Four Essays on Linear and Extreme Dependences in Credit Derivatives and Equity Markets

301 Pages·2014·3.99 MB·English

Four Essays on Linear and Extreme
Dependences in Credit Derivatives and
Equity Markets
INAUGURALDISSERTATION
zur
Erlangung des akademischen Grades eines
Doctor rerum politicarum (Dr. rer. pol.)
der
Wirtschafts- und Sozialwissenschaftlichen Fakulta¨t
der
Technischen Universita¨t Dortmund
vorgelegt von
Hendrik Supper
Master of Science
aus Kamen
Juli 2014
Table of Contents
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 Introduction 1
2 IsTailRiskPricedinCreditDefaultSwapPremia? 10
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 ModelingextremeCDSspreadco-movements . . . . . . . . . . . . . . . 15
2.2.1 CDSdataandstylizedfactsofCDSspreads . . . . . . . . . . . . 15
2.2.2 Univariatemodeling ofCDSspreads . . . . . . . . . . . . . . . . 25
2.2.3 Jointmodeling ofCDSspreadswiththeDACmodel . . . . . . . 26
2.2.4 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Empiricalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.1 Maindependentandindependentvariables . . . . . . . . . . . . 37
2.3.2 IstailriskpricedinCDScontracts? . . . . . . . . . . . . . . . . 41
2.3.3 Robustnesschecks . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3 DoCDSspreadsmovewith commonalityinliquidity? 65
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.1 CDSdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2.2 Measuresofcreditrisk . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.3 Liquidity variables . . . . . . . . . . . . . . . . . . . . . . . . . 71
i
TABLEOFCONTENTS ii
3.2.4 Descriptivestatistics . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3 LiquidityandCDSspreadmovements: Empiricalevidence . . . . . . . . 84
3.3.1 Time-seriesevidence . . . . . . . . . . . . . . . . . . . . . . . . 84
3.3.2 Panel-dataevidence . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4 Robustnesstests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4 Dynamic Dependence in Prices, Liquidity, and Credit Risk. A Vine Copula
Approach. 103
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2 Econometricmethodology . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2.1 Univariate models for returns, bid-ask spreads, and default inten-
sities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2.2 Dependencemodeling withdynamicR-vinecopulas . . . . . . . 110
4.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3.1 Datasources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3.2 ExtractingdefaultintensitiesfromCDSspreads . . . . . . . . . . 117
4.3.3 Descriptivestatistics . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4 Empiricalstudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.4.1 Anecdotalevidence . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.4.2 Forecastingliquidity- andcredit-adjusted Value-at-Risk . . . . . 135
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5 Extremedependenceinfinance: Doesthechoiceofestimatormatter? 158
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.2 Copulasandtaildependence . . . . . . . . . . . . . . . . . . . . . . . . 162
5.3 Simulationstudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.3.1 Modelsunderstudy . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.3.2 Simulation design . . . . . . . . . . . . . . . . . . . . . . . . . 168
5.3.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 171
TABLEOFCONTENTS iii
5.4 Replicationstudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.4.1 Replicationinawidesense: Differencesindataandmethodology 193
5.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
A SupplementaryMaterialforChapter2 218
B SupplementaryMaterialforChapter3 233
C SupplementaryMaterialforChapter4 236
D SupplementaryMaterialforChapter5 246
E PublicationDetails 272
F Bibliography 275
List of Tables
2.1 DescriptivestatisticsofCDSspreads. . . . . . . . . . . . . . . . . . . . 17
2.2 DescriptivestatisticsoflogdifferencesofCDSspreads. . . . . . . . . . . 20
2.3 Time-seriesanalysisoflogdifferencesofCDSspreads. . . . . . . . . . . 23
2.4 ParameterestimatesformarginalandDACmodels. . . . . . . . . . . . . 30
2.5 Descriptivestatistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6 Baselinetime-seriesregressions. . . . . . . . . . . . . . . . . . . . . . . 42
2.7 Time-seriesregressionswithadditionalcontrols. . . . . . . . . . . . . . . 43
2.8 Panelbenchmarkregressions. . . . . . . . . . . . . . . . . . . . . . . . . 46
2.9 Univariatesorts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.10 Sub-sampleanalysis: Crisisvs. pre-crisisperiod. . . . . . . . . . . . . . 50
2.11 Robustnesschecksusingalternativeriskmeasures. . . . . . . . . . . . . 56
3.1 TemporalvariationinCDSmidquotes,liquiditymeasures,andcommon-
