Master Thesis Capital Structure Arbitrage Strategies

241 Pages·2004·1.91 MB·English

by  Bruno Stephan

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
I Descriptive Part 1
1 Theoretical and Practical Background 2
1.1 Bond Pricing Models based on Equity Price Behavior . . . . . . . . . . . . . . 2
1.1.1 Structural Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Reduced-form Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2 Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.2.1 Brief Survey on Pricing Models . . . . . . . . . . . . . . . . . . . . . . 28
1.2.2 Risks and the Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.2.3 Arbitrage Technique - Delta Hedging . . . . . . . . . . . . . . . . . . . 31
1.2.4 Portfolio Risk Management . . . . . . . . . . . . . . . . . . . . . . . . 36
1.3 Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.3.1 Basics about Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . 38
1.3.2 Terminologies and Definitions . . . . . . . . . . . . . . . . . . . . . . . 39
1.3.3 Credit Derivative Types . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.3.4 Credit Derivative Structures and Applications . . . . . . . . . . . . . . 45
1.3.5 The Market and the Use of Credit Derivatives . . . . . . . . . . . . . . 50
1.3.6 Credit Derivatives can complete Financial Market Information . . . . . 55
1.3.7 Credit Default Swap Basics . . . . . . . . . . . . . . . . . . . . . . . . 55
1.3.8 Credit Default Swap Valuation . . . . . . . . . . . . . . . . . . . . . . 62
1.3.9 Credit Default Swap Summary . . . . . . . . . . . . . . . . . . . . . . 103
i
CONTENTS ii
2 Capital Structure Arbitrage and Hedging 105
2.1 Main Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.1.1 Equity and Debt Market . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.1.2 Equity and Credit Market . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.1.3 Credit and Debt Markets . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.2 The Market for Capital Structure Arbitrage and Hedging Strategies . . . . . . 122
2.2.1 The Participants of the Capital Structure Arbitrage Strategies Market . 123
2.2.2 TheRuleof BanksandHedgeFundsinCapital StructureArbitrageand
Hedging Strategies market . . . . . . . . . . . . . . . . . . . . . . . . . 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
3.1 The Rationale of empirical Capital Structure Arbitrage Analysis . . . . . . . . 133
3.1.1 RelationshipbetweentheCreditSpreadandtheVolatilitySkewimplied
by the Merton Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
3.2 Cointegration Econometrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.2.1 Stationary and Nonstationary Stochastic Process . . . . . . . . . . . . 142
3.2.2 Vector Autoregressive Models . . . . . . . . . . . . . . . . . . . . . . . 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 Empirical Relationship between CDS and Equity Prices . . . . . . . . . 170
4 Conclusion 178
A Detailed Proofs 182
A.1 Notations: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
A.2 Proof of formula (9) in Hull et al. (2003a) . . . . . . . . . . . . . . . . . . . . 183
A.3 Proof of formula (8) in Hull et al. (2003a) . . . . . . . . . . . . . . . . . . . . 188
A.4 The credit spread of a risky bond implied by the Merton model . . . . . . . . 189
A.5 A formula for the implied put option volatilities . . . . . . . . . . . . . . . . . 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.1 Unit Roots Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
C.2 Granger Causality Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
C.3 VAR Especification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
C.4 Innovation Accounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
C.5 Cointegration Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
C.6 VAR and VECM representations . . . . . . . . . . . . . . . . . . . . . . . . . 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 -
UniversityofLausanne,whoopenedoureyesinfinanceduringhisveryspecialandoutstanding
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
helpfulcommentsandDr. WilhelmTrinder,KPMGFrankfurt/Main,whosupportedusduring
ourapproachtofindaninterestingtopicandreviewedtheversionsofthethesis. Wewouldlike
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
MenaJacquierandSandrineZauggfortheiralwayswarmwelcomeandfriendlyadministrative
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
derivativesduringhisveryoutstandingAppliedCorporateFinancecourse. Amongstthemany
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
somepartsofthethesis. FurthermorewewouldliketothankthemembersofAXAInvestment
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.
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PREFACE v
Mirta Sataka Bugarin and Professor Dr. Francisco Cribari-Neto, Brasília - Brazil who taught
us how to do scientific 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. Whenaleverage indicator is usedina sub-sampletheresults areevenmore
signficant than before.
vi
Introduction
The objective of the thesis is the theoretical and practical background of capital structure
arbitrageandhedgingstrategies,andtheempiricalevidenceofkeyrelationshipsapplyingthese
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
leadstoananalysisoftherelationshipbetweencreditspreadsandtheimpliedequityvolatility
surface - so-called the volatilityskew- or equityprices. 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 skewor 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.
The thesis will be a first step in the relatively new area of capital structure arbitrage
strategies with empirical analysis on the relationship between CDS rates, equity and equity
options. Theempirical resultforatelecommunicationsectorfirm, FranceTelecom, showsthat
there exists a long-run relationship between CDS rates and the corresponding equityvolatility
skew. This relationship, detected by cointegration tests, indicates that short-run dynamic
deviations of these two variables (CDS rates and volatility skew) will revert to an equilibrium
in a long-term; the variables are thus found to be cointegrated and the relationship between
them is mean-reverting. When a proxy for the leverage is used the long-run relationship is
even more significant, meaning that the relationship mean-reverts faster than before.
Therefore the thesis is organized in two parts, a descriptive part and an empirical analysis
