Essays in Asset Management and Risk Management Universität Hamburg Fakultät Wirtschafts- und Sozialwissenschaften Dissertation Zur Erlangung der Würde des Doktors der Wirtschafts- und Sozialwissenschaften vorgelegt von Diplom-Wirtschaftsmathematiker Martin Philipp Wambach aus Osnabrück Hamburg 2013 Vorsitzender: Prof. Dr. Michel Clement Erstgutachter: Prof. Dr. Wolfgang Drobetz Zweitgutachter: Prof. Dr. Alexander Szimayer Datum der Disputation: 09.07.2013 Contents Danksagung vii 1 Synopsis1 1.1 Motivation...................................2 1.2 Value Added of Rebalancing.........................2 1.3 Optimal Rebalancing.............................4 1.4 Rebalancing Across Different Asset Allocations..............5 1.5 Portfolio Insurance..............................5 1.6 Time-Varying Risk of Global Shipping Markets..............7 References...................................... 10 2 Value Added of Rebalancing 11 Abstract........................................ 12 2.1 Introduction.................................. 12 2.2 Data Description................................ 15 2.2.1 Dataset................................. 15 2.2.2 Descriptive Statistics......................... 16 2.3 Implemented Rebalancing Strategies.................... 18 2.4 Statistical Inference.............................. 20 2.5 Empirical Simulation Results........................ 23 2.5.1 Returns................................. 23 2.5.2 Risk................................... 28 2.5.2.1 Volatility........................... 28 2.5.2.2 Semi-Volatility....................... 29 2.5.3 Risk-Adjusted Performance Measures................ 31 2.5.3.1 Sharpe Ratio........................ 31 2.5.3.2 Omega Measure...................... 34 2.5.3.3 Sortino Ratio........................ 35 2.6 Robustness Checks.............................. 37 2.6.1 Transaction Costs........................... 37 2.6.2 Variation of the No-Trade Interval for Threshold and Range Re- balancing................................ 37 2.6.3 Variation of the Average Block Length............... 38 2.7 Conclusion................................... 38 References...................................... 43 i Contents ii 3 Optimal Rebalancing 44 Abstract........................................ 45 3.1 Introduction.................................. 45 3.2 Implemented Rebalancing Strategies.................... 48 3.3 Methodology.................................. 50 3.3.1 Data................................... 50 3.3.2 Settings................................. 50 3.3.3 Motivation............................... 52 3.3.4 Test Design............................... 53 3.4 Empirical Simulation Results........................ 56 3.4.1 Periodic Rebalancing......................... 56 3.4.2 Interval Rebalancing......................... 60 3.4.3 Optimal Rebalancing......................... 63 3.4.4 Impact of Time Series Characteristics on Portfolio Performance. 67 3.5 Conclusion................................... 68 References...................................... 72 4 Rebalancing Across Asset Allocations 73 Abstract........................................ 74 4.1 Introduction.................................. 74 4.2 Data and Descriptive Statistics........................ 76 4.3 Implemented Rebalancing Strategies.................... 77 4.4 Analyzed Asset Allocations.......................... 78 4.5 Simulation Set-Up............................... 79 4.5.1 Resampling Procedure........................ 79 4.5.2 Construction of Confidence Intervals................ 81 4.6 Empirical Results............................... 83 4.6.1 Sharpe Ratio.............................. 84 4.6.2 Sortino Ratio.............................. 87 4.6.3 Omega Measure............................ 88 4.7 Conclusion................................... 89 References...................................... 92 5 Portfolio Insurance 93 Abstract........................................ 94 5.1 Introduction.................................. 94 5.2 An Overview of Portfolio Insurance Strategies............... 97 5.2.1 Stop-Loss Portfolio Insurance Strategy............... 97 5.2.2 Synthetic Put Portfolio Insurance Strategy............. 98 Contents iii 5.2.3 Constant Proportion Portfolio Insurance Strategy......... 99 5.2.4 Time Invariant Portfolio Protection Strategy............ 