alityinliquidity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 Industry-specificCDSmidquotesandliquidity measures. . . . . . . . . . 82
3.3 Market-wideandindustry-specificestimatesofCDSliquiditycommonality. 83
3.4 Time-seriesregressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.5 Panelbenchmarkregressions. . . . . . . . . . . . . . . . . . . . . . . . . 90
3.6 Panelbenchmarkregressionswithadditionalcontrolvariables. . . . . . . 93
3.7 Sub-sampleanalysis: Pre-crisisvs. crisisperiod. . . . . . . . . . . . . . . 95
3.8 Robustnesschecksusingindustry-, firm-,andyear-fixedeffects. . . . . . 98
3.9 Robustnesschecksusingrelativebid-askspreads. . . . . . . . . . . . . . 100
iv
LISTOFTABLES v
4.1 Summary statistics for mid prices, bid-ask spreads, and default intensi-
ties/probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2 Summarystatisticsforlog-differencesofmidprices,bid-askspreads,and
defaultintensities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.3 Cross-sectionaldistribution ofparameterestimates. . . . . . . . . . . . . 130
4.4 Averageparameterestimatesformarginaldistributions. . . . . . . . . . . 144
4.5 Temporalvariation ofselectedparametricpair-copulas. . . . . . . . . . . 146
4.6 Treewiseselectionofparametricpair-copulas. . . . . . . . . . . . . . . . 147
5.1 Descriptivestatisticsoftrueandestimatedlowertaildependence. . . . . . 172
5.2 Performanceoflowertaildependenceestimators. . . . . . . . . . . . . . 177
5.3 Mean squared errors of lower tail dependence estimators for different
samplesizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.4 Alternativeperformancemetrics. . . . . . . . . . . . . . . . . . . . . . . 186
5.5 Rankingandoverallperformanceoflowertaildependenceestimators. . . 191
5.6 Summarystatistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.7 Univariatesorts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
5.8 Dependentportfolio sorts: Lowertaildependenceandregularbeta. . . . . 206
5.9 Dependentportfolio sorts: Lowertaildependenceanddownsidebeta. . . 208
5.10 Dependentportfolio sorts: Lowertaildependenceandcoskewness. . . . . 209
5.11 MultivariateFama-MacBeth(1973)regressions. . . . . . . . . . . . . . . 211
List of Figures
2.1 Time evolution of CDS spreads, log differences of CDS spreads, and eq-
uityreturns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 CDSspreadsversuslogdifferencesofCDSspreadsandequityreturns. . . 21
2.3 Copulacorrelations andCDStailbetas. . . . . . . . . . . . . . . . . . . 33
2.4 Single-bankCDStailbetaestimates. . . . . . . . . . . . . . . . . . . . . 35
2.5 AlternativeriskmeasuresandCDStailbeta. . . . . . . . . . . . . . . . . 53
2.6 MESmodelsandCDStailbeta. . . . . . . . . . . . . . . . . . . . . . . 58
2.7 Tailriskwithanalternativeindex. . . . . . . . . . . . . . . . . . . . . . 62
3.1 CDSmidquotesandbid-askspreads. . . . . . . . . . . . . . . . . . . . 78
3.2 CDSmidquotesandliquidity commonalities. . . . . . . . . . . . . . . . 80
4.1 Timeevolution ofcross-sectionaldata. . . . . . . . . . . . . . . . . . . . 126
4.2 Dynamiccorrelationsandtaildependences. . . . . . . . . . . . . . . . . 133
4.3 Time evolution of stock returns, bid-ask spreads, and default intensities
offirmsincludedintheValue-at-Riskstudy. . . . . . . . . . . . . . . . . 140
4.4 Realizedportfolio lossesandValue-at-Riskforecasts. . . . . . . . . . . . 149
4.5 Decomposingliquidity- andcredit-adjusted Value-at-Risk. . . . . . . . . 151
4.6 RealizedportfoliolossesandValue-at-Riskforecastsfromalternativede-
pendencemodels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.7 DynamicR-vinecopulamodelversusalternativedependencemodels. . . 154
5.1 Averagemeansquarederrorsfordifferentsamplesizes. . . . . . . . . . . 183
5.2 Averagealternativeperformancemetricsfordifferent samplesizes. . . . . 188
vi
LISTOFFIGURES vii
5.3 Numberoffirmsacrosssampleperiod. . . . . . . . . . . . . . . . . . . . 195
5.4 Aggregatelowertaildependenceovertime. . . . . . . . . . . . . . . . . 201
5.5 Comparingaggregatelowertaildependenceacrossestimators. . . . . . . 202
Chapter 1
Introduction
Linear and extreme dependences are ubiquitous in financial markets. While linear
correlations and covariances have been well investigated in the literature and established
as a critical input in financial management, the notion of extreme dependences between
financial variables has mainly been fostered during the recent financial crisis. Extreme
dependences capture the behavior of variables during tail events and their neglection is
thought to be one of the main reasons for the severity of the financial crisis. The dis-
sertation investigates the linear and extreme dependence structures in credit derivatives
and equity markets and studies their possible implications for asset pricing and portfolio
management.