part. The completion of financial market information by using credit derivatives and, more
specifically credit default swaps, as well as the consequences to the financial market from
capital structure arbitrage strategies are discussed in the descriptive part of the thesis. The
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INTRODUCTION viii
relationoftheempiricalresultstotherecenttradingapplicationsofcapitalstructurearbitrage
strategies are analysed and discussed in the empirical analysis part.
For a better understanding of the relatively new area of capital structure arbitrage strate-
gies the descriptive part includes all relevant key facts on the bond pricing models based on
equity price behavior, such as structural and reduced-formapproaches. For example, to hedge
the credit risk of convertible bonds with credit default swaps is also a favorite strategy with
capital structure characteristics but is more known as classical convertible arbitrage. Merely
the fact that in the near past the credit default swap market overcame the asset swap market
in terms of liquidity brings this strategy also more in the light of capital structure arbitrage.
Therfore an overview of convertibles is discussed as well in the descriptive part. Furthermore,
before discussing in detail the market, the structures, valuation models and the implementa-
tion issues of credit default swaps, some basics about the important area of credit derivatives
are presented in the descriptive part of the thesis. In the end of the descriptive part the main
strategies and the market for capital structure arbitrage strategies is discussed.
The empirical analysis part includes the results of the cointegration analysis of the rela-
tionships described before. For these analysis the vector autoregression (VAR) and vector
error-correction (VEC) methodologies and Granger causality as well other significant tests
were used to show that the implied volatility skew is causing the CDS rates significantly in
the long run especially in a leverage cycle of a firm. The descriptive statistics, discussion of
the results and the conclusion is made in this part.
Capital structure arbitrage strategies currently are the fastest growing sector in the hedge
fund market and in proprietary trading departments in large banks. For example, the number
of hedge funds exploiting capital structure arbitrage strategies is expected to grow from 30 to
approximately 200 funds until end of this year, according to Currie and Morris (2002). Addi-
tionally, Germany will open their financial market for hedge funds by a change in legislation
for beginning 2004. This will also have an impact for the leading investment banks inside and
outside Europe, which are highly active in such strategies, and therefore an increase in debt
instruments versus equity instruments trading is expected.
One of the main reason is given by the fact that after the -world wide- equity bubble in
2000, investment-grades as well as high-yield default rates increased dramatically with respect
to previous years. On the other side, the past months have been the best period for corporate
bonds in at least 20 years, according to Zuckerman (2003). Trading debt versus equity of
distressed companies has been highly attractive subsequently the bubble, because in times of
widening credit spreads the correlation between movements in credit spread and the equity
INTRODUCTION ix
price increases, see Currie and Morris (2002). Another reason why investors are currently
getting involved in capital structure arbitrage is related to the development of the credit
default market.
By far the main users of credit derivatives are large banks, followed by securities firms
and insurance companies. While banks and securities firms act both as sellers and buyers of
protection, insurance companies, which have reportedly increased their market participation
substantially in recent years, are primarily protection sellers, presumably using their exper-
tise in evaluating and diversifying risk. Hedge funds are also relatively active participants,
arbitraging perceived mis-pricing between the cash and the derivatives markets. Other par-
ticipants include pension funds and mutual funds, but their participation in the market is
very small. In terms of volume, according to the credit derivatives survey, Risk (2003), in
the course of the year 2002 the credit derivatives market in terms of total notional amount
of outstanding contracts has grown by more than 50% to $ 2,306 trillion and is expected to
double until the end of 2004 up to $ 4.8 trillion, see also British Banker Association (BBA)
forecasts.
The CDS capture nearly the half of the market share and become the dominant financial
instrumentinthecreditderivativesmarket. CBOsandCDOs arealsomoreandmoreusedfor
balancesheetre-organisation. TheriskreplicationofCDOsviaportfoliosofCDSsisoneofthe
key transaction and one of the major reason why the CDS market remains more liquid than
the markets for other credit derivative instruments. Furthermore, besides all these reasons
and the fact that the CDS is the key instrument for completing market information, the CDS
market is at the moment more liquid than the corresponding cash market for bonds and asset
swaps, so that the CDS rate is the key information for the creditworthiness of companies and
reflects the credit quality better than credit spreads in financial market.
Moreover, the results of Hull et al. (2003) and Zou (2003) provide new findings and
alternatives for the relation between credit spreads and implied equity volatility surfaces,
which we will also focus on throughout the thesis. Additionally, resent research interests
as focused the sector such as the forthcoming works from Berd (2003) and Ilinski (2003)
developing models to extract CDS rates from implied equity volatility surfaces. These models
are based mainly on Merton approaches, but they use reduced form models or mixed versions
as well, sometimes additional statistical models are also involved. None of these models is
completely public at the moment but in the near future a lot of forthcoming papers will be
produced by the industry and will be very interesting for academics as well.
Because of the overall development during the last years within the important area of
capital structure arbitrage strategies the objective of the thesis is to do a first step in this