial signals exists for both value and glamour stocks on all the markets examined in this study, except Malaysia. The ﬁnancial signals effect, however, is relatively small on all these Asian markets. This may be the result of investors’ perceptions that the quality of ﬁnancial statement information in Asia is poor. Unlike the results of US studies, the ﬁnancial signals effect for value stocks is not larger than the effect for glamour stocks. This ﬁnding does not contradict the idea that value ﬁrms should exhibit a relatively large ﬁnancial signals effect because their price reaction to ﬁnancial statement information is relatively slow. This idea still holds because the negative value premiums that the present study found on these markets could have constrained the ﬁnancial signals effect for value ﬁrms. The results of the present study also show that a zero-investment, winner– loser strategy for high-BTM stocks would have generated average returns ranging from 5% (Taiwan) to 20% (Korea), with 16% (Singapore) being the

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median, while a zero-investment strategy for low-BTM stocks would have generated average returns ranging from 7% (Korea) to 25% (Taiwan), with 17% (Thailand) being the median. The zero-investment returns are not expected to be larger than the benchmark-adjusted returns of sophisticated investment funds, such as hedge funds and emerging market funds. The median zero-investment returns (i.e., 16% for value ﬁrms and 17% for glamour ﬁrms) are larger than the returns for Asian hedge funds (12%) and emerging equity market funds (11.3%), although the extra returns are not as large as those reported in Piotroski (2000) and Mohanram (2003). The results of the present study suggest that the use of multiple ﬁnancial signals can also lead to substantial return enhancements on Asian markets. Such return enhancement may not persist over time, however, largely because investors will sooner or later arbitrage away the abnormal returns obtained using a simple ﬁnancial statement analysis. Furthermore, future stock performance might be sensitive to other economic factors that were not considered in this study.

NOTES 1. See Piotroski (2000), and Mohanram (2003). Recent valuation studies using a ﬁnancial statement analysis also include Nissim and Penman (2001), Beneish, Lee, and Tarpley (2001), Liu, Nissim, and Thomas (2002), and Lewellen (2002). 2. Recent studies include Petkova and Zhang (2002), who highlight the possibility that value stocks are relatively more (less) risky than growth stocks in bad (good) times, and Nagel (2003) who describe what types of value ﬁrms provide stringent limits on arbitrage and, therefore, are more subject to investors’ irrational expectations about their future returns. 3. For example, a negative value premium is found in Argentina, Colombia, Mexico (Fama & French, 1998), and Turkey (Gonenc & Karan, 2003), while an insignificant value premium is found in Taiwan, Thailand (Chui & Wei, 1998), New Zealand (Pinfold, Wilson, & Li, 2001), and Pakistan (Fama & French, 1998). Hong and Lee (2003) did not ﬁnd earnings and price momentum in Korea, Singapore, Taiwan, and Malaysia, which suggests a non-positive value premium in these markets. For similar ﬁndings of a non-positive book-to-market effect on Asian markets, see Chui and Wei (1998). Non-positive value premiums for these markets are also reported in Table 2 of the present study. 4. He also shows that a zero-investment, winner–loser strategy of longing the value stocks with strong ﬁnancial signals and simultaneously shorting those with weak ﬁnancial signals (lowest three F-SCORE deciles) could have generated 23% (43.2%) in a 1-year (2-year) horizon.

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5. He also suggests that a zero-investment, winner–loser strategy could have generated 20.3% (13.2%) returns in a 1-year (2-year) horizon. 6. For a similar argument for using more ﬁnancial proxies, see Chan and Lakonishok (2004). 7. This ﬁnding contrasts with the corresponding statistics in Piotroski (2000). 8. Mohanram (2003) considers alternative ways to deal with delisted stocks. However, as in Piotroski (2000), the results in Mohanram (2003) are not sensitive to these alternative adjustments for delisted stocks. 9. For similar applications, see Kothari and Warner (1997), Piotroski (2000), and Mohanram (2003). 10. The median return (i.e., 12%) is estimated as follows: First, monthly excess return is computed as simple average excess returns of the 5th and 6th performance deciles (i.e., 0.5*0.41%+0.5*0.87% ¼ 0.64%); second, the monthly gross return (1%) is computed by adding an assumed monthly risk-free rate (0.36%) to the excess monthly return (0.64%); and third, a median annualized return (12%) is obtained by simply annualizing the gross monthly return.

ACKNOWLEDGMENTS The authors wish to thank A. Chen (the editor), S. Courtenay, R. Grieves, A. Y. Wang, J. J. Williams, and session participants at the 2004 AsFA/TFA/ FMA Conference (Taiwan) and the 2004 FMA Conference (New Orleans) for their valuable comments. The authors also wish to thank the comments of anonymous referees, the research assistance of C. Roongsangmanoon and the ﬁnancial support of the Nanyang Business School.

REFERENCES Barry, C. B., Glarier, E., Lockwood, L., & Rodriguez, M. (1999). Size and book-to-market effects: Evidence from emerging equity markets. Working Paper. Texas Christian University, Dallas, TX. Beneish, M. D., Lee, C. M., & Tarpley, R. L. (2001). Contextual fundamental analysis through the prediction of extreme returns. Review of Accounting Studies, 6, 165–189. Chan, L. K. C., & Lakonishok, J. (2004). Value and growth investing: Review and update. Financial Analysts Journal, 60, 71–87. Chui, A., & Wei, J. (1998). Book-to-market, ﬁrm size, and the turn-of-the-year effect: Evidence from pacific-basin emerging markets. Pacific-Basin Journal of Finance, 6, 275–293. Fama, E. (1998). Market efﬁciency, long-term returns and behavioral ﬁnance. Journal of Financial Economics, 48, 283–306. Fama, E., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47, 427–465. Fama, E., & French, K. R. (1995). Size and book-to-market factors in earnings and returns. Journal of Finance, 50, 131–155.

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Fama, E., & French, K. R. (1998). Value versus growth: The international evidence. Journal of Finance, 53, 1975–1999. Fung, H. G., Xu, X., & Yau, J. (2002). Global hedge funds: Risk, return and market timing. Financial Analysts Journal, 58(6), 19–30. Gonenc, H., & Karan, M. B. (2003). Do value stocks earn higher returns than growth stocks in an emerging market? Evidence from the Istanbul stock exchange. Journal of International Financial Management and Accounting, 14, 54–75. Hong, D., & Lee, C. (2003). Earnings momentum in international markets. Working Paper. Cornell University, Ithaca, New York. Koh, F., Koh, W. T. H., & Teo, M. (2003). Asian hedge funds: Return persistence. Working Paper. Singapore Management University, Singapore. Kothari, S. P., & Warner, J. (1997). Measuring long-horizon security price performance. Journal of Financial Economics, 43, 301–339. Lakonishok, J., Shleifer, A., & Vishny, R. (1994). Contrarian investment, extrapolation and risk. Journal of Finance, 49, 1541–1578. Lewellen, J. (2002). Predicting returns with financial ratios. Working Paper 4374-02. MIT Sloan School of Management, Cambridge, MA. Liu, J., Nissim, D., & Thomas, J. (2002). Equity valuation using multiples. Journal of Accounting Research, 40–41, 135–172. Mohanram, P. S. (2003). Is fundamental analysis effective for growth stocks. Working Paper. Stern School of Business, New York University, New York. Nagel, S. (2003). Short sales, institutional investors, and the book-to-market effect. Working Paper London Business School, London, UK. Nissim, D., & Penman, S. (2001). Ratio analysis and equity valuation: from research to practice. Review of Accounting Studies, 6, 109–154. Petkova, R., & Zhang, L. (2002). Is value riskier than growth? Working Paper. University of Rochester, Rochester, New York. Pinfold, J. F., Wilson, W. R., & Li, Q. (2001). Book to market and size as determinants of returns in small illiquid markets. Working Paper. Massey University, Massey, New Zealand. Piotroski, J. D. (2000). Value investing: The use of historical ﬁnancial statement information to separate winners from losers. Journal of Accounting Research, 38, 1–41.

AN ANALYSIS OF STOCK PARTICIPATION ACCRETING REDEMPTION QUARTERLY-PAY SECURITIES K. C. Chen, Friderica Widyasari Dewi and Lijie Zhu ABSTRACT Stock Participation Accreting Redemption Quarterly-pay Securities (SPARQS), a service mark of Morgan Stanley, represent another form of equity-linked structured notes. The SPARQS generally provide the investors with higher interest payments that substantially exceed the market interest rate for corresponding standard bonds, in exchange for a call feature. The call option limits the potential appreciation of the SPARQS in case the underlying common stock price rises. Moreover, the SPARQS are mandatorily convertible at maturity that entail more risk than ordinary debts due to the possibility that investors might not receive their principal amount in case the underlying common stock price declines. This paper derives a general pricing formula for the SPARQS using the binomial tree approach. An empirical test of a specific SPARQS issue indicates that the binomial tree model is quite accurate.

Research in Finance, Volume 22, 141–160 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22005-1

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During the last two decades, investors have witnessed a rich variety of securities innovations. On the whole, this array of innovative securities is designed to provide investors with additional potential payoffs not present in other securities, and at the same time to ease some of the ﬁnancing costs to the issuer (see Finnerty, 1988, 1992). To take advantage of these beneﬁts, corporations have expanded beyond traditional hybrids and are issuing customized securities that meet specific ﬁrm needs. Among the myriad of customized securities, structured products, especially structured notes, have proliferated rapidly not only in the US (Peng & Dattatreya, 1995) but also in Europe (Burth, Kraus, & Wohlwend, 2001). According to Peng and Dattatreya (1995), the US new issue structured notes issued by agencies and corporations amounted to $90 billions in 1994. Structured notes are typically intermediate-term ﬁxed-income securities with embedded derivative elements whose coupon and/or principal payments create cash ﬂows similar to those created by the direct purchase of derivative instruments and at the same time provide returns and exposures to markets in a manner not readily available through traditional ﬁxedincome instruments. For instance, the derivative component of a structured note can be embedded either in the redemption value of the note or in the interest payments. The note’s performance, and hence its coupon payments or principal repayment at maturity, is linked to the performance of a single asset, a basket of assets, or a market index. The principal and coupon payments can be fully or partially at risk depending on the risk exposure desired. Among many permutations of structured notes, the most common structured notes are credit-linked notes, commodity-linked notes, equity-linked notes, interest-rate-linked notes, and principal-protected notes (e.g., see Braddock, 1997; Braddock & Krouse, 2002; Das, 2000; Fabozzi, 1998). Like derivatives, structured notes are used to modify or create synthetic exposure or otherwise manage market risk, credit risk, or both. According to Telpner (2004), with structured notes, investors can implement strategies based on their views about the direction of interest rates; the range, the volatility, and the shape of long-term versus short-term rates; and the direction of equity and commodity markets and prices. Structured notes per se are not a recent innovation. Both callable bonds and convertible bonds, which possess some common derivative characteristics as of structured notes, have existed for a long time. However, the current generation of structured notes is often much more complex as the result of embedding highly engineered derivative components. According to Burth et al. (2001), there are basically two types of structured products:

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instruments with a convex payoff and instruments with a concave payout. Convex products guarantee a minimum payoff at expiration but yield a certain upside potential at the same time. Such a strategy can be replicated through a riskless investment in combination with one or more call options on an underlying asset (typically a stock market index). Some earlier convex products are market-index certificates of deposit (Chance & Broughton, 1988; Chen & Kensinger, 1990), S&P 500 Index subordinated notes (SPINs, Chen & Sears, 1990), and stock-index growth notes (SIGNs, Finnerty, 1993). On the contrary, concave products combine a position in the underlying asset with a short position in a call option on the same asset. The call option premium will increase the return on the structured note, most likely through increased coupon payments. This strategy, however, cannot easily be implemented by small investors because it implies a short position in a corresponding derivative instrument. Equity-linked securities (ELKS, Chen & Chen, 1995) and reverse convertibles (Wilkens, Erner, & Roder, 2003) are two examples of concave products without principal protection. One of the recently issued structured notes is Stock Participation Accreting Redemption Quarterly-pay Securities (SPARQS). The SPARQS, a service mark of Morgan Stanley, have been linked to scores of companies since their inception in 2001. The underlying companies, however, are not involved in the offering and will have no obligation of any kind with respect to the SPARQS. These instruments generally provide the investors with higher interest payments that substantially exceed the market interest rate for corresponding standard bonds, in exchange for a call feature. This embedded call option limits the upside potential of the SPARQS in case the underlying common stock appreciates in value. Moreover, the SPARQS are mandatorily convertible at maturity that entail more risk than ordinary debts due to the possibility that investors might not receive their principal amount in case the underlying common stock price declines. Therefore, the SPARQS can be deemed as another type of reverse convertibles or equitylinked notes without principal protection. Since the SPARQS typically are highly rated as senior notes that reﬂect investors’ desire for credit enhancement, the issuance of the SPARQS raises some intriguing questions related to the valuation of the SPARQS and the motives of issuing and purchasing the SPARQS. The remaining of this paper is organized as follows: Section 1 describes the characteristics of the SPARQS. A theoretical valuation of the SPARQS using a binomial tree approach is discussed in Section 2. Section 3 presents the empirical test result on the SPARQS valuation model. Concluding remarks then follow.

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1. OVERVIEW OF THE SPARQS 1.1. Specifications To illustrate how the SPARQS work, we arbitrarily choose the 7% SPARQS mandatorily exchangeable for shares of common stock of Best Buy issued on July 24, 2003. Best Buy is the number one specialty retailer of consumer electronics and home–ofﬁce products. Morgan Stanley issued 1,032,200 shares of this particular instrument due August 1, 2004 for a net proceeds of $21,589,520. The principal amount and issue price of each SPARQS is $21.45, which is equal to one-half of the closing price of Best Buy common stock on July 23, 2003. Each SPARQS will receive 7% interest (equivalent to $1.5015 per year), paid quarterly beginning November 1, 2003, on the $21.45 principal amount. The Best Buy SPARQS was listed on the American Stock Exchange under the ticker symbol ‘‘BYS.’’ Unlike ordinary debt securities, the SPARQS do not guarantee any return of principal at maturity. On August 1, 2004, the maturity date, each SPARQS would be mandatorily converted into one-half of a share of Best Buy common stock. This conversion privilege, however, is not applicable prior to maturity. In addition, the SPARQS became callable effective from February 1, 2004 until maturity. Upon call, each SPARQS holder would receive a cash call price that produces an annually compounded yield to call of 23% on the issue price. The calculation of the yield to call takes into account the issue price of the SPARQS, the time to the call date, and the amount and timing of interest payments on the SPARQS as well as the call price. As reported in the Prospectus (Morgan Stanley Dean Witter & Co., 2003), the call price on the earliest call day and at maturity is $23.0278 and $24.7684, respectively. Therefore, the call right retained by Morgan Stanley caps the maximum return (including interest payments) that investors may realize on the SPARQS at 23% per annum on the issue price of the SPARQS to the call date. 1.2. Tax and Hedging Issues According to the Prospectus, there is no direct legal authority as to the proper tax treatment of the SPARQS, and therefore significant aspects of the tax treatment of the SPARQS are uncertain. Pursuant to the terms of the SPARQS, a SPARQS is treated as an investment unit consisting of (a) a terminable forward contract and (b) a deposit (equal to the issue price) with

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the issuer, Morgan Stanley, of a ﬁxed amount of cash to secure the SPARQS holder’s obligation under the terminable forward contract. The terminable forward contract requires the SPARQS holder to purchase Best Buy common stock from the issuer at maturity, and allows the issuer to terminate the terminable forward contract by exercising its call right and returning to the holder the deposit plus an amount of cash equal to the difference between the call price and the deposit. Based on the characterization set forth above, quarterly interest payments on the SPARQS will be taxable as ordinary income at the time accrued or received. The SPARQS holder’s tax basis will be zero in the terminable forward contract and 100% of the issue price in the deposit, respectively. The net proceeds, $21,589,520, Morgan Stanley received from the sale of the SPARQS will be used for general corporate purposes and, in part, in conjunction with hedging its obligations contingent upon the performance of the embedded derivative components under the SPARQS. As discussed above, Morgan Stanley’s maximum loss on the SPARQS is 23% per annum whenever call is triggered. Therefore, through out the life of the SPARQS, the issuer could hedge its anticipated exposure in connection with the SPARQS by taking positions in Best Buy stock and/or option contracts on Best Buy stock. The hedging activities are more likely to take place especially when the Best Buy stock price has a propensity to rise.

1.3. The Demand for the SPARQS For investors, the SPARQS offer a number of beneﬁts that are also prevalent for structured notes. First, the SPARQS are listed on the American Stock Exchange, thus providing liquidity for investors. Second, as in the primary market, most of the buyers are equity income funds and wealthy investors. The SPARQS relatively high-coupon rate along with their senior note rating attract investors which would not be attracted by the lower yield on the underlying yet still want exposure to the underlying common stock. With the lowest interest rates in 40 years, investors have been scrambling in search of enhanced yield opportunities. Third, structured products play an important role in the implementation of advanced investment strategies for private investors to whom replicating strategies are usually limited by a lack of available instruments, by short-selling restrictions, or by transaction costs. Table 1 contains a partial list of SPARQS that were traded on the American Stock Exchange on April 18, 2005. There were more than 20 SPARQS

146

Table 1. Coupon Rate (%)

10 10 10 6 8 8 8 10 9 10 7 8 10 6

a

Underlying Company

Ticker Symbol

Expiration Date

Average three-month Daily Trading Volume

Issue Size (millions)

Dividend Yielda (%)

Apple Computer Jetblue Airways Nvdia Corporation EMC Motorola Texas Instruments Valero Energy Abercrombie & Fitch Lyondell Chemical Avaya Biogen IDEC Consol Energy Goodyear Tire & Rubber International Game & Technology National Semiconductor Newmont Mining Nokia Qualcomm Xilinx Yahoo

ALR JTM SND ECC MLQ TXM ERV ABH LSM AYS BIS ECN GDY

04/15/2006 06/15/2005 12/01/2005 08/15/2005 01/15/2006 01/15/2006 04/15/2006 01/30/2006 01/30/2006 07/15/2005 11/01/2005 03/01/2006 11/01/2005

1,500 4,622 7,961 4,097 6,019 4,355 11,916 7,093 4,890 4,811 9,785 6,967 4,734

16.596 19.102 44.781 14.000 34.880 28.668 31.753 13.855 40.764 31.620 11.000 27.000 13.622

0 0 0 0 1.08 0.44 0.47 0.92 3.69 0 0 1.33 0

MIS

12/01/2005

6,337

16.638

1.98

NSN NEH NKS QSQ XLS MYA

05/15/2005 05/15/2005 11/01/2005 11/01/2005 07/15/2005 07/15/2005

5,749 4,388 7,355 2,677 8,149 2,583

28.742 15.442 32.000 14.280 10.905 16.955

0.43 1.01 2.97 0.86 0.71 0

The average daily trading volume over three months on April 18, 2005.

K. C. CHEN ET AL.

10 6.25 7 6 8 8

A Partial List of SPARQS Traded on the American Stock Exchange on April 18, 2005.

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issues outstanding because some of them were not traded on that day. Also included in Table 1 are their respective coupon rate, the underlying company, expiration date, average three-month daily trading volume, issue size, and the underlying stock’s dividend yield. It can be seen that the SPARQS represent an important source of ﬁnancing for Morgan Stanley, which had raised approximately $463 million from the SPARQS listed in Table 1. In addition, the SPARQS coupon rates are much higher than their corresponding dividend yield counterparts with an average spread of 7.5%.

2. VALUATION OF SPARQS By design, the SPARQS are medium-term debt securities with embedded call and conversion options. In the literature, Ingersoll (1977a, b) and Brennan and Schwartz (1977, 1980) use the contingent claims approach pioneered by Merton (1974) to value ﬁxed-income securities that are both callable and convertible. Ingersoll (1977a) derives a closed form solution for a callable convertible bond whose call price and conversion terms are ﬁxed, whereas Brennan and Schwartz (1977) use ﬁnite difference methods to account for call protection periods and nonconstant call prices. To model the SPARQS, we employ the binomial tree approach proposed by Cox, Ross, and Rubinstein (1979). We choose this approach for two reasons. First, the SPARQS issued by Morgan Stanley are not identical to the traditional callable, convertible bonds modeled by Ingersoll (1977a) and Brennan and Schwartz (1977) because there is no dilution effect upon conversion, as the underlying company is not involved. Second, the binomial tree approach is particularly useful here because the SPARQS become callable six months prior to maturity. The dynamic call feature and the mandatory call protection can be ﬂexibly implemented within the binomial tree framework. We ﬁrst start by dividing the life of the SPARQS, T, into N small time steps of length Dt, i.e., T ¼ NDt: In each time step there is a binomial stock price movement with the stock price moving either upward from S to mS or downward from S to dS. The probability of an up movement is denoted by p and the probability of a down movement is 1p. In a risk-neutral world, Cox et al. (1979) show the following relations: m ¼ es

pﬃﬃﬃﬃ Dt

; d ¼ es

pﬃﬃﬃﬃ Dt

; p¼

ad ; and a ¼ erDt md

(1)

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pﬃﬃﬃﬃﬃ where s Dt is the standard deviation of the return on the stock price in a short period of time of length Dt and r is the risk-free interest rate. Denote the jth node at time iDt as the (i, j) node, where 0pipN and 0pjpi. The call price at the (i, j) node is Ci,j and the stock price at the (i, j) node is Si,j, which equals S0mjdij where S0 is the stock price at time zero. The value of the SPARQS at the (i, j) node, fi, j, can be evaluated by starting at the end of the tree (time T) and proceeding backward through the tree. At maturity (T ¼ NDt), each SPARQS is mandatorily exchangeable for one-half of a share of the underlying common stock if the issuer does not call it; however, if the SPARQS is called, the SPARQS holder will receive a cash call price. Therefore, the maturity-day payoff for a SPARQS at the (N, j) node, which includes accrued interest for the last time step regardless whether it is called or not, can be expressed as follows: S N; j f N; j ¼ min C N; j ; (2a) þ I N; j 2 f N; j

S N; j S N; j max 0; C N; j þ I N; j ¼ 2 2

(2b)

where CN, j is the call price at note (N, j), SN, j is the stock price at note (N, j), and IN, j is the accrued interest for the time step of length from (N1)Dt to NDt. Algebraically, Eq. (2a) indicates that the SPARQS holder writes an intermediate-term, out-of-the-money covered call option on one-half of a share of the underlying common stock and sells it to the issuer in exchange for an option premium in the form of an ‘‘above market’’ coupon rate. In sum, the SPARQS provide a ‘‘one-stop shopping’’ of covered call or the ‘‘buy-write’’ strategy, which may save investors transaction costs. Since in a risk-neutral world, the option’s value is given by its expected payoff discounted at an appropriate risk-free interest rate for the length of time considered, the rollback value of the SPARQS at each node, assuming no early exercise at this node, can be calculated as follows: h i f i; j ¼ erDt pf iþ1; jþ1 þ ð1 pÞf iþ1; j for 0pipN 1 and 0pjpi (3) where f i; j denotes the rollback value of the SPARQS at the (i, j) node. However, the valuation of the SPARQS is further complicated because effective from February 1, 2004 to maturity, Morgan Stanley would have the right to call the SPARQS at any time. The call price can be modeled within the binomial tree framework that resembles the discrete time model

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speciﬁed in the Prospectus; that is, upon call each SPARQS holder will receive a cash call price that produces a continuously compounded yield to call of 20.7% (equivalent to 23% compounded annually) on the issue price as follows: Issue price ¼

m X

I z eyzDt þ eymDt C m

(4)

z¼1

where Iz is the accrued interest for the zth time step, m is the mth time step when call is made, Cm is the call price, and y is the continuously compounded yield to call. As implied by Eq. (4), the longer the call delays, the higher the call price. In the following analysis, we assume that Morgan Stanley will call the SPARQS as soon as the call policy is triggered. Denoting time kDt as the ﬁrst call date, the value of the SPARQS at the (i, j) node between time intervals kDt and (N1)Dt depends on whether the call option is exercised or not. If called, its value equals call price plus accrued interest for this time step only because the SPARQS holder will cease receiving future interests; otherwise, its value is given by the rollback value, f i; j ; plus accrued interest for this time step and the rollback interest value. Thus, the value of the SPARQS on and after the ﬁrst call date but prior to maturity can be expressed as follows: ( C i; j þ I i; j if called f i; j ¼ for kpipN 1 and 0pjpi (5) f i; j þ I i; j if not called where I i;j ¼ I i;j þ I i;j ; and I i;j is the rollback interest value discounted at a risky rate to reﬂect the issuer’s credit risk. During the call protection period from time zero to time (k1)Dt, the value of the SPARQS at the (i, j) node is simply given by its rollback value expressed in Eq. (3) plus accrued interest for the time step and the rollback interest value as follows:

f i; j ¼ f i; j þ I i; j

for 0pipk 1 and 0pjpi

(6)

Since the underlying Best Buy common stock pays quarterly dividends, we need to adjust the binomial tree for discrete dividends. Following Hull (2003), the stock price, S, has two components: a stochastic component, S*, and a part corresponding to the present value of all future dividends during the life of the option. Assuming only one dividend payment for the time

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being, the value of the stochastic component at time iDt can be written as ( when iDt4tDt S ¼S rðtDtiDtÞ (7) S ¼ S De when iDtptDt

where tDt is the ex-dividend date, D is the dividend payment, and r is the risk-free interest rate. A binomial tree can then be constructed to model S* with the same parameters m, d, and p as deﬁned in Eq. (1). Next, by adding to the stock price at each node the present value of the future dividend (if any), the tree can be converted into another tree that models S. This approach, which guarantees that the tree recombines, can be extended to deal with multiple dividend payments. Another issue that deserves attention is the choice of the discount rate used in conjunction with the tree. So far, the discount rate used in the above analysis has been the risk-free rate of interest. According to Tsiveriotis and Fernandes (1998) and Hull (2003), if a convertible bond is certain to be converted at maturity, it is then appropriate to use the risk-free interest rate as the discount rate. Contrarily, if the convertible is certain to remain a bond, it is then appropriate to use a risky discount rate that reﬂects the credit risk of the issuer. Since the SPARQS is either callable or convertible at maturity, its value can be calculated as the sum of two components: a component that arises when it ends up as debt when called (i.e., the ﬁrst payoff of the minimum operator in Eq. (2a)) and a component that arises when it ends up as equity when converted (i.e., the second payoff of the minimum operator in Eq. (2a)). We then apply a risky discount rate for the bond component and a risk-free discount rate to the equity component.

3. APPLICATION OF THE SPARQS VALUATION MODEL The sample period covers the entire life of the Best Buy SPAQRS, spanning from July 25, 2003 (the day after issuance) to July 29, 2004 (two days before maturity). Fig. 1 depicts both Best Buy common stock price and SPARQS market price plots during the sample period. As shown, the Best Buy SPARQS was not as volatile as its underlying common stock because the former’s embedded call feature might have handicapped its own price performance. As indicated in Section 2, the theoretical SPARQS value is determined by six factors: (1) Best Buy common stock price, S, (2) time to maturity, T, and

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70 34 32

60

30

55

28

50 45

26

40

24

35

22

30

20 7/25/03

7/29/04

Dates Best Buy Price

Fig. 1.

SPARQSMarketPrice

Best Buy Stock Price

65

SPARQS Price

Plots of Best Buy Common Stock Price and SPARQS Market Price During the Sample Period.

N steps of time intervals, (3) call price, (4) the risk-free interest rate, r, to discount the equity component values, (5) the risky discount rate for the bond component values and coupon interest payments, and (6) the volatility of Best Buy stock prices, s. Before proceeding to test the SPARQS valuation model, a numerical example is presented in Table 2 to illustrate how the model works. The parameters of the numerical example include the data collected on August 1, 2003 as follows: (1) the SPARQS is mandatorily convertible to one-half of a share of Best Buy stock at maturity, which is one year from August 1, 2003; (2) the one-year time horizon is divided into four time steps, with each representing three months; (3) the SPARQS becomes callable after six months and at maturity with a call price of $23.876 and $24.768 (taken from the Prospectus), respectively; (4) the initial Best Buy stock price is $42.85; (5) the continuously compounded risk-free rate is 1.3706%; (6) the continuously compounded risky discount rate is 5.354%; (7) Best Buy’s volatility is 37.82% per annum; (8) Best Buy pays $0.10 dividend at the end of each time step; and (9) the SPARQS pays $0.3754 interest at the end of each time step. Based on the above parameters, we ﬁrst compute m, d, and p as deﬁned in Eq. (1) and get m ¼ 1:2081; d ¼ 0:8277; and p ¼ 0:4709: Next, a binomial tree of stock price with dividend adjustments following the procedure described in Eq. (7) is constructed in Table 2, which is then used to value the

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Table 2. Numerical Example using the SPARQS Valuation Model.

X

Y

Z

21.425 20.364 12.605 6.344 1.415

51.686 22.718 10.466 10.861 1.392

35.537 18.548 14.591 2.485 1.472

62.260 24.217 5.914 17.364 0.939 42.750 21.044 14.585 5.348 1.111 29.383 15.802 14.691 0.000 1.111

90.532* 25.143 0.000 24.768 0.375

75.055 24.251 0.000 24.439 W 62.058 0.375 25.143 0.000 24.768 51.485 0.375 23.472 11.217 11.509 42.549 0.746 21.650 21.274 0.000 35.336 0.375 18.424 17.678 0.000 29.183 0.746 14.967 14.591 0.000 24.272 0.375 12.873 12.127 0.000 20.025 0.746 10.388 10.013 0.000 0.375

Note: Parameters used in the numerical example: (1) the SPARQS is mandatorily convertible to one-half of a share of Best Buy stock at maturity, which is one year from August 1, 2003; (2) the one-year time horizon is divided into four time steps, with each representing three months; (3) the SPARQS becomes callable after six months and at maturity with a call price of $23.876 and $24.768 (taken from the Prospectus), respectively; (4) the initial Best Buy stock price is $42.85; (5) the continuously compounded risk-free rate is 1.3706%; (6) the continuously compounded risky discount rate is 5.354%; (7) Best Buy’s volatility is 37.82% per annum; (8) Best Buy pays $0.10 dividend at the end of each time step; (9) the SPARQS pays $0.3754 interest at the end of each time step; and (10) m ¼ 1:2081; d ¼ 0:8277; p ¼ 0:4709: The top number at each node is the stock price; the second number is the value of the SPAQRS; the third number is the component of the SPARQS that ultimately becomes equity; the fourth number is the component of the SPARQS that ultimately becomes debt; and the ﬁfth number is the sum of accrued interest and the rollback interest value.

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SPARQS. The top number at each node is the stock price; the second number is the value of the SPAQRS; the third number is the component of the SPARQS that ultimately becomes equity; the fourth number is the component of the SPARQS that ultimately becomes debt; and the ﬁfth number is the sum of accrued interest and the rollback interest value. At node W, we test whether the SPARQS will be called or converted. Since onehalf of the stock price, 31.029, is higher than the call price of 24.768, the SPARQS is called. Its equity component value becomes zero and the bond component value is 24.768. Adding both component values with accrued interest, the SPARQS value becomes 25.143. As we rollback through the tree to time step 3, we test whether the SPARQS will be called. At node X, since one-half of the stock price, 37.527, is higher than the call price of 23.876, the SPARQS is called. Therefore, the value of the SPARQS equals call price plus accrued interest for this time step only. At node Y where the SPARQS is not subject to call, rollback using Eq. (3) yields the value of the equity component and the bond component as 5.914 and 17.364, respectively. The value of the interest component, 0.939, includes both accrued interest and the rollback interest value. The sum of these three components gives 24.217 as the value of the SPAQRS. Continuing in this way, the value of the SPARQS at the initial node, Z, is 20.364. Now, we can proceed to test the SPARQS valuation model. Among the aforementioned six factors that determine the SPARQS value, the ﬁrst three factors can be either observed or calculated. When constructing the binomial tree of Best Buy stock prices we divide the remaining life of the SPARQS into 300 steps of small time length. Although in practice, N ¼ 30 usually gives reasonable results, we choose a much larger number of time steps because the initial maturity is one year from the issue day. Regarding the last three factors, the risk-free rate, r, can be estimated by the annualized yield to maturity for the August 2004 Treasury Strips with a maturity date closest to that of the SPARQS. The risky discount rate that reﬂects Morgan Stanley’s credit risk is proxied by Morgan Stanley’s 7.75% note due January 2005, whose yields to maturity are collected from the Standard and Poor’s Bond Guide. Finally, the volatility of Best Buy stock prices, s, will be estimated by using two approaches. The ﬁrst approach is based on implied volatility (ISD). On a given sample day (one day before pricing), the implied volatilities for Best Buy January 2005 at-the-money and close-to-the money leap call options are collected from www.ivolatility.com. The average of these implied volatilities on that day is then used on the subsequent day to

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45%

Volatility

40% 35% 30% 25% 20% 7/25/03

Fig. 2.

Dates

7/29/04

Implied (ISD) and Historical (HSD) Volatility Plots for Best Buy Common Stock.

value the SPARQS. On the contrary, the historical volatility (HSD) is an expost value, based on the standard deviation of the logs of the previous (prior to valuation) 60 trading days’ percentage changes in Best Buy stock prices. Because HSD is a moving average measure of volatility that changes very slowly, we arbitrarily choose 60 trading days for the estimating period that spans around three months. The annualized equivalent of this daily standard deviation is then used as a proxy. Fig. 2 depicts time-series plots for both ISD and HSD estimates for the Best Buy SPARQS. As shown, the 60-day HSDs are more volatile than their ISD counterparts over the sample period. The HSDs are higher than the ISDs during the ﬁrst three months after issuance, but stay lower than the ISDs during the rest of the sample period. Table 3 presents a comparison between the market prices and the theoretical values for the Best Buy SPARQS using the ISD measure. To allow comparisons of prices across various dollar levels, the statistics are computed on a percentage, rather than absolute, basis. The sample period is further subdivided into two intervals to examine the stationarity of the sample statistics. The ﬁrst interval represents the call protection period from the day after issuance (July 25, 2003) to the day before the SPARQS become callable (January 31, 2004), and the second interval covers the period when the SPARQS are both callable and convertible. As shown in Table 3, the average SPARQS market price is 23.00 and the average SPARQS model price is 23.15 for the entire sample period, with a mean pricing error of only

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Table 3. Statistical Results of Comparisons between Market Prices and Theoretical Values for the SPARQS Based on Implied Volatility. Category

1. 2. 3. 4. 5.

7. 8. 9. 10. 11.

12. 13. 14. 15. 16.

Average Price

Standard Deviation

t-Statistics

Best Buy stock price SPARQS market price Theoretical SPARQS price Pricing error ISD

July 25, 2003 to July 29, 2004 (255 observations) 51.84 3.62 23.00 0.74 23.15 0.65 0.65% 1.17% 35.74% 2.23%

Best Buy stock price SPARQS market price Theoretical SPARQS price Pricing error ISD

July 25, 2003 to January 30, 2004 (131 observations) 52.31 4.41 22.52 0.49 22.75 0.50 1.03% 1.20% 0.075 37.11% 1.04%

Best Buy stock price (S0) SPARQS market price Theoretical SPARQS price Pricing error ISD

February 2, 2003 to July 29, 2004 (124 observations) 51.33 2.43 23.51 0.60 23.56 0.50 0.25% 1.01% 0.022 34.30% 2.23%

0.035

0.65% that is not significantly different from zero with t ¼ 0:035: The same conclusion also holds for both subperiods with 1.03% mean pricing error (t ¼ 0:075) for the ﬁrst subperiod and 0.25% mean pricing error (t ¼ 0:022) for the second subperiod. Table 4 presents a comparison between the market prices and the theoretical values for the Best Buy SPARQS using the HSD measure. As shown, the average SPARQS market price is 23.00 and the average SPARQS model price is 23.16 for the entire sample period, with a mean pricing error of 0.72% that is not significantly different from zero with t ¼ 0:087: The same conclusion also holds for both subperiods with 0.81% mean pricing error (t ¼ 0:057) for the ﬁrst subperiod and 0.63% mean pricing error (t ¼ 0:051) for the second subperiod. The theoretical SPARQS values using ISD and HSD, respectively, are plotted against their actual market price counterparts in Fig. 3 wherein the

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Table 4. Statistical Results of Comparisons between Market Prices and Theoretical Values for the SPARQS Based on Historical Volatility. Category

1. 2. 3. 4. 5.

7. 8. 9. 10. 11.

12. 13. 14. 15. 16.

Average Price

Standard Deviation

t-Statistics

Best Buy stock price SPARQS market price Theoretical SPARQS price Pricing error HSD

July 25, 2003 to July 29, 2004 (255 observations) 51.84 3.62 23.00 0.74 23.16 0.70 0.72% 1.18% 33.49% 5.12%

Best Buy stock price SPARQS market price Theoretical SPARQS price Pricing error HSD

July 25, 2003 to January 30, 2004 (131 observations) 52.31 4.41 22.52 0.49 22.70 0.56 0.81% 1.23% 0.057 36.34% 4.73%

Best Buy stock price SPARQS market price Theoretical SPARQS price Pricing error HSD

February 2, 2003 to July 29, 2004 (124 observations) 51.33 2.43 23.51 0.60 23.65 0.46 0.63% 1.11% 0.051 30.48% 3.55%

0.038

straight line maps the actual SPARQS value to the vertical axis. Panel A shows that the theoretical SPARQS values using ISD tend to fall fairly close to the line. So do the theoretical SPARQS values using HSD in Panel B. Frequency distributions of the pricing errors of each of the ISD and HSD models are also depicted as histograms in Fig. 4. As shown, both ISD and HSD models exhibit similar shapes of distributions with a majority of observations lying above but not far from zero. Overall, the above results indicate that on average, the Best Buy SPARQS issue had been slightly overpriced by the binomial tree model prices during the sample period. This insignificant mispricing could be partially attributed to (1) the SPARQS thin trading liquidity in the secondary market, which is evidenced in Table 1 where the average three-month daily trading volume is less than 10,000 shares for most SPARQS issues and (2) the effect of ‘‘onestop shopping’’ of covered call strategy in the reduction of transaction costs.

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25 SPARQS

Model Price

24

23

22

21

20 20

21

(a)

22 23 Market Price

24

25

25 SPARQS

Model Price

24

23

22

21

20 20 (b)

21

22 23 Market Price

24

25

Fig. 3. Theoretical SPARQS Values vs. Market Prices. (a) Theoretical SPARQS Values are Derived using ISD. (b) Theoretical SPARQS Values are Derived using HSD.

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100 ISD 90

HSD

80

Frequency

70 60 50 40 30 20 10 0 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

Pricing Error

Fig. 4.

Frequency Distribution of the Pricing Errors.

Nevertheless, the extremely small pricing errors resulting from the use of either ISD or HSD provide strong evidence of the effectiveness of the binomial tree model in pricing the SPARQS.

4. CONCLUDING REMARKS SPARQS represent another equity-linked structured notes. The SPARQS generally carry higher coupon rates and senior note rating than conventional bonds, and are callable after a brief call protection period and mandatorily convertible at maturity if not called. Therefore, the call feature limits the potential appreciation of the SPARQS in case the underlying common stock price rises, and the conversion option provides no guarantee for any return of principal at maturity. Nevertheless, the SPARQS like all other structured notes indeed offer a number of beneﬁts to the investors that are not readily available from other instruments. We derive a valuation model for the SPARQS by employing the binomial tree approach pioneered by Cox et al. (1979). The binomial tree model is chosen over the conventional contingent claims approach because there is no dilution effect, as the underlying company is not involved in issuing

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additional common shares upon SPARQS conversion. The application of the valuation model to a specific SPARQS issue linked to Best Buy common stock provides strong evidence of the accuracy of the binomial tree model with mean pricing errors ranging from 0.65% to 0.72% during the sample period.

ACKNOWLEDGMENT The authors would like to thank the editor for valuable comments and suggestions. All errors remain ours.

REFERENCES Braddock, J. C. (1997). Derivatives demystified: Using structured financial products. New York, NY: Wiley. Braddock, J. C., & Krause, B. D. (2002). A practitioner’s guide to structuring listed equity derivative securities. In: J. C. Francis, W. W. Toy & J. G. Whittaker (Eds), The handbook of equity derivatives. New York, NY: Wiley. Brennan, M., & Schwartz, E. (1977). Convertible bonds: Valuation and optimal strategies for call and conversion. Journal of Finance, 32, 1699–1715. Brennan, M., & Schwartz, E. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative Analysis, 15, 907–929. Burth, S., Kraus, T., & Wohlwend, H. (2001). The pricing of structured products in the Swiss market. Journal of Derivatives, 9(2), 30–40. Chance, D. M., & Broughton, J. B. (1988). Market index depository liabilities: Analysis, interpretation, and performance. Journal of Financial Services Research, 1(4), 335–352. Chen, A. H., & Kensinger, J. W. (1990). An analysis of market-index certificates of deposit. Journal of Financial Services Research, 4(2), 93–110. Chen, A. H., & Chen, K. C. (1995). An anatomy of ELKS. Journal of Financial Engineering, 4(4), 399–412. Chen, K. C., & Sears, R. S. (1990). Pricing the SPIN. Financial Management, 19(2), 36–47. Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simpliﬁed approach. Journal of Financial Economics, 7(3), 229–263. Das, S. (2000). Structured products and hybrid securities. New York, NY: Wiley. Fabozzi, F. J. (1998). Overview. In: F. J. Fabozzi (Ed.), The handbook of structured financial products (pp. 1–5). New Hope, PA: McGraw-Hill. Finnerty, J. D. (1988). Financial engineering in corporate ﬁnance: An overview. Financial Management, 17(4), 14–33. Finnerty, J. D. (1992). An overview of corporate securities innovation. Journal of Applied Corporate Finance, 4(4), 233–239. Finnerty, J. D. (1993). Interpreting SIGNs. Financial Management, 22(2), 34–47. Hull, J. C. (2003). Options, futures, and other derivatives. Upper Saddle River, NJ: Pearson Prentice-Hall.

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Ingersoll, J. (1997a). A contingent-claims valuation of convertible securities. Journal of Financial Economics, 4, 289–321. Ingersoll, J. (1997b). An examination of corporate call policies on convertible securities. Journal of Finance, 32, 463–478. Merton, R. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, 449–470. Morgan Stanley Dean Witter & Co. (2003). Prospectus global medium-term notes, series C senior ﬁxed rate notes: 7% SPARQS due August 1, 2004. Mandatorily Exchangeable for Shares of Common Stock of Best Buy Co., Inc., July 30. Peng, S. Y., & Dattatreya, R. E. (1995). The structured note market. Burr Ridge, IL: Irwin. Telpner, J. S. (2004). A survey of structured notes. Journal of Structured and Project Finance, 9(4), 6–19. Tsiveriotis, K., & Fernandes, C. (1998). Valuing convertible bonds with credit risk. Journal of Fixed Income, 8(2), 95–102. Wilkens, S., Erner, C., & Roder, K. (2003). The pricing of structured products in Germany. Journal of Derivatives, 11(1), 55–69.

INVESTMENT INCENTIVES IN PROJECT FINANCE IN THE PRESENCE OF PARTIAL LOAN GUARANTEES Van Son Lai and Issouf Soumare´ ABSTRACT In this paper, we study the role of government financial guarantees as catalyst for project finance (PF). On the one hand, the government’s incentive compatibility and participation constraint determine the optimal portion of the loan to be backed. On the other, the borrowing interest rate satisfies the debtholders’ participation constraint. The project’s sponsor may choose to underinvest or overinvest depending on its own capital contribution, the risk technology, the risk measurement errors, and the proportion of guarantee provided by the government. We derive the project optimal investment level as well as the government partial loan guarantee coverage. We also discuss the impact of the risk measurement errors on the project’s credit spreads.

1. INTRODUCTION Project ﬁnance (PF) is an increasingly important method of ﬁnancing large-scale capital-intensive projects, such as power plants, oil pipelines, Research in Finance, Volume 22, 161–186 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22006-3

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automated steel mills, roads, ports, tunnels, etc. The demand for ﬁnancing often exceeds the supply capacity of the project sponsor and of local capital markets (Farrell, 2003). Unlike in traditional ﬁnancing methods, PF lenders have limited or zero-recourse to or right to attach claims against the assets of the project sponsor. As pointed out by Pollio (1998), among others, while allowing for better risk sharing, PF is value enhancing for both the project sponsor and lenders. Lenders need to evaluate and audit only the project assets rather than having to assess both project and sponsor assets, as would be the case with other ﬁnancing vehicles. Nonetheless, PF is a favored option for governments worldwide in managing risk optimally and reducing agency costs.1 Undeniably, credit risk is one of the primary risks facing banks and other creditors. One way for lenders to hedge credit risk is to require ﬁnancial guarantees for the loans they make. A ﬁnancial guarantee is a promise from a third party to make good on payments to the fund provider when the borrower defaults. To have access to funds at lower costs, ﬁrms resort to ﬁnancial guarantees to improve their credit rating and debt capacity. Government agencies and international organizations such as the World Bank are some of the main providers of ﬁnancial guarantees, especially to back large-scale projects ﬁnancing (e.g., Dailami & Leipziger, 1998; Ehrhardt & Irwin, 2004). There is a substantial literature on PF with diverse objectives. Shah and Thakor (1987) use asymmetry of information to explain why project ﬁnancing involves higher leverage than conventional ﬁnancing and why highly risky assets are project-ﬁnanced. They also derive conditions under which a ﬁrm chooses a specific organizational structure over others. Flannery, Houston, and Venkataraman (1993) study the simultaneous effect of corporate tax and organizational form on the agency cost of debt. Chemmanur and John (1996), in the context of corporate control rights, analyze the interrelationship between the corporate organization structure, the capital structure, and the ownership structure of a ﬁrm with multiple projects. However, none of these papers include in their studies ﬁnancial guarantees commonly used in PF. In this paper, we propose a model to study the dynamics between equity holders represented by the project sponsor, debtholders, and the government in structuring a PF. The sponsor undertakes a new project and requires outside ﬁnancing in the form of debt. The government participates in this endeavor by providing a partial loan guarantee (see Lai, 1992, 1995). Recently, Garcia-Alonso, Levine, and Morga (2004) provide an alternative explanation for the government limited guarantee coverage to exporting ﬁrms. The allowance for partial guarantee in our framework is a noteworthy

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contribution. Furthermore, we introduce the presence of measurement errors on the risk level of the project a` la Flannery (1991). The project sponsor knows perfectly the risk level of the project. But debtholders and the government estimate risk with error. The shareholders maximize their wealth with respect to the investment level, the risk technology and their capital contribution. The borrowing interest rate is obtained endogenously from the participation constraint of the debtholders, whereas the percentage of guarantee coverage is decided by the government. Our results raise several policy implications for both public and private decision makers. First, since securing project ﬁnancing with government loan guarantee lowers its debt credit spread, the ﬁrm overinvests. The additional investment is made mainly by debt issue, which increases the project debt ratio. Kleimeier and Megginson (2001) and Esty (2003) document that PF are heavily levered, with an average debt ratio approximating 70%.2 Second, we consider corporate tax payments by the ﬁrm as in Green and Talmor (1985) and in Flannery et al. (1993). Green and Talmor (1985) describe situations in which tax liabilities are short positions comprising the call option on the value of the ﬁrm held by equity holders. Therefore, without loan guarantee, the ﬁrm will be inclined to underinvest in risky projects. This underinvestment gives rise to less tax revenues to the government. That’s why the government provides ﬁnancial guarantees to increase tax revenues in the future. By guaranteeing the loan today, the government improves the credit rating of the project. The ﬁrm is then able to borrow at lower costs, which induces higher investments. Galai and Wiener (2003) made the opposite argument. They examine the government decisions to lend money to the ﬁrm and ﬁnd that with corporate taxes, the government can induce ﬁrms to underinvest. Our result contradicts those in Galai and Wiener (2003) because in our setup, instead of directly making the loan, the government guarantees the loan. Third, several other results emerge from our analysis. The government is facing two dilemmas. On the one hand, the loan guarantee enables the ﬁrm to be more indebted (higher tax shields) which reduces government’s tax revenues. On the other, without obtaining a loan guarantee, the ﬁrm will underinvest, and thus less cash ﬂows subject to corporate taxes. In sum, there is an optimal level of loan guarantee to be provided by the government to maximize the net social beneﬁt. Contrary to what we would expect the government to do in fostering project development, its optimal coverage decreases when the project is too risky. The explanation is that for a highrisk project, marginally, it is too costly to guarantee the debt. The marginal cost not compensated by the marginal tax gain, therefore, it is better for the

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government to not cover a higher portion of the loan. However, when the government increases its guarantee coverage, the borrowing interest rate decreases and the ﬁrm increases its investment. Unfortunately, the government will not always act so, because the marginal gain is not necessarily superior to the marginal cost of the guarantee. When the government estimates the project risk with bigger errors, it is beneﬁcial for the ﬁrm to implement very risky projects. Below a certain threshold, shareholders even looses wealth. To beneﬁt from the government guarantee, they increase the ﬁrm risk above a given threshold. A guarantee coverage up to 80% seems desirable for the government. The investment curve takes various shapes. On the one hand, when the debtholders’ assessment of the project risk is lower than the true risk level of the ﬁrm, the investment pattern takes a concave shape. Intuitively, since lenders will charge less, the ﬁrm can only extract less guarantee from the government. Therefore, increasing the investment level creates marginally more wealth for the government than for the ﬁrm’s shareholders, a reason why the marginal investment level tends to decrease with the risk level of the ﬁrm. On the other, when debtholders’ assessment of the project risk is higher than the true value, the investment has a convex shape especially above a minimum risk threshold. Indeed, since the borrowing rate is high, to reduce the borrowing cost, the ﬁrm obtains more ﬁnancial guarantee from the government. Therefore, when the marginal gain to the ﬁrm is more than the marginal tax burden, the ﬁrm has more incentive to overinvest. In this case, the marginal investment is increasing with the project risk. Further, we ﬁnd the interest rate paid for the debt to be a decreasing function of the portion ﬁnanced by the sponsor. Indeed, if the sponsor is ﬁnancing a large part of the investment, the demand for external funds will be lower, thus by the law of supply and demand, the interest rate should be lower. The incentive for the project manager to increase risk declines with its capital contribution, unless there is a government guarantee. Furlong and Keeley (1989) found that for a value maximizing bank, incentives to increase asset risk decline as its capital increases. Meanwhile, Homo¨lle (2004) asserts that bank with insured deposits, subordinated uninsured debt, and ﬁxed (or variable) equity decreases asset risk as a response to a higher capital requirement. Albeit, obtained for banks, these ﬁndings are in line with our model prediction when there is no loan guarantee. However, when we introduce the guarantee instrument, we ﬁnd opposite results. The remainder of the paper is structured as follows. Section 2 presents the model. We solve the shareholders problem for an all equity ﬁnancing case and study the debt-equity ﬁnancing mix with the government loan

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guarantee. Section 3 provides a general discussion of the ﬁndings. Section 4 concludes. The proofs are presented in the Appendix.

