Hedge funds [Elektronische Ressource] : alternative investment strategies and portfolio models / Wolfgang Mader

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Hedge FundsAlternative Investment Strategies andPortfolio ModelsWolfgang MaderErstgutachter: Prof. Dr. Manfred SteinerZweitgutachter: Prof. Dr. Gun¨ ter BambergVorsitzender der mundlic¨ hen Prufung:¨ Prof. Dr. Hans Ulrich BuhlDatum der mundlic¨ hen Prufung:¨ 22. Juli 2005Dissertation zur Erlangung des Grades eines Doktors derWirtschaftswissenschaften (Dr. rer. pol.) durch die WirtschaftswissenschaftlicheFakult¨at der Universit¨at AugsburgContentsList of Figures VIIIList of Tables XIIList of Abbreviations XVList of Symbols XIX1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives and Structure . . . . . . . . . . . . . . . . . . . . . . . . . 32 Hedge Funds 72.1 Hedge Funds Defined . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Hedge Funds in the Alternative Investment Universe . . . . . . . . . 102.3 Key Characteristics of Hedge Funds . . . . . . . . . . . . . . . . . . . 122.3.1 Financial Instruments . . . . . . . . . . . . . . . . . . . . . . 122.3.2 Sources of Return . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.3 Absolute Return Targets . . . . . . . . . . . . . . . . . . . . . 152.3.4 Performance Fees . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.5 Co-Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.6 Liquidity of Hedge Fund Investments . . . . . . . . . . . . . . 202.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Publié le : lundi 1 janvier 2007
Lecture(s) : 46
Source : WWW.OPUS-BAYERN.DE/UNI-AUGSBURG/VOLLTEXTE/2007/635/PDF/MADER_HEDGE_FUNDS.PDF
Nombre de pages : 316
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Hedge Funds
Alternative Investment Strategies and
Portfolio Models
Wolfgang Mader
Erstgutachter: Prof. Dr. Manfred Steiner
Zweitgutachter: Prof. Dr. Gun¨ ter Bamberg
Vorsitzender der mundlic¨ hen Prufung:¨ Prof. Dr. Hans Ulrich Buhl
Datum der mundlic¨ hen Prufung:¨ 22. Juli 2005Dissertation zur Erlangung des Grades eines Doktors der
Wirtschaftswissenschaften (Dr. rer. pol.) durch die Wirtschaftswissenschaftliche
Fakult¨at der Universit¨at AugsburgContents
List of Figures VIII
List of Tables XII
List of Abbreviations XV
List of Symbols XIX
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives and Structure . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Hedge Funds 7
2.1 Hedge Funds Defined . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Hedge Funds in the Alternative Investment Universe . . . . . . . . . 10
2.3 Key Characteristics of Hedge Funds . . . . . . . . . . . . . . . . . . . 12
2.3.1 Financial Instruments . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 Sources of Return . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 Absolute Return Targets . . . . . . . . . . . . . . . . . . . . . 15
2.3.4 Performance Fees . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.5 Co-Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.6 Liquidity of Hedge Fund Investments . . . . . . . . . . . . . . 20
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
IIIContents IV
3 Hedge Fund Strategies 25
3.1 Risks in Hedge Fund Investing . . . . . . . . . . . . . . . . . . . . . . 25
3.1.1 Industry-Inherent Risk Factors . . . . . . . . . . . . . . . . . 26
3.1.2 Strategy-Specific Risk Factors . . . . . . . . . . . . . . . . . . 31
3.2 Hedge Fund Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Equity Hedge . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1.1 Equity Hedge Subgroups . . . . . . . . . . . . . . . . 35
3.2.1.2 Investment Approaches . . . . . . . . . . . . . . . . 37
3.2.1.3 Equity Hedge Trades . . . . . . . . . . . . . . . . . . 38
