School of HEC at University of Lausanne Institute of Banking and Finance Master of Science in Banking and Finance Master Thesis Capital Structure Arbitrage Strategies: Models, Practice and Empirical Evidence Oliver Berndt and Bruno Stephan Veras de Melo November 2003, Lausanne, Switzerland Supervised by Professor Salih Neftci, CUNY, New York and School of HEC at University of Lausanne Co-supervised by Dr. Norbert Dörr, Credit Risk Management, Deutsche Bank AG, London and Dr. Wilhelm Trinder, Financial Risk Management, KPMG, Frankfurt/Main Contents Abstract vi Introduction vii Notation xvi IDescriptivePart 1 1 Theoretical and Practical Background 2 1.1BondPricingModelsbasedonEquityPriceBehavior.............. 2 1.1.1 Structural Models.............................. 3 1.1.2 Reduced-formModels............................ 22 1.2 Convertible Bonds ................................. 25 1.2.1 BriefSurveyonPricingModels...................... 28 1.2.2 RisksandtheGreeks............................ 29 1.2.3 ArbitrageTechnique-DeltaHedging................... 31 1.2.4 PortfolioRiskManagement........................ 36 1.3 Credit Derivatives.................................. 38 1.3.1 BasicsaboutCreditDerivatives...................... 38 1.3.2 Terminologies and Definitions....................... 39 1.3.3 CreditDerivativeTypes.......................... 42 1.3.4 CreditDerivativeStructuresandApplications.............. 45 1.3.5 TheMarketandtheUseofCreditDerivatives.............. 50 1.3.6 CreditDerivativescancompleteFinancialMarketInformation..... 55 1.3.7 CreditDefaultSwapBasics........................ 55 1.3.8 CreditDefaultSwapValuation...................... 62 1.3.9 CreditDefaultSwapSummary...................... 103 i CONTENTS ii 2 Capital Structure Arbitrage and Hedging 105 2.1 Main Strategies ................................... 105 2.1.1 EquityandDebtMarket.......................... 105 2.1.2 EquityandCreditMarket......................... 111 2.1.3 CreditandDebtMarkets..........................114 2.2TheMarketforCapitalStructureArbitrageandHedgingStrategies...... 122 2.2.1 The Participants of the Capital Structure Arbitrage Strategies Market . 123 2.2.2 The Rule of Banks and Hedge Funds in Capital Structure Arbitrage and HedgingStrategiesmarket......................... 125 2.2.3 The Consequences to the Financial Market from Capital Structure Ar- bitrage Strategies .............................. 128 II Empirical Analysis 132 3 Cointegration Analysis 133 3.1TheRationaleofempiricalCapitalStructureArbitrageAnalysis........ 133 3.1.1 Relationship between the Credit Spread and the Volatility Skew implied bytheMertonModel............................ 140 3.2CointegrationEconometrics............................ 141 3.2.1 StationaryandNonstationaryStochasticProcess............ 142 3.2.2 VectorAutoregressiveModels....................... 146 3.2.3 Cointegration ................................ 148 3.3 Descriptive statistics................................ 150 3.4 Cointegration Results................................ 153 3.4.1 Description of the Tests .......................... 155 3.4.2 Empirical Relationship between CDS Rates and the Volatility Skew . 157 3.4.3 EmpiricalRelationshipbetweenCDSandEquityPrices.........170 4 Conclusion 178 A Detailed Proofs 182 A.1Notations:...................................... 182 A.2Proofofformula(9)inHulletal.(2003a).................... 183 A.3Proofofformula(8)inHulletal.(2003a).................... 188 A.4ThecreditspreadofariskybondimpliedbytheMertonmodel........ 189 A.5Aformulafortheimpliedputoptionvolatilities................. 190 CONTENTS iii B VAR and VECM representations of section 3.4.2 192 C VAR and VECM representations of section 3.4.2 195 C.1UnitRootsTest................................... 195 C.2 Granger Causality Test............................... 196 C.3 VAR Especification................................. 196 C.4 Innovation Accounting............................... 197 C.5 Cointegration Tests ................................. 200 C.6VARandVECMrepresentations......................... 201 D VAR and VECM representations of section 3.4.3 204 Bibliography 207 Acknowledgement Special thanks are due to our supervisor Professor Salih Neftci, CUNY New York and HEC - University of Lausanne, who opened our eyes in finance during his very special and outstanding Financial Engineering course. Secondly, we would like to thank to our co-supervisors Dr. Norbert Dörr, Deutsche Bank AG London, who provided us with internal documents and helpful comments and Dr. Wilhelm Trinder, KPMG Frankfurt/Main, who supported us during our approach to find an interesting topic and reviewed the versions of the thesis. We would like to thank all our colleagues at the Master of Science in Banking and Finance (MBF) program at the