2. THE MODEL We consider a sponsor undertaking a new project. The project is a standalone ﬁrm, meaning that the project is an independent and separate entity. The only commitment of the sponsor is its capital contribution. The project ~ requires an initial investment I and the project cash ﬂows CðIÞ are characterized by the following stochastic technology: ~ ðIÞ ~ CðIÞ ¼ yf

(1)

where f(.) is a twice differentiable concave function and y~ a random variable capturing the stochastic nature of the cash ﬂows. We assume the dynamics of y~ to follow a geometric Brownian motion with mean y. Therefore, with Z denoting the standard Wiener process, the cash ﬂows follow a geometric Brownian motion process as well ~ ~ dCðIÞ ¼ CðIÞ½m dt þ s dZðtÞ

(2)

One of the concerns from the practice is the uncertainty surrounding the valuation of future cash ﬂows. We are aware of these issues, but since it is not the main focus of our study, we assume the cash ﬂows to follow a geometric Brownian motion process with instantaneous mean return m and return volatility s. This risk level is chosen or known by the project sponsor. For the rest of the paper we will use contingent claims analysis (CCA) to price the different payoffs (see Harrison & Kreps, 1979; Merton, 1974 for the use of CCA in pricing assets). Under the risk neutral probability, Q, the process of the cash ﬂows becomes ~ ~ dCðIÞ ¼ CðIÞ½r dt þ s dZ Q ðtÞ

(3)

where r is the risk-free interest rate in the economy assumed to be nonstochastic, and ZQ the Wiener process under the risk neutral measure. The project is owned by a sponsor and the project cash ﬂows are used to pay its debt. In this ﬁnancing framework, often referred to as non- or limited recourse ﬁnancing, lenders depend on the performance of the project itself for repayment rather than the credit of the sponsor. We assume a simple capital structure for the project, consisting of a single debt and equity contracts. There are no dividend payments nor intermediate payments on the debt before it matures. The maturity of the project is T. We assume the

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existence of corporate taxes and also trading takes place continuously with no transaction costs, and the market is frictionless. We also introduce the government, who guarantees the loan payment in case of default by the project. The government guarantees only a proportion of the loan and not the entire amount of the debt. Multiple risk technologies are available for executing the new project. However, it is possible that debtholders and the government estimate the risk of the project with error. In general, the debts in PF are mainly bank loans, hence a better assessment of risk and monitoring. Therefore, the risk measurement error is lower with banks. Let’s note also that the free cash ﬂow problem should not be a concern under project ﬁnancing.

2.1. All Equity Financed Project ~ We start with an all equity ﬁnanced ﬁrm. The project with value CðIÞ ¼ ~yf ðIÞ is held entirely by its shareholders (the sponsor). The total initial debt value is zero. For simplicity, we assume the shareholders to be in charge of the company (i.e., they are ‘the manager’). Albeit interesting, we do not study the agency conﬂicts between shareholders and the project’s manager, since it is not the main focus of this study. At the initial date t ¼ 0; the sponsor initiates an independent new project ﬁnanced entirely by his own money. He invests I dollars in the new project and expects to beneﬁt from it. The project yields a net profit after tax equal to ~ tc maxðCðIÞ ~ elT I; 0ÞÞ I V ðIÞ ¼ E Q erT ðCðIÞ pﬃﬃﬃﬃ ¼ yf ðIÞð1 tc Nðd 0 ÞÞ þ tc eðrþlÞT IN d 0 s T I ð4Þ p ﬃﬃﬃﬃ where d 0 ¼ ½lnðyf ðIÞ=I þ ðl þ r þ s2 =2ÞT=s T ; elT is the tax code depreciation allowance, and tc the corporate tax rate assumed constant,3 EQ represents the expectation under the risk neutral probability Q, and N(x) is the cumulative standard normal distribution function evaluated at x. The tax amount paid by the ﬁrm is equivalent to a call option on the project cash ﬂow with exercise price the tax depreciation, e.g., Green and Talmor (1985). To determine the optimal investment level I, the sponsor maximizes his net wealth from the project, i.e., I ¼ arg max V ðIÞ I

(5)

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We solve this optimization problem and obtain an investment level n o pﬃﬃﬃﬃ I ¼ arg yf 0 ðIÞð1 tc Nðd 0 ÞÞ þ tc eðrþlÞT N d 0 s T 1 ¼ 0

(6)

where f 0 is the ﬁrst differential of f with respect to I. If we assume a decreasing return to scale production technology, f ðIÞ ¼ I g ; with 0pgp1, and no depreciation of capital, l ¼ 1; then I ¼ ½ygð1 tc 1=ð1gÞ From this simpliﬁed expression for the level of investment, it is clear that when the tax rate is high, the ﬁrm will underinvest. It is worth noticing that in some countries and for some strategic projects, the government will regulate the output price. In our framework, y represents the output price. Therefore, if the price y is high, the ﬁrm will invest more (see Fig. 1 for y ¼ 4 versus y ¼ 3). Fig. 1 plots the changes in the investment levels and the value to shareholders when the risk technology of the project varies. When s increases, there are more tax payments since the value of the call (tax value) increases; therefore, it is better for the sponsor to underinvest since the additional investment will only bring more rents to the government in the form of tax revenues. This is consistent with the ﬁndings of Green and Talmor (1985). However, in spite of agency conﬂicts, the tax advantage of debt will induce the ﬁrm to borrow. The next section incorporates the guaranteed debt in the framework and study the interactions between shareholders, debtholders, and the government.

2.2. Equity-Debt Financing Mix with Government Loan Guarantee Now, instead of ﬁnancing the project alone, we assume that the sponsor requires outside ﬁnancing in the form of debt. The project requires an initial investment of I amount, ﬁnanced partly by the sponsor in the proportion a, and the rest 1a is ﬁnanced by debt. In other words, the shareholders decide to infuse a capital level aI and borrow (1a)I to ﬁnance the new project. We assume that aI is entirely ﬁnanced by the existing shareholders, meaning that no new shares are issued or there are no new shareholders in our model. Thus the initial amount of debt required to start the project is (1a)I. We also assume the intervention from a public authority as it is the case in most project ﬁnancing (see Kleimeier & Megginson, 2001; and Esty, 2003, 2004 for extensive reviews on PF). The government participates here, by

168

=3 Investment in an all equity project

Value to shareholders

68

14.8 14.6 14.4 14.2

64 62

Equity

Investment

66

60 58 56 54 0.1

0.2

0.3

0.4

0.5 0.6 sigma

0.7

0.8

0.9

1

14 13.8 13.6 13.4 13.2 13 12.8 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sigma =4

290

62 61

280 Equity

Investment

60 270 260

59 58 57

250

56 240

55

230 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 sigma

1

54

0.1 0.2 0.3

0.4 0.5

0.6 0.7 0.8

0.9

1

sigma

Fig. 1. The Optimal Investment Levels and the Value to Shareholders. These Graphs Plot the Investment Levels and the Value to Shareholders in an All Equity Financed Project as a Function of the Risk Level of the Project. The Parameters Values are g ¼ 0:80; l ¼ 0:20; tc ¼ 0:15; r ¼ 0:03; T ¼ 1:

VAN SON LAI AND ISSOUF SOUMARE´

Value to shareholders

Investment in an all equity project

Investment Incentives in Project Finance

169

guaranteeing the loan, hence subsidizing the project. The government action can also be indirect, i.e., by asking a multinational institution, such as the World Bank, to provide credit enhancement. 2.2.1. The Value to Shareholders With debt ﬁnancing, the shareholders’ net wealth in the new project is4 ~ eRt ð1 aÞI V ¼ E Q egT max ðCðIÞ ~ ðeRT 1Þð1 aÞI elT I; 0Þ; 0Þ aI ð7Þ tc max ðCðIÞ where l is the depreciation rate of the capital and R the ﬁnancing cost of the debt, which is equal to the risk-free rate augmented by a premium p: R ¼ r þ p: The ﬁrst two terms in the expression of shareholders’ wealth represent the net profit before taxes, the third term represents the adjustment for taxes, and the last term represents the initial investment brought by shareholders. The ﬁrm beneﬁts from the tax shields on the interests paid on its debt and also from the depreciation of its initial capital. In fact, eRT(1a)I is the face value of the debt, and (eRT1)(1a)I represents the interest payments. Similar to the case of an all equity ﬁnanced project, the amount of tax paid is equivalent to a call option with a different exercise price. Similar to Flannery et al. (1993), we assume the debt face value to be lower than the tax deductible amount, i.e., eRT ð1 aÞIpðeRT 1Þð1 aÞI þ elT I ) aX1 elT

(8)

From Eq. (8), in default states, no tax payment occurs. ~ eRT ð1 aÞIX0; thus Under condition (8), V+aIX0 only if CðIÞ ~ eRT ð1 aÞI; 0Þ V ¼ E Q erT max ðCðIÞ ~ ðeRT 1Þð1 aÞI elT I; 0Þ aI ð9Þ tc E Q erT max ðCðIÞ A` la Black and Scholes (1973), the solution of Eq. (9) is V ¼ ½CðIÞNðd 1 Þ eðRrÞT ð1 aÞINðd 2 Þ tc ½CðIÞNðd 3 Þ erT ððeRT 1Þð1 aÞI þ elT IÞNðd 4 Þ aI

ð10Þ

with pﬃﬃﬃﬃ lnðCðIÞ=eRT ð1 aÞIÞ þ ðr þ s2 =2ÞT pﬃﬃﬃﬃ ; d2 ¼ d1 s T s T pﬃﬃﬃﬃ lnðCðIÞ=ððeRT 1Þð1 aÞI þ elT ÞÞ þ ðr þ s2 =2ÞT pﬃﬃﬃﬃ ; d4 ¼ d3 s T d3 ¼ s T d1 ¼

VAN SON LAI AND ISSOUF SOUMARE´

170

2.2.2. The Government Incentive and Participation Constraints The government participates in the project by providing partial loan guarantees. The incentive for the government is to gain positive beneﬁts in the form of taxes if the project succeeds.5 The government by its presence in the project expects to raise more taxes in the future. The government insures a portion o of the loan, with 0pop1. As mentioned previously, the government assesses the risk level of the ﬁrm with an error Z, thus the risk level estimated by the government is s+Z. In that case the value of the guarantee provided by the government is6 ~ Guarantee ¼ E Q erT max oeRT ð1 aÞI CðIÞ; 0 (11) This expression is similar to the one in Merton (1977) except that we use a partial guarantee of o instead of 100% coverage. The government is guaranteeing the debt because it expects to raise more taxes to fulﬁll its social agenda. The tax revenue to the government is ~ ðeRT 1Þð1 aÞI elT I; 0 TaxRevenue ¼ tc E Q erT max CðIÞ (12) where tc is the corporate tax rate. The net gain to the government, W, is the difference between the tax gain and the cost of the guarantee, i.e., W ¼ TaxRevenueGuarantee. Therefore, the participation constraint of the government is such that its net gain is positive, WX0. Using CCA, the explicit expression of the net wealth to the government is W ¼ tc CðIÞNðd Z3 Þ erT ððeRT 1Þ ð1 aÞI þ elT IÞNðd Z4 Þ ð13Þ oeðRrÞT ð1 aÞINðd Z8 Þ CðIÞNðd Z5 Þ with o representing the percentage of loan guarantee by the government, d3Z, and d4Z are obtained as in Eq. (10) above with s replaced by s+Z, and d Z5 ¼

lnðCðIÞ=oeRT ð1 aÞIÞ þ ðr þ ðs þ ZÞ2 =2ÞT pﬃﬃﬃﬃ ; ðs þ ZÞ T

pﬃﬃﬃﬃ d Z6 ¼ d Z5 ðs þ ZÞ T

The government will insure a portion o of the loan such that the marginal net gain is zero, which constitutes the incentive compatibility condition of the government. Thus, under the incentive compatibility of the government, the marginal tax gain is equal to the marginal guarantee cost @W =@o ¼ 0 ) @TaxRevenue=@o ¼ @Guarantee=@o which implies Nðd Z6 Þ @R ¼ p0 @o Tðtc Nðd Z4 Þ þ Nðd Z6 ÞoÞ

(14)

Investment Incentives in Project Finance

171

or o¼

tc Nðd Z4 Þ 1 T@R=@o Nðd Z6 Þ

(15)

The quantity o is obtained as the trade-off between the changes in the marginal borrowing rate and the marginal tax gain. Recall from the shareholders’ wealth equation (7), the tax revenue to the government decreases with the interest payments. Therefore, the government is more willing to insure a larger portion of the debt when it can inﬂuence significantly the cost of borrowing. In addition, for lower corporate tax rates, the government will guarantee a larger portion of the debt. This reduces the interest payments made by the ﬁrm, which yields more taxable income (cash ﬂow minus interest payments). The government is then making a trade-off between the tax rate and the net taxable income. At the same time, when o increases, the cost of guarantee to the government increases as well, even though the borrowing interest rate is reduced. Therefore, there is an optimal level of o from the government standpoint.

2.2.3. The Debtholders’ Participation Constraint The participation constraint of the debtholders is obtained when the debt amount (Ia)I is lower or equal to the present value of the future payments to them. The value today of all future payments to them is ~ D ¼ ð1 aÞIeðRrÞT E Q erT maxðeRT ð1 aÞI CðIÞ; 0Þ ~ 0Þ ð16Þ þ E Q erT maxðoeRT ð1 aÞI CðIÞ; The ﬁrst two terms represent the value of the risky debt. Similar to Merton (1974), the value of the risky debt is equal to the value of the risk-free debt minus a put option. The third term is the value of the guarantee. When o ¼ 1; the debt is risk-free and R ¼ r: As mentioned earlier, it is likely that debtholders estimate the risk of the project with an error term e. Thus, shareholders know the true level of the project risk, s, whereas debtholders estimate of the project’s risk is s+e. Using option-pricing theory, the expression of D becomes D ¼ ð1 aÞIeðRrÞT eðRrÞT ð1 aÞINðd 2 Þ CðIÞNðd 1 Þ þ oeðRrÞT ð1 aÞINðd 6 Þ CðIÞNðd 5 Þ ð17Þ

172

VAN SON LAI AND ISSOUF SOUMARE´

with d 1 and d 2 given similar to the expressions of d1 and d2 in Eq. (10), except that the volatility is changed to s+e, and d 5 ¼

lnðCðIÞ=oeRT ð1 aÞIÞ þ ðr þ ðs þ Þ2 =2ÞT pﬃﬃﬃﬃ ; ðs þ Þ T

pﬃﬃﬃﬃ d 6 ¼ d 5 ðs þ Þ T

In equilibrium, the participation constraint of the debtholders is D ¼ ð1 aÞI: The credit spread, Rr, is obtained from this later equilibrium condition as follows: 1 1 ðCðIÞ=ð1 aÞIÞ½Nðd 5 Þ Nðd 1 Þ R r ¼ log (18) T Nðd 2 Þ þ oNðd 6 Þ From Eq. (14), R decreases when o increases meaning that the borrowing cost is reduced when more guarantee is provided. Taking the partial differentials of D and using the debtholders’ participation constraint condition, we get

@R 1 1 ¼ 1 ðRrÞT @a Tð1 aÞ e ðNðd 2 Þ þ oNðd 6 ÞÞ Nðd 6 Þ @o p0 ð19Þ TðNðd 2 Þ þ oNðd 6 ÞÞ @a

@R 1 1 ðNðd 6 Þ Nðd 1 ÞÞC 0 ðIÞ=ð1 aÞ ¼ 1 @I TI eðRrÞT ðNðd 2 Þ þ oNðd 6 ÞÞ Nðd 6 Þ @o X0 TðNðd 2 Þ þ oNðd 6 ÞÞ @I pﬃﬃﬃﬃ @R CðIÞ T ðnðd 1 Þ nðd 5 ÞÞ ¼ @s ðNðd 2 Þ þ oNðd 6 ÞÞeðRrÞT Tð1 aÞI Nðd 6 Þ @o X0 TðNðd 2 Þ þ oNðd 6 ÞÞ @s

ð20Þ

ð21Þ

The ﬁrst term in the expression of @R/@a is negative and the sign of the second term equals to sign(@o/@a). Since @o/@a40, it implies @R/@ao0. The intuition is as follows. When the project sponsor ﬁnances the project with more equity the demand for loan decreases, and from the equilibrium demand and supply the cost of borrowing decreases.

Investment Incentives in Project Finance

173

For I sufﬁciently large, the ﬁrst term of @R/@I is positive and the sign of the second term equals to sign(@o/@I). Since @o/@Io0, it implies @R/@I40. Intuitively, when the implementation of the project calls for higher investment, the ﬁrm requires more debt, therefore, the cost of borrowing increases as the demand for funds is high. Finally, the ﬁrst term of @R/@a has a positive sign and the sign of the second term equals to sign(@o/@s). And since @o/@so0, it implies @R/@s40. When the risk of the project is high, lenders require a higher premium for their funds. 2.2.4. The Firm’s Optimization Problem On the one hand, the value of o is obtained from the government incentive and participation constraints. The government maximizes his net wealth to determine the optimal portion of the loan to insure. On the other, the borrowing cost R is obtained from the participation constraint of the debtholders. The ﬁrm then maximizes its shareholders’ wealth under those constraints. Therefore, the optimization problem of the project’s sponsor is to maximize the shareholders’ wealth, max V ða; I; sÞ a;I;s

(22)

where R is obtained from the participation constraint of the debtholders, R ¼ arg{D ¼ (1a)I}, and o obtained from the participation constraint and incentive compatibility of the government, o ¼ arg{max W,WX0}.7 This kind of optimization with three arguments, a the project’s sponsor contributed capital, I the investment level, and s the project’s risk level, determined endogenously, to our knowledge, has not been tackled in the extant literature. We next discuss the numerical results of our optimization exercise.

3. NUMERICAL RESULTS AND GENERAL DISCUSSION Naturally, to obtain a higher guarantee coverage for each loan, the ﬁrm will overstate its risk level to the government, therefore reducing its borrowing cost and/or increasing its debt capacity.8 On the contrary, vis-a`-vis the debtholders, the ﬁrm tends to understate the risk level, thereby beneﬁting from a better credit rating. We analyze different cases of risk measurement errors by debtholders and the government. We assume many possible cases:

VAN SON LAI AND ISSOUF SOUMARE´

174

(i) when the ﬁrm is successful in misleading both the government and debtholders, ¼ 10%; Z ¼ 10%; (ii) no measurement errors on the risk estimation, ¼ 0; Z ¼ 0; and (iii) debtholders and the government overestimate the risk level of the ﬁrm, ¼ 15%; Z ¼ 15%: The rationale may be that debtholders learn and infer the risk level from the guarantee promise of the government. Therefore, they use the same risk assessment as the government. For all the results we present, we use T ¼ 1; since we assume a oneperiod framework. Even though the average maturity for PF varies between 8 and 12 years, using T ¼ 1 does not affect the qualitative results. We use a tax rate of tc ¼ 0:15 and l ¼ 0:20 corresponding to a depreciation code allowance of el ¼ 0:82: In fact, these numbers are close to those used by Flannery et al. (1993).

3.1. Risk Shifting, Moral Hazard, and Investment Incentives Fig. 2 plots the levels of investment, equity value, and borrowing costs. Depending on the initial capital contribution from the project sponsor, the optimal investment levels take many different forms. If the project sponsor has more equity stake in the ﬁrm, his incentive to take risk is less. Therefore, the ﬁrm can forego some growth opportunities. The rationale being that, by investing more in the project, the sponsor creates more tax revenues for the government but is not able to extract additional beneﬁts from the increased investment. It is then optimal for the project shareholders to prefer lower levels of investment. In contrast, the lower the initial capital participation by Value to shareholders

Borrowing cost

75

0.5

70

0.4

65

0.3

Rate

360 340 320 300 280 260 240 220 1

Equity

Investment

Investment

60

50 1 0.8 0.6 0.4 alpha

0.2 0

0.2

0.4

0.6

sigma

0.8

1

0.2 0.1

55

0.8 0.6 0.4 alpha

0.2 0

0.2

0.4

0.6

sigma

0.8

1

0 1

0.8 0.6 0.4 alpha

0.2 0

0.2

0.4

0.6

0.8

1

sigma

Fig. 2. The Optimal Levels of Investment, Equity, and Borrowing Cost in Presence of Loan Guarantee. These Graphs Plot the Investment Levels, the Value to Shareholders and the Borrowing Costs as Function of the Risk Levels of the Project and the Capital Contribution of the Project Sponsor. The Parameters Values are g ¼ 0:80; y ¼ 4; l ¼ 0:20; tc ¼ 0:15; r ¼ 0:03; ¼ 0:00; Z ¼ 0:00:

Investment Incentives in Project Finance

175

the project sponsor, the higher is his incentive to overinvest. These ﬁndings are consistent with previous literature on risk shifting and moral hazard, e.g., Galai and Masulis (1976), Jensen and Meckling (1976), and Myers (1977). Esty (2003) documents that PF companies have on average a debt-to-total capitalization of 70% compared to 33% for similar-sized ﬁrms listed in the Compustat database. Thus, we purport to capture in our framework this particular PF characteristic by the low level of the sponsor’s own capital. Indeed, when the sponsor has less capital in the project, increasing the risk level of the project is beneﬁcial for him, since it can cash on potential growth options. However, as depicted in Fig. 3, depending on the degree of the risk measurement errors, the investment curve takes various shapes, hence, both underinvestment and overinvestment can occur. When the debtholders’ assessment of the ﬁrm risk is lower than the true risk level of the ﬁrm, the investment has a concave shape. Since debtholders require a lower return, the ﬁrm will be able to extract less guarantee from the government. Therefore, increasing the investment level produces marginally more tax revenues for the government than for the ﬁrm itself, a reason why the marginal investment level tends to decrease with the risk level of the ﬁrm. In general, the equity value decreases with a, the percentage of the investment borne by the sponsor, which supports the moral hazard argument. Indeed, having more stake in the project (for high a), the sponsor can barely extract wealth from debtholders and the government. When a increases, the ﬁrm not only loses the tax shield advantage, but also beneﬁts less from the government guarantee. Furthermore, the value to shareholders increases with the project risk s for low a, and the opposite tendency occurs for high a. However, when debtholders’ assessment of the ﬁrm risk level is higher than the true one, the investment curve has a convex shape, especially for risk above a risk threshold. The intuition for that is as follows. Since the borrowing cost is high, to reduce its borrowing cost, the ﬁrm relies heavily on guarantees. When the marginal gain to the ﬁrm exceeds the marginal tax outlets, the ﬁrm has higher incentive to overinvest to take advantage of the government guarantee. In this case, the marginal investment is increasing with the project risk. When the difference in estimating the project risk between the ﬁrm and the government is large, it is beneﬁcial for the ﬁrm to implement very risky projects. Below some threshold, shareholders even lose wealth. To profit from the government guarantee, it is in their interest to increase the ﬁrm risk above a given threshold. With higher project risk, the expected tax revenues to the government also increase. This explains why the government ﬁnds proper to guarantee the debt.

VAN SON LAI AND ISSOUF SOUMARE´

176

=−0.10, η=0.10 Investment

Equity

440

85 alpha=0.2

alpha=0.2

420

80

380

75

360

Equity

Investment

400

340 320

alpha=0.5

300

alpha=0.5

65

280

60

260 240 0.2

70

alpha=0.8

alpha=0.8 0.3

0.4

0.5

0.6 sigma

0.7

0.8

0.9

55 0.2

1

0.3

0.4

0.5

0.6 sigma

0.7

0.8

0.9

1

0.9

1

=0.00, η=0.00A Investment

360 340

72 68 Equity

Investment

300

66 64

alpha=0.5

62

alpha=0.5

280

60 alpha=0.8

58

260

alpha=0.8 0.2

0.3

0.4

0.5 0.6 sigma

0.7

0.8

56 0.9

54 0.1

1

290

64

280

62 Equity

270 alpha=0.8

260

0.2

0.3

0.4

=0.15, η=0.15

Investment

Investment

alpha=0.2

70

320

240 0.1

Equity

74 alpha=0.2

0.5 0.6 sigma

0.7

0.8

Equity alpha=0.5

60 alpha=0.8

58

250 56

alpha=0.2

240

220 0.1

alpha=0.2

54

230

alpha=0.5 0.2

0.3

0.4

0.5 0.6 sigma

0.7

0.8

0.9

1

52 0.1

0.2

0.3

0.4

0.5 0.6 sigma

0.7

0.8

0.9

1

Fig. 3. The Optimal Investment Levels and the Value to Shareholders in Presence of Loan Guarantees. These Graphs Plot the Levels of Investment and the Value to Shareholders for Different Values of a as Function of the Risk Level of the Project. The Parameters Values are g ¼ 0:80; y ¼ 4; l ¼ 0:20; tc ¼ 0:15; r ¼ 0:03:

For intermediate levels of capital contribution from the sponsor, the ﬁrm can choose an optimal risk level. The ﬁrm weights the bankruptcy risk against the gain from the guarantee. Up to a given risk level, the ﬁrm gains from the guarantee which decreases its borrowing cost. However, beyond an optimal risk level, by taking more risk, the ﬁrm increases the tax revenues to the government, but is unable to improve its shareholders’ wealth. Thus, the ﬁrm can underinvest below and above the optimal risk level.

Investment Incentives in Project Finance

177

Overall, our analysis demonstrates that both underinvestment and overinvestment scenarios can occur even under the presence of a government loan guarantee. The crucial determinants are the risk technology, the initial capital contribution of the project’s sponsor, and the degree of risk measurement errors by the other stakeholders. 3.2. Loan Guarantees and Investment Incentives Table 1 shows an increase in the guarantee proportion o when the project owner contributed capital a is large. Indeed, when a is large, less debt has to be insured, therefore, to increase the taxable income, the government can guarantee a larger portion of the loan. Note however, even though the guarantee portion is large, the investment level is lower than the case with small a. The government is facing two dilemmas here. On the one hand, from the provision of the loan guarantee, the ﬁrm becomes more indebted, hence uses more tax shields, which results into a reduction in the tax payment to the government. On the other, without the loan guarantee, the ﬁrm will underinvest, and thus will bring in less cash ﬂows subject to corporate taxes (taxable income). In sum, there is an optimal level of loan guarantee which maximizes the government net wealth. Table 1.

Optimal Values of o, R, I, and V in Presence of Loan Guarantees. R

o

s

0.20 0.40 0.70

0.20

a 0.50

0.80

0.2361 0.0509 0.0001

0.2361 0.0874 0.0100

0.9999 0.2361 0.0260

s

0.20 0.40 0.70

0.20

a 0.50

0.80

0.0300 0.0314 0.1886

0.0300 0.0300 0.0443

0.0300 0.0300 0.0300

0.20

a 0.50

0.80

62.97 68.99 69.87

62.46 61.72 62.62

62.06 61.17 58.24

I

s

0.20 0.40 0.70

V

0.20

a 0.50

0.80

290.00 323.00 331.00

284.00 277.00 278.00

282.00 272.00 253.00

s

0.20 0.40 0.70

Note: These tables show the optimal values of optimal o, R, I and V for different values of a and s. The parameter values are g ¼ 0:80; y ¼ 4; l ¼ 0:20; tc ¼ 0:15; r ¼ 0:03; ¼ 0:00; Z ¼ 0:00:

178

VAN SON LAI AND ISSOUF SOUMARE´

When a is low, the ﬁrm begs for more guarantee. Unfortunately, for risky projects, the optimal guarantee percentage from the viewpoint of the government is small, almost close to zero. Recall that, the government provides the guarantee as long as the marginal tax beneﬁt exceeds (or equals to) the marginal guarantee cost. Beyond the optimal percentage of the guarantee coverage o, the ﬁrm’s investment is profitable to shareholders, but not to the government, since the government net wealth decreases. The optimal o increases with the capital contribution of the sponsor, a, and decreases with the risk level of the project, s. The borrowing interest rate R increases with the risk level of the project. However, the level of R is higher for low a than for high a. The intuition is as follows. When a is large, the demand for investment fund is lower, therefore in equilibrium the cost of borrowing decreases. When the project is too risky, the resulting probability of default is high, thus debtholders demand higher credit spread on the loan. Even under a government guarantee, these patterns hold. If the guarantee coverage were full, i.e., the cost of borrowing would be the risk-free rate. Again, the government decides the coverage level based on its welfare maximization. By reneging its role of fostering project development, the government optimal coverage decreases when the project is too risky. The explanation is that for a high-risk project, it is too costly marginally to guarantee the debt. Since the marginal cost is not compensated by the marginal tax gain, it is better for the government not to provide any additional guarantee. Fig. 4 plots the changes in the investment level, the shareholders’ value, the borrowing cost, and the net wealth of the government for different values of o. As we can see from the exhibits, increasing o decreases the borrowing cost, leads to overinvestment by the ﬁrm, and improves the value to shareholders, but the wealth of the government decreases. Therefore, although it beneﬁts the ﬁrm, the net gain to the government is not improved. For all the cases presented, the full guarantee coverage is not viable for the government. Indeed, except in panel (b) corresponding to the no-measurement error case, when o exceeds 90%, the net gain to the government becomes negative.

Fig. 4. The Optimal Levels of Investment, Equity, Borrowing Cost, and Government Wealth. These Graphs Plot from Left to Right, the Investment Levels, the Value to Shareholders, the Borrowing Costs, and the Net Wealth of the Local Government as Function of Exogenous Levels of o. The Parameters Values are g ¼ 0:80; y ¼ 4; l ¼ 0:20; tc ¼ 0:15; r ¼ 0:03; a ¼ 0:20; s ¼ 0:50:

Value to shareholders

78.5

440

410

77

400

76.5

390 380

76

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

0.037

20

0.036

15

0.035 0.034

0 -5

0.031

-10

0.03

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega Value to shareholders

460

0.07

77

0.065

76 Rate

Equity

74

340

0.055 0.05

71

0.04

70

0.035

69

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega Investment

0.03

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega Value to shareholders

75 70

Rate

Equity

400 350

65

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

Government net wealth

0.13

25

0.12

20

0.11

15

0.1

10

0.09 0.08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

5

W>0

0 -5

0.05

-10

0.04

-15

0.03 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

-20

W<0

179

55 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

0.06 60

250

(c)

5

0.07

300

200

10

Borrowing cost

80

450

Government net wealth

15

ε=0.15, η=0.15

500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

0.045

72

360

320

75

25

W<0

20

0.06

73

380

(b)

-15

Borrowing cost 0.075

78

400

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

W>0

5

0.032

79

420

10

0.033

480

440 Investment

25

ε=0.00, η=0.00

Investment

Investment

30

0.038

Wealth

420

77.5

Government net wealth

0.039

Wealth

430

78 Rate

Equity

Investment

450

(a)

Borrowing cost

79

460

Wealth

470

Investment Incentives in Project Finance

ε=−0.10, η=0.10 Investment

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 omega

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It is worth mentioning that we use the maximum wealth for the government objective welfare function (incentive compatibility). If instead the objective of the government were to keep his wealth positive (participation constraint), the optimal o would be higher. This objective is consistent with the government policy to encourage the implementation of a project if it earns a positive net gain. This argument holds especially if the project requires a minimum investment level for a go-ahead. To beneﬁt from the project, the government has to provide a sufﬁcient level of guarantee. 3.3. The Impact of Loan Guarantees on Credit Ratings Table 2 shows the changes in the ﬁrm’s investment decision for different credit ratings proxied by the debt interest rate premium or credit spread, Rr. For this purpose, we compute the percentage of loan guarantee needed to maintain the same R. When the risk measurement errors between the ﬁrm and its stakeholders (debtholders and the government) have the structure ¼ 0:10; Z ¼ 0:10; to maintain a risk premium of 100 basis points, the partial guarantee required from the government is 67% of the loan face value, whereas in absence of measurement errors ( ¼ 0:00; Z ¼ 0:00) it would be 84%. For positive measurement errors from both stakeholders, ¼ 0:15; Z ¼ 0:15; the guarantee level would be 89%. To maintain a risk premium or credit spread of 200 basis points, the partial guarantee will be 0% for the risk measurement error structure ¼ 0:10; Z ¼ 0:10; 79% for ¼ 0:00; Z ¼ 0:00; and 86% for ¼ 0:15; Z ¼ 0:15: In sum, we can conclude that the credit rating of the project debt improves in presence of a loan guarantee. However, the degree of the credit enhancement depends on the structure of the risk measurement errors.

4. CONCLUSION This paper studies the dynamics between the project’s sponsor, the debtholders, and the government in structuring a new PF. The project sponsor requires outside ﬁnancing in the form of debt and the government acts as a stakeholder by providing a partial loan guarantee. The borrowing cost is obtained endogenously from the participation constraint of the debtholders, and the percentage of guarantee coverage is decided by the government. The government is facing two dilemmas. On the one hand, following the obtention of the loan guarantee, the ﬁrm becomes more indebted which results in a reduction of the tax payment to the government. On the other,

Investment Incentives in Project Finance

Table 2.

181

Optimal Policies for Given Categories of Credit Ratings in Presence of Loan Guarantees.

(a) ¼ 0:10; Z ¼ 0:10 p(bp) I V o W

0

25

50

75

100

125

150

175

200

467.79 463.96 460.17 456.40 452.67 448.96 445.28 441.63 438.01 78.65 78.10 77.55 77.00 76.46 75.93 75.39 74.86 74.33 0.8104 0.7851 0.7558 0.7202 0.6734 0.5982 0.0000 0.0000 0.0000 11.06 13.15 15.39 17.85 20.69 24.32 30.11 29.88 29.66

(b) ¼ 0:00; Z ¼ 0:00 p(bp) I V o W

0

50

100

150

200

300

400

500

600

467.79 460.17 452.67 445.28 438.01 423.81 410.05 396.72 383.79 78.65 77.55 76.46 75.39 74.33 72.25 70.22 68.26 66.34 0.8851 0.8629 0.8394 0.8143 0.7871 0.7238 0.6376 0.4490 0.0000 12.10 13.55 14.95 16.32 17.64 20.17 22.53 24.75 24.42

(c) ¼ 0:15; Z ¼ 0:15 p(bp) I V o W

0

100

200

300

500

700

900

1100

1200

467.79 452.67 438.01 423.81 396.72 371.27 347.39 324.98 314.30 78.65 76.46 74.33 72.25 68.26 64.47 60.88 57.48 55.85 0.9184 0.8897 0.8600 0.8292 0.7628 0.6869 0.5929 0.4465 0.0000 5.48 2.26 0.77 3.64 8.90 13.55 17.66 21.25 22.78

Note: Here the values of the investment, the equity, the required level of o to achieve the given R, and the net wealth of the government when the risk premium takes different values are given. R ¼ r þ p, where p represents the risk premium expressed in basis points (bp). The parameters values are g ¼ 0:80; y ¼ 4; l ¼ 0:20; tc ¼ 0:15; r ¼ 0:03; a ¼ 0:20; s ¼ 0:50: With these parameter values, the investment and equity levels in an all equity ﬁnanced project are I 0 ¼ 264:82; V 0 ¼ 60:10; respectively. The bold ﬁgures highlight the results for 100 and 200 basis points.

without the loan guarantee, the ﬁrm will underinvest, and thus less cash ﬂows will be subject to corporate taxes. In sum, there is an optimal level of loan guarantee to be provided by the government to maximize the net social beneﬁt. Contrary to what we would expect the government not to renege its role of fostering project development, its optimal coverage decreases when the project is too risky. The explanation is that for high-risk project, it is marginally too costly to guarantee the debt. The marginal cost is not compensated by the marginal tax gain, therefore it is better for the government not to cover a high percentage of loan. Consistent with previous ﬁndings on risk shifting and moral hazard (e.g., Galai & Masulis, 1976; Jensen & Meckling, 1976; Myers, 1977), the optimal

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investment levels take different forms depending on the initial capital contribution from the project sponsor. When the project is ﬁnanced entirely with equity, the ﬁrm tends to underinvest when the risk of the project increases. However, as documented by Esty (2003) among others, PFs are highly levered and usually beneﬁt from the government guarantees. Our theoretical model helps explain these puzzling ﬁndings. Especially, we show that in presence of government loan guarantees, the ﬁrm is able to reduce its ﬁnancing costs. We also discuss the relationship between the risk measurement errors, the project’s rating, and the government guarantee. By and large, our analysis demonstrates that both underinvestment and overinvestment scenarios can occur even under the presence of the government loan guarantees. The crucial elements here are the risk technology, the initial capital contribution of the project’s sponsor, and the degree of risk measurement errors by the other stakeholders (government and/or debtholders).

NOTES 1. For example, the proposed Energy Policy Act of 2003 of the American Congress intends to modernize America’s energy production and distribution systems. This follows closely the Bush–Cheney’s National Energy Policy (2001). Obviously, these infrastructures will be mostly ﬁnanced by project companies. 2. Kleimeier and Megginson (2001) compare empirically portfolios of PF loans to comparable samples of non-PF loans. They ﬁnd that PF loans have longer maturities, and are more likely to have third party guarantees. Moreover, projects funded with PF loans are heavily leveraged with an average loan to project value ratio of 67%. Esty (2003) found that PF creates value by reducing agency costs associated with large, transaction-specific assets, and by reducing the opportunity cost of underinvestment due to leverage and incremental distress costs. 3. We ignore the American optionality feature of taxation, since it is not the main focus of our study. 4. We assume, as is usually done in the corporate ﬁnance literature, appropriate assumptions on the utility functions so that maximizing utility is equivalent to maximizing net equity. 5. This is a simpliﬁcation of the social objective of the government. Indeed, there are intangible social beneﬁts taken into account by the public authority. We assume the tax rate to proxy for all these features. 6. Merton (1977) is the ﬁrst to establish an isomorphism between a put option and a ﬁnancial guarantee. A ﬁnancial guarantee is a put option written by the guarantor and granted to the bondholder. 7. The optimization is performed numerically using Matlab optimization toolbox. 8. In contrast to Turnbull (1979), here the debt capacity is equal to the optimal debt level. Nevertheless, we recognize that the debt capacity is usually lower than the

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optimal desired debt level of the ﬁrm, because the borrowing cost included the expected tax on interest obtained by the debtholders. Therefore, if we assume R+k, where k represents the portion of borrowing cost added because of this tax issue, the debt capacity here should be lower than the optimal debt level.

ACKNOWLEDGEMENTS We acknowledge the ﬁnancial support from the Institut de Finance Mathe´matique of Montreal (IFM2) and the Fonds Quebecois de la Recherche sur la Societe et la Culture (FQRSC). All errors are the authors’ sole responsibility.

REFERENCES Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(May/June), 637–654. Chemmanur, T. J., & John, K. (1996). Optimal incorporation, structure of debt contracts, and limited-recourse project ﬁnancing. Journal of Financial Intermediation, 5, 372–408. Dailami, M., & Leipziger, D. (1998). Infrastructure project ﬁnance and capital ﬂows: a new perspective. World Development, 26, 1283–1298. Ehrhardt, D., & Irwin, T. (2004). Avoiding customer and taxpayer bailouts in private infrastructure projects: Policy toward leverage, risk allocation and bankruptcy. World Bank Policy Research Paper 3274, April. Esty, B. C. (2003). The economic motivations for using project finance. Working Paper, HBS. Esty, B. C. (2004). Why study large projects? An introduction to research on project ﬁnance. European Financial Management, 10, 213–224. Farrell, L. M. (2003). Principal-agency risk in project ﬁnance. International Journal of Project Management, 21, 547–561. Flannery, M. J. (1991). Pricing deposit insurance when the insurer measures bank risk with error. Journal of Banking and Finance, 15, 975–998. Flannery, M. J., Houston, J. F., & Venkataraman, S. (1993). Financing multiple investment projects. Financial Management, 22(Summer), 161–172. Furlong, F. T., & Keeley, M. C. (1989). Capital regulation and bank risk-taking: A note. Journal of Banking and Finance, 13, 883–891. Galai, D., & Masulis, R. (1976). The option pricing model and risk factor of stock. Journal of Financial Economics, 3, 53–81. Galai, D., & Wiener, Z. (2003). Government support of investment projects in the private sector: A microeconomic approach. Financial Management, 32(Autumn), 33–50. Garcia-Alonso, M. C., Levine, P., & Morga, A. (2004). Export credit guarantees, moral hazard and exports quality. Bulletin of Economic Research, 56, 311–327. Green, R. C., & Talmor, E. (1985). The structure and incentive effects of corporate tax liabilities. Journal of Finance, 40, 1095–1114.

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Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20, 381–408. Homolle, S. (2004). Bank capital regulation, asset risk, and subordinated uninsured debt. Journal of Economics and Business, 56, 443–468. Jensen, M. C., & Meckling, W. (1976). Theory of ﬁrm: managerial behavior, agency costs and ownership structure. Journal of Financial Economics, 3, 305–360. Kleimeier, S., & Megginson, W. L. (2001). An empirical analysis of limited recourse project finance. Working Paper, The University of Oklahoma. Lai, V. S. (1992). An analysis of private loan guarantees. Journal of Financial Services Research, 6, 223–248. Lai, V. S. (1995). On the valuation of private loan guarantees: Wealth effects and government insurance protection. Research in Finance, 12, 141–181. Merton, R. C. (1973). The theory of rational option pricing. Bell Journal of Economics and Management Science, 4(Spring), 141–183. Merton, R. C. (1974). On pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, 449–470. Merton, R. C. (1977). An analytic derivation of the cost of deposit insurance and loan guarantees: An application of modern option pricing theory. Journal of Banking and Finance, 1, 3–11. Myers, S. C. (1977). Determinants of corporate borrowing. Journal of Financial Economics, 5, 147–175. Pollio, G. (1998). Project ﬁnance and international energy development. Energy Policy, 26, 687–697. Shah, S., & Thakor, A. V. (1987). Optimal capital structure and project ﬁnancing. Journal of Economic Theory, 42, 209–243. Turnbull, S. M. (1979). Debt capacity. Journal of Finance, 34, 931–940.

APPENDIX Proofs Let’s deﬁne the value of the standard call and put as follows CallðX ; F Þ ¼ XNðx1 Þ erT FNðx2 Þ PutðX ; F Þ ¼ erT FNðx2 Þ XNðx1 Þ with x1 ¼

lnðX =F Þ þ ðr þ s2 =2ÞT pﬃﬃﬃﬃ ; s T

pﬃﬃﬃﬃ x2 ¼ x 1 s T

where X is the underlying asset value and F the exercise price in Black and Scholes (1973) and Merton (1973) world. The other notations are standard and are deﬁned in the main text.

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The partial derivatives of the call and the put are @CallðX ; F Þ @CallðX ; F Þ ¼ Nðx1 Þ; ¼ erT Nðx2 Þ @X @F @PutðX ; F Þ @PutðX ; F Þ ¼ Nðx1 Þ 1; ¼ erT ½1 Nðx2 Þ @X @F pﬃﬃﬃﬃ @CallðX ; F Þ @PutðX ; F Þ ¼ ¼ X T nðx1 Þ @s @s where n(x) ¼ @N(x)/@x. The values of debt, tax revenue, and guarantee are deﬁned as D ¼ ð1 aÞIeðRrÞT PutðCðIÞ; eRT ð1 aÞIÞ þ PutðCðIÞ; oeRT ð1 aÞIÞ TaxRevenue ¼ tc CallðCðIÞ; ðeRT 1Þ ð1 aÞI þ elT IÞ Guarantee ¼ PutðCðIÞ; oeRT ð1 aÞIÞ Using the formulae for the put and call and the participation constraint condition of debtholders, the partial differential of D with respect to a, I, and s, respectively are @D @R ðRrÞT ¼ I ¼e I Nðd 2 Þ Tð1 aÞ I @a @a @R @o ðRrÞT o oI þ ð1 aÞI Tð1 aÞ I þe Nðd 6 Þ @a @a @D @R ðRrÞT ¼ ð1 aÞ ¼ Nðd 2 Þe þ ð1 aÞ Tð1 aÞ I @I @I þ ðNðd 1 Þ Nðd 5 ÞÞgyI g1 @R @o ðRrÞT o oð1 aÞ þ ð1 aÞI þe Tð1 aÞ I Nðd 6 Þ @I @I @D @R ¼ 0 ¼ Nðd 2 Þ þ oNðd 6 Þ eðRrÞT Tð1 aÞ I @s @s pﬃﬃﬃﬃ CðIÞ T nðd 1 Þ nðd 5 Þ @R þ eðRrÞT ð1 aÞ INðd 6 Þ @s We obtain the expressions of @R/@a, @R/@I, and @R/@s from these equations. Also the partial differential of the tax revenue and the guarantee with

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186

respect to o are @TaxRevenue @R ¼ eðRrÞT ð1 aÞItc Nðd 4 ÞT @o @o

@Guarantee @R ðRrÞT ¼e ð1 aÞINðd 6 Þ 1 þ To @o @o

PRICING OPTIONS WITH PRICE LIMITS AND MARKET ILLIQUIDITY Chuang-Chang Chang, Huimin Chung and Tin-I Wang ABSTRACT The effects of price limits and market illiquidity are crucial for pricing derivatives based on some underlying assets traded in the markets with a price limit rule and an illiquidity phenomenon. We develop models to value options for the cases of either the underlying assets encountering price limits and market illiquidity, or when the underlying assets are imposed with price limits and the options themselves show market illiquidity in this paper. The Black–Scholes (1973) model, the Krakovsky (1999) model, and the Ban, Choi, and Ku (2000) model are presented as special cases of our model. Our numerical results show that both the price limit and market illiquidity significantly affect the option values.

1. INTRODUCTION To stabilize ﬁnancial market prices, many exchanges adopt daily price limits. Price limits are imposed in futures and options markets of the United States

Research in Finance, Volume 22, 187–214 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22007-5

187

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and in many stock exchanges around the world including: Austria, Belgium, France, Italy, Japan, South Korea, Malaysia, Mexico, the Netherlands, South Africa, Spain, Switzerland, Taiwan, and Thailand (Roll, 1989). Although a price limit rule restricts the ﬂuctuations of stock prices within a predetermined range in each trading day, the effectiveness of a price limit on trading prices under stressful market condition is widely debated.1 The trading of derivatives is now one of the fastest growing areas in many emerging markets. Many derivatives such as futures and options that are traded in emerging markets have price limits imposed on their underlying stocks.2 However, very little is known regarding the effect of price limits on the values of derivatives. Applying the ‘‘vanishing transaction cost’’ technique and adopting the solution of an initial boundary value problem, Ban, Choi, and Ku (2000) successfully derive a partial differential equation (PDE) to value European options in a market with a daily price limit. However, they do not illustrate how to implement their model, and the quantitative impact of a price limit on option prices remains an open question. In addition to price limits, another important market friction that affects the price of options is the illiquidity problem. The trading volume of some of the underlying stocks in emerging markets is very thin. For derivatives whose underlying trades in thin markets, pricing market liquidity into derivatives has become very essential.3 Most option pricing models are developed under the assumption that the underlying assets are traded in a liquid market, but one exception is Krakovsky (1999). He shows how to incorporate the market liquidity of the underlying asset into the option values. He derives a liquidity-adjusted Black–Scholes (1973) equation that is a non-linear PDE for computing the replicating cost of a European contingent claim. His pricing PDE shows that market liquidity affects the option values through the gamma of the position, which is reﬂected in the local volatility. To our knowledge, there are no papers that have developed models to value options based on underlying assets having both properties of price limits and market illiquidity, which is very common in the emerging markets. In this paper, we propose a new approach that can incorporate both market illiquidity and daily price limits into derivative pricing. We assume that the liquidity problem could happen either in the stock market or in the option market, and the underlying stock prices are imposed with price limits. We also use ﬁnite difference methods to illustrate how market illiquidity and price limits affect the option values. The remainder of this paper is organized as follows: Section 2 constructs the valuation models. Section 3 illustrates how to implement the models

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189

developed in Section 2 by using a ﬁnite difference method. Section 4 presents and analyzes the numerical results. Some discussions are given in Section 5. Section 6 draws conclusions.