3.2.1.4 Equity Hedge Risk Factors. . . . . . . . . . . . . . . 40
3.2.2 Convertible Arbitrage. . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Fixed Income Arbitrage . . . . . . . . . . . . . . . . . . . . . 49
3.2.4 Mortgage-Backed Securities Arbitrage. . . . . . . . . . . . . . 55
3.2.5 Merger Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.6 Distressed Securities . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.7 Global Macro . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2.8 Short Selling. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.9 Emerging Markets . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2.10 Managed Futures . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2.11 Closed-end Fund Arbitrage . . . . . . . . . . . . . . . . . . . . 84
3.2.12 Depository Receipts Arbitrage . . . . . . . . . . . . . . . . . . 88
3.2.13 Regulation D . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.3 Fund of Hedge Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.1 Advantages of Funds of Hedge Funds . . . . . . . . . . . . . . 92
3.3.2 Disadvantages of Funds of Hedge Funds . . . . . . . . . . . . 95
3.3.3 Hedge Fund Selection . . . . . . . . . . . . . . . . . . . . . . . 97
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4 Description and Analysis of Hedge Fund Data 104Contents V
4.1 Hedge Fund Databases and Index Providers . . . . . . . . . . . . . . 104
4.1.1 Desirable Properties of Hedge Fund Indices . . . . . . . . . . . 105
4.1.2 Hedge Fund Index Providers . . . . . . . . . . . . . . . . . . . 108
4.1.3 Hedge Fund Databases and Index Methodologies. . . . . . . . 118
4.2 Biases in Hedge Fund Index Data . . . . . . . . . . . . . . . . . . . . 126
4.2.1 Biases in Hedge Fund Databases . . . . . . . . . . . . . . . . . 126
4.2.1.1 Problems with Hedge Fund Data . . . . . . . . . . . 127
4.2.1.2 Survivorship Bias . . . . . . . . . . . . . . . . . . . . 128
4.2.1.3 Selection Bias . . . . . . . . . . . . . . . . . . . . . . 131
4.2.1.4 Instant-History Bias . . . . . . . . . . . . . . . . . . 132
4.2.1.5 Stale-Price Bias . . . . . . . . . . . . . . . . . . . . . 133
4.2.1.6 Consequences of Hedge Fund Database Biases . . . . 134
4.2.2 Weighting Schemes for Hedge Fund Indices . . . . . . . . . . . 139
4.2.3 Fund of Hedge Funds Data . . . . . . . . . . . . . . . . . . . . 140
4.3 Data Selection from the Hedge Fund Index Universe . . . . . . . . . . 144
4.4 Statistical Properties of Fund of Hedge Fund Index Data . . . . . . . 148
4.4.1 Return Definitions . . . . . . . . . . . . . . . . . . . . . . . . 150
4.4.2 Unconditional Return Distributions . . . . . . . . . . . . . . . 153
4.4.2.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . 153
4.4.2.2 Parameter Estimates . . . . . . . . . . . . . . . . . . 160
4.4.2.3 Tests for Normality . . . . . . . . . . . . . . . . . . . 162
4.4.3 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . 166
4.4.3.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . 166
4.4.3.2 Autocorrelation . . . . . . . . . . . . . . . . . . . . . 168
4.4.3.3 Unsmoothing of Hedge Fund Data . . . . . . . . . . 171
4.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5 Portfolio-Selection including Hedge Funds 176Contents VI
5.1 Traditional Portfolio Selection . . . . . . . . . . . . . . . . . . . . . . 177
5.2 Problems with Traditional Portfolio-Selection . . . . . . . . . . . . . 181
5.2.1 Investor Preferences . . . . . . . . . . . . . . . . . . . . . . . 181
5.2.2 Return Distributions . . . . . . . . . . . . . . . . . . . . . . . 183
5.2.3 Dependence Structures . . . . . . . . . . . . . . . . . . . . . . 184
5.2.3.1 Linear Correlation . . . . . . . . . . . . . . . . . . . 184
5.2.3.2 Empirical Evidence against Linear Correlation . . . . 187