Linear dependences in the form of correlations and covariances between the returns
onfinancialassetshavebeenarecurringtopicinbothresearchandpracticalapplications.
The consideration and the reliable estimation of correlations and covariances play a cru-
cial role in asset pricing, portfolio selection, and risk management. For example, most
asset pricing theories rely on the assumption that the risk premium of an asset is deter-
mined by the covariance between the future return on the asset and one or more bench-
mark portfolios. The capital asset pricing model (CAPM) of Sharpe (1964) and Lintner
(1965)predictsthatexpectedexcessreturnsonanassetareproportionaltothecovariance
of the asset returns with the returns on a portfolio composed of all available assets in
the market. Similarly, the asset pricing studies in FamaandFrench (1993) and Carhart
1
CHAPTER1. INTRODUCTION 2
(1997)showthattheriskpremium ofanassetdependsonthecovariancebetweentheas-
setreturnsandthereturnsonseveralbenchmarkportfoliosaccountingformarketreturns,
size effects, differences in book-to-market equity, and momentum in stock returns. More
recently,AcharyaandPedersen(2005)extendtheCAPMtotheinclusionofliquidityrisk
and document return premia due to the covariance between individual and market-wide
liquidity, individual stock returns and market-wide liquidity, and between individual liq-
uidity and market returns. Moreover, portfolio selection and asset allocation are widely
based on the mean-variance approach proposed by Markowitz (1959) and, hence, rely on
the estimation of the potentially large number of correlations between the returns on the
underlyingassets. Moreprecisely,derivingtheoptimalportfoliointheMarkowitz(1959)
framework requires a forecast of the covariance matrix of the asset returns to obtain the
corresponding portfolio variances that are used to identify the mean-variance combina-
tionwhichmaximizestheinvestor’sutility. Furthermore,lineardependencesareessential
in risk management applications such as, e.g., the calculation of portfolio Value-at-Risk
and Expected Shortfall as well as the computation of optimal hedge ratios. While the
former requires the estimation of the correlation between the risk factors of the portfolio,
the latter relies on the covariance between the returns of the assets in the hedge. More
recently, linear dependences are found to be of prime importance in the measurement of
systemicrisk. Inthiscontext,Acharyaetal.(2010)definethemarginalexpectedshortfall
(MES) as the average return of a particular firm during the 5% worst days for the market
andshowthatMESpredictssystemicrisk. BrownleesandEngle(2012)buildonthisidea
and propose an econometric approach for the estimation of MES that explicitly models
thecorrelation betweenfirmandmarketreturns.
The statistical properties of correlations have been extensively studied in the econo-
metricsliterature. Ithasnowbecomecommonknowledgethatcorrelationschangethrough
time and are asymmetric in the sense that the correlation between asset returns tends
to be greater during market downturns than during market upturns. While the first ev-
idence on time-varying variances and covariances dates back to the seminal studies of
Mandelbrot (1963) and Fama (1965), it was not until the work of Bollerslevetal. (1988)