2. THE MODEL 2.1. Geometric Brownian Motion with a Boundary (Intraday Model) To put price limits into option pricing, we adopt the dynamic process for the underlying asset proposed by Ban et al. (2000) as follows: 8 dSðtÞ ¼ sðSðtÞÞI ða;bÞ ðSðtÞÞ dBt þ mðSðtÞÞI ða;bÞ ðSðtÞÞ dt > > > > < þd1 dft d2 dct (1) > I fag dt ¼ r1 df > > > : I dt ¼ r dc fbg 2 t where f and c are the so-called local times at a and b, respectively. We denote the probability space as ðW ; BðW ÞÞ; where W is the space consisting of all continuous functions deﬁned on [0, N] and BðW Þ is the usual Borel sﬁeld of W. The term r can be interpreted as how sticky the boundary is and r40 indicates that the boundary is not an instantaneous reﬂection, whereas d40 indicates that the boundary is not absorbing. To exclude the arbitrage opportunity that incurs under a price limit environment, Ban et al. (2000) discretize the time interval and employ the Leland (1985) transaction cost model. They then let the transaction cost vanish sufﬁciently fast enough when the time interval approaches zero. This method is the so-called ‘‘vanishing transaction cost technique’’ that makes it possible to derive a pricing PDE with a boundary condition to price options when the underlying assets that have price limit. For a multiday case, we merely assume that any given day is like any other day except that the range of movement is determined by the closing price of the previous day. This implies that the new process cannot be Markov,4 and it causes some complication in the economic behavior of the model. Let S(t) be the process at Sð0Þ ¼ s0 and let [(n1)T, nT] be the time interval for the nth day. To make the structure clear, we summarize the assumptions as follows: (1). For the nth day, we assume the price process to be a geometric Brownian motion with a boundary as described in Eq. (1) and with the movement range [a, b] ¼ ½ð1 aÞS ðn1ÞT ; ð1 þ bÞS ðn1ÞT ; where a and b

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CHUANG-CHANG CHANG ET AL.

are ﬁxed positive constants for the upper and lower price limit percentages: for example, a ¼ b ¼ 7% in Taiwan’s stock market. (2). The closing price of the nth trading day is equal to the starting price of the (n+1)st trading day. (3). The process for any trading day is the same as the process for any other trading day except that the movement range is changed.

2.2. Pricing Options with Underlying Assets Imposed with Price Limits and Market Illiquidity To price market liquidity into derivatives, we have to modify the dynamic process described in Eq. (1). Furthermore, we assume ri 40; and hence the boundary shown in Eq. (1) does not instantaneously reﬂect this. We employ the deﬁnition of market liquidity of an underlying asset, proposed by Krakovsky (1999), as the asset notional (total amount of stocks or bonds) that has to be traded in the market to drive the asset price by one point. We can express it as follows: @N @S where N is the notional traded to the market.5 To derive a Leland type result, we have to ﬁnd a hedging strategy that makes the hedging error tend to zero as Dt ! 0: To handle the effect of market liquidity and the local times as Dt ! 0; we rewrite the dynamic process of the underlying asset price given in Eq. (1) as follows: L¼

dS d1 ¼ mI ða;bÞ ðSÞ dt þ sI ða;bÞ ðSÞ dBt þ I fag ðSÞ dt S r1 d2 1 dN I fbg ðSÞdt þ LS r2

ð2Þ

Using Taylor series expansion, dN can be expressed as dN ﬃ

@N @N 1 @2 N @N dS þ dt þ 2 ðdSÞ2 ¼ OðdtÞ þ dS @S @t 2@ S @S

(3)

where O(dt) is a collection of terms of order dt consisting of drift terms and Ito terms. In a discretized format (for a time period Dt), dN can be denoted as: DN ¼ OðDtÞ þ

@N DS @S

(4)

Pricing Options with Price Limits and Market Illiquidity

191

Over a small interval Dt, the stock process (2) then satisﬁes the ﬂowing discrete-time equation: DS d1 ¼ mI ða;bÞ ðSÞDt þ sI ða;bÞ ðSÞFðDtÞ1=2 þ I fag ðSÞDt S r1 d2 1 @N DS þ OðDtÞ I fbg ðSÞDt þ L @S S r2

ð5Þ

Here, F is a normally distributed random variable with mean zero and variance one. Eq. (5) can be changed as follows: DS 1 @N DS ¼ sI ða;bÞ ðSÞFðDtÞ1=2 þ þ OðDtÞ S L @S S

(6)

Hence, we have sI ðSÞ DS ða;bÞ FðDtÞ1=2 þ OðDtÞ ¼ (7) S 1 1=L @N=@S 2 The Ito term DS=S that we need in Eq. (7) can be directly obtained from 2 s2 I ða;bÞ ðSÞ DS 2 ¼ (8) 2 F Dt S 1 1=L @N=@S Let f be the ‘value’ of the contingent claim in our setting. In order to derive a valuation formula, we construct a hedging portfolio, P, which consists of N ¼ @f =@S shares of stocks and B ¼ f ð@f =@SÞS dollars of a risk-free security over the interval Dt. Over the interval Dt, the change in the value of portfolio P is DP ¼ NDS þ BrDt þ OðDt2 Þ DS þ ðf f S SÞrDt þ OðDt2 Þ ¼ f SS S

ð9Þ

where the term OðDt2 Þ comes from the continuous compounding of interest. The change in the value of the contingent claim f is Df ¼ f S S

2 DS 1 þ f SS S 2 DS=S þ f t Dt þ OðDt3=2 Þ S 2

(10)

Note that the expression OðDt3=2 Þ is written as in the equation for DS=S using the same argument together with the fact that the price movement is bounded. The hedging error DH over the interval Dt is DH ¼ DP Df kðS þ DSÞDN (11)

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CHUANG-CHANG CHANG ET AL.

where k represents the rate of transaction cost which is proportional to the value of assets traded. We can also assume that k vanishes sufﬁciently fast as Dt becomes zero. Precisely, we assume k is OðDtÞ: Applying Taylor’s theorem for a small DS and Dt, we have kðS þ DSÞDN ¼ kjðS þ DSÞðf S ðS þ DS; t þ DtÞ f S ðS; tÞÞj ¼ kjðS þ DSÞf SS ðS; tÞDSj þ OðDt3=2 Þ DS þ OðDt3=2 Þ ¼ kf SS S2 S

ð12Þ

Therefore, 2 1 2 DS DH ¼ ðf f s SÞrDt f SS S 2 S DS 3=2 þ O Dt f t Dt K f SS S2 S

ð13Þ

Substituting the terms of DS=S and ðDS=SÞ2 given in Eqs. (7) and (8) into Eq. (13), we have s2 I ða;bÞ F2 Dt 1 DH ¼ ðf f s SÞrDt f ss S 2 2 ð1 ð1=LÞ@N=@SÞ2 1=2 sI FðDtÞ ða;bÞ f t Dt kf ss S2 þ OðDtÞ ð1 ð1=LÞ@N=@SÞ

ð14Þ

We can observe that the terms which represent the boundary conditions become OðDt2 Þ due to the fact that k ¼ OðDtÞ: Taking the expectation for DH, we have EðDHÞ ¼

s2 I ða;bÞ ðSÞ 1 ðf f s SÞr f ss S 2 ft 2 ð1 ð1=LÞ@N=@SÞ2 ! rﬃﬃﬃ! sI ða;bÞ ðSÞ 2 k 2 f S Dt þ OðDtÞ p ðDtÞ1=2 SS ð1 ð1=LÞ@N=@SÞ

ð15Þ

When we take Dt ! 0; the last term in the above equation vanishes as k ¼ OðDtÞ: We now have EðDHÞ ¼ OðDtÞ

(16)

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193

Since EðDH 2 =Dt2 ÞoC for some constant C and the law of large numbers, we can demonstrate that TDt X

DH t ! 0; a:s:

(17)

t¼0

where DHt is the hedging error over ½t; t þ Dt and T is the time to maturity of the option. Therefore, the hedging error over the period [0,T] vanishes almost surely as Dt ! 0: We then have N ¼ ð@f =@SÞ and let f satisfy the following equation s2 I ða;bÞ ðSÞ 1 ðf f S SÞr f SS S 2 2 f t ¼ 0 2 1 1=L @2 f =@S2

(18)

Following the argument of Wilmott, Dewynne, and Howison (1993), we can conclude that the expectation of the inﬁnitesimal hedging error becomes zero. The above equation can be rewritten as follows: 8 @f 1 s2 S2 @2 f @f > > ðS; tÞ þ rS ðS; tÞ rf ðS; tÞ ¼ 0 > ðS; tÞ þ 2 2 2 > > @t 2 @S ð1 ð1=LÞ@ f =@S Þ @S > > > > < f ðS; TÞ ¼ Y ðSÞ @f @f > ða; tÞ þ ra ða; tÞ rf ða; tÞ ¼ 0 > > > @t @S > > > @f @f > > : ðb; tÞ þ rb ðb; tÞ rf ðb; tÞ ¼ 0 @t @S (19) We can justify that the solution to Eq. (19) is the value of the contingent claim.6 We should emphasize that our pricing PDE reduces to the Black and Scholes pricing PDE when the price limit is removed and the trading volume is large. Additionally our pricing PDE also reduces to the Krakovsky model (with price limits) or the Ban, Choi, and Ku model (without market illiquidity).

2.3. Pricing Options with Underlying Assets Imposed by Price Limits and the Option Itself shows Market Illiquidity In the previous sub-section, we explained the price PDE with speciﬁc boundary conditions for pricing options based on the underlying assets having properties of price limits and market illiquidity. This sub-section

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considers another case in which option valuations are under the constraints of the underlying assets with price limits and the option itself with market illiquidity. These options are traded in many emerging derivative markets, such as Taiwan’s covered warrant market. Moreover, recent studies have showed that the liquidity of options appears to affect the price of options. In particular, Bollen and Whalley (2003) demonstrate that net buying pressure effects account for the higher implied volatility of out-of-money index put options. We also assume that a stock price in a single day is represented in Eq. (1). We have to ﬁnd a hedging strategy that makes the hedging error tend to zero as Dt ! 0: To handle the local times as Dt ! 0; we write the stock price process as follows. dS d1 d2 ¼ mI ða;bÞ ðSÞ dt þ sI ða;bÞ ðSÞ dBt þ I fag ðSÞ dt I fbg ðSÞ dt S r1 r2

(20)

Over a small interval, this above process satisﬁes the following discrete equation: DS d1 ¼ mI ða;bÞ ðSÞDt þ sI ða;bÞ ðSÞFðDtÞ1=2 þ I fag ðSÞDt S r1 d2 I fbg ðSÞDt þ OðDt3=2 Þ r2

ð21Þ

and

DS S

2

¼ sI ða;bÞ ðSÞF2 Dt

(22)

where F is a normally distributed random variable with mean zero and variance one. The market illiquidity of an option has the same deﬁnition of the underlying asset’s illiquidity as shown in Section 2.2. Suppose that f is the price of a call option or other derivative contingent on S; then f must be some function of S, t, and l. Applying Ito’s lemma obtains df ¼

@f 1 @2 f @f 1 dS þ dt þ dn ðdSÞ2 þ 2 @S 2 @S @t l

The discrete-time version of Eq. (23) is as follows: 2 DS 1 1 2 DS Df ¼ f S S þ f SS S þ f t Dt þ Dn þ O Dt3=2 S 2 S l

(23)

(24)

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195

Like the case with delta hedging in the Black–Scholes (B–S) framework, let P be a portfolio consisting of n ¼ ð@S=@f Þ derivatives and B ¼ S ð@S=@f Þf dollars of a risk-free security over the interval Dt. Over the interval Dt, the change in the value of portfolio P is DP ¼ S f Df þ BrDt þ OðDt2 Þ ! 2 DS 1 1 2 DS þ f ss S þ f t Dt þ Dn ¼ Sf f s S S 2 S l þ ðS Sf f ÞrDt þ OðDt3=2 Þ

ð25Þ

and DS ¼ S

DS S

The hedging error DH over the interval Dt is DH ¼ DP DS kðf þ Df ÞDS f

(26)

where k represents the rate of transaction cost which is proportional to the value of options traded. Here, we assume that k vanishes sufﬁciently fast as Dt becomes zero. Precisely, we assume that k is OðDtÞ: Applying Taylor’s theorem for a small DS and Dt, we have kðf þ Df ÞDSf ¼ kjðf þ Df ÞðS f ðf þ Df ; t þ DtÞ S f ðf ; tÞÞj ¼ kjðf þ Df ÞS ff Df j þ OðDt3=2 Þ ¼ k S ff f Df þ OðDt3=2 Þ

ð27Þ

We next have 2 1 DS þ Sf f t Dt k Sff f Df þ OðDt3=2 Þ DH ¼ ðS S f f ÞrDt þ Sf f SS S 2 2 S 1 ¼ ðS S f f ÞrDt þ Sf f SS S 2 ðs2 I ða;bÞ F2 DtÞ þ Sf f t Dt 2 1 þ S f Dn kjS CC f ðf S SsI ða;bÞ FDt1=2 l 1 1 þ f SS S 2 s2 I ða;bÞ F2 Dt þ DnÞj þ OðDt3=2 Þ ð28Þ 2 l Observe that the terms which represent the boundary conditions become OðDt2 Þ due to the fact that k ¼ OðDtÞ: Therefore, taking an expectation for

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DH, we have 2

3 1 ðS Sf f Þr þ S f f ss S2 s2 I ða;bÞ ðSÞ þ S f f t 7 6 2 7 6 rﬃﬃﬃ 6 1 Dn 2 1=2 7 7 6 K S ff f ðf s SsI ða;bÞ þS f Dt 7Dt þ O Dt3=2 EðDHÞ ¼ 6 (29) 7 6 l Dt p 7 6 7 6 1 Dn 5 4 1 þ f ss S 2 s2 I ða;bÞ þ Þ 2 l Dt

Finally, taking Dt ! 0; the last term in the above equation vanishes as k ¼ OðDtÞ: Hence, we have EðDHÞ ¼ OðDt3=2 Þ

(30)

Since EðDH 2 =Dt3 ÞoC for some constant C, the law of large numbers, referred to in Feller (1971), implies TDt X

DH t ! 0; a:s.

(31)

t¼0

where DHt is the hedging error over ½t; t þ Dt and T is the time to maturity of the option. Therefore, the hedging error over the period [0, T] vanishes almost surely as Dt ! 0: We then let N ¼ ð@S=@f Þ and requires f to satisfy 1 1 Dn ¼0 ðS Sf f Þr þ S f f ss S2 s2 I ða;bÞ ðSÞ þ S f f t þ S f 2 l Dt

(32)

or 1 1 ðf s S f Þr þ f ss S2 s2 I ða;bÞ ðSÞ þ f t Sft ¼ 0 (33) 2 l Following the argument of Wilmott et al. (1993) and Ban et al. (2000), we can conclude that the expectation of the inﬁnitesimal hedging error becomes zero. The above equation can be rewritten as 8 @f 1 2 2 @2 f @f 1 @2 S > > rf ðS; tÞ ¼ 0 ðS; tÞ þ rS ðS; tÞ > ðS; tÞ þ s S 2 > @t 2 @S l @f @t > @S > > > > > < f ðS; TÞ ¼ Y ðSÞ @f @f 1 @2 S (34) ða; tÞ þ ra ða; tÞ rf ða; tÞ ¼ 0 > > > @t @S l @f @t > > > > > @f @f 1 @2 S > > rf ðb; tÞ ¼ 0 : ðb; tÞ þ rb ðb; tÞ @t @S l @f @t

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197

Eq. (34) provides the solution of options with underlying assets imposed by price limits and the option itself encounters market illiquidity.

3. NUMERICAL IMPLEMENTATION 3.1. Multiday Valuation Framework We use the multiday framework of Ban et al. (2000) to compute the value of the contingent claim at the end of the nth trading day. Suppose that the contingent claim Y(y) at the expiry date t ¼ NT is given. The valuation process can be hence divided into two steps. First, the value f(S, nT) of the contingent claim is computed at the end of each trading day. Second, we compute f(S, t) for t 2 ½0; T: Given the above description, the process can be stated as follows: Step 1: Suppose f(z, nT) is given for all z 2 ½x na; x þ na: Compute f(y, (n1)T) for each y 2 ½x ðn 1Þa; x þ ðn 1Þa; consider the movement range [ya, y+a] of the single day (nth day), and restrict f(z, nT) to z 2 ½x na; x þ na (Fig. 1). Using this we can compute f(y, NT), f(y, (N1)T),y, f(y, T). Step 2: By Step 1, we have found f(y, T) for y 2 ½x a; x þ a; and then we apply an intraday valuation to compute f(y, t) (see Fig. 2).

Fig. 1.

Possible Movement Range of Logs.

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Fig. 2.

Valuation of Contingent Claim at y.

3.2. Numerical Implementations for the Price Limit Model This section shows how to use the explicit ﬁnite difference method to implement our valuation framework. The pricing equation for options with underlying assets that have price limits can be restated as follows: 8 @f 1 2 2 @2 f @f > > > ðS; tÞ þ s S ðS; tÞ þ rS ðS; tÞ rf ðS; tÞ ¼ 0 > @t 2 > 2 @S @S > > > > < f ðS; TÞ ¼ Y ðSÞ (35) @f @f > ða; tÞ þ ra ða; tÞ rf ða; tÞ ¼ 0 > > @t @S > > > > @f @f > > : ðb; tÞ þ rb ðb; tÞ rf ðb; tÞ ¼ 0 @t @S To implement the ﬁnite difference methods more efﬁciently, we treat ln S rather than S as the underlying variable. After deﬁning Z ¼ ln S; Eq. (35)

Pricing Options with Price Limits and Market Illiquidity

can be rewritten as 8 @f 1 @2 f s2 @f > > > ðZ; tÞ þ s2 2 ðZ; tÞ þ ðr Þ ðZ; tÞ rf ðZ; tÞ ¼ 0 > > @t 2 @Z 2 @Z > > > > < f ðZ; TÞ ¼ Y ðZÞ @f @f > > @t ða; tÞ þ r @Z ða; tÞ rf ða; tÞ ¼ 0 > > > > > @f @f > > ðb; tÞ rf ðb; tÞ ¼ 0 : ðb; tÞ þ r @t @Z

199

(36)

For an interior point (i, j ) on the grid, we use a central difference as the approximation for the term of @f =@S: It can be expressed as follows: f iþ1; jþ1 f iþ1; j1 @f ¼ (37) @Z 2DZ For the term @f =@t; we use a forward difference approximation so that the value at time iDt is related to the value at time (i+1)Dt. Hence, we have f iþ1; j f i; j @f ¼ (38) @t Dt The term of @2 f =@Z2 is the second derivative of the option with respect to ln S. The approximation for this term is achieved as follows: f iþ1; jþ1 f iþ1; j1 2f iþ1; j @2 f ¼ 2 DZ2 @Z Substituting Eqs. (37)–(39) into Eq. (11), we have f iþ1; j f i; j s2 f iþ1; jþ1 f iþ1; j1 þ ðr Þ Dt 2 2DZ 1 2 f iþ1; jþ1 þ f iþ1; j1 2f iþ1; j þ s ¼ rf i; j 2 DZ 2

(39)

ð40Þ

for j ¼ 1,2,y,M1 and i ¼ 0,1,y,N1. Rearranging all of the terms, we obtain 3 2 1 s2 s2 6 2DZ r 2 þ 2DZ 2 f iþ1; jþ1 7 7 6 7 6 7 6 1 s2 Dt 7 6 þ f iþ1; j f i; j ¼ 2 7 6 Dt DZ rDt þ 1 6 7 7 6 2 2 1 s s 5 4 r þ f þ iþ1; j1 2 2DZ 2 2DZ

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The upper boundary condition becomes

Dt 1 r r þ f iþ1; j1 f i; j ¼ f iþ1; j 1 þ rDt Dt DZ DZ for j ¼ M and i ¼ 0,1,y,N1. Furthermore, the lower boundary condition becomes

Dt 1 r r f f i; j ¼ þ f 1 þ rDt Dt DZ iþ1; j DZ iþ1; jþ1 for j ¼ 0 and i ¼ 0,1,y,N1.

3.3. Numerical Implementations for Pricing Options Based on Underlying Assets with Price Limits and Market Illiquidity The pricing equation for options based on underlying assets with price limits and market illiquidity is shown in Eq. (19). As mentioned earlier, to implement the ﬁnite difference methods more efﬁciently, we treat the variable as lnS rather than S. After deﬁning Z ¼ ln S; Eq. (19) becomes 8 @f @f 1 s2 @f > > ðZ; tÞ þ r ðZ; tÞ ðZ; tÞ > > 2 2 @Z > @t @Z 2 > 1 @f @ f > > 1þ > > > Lðexp ZÞ2 @Z @Z 2 > > > > > s2 @2 f > 1 > þ > 2 @Z2 ðZ; tÞ rf ðZ; tÞ ¼ 0 > < 2 1 @f @2 f 1þ (41) > Lðexp ZÞ2 @Z @Z 2 > > > > f ðZ; TÞ ¼ Y ðZÞ > > > > > @f @f > > ða; tÞ þ r ða; tÞ rf ða; tÞ ¼ 0 > > @t @Z > > > > @f @f > > : ðb; tÞ þ r ðb; tÞ rf ðb; tÞ ¼ 0 @t @Z Substituting Eqs. (37), (38), and (39) into Eq. (40), we have

rDt þ 1 1 s2 1 s2 f i; j ¼ A þ ðr Þ n Bþ n C Dt 2D 2D

(42)

Pricing Options with Price Limits and Market Illiquidity

201

where f iþ1;j Dt f iþ1;jþ1 f iþ1;j1 B¼ 2DZ f iþ1;jþ1 þ f iþ1;j1 2f iþ1;j C¼ DZ 2

2 1 D¼ 1þ ðB CÞ LðexpðZ a þ j DZ Þ2 A¼

for j ¼ 1,2,y,M1 and i ¼ 0,1,y,N1. The upper boundary condition becomes

Dt 1 r r þ f f i; j ¼ f 1 þ rDt Dt DZ iþ1; j DZ iþ1; j1 for j ¼ M and i ¼ 0,1,y,N1. Additionally, the lower boundary condition becomes

Dt 1 r r f f i; j ¼ þ f 1 þ rDt Dt DZ iþ1; j DZ iþ1; jþ1 for j ¼ 0 and i ¼ 0,1,y,N1. Fig. 3 shows the basic structure for pricing options using the explicit method. Eqs. (40) and (42) only holds for j ¼ 1,2,y,M1, i.e. for an interior point, since f i;1 and f i;Mþ1 are not deﬁned. Thus, there are M1 equations for M+1 unknowns, the fi, j. The remaining two equations comes from the two boundary conditions for j ¼ 0 and M. The two endpoints are treated separately.If we know fi, j for all j, then Eqs. (40) and (42) can compute the value of fi+1, j. Since we know f 0; j ; the payoff function, we can easily calculate f 1; j ; which is the option value at one time step before expiry. Using these values, we can step-by-step go back down the grid as far as we want. This completes the procedures of calculation using the ﬁnite difference methods.

3.4. Numerical Implementation of the Adjusted B–S Model with Stock Price Limits and Option Illiquidity To price options with an underlying asset that has price limits and the option itself encounters market illiquidity, we use the implicit ﬁnite difference method since it no longer suffers from the restriction on the time-steps.

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Option price

3 2 2 1 1 0

20%

30%

40% volatility

b-s price

price limit=15%

price limit=5%

price limit=2%

50%

60%

price limit=7%

Fig. 3. The Prices of a European Call Option under Different Price Limits. Note: The Continuously Compounded Risk-Free Interest Rate is r ¼ 0:02; the Stock Price is 50, the Exercise Price is 50, and the Time to Expiration is 0.05952 (Half-Month), respectively.

Hence, we can choose a small asset step and a large time-step while the implicit ﬁnite difference method still can give a stable result. The calculating procedures are similar to those of the explicit ﬁnite difference method. The only difference is its delta and gamma at the time-step i. Fig. 4 shows the basic structure for pricing options using the implicit ﬁnite difference method. The pricing equation for options with underlying assets that have price limits and when the option itself encounters market illiquidity is given in Eq. (34). Like the previous section, we treat the state variable as lnS rather than S due to computational efﬁciency. We deﬁne Z ¼ ln S; and hence Eq. (19) becomes 8 > @f s2 @f 1 2 @2 f 1 exp Z @Z exp Z @2 f > > þ r þ s ¼ rf > > @t D @t 2 @Z 2 @Z 2 l > D2 @Z@t > > > > > < f ðexp Z; TÞ ¼ Y ðexp ZÞ @f @f 1 exp Z @Z exp Z @2 f ðexp a; tÞ þ r ðexp a; tÞ rf ¼ 0 > > > @t @Z l D @t D2 @Z@t > > > > 2 > > > @f ðexp b; tÞ þ r @f ðexp b; tÞ 1 exp Z @Z exp Z @ f rf ¼ 0 > : @t @Z l D @t D2 @Z@t (43)

Pricing Options with Price Limits and Market Illiquidity

203

10%

Price limit effect

0% -10%

20%

30%

40%

50%

60%

-20% -30% -40% -50% volatility price limit=2%

price limit=5%

price limit=7%

price limit=15%

Fig. 4. Price Limit Effect under Different Percentage of Price Limits. Note: The Continuously Compounded Interest Rate is r ¼ 0:02; the Stock Price is 50, the Exercise Price is 50, and the Time to Expiration is 0.05952 (Half-Month). Furthermore, the Price Limit Effect is Deﬁned as Follows: Price Limit Effect ¼ (Option Price with Price Limits – B–S price)/B–S price.

where D ¼ @f =@Z: For an interior point (i, j) on the grid, we use a central difference as the approximation to the term of @f =@S f i; jþ1 f i; j1 @f ¼ @Z 2DZ

(44)

The term of @2 f =@Z2 is the second derivative of the option with respect to the ln S. We use the following equation to approximate it. f i; jþ1 þ f i; j1 2f i; j @2 f ¼ 2 @Z DZ2

(45)

Substituting Eqs. (47), (53), and (54) into Eq. (52), we obtain ai; j f iþ1; j1 þ f iþ1; j þ bi; j f iþ1; jþ1 þ ci; j DZ ¼ d i; j f i; j1 þ ei; j f i; j þ hi; j f i; jþ1

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where exp Z 2lDZD2iþ1; j exp Z G i; j ¼ lD ai; j ¼ EE i; j EE i; j ¼

bi; j ¼ EE i; j ðr s2 =2ÞDt s2 Dt EE i; j 2DZ 2DZ 2 s2 Dt ei; j ¼ 1 þ rDt þ DZ2 2 ðr s =2ÞDt s2 Dt hi; j ¼ þ EE i; j 2DZ 2DZ 2 d i; j ¼

for j ¼ 1,2,y,M1 and i ¼ 0,1,y,N1. The terms of EEi,j and Gi,j represent speciﬁc variables belonging to this model, respectively. We can approximate the delta from our grid as follows: Di; j ﬃ Diþ1; j ¼

f iþ1; jþ1 f iþ1; j1 2DZ

(46)

The upper boundary condition then becomes 2EE i; j f iþ1; j1 þ ð1 þ 2EE i; j Þf iþ1; j Gi; j DZ rDt rDt 2EE i; j f i; j1 þ 1 þ rDt þ 2EE i; j f i; j ¼ DZ DZ

ð47Þ

for j ¼ 1,2,y,M1 and i ¼ 0,1,y,N1. Additionally, the lower boundary condition becomes ð1 2EE i; j Þf iþ1; j þ 2EE i; j f iþ1; jþ1 Gi; j DZ rDt rDt 2EE i; j f i; j þ þ 2EE i; j f i; jþ1 ¼ 1 þ rDt þ DZ DZ for j ¼ 1,2,y,M1 and i ¼ 0,1,y,N1.

ð48Þ

Pricing Options with Price Limits and Market Illiquidity

205

4. NUMERICAL RESULTS 4.1. The Magnitude of the Price Limit Effect on Option Values We ﬁrst investigate the effects of price limits imposed on the underlying an asset on option values. Our theoretical model of option pricing in the presence of price limits can be directly applied to the options on futures in the U.S., as futures contracts in the U.S. are subject to price limit rules. Futures markets in the U.S. have a daily 20% price limit, while in some markets, such as the Taiwan Stock Exchange, the daily price limit range is lower.7 Taiwan once set the daily price limit to 3.5%, but at present it is 7%. Because of the large difference in the range of price limits set by exchanges, theoretical values of options under daily price limit ranges of 2%, 5%, 7%, and 10% are analyzed in our numerical study and are reported in Tables 1 and 2. In each table the options price is calculated by setting the parameter value of volatility (standard deviation) of the underlying asset equal to 20%–60% by a step of 10%. To gauge the potential price limit effect on the options price, the price limit effect is calculated as the theoretical price minus the B–S price and then divided by the B–S price. The row labeled ‘‘price limit effect’’ represents the potential overpricing of the B–S model. Table 1 reports the theoretical price and compares it with the B–S price when the underlying asset is subject to a 2% price limit, while the cases of 5%, 7%, and 10% price limits are reported in Table 2. From Table 1, it is clear that the numbers in the rows labeled ‘‘price limit effect’’ are all negative, indicating that the B–S model over-prices options in markets where price limits are imposed on the underlying stocks. Furthermore, the effect of price limits increases as the volatility of the underlying stock increases. For the case of a 2% daily price limit, the effect is very large (on average 31% for in-the-money options, 46% for at-the-money options, and 62% for out-of-the-money options), whereas the price limit effect is relatively small when the daily price limit is 10%. Comparing across Tables 1 and 2, it shows that the price limit effect on the option values does not increase as the time to expiration increases. This is particularly true when time to maturity is larger than half a year; the price limit effect on the option price remains very stable when the time to maturity is large. The results are also important for the derivative warrants, since unlike standard exchangetraded options, they tend to have a longer maturity. Fig. 3 shows that the difference between the B–S price and price with the price limit becomes large when the volatility increases from 20% to 60%.

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Table 1. The Price Limit Effect on Option Values when the Underlying Asset is Subject to a 2% Price Limit. Volatility/Time to Expiration

5 Days

10 Days

15 Days

30 Days

126 Days

Panel A: In-the-money (S ¼ 50; K ¼ 48) 20% Price limit effect 0.40% 30% Price limit effect 3.12% 40% Price limit effect 8.31% 50% Price limit effect 14.67% 60% Price limit effect 21.25%

0.75% 1.00% 1.48% 2.23% 5.01% 6.14% 7.88% 10.27% 12.32% 14.24% 17.16% 20.85% 20.82% 22.94% 26.80% 31.21% 28.80% 30.89% 35.50% 40.11%

Panel B: At-the-money (S ¼ 50; K ¼ 50) 20% Price limit effect 2.78% 30% Price limit effect 12.98% 40% Price limit effect 24.71% 50% Price limit effect 35.43% 60% Price limit effect 44.67%

3.10% 13.52% 25.98% 38.13% 47.99%

3.19% 13.65% 25.86% 37.07% 46.20%

3.25% 13.71% 25.88% 37.31% 46.86%

3.57% 13.68% 25.38% 36.49% 45.72%

Panel C: Out-of-the-money (S ¼ 50; 20% Price limit effect 30% Price limit effect 40% Price limit effect 50% Price limit effect 60% Price limit effect

10.17% 27.90% 44.42% 58.00% 67.61%

8.39% 24.84% 40.52% 52.93% 62.01%

6.56% 21.17% 35.96% 48.44% 58.18%

4.64% 16.69% 30.02% 41.82% 51.23%

K ¼ 52) 17.27% 36.14% 51.50% 62.88% 71.34%

Note: We set S ¼ 50; K ¼ 48; 50and52; r ¼ 0:02; volatility ranges from 20% to 60%; and the lengths of expiration are 0.0198 (ﬁve days), 0.03967 (ten days), 0.05952 (half-month), 0.119 (one month), and 0.5 (six months). The price limit effect is deﬁned as follows: Price limit effect ¼ option price with price limit B S price/B S price.

Fig. 4 presents the percentage price differences between the model under a price limit and the B–S model. The results show that the price limit effect is mostly signiﬁcant when the price limit is 2%, while the price effect vanishes as the price limit is 15%. The volatility is a measure of how uncertain we are about future stock price movement. Under the circumstance of a stringent daily price limit, the probability of the price hitting the upper or lower limit in the middle of the trading day increases as the volatility increases, which makes the price limit effect increase. Since the daily price limit range is 20% in the U.S. futures markets, the pricing error of the B–S price is relatively small. Nevertheless, it remains important to note that there can be a signiﬁcant price limit effect on options prices under extreme volatile market condition. The daily price range is 7% in the Taiwan Stock Exchange. In this case, the price limit signiﬁcantly affects the option values when the volatility of

Pricing Options with Price Limits and Market Illiquidity

207

Table 2. The Price Limit Effect on Option Values when the Underlying Asset is Subject to 5%, 7%, and 10% Price Limits. Volatility/Time to Expiration

5 Days

10 Days

15 Days

30 Days

126 Days

Panel A: 5% Daily price movement limit 20% Price limit effect 0.04% 30% Price limit effect 0.17% 40% Price limit effect 0.55% 50% Price limit effect 2.81% 60% Price limit effect 6.41% Panel B: 7% Daily price movement limit 20% Price limit effect 0.10% 30% Price limit effect 0.03% 40% Price limit effect 0.16% 50% Price limit effect 0.38% 60% Price limit effect 1.22%

0.02% 0.10% 0.70% 3.16% 6.87%

0.01% 0.08% 0.74% 3.26% 7.01%

0.01% 0.06% 0.78% 3.35% 7.13%

0.02% 0.16% 1.16% 3.50% 6.99%

0.05% 0.02% 0.07% 0.44% 1.43%

0.03% 0.01% 0.04% 0.45% 1.50%

0.02% 0.01% 0.01% 0.47% 1.56%

0.03% 0.02% 0.11% 0.58% 1.70%

Panel C: 10% Daily price movement limit 20% Price limit effect 0.01% 30% Price limit effect 0.02% 40% Price limit effect 0.02% 50% Price limit effect 0.02% 60% Price limit effect 0.05%

0.02% 0.02% 0.02% 0.01% 0.08%

0.02% 0.02% 0.02% 0.01% 0.09%

0.02% 0.02% 0.02% 0.02% 0.10%

0.02% 0.02% 0.02% 0.02% 0.11%

Note: We set S ¼ 50; K ¼ 50; r ¼ 0:02; volatility ranges from 20% to 60%; and the lengths of expiration are 0.0198 (ﬁve days), 0.03967 (10 days), 0.05952 (half-month), 0.119 (one month), and 0.5 (six months). The price limit effect is deﬁned as follows: Price limit effect ¼ option price with price limit B S price/B S price.

the underlying stock price is high (say over 50%). We should emphasize that many stocks traded in the Taiwan Stock Exchange have volatility higher than 50%. Therefore, the price limit effect on option values is not negligible and in this case, the potential model errors of the B–S model remain large. We also investigate how the price limit affects the delta of options. Table 3 shows that for out-of-the-money and at-the-money options, the deltas under price limit effects on underlying assets are smaller than those of the Black and Scholes model. However, the deltas for in-the-money options with the underlying asset imposed by a price limit are larger than those of the B–S model. These results are useful for option issuers when the underling asset is imposed by a price limit. Particularly, the results are informative when conducting dynamic hedging.

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Table 3. The Price Limit Effect on the Option Delta when the Underlying Asset is Subject to a 2% Price Limit. Volatility

5 Days

10 Days 15 Days 30 Days 126 Days

Panel A: In-the-money options (S ¼ 50; K ¼ 48) 20% Price limit effect 0.16% 30% Price limit effect 3.15% 40% Price limit effect 7.52% 50% Price limit effect 12.47% 60% Price limit effect 17.04%

0.50% 3.60% 7.38% 10.96% 13.93%

0.66% 3.51% 6.69% 9.48% 11.79%

0.75% 2.99% 5.13% 6.89% 8.23%

0.57% 1.42% 1.64% 1.25% 0.45%

Panel B: At-the-money options (S ¼ 50; K ¼ 50) 20% Price limit effect 0.07% 30% Price limit effect 0.16% 40% Price limit effect 0.39% 50% Price limit effect 0.74% 60% Price limit effect 1.15%

0.06% 0.18% 0.55% 1.06% 1.71%

0.05% 0.22% 0.66% 1.32% 2.06%

0.03% 0.28% 0.92% 1.79% 2.78%

0.00% 0.52% 1.72% 3.37% 5.23%

2.83% 11.21% 17.81% 22.44% 25.96%

2.66% 9.04% 14.51% 19.51% 24.07%

2.03% 6.23% 10.26% 13.90% 16.74%

0.88% 3.07% 5.79% 8.73% 11.57%

Panel C: Out-of-the-money options (S ¼ 50; K ¼ 52) 20% Price limit effect 2.16% 30% Price limit effect 15.70% 40% Price limit effect 25.89% 50% Price limit effect 35.21% 60% Price limit effect 41.91%

Note: We set S ¼ 50; K ¼ 48; 50; and52; r ¼ 0:02; volatility ranges from 20% to 60%; and the lengths of expiration are 0.0198 (ﬁve days), 0.03967 (10 days), 0.05952 (half-month), 0.119 (one month), 0.5 (six months). The price limit effect is deﬁned as follows: Price limit effect ¼ option delta with price limit B S delta price/B S delta price.

4.2. The Effect of the Underlying Asset with Market Illiquidity Another interesting issue is how the underlying asset with market illiquidity affects the option value. To investigate the convergence properties of the ﬁnite difference method, we calculate the numerical values of options for various time steps. A numerical study is presented for the case of an at-themoney call when the stock price and the exercise price are both equal to 50. The time to expiration is 0.0198 (ﬁve days), the risk-free rate (r) is 2%, and the volatility of the underlying asset is 50%. The liquidity measure is set to 50,000, which corresponds to the case where the underlying stock has high liquidity. Fig. 5 demonstrates that convergence is achieved as the number of time steps exceeds 250. In other words, the option price calculated by our model is similar to that of the B–S model when the liquidity of the underlying asset is large. Furthermore, the B–S option pricing model is a

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2.02

Option price

2 1.98 1.96 1.94 1.92 1.9

50

100

150

200

250 300 350 Number of asset steps

liquidity=50000

Fig. 5.

400

450

500

B-S price

The Convergence of the Liquidity-Adjusted B–S Model.

special case of our model. The reasonable range of the liquidity number through our examination is allocated between 10 and 100,000. We ﬁnd that the option price increases as the liquidity of the stock decreases from Tables 4 and 5. Due to the non-linear characteristics of our pricing equation, hedging a large position affects the market prices more deeply than hedging a small position. We can see thatmarket liquidity affects the pricing through the gamma of the position @2 f @S2 as shown in Eq. (19). For example, a short gamma position has a higher effective volatility and a higher option price. This phenomenon occurs because when the market goes up (down), one has to increase (decrease) the hedging positions to stay delta-neutral, which will noticeably increase market volatility if the position is sizeable and the market is relatively illiquid. For a long gamma position, the same reason is valid, only in the reverse direction. If we consider the market to have price limits, then the effective volatility from a short gamma position or a long gamma position will decrease as the range of the price limit shortens (see Fig. 6).

4.3. The Effect of Option Illiquidity As mentioned earlier, it is very common for the derivatives that trade in emerging markets to have a market illiquidity problem. This subsection presents the numerical analysis of the effect of option illiquidity on option

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Table 4. Comparing the Adjusted B–S Model with Stock Price Limits and Stock Illiquidity with the Liquidity-Adjusted B–S Model (Maturity T ¼ 0:0198 years (ﬁve days)). The Size of Liquidity

100,000 10,000 1,000 100 50 40 30 20 10

B–S Price

1.41424 1.41424 1.41424 1.41424 1.41424 1.41424 1.41424 1.41424 1.41424

Model with Stock Illiquidity

Model with Price Limit and Stock Illiquidity

Option price

Price effect (%)

Option price

Price effect (%)

1.41238 1.4142 1.41263 1.4149 1.41743 1.41869 1.42078 1.42498 1.43758

0.1318 0.0031 0.1141 0.0464 0.2253 0.3144 0.4622 0.7592 1.6501

1.40977 1.40816 1.41005 1.41285 1.41596 1.41752 1.42011 1.42343 1.42543

0.3163 0.4302 0.2965 0.0985 0.1214 0.2317 0.4148 0.6496 0.7910

Note: A numerical analysis of an option price is conducted for the case where the stock price is S ¼ 50; the exercise price is K ¼ 50; the volatility of a stock price is 50%; the continuously compounded interest rate is r ¼ 0:02; the time to expiration is 0.0198 (ﬁve days), and the daily price movement is 7%. The price effect is deﬁned as follows: Price effect ¼ option price B S price/B S price.

values. We ﬁrst test how well our model converges. Fig. 7 demonstrates that price convergence is achieved as the number of asset steps exceeds 250. In other words, the option price calculated by our model, when considering the option itself has market illiquidity is very close to that of the B–S model when the liquidity of the option market is good. The results are presented for an option liquidity measure ranging from 1,000 to 100,000. Fig. 8 shows that the option price decreases as the liquidity of the option increases. The difference between the B–S price and the adjusted B–S price increases as the degree of liquidity decreases in an option market with imperfect liquidity. This is because a trader will not pay more to buy an option if he/she worries about the holding costs of the option when the market has a liquidity problem, which makes the option price lower than the B–S price. Therefore, if the options market is imperfectly liquid, then the trader sells the contingent claim to hedge the position in the underlying asset, which accelerates the downturn of the option price (as he/she sells) (see Fig. 8).

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Table 5. Comparing the Adjusted B–S Model with Stock Price Limits and Stock Illiquidity with Liquidity-Adjusted B–S Model (Maturity T ¼ 0.03967 years (10 days)). The Size of Liquidity

B–S Price

100,000 10,000 1,000 100 50 40 30 20 10

Model with Stock Illiquidity

Model with Price Limit and Stock Illiquidity

Option price

Price effect (%)

Option price

Price effect (%)

1.9939 1.99394 1.99431 1.99805 2.00219 2.00426 2.00769 2.01454 2.03433

0.5573 0.5553 0.5369 0.3503 0.1439 0.0406 0.1304 0.4721 1.4591

2.00503 2.00505 2.00527 2.00752 2.01002 2.01128 2.01322 2.01745 2.02969

0.0022 0.0012 0.0098 0.1220 0.2467 0.3095 0.4062 0.6172 1.2277

2.00507 2.00507 2.00507 2.00507 2.00507 2.00507 2.00507 2.00507 2.00507

Note: We set the stock price to be S ¼ 50; the exercise price is K ¼ 50; the volatility of the stock price is 50%; the continuously compounded interest rate is r ¼ 0:02; the time to expiration is 0.03967 (ﬁve days), and the daily price movement is 7%. The price effect is deﬁned as follows: Price effect ¼ option price B S price/B S price.

2.02

Option price

2.015 2.01 2.005 2 1.995 1.99 1.985 1.98

20

30

40

50

100

1000

10000

100000

The size of liquidity B-S price

price limit and stock liquidity

stock liquidity

Fig. 6. The Price of European Call Options under Different Models. Note: We Set the Continuously Compounded Interest Rate to be r ¼ 0:02; the Stock Price is 50, the Exercise Price is 50, the Time to Expiration is 0.0198 (Five Days), and the Volatility of the Underlying Asset is 50%.

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Option price

1.98 1.97 1.96 1.95 1.94 1.93 1.92 1.91

50

100

150 200 Number of asset steps B-S price

Fig. 7.

250

300

liquidity=100000

The Convergence of the Adjusted B–S Model with Option Illiquidity.

Fig. 8. The Prices of European Call Options under Different Models. Note: We Set the Continuously compounded Interest Rate (r) to be Equal to 0.02, While the Stock Price, the Exercise Price, and the Time to Expiration are Set to 50, 50, and 0.0198 (10 days), respectively.

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5. CONCLUSION This paper uses the vanishing transaction cost technique to derive an option pricing model that simultaneously considers the effects of price limits and market illiquidity. We obtain two generalized non-linear B–S pricing of PDEs for the cases when (1) the underlying assets encounter price limits and market illiquidity, or (2) the underlying assets are imposed on price limits and the option itself shows market illiquidity. We ﬁnd that the price difference between those of the B–S model and the adjusted B–S model increases as the volatility of the underlying asset increases. Additionally, the option value increases as the liquidity of the underlying asset decreases, whereas the option value decreases as the liquidity of the option itself decreases. In general, we ﬁnd that both price limits and market illiquidity signiﬁcantly affect the option values.

NOTES 1. See Harris (1998), Kim and Rhee (1997), and Ma, Rao, and Sears (1989) for an overview of the price limit literature. 2. Since the price limit mechanism restricts the possible price variation of a certain trading day, the extent that the price of options being in-the-money at expiration day might be reduced is due to the price limit effects. Consider the example of the call warrants on AU Optronics Corp. AUO is a world-leading manufacturer of large-size thin ﬁlm transistor liquid crystal display (TFT-LCD) panels. On February 19, 2004, the theoretical B–S options value of the AUO call warrant expiring on April 6 was 13.38 with an implied volatility of 70%, while the market price of it was 12.58. The under-pricing of options on high volatility stock might be due to the price limit effects. 3. For the case of the illiquidity in the underlying stocks, on October 4, 2000, the stock liquidity of Acer Co. sharply fell from an average level of 344 to a level of 2.77, yet while facing this illiquidity shock, the market price of the warrant stayed at 6.2, a nearly 2% higher than the B–S theoretical value. The liquidity is measured as 10–4 times (daily trading volume/price change). 4. For the proof, one can refer to Theorem 2 in Ban et al. (2000). 5. In an economy with a ﬁnite number of hedgers and speculators, Galy (2003) derives a theoretical model that values derivatives in the presence of illiquidity. In his model, the prices of derivatives are no longer independent of the size of the trade; illiquidity is crucial to the option price. However, Galy does not provide an explicit pricing equation for options pricing in the presence of illiquidity. Our approach has the advantage that it can be directly applied and conveniently implemented to investigate the quantitative impacts of illiquidity on option prices. 6. One can refer to Theorem 5 in Ban et al. (2000) for the proof.

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7. For index futures traded in CME, the absolute price limits are set on a quarterly basis and are based on percentages of 5%, 10%, 15%, and 20%. The maximum daily limit is thus 20%. Price limits are in effect for down markets only during regular trading hour (RTH) sessions. Electronic Trading Hours (ETH) trading and E-mini stock index products have both up and down price limits.

ACKNOWLEDGMENTS An earlier version of this paper was presented at the 2005 Annual Meeting of Taiwan Financial Engineering Association and National Central University. We are especially grateful to Pin-Hung Chow for helpful comments and discussions.

REFERENCES Ban, J., Choi, I.-H., & Ku, H. (2000). Valuation of European options in the market with daily price limit. Applied Mathematical Finance, 7, 61–74. Black, F., & Scholes, M. (1973). The pricing of option and corporate liabilities. Journal of Political Economy, 81(3), 637–659. Bollen, N. P. B., & Whaley, R. E. (2003). Does net buying pressure affect the shape of implied volatility functions? Journal of Finance, 58(3), 943–973. Galy, S. (2003). Illiquidity and the shape of implied volatility function. Working paper. Harris, L. (1998). Circuit breakers and program trading limits: What have we learned? In: R. E. Litan & A. M. Santomero (Eds), Brookings-Wharton papers on financial services (pp. 17–63). Washington, DC: Brooking Institutions Press. Kim, K. A., & Rhee, S. G. (1997). Price limit performance: Evidence from Tokyo stock exchange. Journal of Finance, 52, 885–901. Krakovsky, A. (1999). Pricing liquidity into derivatives. Risk, 6(2), 65–67. Leland, H. E. (1985). Option pricing and replication with transaction costs. Journal of Finance, 40, 1283–1301. Ma, C. K., Rao, R. P., & Sears, R. S. (1989). Limits moves and price resolution: The case of the treasury bond futures markets. Journal of Future Markets, 9, 321–335. Roll, R. (1989). Price volatility, international market links, and their implications for regulatory policies. Journal of Financial Service Research, 3, 211–246. Wilmott, P., Dewynne, J., & Howison, S. (1993). Option pricing. Oxford: Oxford Financial Press.

THE INCREASING INTEGRATION AND COMPETITION OF FINANCIAL INSTITUTIONS AND OF FINANCIAL REGULATION James A. Wilcox ABSTRACT Deregulation and other factors permit and encourage financial institutions to become more integrated, both within their own (financial) industries, such as banking and insurance, and across these industries. Financial regulators have responded with like integration. As financial institutions increasingly compete with firms from other industries and areas, financial regulators similarly compete more across borders. The resulting competition in financial regulation enhances innovation, choice, and efficiency. The advent of home-run regulation, which in general allows financial institutions to adhere only to the financial regulations of their home area and is spreading across the US and Europe, may allow numerous regulatory regimes within a given market.

Both the real and the ﬁnancial sides of the world economy became considerably more integrated and less regulated over the past three decades. Over the same period, the operations and structures of ﬁnancial institutions Research in Finance, Volume 22, 215–238 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22008-7

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and their regulation have changed greatly and rapidly. Even so, the actual evolutions and revolutions in the ﬁnancial sector have often not been able to match the forecasts for them.1 Though the extent and speed of change in the ﬁnancial sector may have often fallen short of consensus forecasts, nonetheless, many more ﬁnancial services have come to be supplied by individually more integrated ﬁnancial institutions. While it remains to be seen whether the oft-foretold era of the ﬁnancial supermarket has ﬁnally arrived, both ﬁnancial institutions and ﬁnancial regulation have become more integrated in recent years.2 As ﬁnancial (de) regulation has proceeded worldwide for the past three decades, ﬁnancial institutions, especially the larger ones, have expanded the ranges of the products and services they offer and the geographical areas over which they offer them. That deregulation has spurred increasing competition between banks and also between banks and nonbank ﬁnancial institutions. It has similarly sharpened competition between all ﬁnancial institutions across political borders. Just as ﬁnancial institutions seek, subject to their regulation, their optimal scales and scopes, so too do ﬁnancial regulators. As ﬁnancial institutions have become more (horizontally) integrated, in recent years so too have their regulators. The Financial Services Authority (FSA) in the UK now oversees the ﬁrms of several ﬁnancial industries. Other advanced countries have also integrated their various ﬁnancial regulators into single regulatory agencies. Though the US has not yet integrated them, its several ﬁnancial regulators each now regulate ﬁnancial institutions that have expanded the scopes of their operations. Thus, for example, the Federal Reserve System now inspects newly authorized, wide-ranging ﬁnancial holding companies. Similarly, the US Ofﬁce of the Comptroller of the Currency (OCC) regulates commercial banks and their subsidiaries that now face fewer restrictions on the products and services that they can offer. That same deregulation brought with it increased competition between regulators of the same type of ﬁnancial institutions (e.g., banks) that have different home bases (US states or countries) and between regulators of different types of ﬁnancial institutions (banks and insurance companies from either the same or different home bases). While it may often be difﬁcult to identify which event or action by a ﬁnancial institution or regulator initially served as a stimulus, the volleying of actions and reactions of ﬁnancial institutions and their regulation can often readily be identiﬁed. In some cases, technological advances in telecommunications or computing or macroeconomic events such as high nominal interest rates, likely served as the stimuli. Responses by ﬁnancial

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institutions were then volleyed by their regulators, often in the form of loosened regulations. These replies often led to further adjustments by ﬁnancial institutions and subsequent adjustments by ﬁnancial regulators. These adjustments included not just offerings of new ﬁnancial products and services, but also included the basic restructuring of the ﬁnancial institutions and of ﬁnancial regulators themselves. Section 1 below points out some of the factors that have propelled the increasing integration of and competition between ﬁnancial institutions. Section 1 also points out how and why ﬁnancial regulations should and have responded in kind – by becoming more integrated and competing more. Section 2 describes the aspects of the ﬁnancial systems of the US and Europe that already offer alternative regulators to ﬁnancial institutions. Section 3 notes some of the recent market and regulatory developments that illustrate the continuing shifts that are associated with competition between ﬁnancial institutions and between ﬁnancial regulators. Section 4 then analyzes a number of beneﬁts that are associated with competition in ﬁnancial regulation. It concludes with a delineation of the prior and the novel aspects of those beneﬁts. Section 5 draws together these perspectives and indicates what might be next for ﬁnancial regulations and thus for the ﬁnancial institutions that they regulate.