Institute of Banking and Finance (IBF), School of HEC at University of Lausanne and the members of the Financial Asset Management and Engineering (FAME) program for there participation on our sometimes tiny problems. Especially we would like thank our secretaries Mena Jacquier and Sandrine Zaugg for their always warm welcome and friendly administrative support and help; the Director of IBF and of the MBF, Professor Michael Rockinger, who was also our professor in the Options & Futures course; the former MBF Director Professor Dider Cossin, now Professor at IMD, who taught and motivated us on how to apply credit derivatives during his very outstanding Applied Corporate Finance course. Amongst the many people who gave us the opportunity to discuss our ideas and provided valuable feedback or supported us with some helpful material we would like to thank immensely Dr. Alexander Passow, GOTTEX and FAME, Lausanne for his advise and help during all phases of the project, in particular for his insights in capital structure arbitrage strategies and for reading some parts of the thesis. Furthermore we would like to thank the members of AXA Investment Managers in Paris and London, Antoine Josserand, Olivier Lamotte, Jerome Vierling and in particular Guillaume Boulanger for providing us the data we needed for our project. Without this data we would never have been able to show the results we have in the empirical evidence part of the thesis. Furthermore, we would like to thank Dr. Lutz Schloegel, Lehman Brothers London, Dr. Günter Umlauf, KPMG London, Dr. Stefan Kremp, KPMG Frankfurt/Main, Ira Jersey, CSFB New York, Kirill Ilinski, JPMorgan New York, Joe Zou, Goldman Sachs New York and Ali Hirsa, Morgan Stanley New York. We also have to thank very gratefully our earlier mentors Professor Dr. Felix Ali Mehmeti, Valenciennes - France and Professor Dr. iv PREFACE v Mirta Sataka Bugarin and Professor Dr. Francisco Cribari-Neto, Brasília - Brazil who taught ushowtodoscientific research. Last but not least, personal support from our partners and relatives was fantastic during the MBF program and during the last four month while doing this project. Abstract The objective of the thesis is the theoretical and practical background of capital structure arbitrage strategies and the empirical evidence of key relationships applying these strategies. Capital structure arbitrage involves taking long and short positions in different financial in- struments of a company’s capital structure, particularly between a company’s debt and equity products. In general, capital structure arbitrage strategies can be viewed as an example of the interaction between market risk and credit risk, which often leads to an analysis of the relationship between the credit spreads and its proxy credit default swaps (CDS), the implied equity volatility skew, and the level of leverage. As an example the long-term relationship between France Telecom’s CDS rates and volatility skew is analysed by means of cointegra- tion tests. The results indicate that volatility skew and CDS rates are cointegrated over a three-year period. When a leverage indicator is used in a sub-sample the results are even more signficant than before. vi Introduction The objective of the thesis is the theoretical and practical background of capital structure arbitrage and hedging strategies, and the empirical evidence of key relationships applying these strategies. Capital structure arbitrage and hedging involves taking long and short positions in different instruments and asset classes of a company’s capital structure, in particular between a company’s debt and equity products. In general, capital structure arbitrage strategies can be viewed as an example for a the interaction between market risk and credit risk, which often leads to an analysis of the relationship between credit spreads and the implied equity volatility surface - so-called the volatility skew - or equity prices. Because of the lions share of the credit default swaps within the credit derivatives market and the general tremendous growth of this market during the last years, typical capital structure arbitrage strategies such as credit default swap (CDS) versus cash equities or equity options lead to the relationship between credit default swap rates and the volatility skew or equity prices. With the knowledge of these relationships and detailed information of the leverage cycles of firms, the implementation of a capital structure arbitrage strategy can be set as a convergence trade. Thethesiswillbeafirststepintherelativelynewarea of capital structure arbitrage strategies with empirical analysis on the relationship between CDS rates, equity and equity options. The empirical result for a telecommunication sector firm, France Telecom, shows