5.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.3 Modeling Multivariate Return Distributions . . . . . . . . . . . . . . 192
5.3.1 Marginal Distributions . . . . . . . . . . . . . . . . . . . . . . 193
5.3.1.1 Moments of Univariate Distribution Functions . . . . 194
5.3.1.2 Kernel Densities . . . . . . . . . . . . . . . . . . . . 195
5.3.2 Copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.3.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . 196
5.3.2.2 Important Copula Properties . . . . . . . . . . . . . 199
5.3.2.3 Different Copula Functions . . . . . . . . . . . . . . 200
5.3.2.4 Fitting Copula Functions . . . . . . . . . . . . . . . 211
5.3.2.5 Selecting Copula Functions . . . . . . . . . . . . . . 213
5.4 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
5.4.1 Technical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . 216
5.4.2 Portfolio Constituents . . . . . . . . . . . . . . . . . . . . . . 222
5.4.3 Modeling Multivariate Return Distributions . . . . . . . . . . 222
5.4.3.1 Marginal Distributions . . . . . . . . . . . . . . . . . 222
5.4.3.2 Multivariate Distributions . . . . . . . . . . . . . . . 226
5.4.4 Portfolio Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 230
5.4.4.1 Simulation Approach . . . . . . . . . . . . . . . . . . 231
5.4.4.2 Minimum Risk Portfolios . . . . . . . . . . . . . . . 233
5.4.4.3 Efficient Portfolios . . . . . . . . . . . . . . . . . . . 236Contents VII
5.4.4.4 Impact of Modeling . . . . . . . . . . . . . . . . . . 243
5.4.4.5 Benefits of Hedge Funds . . . . . . . . . . . . . . . . 250
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
6 Summary and Conclusion 257
Bibliography 262List of Figures
1.1 Structure of this work . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Traditional investments in the investment universe . . . . . . . . . . . 9
2.2 Systematization of alternative investments . . . . . . . . . . . . . . . 11
2.3 Key characteristics of hedge funds . . . . . . . . . . . . . . . . . . . . 12
2.4 Relative return model vs. absolute return model . . . . . . . . . . . . 16
2.5 Dates and periods affection hedge fund liquidity . . . . . . . . . . . . 23
3.1 Systematization of risk factors in hedge fund investing . . . . . . . . 26
3.2ization of equity strategies . . . . . . . . . . . . . . . . . . . 36
3.3 Advantages and disadvantages of funds of hedge funds . . . . . . . . 92
3.4 Typical hedge fund selection process . . . . . . . . . . . . . . . . . . 98
3.5 Important topics in a hedge fund due diligence . . . . . . . . . . . . . 102
4.1 Objectives and problems of hedge fund benchmark construction . . . 106
4.2 Problems with hedge fund data and resulting biases . . . . . . . . . . 128
4.3 Different reasons for biases and the resulting consequences . . . . . . 135
4.4 Constituents and weighting schemes of hedge fund indices. . . . . . . 141
4.5 Advantages and disadvantages of fund of hedge fund indices . . . . . 142
4.6 Performance of fund of hedge funds indices since 1997 . . . . . . . . . 148
4.7 Differences between simple and log returns . . . . . . . . . . . . . . . 151
4.8 Histograms for fund of hedge fund index returns since 1997 . . . . . . 157
VIIIList of Figures IX
4.9 Boxplots for fund of hedge fund index returns since 1997 . . . . . . . 159
4.10 Quantile-quantile plots for fund of hedge fund index returns . . . . . 163
4.11 Autocorrelation plots for fund of hedge fund index returns . . . . . . 170
5.1 Assumptions that lead to traditional portfolio selection . . . . . . . . 179
5.2 Bivariate densities with standard normal marginals . . . . . . . . . . 187
5.3 Portfolio modeling approach . . . . . . . . . . . . . . . . . . . . . . . 192
5.4 Bivariate densities of Gaussian copulas with different correlation co-
efficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.5 Bivariate densities of t-copulas with different degrees of freedom . . . 204
5.6 Bivariate densities of t-copulas with different correlation coefficients . 205
5.7 Bivariate densities of Clayton copulas with different coefficients β . . 207C
5.8 Bivariate densities of Frank copulas with different coefficients β . . . 208F
5.9 Bivariate densities of Gumbel copulas with different coefficients β . . 209G
5.10 Empirical copula function . . . . . . . . . . . . . . . . . . . . . . . . 210
5.11 Return series for different potential portfolio constituents . . . . . . . 223
5.12 Empiricaldistributionfunction(black)andcorrespondingcumulative
kernel densities (grey) . . . . . . . . . . . . . . . . . . . . . . . . . . 224
5.13 Marginal distributions represented by kernel densities . . . . . . . . . 225
5.14 Log-Likelihood for different degrees of freedom ν of the t-copula . . . 227
5.15 Illustration of the AD measure for a Gumbel copula . . . . . . . . . . 229
5.16 Dependence structure from a Gumbel copula . . . . . . . . . . . . . . 229
5.17 Bivariate scatter plots for stock and bond returns . . . . . . . . . . . 231
5.18 Bivariate scatter plots for stock and hedge fund returns . . . . . . . . 232
5.19 Bivariate scatter plots for bond and hedge fund returns . . . . . . . . 232
5.20 Standard deviations of all minimum risk portfolios . . . . . . . . . . . 235
5.21 Standard deviation - efficient frontier for Gaussian copula . . . . . . . 238
5.22 Standard deviation - efficient frontier for Gumbel copula . . . . . . . 238
5.23 MAD - efficient frontier for Gaussian copula . . . . . . . . . . . . . . 239List of Figures X
5.24 MAD - efficient frontier for Gumbel copula . . . . . . . . . . . . . . . 239
5.25 Shortfall probability - efficient frontier for Gaussian copula . . . . . . 240
5.26 Shortfall probability - efficient frontier for Gumbel copula . . . . . . . 240
5.27 Minimum Regret - efficient frontier for Gaussian copula . . . . . . . . 241
5.28 Minimum Regret - efficient frontier for Gumbel copula . . . . . . . . 241
5.29 CVaR - efficient frontier for Gaussian copula . . . . . . . . . . . . . . 242
5.30 CVaR - efficient frontier for Gumbel copula . . . . . . . . . . . . . . . 242
5.31 Differences in standard deviation for the efficient frontiers (Gaussian
copula minus Gumbel copula results) . . . . . . . . . . . . . . . . . . 245
5.32 Differences in weights for the standard deviation - efficient frontiers
(Gaussian copula minus Gumbel copula results) . . . . . . . . . . . . 245
5.33 Differences in MAD for the efficient frontiers (Gaussian copula minus
Gumbel copula results) . . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.34 Differences in weights for the MAD - efficient frontiers (Gaussian
copula minus Gumbel copula results) . . . . . . . . . . . . . . . . . . 246
5.35 Differencesinshortfallprobabilityfortheefficientfrontiers(Gaussian
copula minus Gumbel copula results) . . . . . . . . . . . . . . . . . . 247
5.36 Differences in weights for the shortfall probability - efficient frontiers
(Gaussian copula minus Gumbel copula results) . . . . . . . . . . . . 247
5.37 Differences in minimum regret for the efficient frontiers (Gaussian
copula minus Gumbel copula results) . . . . . . . . . . . . . . . . . . 248
5.38 Differences in weights for the minimum regret - efficient frontiers
(Gaussian copula minus Gumbel copula results) . . . . . . . . . . . . 248
5.39 DifferencesinCVaRfortheefficientfrontiers(Gaussiancopulaminus
Gumbel copula results) . . . . . . . . . . . . . . . . . . . . . . . . . . 249
5.40 Differences in weights for the CVaR - efficient frontiers (Gaussian
copula minus Gumbel copula results) . . . . . . . . . . . . . . . . . . 249

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