1. INTEGRATION OF THE WORLD ECONOMY AND FINANCIAL INSTITUTIONS AND THEIR REGULATION This section identiﬁes some of the principal factors that have propelled the increasing integration of and competition between ﬁnancial institutions. It also points out why and how ﬁnancial regulations have responded in kind, that is by also becoming more integrated and competing more. A number of factors have contributed importantly to these developments over the past three decades. Both the real and the ﬁnancial sides of the world economy have become much more integrated. Stocks and ﬂows of real and ﬁnancial assets across (and probably within) national borders have grown enormously for the past decade and, indeed, for the past half century. Financial markets have been deregulated to varying degrees all over the world. Financial institutions are now less constrained in their products and services, prices, and locations. Many large, sophisticated, liberalized ﬁnancial sectors were liberalized even further and entire nations’ stultiﬁed ﬁnancial systems were reconﬁgured

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and reconstructed following various, very large shocks, such as the demise of the Soviet Union, ﬁnancial crises, hyperinﬂations, and so on. Technological advances in the telecommunications and computing industries were widespread and rapid. They in turn fostered further technical advances in ﬁnance. The combination of these advances significantly reduced the costs of conducting and combining many ﬁnancial activities. As a consequence, ﬁnancial institutions have become increasingly integrated across (ﬁnancial) activities and across geographical (or political) borders. To regulate ﬁrms with greater diversities, or scopes, of products and services, regulators have similarly integrated, in that more and more activities are under the purview of fewer regulatory bodies. The same forces that elicited greater scopes in the offerings of products and services by ﬁnancial institutions have also elicited greater geographical areas over which ﬁrms can efﬁciently operate. Restrictions that impeded US banks from operating across state borders and European banks from operating across national borders have both been whittled down. In connection with the resulting increases in cross-border competition between ﬁrms, competition across borders in ﬁnancial regulation has also intensiﬁed. We refer to the ability of state-chartered banks in the US and banks of European Union (EU) member states to answer, generally, to only the ﬁnancial regulations of their home states as ‘‘home-run regulation.’’ Like dual banking in the US and more specifically its modern reincarnation under the 1997 amendments to the Riegle–Neal Act, home country control in the EU may be described as home-run regulation. In the EU home-run regulation permits each banking institution’s branches, operating sideby-side with host-country bank branches in a given EU member country (e.g., in Britain), to operate subject largely to the regulations of its home country (e.g., those of Britain, Spain, and potentially up to 25, countries). Home-run regulation creates competition in regulation, since ﬁnancial institutions directly and their customers indirectly via their choices of ﬁnancial institutions in a given geographical area can choose which of two (or more) sets of regulations will pertain to them. Some circumstances suggest that, rather than having home-run regulation with a myriad of choices of regulators, there are beneﬁts to having ﬁnancial regulations be imposed uniformly across borders. The Tiebout perspective suggests that regulatory authority should devolve to the smallest unit that internalizes externalities.3 That perspective posits a trade-off between the beneﬁts of local variations in regulations and the costs of localities’ not sufﬁciently internalizing the costs of the externalities associated with local regulations.4

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The spate of bank and thrift failures in the US illustrated how expensive it was, and might be again, not to internalize competitive and safety-net-related externalities associated with regulatory competition. Thus, at the same time that competition in ﬁnancial regulation increased in some spheres, it has been harnessed or eliminated in other spheres. A result of the failures in the US was that some ﬁnancial regulation then came under the purview of the federal government and thus, in effect, pertained to all US banks and thrifts. International agreement on the Basel Accord effectively shifted some regulation, such as that of capital, from a national to a supranational body. The growth of cross-border competition between ﬁnancial institutions over the past generation made the externalities associated with their operations even more apparent. One impetus to the Basel Accord of the late 1980s and its presumed revision after 2005 has been that differential regulation tilted the competition between ﬁrms. Moving toward more uniform standards may have also tilted the global ﬁnancial system away from systemic risks. The original Tiebout formulation related to geographically oriented regulation. As we shall see below, in the ﬁnancial sectors of the US and of Europe, an important aspect of regulatory competition may also occur within a given geographic area, such as a US state or an EU member state. While such regulatory competition is hardly new to the US, it has come only more recently to the EU. In the US, for well over a century, banks in a given area have had the option of being regulated by either a local (i.e., state) or a federal agency. Now, within the EU, generally, banks can operate abroad while generally being subject only to home-run regulation.

2. HOME-RUN REGULATION IN THE US AND IN EUROPE Financial regulation may be almost completely centralized at the national (i.e., federal in the US) level or may be almost entirely local.5 These extreme cases, the intermediate cases between them, and variations that permit simultaneous operation of both extremes can have beneﬁts and costs that differ considerably. Among the factors that would likely affect assessments about each case are its beneﬁts and costs of tailoring of regulations to local preferences, of fostering laboratories for private and public experimentation, of costs imposed on businesses and customers of operating across localities, of restrictions on entry and competition, and of the stabilizing effects of cross-locality ﬁnancial operations.

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Among the alternatives to the extreme cases are (1) voluntary cooperation that seeks to minimize some variations of regulations across the borders of US states or EU member states and (2) ‘‘mixed’’ systems, wherein different government entities charter ﬁnancial institutions to operate side-by-side in a given geographical area under different sets of regulations. The longstanding dual banking system in the US is an example of a mixed system where an agency of the federal government charters and regulates ‘‘national’’ banks, while simultaneously localities (agencies of state governments) charter and regulate ‘‘state’’ banks. Below, we describe and discuss how the US dual banking system has operated in the past. We also address the newer, US and European analog that may supplant dual banking regulation – home-run regulation. Home-run regulation has now emerged as a potentially powerful new force in the ﬁnancial sectors of the US and Europe. The 1997 amendments to the Riegle–Neal Act permit, with respect to some aspects of interstate banking and branching, state chartered banks to operate some interstate banking and branching operations under the regulations of their chartering state while being exempt from host state regulations.6 Similarly, the EU has developed mixed systems of ﬁnancial regulation where, within some broad guidelines, ﬁnancial institutions (including banks, insurance companies, etc.) from one country may operate in other countries under their home country regulations, while remaining largely exempt (at least for speciﬁed activities) from the regulations of the host country.

2.1. Dual Banking in the US In the US, state and national banks can operate side-by-side in a given geographical area. They operate under overlapping, but importantly (actually or potentially) distinct sets of regulations. Thus, state banks have long been able to operate independently of the regulations that were designed for national banks, and vice versa. That provided banks and their customers in effect with a choice of operating under a state or a national bank charter. (Some bank holding companies even owned some banks that were state chartered and some banks that were nationally chartered.) Having a dual banking system requires that the regulations that apply to state and national banks do, or at least can, differ somewhat. A ‘‘pure’’ dual banking system might subject state banks only to state regulations. Analogously, national banks would be subject solely to the regulations for national banks and not to states’ ﬁnancial regulations. Past

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and current versions of dual banking in the US differ markedly from this ‘‘pure’’ form of dual banking. The regulations that apply to each bank charter have historically been far from completely distinct. In practice, state banks are subject to federal banking regulations (as opposed to those promulgated for national banks) and national banks are subject to some state regulations. In addition, and consistent with the federal form of government in the US, both national and state banks, large and small, local and interstate, are in effect subject to various federal banking regulations and regulators. For example, although federal deposit insurance technically may be voluntary, in practice, virtually all banks provide it for their customers. Further, national banks must be members of the Federal Reserve System and many state banks, especially the larger ones, also choose to be members. As a result, nearly all state banks are also subject to the regulations of either the Federal Deposit Insurance Corporation (FDIC) or the Federal Reserve System. Additional aspects of dual banking in the US extend the effective reach of the regulator of national banks. For example, the vast majority of states have more or less complete ‘‘parity or wild card’’ laws that grant their state banks the same powers as national banks and that exempt their state banks from restrictions and costs that may not be binding on national banks. Such parity laws may be interpreted as attempts by states to protect the competitiveness of the state banks and the state bank charters. Similarly, some state regulations do apply to national banks. National banks are subject to state laws for non-banking matters such as contract law, criminal law, torts, zoning, etc. (OCC, 2004). In addition, although courts routinely rule that state laws that conﬂict with federal laws (and federal regulations that apply those laws) do not apply to national banks, Congress can ‘‘federalize’’ state law by making state laws on specific topics applicable to national banks. For instance, the Glass–Steagall Act, which was enacted in 1933, decreed that national banks would have the branching rights that were available to state banks in that jurisdiction (Rose, 1989). Occasionally, the federalization of state laws may take place through ‘‘opt outs’’ and ‘‘opt ins.’’ The Riegle–Neal Act, formally known as the Interstate Banking and Branching Efﬁciency Act (IBBEA) of 1994, established a federal default under which (1) bank holding companies (BHCs) may acquire existing banks across state lines and (2) BHCs and banks may not open de novo banks and branches across state lines. However, the Act also provided that states may pass legislation (applicable to national banks) to ‘‘opt out’’ of interstate banking and/or to ‘‘opt in’’ into interstate branching. As a ‘‘penalty’’ for opting out, however, the law required that the BHCs that were

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headquartered in states that opted out could not engage in the acquisition of out-state banks. In addition, without any federal penalty, states may have legislation to permit, restrict, or forbid de novo interstate banking and branching by both state and national banks (Calem & Nakamura, 1998, p. 600). Thus, the US dual banking system has not entailed completely distinct regulations for state and national banks. 2.2. Home Country Control in the EU In the 1980s, the EU (actually, its predecessor, the European Community) launched the ‘‘Single Market’’ program to remove barriers to the free movement of goods, persons, services (including ﬁnancial services), and capital among its member states. In banking and ﬁnance, the Second Banking Directive (1989), along with other EU legislation, greatly eased the entry of banks from one EU country into the others and established a mixed regulatory system for EU banking. EU banking legislation now provides a framework of minimum requirements (capital requirements, deposit insurance, etc.) that have to be met by banks headquartered in any EU country and a list of permissible activities for EU banks. This list is rather comprehensive by the standards of US commercial banks. The list includes deposit taking, lending (consumer, commercial, mortgage, etc.), leasing, credit cards, investment banking, portfolio management, derivatives trading, and several other activities (European Union, 2004). Each EU country may permit, regulate, restrict, or forbid the activities included in that list (and other activities not included in that list) for banks headquartered within its territory. However, a country may neither (1) restrict the establishment of branches of banks headquartered in other EU countries, nor (2) prevent those branches from carrying out activities that are included in that list if they are permitted in the country where they are headquartered. Thus, Britain may restrict British commercial banks from engaging in investment banking, but it may not prevent the branches of a Spanish commercial bank in Britain from engaging in investment banking, if that activity is permitted in Spain. Further, EU banking law seeks to minimize the numbers of laws and regulators that banks operating outside of their country need to deal with. Under the principle of home country control, a bank’s branches outside of their home country are largely supervised by the bank’s home country regulator and not by those of the host countries.7 However, each host country still retains the right to forbid and restrict activities not included in the list of permissible activities for EU banks.

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The US approach to home-run regulation differs somewhat from that of the EU. One notable difference is in charter choice. Although EU bank consumers may, in effect, change laws and regulators by using the local branches of a bank headquartered in a different EU country, EU banks themselves are restricted in their ability to change, or ‘‘ﬂip,’’ charters in that they would have to move their headquarters to another country or merge with a foreign bank. Another difference involves the use of mixed regulation outside of depository institutions. In the US, mixed regulation is largely restricted to depository institutions (e.g., commercial banks, thrifts, and credit unions). In the EU, home-run regulation (in the form of home country control) applies to a broader array of ﬁnancial services and institutions. For instance, home-run regulation applies to insurance and securities institutions. The list of activities of EU banks that fall under home-run regulation includes a broad range of activities (investment banking, etc.) for which home-run regulation does not apply in the US. Similarly, the ongoing project for an EU business charter (Societas Europaea) shows how European regulatory practices may both retrace earlier US paths and point toward venues for expanding dual chartering in the US. The EU business charter would permit businesses that operate across more than one European country to operate under a single European charter and under (something closer to) a single regulatory environment. This project retraces earlier American paths by introducing an EU charter that is not linked to any member country (akin to the national bank charter in the US). The EU charter departs from the US tradition since the charter would not be limited to commercial banking, but would be open to other areas of business activity. The European example raises the issue of whether the beneﬁts of home-run regulation justify its being extended beyond banking, for instance to the insurance or securities industries in the US.

3. CHARTER CHANGES AND CHANGES OF CHARTERS Competition in ﬁnancial regulation requires that ﬁrms have some choice of the regulations that will pertain to them. Over time, the ‘‘market shares’’ of ﬁnancial institutions, assets, or activities that are under the aegis of each of the ﬁnancial regulations inevitably shift. The ratio of state banks to total bank assets will change over time as certain banks grow disproportionately

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and as banks ﬂip from one charter to another in order to change the body of regulation that will pertain to them. Some shifts in market shares will be transient, while others will be more longstanding and perhaps continual. In evaluating the future prospects for a given set of regulations, it will often be crucial to distinguish between these types of shifts and responding effectively will often require identifying the sources of the shifts. In the case of the US dual banking system, the balance can and does vary through time for various reasons. Changes in general or specific market conditions, in banks’ strategies, in banks’ leadership, and other factors may lead enough banks or large banks with enough assets to change charters and thereby change noticeably the numerical balance between state and national banks and assets. Changes in the numerical balance may also occur over time as a result of changes in the relative opportunities and constraints associated with state and national charters. As one charter’s regulations prove increasingly attractive, the balance ought to shift noticeably toward that charter. The resulting regulatory competition provides banks and their customers with incentives to prefer certain charters and banks. Periodically, changes in the regulation of state or national banks may noticeably alter market shares for the two charters. For example, the 1994 Riegle–Neal Act and the 1997 amendments to Riegle–Neal may have each ultimately importantly affected (in opposite directions, however) the average ratio of total bank assets that were in state banks. Each regulation on its own may have shifted the balance, or equilibrium ratio, but neither may have set off a continual slide in market shares. Since a bank’s changing its charter is not undertaken lightly or quickly, attaining new equilibrium levels may take years. Thus, while a change from one equilibrium level of a market share to another may look like a continuing decline, the apparent trend may only be the manifestation of a multi-year adjustment to a new, sustainable balance between two (or more) viable charters. The ratio of state to total bank assets may change as one charter adapts more quickly to changed circumstances. When large changes occur, either in one of the charters or in the banks of the economies in which they operate, large incentives arise for that charter to innovate in order to enhance its charter and thereby recover some or its entire lost market share. Thus, even large shifts of assets toward one charter at the expense of the other charter may not signal that either is imperiled. In addition, even now, if one of the largest US banks changes its charter, it may noticeably alter market shares. History and logic indicate that if one charter becomes far more attractive than the other, the other charter is the more likely to react. The less pressing

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the crisis is, the less the charter reacts; the more likely is doom, the larger is the response. The 1997 amendments to the Riegle–Neal Act can be seen in this light. While the Riegle–Neal Act might have shifted the balance toward the national charter, the 1997 amendments, which allowed state banks to adhere to the regulations of the state of their headquarters, were designed to attenuate that shift.

4. BENEFITS OF COMPETITION IN FINANCIAL REGULATION This section specifically addresses the beneﬁts of competition in regulation in the US dual banking system. The beneﬁts, however, would generally accrue to the EU version and to the other versions of home-run regulation in other ﬁnancial industries. 4.1. Overview Consumers and policymakers have long recognized the beneﬁts of competition among ﬁrms: Enhanced innovation, choice, and efﬁciency. Competing ﬁrms have incentives to produce new and better products and services for their customers. Competing ﬁrms offer customers choices among ﬁrms and among products and services. Competing ﬁrms strive to operate more efﬁciently in order to attract more customers with lower prices. The US dual banking system provides an example of how ﬁnancial regulation can also beneﬁt from competition. Dual banking allows banks to choose between state and national charters, which entail different laws, regulations, and regulators.8 This section describes how competition in ﬁnancial regulation beneﬁts banks, their customers, and local and national economies by enhancing innovation, choice, and efﬁciency in bank activities and regulation. Some recent studies and trade associations argue that competition in regulation would provide beneﬁts to other ﬁnancial industries, such as insurance, as well. The remainder of this section proceeds as follows. Section 4.2 describes how competition in ﬁnancial regulation enhances innovation. Banks and their regulators have powerful economic incentives to mimic others’ successful innovations. Vibrant competition between charters encourages both innovations that can at least temporarily differentiate charters and ensuing adaptations that restore their similarities. Section 4.3 describes how

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competition in ﬁnancial regulation enhances choice. Section 4.4 describes how competition in ﬁnancial regulation enhances efﬁciency. By providing the option of national regulation, dual banking facilitates uniform national markets. National regulation reduces costs for banks that operate across state lines and for their customers, streamlines interstate bank transactions, eases entry by and sharpens competition from out-of-state banks, cushions downturns in local and regional economies, and helps channel funds to areas that offer the greatest beneﬁts to borrowers and the greatest rewards to savers and thereby raises national production and wealth. By providing the option of state regulation, dual banking facilitates state bank regulations that are tailored to local conditions. Competition in ﬁnancial regulation also spurs regulatory efﬁciency and stability. Section 4.5 discusses the critical role of preemption in sustaining competition in ﬁnancial regulation. Section 4.6 describes how competition in ﬁnancial regulation has been extended beyond US banking to the banking, insurance, and securities industries in the EU. Section 4.7 summarizes the beneﬁts of competition in ﬁnancial regulation.

4.2. Competition Enhances Innovation 4.2.1. Dual Banking Encourages Innovation The state and national components of the US dual banking system serve as ‘‘laboratories’’ for innovations both in bank products and services and in public policies. These laboratories consist of state banks and their regulators in each of the 50 states and the District of Columbia as well as national banks and the national bank regulator, the OCC. These numerous laboratories, innovating largely independently of one another, can simultaneously test a wide range of bank products and services and public policies. States differ considerably in their sizes, in their current economic conditions, in their average per capita incomes, and in the relative importance to their economies of manufacturing, ﬁnancial services, tourism and entertainment, agriculture, international trade, and other sectors. As a result, these statewide laboratories can provide information about how various innovations perform under widely differing conditions. An advantage of the US dual banking system is that it provides a venue for innovations small and large. Since there are far more state bank regulators and state banks, innovations are likely to be more numerous in the state component of the dual banking system. In contrast, innovations by national banks and their regulators are likely to be fewer in number but

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national, and thus larger, in scale. While many innovations in bank products and services and in bank regulation may have costs and beneﬁts that are justiﬁed even in quite small markets, some innovations may have sufﬁciently large development or implementation costs that only a large, multistate market would justify incurring those costs. Just as all innovation involves risk, so, too, does failing to innovate. When technology and economic conditions change rapidly, opportunities for successful innovation are the greatest. So, too, are the beneﬁts of shedding outdated and inefﬁcient practices and regulations. The dual banking system has a built-in shock absorber for innovations that work less well. An innovation in one part of the US dual banking system, for example an innovation in the bank activities permitted by one state bank regulator, won’t be adopted universally and instantly elsewhere. For a time, then, a significant share, and very often an overwhelming share, of banks won’t participate in the innovation. The non-participating banks then serve as shock absorbers when innovations are less successful. Thus, adverse repercussions on customers, banks, and economies of less successful innovations at the state level are limited by having national banks. Similarly, the adverse repercussions of less successful national innovations are limited by having state banks in every state that did not participate in the innovation. Thus, the dual banking system provides incentives to innovate and opportunities to beneﬁt from innovations, while simultaneously mitigating the risks associated with innovations.

4.2.2. Dual Banking Transmits more Innovations more Rapidly In addition to encouraging innovations, the dual banking system provides banks and their regulators with powerful economic incentives to mimic others’ successful innovations. A successful innovation by state banks (or their regulator) in one state likely tilts the competition in favor of the state banks at the expense of national banks in that state. National banks are then likely to prod the OCC to permit (or adopt) that innovation. If the OCC determines that the innovation sufﬁciently maintains national banks’ safety and soundness, it may permit (or adopt) that innovation, thereby providing national banks in all states with access to the innovation. As a consequence, state banks in other states would likely prod their own regulators to follow suit, so that they can compete effectively with the national banks in their own states. In this way, dual banking transmits more successful innovations more rapidly to state and national banks that do not compete directly with the state bank or state regulator that initiated the innovation.

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4.2.3. Vibrant Competition Spurs Charters to be Similar The permissible activities and regulatory costs of state and national banks need not differ persistently for the dual banking system to be competitive and healthy. During periods of large or rapid changes in technologies, economic conditions, or ﬁnancial developments, innovations in activities and costs may produce noticeable differences across bank charters. Historically, innovations like checking accounts, in-state branching, interest-bearing checkable deposits, and adjustable rate mortgages (ARMs) all originated in state banks. As each succeeded, it spread to other states and to national banks. More recently, innovations like insurance sales, discount securities brokerage, and real estate brokerage have been spreading across the banking system. Vibrant competition between the state and national charters whittles away at the differences across charters via the most sincere form of ﬂattery – imitation.9 A key then to a vibrant dual banking system is not how different the two kinds of charters are at any point in time, but, rather, how readily successful innovations are diffused throughout both the state and national bank systems. In that regard, then, the similarity of charters signals the vigor of the competition between national and state charters. The narrow bands within which the shares of state banks and state bank assets ﬂuctuated over the past century attest to the balance between state and national charters. State banks comprised 71 percent of all commercial banks in 1900, 65 percent in 1950, and 74 percent in 2003 (when there were ca. 5,800 state banks and ca. 2,000 national banks). State banks’ shares of bank assets ﬂuctuated within an even narrower band. State bank assets comprised 45 percent of all commercial bank assets in 1900, 43 percent in 1950, and 44 percent in 2003.

4.3. Competition Enhances Choice Competition between the national and state bank regulators in each state enhances the choices available to banks and their customers. The previous section noted that successful innovations are diffused as time passes, thereby simultaneously increasing the choices of banks and their customers and increasing the similarities of state and national charters. Before an innovation has spread far, however, charters may differ enough that bank customers can recognize differences in bank regulations. For instance, after a state charter ﬁrst permitted ARMs but before the national charter did, customers readily noticed the difference in mortgage offerings. Typically,

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however, bank customers sense little difference between banks that stem from differences in their charters. In general, however, dual banking may provide more choices to banks and their customers than may be apparent. Consider the following hypothetical example: Suppose that the regulator of national banks in effect caps agricultural loans at 10 percent of assets and caps holdings of ﬁxed-rate mortgage loans at 10 percent of assets at each national bank. Suppose also that a state bank regulator, instead, caps agricultural loans at 20 percent of assets and ﬁxed-rate mortgage loans at 5 percent of assets at each of its state banks. Such differences in caps might reﬂect regulators’ recognition of the differences in the credit and interest rate risks of agricultural and ﬁxed-rate mortgage loans and differences in their relative expertise in supervising these two types of loans. These two regulatory policies might lead state and national banks to be equally safe and sound. Nonetheless, the differences in bank regulations allow different banks to focus on, or specialize in, different products. Some customers may prefer to deal with a single bank that focuses on their primary bank product (i.e., their agricultural or mortgage loan). Other customers may prefer to obtain their bank products from several banks, each of which specializes in a different product. Other customers may prefer banks that do not specialize at all. As a result of the regulatory differences that allow banks to specialize more, bank customers have more choice in that they now have access to specialized banks that they would otherwise not have. The dual banking system also expands choice for banks and their customers who operate across state lines. Differences in regulations across states increase costs for banks that do business across state lines. To the extent that national banks can avoid some of those cross-state-related costs, national banks might have a cost advantage over state banks in providing interstate banking services. As these costs affect the fees and rates that banks charge, customers that need their banks to have cross-state operations are likely to gravitate toward national banks. Customers that do not need such operations are likely to gravitate toward state banks that have other offsetting advantages relative to national banks.

4.4. Competition Enhances Efficiency 4.4.1. Dual Banking Facilitates Uniform National Markets The US dual banking system provides banks with the option of national regulation. For banks that want to operate across state lines, national

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regulation reduces costs for banks and for their customers, streamlines interstate bank transactions, eases entry by and sharpens competition from outof-state banks, cushions downturns in local and regional economies, and helps channel funds to areas that offer the greatest beneﬁts to borrowers and the greatest rewards to savers and thereby raises national production and wealth. Absent national regulation, banks that operate across state lines incur more costs. They incur costs associated with complying with each state’s relevant regulations of banks’ products and services and all of their attendant contracts and documentation, banks’ policies and practices, and any other aspects of banks’ businesses. If the differences in relevant regulations across states were relatively minor, banks might adopt products, services, and other aspects of their businesses that were common across states, and comply with disclosure and other regulations by having state-specific contracts, documentation, and so on. If the differences in relevant regulations across states were larger, however, banks that wanted to operate across state lines would have to develop and offer state-specific products, services, and other aspects of their businesses. Either way, the absence of national regulation would raise the costs of serving bank customers across state lines. These higher costs would affect not only large, interstate banks, but also the increasing numbers of smaller banks whose markets cross state lines. Higher costs for banks (or other ﬁnancial institutions) that operated across state lines would in turn raise costs paid by customers and reduce their access to ﬁnancial services. Estimates of the aggregate amount of these costs are hard to come by. We do, however, have evidence about the costs associated with a few individual activities and banks. The Financial Services Roundtable estimates that the national uniformity of credit reporting standards (as dictated by the Fair Credit Reporting Act (FCRA) of 1970 and the Fair and Accurate Credit Transactions (FACT) Act of 2003) saves the average consumer $195 per year. Many banks recently provided the OCC with estimates of how complying with various state laws increased their costs. Six banks estimated at $44 million the total cost of implementing a California law that mandated a minimum payment warning. Other banks estimated they would need 250 programing days to update computer systems to comply with anti-predatory lending laws in three states plus the District of Columbia. One bank estimated that complying with mandated annual statements for credit card customers would cost $7.1 million.10 National regulation also enhances the convenience of interstate bank transactions. Some customers value bank products and services that are uniformly available across state lines. Among them are businesses with customers in more than one state,11 business travelers, tourists, residents of

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border towns, people who move to other states, and customers who want products and services that are not otherwise available in their own states. By making it easier for out-of-state banks to enter local markets, national regulation increases competition. In the absence of national regulation, regulations that vary across states act as ‘‘hidden barriers to trade’’ that restrict entry by out-of-state competitors and thereby limit competition and correspondingly reduce the beneﬁts to banks and their customers that would ﬂow from competition.12 Entry by out-of-state banks may also be deterred by uncertainty about whether future state regulations would force interstate banks to truncate national products to ﬁt state-specific regulations. Because it facilitates interstate banking, national regulation can also help cushion downturns in local economies. The health of local banks tends to mirror the health of their local economies, because their loans and deposits are concentrated in their local markets. As a result, downturns in their local economies tend to reduce the credit available from local banks when it would be most valuable to some creditworthy borrowers. In contrast, the health of an interstate bank is less affected by the health of a local economy, because its loans and deposits tend to be more geographically diversiﬁed. Hence, when both local economies and local banks are troubled, interstate banks are less likely to be troubled and more likely to be able to provide credit to local households and businesses when they need it the most. Interstate banks may also better channel funds from less dynamic, lowerreturn sectors and regions to more vigorous, higher-return sectors and regions. Better channeling of funds to areas that offer the greatest beneﬁts to borrowers and the greatest rewards to savers raises national production and wealth. 4.4.2. Dual Banking Allows Regulations to be Tailored to Local Conditions State bank regulators may have sufﬁciently superior local knowledge that they can tailor regulations more effectively to their states’ economies while keeping their banks safe and sound. For example, some states’ regulators may be more adept at supervising banks with more agricultural loans (and less adept at supervising banks with other risks). Other states’ regulators may be more adept with other categories of loans. As a result, state bank charters might appropriately differ not only from the national charter but also from the charters of other states. Banks within a state would beneﬁt not only from having a charter that was tailored more effectively to ﬁt local conditions, but also from having a choice of charters. Banks within a state often differ considerably in their business strategies and thus in their mixes of products, services, and customers. As a result, some banks in each state likely ﬁnd that they can service

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their customers best through a state charter, while other banks can do so best through a national charter. 4.4.3. Dual Banking Spurs Regulatory Efficiency and Stability Competition in ﬁnancial regulation compels regulators to monitor closely which practices and regulations most beneﬁt ﬁnancial institutions and their customers, to assess whether their operations and regulations are appropriate, and to restrain their operational costs. The dual banking system, then, pressures bank regulators to pass along these efﬁciencies to banks and, ultimately, to bank customers. The dual banking system also encourages regulators to be appropriately ﬂexible in their dealings with banks. If a regulator routinely denied requests by banks to launch innovative products and services, introduced ever more costly regulations, or enforced regulations inefﬁciently, banks and their customers would suffer unduly. Customers would abandon those banks and move to other banks and to nonbank ﬁnancial institutions. Similarly, banks would abandon those regulators by ‘‘ﬂipping’’ charters. In such cases, the option of banks’ ﬂipping charters puts a healthy restraint on regulation. At the same time that it provides incentives for regulatory innovation and efﬁciency, the dual banking system also reduces uncertainty about regulation. Banks value regulatory predictability and are more likely to ﬂip away from charters that impose unduly volatile regulations. Regulators are conscious of banks’ concerns about regulatory predictability and consequently weigh carefully changes in regulations. A concern with regulatory competition involves the possibility of ‘‘competition in laxity’’ among regulators – that regulators may sacriﬁce safety and soundness to attract banks to their respective charters. The Federal Deposit Insurance Corporation Improvement Act (FDICIA) of 1991 was designed to reduce the possibility that regulators would be lax. FDICIA provided for more involvement by the federal government in the regulation and supervision of all federally insured banks, both state and national. For example, the Act imposes ‘‘prompt corrective action’’ on all bank regulators. As a result of this and other provisions of the Act, many analysts regard FDICIA as having reduced the possibility of competition in laxity.

4.5. Preemption is Critical for Regulatory Competition To reap the beneﬁts of competition, it is critical that bank regulators be able to differentiate their charters; that is, regulations that apply to national

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banks cannot routinely apply to state banks, and vice versa. Without federal preemption of state regulations that conﬂict with national (banking) regulations, national banks would operate under the same regulations that state banks operate under in each state. Therefore, removing preemption would, in effect, eliminate the dual nature of banking and hamper interstate banking. State bank regulators may fear that preemption of state laws will place state banks at a competitive disadvantage and ultimately lead to centralized banking regulation. They argue that if national banks are not subject to the same regulations that states impose on state banks, then state banks will switch to national charters. They further argue that state bank regulators then would not be able to resist mimicking national regulations, thereby effectively centralizing bank regulation. Preemption of state laws, however, need not place state banks, on balance, at a competitive disadvantage. Preemption does mean that some state laws may not apply to national banks. However, these laws may either impose additional costs on banks or grant them additional beneﬁts. That some specific costs or beneﬁts associated with national banks are more favorable to either state banks or national banks does not mean that, on balance, either charter is at a competitive disadvantage. Rather than considering some costs or beneﬁts of a charter in isolation, meaningfully comparing charters requires taking into account the balance of all of a charter’s costs and beneﬁts. Of course, different banks will value the costs and beneﬁts of the state and national bank charters differently, depending on the banks’ business strategies and environments, their products and services, and their customers. Thus, some banks will prefer state charters and other banks will prefer national charters. If the market share of either type of charter drops appreciably, then regulators should consider whether their charter has responded effectively enough to its competition.

4.6. Competition in Financial Regulation in Europe Competition in ﬁnancial regulation has spread beyond US banking. For instance, the EU has implemented its own version of a dual banking system. EU legislation speciﬁes a list of permissible activities for banks, including deposit-taking, lending, investment banking, portfolio management, derivatives trading, and several other activities. Each EU country may permit, regulate, restrict, or forbid these and other activities for banks

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headquartered within its borders. However, a country may neither (1) restrict within its borders the establishment of branches of banks headquartered in other EU countries, nor (2) prevent those branches from carrying out activities permitted in their home country, if the activities are included in the EU’s list of permissible bank activities. Thus, Italy may restrict Italian commercial banks from engaging in investment banking, but may not prevent branches in Italy of a Spanish commercial bank from engaging in investment banking, if investment banking is permitted in Spain. In addition, under the principle of home country control, a bank’s branches outside of its home country are supervised by the bank’s home country regulator rather than by that of the host country. In that regard, home country control is a version of dual banking: branches of Spanish and Italian banks that operate side by side (e.g., in Spain, in Italy, or in any other EU country such as Poland) are subject to somewhat different regulations (i.e., those of each home country). In the EU, these principles apply not only to banks, but also to other parts of the ﬁnancial sector, such as the insurance and securities industries. The performances of banking and other ﬁnancial industries in the EU are likely to provide valuable information and insights into the beneﬁts of extending competition in ﬁnancial regulation to nonbank ﬁnancial industries in the US, such as ﬁnance companies and insurance.

4.7. Aspects, Old and New, of the Benefits of Competition in Financial Regulation A number of the beneﬁts that are attributable to competition in ﬁnancial regulation have been recognized for some time. For convenience, several are recapitulated here. Yet, despite the long history of dual banking in the US, a surprising number have not been recognized widely, if at all, before. For decades, that competing regulators are more likely to innovate has been testiﬁed by argument and example. While that point has tended to be advanced by academics, bankers seem to have been more likely to stress that having a choice of charters stiﬂes any tendency for regulations to be excessive: The implicit threat of charter ﬂips corrals any regulatory overzealousness. Occasionally acknowledged is that excessive regulation might lead banks or their customers to shift assets out of banks altogether by using nonbank ﬁnancial institutions. Some of the novel aspects of competition in ﬁnancial regulation arise from the introduction over the past decade of reduced restrictions

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on interstate branching and banking in the US. One of the intriguing, newer aspects of regulatory competition might be termed the ‘‘epidemic’’ feature introduced by the national charter, whereby a state-level regulatory innovation spreads to states near and far via the ‘‘carrier’’ of the nationwide purview of the national charter. This transmission mechanism has received little previous notice. Nor recognized has been the risk-mitigating feature of the ballast provided by the banks of one charter, which are not currently covered by a regulatory innovation in the other charter. Similarly, when regulators compete, banks may perceive not only less regulatory overzealousness on average, but also less risk of that zeal. Banks, more than academics, apparently regard this reduced second moment of regulation as being of great moment. Finally, little notice has been given to the ability of a larger regulator to undertake innovations that have large ﬁxed costs of research, as opposed to the costs of implementation and maintenance.

5. LOOKING BACK AND AHEAD, OR IS DUAL BANKING ‘‘TOO GOOD TO BE TWO?’’ Financial institutions have seized upon the greater opportunities of the past three decades to integrate across banking activities and across nonbanking activities. Much of the deregulation that permitted more integration also stimulated more competition within banking, across banking and nonbanking ﬁnancial institutions – and even across historically nonﬁnancial institutions, and across banks from different countries. Financial regulation responded. Financial regulation has become more integrated, very largely due to the integration of their regulatees and separately due to the forces that led to the increasing integration of ﬁnancial institutions. Financial regulation has become more integrated both across banking and nonbanking ﬁnancial activities and across countries. In the US, the Federal Reserve System is now the regulator of bank holding companies that do more kinds of banking activities and of ﬁnancial holding companies that do more kinds of nonbanking ﬁnancial activities than heretofore. In the UK, the FSA has come to be the regulator of UK ﬁnancial institutions generally. These developments have led to greater competition, not only between ﬁnancial institutions, but also between ﬁnancial regulators. Financial liberalization that allows more of the industries in the US ﬁnancial sector to compete with each other means that the regulations of those industries are

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now more in competition with each other. That holds true both for banking and nonbanking ﬁnancial institutions and regulations. In the US, the Riegle–Neal Act, which dismantled most of the remaining restrictions on interstate banking and branching, was amended in 1997 to permit outof-state, state banks to operate their branches under home-run regulation. In the same spirit, the EU has speciﬁed activities that banks can undertake abroad under home-run regulation. In a contrasting trend, in order to better internalize various externalities, Basel agreements intend to harness the competition between national regulators, and thus of their banks, into agreed-upon channels. In its effective reach across national borders, the Basel Accord and its updated version seek to require uniform standards for the safety and soundness of ﬁnancial institutions around the world. To the extent that some nations remain outside the Basel agreements, there is scope even for competition between ﬁnancial institutions whose regulations do and those that do not comport with the Basel agreements. In the case of the US, which intends to adopt a bifurcated arrangement that subjects its largest banks to Basel II and subjects the remaining US banks to Basel I, scope is introduced for an additional dimension of competition between banks subject to different versions of the Basel agreements. Competition in ﬁnancial regulation can produce a number of beneﬁts, some of which are well known and some of which apparently have not previously been noted. The prime example of such competition has long been the US dual banking system, which has long allowed US banks to choose between two charters. As yet, relatively few ﬁnancial institutions have availed themselves of the home-run regulation that was ushered in by the 1997 amendments to the Riegle–Neal Act in US and the implementation of home country control in the EU. Regardless of the motives for each of these regulatory shifts, their effect eventually may be the end of the dual banking system. If so, the demise of the dual banking system will likely not be due to the failings of the dual system. Nor is it likely to mean the end of competition in ﬁnancial regulation. On the contrary, if for these reasons the dual banking system were to cease to exist as we now know it, its demise is likely more because it was ‘‘too good to be two.’’ That is, home-run regulation opens up the possibility that banking in each US state could be conducted, under one of not just two alternative charters, but rather under any one of 52 charters. (Hypothetically, banks from each of the 50 states plus the District of Columbia plus national banks could be in operation within a single state, each operating under its home-run regulations. Similarly, in the EU, banks in a given

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member state could be operating under any one of one, or soon to be two, dozen different sets of home-run regulations.) Thus, the path for the foreseeable future, if not forever, seems likely to lead toward rather more diversity in charter choice and more competition in ﬁnancial regulation.

NOTES 1. See Wilcox, Cobas and Mote (2003) for comparisons of the forecasted and actual speeds and extent of advances in ﬁnancial products and services. 2. See Wilcox, Barth and Brumbaugh (2000). 3. See Donahue (1997) and Inman and Rubinfeld (1997). 4. For convenience, we use the term ‘‘regulation’’ broadly. Here, regulation refers to regulations, legislation, rules, supervision, or any other governmental authority. 5. In addition, in the US, federal laws, as opposed to the rules that specifically are applied by their regulator (the OCC in the US) to national banks, generally apply equally in practice, both to local (i.e., state-chartered) and to national banks. 6. The national charter remains intact. 7. For the purpose of EU banking legislation, the home country is the country where a bank’s headquarters are located and the host country is the foreign country where the branches are located. For instance, regarding branches located in Britain of a bank headquartered in Spain, Spain is the home country and Britain is the host country. 8. For simplicity, here we do not distinguish among laws, regulations, and supervision. 9. The process by which bank charters mimic one another can at times be almost automatic. State ‘‘wild card’’ or parity laws aim to grant state banks whatever powers are available to national banks within that state. However, these laws do not prevent states from (1) granting state banks additional powers not available to national banks or (2) introducing additional regulations that are binding on state banks and thus not ‘‘covered’’ by parity laws. Also, federal law may explicitly make some state laws binding for national banks within each state (e.g., branching under the Glass–Steagall Act). 10. Several recent studies and surveys highlight how variations in state regulations increase costs for insurance companies that operate in multiple states. In particular, survey respondents report that delays in the approval of new products across 50 states led to significant costs and forgone revenues. 11. These include businesses both large and small, businesses operating in many states or simply across one state border, and businesses that have physical operations in multiple states or that simply deliver goods and services from a single location. 12. International trade analysis highlights how differences in regulations across jurisdictions act as hidden barriers to trade. These hidden barriers may be more important barriers than transportation costs. For instance, ten years after NAFTA was introduced, Canadian provinces traded more with other Canadian provinces (with which they share the Canadian regulatory framework) than they traded with US states that were sometimes thousands of miles closer.

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ACKNOWLEDGMENTS The author thanks the American Bankers Association and the Financial Services Roundtable for research support. The views expressed are those of the author and should not be attributed to the ABA, the FSR, or the members of either organization.

REFERENCES Calem, P., & Nakamura, L. I. (1998). Branch banking and the geography of bank pricing. Review of Economics and Statistics, 80(4), 600–610. Donahue, J. D. (1997). Tiebout? Or not Tiebout? The market metaphor and America’s devolution debate. The Journal of Economic Perspectives, 11(4), 73–81. European Union. (2004). Second banking directive. http://europa.eu.int/smartapi/cgi/sga_doc?smartapi!celexapi!prod!CELEXnumdoc&lg=EN&numdoc=31989L0646&model=guichett Inman, R. P., & Rubinfeld, D. L. (1997). Rethinking federalism. The Journal of Economic Perspectives, 11(4), 43–64. Ofﬁce of the Comptroller of the Currency (OCC). (2004). Final rule: Preemption. http:// www.occ.treas.gov/2004-3bPreemptionrule.pdf Rose, P. S. (1989). The interstate banking revolution. New York: Quorum Books. Wilcox, J. A., Barth, R., & Brumbaugh, D. R., Jr. (2000). The repeal of Glass–Steagall and the advent of broad banking. Journal of Economic Perspectives, 14(2), 191–204. Wilcox, J. A., Cobas, M. G., & Mote, L. R. (2003). A history of the future of banking: Predictions and outcomes. In: B. E. Gup (Ed.), The future of banking (pp. 49–76). New York: Quorum Books.

A MODEL OF LIQUIDITY AND BANK RESERVES Stephen A. Kane and Mark L. Muzere ABSTRACT We consider two economic aspects of required reserves on bank deposits, their impact on bank-intermediated investment versus direct investment and their opportunity cost. We show that Bank reserves serve as a buffer to mitigate inefficient liquidation of a bank’s assets in order to meet the demand for liquidity by investors. Due to some transaction costs or information costs, investors may prefer bank-intermediated investment to direct investment. Banks offer investors competitive deposit returns compared to the liquidation value of investment to attract funds from investors. If the Federal Reserve allows banks to set their individual optimal level of reserves, this might mitigate costs associated with required reserves. If banks implement the social optimum, this may introduce additional fragility into the banking system. We argue that required reserves might lead to deadweight loss if they are set above a bank’s optimally determined reserves.

1. INTRODUCTION In the United States, the Federal Reserve sets a minimum level of required reserves, which depository banks in the Federal Reserve System need to Research in Finance, Volume 22, 239–272 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22009-9

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maintain as a fraction of their demand deposits. We consider two economic aspects of required reserves on bank deposits, their impact on bankintermediated investment versus direct investment, and their opportunity cost. We employ the framework of Diamond and Dybvig (1983) and Bryant (1980) to conduct our analysis. Banks determine their individual optimal level of reserves on demand deposits.1 Investors invest their funds in bank portfolios through bank deposits and directly invest some of their funds in long-term risky assets and short-term securities. Investors may rebalance their portfolios to facilitate diversiﬁcation of their investment and to facilitate consumption. That is, investors may partially withdraw their bank deposits and reinvest the funds in short-term securities. We show that in the social optimum, investment in risk-free securities helps to meet the demand for liquidity by investors and to provide diversiﬁcation beneﬁts. A bank’s reserves may mitigate inefﬁcient liquidation of the bank’s assets to meet demand for liquidity by investors. Due to some transaction costs or information costs, investors may prefer bankintermediated investment to direct investment. Banks offer investors competitive deposit returns compared to costly premature liquidation of investment in order to attract funds from investors. If banks implement the social optimum, they may do so at the cost of additional fragility to the banking system. In the social optimum, our investors do not partially withdraw their bank deposits and reinvest the funds in risk-free securities. Generally, investors decrease their amounts of bank deposits as their degree of risk aversion increases. Our analysis has policy implications. By allowing banks to determine their individual optimal level of reserves, this may mitigate costs of ﬁnancial stress. If the minimum level of required reserves exceeds a bank’s optimally determined level of reserves, this may lead to deadweight loss. Since membership in the Federal Reserve System is voluntary, we argue that required reserves may implicitly earn their opportunity cost through some bank operations and Federal government subsidies. The remainder of the paper is organized as follows; Section 2 describes the model and Section 3 concludes the paper.

2. THE ECONOMY We extend the Diamond and Dybvig (1983) model into a setting in which early liquidation of one dollar assets yields strictly less than one dollar. This

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assumption gives depositors incentive to hold risk-free assets and makes the analysis complicated. There are two assets, a risk-free asset, which is used for lending and borrowing, and equity, which entitles investors to cash ﬂows generated by a productive process.2 The productive process is illiquid because it needs time to generate cash ﬂows. Investor transaction and information costs further contribute to the illiquidity of the securities of the productive process. We assume that there is a continuum of investors, who are uniformly distributed over the unit interval [0,1]. Each investor has an increasing, concave and twice continuously differentiable expected utility function. We denote the utility function by u(c), where c denotes consumption. The utility function satisﬁes the Inada conditions, which means lim u0 ðcÞ ¼ 1 and lim E½u0 ðcÞ ¼ 0

c!0þ

c!1

where E denotes the expectation operator. Our two-period economy is indexed by dates 0, 1, and 2. We might suppose a one year time interval for each period, since two years is a plausible time horizon for a productive process to come to fruition. At date 0, all investors are homogeneous. We normalize the aggregate wealth of investors to one. At date 1, investors are subject to privately observed liquidity shocks. They decide whether or not to discontinue their investment. Investors who discontinue their investment consume the proceeds from their investment. Late consumers consume the proceeds from their investment after the productive process has reached full fruition. We assume a ﬁxed proportion yA(0,1) of early consumers. The parameter y is publicly known. Based on y, each investor has an independent and identically distributed chance of being an early consumer. Thus, the productive process is the only source of aggregate uncertainty. Our banking system consists of banks and a central bank. Banks perform maturity transformation, using short-term liabilities such as demand deposits to ﬁnance long-term projects. Banks determine their individual optimal level of reserves. The banks use short-term securities to store their reserves. Consequently, we assume that there are traders, including the Federal government, of short-term securities. We assume that banks compete only in price, interest rate on deposits, and not in the quality of service they provide or in the characteristics of customers they serve. Consequently, we may assume that there is only one bank which intermediates the productive process. The bank offers investors

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demand deposit contracts that satisfy the sequential service constraint.3 We assume that the bank is a mutual. That is, depositors own the bank. There is one consumption good which may be imported. We use this consumption good as a numeraire. We normalize price of the consumption good to one. Required reserves on demand deposits earn zero explicit interest. Consistent with this observation, one dollar invested in the risk-free asset yields a constant gross return of one. But since membership in the Federal Reserve System is voluntary, the individual participation constraint implies that required reserves implicitly earn at least their opportunity cost through some bank operations and government subsidies. Thus, we assume that the gross return on investment in the risk-free asset satisﬁes rX1. The returns on one dollar invested in the productive process at date 0 are given by ( v at t ¼ 1 if investment is liquidated m r ¼ x at t ¼ 2 if investment is not liquidated at t ¼ 1 where v is a constant liquidation value and x a random variable whose distribution is publicly known. We assume the random variable x has a Bernoulli distribution deﬁned as follows: x ¼ vL in a low state of nature with probability q, and x ¼ vH in a high state of nature with probability 1q, where qA(0,1). The high state may represent a period of economic boom, while the low state may represent a period of economic recession. The expected value of x satisﬁes vL+(1q)vH 4r, or else the risk-free asset will dominate the productive process. We assume that the liquidation value satisﬁes vpvLorovH, which formalizes the cost of illiquidity. Since the return in the low state is strictly less than the return on investment in the risk-free asset, a risk-averse investor allocates positive amounts of the investor’s funds between the productive process and the risk-free asset. The bank offers investors demand deposit contracts. Returns on one dollar deposited in the bank at date 0 are given by ( r1 at t ¼ 1 if a depositor chooses to cash out then b r ¼ r2 at t ¼ 2 otherwise: The date 1 deposit return is constant while date 2 returns are random. The random variable r2 corresponds to a fractional share of assets remaining in the bank, assuming no bank run occurs. The bank makes this promise to investors, but in the case that it is illiquid or is insolvent, the bank may not be able to honor its promise. When the bank is illiquid and the central bank

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elects not to rescue it, then the central bank acts as a supervisory regulator and places the bank into receivership (as would be the case of a state chartered bank that is a member of one of the 12 Federal Reserve Banks). The resolution agency (Federal Deposit Insurance Corporation (FDIC) for state chartered banks in the United States) is a passive entity, since the supervisory regulator determines receivership. We introduce an equilibrium concept for the two-stage game played by the bank and investors. Since there is a continuum of investors, we use an extension of the Nash equilibrium concept to nonatomic games (Schmeidler, 1973). In nonatomic games a single player has no inﬂuence on a situation but the aggregate action of a set of players may change the payoffs.4 We obtain an equilibrium when, given the decision of other agents, an agent does not improve on the agent’s expected utility by making a different decision. A run on a bank is an event when depositors rush to the bank to withdraw their deposits due to the chance that the bank will be illiquid or will fail. The sequential service constraint induces a negative externality when investors run on a bank because investors who arrive late may not receive anything from their bank deposits. Thus, bank run is a Nash equilibrium because each investor decides to withdraw the investor’s bank deposits given that other investors decide to withdraw their bank deposits. The Diamond–Dybvig model may be described as a two-stage game. Consequently, we use the equilibrium concept of subgame perfect Nash equilibrium extended to nonatomic games. We introduce additional uncertainty by letting fXy denote the fraction of investors who withdraw all their bank deposits at date 1. Since the withdrawals of bank deposits occur randomly, we use the random variable f to characterize the aggregate behavior of a fraction of late consumers. The distribution of this random variable is not publicly known because liquidity shocks are private information, and investors withdraw their bank deposits for various reasons. Bank failure, bank illiquidity, personal crisis, natural disasters, or even rumors may induce investors to withdraw their bank deposits. Participants only observe the realization of f, which we denote as f. We let b denote the fraction of bank deposits, which the bank invests in the productive process. The bank allocates the fraction (1b) of its deposits to the risk-free asset. The bank uses investment in the risk-free asset to store its reserves. The fraction of bank deposits invested in the productive process is optimally chosen, which implies that the level of bank reserves is optimally chosen, too. Let a denote the amount of dollars an investor deposits in the bank. Let d denote the amount of dollars the investor invests directly in the productive

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process. The investor invests the remaining amount (1ad) of dollars in the risk-free asset. Suppose f is the fraction of late consumers who withdraw all their bank deposits at date 1. Thus, the amount of bank deposits liquidated to meet the demand for liquidity is given by afr1. We claim that this amount does not exceed the amount of bank reserves (afr1pa(1b)r). If (afr14a(1b)r), the bank would do better by increasing the amount of reserves and investing less in the productive process.5 This argument hangs on the assumption that the productive process is illiquid and premature liquidation of long-term investment is costly. The bank’s date 2 proceeds from its investment are given by abx+[a(1b)rafr1]r, while the bank’s corresponding liabilities are given by (1f)ar2 (f, b, x). The bank is a mutual, so we assume that it distributes all date 2 proceeds from its investment to investors. Thus, the resource constraint is of the form (1f)ar2 (f, b, x) ¼ abx+[a(1b)rafr1]r.

2.1. The Social Optimum An investor acting alone may allocate funds to both the risk-free asset and the long-term risky asset. These portfolio allocations may not be optimal. But investors acting together may beneﬁt from a coalition (bank). We consider the case where the bank acts on behalf of the investors. That is, investors deposit all their funds in the bank and the bank invests the funds on their behalf. By the revelation principle, we assume that investors fully reveal their type by their choices. This resolves the information asymmetry needed to solve Problem 1. The bank solves a representative investor’s problem. (Chang & Velasco, 2000, use a similar argument in a different problem.) Problem 1. The bank chooses per capita consumption c1 and risky investment a to maximize a representative investor’s expected utility yuðc1 Þ þ ð1 yÞE½uðc2 ðy; xÞÞ subject to ð1 yÞc2 ðy; xÞ ¼ ax þ ½ð1 aÞr yc1 r

(1)

a; c1 X0

(2)

Constraint (1) is a consumption version of the resource constraint. The bank invests in the risk-free asset to meet the consumption of early consumers and to facilitate diversiﬁcation of investment (yc1p(1a)r). If yc14(1a)r, the bank would do better by increasing the funds invested in

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the risk-free asset and then invest less in the productive process.6 Constraint (2) ensures that there are no short sales on long-term investment and consumption is never negative. The bank’s investment strategy is similar to an investment strategy using the capital market line (CML) as in the capital asset pricing model (CAPM), where an investor allocates funds between the ‘market’ portfolio and a riskfree asset. The optimal allocation depends on the level of risk and the investor’s degree of risk aversion. We provide a solution to Problem 1 for a speciﬁc utility function. Proposition 1. Assume that an investor’s preferences are represented by a constant coefﬁcient relative risk-aversion utility function of the form uðwÞ ¼ wg =g; where go1 and g6¼0. Then the solution to Problem 1 is given by a¼

ð1 yÞr2 ð1 h1 Þ ð1 yÞ ðh1 ðvH r2 Þ þ r2 vL Þ þ y rh2 ðvH vL Þ

c1 ¼

r2 h2 ðvH vL Þ ð1 yÞ ðh1 ðvH r2 Þ þ r2 vL Þ þ y rh2 ðvH vL Þ

where the parameters h1 and h2 are deﬁned as 1=ð1gÞ q ðr2 vL Þ h1 ¼ ð1 qÞ ðvH r2 Þ

r 2 vL h2 ¼ ð1 qÞ ðvH vL Þ

1=ð1gÞ

A proof of Proposition 1 is provided in the appendix. We see that investment in the risk-free security meets the liquidity demand by investors and offers diversiﬁcation beneﬁts to investors. We consider opportunity cost on required reserves. The question we address is given that membership in the Federal Reserve System is voluntary and banks earn zero interest on their required reserves, why would banks seek membership in the Federal Reserve System? The individual rationality constraint implies that required reserves may implicitly earn at least their opportunity cost through some bank operations and Federal government subsidies. In the United States, Federal Reserve member banks may earn a return on required reserves through government debt trading, foreign exchange trading, other Federal Reserve payment

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services, and afﬁnity relationships (outsourcing) between large and small banks. Banks may also receive a safety-net subsidy that lowers their cost of capital. We note that vault cash residing in Automated Teller Machines (ATMs) network qualiﬁes as required reserves, too. Thus, banks may earn a positive return on required reserves. We pose mathematically the minimum amount S of wealth a bank might earn from some of its operations and subsidies from the Federal government. We deﬁne S to be a solution to the equation ax þ ðð1 aÞr yc1 Þr Max yuðc1 Þ þ ð1 yÞE u c1 ; a 1y lx þ ð1 lÞ yc1 þ S ¼ Max yuðc1 Þ þ ð1 yÞE u c1; l 1y On the left-hand side, the amount c1 is per capita consumption of early consumers and the amount a is the bank’s risky investment. The bank’s required reserves earn positive interest. On the right-hand side, the amount c1 is per capita consumption of early consumers and the amount l is the bank’s risky investment. The bank’s required reserves do not earn positive interest but the bank earns an amount S of subsidy. In practice, S may be substantially larger than the minimum amount. There is difﬁculty in measuring S, since agents may obscure subsidies. In the sequel, we assume that banks earn positive interest from their reserves.

2.2. Demand Deposits and Illiquidity We allow investors to make deposits in the bank and directly invest some of their funds in the illiquid asset. This permits some degree of interaction between the banking system and the capital market. Investors may withdraw their bank deposits in the middle period. We seek to derive implications for the banking system if banks implement the social optimum. (Chang & Velasco, 2000, use a similar argument in a different problem.) We seek to show that if banks implement the social optimum, this may lead to additional fragility in the banking system. We shall show the existence of a socially desirable equilibrium if banks implement the social optimum. But there is also a socially undesired equilibrium, bank run, which may occur if banks implement the social optimum. One way to quell a bank run is through a program such as the FDIC, but this induces moral hazard.

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We assume that there are no side trades in the demand deposit contracts. This assumption ensures that investors do not undermine the bank in its role of providing liquidity (Jacklin, 1987). We provide a detailed description of the two-stage game played by the bank and the investors. The stage-one game is played at date 0. In this subgame, parties presume that a run on the bank is an event with negligible probability. The bank chooses an interest rate on bank deposits and an investment strategy for the funds the investors deposit with the bank. The bank invests these funds in the productive process and risk-free asset. At date 0, all investors are homogenous. The investors do not know their types. An investor deposits some of the investor’s funds with the bank and invests some of the funds directly in the productive process. The investor invests the remaining funds in the risk-free asset. Because the investor does not know the investor’s type, the investor’s expected utility is given by yuðar1 þ ð1 a dÞ rÞ þ ð1 yÞ E½uðð1 cÞ ar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 Þ The stage-two subgame is played at date 1. Investors receive their private liquidity shocks. Investors who consume early liquidate their investment and consume the proceeds. An early consumer’s utility is given by u(ar1+(1ad)r). Since the proportion of early consumers is publicly known, the bank may have a contingency plan for the demand for liquidity by early consumers. Indeed, the bank uses part of its reserves to meet the demand for liquidity by early consumers. Investors who consume at date 2 rebalance their portfolios. They may withdraw part of their bank deposits and reinvest these funds in the risk-free asset. These transactions occur randomly with an unknown distribution. Thus, it is difﬁcult for the bank to have a contingency plan for these transactions. The bank meets these partial withdrawals by partially liquidating its investment in the productive process. A late consumer’s expected utility is given by E½uðð1 cÞar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 Þ We state the utility maximization problems associated with the two-stage game. Problem 2. Given an investor’s planned investment strategy (a, d; c), the bank chooses at date 0, deposit return r1, and risky investment b in order

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to maximize the investor’s expected utility yuðar1 þ dv þ ð1 a dÞ rÞ þ ð1 yÞ E½uðð1 cÞ ar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 Þ subject to uður1 þ ð1 a dÞ rÞpE½uðð1 cÞ ar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 Þ

ð1 yÞ ð1 cÞ ar2 ðy; b; xÞ ¼

car1 ab x þ ½að1 bÞ r a yr1 r v

ð3Þ

(4)

Constraint (3) is an incentive compatibility constraint for late consumers. This means late consumers have no incentive to pretend to be early consumers. Constraint (4) is a restatement of the resource constraint. The funds an investor partially withdraws at date 1 are met by partial liquidation of the bank’s investment in the productive process. Problem 3. Given the bank’s planned investment strategy (r1, b), and the fraction c of bank deposits an investor will withdraw at date 1, the investor chooses at date 0, bank deposits a and risky investment d to maximize the investor’s expected utility yuðar1 þ dv þ ð1 a dÞ rÞ þ ð1 yÞ E½uðð1 cÞ ar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 Þ subject to a þ dpð1 þ mÞ

ð1 yÞ ð1 cÞ ar2 ðy; b; xÞ ¼

car1 ab x þ ½að1 bÞ r a yr1 r v a; dX0

(5)

(6)

(7)

Constraint (5) describes a feasibility condition, where the parameter m describes a limit on the funds an investor can borrow. The parameter m is

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exogenous and its value depends on several factors including the state of the economy. Investors may borrow funds through the bank. Constraint (6) is a restatement of the resource constraint. The bank meets partial withdrawals at date 1 by partial liquidation of the bank’s investment in the productive process. Constraint (7) prevents short sales in an investor’s long-term investment. In the following lemma, we show that if banks implement the social optimum, this may lead to fragility in the banking system. Lemma. We assume thatthe gross return on investment in the risk-free asset satisﬁes 1prpMin 1=q; 1=ð1 qÞ : In the social optimum, the per capita consumption is more than the per capita liquidation value of the economy’s assets (c14av+(1a)r). If banks earn positive interest on their required reserves, a sufﬁciently high interest rate might mitigate ﬁnancial fragility in the banking system. The consumption of early consumers is strictly less than the total return on investment in the risk-free asset (yc1o(1a)r). This means that investment in the risk-free asset may help to facilitate diversiﬁcation of investment. A proof of the lemma is provided in the appendix. In the following proposition we show that, absent bank runs, bank reserves may prevent inefﬁcient liquidation of the bank’s assets to meet the demand for liquidity by investors. In the social optimum, investment in the risk-free asset meets the demand for liquidity and facilitates diversiﬁcation of investment. Here, the bank’s investment in the risk-free asset meets the demand for liquidity by early consumers. Investors achieve asset diversiﬁcation through their investment in the risk-free asset. Proposition 2. The bank’s reserves on demand deposits are equal to the liquidity demand by early consumers (a(1b)r ¼ ayc1). The solution to Problem 3 has no funds invested directly in the productive process (d ¼ 0). A proof of Proposition 2 is provided in the appendix. The bank offers investors competitive deposit returns compared to costly premature liquidation of investment to attract funds from investors. Thus, investors may prefer bank intermediated investment to direct investment. We solve the two-stage game associated with the Diamond–Dybvig model backward. We represent the two-stage game in normal form. That is, in each subgame, investors, their payoffs, and their strategies are speciﬁed. The investors’ payoffs are the values of their utility functions.

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First, we solve the stage-two subgame at date 2. At date 2, investors decide whether to withdraw or not to withdraw their bank deposits. Since these investors consume all the proceeds from their investment at date 2, it is optimal for the investors to withdraw their bank deposits. Thus, there is a unique Nash equilibrium in the stage-two subgame. Second, we solve the stage-one subgame at date 1. At date 1, the investors know their types. Since there is no discounting, the payoffs in the stage-two subgame associated with the investors’ strategy to withdraw their bank deposits are substituted into the payoffs for the stage-one subgame. Since investors get higher expected return when the project is allowed to mature, it is optimal for late consumers not to withdraw their bank deposits at date 1. Thus, the strategy not to withdraw bank deposits at date 1 constitutes a pure strategy Nash equilibrium of the stage-one subgame. The sequential service constraint induces a negative externality, when all investors decide to withdraw their bank deposits at date 1. This is because investors who are far back in the queue may not get anything if the bank becomes insolvent. Thus, it is optimal for an investor to withdraw the investor’s bank deposits at date 1 if a sufﬁciently large number of investors decide to withdraw their bank deposits at date 1. Thus, bank run is a pure strategy Nash equilibrium of the stage-one subgame. These two pure strategy Nash equilibriums are subgame perfect Nash equilibriums.7 We analyze the pure strategy equilibriums of the stage-one subgame. According to Proposition 1, the amount of bank reserves is equal to the demand for liquidity by early consumers (a(1b)r ¼ ayc1). Thus, for any fraction fXy of investors who withdraw all their bank deposits at date 1, the demand for liquidity by the additional fraction (fy) of investors is supported by partial liquidation of the bank’s investment in the productive process. Let fXy to be the largest fraction of investors whose demand for liquidity can be supported by the bank’s assets. This means the bank’s bankruptcy condition is determined from the equation a(fy)r1 ¼ abvcar1. That is, the bank’s bankruptcy condition is given by fn ¼ y þ

bv c r1

(8)

For any fraction fXy of investors who withdraw all their bank deposits at date 1, the demand for liquidity a(fy)r1 is met by partial liquidation of the bank’s investment in the productive process. These funds are reinvested in the risk-free asset, yielding a return of a(fy)r1r at date 2. Using the relations a(fy)r1 ¼ abvacr1 and a(1b)r ¼ ayr1, we rewrite the resource

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constraint in the form: ð1 fÞar2 ðf; b xÞ ¼ abx þ ½að1 bÞr afr1 r ¼ ½ðf n yÞ ðf yÞ ar1 x=v ¼ ðf n fÞar1 x=v. Thus, increasing the fraction of investors who withdraw all their deposits at date 1 has the following effect on date 2 returns. By taking partial derivative of r2(f, b, x) with respect to f, we get @r2 ðf; b; xÞ ðf n 1Þr1 x ¼ @f vð1 fÞ2 If fo1, then date 2 returns are decreasing in f and the bank is susceptible to a run. In the following proposition, we show the existence of a socially desirable equilibrium and one that is socially undesirable. Proposition 3. Let f denote the fraction of investors who withdraw all their bank deposits at date 1. If the bank’s bankruptcy condition satisﬁes fo1, there are two pure strategy Nash equilibriums with the corresponding outcomes f ¼ y and 1. The equilibrium outcome f ¼ y is part of the socially desirable equilibrium. The equilibrium outcome f ¼ 1 is part of the bank run equilibrium. A proof of the Proposition 3 is provided in the appendix. If there is no uncertainty about the productive process, the bank implements the social optimum by offering investors the following demand deposit contract: the deposit return is equal to the per capital consumption (r1 ¼ c1) and the bank’s reserves are equal to the liquidity demand by early consumers (a(1b)r ¼ ayr1). Investors deposit all their funds in the bank, as in the Diamond and Dybvig (1983) model. Late consumers consume only the proceeds from the bank’s investment in the productive process. In the following result we construct necessary conditions if banks implement the social optimum. Corollary. Let (r1, b, a, d, c) denote a solution of the model. If the bank implements the social optimum through demand deposit contracts and an investor invests zero funds directly in the productive process (d ¼ 0), then we have the following results. The bank offers investors competitive deposit returns relative to the liquidation value (r14v) to attract funds from investors. The bank’s risky investment is the same as the social planner’s risky investment a ¼ ab car1 =v :

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An investor’s date 1 consumption is equal to the investor’s total return on bank deposits and on investment in the risk-free asset (c1 ¼ ar1+(1a)r). The total return on an investor’s investment in the risk-free asset is equal to the total return on the social optimum’s investment in the risk-free asset ðcar1 r þ ð1 aÞr2 ¼ ½ð1 aÞr yc1 rð1 yÞ1 Þ: The amount of bank deposits which an investor partially withdraws at date 1 and reinvests in the riskfree asset is zero (c ¼ 0). We express the solution (r1, b, a; c) of the model in terms of the social optimum (c1, a): a¼

ra þ yðc1 rÞ ð1 yÞr

b¼

ð1 yÞra ra þ yðc1 rÞ

r1 ¼

rðra þ ðc1 rÞÞ ra þ yðc1 rÞ c¼0

A proof of the corollary is provided in the appendix.

2.3. Policy Implications We now describe the policy implications of our model. Since required reserves on demand deposits earn zero explicit interest, we might consider required reserves to be a tax on demand deposits. Since membership in the Federal Reserve System is voluntary, we argue that required reserves may implicitly earn their opportunity cost through some bank operations and Federal government subsidies. If the minimum level of required reserves happens to be above a bank’s optimal level of reserves, there may be deadweight loss. Consequently, allowing banks to determine their optimal level of reserves helps to mitigate this loss.

3. CONCLUSION Bank reserves may mitigate inefﬁcient liquidation of a bank’s assets to meet the demand for liquidity by investors. Due to some transaction costs or information costs, investors may prefer bank intermediated investment to

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direct investment. Banks offer investors competitive deposit returns compared to the liquidation value of investment to attract funds from investors. In the social optimum, investment in the risk-free asset helps to meet the liquidity demand of investors and to provide investors with diversiﬁcation beneﬁts. If banks implement the social optimum, this may introduce additional fragility into the banking system. In the social optimum, our investors do not partially withdraw their bank deposits to reinvest in the funds in risk-free securities. Consistent with economic intuition, investors decrease the amount of bank deposits as their level of risk-aversion increases. We argue that required reserves might lead to deadweight loss if they are above a bank’s optimally determined reserves.

NOTES 1. If banks decrease their level of reserves, then this will increase the money supply through a multiplier effect. Consequently, the central bank might decrease the monetary base to keep the money supply and price levels steady. 2. The risky asset might be an index that is a proxy for a portfolio of several risky productive processes in the economy in which a bank may invest. 3. Depositors who seek to withdraw their funds will be served on a ﬁrst come, ﬁrst served basis, until funds have been exhausted (Bagehot, 1999). 4. Interesting examples include the action of voters on the outcome of an election and the action of investors on returns from investment by a bank or by a mutual fund. 5. If the bank reserves satisﬁed (1b)rofr1, the bank would replace the allocation (r1, b) with a new allocation (r1, b0 ), where (1b0 )r ¼ fr1. Since (rv)40, the inequality b0 ob is equivalent to ðr vÞab0 oðr vÞab: We rearrange the terms and get abv ðað1 b0 Þr að1 bÞrÞoab0 v: Substituting (1b0 )r ¼ fr1 into this inequality yields the following date 2 returns under the two strategies:

ð1 f Þar2 ðf 1 ; b; xÞ ¼ abx aðfr1 ð1 bÞrÞ

x y

x ¼ abx ðað1 b0 Þr að1 bÞr oab0 x y ¼ ð1 fÞar2 ðf; b; xÞ

6. If (1a)royc1, the bank would replace the allocation (c1, a) with a new allocation (c1, a0 ), where (1a0 )r ¼ yc1. The new allocation would increase per capita consumption at date 2 without changing per capita consumption at date 1. Since (rv)40, the inequality a0 oa is equivalent to (rv)a0 o(rv)a. We rearrange the terms and get a((1a0 )r(1a)r)v1oa0 . By substituting (1a0 )r ¼ yc1 into this

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inequality, we obtain the following date 2 consumption under the two strategies: ð1 yÞc2 ðy; xÞ ¼ ½a ðyc1 ð1 aÞrÞv1 x ¼ ½a ðð1 a0 Þr ð1 aÞrÞv1 xoa0 x ¼ ð1 yÞc02 ðy; xÞ 7. There are possible (unstable) mixed strategy Nash equilibriums but we do not analyze them because they do not have clear policy implications.

ACKNOWLEDGMENTS We acknowledge the contribution of Parames Laosinchai with whom we have lost contact. We thank Philip Dybvig, Lin Guo, David Humphrey, Jim Moser, Anthony Santomero, James Thomson, Xia Hong Yang, and participants at the Applied Business and Economics Research conference in Acapulco, Mexico, March 2003, for helpful discussions, comments, and suggestions. We are responsible for any errors.

REFERENCES Bagehot, W. (1999). Lombard Street: A description of the money market. New York, USA: Wiley. Bryant, J. (1980). A model of reserves, bank runs, and deposit insurance. Journal of Banking and Finance, 4, 335–344. Chang, R., & Velasco, A. (2000). Banks, debt maturity and ﬁnancial crises. Journal of International Economics, 51, 169–194. Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91, 401–419. Jacklin, C. J. (1987). Demand deposits, trading restrictions, and risk sharing. In: E. C. Prescott & N. Wallace (Eds), Contractual arrangements for inter-temporal trade. Minneapolis: University of Minnesota Press. Schmeidler, D. (1973). Equilibrium points of nonatomic games. Journal of Statistical Physics, 4, 295–300.

APPENDIX The appendix has two parts. The ﬁrst part contains proofs of our technical results. In the second part, we provide an example where a bank implements the social optimum. The values of numerical examples verify the main insights of our model.

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Proofs Proof of Proposition 1. The ﬁrst-order conditions associated with Problem 1 are ðð1 yÞc1 Þg1 ¼ qðavL þ ½ð1 aÞr yc1 rÞg1 þ ð1 qÞ ðavH þ ½ð1 aÞr yc1 rÞg1 qðr2 vL Þ ðavL þ ½ð1 aÞr yc1 ÞrÞg1 ¼ ð1 qÞ ðvH r2 Þ ðavH þ ½ð1 aÞr yc1 rÞg1 These ﬁrst-order conditions are equivalent to the following equations: yrð1 h1 Þ c1 þ ðh1 ðvH r2 Þ þ ðr2 vL ÞÞa ¼ ð1 h1 Þr2 ð1 yÞ ð1 h1 Þc1 ¼ h2 ðvH vL Þa where the parameters h1 and h2 are deﬁned as 1=ð1gÞ qðr2 vL Þ h1 ¼ ð1 qÞ ðvH r2 Þ h2 ¼

r 2 vL ð1 qÞ ðvH vL Þ

1=ð1gÞ

From these two equations we obtain the amount of risky investment and the date 1 per capita consumption. Proof of Lemma. We show that yc1p(1a)r holds with strict inequality. If yc1 ¼ (1a)r then risk-averse late consumers have zero funds invested in the risk-free asset. However, investment in the risky asset offers a lower return in the low state than investment in the risk-free asset. From portfolio theory risk-averse investors would diversify their investment to mitigate this potential loss from their investment. Thus, the aggregate consumption of early consumers satisﬁes yc1 oð1 aÞr We want to show that if date 1 per capita consumption satisﬁes c1pav+(1a)r, then it is not optimal by increasing date 1 per capita consumption without violating the feasibility condition. We take the derivative of the objective function with respect to the date 1 per capita

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consumption c1: @uðc1 Þ @uc2 ðy; vL Þ @uc2 ðy; vH Þ yr q þ ð1 qÞ y @c1 @c1 @c1

(A.1)

Since date 1 per capita consumption satisﬁes c1pav+(1a)r and the aggregate consumption of early consumers satisﬁes yc1oav+(1a)r, we get the following relations: c1 p

av þ ð1 aÞr yc1 avL þ ð1 aÞr yc1 pc2 ðy; vL Þ ¼ oc2 ðy; vH Þ 1y 1y avH þ ð1 aÞr yc1 ¼ 1y

But the utility function is increasing and concave in per capital consumption c1, which implies that its (derivative) marginal utility is decreasing. If rqp1 and r(1q)p1, then the derivative in (A.1) is positive. Thus, increasing the date 1 per capita consumption increases the value of the objective function. This implies that the per capita consumption c1pav+(1a)r cannot be optimal. Proof of Proposition 2. An investor invests the amount (1ad) in the risk-free asset to facilitate diversiﬁcation of this investor’s investment. We assume that the bank and this investor are playing the stage-one game. We assume that the stage-two game has already been played at date 1. Thus, this investor has already chosen the fraction c of bank deposits the investor withdraws at date 1. We show that the bank invests the fraction (1b) of deposits in the risk-free asset to meet the demand for liquidity by early consumers (a(1b)r ¼ ayr1). We suppose this investor makes the allocation (a, d; c) as a best response to the mutual bank’s strategy (r1, b) to maximize this investor’s expected utility. We suppose the bank reserves are below the demand for liquidity by early consumers (a(1b)roayr1). The bank can then replace the strategy (r1, b) with a new strategy (r1, b0 ), where (1b0 )r ¼ yr1, to increase this investor’s expected utility. The bank increases the fraction of bank reserves by increasing investment in the risk-free asset, while decreasing investment in the risky asset. We want to show that this investor’s expected utility is increased under the investor’s old strategy (a, d; c). Since (rv)40, the inequality b0 ob is equivalent to (rv)ab0 o(rv)ab. We rearrange the terms and get ab ½ð1 b0 Þr að1 bÞrv1 oab0 : By substituting ayr1 ¼ a(1b0 )r into this inequality, we obtain the following date 2 returns under the two

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strategies: c2 ðy; xÞ ¼ ð1 cÞar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 ab ðayr1 að1 bÞr þ car1 Þv1 þd x ¼ 1y þ car1 r þ ð1 a dÞr2 ab ½ð1 b0 Þr að1 bÞrv1 car1 v1 þd x ¼ 1y þ car1 r þ ð1 a dÞr2 0 ab car1 v1 þ d x þ car1 r þ ð1 a dÞr2 o 1y ¼ ð1 cÞar2 ðy; b0 ; xÞ þ dx þ car1 r þ ð1 a dÞr2 ¼ c02 ðy; xÞ Thus, we can increase this investor’s consumption at date 2 without changing the investor’s consumption at date 1. Therefore, the liquidity demand by early consumers satisﬁes yr1 pð1 bÞr

(A.2)

Next, we show that the amount of bank reserves is less than or equal to the demand for liquidity by early consumers (a(1b)rpayr1). Suppose a(1b)r4ayr1, then the bank can replace the strategy (r1, b) with a new strategy (r10 , b0 ), where a(1b0 )r ¼ ayr10 and r10 ¼ r10 (b, r1, y). We want to show that this investor’s expected utility is increased when this investor responds by choosing the new strategy (a0 , d; c), where a0 ¼ a0 (b, r1, y). First, we consider this investor’s consumption at date 2. We write the corresponding arguments of the utility function as functions of x. More speciﬁcally, we write c2 ðy; xÞ ¼ ð1 cÞar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 aðb cr1 v1 Þ þ d x þ a½ð1 bÞr yr1 r þ car1 r þ ð1 a dÞr2 ¼ 1y c02 ðy; xÞ ¼ ð1 cÞa0 r01 ðy; b0 ; xÞ þ d 0 x þ ca0 r01 r þ ð1 a0 d 0 Þr2 0 a ð1 yr01 cr01 v1 Þ þ d x þ ca0 r01 r þ ð1 a0 dÞr2 ¼ 1y Notice that we have substituted b0 ¼ 1yr10 into c20 (y, x) above. The functions c2(y, x) and c20 (y, x) deﬁne lines in (c2, x) space.

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We compare the slopes and intercepts of these lines. Equating the slopes of these lines yields aðb cr1 v1 Þ a0 ð1 yr01 cr01 v1 Þ þd ¼ þd 1y 1y We write a0 in terms of the other parameters: a0 ¼

aðvb cr1 Þ v r01 ðyv þ cÞ

By comparing the constant terms of these lines, we get the inequality ½að1 bÞr ayr1 r þ car1 r þ ð1 a dÞr2 oca0 r01 r þ ð1 a0 dÞr2 : Substituting the value of a0 into this inequality yields ½að1 bÞr ayr1 þ car1 ar ¼ a½cr1 ðyr1 þ bÞoa0 ðcr01 rÞ aðvb cr1 Þ ðr cr01 Þ ¼ r01 ðyv þ cÞ v Thus, we get the inequality r01 4

cr1 ðr vÞ þ vðyr1 bðr 1ÞÞ ðb þ yr1 Þðyv þ cð1 vÞÞ

(A.3)

We next consider this investor’s consumption at date 1. We impose the condition that consumption under the new strategy is greater than consumption under the old strategy. That is, we have a0 r01 þ ð1 a0 Þr4ar1 þ ð1 aÞr: Substituting a0 ¼ aðvb cr1 Þ=v r01 ðyv þ cÞ into this relation yields the inequality aðvb cr1 Þ ðr01 rÞ=v r01 ðyv þ cÞ4aðr1 rÞ: Thus, we get the inequality r01 4

rðvb cr1 Þ þ ðr1 rÞv ðvb cr1 Þ þ ðr1 rÞ ðyv þ cÞ

(A.4)

From the inequalities in (A.3) and (A.4) we obtain the inequality

cr1 ðr vÞ þ vðyr1 b ðr 1ÞÞ rðvb cr1 Þ þ ðr1 rÞv 0 ; r1 4Max ðb yr1 Þ ðyv þ cð1 vÞÞ ðvb cr1 Þ þ ðr1 rÞ ðyv cÞ (A.5) We have shown that the strategy of choosing the amount of reserves on bank deposits equal to the liquidity demand by early consumers dominates other choices of the amount of bank reserves. Thus, we have ð1 bÞrpyr1

(A.6)

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From (A.2) and (A.6) we conclude that the bank reserves are equal to the demand for liquidity by early consumers ((1b)r ¼ yr1). Next, we show that this investor invests nothing directly in the productive. Given the strategy (a, d; c), which is this investor’s best response to the bank’s choice of (r1, b), we want to show that the bank can change the choice of the deposit return to induce this investor to invest nothing directly in the productive process. We argue that given the strategies (a, d; c) and (r1, b), the bank and this investor can replace these strategies with the new strategies (a0 , d0 ; c) and (r10 , b), where a0 ¼ a+d, d0 ¼ 0, and r10 ¼ r10 (a, d, r1) in order to increase this investor’s expected utility. First, we consider this investor’s consumption at date 2. We write the corresponding arguments of the utility function under the two investment strategies as follows: c2 ðy; xÞ ¼ ð1 cÞar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 ðað1 yr1 Þ car1 v1 Þ þ d x þ car1 r þ ð1 a dÞr2 ¼ 1y c02 ðy; xÞ ¼ ð1 cÞa0 r02 ðy; b0 ; xÞ þ d 0 x þ ca0 r01 r þ ð1 a0 d 0 Þr2 ða þ dÞ ð1 yr01 Þ car01 v1 Þ ¼ x þ cða þ dÞr01 r þ ð1 a dÞr2 1y The functions c2(y, x) and c20 (y, x) deﬁne lines in (c2,x) space. We compare their slopes and intercepts. By comparing their slopes, we get ðað1 yr1 Þ car1 v1 Þ ða þ dÞ ð1 yr01 Þ car01 v1 þ do 1y 1y Thus, we get the inequality r01 o

ðyv þ cÞar1 þ yvd yða þ dÞv þ ca

By comparing the intercepts of these lines, we get car1 rocða þ dÞr01 r: We get the inequality r01 4

ar1 aþd

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STEPHEN A. KANE AND MARK L. MUZERE

Putting these inequalities together we get ar1 ðyv þ cÞar1 þ yvd or01 o yða þ dÞv þ ca aþd

(A.7)

Next, we consider this investor’s consumption at date 1. We want to show that ar1 þ vd þ ð1 a dÞroa0 r01 þ vd 0 þ ð1 a0 d 0 Þr: By substituting a0 ¼ a+d and d0 ¼ 0 into this inequality, we get r01 4

ar1 þ vd aþd

Putting the relations in (A.7) and (A.8) together, we get

ar1 þ vd ar1 ðyv þ cÞar1 þ yvd Max ; or01 o aþd aþd yða þ dÞv þ ca

(A.8)

(A.9)

The correct choice of r10 satisﬁes both conditions (A.5) and (A.9). That is,

ar1 þ vd ar1 ; Max or01 aþd aþd 9 8 ðyv þ cÞar1 þ yvd cr1 ðr vÞ þ vðyr1 bðr 1ÞÞ > > > ; ;> > > = < yða þ dÞv þ ca ðb þ yr1 Þ ðyv þ cð1 vÞÞ oMax > > rðvb cr1 Þ þ ðr1 rÞv > > > > ; : ðvb cr1 Þ þ ðr1 rÞ ðyv þ cÞ This means that the bank and this investor can replace the strategies (a, d, r1) with the strategies (a0 , d0 , r10 ), where a0 ¼ a+d and d0 ¼ 0, to increase this investor’s expected utility. We set the amount of wealth this investor invests directly in the risky asset to zero (d ¼ 0) as shown above. From the ﬁrst-order conditions associated with Problem 3, we obtain the amount of wealth this investor deposits in the bank (a40) and the fraction of deposits this investor withdraws at date 1. Proof of Proposition 3. We focus on the behavior of late consumers since early consumers consume at date 1. This is to simply the algebra, because in a bank run early consumers who are way back in the queue may lose their bank deposits if the bank’s assets are totally liquidated to meet the liquidity demand by depositors who are ahead in the queue. When late consumers withdraw all their bank deposits early, they reinvest these funds in the risk-free asset. For example, if an

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investor withdraws the amount a, this investor gets the amount ar1 because the bank offers investors an interest rate on their deposits. This investor reinvests the amount ar1 in the risk-free asset, yielding a date 2 return of, ar1r, where r is the gross return on investment in the riskfree asset. This means this investor consumes the amount ar1r+(1a)r2 at date 2. If the bankruptcy condition satisﬁes f ¼ 1, then the date 2 returns ar2 (f, b, x) are nondecreasing in the fraction f. This implies that late consumers do not have any incentive to withdraw all their bank deposits at date 1. Thus, we get a pure strategy equilibrium with the outcome given by f ¼ y. If fo1, then the date 2 returns ar2(f, b, x) are decreasing in the fraction f. This scenario includes a bank run. There are two cases to consider if the bankruptcy condition satisﬁes fo1. In the ﬁrst case, the proportion of investors who withdraw all their bank deposits early is less than the bankruptcy condition. (fof). By the incentive compatibility constraint, a late consumer has no incentive to withdraw this consumer’s bank deposits early. In the second case, the proportion of consumers who withdraw all their bank deposits early is equal to or greater than the bankruptcy condition (fXf). Since the productive process is totally liquidated to meet the liquidity demand, the date 2 returns on investment in the productive process will be zero. The sequential service constraint imposes a negative externality on depositors, who want to withdraw their bank deposits early but are far behind in the queue, because they may get nothing from their bank deposits. Thus, it is optimal for a depositor to withdraw all the depositor’s bank deposits early if this depositor believes that a sufﬁciently large number of depositors will withdraw all their bank deposits early. We now formalize the above intuition by the following algebraic arguments. If a depositor withdraws all this depositor’s bank deposits at date 1, this depositor’s expected utility is uðar1 r þ ð1 aÞr2 Þ if fof n n f fn uðar1 r þ ð1 aÞr2 Þ þ 1 uðð1 aÞr2 Þ if fXf n f f

(A.10)

where (f/f) denotes the fraction of depositors who get all their bank deposits and (1f/f) denotes the fraction of depositors who get nothing from their bank deposits. Depositors who get nothing from their bank deposits consume only the proceeds from their investment in the risk-free asset.

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If a depositor performs only partial withdrawal of this depositor’s bank deposits at date 1, this depositor’s expected utility is E½uðð1 cÞar2 ðf; b; xÞ þ car1 r þ ð1 aÞr2 Þ if fof n n f fn 2 uðcar1 r þ ð1 aÞr Þ þ 1 uðð1 aÞr2 Þ if fXf n f f

(A.11)

where (f/f) and (1f/f) are as deﬁned in (A.10). The date 2 returns r2(f, b, x) are deﬁned as ð1 fÞð1 cÞar2 ðf; b; xÞ ¼ ðab car1 v1 Þx þ ½að1 bÞr afr1 r If the fraction of investors who withdraw their bank deposits early satisﬁes, fXf, then some late consumers consume only from their investment in the risk-free asset. We seek to only prove the existence of pure strategy equilibriums, since they have clear policy implications, while mixed strategy equilibriums do not. One of the pure strategy equilibriums is a socially desirable equilibrium, where there is no run on a bank. The other pure strategy equilibrium is a socially undesirable equilibrium, where depositors run on a bank. If fof n ; then we see from (A.10) and (A.11) that uðar1 r þ ð1 aÞr2 ÞoE½uðð1 cÞar2 ðf; b; xÞ þ car1 r þ ð1 aÞr2 Þ That is, the incentive compatibility condition implies that late consumers have no incentive to pretend to be early consumers. This means the fraction f ¼ y of depositors who withdraw all their bank deposits is an equilibrium outcome. If fXf n ; then it is optimal for a depositor to withdraw all of this depositor’s bank deposits early. Indeed, from (A.10) and (A.11) we get n f fn 2 uðcar1 r þ ð1 aÞr Þ þ 1 uðð1 aÞr2 Þ f f n f fn 2 o uðar1 r þ ð1 aÞr Þ þ 1 uðð1 aÞr2 Þ f f where (f/f) and (1f/f) are as deﬁned in (A.10). This means that the fraction f ¼ 1 of depositors who withdraw all their funds at date 1 is an equilibrium outcome. Proof of Corollary. We recall the following information from Proposition 1. The funds an investor invests directly in the risky asset is zero. The bank’s

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reserves are equal to the demand for liquidity by early consumers. We write these statements as d¼0 að1 bÞr ¼ ayr1

(A.12)

If the bank implements the social optimum, then the arguments of the utility functions in the social optimum problem and in the bank’s problem are equal. That is, we compare consumption at date 2 and consumption at date 1 under the two problems. First, we consider consumption at date 2. In Problem 1, the date 2 per capita consumption is c2 ðy; xÞ ¼ ½ax þ ðð1 aÞr yc1 Þr ð1 yÞ1

(A.13)

Applying the results in (A.12) to the date 2 per capita consumption in Problem 3 yields ð1 cÞar2 ðy; b; xÞ þ dx þ car1 r þ ð1 a dÞr2 ¼ ½ðab car1 v1 Þð1 yÞ1 þ dx þ ½að1 bÞr ayr1 rð1 yÞ1 þ car1 r þ ð1 a dÞr2 ¼ ½ðab car1 v1 Þð1 yÞ1 x þ car1 r þ ð1 aÞr2

ðA:14Þ

By equating the components of risky investment in (A.13) and (A.14), we get a ¼ ab car1 v1

(A.15)

By equating the components of the risk-free investment in (A.13) and (A.14), we get ½ð1 aÞr yc1 rð1 yÞ1 ¼ car1 r þ ð1 aÞr2

(A.16)

Second, we consider consumption at date 1. We set an investor’s date 1 consumption equal to the liquidation value of the investor’s investment. Thus, we have c1 ¼ ar1 þ ð1 aÞr (A.17) We proceed to express the variables (r1, b, a, c) in terms of the social optimum (c1, a). By substituting Eq. (A.15) into equation (A.16), we obtain the equation ð1 aÞr yc1 ¼ ð1 yÞ½ðvba vaÞ þ ð1 aÞr: We rearrange this relation into the form ð1 yÞðr vbÞa ¼ ðr ð1 yÞvÞa þ yðc1 rÞ (A.18)

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By substituting Eq. (A.17) into Eq. (A.18), we get ð1 yÞ ðr vbÞ ðc1 rÞ= r1 r ¼ ðr ð1 yÞvÞa þ yðc1 rÞ: We rearrange this relation into the form ð1 yÞðr vbÞðc1 rÞ ¼ ðr1 rÞ½ðr ð1 yÞvÞa þ yðc1 rÞ

(A.19)

Substituting Eq. (A.12) into equation (A.19) yields yð1 yÞðr vbÞðc1 rÞ ¼ ð1 b yÞ r½ðr ð1 yÞvÞa þ yðc1 rÞ

(A.20)

We solve Eq. (A.20) to determine the bank’s risky investment. This equation yields b ¼ ð1 yÞra=ra þ yðc1 rÞ: We substitute this value of b into Eq. (A.12) to determine the deposit return. We have 1 b ¼ yðra þ ðc1 rÞÞ=ra þ yðc1 rÞ: Thus, we get r1 ¼ rðra þ ðc1 rÞÞ=ra þ yðc1 rÞ: From Eq. (A.17) we get the investor’s bank deposits. By substituting the relation r1 r ¼ ð1 yÞrðc1 rÞ=ra þ yðc1 rÞ into the equation a ¼ c1 r=r1 r; we get a ¼ ra þ y ðc1 rÞ=ð1 yÞr: We determine the partial withdrawals from Eq. (A.15). We get car1 ¼ vðab aÞ ¼ 0: Thus, c ¼ 0, since ar1 is not zero. We have expressed the solution of the model in terms of the social optimum.

0.8 0.6 0.4 0.2

aggregate consumption

per capita consumption

1

0.5

1 1.5 risk aversion

1 0.8 0.6 0.4 0.2 0

0.5

1 1.5 risk aversion

1.2 1 0.8 0.6 0.4

2

aggregate consumption

per capita consumption

1.2

2

0.5

1 1.5 risk aversion

2

0.5

1 1.5 risk aversion

2

1 0.8 0.6 0.4 0.2 0

Fig. A1. Plots of Consumption. The parameters are y ¼ 0.25, q ¼ 0.45, vL ¼ 0.20 and vH ¼ 3.25. In the Left Diagrams r ¼ 1 and in the Right Diagrams r ¼ 1.08.

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Example We assume that an investor’s preferences are represented by a constant coefﬁcient of relative risk aversion utility function of the form uðwÞ ¼ wg =g; where go1 and g6¼0. The solution (a, b, r1, c) of the model, which implements the social optimum (a, c1) obtained in Proposition 1 is as given in Proposition 3. We assume that the liquidation value is equal to the return on investment in the low state (v ¼ vL). In the top diagrams, we illustrate the fragility concerns in our model when banks implement the social optimum. That is, the date 1 per capita consumption is greater than the liquidation value of the economy’s assets. As the degree of risk aversion increases, early consumers increase their consumption which is given by the upper curve. Consequently, there is corresponding increase in the liquidation value of the economy’s assets which is given by the lower curve (see Fig. A1). 1 risky investment

risky investment

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Fig. A2. Plots of Risky Investment in the Social Optimum and Bank Deposits. The Parameters are y ¼ 0.25, q ¼ 0.45, vL ¼ 0.20, and and vH ¼ 3.25. In the Left Diagrams r ¼ 1 and in the Right Diagrams r ¼ 1.08.

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In the bottom diagrams, as the degree of risk aversion increases, the consumption of early consumers which is given by the lower curve increases. The corresponding funds invested in the risk-free asset which is given by the upper curve increases to meet this increased consumption. The difference between these curves describes the amount of investment in the risk-free asset, which facilitates diversiﬁcation of investment by late consumers. In the top diagrams, as the degree of risk aversion increases, investors tend to reduce the funds they allocate to risky assets. Consequently, the bank reduces the funds it invests in the productive process (see Fig. A2). In the bottom diagrams, as the degree of risk aversion increases, investors tend to reduce the funds they allocate to risky assets. Consequently, they reduced the funds they deposit with the bank because the bank’s portfolio consists of funds invested in the productive process and in the risk-free asset. In the top diagrams, as the degree of risk aversion increases, investors tend to reduce the funds they allocate to risky assets. Consequently, the

0.85 risky investment

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1.4 deposit return

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Fig. A3. Plots of the Bank’s Risky Investment and Deposit Returns. The Parameters are y ¼ 0.25, q ¼ 0.45, vL ¼ 0.20, and vH ¼ 3.25. In the Left Diagrams r ¼ 1 and in the right diagrams r ¼ 1.08.

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0.8 0.6 0.4 0.2

per capita consumption

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bank reduces the fraction of funds invested in the productive process (see Fig. A3). In the bottom diagrams, as the degree of risk aversion increases, investors tend to reduce the funds they allocate to risky assets. Since investors decrease the funds investors deposit with the bank, the bank increases the deposit return it offers investors in order to attract funds. We notice that if the coefﬁcient of relative risk aversion is less than one, the gross return on bank deposits is less than one. This means that there is a wealth transfer from early consumers to late consumers. If the coefﬁcient of relative risk aversion is greater than one, the gross return on bank deposits is greater than one because the amount of liquidity demanded by these investors is high. In Fig. A4 we illustrate the fragility concerns in our basic model when banks implement the social optimum. That is, the date 1 per capita consumption is greater than the liquidation value of the economy’s assets.

1 0.9 0.8 0.7

0

0.2 0.4 0.6 early consumers

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Fig. A4. Plots of Consumption. The Parameters are q ¼ 0.45, vL ¼ 0.20, and vH ¼ 3.25. In the Left Diagrams r ¼ 1 and in the Right Diagrams r ¼ 1.08. In the top diagrams 1g ¼ 0.65 and in the Bottom Diagrams 1g ¼ 1.55.

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0.8

risky investment, bank deposits

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risky investment, bank deposits

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In the top diagrams, when the degree of risk aversion is low, the date 1 per capita consumption is less than one, but increases as the proportion of early consumers is increased. In the left bottom diagram, as the proportion of early consumers increases, the date 1 per capita consumption is decreased because investors put a higher weight on early consumption. In the right bottom diagram, as the proportion of early consumers increases, the date 1 per capita consumption is increased because the deposit return is increased. In the top diagrams, as the proportion of early consumer’s increases, the bank decreases the amount of risky investment and the investors decrease the funds they deposit with the bank. When the gross return on investment in the risk-free asset is greater than one, investors increase their bank deposits after a certain fraction of early consumers. This is because the corresponding deposit return is increasing (see Fig. A5).

1 0.8 0.6 0.4 0.2 0

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Fig. A5. Plots of Risky Investment in the Social Optimum and Bank Deposits. The Parameters are q ¼ 0.45, vL ¼ 0.25, and vH ¼ 3.25. In the Left Diagrams r ¼ 1 and in the Right Diagrams r ¼ 1.08. In the Top Diagrams 1g ¼ 0.65 and in the Bottom Diagrams 1g ¼ 1.55.

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1

1

0.8

0.8

risky investment

risky investment

In the bottom diagrams, as the proportion of early consumers increases, investors put more weight on early consumption. Thus, investors increase the funds they deposit in the bank in order to beneﬁt from the deposit returns, which are higher than the gross returns on investment in the riskfree asset. The bank reduces investment in the risky asset and increases the funds it invests in the risk-free asset in order to meet the liquidity demand by the early consumers. In the top diagrams, as the proportion of early consumers increases, investors put more weight on early consumption. Consequently, the bank decreases the funds it invests in the productive process and increases the funds it invests in the risk-free asset. The lower curves are for a high degree of risk aversion and the upper curves are for a low degree of risk aversion (see Fig. A6).

0.6 0.4 0.2 0

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1

2

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deposit return

deposit return

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1.5

1 0

0.2 0.4 0.6 early consumers

0.8

0.8

Fig. A6. Plots of the Bank’s Risky Investment and Deposit Returns. The Parameters are q ¼ 0.45, vL ¼ 0.20 and vH ¼ 3.25. In the Left Diagrams r ¼ 1 and in the Right Diagrams r ¼ 1.08. In the Top Diagrams 1g ¼ 1.55 for the Lower Curves and 1g ¼ 0.65 for the Upper Curves. In the Bottom Diagrams 1g ¼ 0.65 for the Lower Curves and 1g ¼ 1.55 for the Upper Curves.

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In the top diagrams, as the proportion of early consumers increases, investors put more weight on early consumption. Consequently, the bank increases the deposit return for investors with a low degree of risk aversion and increases the deposit return for investors with a high degree of risk aversion. The bank now transfers wealth from investors with high degree of risk aversion to investors with a low degree of risk aversion. When the gross return on investment in the risk-free asset is greater than one, the bank offers investors deposit returns, which is competitive relative to the gross return on investment in the risk-free asset in order to attract funds from investors. In the top diagrams, as the liquidation value is increased, the bank increases investment in the productive process. The lower curves are for a high degree of risk aversion and the upper curves are for a low degree of risk aversion (see Fig. A7).

risky investment

0.8 0.6 0.4 0.2 0

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1

bank deposits

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1

0.5

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0

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0

Fig. A7. Plots of the Bank’s Risky Investment and Bank Deposits. The Parameters are y ¼ 0.25, q ¼ 0.45, and vH ¼ 3.25. In the Left Diagrams r ¼ 1 and in the Right Diagrams r ¼ 1.08. In all the diagrams 1g ¼ 1.55 for the Lower Curves and 1g ¼ 0.65 for the Upper Curves.

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1

1

0.8

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risky investment

risky investment

In the bottom diagrams, as the liquidation value is increased, investors increase the funds they deposit with the bank. This is because the bank offers investors competitive deposit returns compared to the liquidation value. The lower curves are for a high degree of risk aversion and the upper curves are for a low degree of risk aversion. In the left top diagram, as the liquidation value is increased, the bank increases the level of risky investment and later decreases it if the degree of risk aversion is low. If the degree of risk aversion is high, the bank decreases the level of risky investment (see Fig. A8). In the left bottom diagram, as the liquidation value is increased, the bank decreases the deposit return and later increases it if the degree of risk aversion is low. When the degree of risk aversion is high the bank increases the deposit return. In the right bottom, as the liquidation value is increased,

0.6 0.4 0.2 0

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Fig. A8. Plots of the Bank’s Risky Investment and Deposit Returns. The Parameters are y ¼ 0.25, q ¼ 0.45, and vH ¼ 3.25. In Left Diagrams r ¼ 1 and in the Right Diagrams r ¼ 1.08. In the Top Diagrams 1g ¼ 1.55 for the Lower Curves and 1g ¼ 0.65 for Upper Curves. In the Bottom Diagrams 1g ¼ 0.65 for the Lower Curves and 1g ¼ 1.55 for the Upper Curves.

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bank deposits

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1 0.6 0.4 0.2 0

1

1.05 gross return

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1.05 gross return

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1.05 gross return

1.1

1.4 deposit return

risky investment

0.9

0.8

0.7

1.2 1 0.8

0.6

1

1.05 gross return

1.1

Fig. A9. Plots of the Investment in the Social Optimum, Bank Deposits, the Bank’s Risky Investment, and Deposit Returns. The Parameters are y ¼ 0.25, q ¼ 0.45, vL ¼ 0.25 and vH ¼ 3.25. In all the Diagrams the Coefﬁcient of Relative Risk Aversion is 1g ¼ 0.65 for the Lower Curve and 1g ¼ 1.55 for the upper curve.

the bank decreases the deposit return when the degree of risk aversion is high and increases the deposit return when the degree of risk aversion low. As the gross return on investment in the risk-free asset is increased, the bank decreases the funds it invests in the productive process. Investors similarly decrease the funds they deposit with the bank and increase the funds they invest in the risk-free asset. The lower curve is for high degree of risk aversion and the upper curve is for low degree of risk aversion. The bank decreases the fraction of deposits it invests in the productive process and increases the fraction of bank reserves. The lower curve is for a high degree of risk aversion and the upper curve is for a low degree of risk aversion. Since investors decrease the funds they deposit with the bank, the bank increases the deposit return it offers investors to attract funds. The lower curve is for a low degree of risk aversion and the upper is for a high degree of risk aversion (see Fig. A9).

AN INVESTIGATION OF THE MID-LOAN RELATIONSHIP BETWEEN BANK LENDERS AND BORROWERS Aron A. Gottesman and Gordon S. Roberts ABSTRACT We investigate the nature of mid-loan relationships between bank-lenders and borrowers, to test whether firms borrow from banks to signal quality. Using the LPC DealScan, CRSP, and Wall Street Journal databases, we test whether borrower abnormal returns are related to bank, borrower, deal, and/or event characteristics during the duration of the loan. We demonstrate that borrower abnormal returns are related to mid-loan bank events, defined as an event resulting in bank abnormal returns beyond a specified threshold. The results suggest that borrowers are affected by bank events mid-loan, even when the event is not directly related to bank default.

1. INTRODUCTION There is a large theoretical literature about how and why bank relationships matter (Diamond, 1991; Rajan, 1992, among others) and an even larger Research in Finance, Volume 22, 273–303 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22010-5

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body of empirical work attempting to verify these effects. Two important lines of research explore the impact of bank mergers (Sapienza, 2002; Berger et al., 1998) and bank distress (Slovin, Sushka, & Polonchek, 1993; Baea, Kang, & Limd, 2002 among others). Within the second line of research, a growing number of theoretical and empirical papers argue that lender quality is relevant. Drawing on earlier research, which demonstrates that loan announcement reaction differs on the basis of lender type, the theoretical literature includes a number of hypotheses as to why lender quality matters:1 (i) Merton (1993) argues that since loan relationships are costly to establish, the value of the relationship is a function of the quality of the lender. A higher quality lender is more likely to remain in existence for the long term, and hence the expected value of the relationship is greater. (ii) Lender quality may be a proxy for monitoring effectiveness. Billet, Flannery, and Garﬁnkel (1995) note that both Chemmanur and Fulghieri (1994) and Diamond (1984) argue that a bank’s reputation depends on its ability to choose and monitor borrowers effectively. Hence, a higher quality lender is simply a lender with better monitoring capabilities, and, therefore, the loan announcement effect on borrowers should be an increasing function of the perceived quality of the lender. (iii) Billet et al. (1995) hold that theoretical models of reputational equilibrium can be applied to the lender–borrower relationship.2 A lender develops a reputation as ‘‘high quality’’ through lending to only a specific risk class, and through providing accurate information to the market about borrower quality. Hence, through borrowing from a high-quality lender, the borrower signals its desire to send a credible signal, implying that the borrower privately believes it is of high quality. The nature of the lender–borrower relationship is of particular interest, as competitive pressures in the structure of the ﬁnancial services industry are changing the nature of the relationship between banks and borrowers. As Boot and Thakor (2000) suggest, this raises questions as to whether ‘‘relationship banking’’ will be replaced with ‘‘transaction banking.’’ Boot and Thakor deﬁne relationship banking as an environment where ‘‘banks invest in building relationships with borrowers’’ and transaction banking as an environment where banks engage in arm’s-length transactions. They argue that greater competition will lead to increased emphasis on relationship loans, but with less ‘‘added value’’ for borrowers. A number of studies examine the inﬂuence of lender quality on borrowers.3 These studies, which are reviewed in the next section, either test

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whether the quality of private lenders inﬂuences borrower abnormal return upon loan announcement, or study the inﬂuence of mid-loan bank events on borrowers. They typically look at events that threaten bank existence. For example, the seminal paper by Slovin et al. (1993) examines a single, negative, extreme, bank event (the de facto failure and subsequent Federal Deposit Insurance Corporation (FDIC) rescue of the Continental Illinois Bank). To make an analogy from the life insurance literature, prior studies address the impact of bank-lender ‘‘mortality’’ on borrowers. Studies ﬁnd evidence suggesting that borrowers are sensitive to potential bank failure. In this paper, we extend this previous literature exploring whether the borrower is sensitive to less dramatic bank events. In this sense, we examine lender ‘‘morbidity,’’ investigating whether borrower abnormal returns are related to bank, borrower, deal, and/or event characteristics during the duration of the loan. Our study differs from earlier ones in a number of important ways that permit it to determine how bank morbidity impacts borrowers. First, we do not exclusively consider situations where the bank is in distress. Instead, we examine more general changes in market perceptions of the bank. Second, we separately test the impacts of both positive and negative bank events on borrowers, to determine if borrower reaction is different for each sub-sample. Earlier evidence that bank relationships are costly to replace is limited as it fails to consider positive events as well. Note that both positive and negative bank events impact the continuation and nature of the bank– borrower relationship. Hence, investors’ revise their prior beliefs following both types of events. To illustrate, consider the perspective of Merton (1993), which states that since loan relationships are costly to establish, the value of the relationship is a function of the quality of the lender. If a negative event occurs, then investors revise their prior beliefs regarding the likelihood of the continuation of the valuable relationship downward, and lower their valuation of the borrower correspondingly. If a positive event occurs, prior beliefs regarding the likelihood of the continuation of the relationship are revised upward, resulting in higher borrower valuation. Third, our mid-loan sample is much larger than in previous studies. Through linking the Loan Pricing Corporation DealScan (LPC), Center for Research in Security Prices (CRSP), and Wall Street Journal (WSJ) databases, we are able to develop a much richer and more informative data set than earlier studies typically based on single cases, or rare events such as a banking system collapse. The empirical tests performed in this study demonstrate that borrower abnormal returns are related to mid-loan bank events, deﬁned as an event

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resulting in bank abnormal returns beyond a speciﬁed threshold.4 However, these results differ for positive and negative bank events. First, for positive bank events, we ﬁnd there is a positive relationship between borrower abnormal return and both borrower standard deviation and borrower size. High-risk borrowers, who value bank reputation for monitoring effectiveness more highly, are more sensitive to mid-loan bank events. Second, the relationship is stronger for regional banks. For negative bank events, we ﬁrst ﬁnd that borrower abnormal return is positively related to both bank abnormal returns and bank standard deviation. The positive relationship with bank abnormal returns conﬁrms borrower sensitivity to mid-loan bank events. The positive relationship with bank standard deviation for negative bank events suggests that borrowers are less sensitive to mid-loan events for higher risk lenders, suggesting the reputational signal associated with lower risk banks is stronger. Second, the relationship is stronger for money-center banks. One interpretation is that the bank–borrower relationship is only valuable for money-center banks. Alternatively, noting evidence that money-center banks are riskier than regional banks, the riskier nature of money-center banks could indicate higher probability of failure, resulting in the borrower return reaction. Because our initial sample uses a threshold technique to identify events, it does not identify specific bank events, unlike earlier studies such as Slovin et al. (1993) and Baea et al. (2002), among others. Hence, one concern is that any borrower abnormal return we identify may not be due to bank events, but are instead due to external factors that inﬂuence both borrower and bank returns, and are not specific to the dates identiﬁed using the threshold methodology. As conﬁrmation of the validity of the threshold technique, we searched the WSJ for bank-specific announcements on each of the postinitiation dates for which abnormal returns crossed the threshold. We repeat the tests for the events identiﬁed in the WSJ for money-center banks exclusively, as the WSJ sub-sample is comparable to the non-WSJ sub-sample for money-center banks but not for regional banks. Results for the WSJ sample are generally similar to the results for the non-WSJ sample, with minor differences. Specifically, for negative money-center events in the WSJ sub-sample we identify a relationship between borrower abnormal returns and bank abnormal returns. In the non-WSJ sub-sample, we identify a relationship between borrower abnormal returns and bank standard deviation. Another concern is that any relationship we identify between borrower abnormal return and borrower standard deviation may suggest that company-specific risk is relevant for asset pricing. If so, we should ﬁnd a universal relationship between borrower abnormal return and borrower

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standard deviation. Our results indicate that such a relationship applies exclusively for the positive regional sub-sample. This suggests that companyspecific risk is not relevant for asset pricing. The rest of this study is organized as follows. Section 2 reviews prior empirical evidence. Section 3 discusses empirical implications. Section 4 describes the data extraction, while Section 5 details the methodology and results. In Section 6, we offer conclusions.

2. PRIOR EVIDENCE Billet et al. (1995) test whether the credit quality of private lenders matters by examining the effect of lender characteristics on borrower abnormal equity return upon loan announcements. They ﬁnd that, while borrower returns associated with bank or non-bank private loans are indistinguishable, in general, borrower abnormal return increases with lender credit quality. Beyond loan announcements, a related strain of literature examines bank ﬁnancial distress to provide further evidence that the relationship with the bank is valuable to the borrower.5 Examining the de facto failure (and subsequent FDIC rescue) of (the money-center) Continental Illinois Bank, Slovin et al. (1993) provide evidence that borrowers incurred average excess returns of 4.2% during the impending insolvency, and 2% following the rescue announcement. Kang and Stulz (1997) ﬁnd that Japanese borrowers experience difﬁculties when major banks undergo ﬁnancial distress. Baea et al. (2002) ﬁnd that adverse shocks to Korean banks during 1997–1998 negatively affected the value of borrowers. They also ﬁnd that the adverse effect is a decreasing function of the ﬁnancial health of both bank and borrower.6 In all of these cases, the probability increases drastically that bank relationships will fall apart. Further, Slovin et al. (1993) is based on a specific dramatic event, occurring in 1984, to a large money-center bank under a specific regulatory regime. Ongena, Smith, and Michalsen (1999) study the Norwegian banking system during a period of distress when the banking system was near collapse. They ﬁnd that, while banks experienced permanent value loss following the distress, borrowers in relationships with the banks experienced small, temporary value loss. Ongena et al. (1999) suggest that the market anticipation of government bailout limited the impact on borrowers. Turning to cases in which banks failed and closed their doors, Bernanke (1983) provides evidence that bank failures and loss of bank relationships may have contributed to the Great Depression. Djankov, Jindra, and

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Lapper (2000) study the valuation effect of East Asian bank insolvency on related industrial borrowers. They discover a relationship between borrower market value and bank closure announcements. Announcement of bank nationalization leads to positive abnormal returns. Announcement of foreign sales leads to initial negative abnormal returns followed by longer-term market premiums. Domestic mergers have no effect on related borrowers.7 In summary, prior work has established the importance of lender quality drawing on a range of different data sets encompassing both normal times and ﬁnancial crises.

3. EMPIRICAL IMPLICATIONS The identiﬁcation of a relationship between borrower and lender mid-loan, even for events that are not expected to lead to default immediately, strengthens the argument that the bank relationship is important for borrowers. The most obvious mid-loan relationship we can test for is a positive relationship between borrower and bank abnormal returns for dates on which the bank experiences an event. Further, if borrower abnormal return on bank event dates is a function of proxies for the importance of the bank relationship for the borrower, this constitutes evidence of a mid-loan relationship. We expect the magnitude of the relationship to be a function of the depth of commitment on the part of the bank.8 Bank commitment can be measured by the degree to which the bank participates in the deal, as well as the deal life and size. When is a bank relationship more or less important to a borrower? To answer this question, we review issues that must be considered when investigating the nature of the relationship. Does the event change the probability of bank failure? We begin by distinguishing between events that directly change the probability of bank failure and those that do not. This distinction manifests itself in two ways. First, in light of the ‘‘too big to fail’’ doctrine, we would expect different reactions to lender quality change, dependent on whether the lender is ‘‘too big to fail’’ or not. Larger banks, proxied by market capitalization, are more likely to be ‘‘too big to fail.’’9 Second, we would expect different reactions to lender quality change dependent on whether the bank is high risk, with an associated greater likelihood of failure.10 Note, however, that there is evidence that reputational effects are stronger for lower risk banks.11 Following Billet et al. (1995), we can measure bank systematic and total risk using standard deviation.12

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Is the event specific to the bank? We can distinguish between events that are specific to the bank and those that affect the market or banking industry in general. Events specific to the bank may have a more direct reputational effect. Does the borrower value the reputation of the bank? We distinguish between borrowers that value the reputational signal provided by the bank loan and those that do not. This distinction manifests itself in two ways. First, we expect larger borrowers to have less need for bank borrowing for signaling purposes, as they have fewer informational asymmetries to overcome.13 Hence, we expect a negative relationship between borrower abnormal returns and borrower size.14 Second, higher risk borrowers have greater need for a reputational signal. Hence, we would expect reputation to be more important to a riskier borrower.15 We can measure bank systematic and total risk using the bank standard deviation.16 Is the bank’s reputation valuable? Finally, we can determine whether the bank’s reputation is valuable by considering whether the loan is secured. We can develop two alternative arguments regarding the reputational value of a secured loan. One view is that there is less reputational value to a secured loan, as the lender is not relying as strongly on its own assessment as it would for an unsecured loan. Therefore, we can argue that one should expect the bank–borrower relationship to be closer if the loan is not secured. Alternatively, one can argue that security is required because the secured borrower is riskier than an unsecured borrower. Hence, the reduction in assessment and monitoring due to the security is offset by the higher risk associated with the secured borrower.

4. DATA EXTRACTION Three sources were used to create the data set. 1. The Loan Pricing Corporation’s DealScan database to extract loan data. 2. The CRSP database for return, market capitalization and index data. 3. The WSJ for event information. Loan deals initiated between 1988 and 1998 were extracted from the DealScan database. The loans selected were between non-ﬁnancial US borrowers and US banks with US parent companies. The vast majority of the loan deals are between borrowers and syndicates of lenders. We use syndicated loans to exploit the database available. Prior studies using syndicated loans to investigate relationships include Houston and James (2001) and Bharath (2002). Finding relationships even for syndicated loans

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reinforces the importance of relationships, as single-bank relationships are likely stronger than those with banks that are part of a syndicate.17 To focus on situations where the importance of the bank to the borrower is not negligible, we retain deals with an average life of at least 2 years, and where lender share is at least 20% of the deal. We do so as the empirical literature suggests that borrower sensitivity is a function of features of the contract. For example, Houston and James (1996, 2001) demonstrate that borrowers relying on a single-bank lender have a much greater sensitivity of investment to cash ﬂow than do borrowers with multiple-bank relationships, while Degryse and Ongena (1999) demonstrate that borrower sales proﬁtability is higher if they maintain a single-bank relationship. Tests of sub-sets of excluded cases generally conﬁrm that borrower abnormal returns are not significantly related to the other variables, conﬁrming our decision to exclude these sub-sets. There are weak indications of a relationship between borrower abnormal returns and borrower standard deviation in highly selective cases in which the lender’s share is low.18 Nonetheless, we choose not to include the numerous low-lender share cases in this study. The relative insensitivity in these cases would lead to the erroneous conclusion that no relationship exists when, as demonstrated in this paper, strong relationships do exist.19 The variables selected for each loan deal are discussed in the next section and in the appendix. Any loan for which all data were not available on DealScan was not included in the sample. When a bank and borrower entered into a loan deal more than once, only the initial loan is retained.20 At this stage, 650 bank–borrower deals were retained. DealScan provides tickers for many of the borrowers. For those borrowers without tickers on DealScan, a CRSP name search was performed. Those borrowers without tickers on either DealScan or CRSP were eliminated. A CRSP name search was performed for each lender. If the lender was not found, a CRSP name search was performed for each lender parent. If neither lender nor parent were found, the lender was eliminated. CRSP daily return data was extracted for each bank and borrower between 1988 and 1998. The vector ‘‘value weighted return – all distributions’’ was extracted as the market index. Any deal for which CRSP data were not available was eliminated. At this stage, 190 bank–borrower deals were retained.21 For each bank, the cumulative, two-trading-day, abnormal returns were calculated for every other trading date.22 Since the purpose of this study is to test whether mid-loan bank events impact the borrower, we identify mid-loan bank events as events that cause large bank abnormal returns. To do so, we specify a bank abnormal returns threshold of 5% (either positive or negative) to identify days with extreme bank abnormal returns.23 Thus, we are able to

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focus on dates with large bank abnormal returns, regardless of cause. Using this methodology, we identify 443 positive bank events and 411 negative bank events.24 We repeated the tests for all models for 5.75%, 6.5%, and 7.25% threshold levels. The results are generally robust to changes in threshold levels. Therefore, we only present evidence for the 5% threshold level. As conﬁrmation of the validity of the threshold technique we use to extract events, we next searched the WSJ in the [2,0] trading day window for bank-specific announcements on each of the post-initiation dates for which abnormal returns crossed the threshold. Hence, some of the threshold abnormal returns have a specific event identiﬁed for them. Further, the type of event is noted. Of the bank events, 398 were identiﬁed in the WSJ.25 Table 1 reports the mean and standard error for all the sub-samples we test. Table 2 reports the actual and percentage difference in means, and the results of t-tests for statistically significant differences in means, for all sub-samples. Owing to the ﬁltering methodology, our data set is composed of abnormal returns above and below the threshold, with no observations between the thresholds. Because of this clustering, regressions are performed on the positive and negative sub-samples separately.

5. METHODOLOGY AND RESULTS We estimate ordinary least square (OLS) regressions in which the dependent variable is borrower abnormal return on the date of extreme bank abnormal returns. The dependent and independent variables are deﬁned in the appendix. We group the independent variables into six categories, based on the issues discussed in Section 3. The categories consist of variables that measure the following:26 Category 1: The extent of the relationship, measured using bank abnormal returns. Category 2: The probability of bank failure, measured using bank standard deviation and bank market capitalization. As discussed in Section 3, bank market capitalization measures the probability of bank failure, as larger banks are more likely to be ‘‘too big to fail.’’ Our use of standard deviation to measure bank systematic and total risk follows Billet et al. (1995).27 Category 3: Whether borrowers value the bank’s reputation, measured using borrower standard deviation and borrower market capitalization. As discussed in Section 3, we expect higher risk and smaller borrowers to have greater need for a reputational signal.

282

FrmAbRet BnkAbRet BankSD lnBnkCap FirmSD lnFrmCap BnkShare

[A]

[B]

[C]

[D]

[E]

[F]

[G]

[H]

[I]

[J]

[K]

[L]

Negative

Positive

MoneyCenter

Regional

WSJ Identiﬁed

NonWSJ Identiﬁed

WSJ Identiﬁed MoneyCenter

NonWSJ Identiﬁed MoneyCenter

WSJ Identiﬁed Regional

NonWSJ Identiﬁed Regional

WSJ Identiﬁed Positive

WSJ Identiﬁed Negative

0.0001 (0.0030) 0.0692 (0.0011) 0.0189 (0.0002) 16.1932 (0.0937) 0.0306 (0.0007) 12.3105 (0.0576) 39.4203 (0.7804)

0.0015 (0.0032) 0.0702 (0.0014) 0.0201 (0.0003) 16.0830 (0.0855) 0.0325 (0.0009) 12.2546 (0.0555) 37.6330 (0.7203)

0.0018 (0.0037) 0.0008 (0.0037) 0.0207 (0.0002) 17.1239 (0.0398) 0.0326 (0.0010) 12.5471 (0.0563) 40.8235 (0.8557)

0.0001 (0.0025) 0.0053 (0.0034) 0.0183 (0.0003) 15.1585 (0.1002) 0.0305 (0.0007) 12.0190 (0.0541) 36.2063 (0.6121)

0.0004 (0.0029) 0.0001 (0.0039) 0.0196 (0.0002) 16.8814 (0.0598) 0.0322 (0.0009) 12.4269 (0.0566) 38.7407 (0.8210)

0.0006 (0.0032) 0.0028 (0.0031) 0.0195 (0.0002) 15.6033 (0.0963) 0.0308 (0.0007) 12.2007 (0.0551) 38.5041 (0.6786)

0.0008 (0.0036) 0.0008 (0.0046) 0.0208 (0.0003) 17.1286 (0.0479) 0.0330 (0.0011) 12.5500 (0.0673) 40.3218 (1.0033)

0.0014 (0.0080) 0.0079 (0.0052) 0.0206 (0.0003) 17.2828 (0.0618) 0.0310 (0.0014) 12.6287 (0.0956) 41.9686 (1.4843)

0.0008 (0.0048) 0.0025 (0.0072) 0.0165 (0.0003) 16.2000 (0.1663) 0.0301 (0.0009) 12.0878 (0.0974) 34.3826 (1.2863)

0.0001 (0.0029) 0.0080 (0.0038) 0.0190 (0.0003) 14.7966 (0.1156) 0.0306 (0.0008) 11.9951 (0.0645) 36.8399 (0.6911)

0.0027 (0.0043) 0.0728 (0.0025) 0.0210 (0.0004) 16.7991 (0.0866) 0.0337 (0.0013) 12.3933 (0.0813) 38.2466 (1.1156)

0.0036 (0.0040) 0.0750 (0.0019) 0.0183 (0.0003) 16.9660 (0.0820) 0.0307 (0.0011) 12.4615 (0.0787) 39.2488 (1.2087)

ARON A. GOTTESMAN AND GORDON S. ROBERTS

Table 1. Mean and Standard Error (in Parentheses) of the Negative and Positive Bank Abnormal Returns Sub-Samples, the Money-Center and Regional Bank Abnormal Returns Sub-Samples, the WSJ and Non-WSJ Reported Bank Events Sub-Samples, the WSJ and Non-WSJ Reported Money-Center Bank Events SubSamples, the WSJ and Non-WSJ Reported Regional Bank Events Sub-Samples, and the Positive and Negative WSJ Reported Bank Events Sub-Samples.

LnDealSz SecuredD WSJexecD SWSJMAD WSJPOD WSJsignD WSJearnD WSJanlyD

No. of observations

4.2234 (0.0828) 18.3531 (0.0572) 0.8984 (0.0145) 0.0831 (0.0132) 0.1339 (0.0163) 0.0924 (0.0139) 0.0600 (0.0114) 0.0600 (0.0114) 0.0115 (0.0051)

4.2111 (0.0807) 18.2814 (0.0528) 0.9011 (0.0140) 0.0374 (0.0089) 0.1626 (0.0173) 0.0967 (0.0139) 0.0352 (0.0086) 0.0923 (0.0136) 0.0308 (0.0081)

4.8184 (0.0899) 18.8052 (0.0586) 0.9095 (0.0137) 0.0973 (0.0141) 0.1629 (0.0176) 0.1561 (0.0173) 0.0860 (0.0133) 0.1154 (0.0152) 0.0226 (0.0071)

3.6212 (0.0608) 17.8319 (0.0395) 0.8901 (0.0148) 0.0224 (0.0070) 0.1345 (0.0162) 0.0336 (0.0085) 0.0090 (0.0045) 0.0381 (0.0091) 0.0202 (0.0067)

4.5377 (0.0902) 18.5776 (0.0587) 0.9097 (0.0138) 0.1227 (0.0158) 0.3056 (0.0222) 0.1944 (0.0191) 0.0972 (0.0143) 0.1574 (0.0175) 0.0440 (0.0099)

3.9849 (0.0714) 18.1491 (0.0503) 0.8918 (0.0140) —

411

443

408

446

398

456

— — — — —

4.8280 (0.1081) 18.8108 (0.0702) 0.9148 (0.0157) 0.1356 (0.0193) 0.2271 (0.0236) 0.2177 (0.0232) 0.1199 (0.0183) 0.1609 (0.0207) 0.0315 (0.0098)

4.8260 (0.1501) 18.8838 (0.1005) 0.8994 (0.0239) —

283

125

— — — — —

3.7375 (0.1361) 17.9348 (0.0795) 0.8957 (0.0286) 0.0870 (0.0264) 0.5217 (0.0468) 0.1304 (0.0315) 0.0348 (0.0172) 0.1478 (0.0332) 0.0783 (0.0252)

3.5808 (0.0669) 17.7962 (0.0453) 0.8882 (0.0173) —

115

331

— — — — —

4.5640 (0.1281) 18.5897 (0.0803) 0.9087 (0.0195) 0.0776 (0.0181) 0.3379 (0.0320) 0.2009 (0.0271) 0.0731 (0.0176) 0.1918 (0.0267) 0.0639 (0.0166)

4.5106 (0.1271) 18.5651 (0.0859) 0.9108 (0.0196) 0.1690 (0.0257) 0.2723 (0.0306) 0.1878 (0.0268) 0.1221 (0.0225) 0.1221 (0.0225) 0.0235 (0.0104)

207

191

An Investigation of the Mid-Loan Relationship

AvgLife

Note: FrmAbRet ¼ ﬁrm abnormal return; BnkAbRet ¼ bank abnormal return; BankSD ¼ bank standard deviation; lnBnkCap ¼ the natural logarithm of the year-end bank market capitalization reported in CRSP; FirmSD ¼ borrower standard deviation; lnFrmCap ¼ the natural logarithm of the year-end borrower market capitalization; BnkShare ¼ the share of the loan deal held by the bank; AvgLife ¼ the average life of the facilities in the deal; lnDealSz ¼ the natural logarithm of the deal size; SecuredD ¼ a dummy variable that equals 1 if the loan is secured and 0 otherwise; WSJexecD ¼ a dummy variable that equals 1 if the type of event is executive related and 0 otherwise; WSJMAD ¼ a dummy variable that equals 1 if the type of event is MA related and 0 otherwise; WSJPOD ¼ a dummy variable that equals 1 if the type of event is production related and 0 otherwise; WSJsignD ¼ a dummy variable that equals 1 if the type of event is capital market related and 0 otherwise; WSJearnD ¼ a dummy variable that equals 1 if the type of event is earning related and 0 otherwise; WSJanlyD ¼ a dummy variable that equals 1 if the type of event is analysis related and 0 otherwise.

283

284

FrmAbRet BnkAbRet BankSD lnBnkCap FirmSD lnFrmCap BnkShare

Difference in Positive/ Negative

Difference in MoneyCenter/Regional

Difference in WSJ/NonWSJ

Difference in WSJ/NonWSJ Money-Center Bank

[A]

[B]

[C]

[D]

[E]

[F]

[G]

[H]

[I]

[J]

[K]

[L]

[M]

[N]

[O]

[P]

[Q]

[R]

Diff.

% Diff.

t-stat

Diff.

% Diff.

t-stat

Diff.

% Diff.

t-stat

Diff.

% Diff.

t-stat

Diff.

% Diff.

t-stat

Diff.

% Diff.

t-stat

0.0013 904.6% 0.30 0.0018 1905.2 -0.42 0.0002 33.8 0.04 0.0006 43.9 0.0029 102.7 0.59 0.0087 110.2 0.1394 201.5 75.38 0.0061 115.2 1.21 0.0011 6.0 3.24 0.0024 13.1 6.94 0.0002 0.9 0.50 0.0002 1.1 0.1102 0.7 0.87 1.9655 13.0 18.18 1.2781 8.2 10.94 0.1542 0.9 0.0015 4.8 1.30 0.0020 6.4 0.0019 6.3 1.58 0.0021 6.9 2.03 1.9 2.86 0.0787 0.6 0.0558 0.5 0.70 0.5281 4.4 6.77 0.2263 4.6173 12.8 4.39 0.2367 0.6 0.22 1.6468 3.9 1.7874 4.5 1.69

0.08 1.17 0.49 0.86 1.05 0.67 0.93

Difference in WSJ/NonWSJ Regional Bank

Difference in Positive/ Negative WSJ Identiﬁed Event

0.0010 641.7 0.17 0.0063 176.6% 1.07 0.0105 131.6 1.35 0.1479 197.1 47.46 0.0024 12.7 4.11 0.0026 14.4 5.69 1.4035 9.5 6.40 0.1669 1.0 1.40 0.0005 1.7 0.34 0.0030 9.8 1.61 0.0927 0.8 0.75 0.0682 0.5 0.60 2.4573 6.7 1.76 1.0023 2.6 0.61

ARON A. GOTTESMAN AND GORDON S. ROBERTS

Table 2. Actual and Percentage Difference in Means, and the Results of t-Tests for Statistically Significant Differences in Means, for the Negative and Positive Bank Abnormal Returns Sub-Samples, the Money-Center and Regional Bank Abnormal Returns Sub-Samples, the WSJ and Non-WSJ Reported Bank Events SubSamples, the WSJ and Non-WSJ Reported Money-Center Bank Events Sub-Samples, the WSJ and Non-WSJ Reported Regional Bank Events Sub-Samples, the Positive and Negative WSJ Reported Bank Events SubSamples.

0.0122 0.3 0.0717 0.4 0.0027 0.3 0.0458 55.1 0.0287 21.4 0.0043 4.7 0.0249 41.4 0.0323 53.7 0.0192 166.5

0.11 0.92 0.13 2.89 1.20 0.22 1.82 1.71 1.93

1.1972 0.9732 0.0194 0.0749 0.0284 0.1225 0.0770 0.0773 0.0024

33.1 11.05 5.5 13.8 2.2 0.96 333.9 4.76 21.1 1.69 364.2 6.37 858.6 5.49 202.7 4.37 12.1 0.25

0.5528 0.4285 0.0179 — — — — — —

13.9 2.4 2.0 — — — — — —

4.86 0.0020 5.58 0.0730 0.90 0.0155 — — — — — — — — — — — —

0.0 0.4 1.7 — — — — — —

0.01 0.60 0.55 — — — — — —

0.1567 0.1386 0.0074 — — — — — —

4.4 0.8 0.8 — — — — — —

1.13 1.54 0.22 — — — — — —

0.0534 0.0246 0.0021 0.0914 0.0656 0.0131 0.0490 0.0697 0.0405

1.2 0.1 0.2 54.1 24.1 7.0 40.1 57.1 172.3

0.30 0.21 0.08 2.92 1.48 0.34 1.72 1.77 1.94

Note: BnkAbRet ¼ bank abnormal return; BankSD ¼ bank standard deviation; lnBnkCap ¼ the natural logarithm of the year-end bank market capitalization reported in CRSP; FirmSD ¼ borrower standard deviation; lnFrmCap ¼ the natural logarithm of the year-end borrower market capitalization; BnkShare ¼ the share of the loan deal held by the bank; AvgLife ¼ the average life of the facilities in the deal; lnDealSz ¼ the natural logarithm of the deal size; SecuredD ¼ a dummy variable that equals 1 if the loan is secured and 0 otherwise; WSJexecD ¼ a dummy variable that equals 1 if the type of event is executive related and 0 otherwise; WSJMAD ¼ a dummy variable that equals to 1 if the type of event is M and A related and 0 otherwise; WSJPOD ¼ a dummy variable that equals 1 if the type of event is production related and 0 otherwise; WSJsignD ¼ a dummy variable that equals 1 if the type of event is capital market related and 0 otherwise; WSJearnD ¼ a dummy variable that equals to 1 if the type of event is earning related and 0 otherwise; WSJanlyD ¼ a dummy variable that equals 1 if the type of event is analysis related and 0 otherwise. Significant difference at 10% level. 5% level. 1% level.

An Investigation of the Mid-Loan Relationship

AvgLife lnDealSz SecuredD WSJexecD WSJMAD WSJPOD WSJsignD WSJearnD WSJanlyD

285

286

ARON A. GOTTESMAN AND GORDON S. ROBERTS

Category 4: Whether the bank’s reputation is valuable to the borrower, measured using a secured dummy. Alternative arguments are presented in Section 3 regarding the reputational value of a secured loan. Category 5: The magnitude of the relationship, measured by bank share, average life, and deal size. We expect the magnitude of the relationship to be a function of the depth of commitment on the part of the bank. Category 6: The type of bank announcement, for the WSJ sub-sample exclusively. These measures include executive-related, merger and acquisition (MA)-related, production-related, capital market-related, earningsrelated, and analysis-related announcements. Tests for pure heteroskedasticity fail to reject the null hypothesis of homoskedasticity.28 Joint tests of heteroskedasticity and speciﬁcation errors are highly significant, even after the data are adjusted for homoskedasticity.29 This is because the models developed in this study, true to precedents such as Billet et al. (1995) and Ongena et al. (1999), omit variables that may explain borrower abnormal returns, such as dividend announcements and changes in production efﬁciency. These variables are omitted from the regressions developed in this study, as the vast majority of them are unreported, particularly for smaller borrowers and for relatively unimportant events. These may lead to some bias in coefﬁcients on variables correlated with these omitted variables.30 We ﬁrst run the regressions for the positive and negative bank abnormal return sub-samples. We then compare the results for the money-center and regional bank sub-samples.31 Finally, we compare the results for events reported in the WSJ and those that are not. Through performing regressions for each of these sub-samples separately, we test whether there are crosssub-sample differences in the relationship between ﬁrm abnormal return and the independent variables. For each sub-sample, we run a set of regressions using a model in which variables in categories 1–5 are included as explanatory variables.32 Further, we run a second model for the negative and positive WSJ identiﬁed moneycenter sub-samples. In this model, variables in category 6 are added as explanatory variables. 5.1. Positive and Negative Bank Abnormal Return Sub-Samples In this section, we report evidence on the relationship between borrower abnormal returns and the explanatory variables. We ﬁrst disaggregate the sample based on whether the 5% threshold bank abnormal return is positive or

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287

negative. Columns A and B of Table 1 report means and standard deviations for the negative and positive bank abnormal returns sub-samples, respectively. Columns A–C of Table 2 display the results of the difference of means test. The results in Table 2 indicate that the mean values of the bank abnormal return variable for the two sub-samples are statistically and economically different at a 1% conﬁdence level. This is expected, given that one employs a positive threshold while the other uses a negative threshold. Moreover, at the same conﬁdence level, there are also significant differences for the bank standard deviation and the ‘‘executive related’’ WSJ reported event dummy. However, the actual difference is small for the bank standard deviation (0.0189 versus 0.0201), suggesting that its economic significance is limited. Further, the bank share variable differs between the two samples at a 10% conﬁdence level. However, the actual difference is very small (39.4203 versus 37.6330), suggesting that the economic significance of the difference is limited. Finally, at a 10% conﬁdence level, there are statistically significant differences for the capital market, earning and analysis-related event announcements. The results of the regression tests for the negative and positive bank abnormal returns sub-samples are reported in columns A and B of Table 3, respectively. Interestingly, the results differ between the positive and negative sub-samples, but both indicate that there is a mid-loan relationship between the borrower and the bank. However, the evidence suggests the relationship differs depending on whether the event affects the bank positively or negatively. We test for robustness of our ﬁnding by replacing the OLS technique with replicating regressions adjusting for heteroskedasticity through correcting for White’s Standard Errors. The coefﬁcient and significance values are generally similar to the OLS results.33 The results in column A suggest that there is a significant positive relationship between borrower and bank abnormal returns for the case where bank abnormal returns are negative. Bank abnormal return is associated with a coefﬁcient of 0.3382, significant at the 1% level. However, the overall regression is not statistically significant (pr(F) ¼ 0.2406). The results in column B strongly suggest that there is a statistically, and economically, significant positive relationship between borrower abnormal returns and borrower standard deviation for the case where bank abnormal returns are positive. Borrower standard deviation is associated with a coefﬁcient 0.7262, significant at the 1% level. This result suggests that risky borrowers, that are in greater need of the reputation signal, are more sensitive to bank events. Further, this is similar to the result reported by Billet et al. (1995) and Best and Zhang (1993).

288

BnkAbRet BankSD LnBnkCap FirmSD LnFrmCap

[A]

[B]

[C]

[D]

[E]

[F]

[G]

[H]

[I]

[J]

Negative

Positive

Negative Money Center

Positive Money Center

Negative Regional

Positive Regional

Negative WSJ Identiﬁed Money Center

Positive WSJ Identiﬁed Money Center

Negative Non-WSJ Identiﬁed Money Center

Positive Non-WSJ Identiﬁed Money Center

0.1079 (0.51) 0.7242 (0.89) 0.0007 (0.30) 0.4816 (1.38) 0.0005 (0.10)

0.0257 0.3738 0.1865 1.2962 0.6869 (0.25) (2.23) (1.19) (1.54) (0.80) 0.2254 1.7628 1.3259 11.7055 1.7498 (0.34) (1.28) (1.26) (2.13) (0.46) 0.0021 0.0153 0.0051 0.0061 0.0011 (1.14) (2.12) (0.72) (0.47) (0.04) 1.2102 0.0530 0.2396 0.2130 1.0861 (4.91) (0.16) (0.89) (0.37) (0.96) 0.0097 0.0034 0.0042 0.0002 0.0050 (2.69) (0.61) (0.79) (0.03) (0.29)

0.4304 0.1727 0.3382 0.0846 (2.66) (0.81) (2.50) (0.90) 0.9754 0.5286 2.4813 1.6018 (1.45) (0.89) (1.81) (1.41) 0.0013 0.0007 0.0089 0.0082 (0.73) (0.37) (1.39) (1.04) 0.1695 0.7262 0.0331 0.4611 (0.82) (3.88) (0.11) (1.45) 0.0007 0.0072 0.0022 0.0109 (0.22) (2.17) (0.46) (1.81)

ARON A. GOTTESMAN AND GORDON S. ROBERTS

Table 3. Results of OLS Regressions of Two-Day Borrower Abnormal Returns on Bank Abnormal Return, Bank Standard Deviation, Bank Market Capitalization, Borrower Standard Deviation, Borrower Market Capitalization, a Secured Dummy, Bank Share, Deal Average Life and Deal Size for the Negative and Positive Sub-Samples, the Negative and Positive Money-Center Sub-Samples, the Negative and Positive Non-Money Sub-Samples, the Negative and Positive WSJ Identiﬁed Money-Center Sub-Samples, and the Negative and Positive Non-WSJ Identiﬁed Money-Center Sub-Samples.

BnkShare AvgLife LnDealSz Intercept No. of observations Adj. R2 pr(F-statistic)

0.0020 (0.18) 0.0001 (0.65) 0.0020 (0.74) 0.0003 (0.07) 0.0007 (0.01)

0.0124 0.0126 (1.12) (0.72) 0.0002 0.0002 (0.84) (0.74) 0.0000 0.0004 (0.00) (0.11) 0.0125 0.0017 (2.59) (0.27) 0.0497 0.0630 (0.70) (0.52)

0.0018 (0.08) 0.0003 (1.00) 0.0008 (0.16) 0.0052 (0.63) 0.1209 (0.78)

0.0074 0.0206 0.0160 (0.55) (1.93) (0.77) 0.0002 0.0002 0.0004 (0.49) (0.92) (1.30) 0.0015 0.0019 0.0018 (0.34) (0.65) (0.45) 0.0020 0.0116 0.0045 (0.29) (2.20) (0.67) 0.0543 0.0325 0.1066 (0.47) (0.36) (0.84)

0.0136 0.0123 (0.70) (0.42) 0.0003 0.0002 (0.82) (0.35) 0.0049 0.0095 (1.15) (1.28) 0.0036 0.0095 (0.49) (0.80) 0.0509 0.1055 (0.37) (0.41)

411

443

204

204

207

239

133

150

0.0060 0.2406

0.0197 0.0366

0.0100 0.2645

0.0018 0.4774

0.0185 0.8084

0.0802 0.0008

0.0163 0.2504

0.0046 0.5113

71 0.0021 0.4642

0.0063 (0.10) 0.0017 (1.71) 0.0040 (0.31) 0.0046 (0.20) 0.0578 (0.13) 54 0.0502 0.7455

Note: BnkAbRet ¼ bank abnormal return; BankSD ¼ bank standard deviation; lnBnkCap ¼ the natural logarithm of the year-end bank market capitalization; FirmSD ¼ borrower standard deviation; lnFrmCap ¼ the natural logarithm of the year-end borrower market capitalization; SecuredD ¼ a dummy variable that equals 1 if the loan is secured and 0 otherwise; BnkShare ¼ the share of the loan deal held by the bank; AvgLife ¼ the average life of the facilities in the deal; lnDealSz ¼ the natural logarithm of the deal size; t-statistics are in the parentheses. Significant difference at 10% level. 5% level. 1% level.

An Investigation of the Mid-Loan Relationship

SecuredD

289

290

ARON A. GOTTESMAN AND GORDON S. ROBERTS

Additionally, column B suggests that there is a statistically significant (at the 5% level) positive relationship between borrower abnormal returns and borrower market capitalization, and a statistically significant (at the 1% level) negative relationship between borrower abnormal returns and deal size. The overall regression is significant at the 5% level (pr(F) ¼ 0.0366). 5.2. Money-Center and Regional Bank Sub-Samples In this section, we disaggregate the data sample into money-center bank and regional bank sub-samples. In this way, we are able to explore whether there is any difference between the two sub-samples. Columns C and D of Table 1 report means and standard deviations for the money-center and regional bank abnormal return sub-samples, respectively. Columns D–F of Table 2 show the results of the difference of means test. The mean values of numerous variables are significantly different at the 1% level. As well, there is significant difference between borrower standard deviations at the 5% level. It is apparent that money-center banks are larger and have greater total risk than regional banks. Borrowers from money-center banks are larger than borrowers from regional banks. The bank share, average life, and deal size are all larger when the lender is a money-center bank. Furthermore, money-center banks are more likely than regional banks to have executive, MA, production, capital market, and earnings-related announcements. The results of the regression tests for the negative and positive moneycenter sub-samples are presented in columns C and D of Table 3, respectively. Results for the negative and positive regional sub-samples are presented in columns E and F of Table 3, respectively. Interestingly, the results are different for the money-center and regional sub-samples. In the positive money-center bank sub-sample (column D), the overall regression is insignificant (pr(F) ¼ 0.4774). However, the relationship for the positive regional bank sub-sample (column F) reﬂects a significant borrower abnormal return and borrower standard deviation relationship similar to that revealed in the positive sub-sample (all data) test. The overall regression in this case is significant at the 1% level (pr(F) ¼ 0.0008). The uniqueness of this relationship to the regional subsample is further evidence, for positive bank events, of a stronger reputational effect for borrowers from smaller banks. The negative money-center bank sub-sample (column C) indicates a borrower abnormal return, bank abnormal return, and bank standard deviation relationship similar to that revealed in the negative sub-sample (column A)

An Investigation of the Mid-Loan Relationship

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test. For the negative regional bank sub-sample (column E), there is no significant relationship between these variables. The uniqueness of the relationship to the money-center bank sub-sample provides further evidence that negative bank effects do not have reputational effects on borrowers. The significant results for the money-center sub-sample, for the negative abnormal bank returns, may be due to one of two effects. Either the bank– borrower relationship is only valuable for money-center banks, or the riskier nature of money-center banks indicates higher probability of failure, resulting in greater borrower sensitivity. Further, our significant results for the negative money-center sub-sample reinforce the view that, although moneycenter banks can be characterized as ‘‘too big too fail,’’ ambiguity surrounds regulator decisions to bailout banks.

5.3. Wall Street Journal/Non-Wall Street Journal Sub-Samples We next disaggregate the sample into WSJ and non-WSJ sub-samples. Through doing so, we are able to distinguish between bank-specific and non-bank-specific events. As discussed in Section 3, an event specific to the bank may have a more direct reputational effect than an event that only affects the bank’s reputation indirectly. We begin by demonstrating that there are many significant differences between the two sub-samples. Suspecting that these differences may be because the WSJ is more likely to report money-center bank events than regional bank events, we further disaggregate into money-center and regional bank sub-sub-samples. 5.3.1. WSJ/Non-WSJ Columns E and F of Table 1 report means and standard deviations for the WSJ reported and non-WSJ reported bank events sub-samples, respectively. Columns G–I of Table 2 report the results of the difference of means test. The results demonstrate that the two sub-samples differ greatly. The WSJ identiﬁed events have significantly larger (at the 1% level) values for bank market capitalization, borrower market capitalization, average life, and deal size. To explain this difference, note that on average, 71.1% of the deals associated with WSJ identiﬁed events involve money-center banks, while only 27.4% of deals associated with the non-WSJ identiﬁed events involve a money-center bank. Hence, the differences between the sub-samples appear to represent money-center versus regional differences, rather than WSJ versus non-WSJ differences. To determine if this explains the differences, we further disaggregate into money-center and regional bank sub-samples.

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5.3.2. WSJ/Non-WSJ and Money-Center/Regional Bank Sub-samples Columns G and H of Table 1 report means and standard deviations for the WSJ reported and non-WSJ reported, money-center sub-samples. Columns J–L of Table 2 report the results of the difference of means test. The results indicate that all of the differences between the WSJ and non-WSJ bank event sub-samples disappear in the money-center bank sub-samples. Next, we turn to the regional bank sub-samples. Columns I and J of Table 1 report means and standard deviations for the WSJ reported and non-WSJ reported regional bank events sub-samples. Columns M–O of Table 2 report the results of the difference of means test. The results demonstrate that in the regional case, the WSJ identiﬁed events are associated with higher market capitalization, and lower bank total risk, significant at the 1% level. At the 10% level, the WSJ identiﬁed events are associated with lower bank share. In summary, the tests here indicate that the WSJ and non-WSJ subsamples are highly similar in the money-center bank event case. Hence, differences in the two sub-samples are likely due to whether the event was identiﬁed in the WSJ. Moreover, the results also indicate that in the regional bank event case, there are differences between the WSJ and non-WSJ subsamples. Based on the above analysis, we test four cases: the WSJ and non-WSJ sub-samples, for the positive and negative cases at the 5% threshold levels, for the money-center case. The results of the regression tests for the WSJ negative and positive sub-samples are presented in columns G and H of Table 3, respectively. Results for the non-WSJ negative and positive subsamples are presented in columns I and J of Table 3, respectively. In addition, we estimate an additional model for the two WSJ sub-samples. The additional model includes a number of ‘‘type of event’’ variables.34 The results of the additional model for WSJ negative and positive cases are presented in columns A and B, respectively, of Table 4. We next discuss differences between the results for the WSJ and non-WSJ cases for the money-center bank sub-sample.

5.3.3. Money-Center Bank Sub-Sample As demonstrated in columns J–L of Table 2, the WSJ and non-WSJ sub-samples are broadly similar for money-center banks. Because of this similarity, differences in the two sub-samples may be attributed to the fact that abnormal return events reported in the WSJ are bank specific, while those not reported in the WSJ are less likely to be bank specific. As

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Table 4. Results of OLS Regressions of Two-Day Borrower Abnormal Returns on Bank Abnormal Return, Bank Standard Deviation, Bank Market Capitalization, Borrower Standard Deviation, Borrower Market Capitalization, a Secured Dummy, and Event Type for the Negative and Positive WSJ Identiﬁed Money-Center Sub-Samples.

BnkAbRet BankSD lnBnkCap FirmSD lnFrmCap SecuredD WSJexecD WSJMAD WSJPOD WSJsignD WSJearnD Intercept

No. of observations Adj. R2 pr(F-statistic)

[A] Negative WSJ Identiﬁed Money-Center

[B] Positive WSJ Identiﬁed Money-Center

0.2773 (1.18) 2.2243 (1.18) 0.0149 (1.98) 0.1200 (0.37) 0.0057 (1.17) 0.0136 (0.68) 0.0053 (0.15) 0.0139 (0.41) 0.0010 (0.03) 0.0089 (0.26) 0.0090 (0.26) 0.1402 (1.06)

0.1842 (1.14) 1.0236 (0.93) 0.0117 (1.67) 0.2872 (1.16) 0.0020 (0.44) 0.0061 (0.33) 0.0635 (2.09) 0.0154 (0.59) 0.0223 (0.87) 0.0115 (0.36) 0.0138 (0.51) 0.1518 (1.27)

133 0.0144 0.6324

150 0.0395 0.1121

Note: BnkAbRet ¼ bank abnormal return; BankSD ¼ bank standard deviation; lnBnkCap ¼ the natural logarithm of the year-end bank market capitalization; FirmSD ¼ borrower standard deviation; lnFrmCap ¼ the natural logarithm of the year-end borrower market capitalization; SecuredD ¼ a dummy variable that equals 1 if the loan is secured and 0 otherwise; WSJexecD ¼ a dummy variable that equals 1 if the type of event is executive related and 0 otherwise; WSJMAD ¼ a dummy variable that equals 1 if the type of event is MA related and 0 otherwise; WSJPOD ¼ a dummy variable that equals 1 if the type of event is production related and 0 otherwise; WSJsignD ¼ a dummy variable that equals 1 if the type of event is capital market related and 0 otherwise; WSJearnD ¼ a dummy variable that equals 1 if the type of event is earning related and 0 otherwise; t-statistics are in the parentheses. Significant difference at 10% level. 5% level.

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discussed in Section 3, reputation effects may differ for bank-specific versus non-bank-specific events. In the positive WSJ case, column H of Table 3, the overall regression is not significant (pr(F) ¼ 0.5113). A similar lack of overall significance characterizes all the regressions for the positive non-WSJ cases (column J). For negative bank abnormal returns, the results differ for the WSJ and non-WSJ sub-samples. In the negative WSJ case (column G), there is a significant coefﬁcient associated with the bank abnormal return variable at the 5% significance level. This coefﬁcient is slightly lower than the coefﬁcients associated with the bank abnormal return variable in the negative moneycenter sub-samples. However, the regression for the negative WSJ case lacks overall significance (pr(F) ¼ 0.2504). In the negative non-WSJ case (column I), there is a large and significant coefﬁcient associated with the bank standard deviation variable, significant at the 5% level, although the regression lacks overall significance (pr(F) ¼ 0.4642). As well, while insignificant, the coefﬁcients associated with bank abnormal return are much larger for the negative non-WSJ case models than for the negative WSJ models. However, the insignificance of these coefﬁcients, combined with the lack of overall significance, suggests that this ﬁnding is of doubtful consequence. Turning to Table 4, for the positive WSJ sub-sample (column B), there is a negative coefﬁcient associated with executive related events, significant at the 5% level. Moreover, there is negative coefﬁcient associated with bank market capitalization significant at the 10% level. However, the overall regression is insignificant, with pr(F) ¼ 0.1121. Conversely, for the negative WSJ sub-sample (column A), there is no significant coefﬁcient associated with the ‘‘type of event.’’ There is 0.0149 coefﬁcient associated with the bank capitalization significant at the 10% level. However, the overall regression is insignificant, with pr(F) ¼ 0.6324. We summarize these ﬁndings as follows. For negative money-center events, there is evidence of bank–borrower relationships in both the WSJ and non-WSJ sub-samples. In the WSJ sub-sample, the relationship is between borrower abnormal returns and bank abnormal returns. In the nonWSJ sub-sample, the relationship is between borrower abnormal returns and bank standard deviation. However, the significance of the overall nonWSJ money-center regressions suggests caution when interpreting these results. Finally, there little evidence that the type of event is relevant, in the WSJ case exclusively. This implies that the bank–borrower relationship is invariant to the types of event.

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6. CONCLUSION This study measures the strength of the mid-loan relationship between borrowers and their bank lenders over the period 1988–1998. Broadly, the evidence suggests that relationship banking remained important during the 1990s, and has not been replaced by transaction banking. This supports Boot and Thakor’s (2000) contention that relationship banking is signiﬁcant, even with a more competitive environment. More particularly, because our sample is not limited to banks experiencing ﬁnancial distress as in prior studies, we are able to demonstrate that prior ﬁndings that negative events (changes in lender quality) occurring to banks have a link to borrowers are robust when such bank events are measured in non-crisis periods. The evidence provides insight into why lender quality matters. Interestingly, the empirical tests imply that the nature of the relationship depends on whether the bank events are positive or negative.35 The empirical differences between the positive and negative bank event sub-samples are manifested in a number of ways. Borrower abnormal return is positively related to borrower standard deviation for positive bank events, while positively related to both bank abnormal returns and bank standard deviation for negative bank events. Separate tests for money-center and regional subsamples suggest that the borrower abnormal return/borrower standard deviation relationship identiﬁed for positive abnormal returns is specific to regional banks. These tests also suggest that the borrower abnormal return/ bank abnormal return and borrower abnormal return/bank standard deviation relationships identiﬁed for negative abnormal returns are specific to money-center banks. Tests suggest that the type of event cannot explain the differences between the positive and negative cases. A number of questions remain about the bank–borrower relationship during the duration of the loan. Why are the reputational effects different for the positive and negative bank abnormal return events? Why do we ﬁnd different bank–borrower relationships for negative abnormal return events, depending on whether the bank event is specific to the bank or not? Existing theory cannot be used to explain these effects. The results presented in this study should motivate further theoretical research on these issues.

NOTES 1. Empirically, Mikkelson and Partch (1986) demonstrate bank borrowers have abnormal announcement returns. James (1987) and Aintablian and Roberts (2000)

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demonstrate that abnormal returns are larger for banks than for other private placements. 2. Reputational equilibrium models include Carter and Manaster (1990) and Diamond (1991). 3. Billet et al. (1995) provide evidence that borrower abnormal return at loan announcement is a positive function of lender credit quality. Further, there is evidence that bank distress mid-loan impacts borrowers (see Slovin et al., 1993; Kang & Stulz, 1997). 4. Categories of mid-loan events studied in this paper include MA-related events, production-related events, capital market-related events, earnings-related events, analysis-related events, and executive-related events. 5. A number of studies investigate how bank events affect other banks, and further contagion effects. These include Furﬁne (2003), Allen and Gale (2000), Calomiris and Mason (1997), and Kaufman (1994), among others. 6. Further evidence of the importance of intermediary reputation exists as well. While initial public offerings are associated with underpricing, there is evidence that the extent of the underpricing is a decreasing function of the underwriter’s quality. See Beatty and Ritter (1986) and Carter and Manaster (1990). 7. Other evidence of the importance of the bank–borrower relationship includes Petersen and Rajan (1994), Berger and Udell (1994), and Cole (1998), who estimate that credit availability for small borrowers is greater when a close bank relationship exists. Loans are received with lower rates and fewer collateral agreements for smaller borrowers with close bank relationships. Allen, Saunders, and Udell (1991) provide evidence that banks gather valuable private information from depositors, which is used in credit decisions. Angelini et al. (1998) report that Italian borrowers with longer banking relationships pay higher interest. Morck and Nakamura (1999) demonstrate that bank-related borrowers are less likely to enter into failure during ‘‘bad times.’’ Gibson (1995) ﬁnds that borrower investment is sensitive to the ﬁnancial health of the borrower’s main bank. 8. See Dennis and Mullineaux (2000) for a discussion of factors measuring the extent to which a bank participates. 9. See Kane (2000) for a discussion of the ‘‘too big to fail’’ doctrine. 10. For a bank classiﬁed as ‘‘too big to fail,’’ these risk measures may not provide a sensitive measure of likelihood of failure, as presumably a ‘‘too big to fail’’: bank will be bailed out if it becomes insolvent. However, given the ambiguous nature of implicit government guarantees, a riskier, ‘‘too big to fail,’’ bank is still more likely to fail than a less risky ‘‘too big to fail’’ bank. 11. See Billet et al. (1995). 12. In addition to the bank standard deviation, we initially included the bank beta as another measure of bank systematic and total risk. This follows Billet et al. (1995) who use beta in their regressions, where abnormal returns is the dependent variable. Note, however, that both Billet et al. (1995) and this study do not ﬁnd a significant coefﬁcient related to the bank beta. This is consistent with the argument that the calculation of abnormal return implicitly neutralizes returns using beta. Hence, we do not expect any further relationship between abnormal returns and beta. Thus, we choose to exclude the bank beta from our regressions.

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13. Gertler and Hubbard (1989) ﬁnd that size and age reduce the adverse selection problem, increasing the borrower’s ability to obtain external ﬁnancing, while Slovin, Johnson, and Glascock (1992) demonstrate that the positive announcement effect is weaker for large borrowers. 14. While we argued earlier that larger deal size indicates a closer bank–borrower relationship, since deal size may proxy borrower size, we might expect either a positive or negative coefﬁcient associated with the deal size variable. 15. Billet et al. (1995) found such a result at deal initiation. 16. While bond rating is another measure of riskiness, the database provides only limited bond rating data. 17. One cause for concern related to using a database consisting of syndicated loans is the potential for differences in the nature of the relationship between the lead bank and the borrower versus the relationship between other syndicate members and the borrower. Differences may occur due to the monitoring role played by the lead bank, which may result in agency problems between the lead bank and syndicate members. Specifically, the lead bank may sell larger proportions of potentially problematic loans to uninformed syndicate members. However, this concern is mitigated by results in Jones, Lang, and Nigro (2000) and Panyagometh and Roberts (2005), who do not ﬁnd evidence of the agency problems described above. 18. Specifically, evidence of a weak (significant at the 10% level) relationship exists for only negative bank abnormal return events, and only when other variables are excluded from the regressions. 19. Data analysis indicates that including the less-than-20% cases would result in over 3,000 additional observations. Since fewer than 1,000 greater-than-20%-lendershare observations are found, the inclusion of the 3,000 insensitive cases would swamp the sensitive cases. 20. There is some evidence that only renewals have abnormal returns (Lummer & McConnell (1989). Others do not ﬁnd evidence to support the initial/renewal distinction. Through retaining only initial loans, we eliminate loan renewals. The data set is therefore less sensitive, a bias against ﬁnding mid-loan relationships. Retaining renewals would bias the data set toward banks and borrowers that enter into relationships frequently. 21. The 190 deals are associated with 42 banks, with the average bank associated with 4.52 borrowers. The median bank is associated with 2 borrowers, the range of borrowers per bank is (2, 24), and the standard deviation of borrowers per bank is 5.705. Of the 190 deals, 40.52% are associated with four banks, Banc One, Bank America, Bank Boston, and Chase Manhattan. 22. Calculating two-day, cumulative abnormal returns for every trading date would have resulted in the ﬁlter identifying more than a single abnormal return date for a single threshold event, due to the overlap of days. For example, if the abnormal return on four consecutive days are: 2%, 5%, 3%, and 1%, then calculating abnormal returns for every trading date would have resulted in the ﬁlter identifying two abnormal return dates: day 1 (2%+5% ¼ 7%) and day 2 (5% + 3% ¼ 8%). Through using every other date, we identify a single abnormal return date, day 1. Note that the methodology may result in failure to identify some abnormal return dates. For example, if the abnormal returns on four consecutive days are: 0, 3%, 3%,

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and 0%, then our ﬁlter will miss the event, though the abnormal returns are beyond the 6% threshold. 23. Tests were also performed using bank abnormal return thresholds greater and less than 5%. We do not report the results of these tests. The results are generally robust to changes in the threshold level. 24. Two hundred and four of the positive bank events and 204 of the negative bank events occurred to money center banks, with the remainder occurring to regional banks. 25. Two hundred and eighty-three of the WSJ identiﬁed events occurred to money center banks. Of these, 150 were positive and 133 were negative. None of the WSJ identiﬁed events are borrower events. This suggests that borrower events do not drive the bank events. 26. In addition, we initially included other variables not directly related to the importance of the relationship. These include the LIBOR spread variable and the borrowing purpose dummies. The LIBOR spread variable was included as an explanatory variable to determine if higher spreads are charged for borrowers taking advantage of the bank’s reputation. The borrowing purpose dummies were included as explanatory variables to test whether the relationship between borrower and bank abnormal return is a function of the specific purpose of the loan. Including the date of event variable allows us to test if the relationship between borrower and bank abnormal return is a function of the specific economic and regulatory environment at the time of the event. Including the days since initiation of the deal, variable allows us to test if the relationship between borrower and bank abnormal return is a function of the amount of time since initiation. However, since the coefﬁcients of these variables are mostly insignificant, we exclude them from our reported regressions. 27. As noted in Section 3, we initially included bank beta as another measure of bank systematic and total risk, following Billet et al. (1995). Since this study (similar to Billet et al., 1995) does not ﬁnd a significant coefﬁcient related to the bank beta, we exclude bank beta from our regressions. 28. Tests include the Breusch and Pagan (1978)/Godfrey (1978) test, where explanatory variables R2 is the test statistic. 29. Tests include White’s (1980) general heteroskedasticity test, where explanatory variables R2 is the test statistic. 30. Gujarati (1995) notes that if the omitted variables are correlated with the included variables, both the constant and variable coefﬁcients are biased and inconsistent. If the omitted variables are uncorrelated, the constant is biased, while the variable coefﬁcients are not. However, variance estimates may be biased as well. 31. A bank is classiﬁed as a money-center bank if it is one of the following (based on Slovin et al., 1999): Bank of America, Bank of Boston, Bankers Trust, Chase Manhattan, Chemical New York, Citicorp, Continental Illinois, Crocker, First Chicago, First Interstate Bancorp, Irving, Manufacturers, Hanover, Marine Midland, Mellon, J.P. Morgan, Security Pacific, and Wells Fargo. 32. In results not reported here, we verify the robustness of our ﬁndings by running two alternative regression speciﬁcations leading to similar coefﬁcients. In the ﬁrst model, variables in categories 1 and 2 are included as explanatory variables. In the second model, variables in categories 1–4 are included as explanatory variables.

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33. The regressions adjusted for White’s Standard Errors, are available from the authors upon request. 34. In the paper, we include six types of events (executive-related, MA-related, production-related, capital market-related, earnings-related, and analysis-related announcements). However, to avoid the perfect multicollinearity problem in regressions, we drop the analysis-related event dummy from regressions. Hence, the null hypothesis ‘‘type of event’’ dummy is ‘‘analyst comments.’’ 35. Note that others have found differences in reactions to positive and negative event sub-samples as well. For example, Chan (2002) examines returns to stocks following the public release of news, and ﬁnds that investors are more likely to underreact to bad news than to good news. 36. Note that we do not control for possible thin trading effects when estimating beta, for the following three reasons. First, earlier papers do not correct for thin trading. Second, thin trading is only an important issue in smaller markets. Third, while there are a number of methods to control for thin trading, there is evidence that these methods do not provide significant improvements over simple market model betas (see Berglund, Liljeblom, & Loﬂund, 1989).

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APPENDIX. VARIABLE DEFINITIONS AND SOURCES Independent Variable Borrower abnormal return: cumulative, two-trading-day, borrower abnormal returns, calculated for every other trading date. Calculated using market model parameters using daily trading day returns from the CRSP valueweighted index over the time period t180 through t31.

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Dependent Variables In this study, we group dependent variables into six categories. The categories are as follows: Category 1. Variables that measures the extent of the relationship. This includes: Bank abnormal return: cumulative, two-trading-day, borrower abnormal returns, calculated for every other trading date. Calculated using market model parameters using daily trading day returns from CRSP over the time period t180 through t31.36 Category 2. Variables that measure the probability of bank failure. These include: Bank standard deviation: the standard deviation of the bank’s daily trading day returns from CRSP during the estimation period t180 through t31. Bank market capitalization: the natural logarithm of the year-end bank market capitalization reported in CRSP. Category 3. Variables that measure whether borrowers value the bank’s reputation. These include: Borrower standard deviation: the standard deviation of the borrower’s daily trading day returns from CRSP during the estimation period t180 through t31. Borrower market capitalization: the natural logarithm of the year-end borrower market capitalization reported in CRSP. Category 4. Variables that measure whether the bank’s reputation is valuable. These include: Bank market capitalization: refer to category 2 for description. Secured dummy: a dummy variable that equals 1 if the loan is reported as secured in DealScan and 0 otherwise. Category 5. Variables that measure the magnitude of the relationship. These include: Bank share: the share of the loan deal held by the bank reported in DealScan.

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Average life: the average life of the facilities in the deal reported in DealScan. Deal size: the natural logarithm of the deal size reported in DealScan. Category 6. Variables that measure the type of bank announcement (WSJ sub-set exclusively). The following event categories based on event reports in the WSJ are included as dummies: Executive related: executive appointments, retirements and resignations. Earnings related: earnings announcements, including outlook statements. MA related: mergers, acquisitions, divestitures, takeover and joint venture–related. Production related: events related to products, competition, and operations management, including layoffs and cost cutting. Capital market-related: capital market-related events, including whether other borrowers invest in it, debt rating changes, dividend announcements, inclusion in indices, Initial Public Offering (IPO)-related announcements, security issues and pricing, and share repurchases. Analysis related.

ZERO–NON-ZERO PATTERNED VECTOR ERROR CORRECTION MODELLING FOR I(2) COINTEGRATED TIME SERIES WITH APPLICATIONS IN TESTING PPP AND STOCK MARKET RELATIONSHIPS T. J. Brailsford, J. H. W. Penm and R. D. Terrell ABSTRACT Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect Research in Finance, Volume 22, 305–326 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22011-7

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causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

1. INTRODUCTION The use of vector error correction models (VECMs) for analysing possible cointegrating relations among economic and ﬁnancial variables has become increasingly important in the literature. The advantage of these models is they have proved to be more computationally effective tools, and therefore less costly, and of more immediate relevance than conventional time series techniques. In particular, VECM modelling has been increasingly employed to examine relationships in ﬁnancial markets, e.g. Diamandis, Georgoutsos, and Kouretas (2000), Granger and Lee (1989), Granger, Huang, and Yang (2000). Conventional full-order VECM models assume non-zero elements in all their coefﬁcient matrices. As the number of elements to be estimated in these possibly over-parameterised models grows with the square of the number of variables, the degrees of freedom will be heavily reduced. This issue becomes problematic if the underlying true VECM has zero entries, as different model estimates can produce different cointegrating relationships, thus leading to weaker and often different inferences. Application of VECM models to economic and ﬁnancial time-series data have revealed that zero coefﬁcient entries are indeed possible e.g. King, Plosser, Stock, and Watson (1991), Penm, Penm, and Terrell (1997). Of note, the VECM is identical to the vector autoregressive (VAR) model with unit roots. An optimal VECM speciﬁcation with zero entries suggests that the cointegrating vectors and the loading vectors may also contain zero entries. However, the existence of zero entries has not been fully discussed in causality and cointegration theory.1 The exact nature of the long-term cointegration relations will be crucially dependent upon ﬁnding those zero coefﬁcient patterns where the true structure does indeed include zero entries. Moreover, the issue also impacts on the detection of indirect causality and/ or Granger non-causality. Penm et al. (1997) have developed a search algorithm to select ZNZ patterned cointegrating and loading vectors in a subset VECM with zero entries

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for an I(1) system. However, that paper did not deal with the application to a higher-order integrated system. Several ﬁnancial variables typically display properties consistent with an I(2) process. Hence there is a lack of guidance on how to deal with zero entries in an I(2) system. This paper provides an algorithm to select ZNZ patterned cointegrating and loading vectors in a ZNZ patterned VECM for an I(2) system. The ZNZ patterned VECM modelling includes the full-order VECMs as a special case. The paper also demonstrates the use of this model to detect Granger causality, Granger noncausality and indirect causality among variables. Thus the contribution of the paper is to specify statistical procedures for analyzing ﬁnancial variables of up to order two within a single VECM environment. The paper is constructed as follows; Section 2 provides VECM modelling for an I(2) system. Section 3 shows that the ZNZ patterned VECM is a more straightforward and effective means of testing for Granger causal relations. In Section 4, to begin the algorithm, the optimal speciﬁcation is identiﬁed for a ZNZ patterned VECM using appropriate model selection criteria. The rank of the long-term impact matrix is then computed using the singular value decomposition (SVD) method with allowance for possible zero entries in the impact matrix. A pattern selection algorithm developed from statistical procedures as suggested in Seber (1977) is then proposed for the search of all acceptable ZNZ patterns of the cointegrating and loading vectors. The acceptable ZNZ patterns of these vectors are discussed in detail. Section 5 then presents two applications of the procedure to ﬁnancial markets. The ﬁrst application deals with a three-variable system concerning the stock market while the second application examines purchasing power parity (PPP) using exchange rate series. Concluding remarks are presented in Section 6.

2. VECM MODELLING FOR AN I(2) SYSTEM We begin by considering the general VAR(p) model of the form: uðtÞ þ

p X

Ct uðt tÞ ¼ ðtÞ

(1)

t¼1

where e(t) is an s 1 independent and identically distributed vector random process with EfðtÞg ¼ 0 and EfðtÞ0 ðt tÞg ¼ V ; t ¼ 0 ¼ 0; t40

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Ct ; t ¼ 1; 2; :::; p are s s parameter matrices; Cp ðLÞ ¼ I þ

p X

Ct L t

t¼1

where it is assumed that the roots of jCp ðLÞj ¼ 0 lie outside or on the unit circle, and L denotes the lag operator. Further, u(t) is integrated of order d [I(d)] if it contains at least one element which must be differenced d times before it becomes I(0). Also call u(t) cointegrated with the cointegrating vector, a, of order g, if a0 u(t) is integrated of order (d–g), where u(t) has to contain at least two I(d) variables.2 Under this I(2) assumption, we have Cp ðLÞ ¼ Cp ð1ÞL þ ðI LÞCp1 ðLÞ ¼ Cp ð1ÞL þ Cp1 ð1ÞL Cp1 ð1ÞL2 þ ðI LÞ2 Cp2 ðLÞ

ð2Þ

Following Engle and Yoo (1991), the equivalent VECM for (1) can be expressed as " # h i uðt 1Þ Cp ð1Þ Cp1 ð1Þ (3) þ Cp2 ðLÞD2 uðtÞ ¼ ðtÞ Duðt 1Þ where u(t) contains variables of three types, namely I(0), I(1) and I(2) and D ¼ (IL). Expression (3) can be rewritten as " # uðt 1Þ C (4) þ Cp2 ðLÞD2 uðtÞ ¼ ðtÞ Duðt 1Þ h where C ¼ Cp ð1Þ;

i Cp1 ð1Þ ; and " # uðt 1Þ C Duðt 1Þ

is stationary and the ﬁrst term in (4) is the error correction term. The term Cp2 ðLÞD2 uðtÞ is the vector autoregressive part of the VECM.

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Because u(t) is cointegrated of order 2, the long-term impact matrix, C ; must be singular. As a result, " # uðt 1Þ 0 0 C ¼ da and a Duðt 1Þ C is stationary, where the rank of C is r, and d and a0 are matrices of dimension (s r) and (r 2 s) respectively. The columns of a are the cointegrating vectors, and the rows of d are the loading vectors. Additive linear and quadratic trends can be assumed to be incorporated into the VECM of (3). The presence or absence of any of these trends will then be selected by using the search algorithm proposed by Penm and Terrell (1984) in conjunction with model selection criteria (see Hansen & Yu, 2001). For simplicity of presentation, these trend terms are not included. Further, to properly characterise the underlying system, the VECM in (3) must be a minimal system Hannan and Deistler, (1988), which has an irreducible transfer function matrix as described in Kailath (1980). For instance, consider the following VECM: " # 0 0 DuðtÞ ¼ uðt 1Þ þ ðtÞ 1 0 " # 0 1 0 uðt 1Þ þ ðtÞ ¼ ð5Þ 1 Since this does not involve at least two I(2) variables in u(t), it is impossible to form a cointegrating relationship. Thus this system does not meet the criteria of the I(2) system. If we then add a redundant term 1 0 Duðt 1Þ 0 1 to both sides of (5), the result is " # " # 0 0 1 0 uðt 1Þ Duðt 1Þ ¼ DuðtÞ þ 1 0 0 1 " # 1 0 þ Duðt 1Þ þ ðtÞ. 0 1

ð6Þ

An irreducible transfer function is the lowest-degree representative of the transfer function which can be realised. Consequently, for a reducible

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transfer function, any redundant terms must be removed and any common factors cancelled out. Since in (6) the term 1 0 Duðt 1Þ 0 1 appears on both sides, then this term is redundant. Hence (6) is a reducible system. Thus (6) cannot properly characterise the underlying system. It is possible to rewrite (6) as 0 0 1 0 uðt 1Þ þ Duðt 1Þ þ ðtÞ D2 uðtÞ ¼ 1 0 0 1 this VECM is not a minimal system, and therefore, it does not meet the criteria for an I(2) system. Model development is more convenient using a VECM, rather than the equivalent VAR if the systems under study include cointegrated time series. Engle and Granger (1987) note that, for I(1) systems, the VAR in ﬁrst difference form will be mis-speciﬁed and the VAR in levels will ignore important constraints on the coefﬁcient matrices. Although, these constraints may be satisﬁed asymptotically, efﬁciency gains and improvements in forecasts are likely to result by imposing them. The analogous conclusion applies to I(2) systems. Comparisons of forecasting performance of the VECMs versus VARs for cointegrated systems indicate that, while in the short-run there may be gains in using unrestricted VAR models, the VECMs produce longrun forecasts with smaller errors when the variables used in the models satisfy the test for cointegration (Engle & Yoo, 1987, LeSage, 1990). Further to these developments, consider a hypothesis where every (i, j)th element, for speciﬁed i and j, is zero in all coefﬁcient matrices in a VAR. If this hypothesis is framed in the VAR expressed by (1), these zero entries will also hold in the error-correction terms and in the vector autoregressive part of the equivalent VECM, say (2). A discussion of this property is provided in Section 3.

3. ZERO ENTRIES IN A VAR AND ITS EQUIVALENT VECM FOR AN I(2) SYSTEM In an I(2) system, the VECM of (3) can be expressed as Cp ð1Þuðt 1Þ þ Cp1 ð1ÞDuðt 1Þ þ Cp2 D2 uðtÞ ¼ ðtÞ

(7)

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If the (i, j)-th entries of Cp ðLÞ; Cp ð1Þ; Cp1 ð1Þ; and Cp2 ðLÞ are cij ðLÞ; cij ð1Þ; fij ð1Þ; and kij ðLÞ respectively, we have: cij ðLÞ ¼ cij ð1ÞL þ jij ð1ÞLð1 LÞ þ kij ðLÞð1 LÞ2

(8)

Now, we deﬁne kij ðLÞ by kij ðLÞ ¼ k0 þ k1 L þ þ kp2 Lp2 ; thus (8) becomes: cij ðLÞ ¼ k0 þ ½cij ð1Þ þ jij ð1Þ þ k1 2k0 L þ ½k2 jij ð1Þ 2k1 þ k0 L2 þ ½k3 2k2 þ k1 L3 þ þ ½kp2 2kp3 þ kp4 Lp2 þ ½2kp2 þ kp3 Lp1 kp2 Lp

ð9Þ

If cij ðLÞ ¼ 0; then the coefﬁcient of Lp ; kp2 is zero. Since the coefﬁcient of Lp1 is zero, this leads to kp3 ¼ 0: Consequently, we have ki ¼ 0; i ¼ 0; 1; . . . ; p 3; and therefore kij ðLÞ ¼ 0: Also, if cij ðLÞ ¼ 0; then cij ð1Þ will also be zero, which leads to fij ð1Þ ¼ 0: Therefore, it can be concluded that if uj does not Granger-cause ui, then any (i, j)th element must be zero for all coefﬁcient matrices in the VAR. Also all (i, j)th coefﬁcient elements in the error-correction terms and in the vector autoregressive part of the equivalent VECM, will also be zeros. Further, from (7) if the (i, j)th element of Cp ðLÞ is non-zero, then at least the (i, j)th element is non-zero in Cp ð1Þ; Cp1 ð1Þ or Cp2 ðLÞ: Thus, we have just demonstrated that if uj does Granger-cause ui, then the (i, j)th element of Cp ðLÞ in the VAR is non-zero. In addition at least a single (i, j)th coefﬁcient element is non-zero in Cp ð1Þ; Cp1 ð1Þ or Cp2 ðLÞ of the equivalent VECM. Analogously, we can achieve a result that if all (i, j)th coefﬁcient elements in the error-correction terms and all (i, j)th coefﬁcient elements in the vector autoregressive part of the VECM are zeros, then every (i, j)th entry is zero for all coefﬁcient matrices in a VAR. The implications of the above outcome are obvious. If uj does not Granger-cause ui, then any (i, j)th entry must be zero for all coefﬁcient matrices in the VAR. Also all (i, j)th coefﬁcient elements in the equivalent VECM are zeros. In a similar way, we can demonstrate that if uj does Granger-cause ui, then the (i, j)th element of Cp ð1Þ in (1) is non-zero. Also, at least a single (i, j)th coefﬁcient element is non-zero in Cp ð1Þ; Cp1 ð1Þ or Cp2 ðLÞ in the equivalent VECM. Of note, an indirect causality from uj to ui through um

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indicates uj causing ui but only through um. Hence, uj Granger-causes um, um Granger- causes ui, and uj does not Granger-cause ui directly. We can easily demonstrate that the VAR in (1) has non-zero (m, j)th and (i,m)th elements and a zero (i, j)th element in Cp ðLÞ: This indirect causality can also be shown in the equivalent VECM, which has at least a single non-zero (m, j)th element and a single non-zero (i,m)th elements in Cp ð1Þ; Cp1 ð1Þ and Cp2 ðLÞ: Also all the (i, j)th elements in the equivalent VECM are zeros. Since Granger causality, Granger noncausality and indirect causality detected from both the ZNZ patterned VECM and its equivalent ZNZ patterned VAR are identical, and the use of the VECM is more convenient, it is obvious the ZNZ patterned VECM is a more straightforward and effective means of testing for the Granger-causal relations. The same beneﬁts will be present if the ZNZ patterned VECM is used to analyse cointegrating relations.

4. SEARCH ALGORITHM In the proposed algorithm for an I(2) system, the identiﬁcation of a ZNZ patterned C and the determination of ZNZ patterned d and a are carried out in the following way. First, the search method proposed by Penm and Terrell (1984) in conjunction with model selection criteria is used to select the optimal ZNZ patterned VECM to determine the ZNZ patterned C : Second, after the ZNZ patterned C is determined, the rank of the matrix C is then computed using the singular value decomposition (SVD) method, and the number of cointegrating vectors in the system will be known. Third, given the ZNZ patterned C has been determined and the rank of C has been computed, we then proceed with the pattern selection algorithm straightforwardly adapted for an I(2) system to obtain all acceptable ZNZ patterned d’s and a’s, which are consistent with the ZNZ patterned C : Although the work proposed here has some aspects in common with the work published in Penm et al. (1997), that approach cannot handle a system which includes some I(2) variables. It is therefore essential that we provide an approach that will cope with such a system. Let pd, pa and pda denote a ZNZ pattern of d, a and da0 , respectively, and pC the ZNZ patterned C deriving from pd and pa. If the (i, j)th entry of the product, pda is zero, and the corresponding (i, j)th entry of pC is also zero, then both pd and pa are acceptable. This pattern selection algorithm for use in cointegration assessment avoids the need to evaluate all possible ZNZ patterned d0 s and a0 s. To begin this pattern selection algorithm we ﬁrst construct a regression tree proposed in Seber (1977) for a, where each node of the tree represents a

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pattern for a. Furthermore, there is a d regression tree embedded in each node of the a tree, with the nodes of this regression tree representing all possible patterns of d. Suitable pattern selection rules are then set up in the algorithm to restrict the search to the acceptable patterns of d and a only. Since these rules avoid searching along unfavourable branches, a complete search through all possible patterns of d and a is not required. Thus a considerable saving of computation time and storage can be achieved. After this pattern selection algorithm is conducted, all acceptable patterns of d and a will be found. The ZNZ patterns of acceptable d0 s and a0 s depend on the pattern of C (determined earlier). Of note, the imposition of zero entries on a does not preclude a similar restriction on d. One example is when the determined C contains a zero row, such as 0 0 0 0 C ¼ 1 1 0 1 where 1 denotes a non-zero entry. In this case zero restrictions will have to be imposed on the ﬁrst row of d. This is because the pattern of C implies that the cointegrating relations in the system do not involve the ﬁrst variable in the system. Noting that the number of zeros in d and a are not ﬁxed even with a given ZNZ patterned C ; many differently patterned d0 s and a0 s can be obtained using the pattern selection algorithm. A simple example can be used for demonstration. Let 2 3 1 1 0 0 0 0 6 7 C ¼ 4 1 1 0 0 0 0 5, 1

1

1

0

0 0

where the rank of C is 2. At least three candidate sets of d and a0 can be obtained, which are 2 3 0 1 0 1 1 0 0 0 6 7 0 0 1 (10) d¼4 5 and a ¼ 1 1 0 0 0 0 1 1 2

0 6 d ¼ 40 1

3 1 7 15 1

and

a0 ¼

1 1

0 1 1 0

0 0

0 0

0 0

(11)

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2

0 6 d ¼ 40 1

3 1 7 15 1

and

a0 ¼

0

0 1

0

0

0

1

1 0

0

0

0

(12)

The cointegrating relationships implied by (10), (11) and (12) are different. While (10) and (11) imply that u1, u2 and u3 are cointegrated, (12) indicates that u1 and u2 are cointegrated and u3 is an I(0) series. It is obvious that we cannot take the zero-maximising approach of choosing the a with the maximum number of zero entries to determine the ZNZ patterns of d and a. If we do, then we select (12), not (10) nor (11), while the true model could certainly be either (10) or (11). As a result, model selection criteria will again be used to determine the optimal ZNZ patterns for d and a. Although (10) and (11), in theory, both indicate that u1, u2 and u3 are cointegrated, in practice different forecasting performance can result from (10) and (11). Using model selection criteria in this situation will allow discrimination between (10) and (11) based on forecasting performance. To obtain the correct speciﬁcation for d and a, we next check to see whether d and a can be uniquely obtained by factorising C : If this is possible, the factorisation can be carried out. If it is not possible, the efﬁcient estimation of I(2) cointegrated systems is employed based on a triangular ECM representation, (e.g., Stock & Watson, 1993) to estimate a. Since any non-zero entry in a could be normalised to unity, the estimation procedure is repeated with all possible normalisations. Again different normalisations in practice may result in different forecasting performances for the model. The normalisation, which produces the smallest value (associated with the best forecast adjusted for the number of independent parameters involved) for model selection, is then selected as the candidate a. After the optimal normalisation is determined for every candidate a, we then estimate the associated acceptable ZNZ patterns of d in the VECM framework and employ model selection criteria again to determine the optimal d and a. In the example given above, model selection criteria will help to select between (10), (11) and (12), since the approach of zero-maximisation should not be used to determine a.

5. PATTERN SELECTION ALGORITHM The pattern selection algorithm for use in cointegration analysis provides us with a means of ﬁnding all acceptable patterns for d and a and without

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evaluating every possible pattern that arises from the relation Cn ¼ da0 : The procedure for constructing regression trees consists of two stages as follows. (A) A g-entry regression tree for a. The ﬁrst step is to construct a g-entry regression tree for a, where g ¼ r 2 s. As noted in Section 4, pd, pa, pda and pC denote a ZNZ pattern of d, a da0 and C ; respectively. For instance, when d¼

0

0

0:8

0:3

0

0

,

then pd can be expressed as

0 0 1 0

1 , 0

where 1 represents a non-zero entry and 0 a zero entry (see Seber, 1977). Analogously pa, pda and pC can be constructed. The root of the tree represents a pattern with all g entries. The mth generation, m ¼ 1,2,y,g1, is taken by interior nodes, of which there are C gm nodes in the mth generation. Those nodes represent the possible pa patterns in which the g entries have non-zero entries. To move from one generation to the next we make use of the rule that the ath offspring in generation m has a–1 offspring in generation m+1, which is the next generation down the tree (see Seber, 1977). In setting up the second and later generations, natural ordering is used to provide the ordering of the nodes from left to right. For instance in the 3-entry case of Fig. 1 we would have in the second generation the 3 non-zero entry subsets, i.e., 1, 2 and 3. A node describes a pattern in terms of the non-zero entries. The regression tree for a can be transversed in natural order (see Seber, 1977) (123)-(12)-(13)-(23)-(1)-(2)-(3). Root 123

12

13

1

23

2

3 Null

Fig. 1.

A Three Variable Regression Tree.

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It is noted that the amount of both computation time and storage increases exponentially as g becomes larger. We therefore propose the following selection criteria to avoid travelling along unfavourable branches during the search. Selection criteria: After the regression tree is constructed we start with the selection. This is undertaken using the following criteria: Let S be a set of non-zero entries of a and denote the pa(S) node as the node representing the pa(S) pattern. Also let U be a subset of S and the pa(U) node represents the pa(U) pattern. (1) For a given pa(S) if there exists a non-zero entry of pC, but the corresponding entry of pda(S) is zero for all possible pd, then this pa(S) is not acceptable. The node representing pa(S) can be ignored and so can the node representing pa(U). (2) If pa(S)0 has one or more zero rows, the pa(S) and the pa(U) nodes can be ignored, because the ranks of a(S) and a(U) are not full, and they need to be. (3) If the non-zero entries of a row of pa0 correspond to either of the following conditions, then pa node can be ignored, because no cointegrating relation can be formed (a) only one I(2) variable; (b) no I(2) variable and only one I(1) variable. (4) If pa0 has two or more identical rows, the node representing pa can be ignored because these identical rows represent the same cointegrating relation. (5) If a pa is examined, then any node represented by Mpa , where M is a r r row permutation matrix, can be ignored. This is because both Mpa and pa represent the same cointegrating relation. There are r!pa patterns representing the same cointegrating relation. (B) An n-entry regression tree for d. In the second step, for each pa we construct an n-entry regression tree for d, where n ¼ s r. The regression tree for d can also be transversed in natural order. Selection criteria: The selection is performed using the following criteria. Let E be a set of non-zero entries of d and denote the pd(E) node as the node representing the pd(E) pattern. Also let R be a subset of E and the pd(R) node represents the pd(R) pattern. (1) For a given pa0 , if there exists a zero entry of pd(E)a, but the corresponding entry of pC is non-zero, then the pd(E) node can be ignored and so can the node representing pd(R).

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(2) If pd(E) has one or more zero columns then these pd(E) and pd(R) nodes can be ignored. This is because the ranks of d(E) and d(R) are not full. (3) If an entry of pda is non-zero but the corresponding entry of pC is zero, then this entry of pda has to be restricted to zero. If either of the following two conditions is met, the pd node can be ignored: (a) If the number of non-zero entries of pd involved is less than the number of restrictions, then there will be no acceptable solution for pd. For instance, consider " # " # a11 a12 a13 a14 d11 0 0 d¼ ; a ¼ d21 d22 a21 a22 a23 0 " # 0 1 1 1 and pC ¼ 0 0 0 1 In this example we have the following three restrictions: d21 a1k þ d22 a2k ¼ 0;

k ¼ 1; 2; 3

Although a0 can be estimated by using the estimation method proposed in this section, there will be no solution for d21 and d22 because we have only two unknowns, d21 and d22. (b) If any non-zero entry of pd has to be zero to satisfy restrictions, then the given pd is unacceptable. For instance, consider " # " # 0 a12 0 0 d11 0 0 d¼ ; a ¼ a21 0 a23 0 d21 d22 " # 0 1 0 0 and pC ¼ 0 1 1 0 Now, we have the restriction d22 a21 ¼ 0 This indicates that d22 ¼ 0. Thus pd is unacceptable.

6. APPLICATIONS In this section, two applications to ﬁnancial market data are presented to illustrate the usefulness of the procedure.

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6.1. The Three-Variable Stock Market System The ﬁrst application examines the relationships among the stock market, money supply and inﬂation. Prior research has shown that these three variables are linked. First, despite the Fisher effect, inﬂation has generally been shown to exhibit a negative relationship with the stock market (e.g. Fama & Schwert, 1977; DeFina, 1991). The reasons that have been advanced to explain this relationship include inﬂationary expectations, ﬁxed price nominal contracts and the tax shield effects associated with depreciable ﬁxed assets. However, as Stulz (1986) argues this relationship is dependent also on money growth. Second, announcements of the money supply have been shown to convey a valuable information signal for the stock market. While there is some conjecture as to the sign of the relationship, it is generally accepted that a negative relationship exists between the money supply and stock returns. The general theory advanced is that the linkage between the money supply and interest rates affects economic activity and corporate profits. However, there are questions over whether the real rate of interest is affected. Two main hypotheses have emerged.3 First, changes in the money supply may alter expectations about monetary policy. For instance, a current increase in the money supply may foreshadow a future tightening of monetary policy from the Central Bank resulting in expectations of higher interest rates, which in turn acts to depress stock prices through both a rise in the real rate and a reduction in economic activity. Second, a continued increase in the money supply relative to the target is likely to raise expectations of higher inﬂation which in turn leads to higher nominal interest rates through the inﬂation premium in nominal rates. As discussed above, higher expected inﬂation decreases stock prices. Both these hypotheses suggest a negative sign on the relationship between money supply and the stock market which is generally supported by the evidence. For instance, Hardouvelis (1988) shows that increases in the money supply induce rises in interest rates. Moreover, Pearce and Roley (1985) and Jain (1988) ﬁnd evidence of a significant negative relationship between unexpected money supply signals and stock market movements. Finally, the third interaction in the system is the linkage between money supply and inﬂation. This relationship is well known and rooted in monetary theory (e.g., Mishkin, 1992). Despite arguments over the inﬂuence of lags and the money multiplier, the economic relationship is well established. Of note, the purpose here is not to test in detail hypotheses surrounding these variables, but rather to illustrate how major relationships in the ﬁnancial markets can be tested.

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The following data are used in the test. We focus on the Australian market due to the ease of data availability and the lack of previous research in this area in the Australian market. The All Ordinaries Index (AOI) is used as the stock market indicator. The AOI is a broad market indicator with coverage of around 320 stocks representing about 90–95% of total market capitalisation. The index is value-weighted and calculated on the basis of market capitalisation of the constituent stocks traded on the Australian Stock Exchange. Money supply is measured by the standard stock of money (M3). Inﬂation is measured as the seasonally adjusted consumer price indices for Australia (CPIAUS). The CPI measures the aggregate price behaviour of all consumer goods and services and is commonly used by government and industry in Australia to adjust for cost-of-living allowances in wage and beneﬁt contracts. Data are collected from DataStream over the period June 1981 through December 1999. While money supply and stock market index data are available over shorter frequencies, the CPI ﬁgures are produced on a quarterly basis, and hence this forms the basis for the sampling frequency. The Dickey and Pantula (1987) procedure is used to test for the presence of more than one unit root. The procedure rejects the hypothesis of three unit roots for both log(CPIAUS) and log(M3) and the hypothesis of two unit roots for log(AOI) (at the 5% level). On the basis of the tests our work proceeds with both log(CPIAUS) and log(M3) having two unit roots and log(AOI) one unit root. We then make use of the procedure described in Section 4 to identify the speciﬁcation for the VECM formed by these variables. For brevity only the results using the HQC criterion, as suggested by Hannan and Quinn (1979), are presented in Table 1.4 In addition, to check the adequacy of the model ﬁt, the strategy suggested in Tiao and Tsay (1989) is used, with the proposed Penm and Terrell (1984) algorithm applied to test the residual vector series, using the HQC criterion. The results in Table 1 support the residual vector being a white noise process. The results indicate that there has been no significant variable omitted. Given the determined speciﬁcation of this VECM, the SVD method is then applied to the estimated matrix C : The estimated singular values indicate that the rank of the matrix C is 2. We then utilise the proposed pattern selection algorithm in conjunction with HQC to select all acceptable ZNZ patterns of d and a. The results indicate that only three sets of d and a are acceptable. Subsequently we utilise the factorisation method which is now available to estimate each acceptable a. After this we estimate each d in the VECM framework. HQC is again utilised to ﬁnally select the optimal d and a as presented in Table 1.

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Table 1. The VECM for the Relationship, Linking Money Supply, Inﬂation and Stock Market Indicator for Australia Selected by HQC Using the GLS Procedurea. Variables: u 1t = log(M3), u 2t = log(CPI AUS), Sample Period: 1981/Q2 to 1999/Q4

0.340 (0.110) 0.148 + (0.105 ) 0.0

∆2 u1t ∆2 u 2t ∆2 u 3t

0 .0

0.0

0.0

0.468 (0.091) 0.0

0.0

0 .0

− 0.105

(0.020) 0 .0

(0.105) 0 .0

(0.070) 0 .0

0.0

0.0

−0.045

1.081

0.0

0.0 ˆ

Residual analysisb Value of HQC

∆2 u1t −1 0.0 ∆2 u 2t −1 + ∆2 u 3t -1 0.0

0 .0

0.388

0.0

0.0

0.0

− 0.045

ˆ ' =

lags

u 3t = log(AOI).

u u u

1 t -1 2 t -1 3 t -1

+

0.0

0.0

0.0

0.0

0.0

0 .0

0.155 (0.092) 0.0 0 .0

0 .0

0.0

0.220

0 .0

0.0

(0.121) 1.081 (0.115)

0.0

0.0 0.0

0.0

∆2 u1t −3 ∆2 u 2t −3 + ∆2 u 3t −3

∆u 1t −1 ∆u 2t −1 = ( t ) ∆u 3t -1

1.0

1.0 −8.433 2.278 0.0 0.0 − 4.789

0 1 1.0 1.019

2 3 1,2 1,3 1.010 1.018 1.031 1.038

2,3 1,2,3 1.029 1.050

Long-term Cointegrating Relationship Identified: ∆log(AOI) is stationary log(M3) = 8.433log(CPIAUS) – 2.278log(AOI) + 4.789∆log(AOI) CPI AUS Granger Causal Patternc : M3 a b c

AOI

Standard errors in parentheses. ∆ denotes first difference. For simplicity, the values of HQC for q>3 are not presented, but can be supplied on request. x Granger-causes y: (Notation : x → y); Feedback exists between x and y: (Notation: x ↔ y).

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The results are generally consistent with economic intuition and prior evidence. The causality identiﬁed in the selected ZNZ patterned VECM conﬁrms that M3 is an independent source of ﬁnancial and economic disturbance, and indirect causality exists from M3 through CPIAUS to AOI. This result supports the impact that money supply has on stock prices through inﬂationary pressures. Of note, the presence of this indirect causality cannot be detected from inspecting the non-zero elements in all their coefﬁcient matrices of a conventional full-order VECM. Among CPIAUS, M3 and AOI, two cointegrating vectors are found. The ﬁrst selected cointegrating vector means that Dlog(AOI) is stationary. The second selected cointegrating vector conﬁrms that log(CPIAUS), log(AOI) and Dlog(AOI) are cointegrated with log(M3).5 The positive sign between log(M3) and log(CPIAUS) and the negative sign between log(M3) and log(AOI) are consistent with the hypotheses discussed above that increases in the money supply lead to an increase in inﬂation with a consequent negative effect on the stock market.

6.2. Purchasing Power Parity The second application concerns testing of PPP, using the bilateral exchange rate between the Australian and the US Dollar. Formally the PPP condition can be expressed as E t ¼ Pt =Pt ; where E t denotes units of domestic currency per unit of foreign currency, Pt domestic price level and Pt foreign price level. The theory of cointegration has been utilised to test for PPP in an I(1) system. Following Engle and Granger (1987), logðE t Þ and logðPt =Pt Þ are characterised as integrated of order 1. If there is a long-term cointegrating 0 relationship between them, where a0 X t ¼ ða1 ; a2 Þ½logðE t Þ; logðPt =Pt Þ ¼ t with t as stationary, then it can be concluded that in the I(1) system the necessary condition for the PPP hypothesis is acceptable in the long-term. If a0 ¼ 1 1 ; then both sufﬁcient and necessary conditions for PPP are acceptable (e.g. Corbae & Ouliaris, 1990; Oh, 1996). Dutt and Ghosh (1995) adopt the Phillips–Hansen Fully Modiﬁed Ordinary Least Squares procedure to regress logðE t Þ against logðPt =Pt Þ: The Phillips–Hansen procedure corrects for both endogeneity in the data and asymptotic bias in the coefﬁcient estimates. The Phillips and Ouliaris (1990) test is then applied to determine the order of integration of the residuals for the necessary condition. Following early work on PPP relationships such as Gailliott (1971), cointegration theory has been used in recent years to test for PPP. Fisher and

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Park (1991) have tested bilateral exchange rates for the currencies of 10 major industrial economies and found support for the necessary condition for PPP in the exchange-rate behaviour of many of them. Conejo and Shield (1993) test for PPP in Latin American exchange rates and ﬁnd that the necessary condition for PPP holds for Brazil and Mexico. Typically, the ratio logðPt =Pt Þis treated as one variable, which does not necessarily have the same integration order as logðPÞ and logðP Þ (e.g., Corbae & Ouliaris, 1990; Oh, 1996). However, using the three variables – log(E), logðPÞ and logðP Þ – in one model does not necessarily result in the same order of integration for each variable. For instance, log(E) is wellknown to be I(1), but both logðPÞ and logðP Þare often found to be I(2). These results imply a need for an I(2) model, rather than the more conventional I(1) approach. To illustrate, the quarterly seasonally adjusted consumer price indices for Australia (CPIAUS) and the United States (CPIUS), and the exchange rates (EXCH) per US Dollar from March 1976 through December 2004 are used. The data are obtained from DataStream. The u vector comprises log(CPIAUS), log(CPIUS) and log(EXCH). The unit root tests indicate that both log(CPIAUS) and log(CPIUS) are I(2) while log(EXCH) is I(1). The results identiﬁed by HQC are presented in Table 2.6 The selected pattern of the cointegrating vector contains some interesting ﬁndings. The selected cointegrating vector conﬁrms that both the inﬂation variables, log(CPIAUS) and log(CPIUS) are cointegrated with log(EXCH). The same sign occurring in log(EXCH) and log(CPIAUS), as shown in Table 2, indicates that, ceteris paribus, an increase in CPIAUS is associated with a depreciation of the Australian Dollar relative to the US Dollar. That is, consistent with standard economic theory, an increase in local inﬂation is associated with a depreciation of the local exchange rate. Similarly, the opposite sign occurring in log(EXCH) and log(CPIUS) indicates that, ceteris paribus, an increase in CPIUS is associated with a depreciation in the US Dollar. Again, this is consistent with economic theory. The presence of the long-term cointegrating relationships is consistent with PPP holding within this I(2) system. In looking for causal relations among the nominal exchange rate, domestic and foreign price levels, the VECM we have selected indicates direct Granger causation exists from CPIUS to CPIAUS. That is, inﬂation in the US price levels generally produces a direct response in the Australian CPI, as the US economy is the hub of the world economy in which Australia is involved. The feedback between CPIAUS and EXCH is consistent with both changes in local inﬂation impacting on the exchange rate and changes in the

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Table 2. The VECM for the Relationship, Linking Exchange Rates and Consumer Price Indices, between Australia and the USA Selected by HQC Using the GLS Procedurea. Variables: u 1t = log(CPI AUS), u 2t = log(CPI US), u 3t = log(EXCH AUS/US) Sample Period: 1976/Q1 to 2004/Q4

∆2u1t ∆2u2t + ∆2u3t

0.732 (0.080) 0.0 0.0

−0.388 (0.148) 0.253 (0.908) 1.729 (1.118)

0.332 (0.075) 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 ˆ = −0.278 0.0

0.0 0.0 0.0

∆2u1t −1 ∆2u2t −1 + ∆2u3t-1

∆ 2 u1t −3 ∆ 2 u 2t −3 + ∆ 2 u 3t −3

0.482 (0.096) 0.0 −1.205 (0.611)

0.0

0.0

0.0

0.0

0.0

0.0

0.242 (0.120) 0.0

−0.278 (0.151) 0.0

−0.085 (0.051) 0.0

0.0

0.0

0.0

+

u1t-1 /10. u 2t-1 /10. = ( t ) u 3t-1 /10.

and ˆ ' = [ −0.871 1.0 0.305 0.0 0.0 0.0 ]

Residual analysisb lags 0 1 2 3 1,2 1,3 Value of HQC 1.0 1.010 1.009 1.012 1.011 1.015 Long-term Cointegrating Relationship Identified: 1)

∆2u1t −2 ∆2u2t −2 ∆2u3t-2

2,3 1.018

1,2,3 1.021

0.305log(EXCH) = 0.871log(CPIAUS) – log(CPIUS)

Granger Causal Pattern c :

CPIAUS CPIUS

EXCH

a

Standard errors in parentheses. ∆ denotes first difference. For simplicity, the values of HQC for q>3 are not presented, but can be supplied on request. Also, the results confirm that the estimated residual process is a white noise process, and a deterministic trend does not exist in the proposed model. c x Granger-causes y: (Notation : x → y); Feedback exists between x and y: (Notation: x ↔ y). b

exchange rate impacting on local inﬂation. The one-way causation from CPIUS to EXCH reﬂects the dominant impact of the US economy on a country heavily reliant on trade through the exchange rate. Thus a shock to the US economy results in a direct response of the exchange rate, changing the value of the local currency relative to the US Dollar. These observations

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in turn offer some insight into the dynamics among the variables despite PPP holding in the long run.

7. CONCLUSION The use of cointegration to examine relationships among ﬁnancial variables is of increasing importance. However, current techniques do not explicitly allow restrictions requiring zero entries, whereas applications of VECM models to ﬁnancial market data have revealed that the beneﬁt of imposing such restrictions where the underlying true VECM structure contains zero entries. In such cases, the use of standard full order VECM models is likely to lead to weaker inferences. In this paper, an effective algorithm has been developed to select the optimal ZNZ patterned cointegrating and loading vectors in a subset VECM with zero entries for an I(2) system. Several ﬁnancial series are potentially of order I(2) and hence the procedure here has substantial applicability. Two case studies are analysed to demonstrate the usefulness of this algorithm. The ﬁrst case study deals with the inter-relationships between the stock market, money supply and inﬂation and the results are generally consistent with both theory and prior evidence. In the second case study, PPP is examined between the Australian and US Dollars. The results support the necessary condition for PPP to hold. These case studies are not designed to be an exhaustive assessment of all hypotheses, but rather to illustrate in a limited context the power of the ZNZ VECM approach. Even so, they demonstrate that the proposed algorithm is effective and leads to an efﬁcient analysis of the cointegrating relationships within an I(2) system.

NOTES 1. Johansen (1991) undertakes hypothesis testing for specific ZNZ patterned cointegrating vectors and loading vectors. However that approach depends on a priori hypotheses on the ZNZ patterns of cointegrating vectors and loading vectors. It is difﬁcult to use Johansen’s method to obtain the correct ZNZ patterns for the cointegrating and loading vectors when there are a large number of possible hypotheses. This is especially the case if the number of cointegrating vectors in the system and the number of variables involved in the cointegrating relations are also large. 2. In this paper, only the case of d ¼ 2 is considered, although the procedure can be generally applied to models with d42. 3. We could propose another hypothesis, suggesting that money supply expansion leads to increased general price levels. This creates spillovers into company profitability, thereby affecting stock prices.

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4. The results are obtained using GLS estimation on a SUN 7800 running Unix. 5. We also check the adequacy of the model ﬁt to the additional two models. For the ﬁrst model, we remove Dlog(AOI) from the two selected cointegrating relations in the VECM described in Table 1, and then apply the residual analysis to the ﬁrst model. The HQC criterion indicates that the residual vector being a VAR process with a longest lag 4, and thus not being a white noise process. For the second model, we only remove Dlog(AOI) from the cointegrating relation which previously included log(M3), log(CPIAUS), log(AOI) and Dlog(AOI), and then undertake the residual analysis. The HQC criterion indicates that the residual vector is a VAR process with lag 1, and thus not a white noise process either. The ﬁndings show that Dlog(AOI) is critically involved in each cointegrating relation, and therefore cannot be removed, even if Dlog(AOI) is stationary. 6. We investigate PPP between the US Dollar and the Japanese Yen by using an I(2) model. The unit root tests reject the hypothesis of two unit roots for the CPI in Japan (CPIJapan). Subsequently it is assumed that log (CPIJapan) has one unit root. However Section 2 shows that an I(2) system requires both log(CPIUS) and log (CPI Japan) to be I(2); therefore the proposed procedure cannot be applied to the I(2) model. Brailsford, Penm, and Terrell (2004) have tested PPP between the US Dollar and the Japanese Yen in an I(1) model, which includes price ratios, interest rate ratios and the exchange rate. The results indicate that PPP does exist in the long run if the interest rate ratio variable is involved.

REFERENCES Brailsford, T. J., Penm, J. H. W., & Terrell, R. D. (2004). A new approach to testing PPP: Evidence from the Yen. Research in Finance, 21, 135–154. Conejo, C., & Shield, M. P. (1993). Relative PPP and the long-term terms of trade for ﬁve Latin American countries, a cointegration approach. Applied Economics, 25(12), 1511–1515. Corbae, D., & Ouliaris, S. (1990). A test of long-run purchasing power parity allowing for structural breaks. The Economic Record, 167, 26–33. DeFina, R. (1991). Does inﬂation depress the Stock market? Business Review, Federal Reserve Bank of Philadelphia, Nov–Dec, 3–12. Diamandis, P. F., Georgoutsos, D. A., & Kouretas, G. A. (2000). The monetary model in the presence of I(2) components: Long-run relationships, short-term dynamics and forecasting of the Greek Drachma. Journal of International Money and Finance, 19, 917–941. Dickey, D. A., & Pantula, S. G. (1987). Determining the order of differencing in autoregressive processes. Journal of Business and Economic Studies, 5(4), 455–461. Dutt, S. D., & Ghosh, D. (1995). Purchasing power parity doctrine, weak and strong form tests. Applied Economics Letters, 2(3), 16–20. Engle, R. F., & Granger, C. W. J. (1987). Cointegration and error correction, representation, estimation and testing. Econometrica, 55, 69–104. Engle, R. F., & Yoo, B. S. (1987). Forecasting and testing in cointegrated system. Journal of Econometrics, 35, 143–159. Engle, R. F., & Yoo, B. S. (1991). Cointegrated economic time-series, An overview with new results. In: R. F. Engle & C. W. J. Granger (Eds), Long-Run Economic Relationships. New York: Oxford University Press.

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Fama, E. F., & Schwert, G. W. (1977). Asset returns and inﬂation. Journal of Financial Economics, 7, 115–146. Fisher, E. O., & Park, J. Y. (1991). Testing purchasing power parity under the null hypothesis of cointegration. The Economic Journal, 101, 1476–1484. Gailliott, H. J. (1971). Purchasing power parity as an explanation of long-term changes in exchange rates. Journal of Money, Credit and Banking, 2, 348–357. Granger, C. W. J., & Lee, T. H. (1989). Multicointegration. Advances in Econometrics, 8, 71–84. Granger, C. W. J., Huang, B.-N., & Yang, C.-W. (2000). A bivariate causality between Stock prices and exchange rates: Evidence from recent Asian ﬂu. Quarterly Review of Economics and Finance, 40, 337–354. Hannan, E. J., & Deistler, M. (1988). The statistical theory of linear systems. New York: John Wiley. Hannan, E. J., & Quinn, B. G. (1979). The determination of the order of an Autoregression. J. Roy. Statist. Soc., B 41, 190–195. Hansen, M. H., & Yu, B. (2001). Model selection and the principle of minimum description length. Journal of the American Statistical Association, 96(454), 746–774. Hardouvelis, G. A. (1988). Economic News, exchange rates and interest rates. Journal of International Money and Finance, 7, 23–35. Jain, P. C. (1988). Response of hourly stock prices and trading volume to Economic News. Journal of Business, 61, 219–231. Johansen, S. (1991). Estimation and hypothesis testing of cointegrating vector in Gaussian vector autoregression models. Econometrica, 59, 1551–1580. Kailath, T. (1980). Linear systems. Englewood Cliffs, NJ: Prentice Hall. King, R., Plosser, C., Stock, J. H., & Watson, M. W. (1991). Stochastic trends and Economic ﬂuctuations. American Economic Review, 81, 819–840. LeSage, J. P. (1990). A comparison of the forecasting ability of ECM and VAR models. Review of Economics and Statistics, 72, 664–671. Mishkin, F. S. (1992). The economics of money, banking and financial markets (3rd ed.). New York: Harper Collins. Oh, K. Y. (1996). Purchasing power parity and unit root tests using panel data. Journal of International Money and Finance, 15(3), 405–418. Pearce, D. K., & Roley, V. V. (1985). Stock prices and Economic News. Journal of Business, 58, 49–67. Penm, J. H. W., & Terrell, R. D. (1984). Multivariate subset autoregressive modelling with zero constraints for detecting overall causality. Journal of Econometrics, 24, 311–330. Penm, J. H., Penm, J. H. W., & Terrell, R. D. (1997). The selection of ZNZ patterned Cointegrating vectors in error-correction modelling. Econometric Reviews, 16(3), 281–304. Phillips, P. C. B., & Ouliaris, S. (1990). Asymptotic properties of residual based tests of cointegration. Econometrica, 58, 165–193. Seber, G. A. F. (1977). Linear regression analysis. New York: Wiley. Stock, J. H., & Watson, M. W. (1993). A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica, 61, 783–820. Stulz, R. M. (1986). Asset pricing and expected inﬂation. Journal of Finance, 41, 209–223. Tiao, G. C., & Tsay, R. S. (1989). Model speciﬁcation in multivariate time-series. Journal of Royal Statistical Society, B 51, 157–213.

EXCHANGE RATE COINTEGRATION ACROSS CENTRAL BANK REGIME SHIFTS Jose A. Lopez ABSTRACT Foreign exchange rates are examined using cointegration tests over various time periods linked to regime shifts in central bank behavior. The number of cointegrating vectors appears to vary across these regime changes within the foreign exchange market. For example, cointegration is not generally found prior to the Plaza Agreement of September 22, 1985, but it is present after that date. The significance of these changes is evaluated using a likelihood ratio procedure proposed by Quintos (1994). The changing nature of the cointegrating relationships indicate that certain aspects of central bank activity do have long-term effects on exchange rates.

1. INTRODUCTION ‘‘Nevertheless, the empirical evidence, although allowing for the possibility of short-lived effects, does not ascribe to [central bank] intervention a long-lasting effect on the foreign exchange market.’’ Edison (1993)

Research in Finance, Volume 22, 327–356 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(05)22012-9

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The above quote is the concluding sentence of Edison’s survey on the efﬁcacy of central bank intervention in the foreign exchange market. The short-term impact of central bank intervention has been extensively studied, even down to the level of continuous time data (Goodhart & Hosse, 1993). However, the long-term impact of central bank behavior in the foreign exchange market has not been as carefully examined. The long-term behavior of exchange rates is an important area of economic research and has been addressed by Engel and Hamilton (1990), Mark (1995) and others. An important element of long-term exchange rate dynamics is the regime shifts in central bank behavior, such as the Plaza Agreement of 1985. In this paper, the long-term impact of such regime shifts is examined using cointegration procedures. Cointegration, as introduced by Engle and Granger (1987), is used to test for the existence of long-term relationships among nonstationary economic variables. Exchange rates are considered to be nonstationary time series, as ﬁrst established by Meese and Singleton (1982), and systems of exchange rates may exhibit cointegrating relationships. However, as pointed out by Granger (1986), ﬁnancial asset prices determined in efﬁcient markets should not be cointegrated. That is, if they were cointegrated, one could forecast a given series on the basis of other series in the cointegrated system, and the efﬁcient markets hypothesis would not hold. Several studies have tested for cointegration in systems of foreign exchange rates, such as Hakkio and Rush (1989), Coleman (1990), Copeland (1991), Baillie and Bollerslev (1989), and Diebold, Gardeazabal, and Yilmaz (1994).1 Using various cointegration testing procedures, these studies achieve different results. Specifically, Baillie and Bollerslev (1989) ﬁnd cointegration in a system of seven daily exchange rates, but Diebold et al. (1994) ﬁnd no cointegration in this system once a trend is explicitly modeled. This paper attempts to extend these studies by incorporating structural breakpoints into the cointegration analysis. Structural breaks in data series, particularly in asset price series, usually indicate fundamental changes in the underlying data generating processes. Such breaks may significantly alter the equilibrium relationships between data series, and tests of the long-term behavior of these series should take account of them.2 The breakpoints examined are linked to specific regime shifts in central bank behavior in the foreign exchange market. Generally, studies of such central bank activities have been limited to intervention, ofﬁcial sales or purchases of foreign assets against domestic assets. Much research has found these activities to have little, if any, impact on the behavior of exchange rates. This paper focuses instead on transactions or ofﬁcial announcements by central banks that, in

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essence, indicate a regime shift in their behavior. Examples of such intervention activities are the formation of the European Monetary System in March 1979 and the Plaza Agreement of September 1985. Five such episodes are examined in this paper. With respect to the cointegration analysis, such regime shifts may be considered as structural breaks that fundamentally alter any long-term equilibrium relationships, which may exist. Thus, the number of cointegrating vectors present in the periods before and after the speciﬁed structural break may differ. Quintos (1994, 1995) presents a procedure for testing whether such differences in the number of cointegrating vectors induced by structural breaks are statistically significant. She specifically states that the procedure addresses structural breaks that potentially change the definition of a system’s equilibrium relationship. She suggests that such a change could be brought about by fundamental changes in the behavior of institutions, such as central banks. The main ﬁnding of this paper is that the speciﬁed incidents of central bank regime shifts do impact the long-term behavior of exchange rates. Varying numbers of cointegrating relationships are found before and after the structural breaks, and the changes are mostly found to be significant. For example, no cointegrating relationships are found in the period before the Plaza Agreement of September 22, 1985, but after that date, evidence of cointegration is found. Since the Plaza Agreement signaled concerted intervention by central banks to cause a dollar depreciation, it is not surprising that new long-term relationships (or market equilibria) between exchange rates arose in the post-Plaza period. Similar results are found for other breakpoints and for a subsystem of exchange rates consisting solely of EMS currencies. Section 2 describes the exchange rate data used as well as the proposed structural breakpoints examined. Section 3 outlines the cointegration techniques used in the analysis. Section 4 summarizes the literature on cointegration tests of exchange rates and presents the cointegration results for the various speciﬁed time periods and currencies. Section 5 concludes.

2. THE DATA AND STRUCTURAL BREAKPOINTS The spot foreign exchange rates used in this paper are the Federal Reserve Bank of New York (FRBNY) rates as recorded at noon in the New York foreign exchange market. The eight exchange rates examined are the British pound (BP), the German mark (DM), the Japanese yen (JY), the French

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franc (FR), the Swiss franc (SF), the Canadian dollar (CD), the Dutch guilder (NG) and the Italian lira (LI); see Figs. 1–8. The ﬁrst six exchange rates are historically the most actively traded, as per various central bank surveys; see FRBNY (1992) and Bank for International Settlements (1998). The exchange rates are expressed as the natural log of foreign currency units per US dollar, and the ﬁrst differences of these series are the daily rates of return for dollar-based investors; i.e., Dyt ¼ 100 log(st)100 log(st–1).

Fig. 1.

Daily Spot BP/S Exchange Rate 1974–1992.

Fig. 2.

Daily Spot DM/S Exchange Rate 1974–1992.

Exchange Rate Cointegration

Fig. 3.

Daily Spot JY/S Exchange Rate 1974–1992.

Fig. 4.

Daily Spot FR/S Exchange Rate 1974–1992.

331

Cointegration tests examine the long-term behavior of economic data. Thus, as discussed by Hakkio and Rush (1991), the length of the ‘‘longterm’’ is an immediately relevant question. They argue that the proper length of the ‘‘long-term’’ must be determined in light of the economic

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Fig. 5.

Daily Spot NG/S Exchange Rate 1974–1992.

Fig. 6.

Daily Spot LI/S Exchange Rate 1974–1992.

question being addressed. Two factors can be used to determine the proper time interval over which to examine exchange rates: One is market based and the other is forecast based. Given the massive daily trading volume in the foreign exchange markets, new information is quickly incorporated into exchange rates; this suggests a rather short period of calendar time for the

Exchange Rate Cointegration

Fig. 7.

Daily Spot SF/S Exchange Rate 1974–1992.

Fig. 8.

Daily Spot CD/S Exchange Rate 1974–1992.

333

‘‘long-term’’ horizon of exchange rate determination. Second, forecasts based on daily data that are usually made only several months ahead, as in Diebold et al. (1994). Given these two reasons, time periods longer than one year (approximately 250 observations) seem to be appropriate horizons over which to examine the long-term behavior of daily exchange rates. As shown

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Table 1.

Summary of the 11 Time Periods Examined.

Post-1973 period Pre-‘‘Dollar Rescue’’ period Post-‘‘Dollar Rescue’’ period Pre-EMS period Post-EMS period Pre-Peak period Post-Peak period Pre-Plaza period Post-Plaza period Pre-Louvre period Post-Louvre period

Start date

End date

Observations

01/04/74 01/04/74 11/02/78 01/04/74 03/14/79 01/04/74 02/26/85 01/04/74 09/23/85 01/04/74 02/23/87

12/31/91 11/01/78 12/31/91 03/13/79 12/31/91 02/25/85 12/31/91 09/20/85 12/31/91 02/20/87 12/31/91

4,513 1,213 3,300 1,301 3,212 2,791 1,722 2,938 1,575 3,291 1,222

in Table 1, the principal time periods examined in this paper meet this criterion. In addition to a period’s length, the choice of its endpoints is also important. With respect to cointegration tests, Sephton and Larsen (1991) conclude that the evidence for cointegration is ‘‘fragile’’ and exhibits ‘‘temporal sensitivity’’ since different subsample periods provide differing results. Given this result, testing for cointegration over an arbitrarily chosen time period, as in Baillie and Bollerslev (1989) and other studies, does not seem appropriate. An alternative method for selecting a period’s endpoints is to impose structural breaks exogenously in the spirit of Perron (1989). In this paper, the endpoints of the 18-year period examined are determined by an approximation to the start of the current ﬂoating-rate regime and by data availability at the time the study was initiated, and the ﬁve proposed structural breakpoints examined are linked to regime shifts in central bank behavior in the foreign exchange market. The ﬁrst breakpoint suggested is November 1, 1978.3 On that date, a socalled ‘‘dollar-rescue package’’ was enacted by the US to at least halt the depreciation of the dollar. The package consisted of tightened monetary policy and the creation of an intervention fund. The ensuing sustained and coordinated intervention temporarily raised the value of the dollar, but it returned to its previous level by the year end. The outcome of this intervention was interpreted to mean that substantial effects could be achieved, but that these effects would be temporary unless supported by genuine policy changes. This change in central bank behavior is included in the subsequent analysis to determine whether it did have a long-term impact.

Exchange Rate Cointegration

335

The second proposed breakpoint, March 13, 1979, marks the formation of the European Monetary System (EMS). The original members agreed to ﬁx their mutual exchange rates within certain bands and ﬂoat jointly against the dollar. Although other exchange rate agreements had existed among European currencies, the EMS marked the formation of a new and more strongly codiﬁed system. The third suggested breakpoint, February 25, 1985, primarily arises from the data. Five of the six European exchange rates achieve their post-1973 maximum on that day, and the sixth SF achieves its post-EMS maximum eight days later on March 5, 1985. According to ﬁnancial news reports at the time, market participants could not cite any particular event that led to the dollar’s rapid depreciation. However, the German Bundesbank and other European central banks, as well as the Federal Reserve to a lesser extent, intervened heavily throughout the ﬁrst quarter of 1985 to halt the appreciation of the dollar. This intervention activity by the US was directly linked to the change in the Secretary of the Treasury; Brady was willing to intervene while Regan was not. Most of these intervention operations were widely reported and signaled the central banks’ intentions to market participants. The fourth breakpoint examined is September 23, 1985, the ﬁrst trading day after the announcement of the Plaza Agreement. In this agreement, the G-5 central banks stated that ‘‘some further orderly appreciation of the main non-dollar currencies against the dollar is desirable’’ and that they would ‘‘stand ready to cooperate more closely to encourage this when to do so would be helpful.’’4 After this announcement, the dollar continued its prolonged depreciation as central banks intervened actively in the foreign exchange markets. The ﬁfth breakpoint is February 22, 1987, the day after the Louvre Accord. The G-7 central banks, excluding Italy, ‘‘agreed to cooperate closely to foster the stability of exchange rates around current levels.’’5 In essence, the central banks agreed to stop the depreciation of the dollar and maintain a reference range for the major non-dollar currencies by intervening in the market, as necessary. Given the dataset’s endpoints and these ﬁve breakpoints, the data can be subdivided into the entire post-1973 period, the pre- and post- ‘‘dollar rescue’’ periods, the pre- and post-EMS periods, the pre- and post-peak periods, the pre- and post-Plaza periods and the pre- and post-Louvre periods. Overall, the long-term behavior of exchange rates is examined in these 11 periods; Table 1 lists the endpoints and the number of observations for each period, and Fig. 9 provides a graphical representation of the periods.

336

JOSE A. LOPEZ

Fig. 9.

Timeline of Proposed Structural Breakpoints.

3. OVERVIEW OF COINTEGRATION PROCEDURES 3.1. Unit Root Test Results Cointegration examines the relationships between nonstationary, or I(1), variables. The nonstationarity of post-1973 exchange rates was initially documented by Meese and Singleton (1982) and has been veriﬁed by many authors. In this paper, three types of unit root tests are used to examine the nonstationarity of exchange rates: Dickey and Fuller (1979) tests, augmented Dickey–Fuller tests (Fuller, 1976) and Phillips and Perron (1988) tests. Diebold and Nerlove (1990) state that the augmented Dickey–Fuller test is the most attractive unit root test. The unit root tests are applied to the eight exchange rates in all 11 periods, and the null hypothesis of unit root behavior cannot be rejected in almost all time periods at the one-sided 1 and 5% levels.6 That is, the null hypothesis of r ¼ 1 cannot be rejected in favor of the alternative hypothesis ro1, where r is the autoregressive parameter. The only period in which the unit

Exchange Rate Cointegration

337

root hypothesis may be rejected is the post-peak period. Given these results, the various exchange rate series will be considered to be I(1) variables. 3.2. The Johansen Procedure Various tests for the presence of cointegration among I(1) variables have been proposed beginning with Engle and Granger (1987). The test procedure used in this paper is a multivariate procedure based on maximum likelihood methods introduced in Johansen (1988, 1991) and expanded upon in Johansen and Juselius (1990). The Johansen procedure examines a vector autoregressive (VAR) model of Xt, an (n 1) vector of I(1) time series. The error-correction form is written in ﬁrst differences as DX t ¼ G1 DX t1 þ þ Gk1 DX tk þ m þ t ; t N ð0; LÞ; t ¼ 1; . . . ; T

(1)

where Gi for i ¼ 1, y, k1 and P are (n n) matrices, m is a (n 1) vector of constants, et is a (n 1) error vector and L is its (n n) covariance matrix. Since some or all of the elements of Xt are I(1), DXt is an I(0) process. Thus, the stationarity of the right side of the equation is achieved only if PXtk is stationary. The Johansen procedure tests the rank of P, which determines the number of cointegrating vectors present in the system. If rank (P) ¼ n, Xtk must be a stationary process, and no cointegrating vectors are present. If rank (P) ¼ 0, then P ¼ 0, and the model reduces to a standard VAR in differences. However, if rank (P) ¼ ron, then P ¼ ab0 where both a and b are (n r) matrices. b is the matrix of cointegrating vectors, and the number of such vectors is r. The cointegrating vectors have the property that bj0 Xt, j ¼ 1, y, r is stationary even though Xt is nonstationary; these vectors represent the long-term relationships present in the system. Thus, the number of long-term equilibrium relationships present in a system is equal to the number of cointegrating vectors. Note, however, that a and b cannot be separately identiﬁed since for any non-singular matrix P, the product of aP and b(P0 )1 is also P. The Johansen cointegration tests used in this paper examine the null hypothesis against the alternative that no cointegrating vectors are present in the system Xt. The two null hypotheses tested are that r cointegrating vectors are present in the system under the assumption that either m ¼ 0 or m 6¼ 0. The statistic chosen for testing these null hypotheses is the trace

338

JOSE A. LOPEZ

statistic. It tests for the presence of r cointegrating vectors in a system against the alternative hypothesis that Xt is stationary; i.e., the system has r ¼ n cointegrating vectors. The trace statistic is a likelihood ratio (LR) statistic of the form trðrÞ ¼ T

n X

ln 1 b li ,

(2)

i¼rþ1

where the b li 0 s are the ordered solutions to the eigenvalue problem 9lS kk Sk0 S1 00 S 0k 9 ¼ 0. The Sij matrices are the residual moment matrices derived from the postulated error-correction model. The distributions of the various forms of the trace statistic depend only on (n–r) and are tabulated in Osterwald-Lenum (1992). 3.3. The Quintos Procedure for Testing Rank Constancy Quintos (1994, 1995) presents a procedure for testing the rank constancy of the cointegrating matrix P over sample subperiods; that is, the procedure tests whether the number of cointegrating vectors varies across sample subperiods. If the rank does vary, then the number of driving forces in the economic system changes across the breakpoint. Both long-run and shortrun coefﬁcients in the error-correction model may change as well. The relevant test statistics are simply weighted averages of Johansen’s LR statistics, and the weights are the subperiod sample sizes. The test procedure is briefly summarized below. The Quintos procedure permits one to test a wide variety of null hypotheses, but only a small subset of the available options will be tested in this paper. For example, the procedure allows for J structural breaks in the system, but throughout this paper, J ¼ 1. Furthermore, the procedure allows the breakpoints to be endogenous to the process, but in this paper, the breakpoints used will be exogenously imposed as in Perron (1989). The main hypothesis tested in this paper is that the number of cointegrating vectors (or equilibrium relationships) remains constant across time; that is, H q0 : q1 ¼ q ¼ q2 ; where q is the number of cointegrating vectors in the entire period, q1 and q2 are the number of cointegrating vectors in the pre- and post-breakpoint periods, and 0pqon: Note that the coefﬁcients of P are allowed to vary across subperiods. Different LR statistics are used for the different permutations of the ranks of the full and subperiod P matrices. For qoq1 and qoq2, the LR test

Exchange Rate Cointegration

339

statistic used is LR ¼ p1

q1 X

q2 X ln 1 b l1i p2 ln 1 b l2i

i¼qþ1

(3)

i¼qþ1

where p1 and p2 are the number of observations in each subperiod and the b lji, j ¼ 1,2 are the eigenvalues of the respective, estimated P matrices. The distribution of this statistic is a function of scaled, n-dimensional Brownian motions and depends upon the variables n, q, q1 and q2. For q4q1 and q2, the relevant LR statistic is q q X X ln 1 þ b l1i þ p2 ln 1 þ b l2i LR# ¼ p1 (4) i¼q1 þ1

i¼q2 þ1

2

which is distributed w ð2q2q1 2q2 Þn: These statistics can also be used in case of an equality between q and either one of the subperiod ranks. For the case q1oqoq2, the relevant LR statistic is q2 q X X LR1 ¼ p1 ln b l1i p2 ln 1 b l2i (5) i¼q1 þ1

i¼qþ1

and for the case q2oqoq1, the LR statistic is q1 q X X LR2 ¼ p1 ln 1 b l1i þ p2 ln 1 b l2i i¼qþ1

(6)

i¼q2 þ1

Both of these statistics have distributions that are mixtures of a w2 distribution and a function of scaled Brownian motions.7

4. EMPIRICAL TEST RESULTS 4.1. Previous Cointegration Tests of Exchange Rates Four studies have tested for the presence of cointegration in systems of foreign exchange rates: Hakkio and Rush (1989), Copeland (1991), Baillie and Bollerslev (1989) and Diebold et al. (1994). The ﬁrst two explicitly test for the efﬁciency of the foreign exchange markets; as mentioned before, the presence of cointegration among exchange rates would contradict the efﬁcient markets hypothesis by implying that current rates can be predicted by past deviations from the long-run cointegrating relationships. The second two papers focus on modeling and forecasting exchange rates.

340

JOSE A. LOPEZ

Hakkio and Rush (1989) use the Engle–Granger cointegration procedure to examine monthly spot rates for BP and DM from July 1975 to October 1986. They conclude that the two rates are not cointegrated at the 5% significance level; this result is consistent with the market efﬁciency hypothesis. However, further tests involving the error-correction representation of the system leads the authors to reject the market efﬁciency hypothesis for these two currencies. Copeland (1991) examines bivariate systems of exchange rates for cointegration using the Johansen (1988) procedure. The data used are daily spot rates for BP, DM, JY, FR and SF over the period 1976–1990. Copeland ﬁnds no cointegration among the 10 currency pairs at the 5% significance level, which supports the efﬁcient market hypothesis. Baillie and Bollerslev (1989) examine daily opening spot rates from the New York market for the period March 1, 1980 to January 28, 1985. The seven currencies used are BP, DM, JY, FR, LI, SF and CD. One cointegrating vector is found in this system using the Johansen (1988) procedure. They conclude that the deviations from the long-term relationship between these spot rates are an important component of the next period’s observed rates; thus, the efﬁcient markets hypothesis is violated. The authors further conclude that an error-correction model is appropriate for modeling foreign exchange rates. However, using the Johansen procedure, Diebold et al. (1994) ﬁnd no cointegration in this dataset. Furthermore, in a forecasting exercise, the authors ﬁnd no improvements in forecast performance by the ﬁtted error-correction model relative to the simple martingale model. A similar result is found for the entire post-1973 period. The cointegration tests in this paper extend the latter two results by using a longer time period and a larger currency system. Furthermore, a subsystem of exchange rates consisting of the four EMS currencies is tested for the presence of cointegrating vectors. This cointegration analysis incorporates the structural breaks discussed in Section 2. The cointegration results are derived using the Johansen procedure and the 5% critical values from Osterwald-Lenum (1992). The Quintos procedure described in Section 3 is applied to these cointegration results to determine whether the number of cointegrating vectors (or equilibrium relationships) changed significantly between the pre- and post-breakpoint periods.

4.2. Cointegration Test Results: Post-1973 Period To test for cointegration, error-correction models are ﬁt to all the exchange rate systems under study. The orders of the VAR’s are determined by

Exchange Rate Cointegration

341

minimizing the multivariate Schwarz information criterion (SIC). In all cases examined, the order chosen is two;8 that is, DX t ¼ G1 DX t1 þ PX t2 þ m þ t

(7)

A summary of these cointegration results is presented in Table 2. The results of the cointegration analysis for the full system of exchange rates are presented in Tables 3–13, and the results for the EMS subsystem are in Tables 14–24. As noted above, the appropriate critical values depend on whether m is present in the data. Since this cannot be determined a priori, the calculated test statistics are compared to the critical values based on both assumptions. Tables 3–24 explains Johansen Cointegration Test Results. The 5% critical values for the two forms of the H(r) hypothesis tests using the trace statistic are listed below. The source for these critical values is Osterwald-Lenum (1992). If a trace statistic for the H(r) hypotheses is significant under m ¼ 0, it is marked with *; if it is significant under m6¼0, it is marked with **; and if it is significant for both, it is marked with ].

Dimension of P (nr) 1 2 3 4 5 6 7 8

H(r) m¼0

m 6¼ 0

8.176 17.953 31.525 48.280 70.598 95.177 124.253 157.109

3.762 15.410 29.680 47.410 68.524 94.155 124.243 155.999

The 11 time periods, as determined by the ﬁve structural breakpoints discussed in Section 3, as well as the entire post-1973 period are tested for the presence of cointegration. Two significant results arise from this analysis. First, for the entire post-1973 period, one cointegrating vector is found; thus, indicating that this system of exchange rates has at least one long-term cointegrating relationship. This result differs from that of Diebold et al. (1994), which excludes the NG from the analysis. Second, the cointegration results for the pre-breakpoint periods generally indicate the absence of any long-term relationships, except for the pre-EMS

342

JOSE A. LOPEZ

Table 2.

Summary of the Johansen Cointegration Results for the Systems of FX Rates.

Time period

Number of Cointegrating Vectors

Post-1973 period Pre-‘‘Dollar Rescue’’ period Post-‘‘Dollar Rescue’’ period Pre-EMS period Post-EMS period Pre-peak period Post-peak period Pre-Plaza period Post-Plaza period Pre-Louvre period Post-Louvre period

Table 3.

Full System

EMS Subsystem

1 0 1 1 1 0 3 0 3 0 0

2 1 2 1 1 1 1 0 1 0 0

Johansen Cointegration Test Results for the Full System in the Post-1973 Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

1.4816 5.7237 16.9077 32.3175 47.9406 68.6433 110.0213 160.2744]

period. However, the post-breakpoint periods generally indicate the presence of one or more cointegrating relationships, with the exception of the post-Louvre period. These results seem to indicate that the ‘‘dollar rescue,’’ peak and Plaza breakpoints change the nature of the underlying long-term relationships in the foreign exchange market; these regime shifts in central bank behavior had a long-term impact on the exchange rates. The Louvre breakpoint also seems to have had an impact, but its nature is unclear. It seems that the EMS breakpoint did not have an impact on the entire system of exchange rates.

Exchange Rate Cointegration

Table 4.

343

Johansen Cointegration Test Results for the Full System in the Pre-Dollar Rescue Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

0.1340 6.7796 17.0687 31.0271 49.4256 69.2059 105.3181 155.8310

Table 5.

Johansen Cointegration Test Results for the Full System in the Post-Dollar Rescue Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

2.6645 6.3700 5.8702 31.4557 58.5751 88.2633 120.9527 164.0304]

Table 6.

Johansen Cointegration Test Results for the Full System in the Pre-EMS Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

1.6814 4.9382 14.6901 25.4597 42.0717 65.8132 104.4806 156.4098**

344

Table 7.

JOSE A. LOPEZ

Johansen Cointegration Test Results for the Full System in the Post-EMS Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

2.4110 6.2067 17.3797 31.3092 54.8606 79.4686 112.3466 162.6838]

Table 8.

Johansen Cointegration Test Results for the Full System in the Pre-Peak Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

0.1244 4.9693 10.4071 23.2316 40.5152 58.5681 90.7833 137.8266

Table 9.

Johansen Cointegration Test Results for the Full System in the Post-Peak Period.

R

Trace Statistics H(r)

7 6 5 4 3 2 1 0

3.3206 9.5549 22.5927 44.2406 68.5852** 98.0516] 142.3415] 267.1033]

Exchange Rate Cointegration

Table 10.

345

Johansen Cointegration Test Results for the Full System in the Pre-Plaza Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

0.0348 5.0068 11.7034 24.1218 40.5794 60.4225 91.0500 127.0183

Table 11.

Johansen Cointegration Test Results for the Full System in the Post-Plaza Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

4.2605 13.2175 23.0940 42.2340 64.5921* 95.3069] 133.2467] 179.5316]

Table 12.

Johansen Cointegration Test Results for the Full System in the Pre-Louvre Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

1.5130 6.1328 11.7505 25.0944 39.9255 59.9189 90.8637 128.4835

346

Table 13.

JOSE A. LOPEZ

Johansen Cointegration Test Results for the Full System in the Post-Louvre Period.

r

Trace Statistics H(r)

7 6 5 4 3 2 1 0

1.5472 6.9431 16.7302 31.8432 49.6656 77.4124 110.6171 150.850

Table 14.

Johansen Cointegration Test Results for the EMS Subsystem in the Post-1973 Period.

r

Trace Statistics H(r)

3 2 1 0

1.6127 14.8994 32.5348] 63.8383]

Table 15.

Johansen Cointegration Test Results for the EMS Subsystem in the Pre-Dollar Rescue Period.

r

Trace Statistics H(r)

3 2 1 0

1.1814 4.8994 16.3359 48.6840]

These results indicate that the equilibrium relationship found in the entire post-1973 period has not necessarily remained constant. The varying number of cointegrating vectors in the pre- and post-breakpoint periods indicates that the underlying market equilibria for this system of exchange rates are affected by these structural breaks. To further explore the impact of these structural breaks, a subsystem of EMS currencies (i.e., DM, FF,

Exchange Rate Cointegration

Table 16.

347

Johansen Cointegration Test Results for the EMS Subsystem in the Post-Dollar Rescue Period.

r

Trace Statistics H(r)

3 2 1 0

1.7818 12.8313 29.7344] 58.5574]

Table 17.

Johansen Cointegration Test Results for the EMS Subsystem in the Pre-EMS Period.

r

Trace Statistics H(r)

3 2 1 0

2.2075 6.3416 18.1843 54.9489]

Table 18.

Johansen Cointegration Test Results for the EMS Subsystem in the Post-EMS Period.

r

Trace Statistics H(r)

3 2 1 0

2.2459 15.7156** 36.5782] 71.0912]

Table 19.

Johansen Cointegration Test Results for the EMS Subsystem in the Pre-Peak Period.

r

Trace Statistics H(r)

3 2 1 0

0.4921 8.5004 26.7178 50.7560]

348

Table 20.

JOSE A. LOPEZ

Johansen Cointegration Test Results for the EMS Subsystem in the Post-Peak Period.

r

Trace Statistics H(r)

3 2 1 0

5.5125 14.3179 30.6567** 69.0913]

Table 21.

Johansen Cointegration Test Results for the EMS Subsystem in the Pre-Plaza Period.

r

Trace Statistics H(r)

3 2 1 0

0.0001 8.0007 19.7551 45.2917

Table 22.

Johansen Cointegration Test Results for the EMS Subsystem in the Post-Plaza Period.

r

Trace Statistics H(r)

3 2 1 0

2.9823 10.8225 25.8553 51.5630]

Table 23.

Johansen Cointegration Test Results for the EMS Subsystem in the Pre-Louvre Period.

r

Trace Statistics H(r)

3 2 1 0

1.1206 10.4934 22.0338 46.7566

Exchange Rate Cointegration

Table 24.

349

Johansen Cointegration Test Results for the EMS Subsystem in the Post-Louvre Period.

r

Trace Statistics H(r)

3 2 1 0

1.3289 7.7759 20.1681 39.7472

NG and LI) is tested for the presence of cointegration. The results of the cointegration analysis for the EMS subsystem are different from those of the full system. At least two cointegrating relationships are indicated over the entire post-1973 period for this subsystem. In addition, cointegration is present in all subperiods, except for the pre-Plaza period and the pre- and post-Louvre periods. Overall, these results indicate that the cointegration present in the entire system is driven by the cointegration present in the EMS subsystem.

4.3. Quintos Rank Constancy Tests To determine whether these differences in the number of cointegrating vectors are significant, the Quintos tests described in Section 3 is applied to the cointegration results. 4.3.1. Full System of Exchange Rates Table 25 contains the results of the Quintos tests applied to the cointegration results for the full system of exchange rates over the entire post-1973 period. Given the various combinations of the estimated full and subperiod ranks examined, various LR statistics described in Section 4 are used. For all cases, other than the EMS breakpoint, the null hypothesis of rank constancy with unstable coefﬁcients is rejected. Several implications immediately follow from these results. The most prominent is that these episodes of central bank intervention did have an impact on the long-term relationships (or equilibria) in this system of exchange rates. Thus, certain central bank activities can have a long-term impact on the foreign exchange market. The meaning of these results for the individual breakpoints requires further study. The ‘‘dollar rescue’’ package, as described in Section 2, did not have a strong impact on the market since shortly after its enactment, the

350

Table 25.

JOSE A. LOPEZ

Quintos Cointegration Test Results for the Full System in the Post-1973 Period.

Breakpoint

q

q1

q2

LR Statistic

‘‘Dollar Rescue’’ EMS Peak Plaza Louvre

1 1 1 1 1

0 1 0 0 0

1 1 3 3 0

LR] ¼ 48.51 — LR*1 ¼ 11,515 LR*1 ¼ 13,014 LR] ¼ 76.27

Significant at the 5% level.

market countered all of the gains the package provided. Yet, according to the Quintos test results, the cointegrating relationships across this breakpoint did change. On the other hand, the EMS breakpoint, which one would expect to have an impact on the system since it explicitly imposes a longterm relationship on the exchange rates, does not change the rank of the cointegrating matrix. The results for the peak, Plaza and Louvre breakpoints are as expected; these breakpoints seem cause a significant change in the cointegrating relationships in the system. Furthermore, the similarity between the peak and Plaza breakpoints is as expected. To supplement these full-period results while recognizing the drop in power due to reduced sample size, subperiods around these breakpoints are examined in order to isolate the effects of a single breakpoint. The relevant test results are contained in Table 27.9 This subperiod analysis seems to cast some light on the impact of the ‘‘dollar rescue’’ breakpoint. The null of rank constancy with unstable coefﬁcients is rejected for the start-EMS breakpoint period and cannot be tested for the longer start-peak and start-Plaza breakpoint periods. These results seem to indicate that the ‘‘dollar rescue’’ breakpoint had little overall impact and that its impact with respect to the entire post-1973 period is mainly due to the events surrounding the peak and Plaza breakpoints. However, the results for subperiods surrounding the EMS, peak and Plaza breakpoints indicate that they did impact the system’s cointegrating relationships. 4.3.2. EMS Subsystem of Exchange Rates Table 26 contains the results of the Quintos test applied to the cointegration results for the EMS subsystem of exchange rates over the entire post-1973 period. For all cases, the null hypothesis of rank constancy with unstable coefﬁcients is clearly rejected. Several implications follow from this set of

Exchange Rate Cointegration

351

Quintos Cointegration Test Results for the EMS Subsystem in the Post-1973 Period.

Table 26. Breakpoint

q

q1

q2

LR Statistic

‘‘Dollar Rescue’’ EMS Peak Plaza Louvre

2 2 2 2 2

1 1 1 0 0

2 1 1 1 0

LR] ¼ 11.71* LR] ¼ 27.80* LR] ¼ 34.47 LR] ¼ 52.07 LR] ¼ 67.65

Significant at the 5% level.

Table 27.

Quintos Cointegration Test Results for the Full System in the Deﬁned Subperiods.

Subperiod

q

q1

q2

LR Statistic

‘‘Dollar Rescue’’ Start-EMS Start-Peak Start-Plaza

1 0 0

0 0 0

1 0 0

LR] ¼ 48.51 — —

EMS Start-Peak Start-Plaza ‘‘DR’’-Peak ‘‘DR’’-Plaza

0 0 0 0

1 1 1 1

0 0 0 0

LR ¼ 54.06 LR ¼ 54.06 LR ¼ 55.94 LR ¼ 55.94

Peak Start-Plaza ‘‘DR’’-Plaza EMS-Plaza

0 0 0

0 0 0

3 3 3

LR ¼ 167.05 LR ¼ 167.05 LR ¼ 167.05

Plaza Start-Louvre ‘‘DR’’-Louvre EMS-Louvre Peak-Louvre

0 0 0 1

0 0 0 3

2 2 2 2

LR ¼ 124.25 LR ¼ 124.25 LR ¼ 124.25 LR ¼ 154.64

Louvre ‘‘DR’’-End EMS-End Peak-End Plaza-End

1 1 3 3

0 0 1 2

0 0 0 0

LR] ¼ 75.65 LR] ¼ 77.02 LR] ¼ 200.32 LR] ¼ 154.65

Note: The critical values were provided by Carmela Quintos and are based on 1000 Monte Carlo repetitions. Significant at the 5% level.

352

JOSE A. LOPEZ

results. The proposed central bank regime shifts seem to have an impact on the long-term relationships present in this subsystem of exchange rates. The ‘‘dollar rescue’’ breakpoint results are mixed in which the null hypothesis is rejected at the 5% significance level but not at the 1% level. The result that the ‘‘dollar rescue’’ period may not impact the EMS subsystem as strongly as the whole system is understandable since the event did not focus specifically on the EMS currencies. To supplement these results, subperiods around these breakpoints are examined as before, while still acknowledging the decline in power due to reduced sample size. The results of this analysis are contained in Table 28. Table 28.

Quintos Cointegration Test Results for the EMS Subsystem in the Deﬁned Subperiods.

Subperiod

q

q1

q2

LR Statistic

‘‘Dollar Rescue’’ Start-EMS Start-Peak Start-Plaza

1 1 0

1 1 1

2 0 0

LR ¼ 27.57 LR ¼ 31.24 LR ¼ 31.33

EMS Start-Peak Start-Plaza ‘‘DR’’-Peak ‘‘DR’’-Plaza

1 0 0 0

1 1 2 2

0 0 0 0

LR] ¼ 19.10 LR ¼ 14.92 LR ¼ 60.83 LR ¼ 60.83

Peak Start-Plaza ‘‘DR’’-Plaza EMS-Plaza

0 0 0

1 0 0

1 1 1

LR ¼ 65.86 LR ¼ 19.14 LR ¼ 19.14

Plaza Start-Louvre ‘‘DR’’-Louvre EMS-Louvre Peak-Louvre

0 0 0 1

0 0 0 1

0 0 0 0

— — — LR] ¼ 22.93

Louvre ‘‘DR’’-End EMS-End Peak-End Plaza-End

2 1 1 1

0 0 1 0

0 0 0 0

LR] ¼ 63.03 LR] ¼ 41.05 LR] ¼ 19.28 LR] ¼ 42.20

Note: The critical values were provided by Carmela Quintos and are based on 1,000 Monte Carlo repetitions. Significant at the 5% level.

Exchange Rate Cointegration

353

The interesting result here regards the Plaza breakpoint. The subperiods examined for this breakpoint begin at the four previous breakpoints and end at the Louvre breakpoint; i.e., the post-Louvre period is excluded from the analysis. For the ﬁrst three startpoints, q ¼ q1 ¼ q2; thus, the null of rank constancy cannot be rejected. For the subperiod starting at the peak breakpoint, the null can be rejected. These results seem to indicate that, for the EMS subsystem, the effects of Plaza breakpoint were not as strong as for the whole system.

5. CONCLUSIONS The long-term impact of central bank activities, broadly deﬁned, on the foreign exchange market is an issue that has not been directly examined. This paper attempts to address this question using cointegration analysis that incorporates structural breaks linked to regime changes in central bank behavior. The ﬁve breakpoints examined are instances of changes in central bank behavior that may have substantially altered the long-term relationships among the eight currencies examined. Using the Johansen procedure, cointegrating relationships are found for the full system of exchange rates and a subset consisting of four EMS currencies. The number of cointegrating vectors in the periods before and after the suggested breakpoints are found to be different in several cases. Furthermore, these differences are found to be statistically significant using the testing procedure proposed by Quintos (1994, 1995). Structural changes of the type that alter the definition of the system’s equilibria seem to have occurred at these breakpoints. Thus, regime shifts in central bank behavior do have a long-term impact on foreign exchange rates. Further research into this ﬁnding is warranted, both along methodological and theoretical lines. With respect to methodological issues, the rich structure of the Quintos test procedure should be used to endogenize the breakpoints as well as test for more than one breakpoint at a time. In addition, extensions of the cointegration results, such as fractional cointegration analysis proposed by Baillie and Bollerslev (1994), should be examined. With respect to theoretical issues, another outstanding question is what the existence of cointegrating vectors implies with respect to models of exchange rate determination. If cointegration is a feature of the data, models incorporating it must be constructed and possibly be made robust to structural breaks.

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NOTES 1. Several papers, such as Baillie and Selover (1987) as well as Papell (1997), examine cointegration in systems of foreign exchange rates and other macroeconomic variables. The focus here, however, is in systems of foreign exchange rates only. 2. Granger and Escribano (1986) ﬁnd evidence that exceptional events in the gold and silver markets cause these two price series, which should not be cointegrated under the efﬁcient markets hypothesis, to be cointegrated during certain time periods. 3. This breakpoint is explicitly examined in Loopesko (1984). In-depth summaries of the events surrounding all ﬁve breakpoints are provided in Dominguez and Frankel (1993). 4. G-5 Announcement of September 22, 1985. The G-5 countries are Britain, France, Japan, the US and Germany. 5. G-7 Announcement of February 22, 1987. The G-7 countries are the G-5 countries plus Canada and Italy. 6. The unit root test results are available upon request. 7. Carmela Quintos was kind enough to provide the critical values necessary for some of the hypothesis tests conducted in this paper. 8. In the interest of space, the VAR estimation results are not presented. The various SIC statistics and the estimated VAR parameters are available upon request. 9. Complete test results are available upon request.

ACKNOWLEDGMENTS The views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of San Francisco or the Federal Reserve System. I thank Frank Diebold for his extensive comments and suggestions on an earlier draft of this paper and Carmela Quintos for generously providing the necessary tables of critical values. I also thank Roberto Mariano, Jesus Felipe, Lorenzo Giorgianni as well as seminar participants at the University of Pennsylvania, the Federal Reserve Bank of New York and a meeting of the Multinational Finance Society for helpful comments. Finally, I thank Julie Goldsmith, my wife, for all of her loving support over my many years as an economist.

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