100 5.2.5 Dynamic Value-at-Risk Portfolio Insurance Strategy....... 101 5.2.6 Distinguishing Characteristics of Portfolio Insurance Strategies. 102 5.3 Historical Simulation Methodology..................... 104 5.3.1 Data and Design of the Empirical Analysis............. 104 5.3.2 Performance Measures........................ 105 5.3.3 Testing for Statistical Significance.................. 106 5.4 Historical Simulation Results........................ 110 5.4.1 Main Simulation Results....................... 110 5.4.2 Robustness Tests........................... 116 5.5 Monte Carlo Simulations........................... 121 5.5.1 Design of the Analysis........................ 121 5.5.2 Testing for Statistical Significance.................. 122 5.5.3 Monte Carlo Simulation Results................... 122 5.6 Conclusions.................................. 127 References...................................... 131 6 Time-Varying Risk in Shipping 132 Abstract........................................ 133 6.1 Introduction.................................. 133 6.2 Theoretical Foundations........................... 136 6.3 Empirical Methodology............................ 139 6.4 Data and Descriptive Statistics........................ 141 6.5 Empirical Results............................... 147 6.5.1 GARCH-X Model........................... 147 6.5.2 EGARCH Model............................ 152 6.5.3 EGARCH-X Model.......................... 156 6.6 Conclusion................................... 159 References...................................... 163 List of Tables Value Added of Rebalancing I Descriptive Statistics............................. 17 II Classification of Implemented Rebalancing Strategies.......... 18 III Development of Net Asset Values: United States.............. 24 IV Average Annualized Returns of Periodic Rebalancing........... 26 V CIs: Average Annualized Returns of Periodic Rebalancing........ 27 VI Average Annualized Risk of Periodic Rebalancing............. 28 VII CIs: Average Annualized Risk of Periodic Rebalancing.......... 30 VIII Average Annualized Sharpe Ratios..................... 32 IX CIs: Average Annualized Sharpe Ratio................... 33 X Skewness and Kurtosis of Rebalancing Strategies............. 34 XI CIs: Average Downside Risk-Adjusted Performance of Periodic Rebalancing 36 Optimal Rebalancing I Classification of Implemented Rebalancing Strategies.......... 49 II Descriptive Statistics............................. 51 III Average Risk-Adjusted Performance of Periodic Rebalancing....... 57 IV CIs: Average Risk-Adjusted Performance of Periodic Rebalancing.... 58 V CIs: Average Risk-Adjusted Performance of Threshold Rebalancing... 61 VI CIs: Average Risk-Adjusted Performance of Range Rebalancing..... 62 VII CIs: Average Risk-Adjusted Performance of Optimal Rebalancing.... 64 Rebalancing Across Asset Allocations I Descriptive Statistics............................. 76 II Classification of Implemented Rebalancing Strategies.......... 78 III Average Sharpe Ratios Across Different Asset Allocations........ 84 Portfolio Insurance I Main Properties of Portfolio Insurance Strategies............. 103 II Historical Simulation Results........................ 112 III Hist. Simulation Results for CPPI and TIPP Strategies with Different Multipliers................................... 114 IV Hist. Simulation Results for the Dynamic VaR-Strategy with Diff. Confi- dence Levels.................................. 115 V Robustness Checks for Historical Simulation Results........... 117 iv List of Tables v VI Hist. Simulation Results for the Dynamic VaR-Strategy with Diff. Confi- dence Levels.................................. 119 VII Monte-Carlo Simulations........................... 123 Time-Varying Risk in Shipping I Determinants of the Shipping Market.................... 137 II Descriptive Statistics of Daily Changes of Baltic Exchange Indices... 143 III Impact of Macroeconomic Factors on Freight Rate Volatility....... 145 IV Descriptive Statistics of Daily Changes of Macroeconomic Variables.. 146 V Descriptive Statistics of Daily Changes of Macroeconomic Variables.. 147 VI Results of Estimated GARCH-X models for Daily Baltic Exchange Indices149 VII Results of Estimated EGARCH model for Daily Changes of Baltic Ex- change Indices................................. 154 VIII Results of Estimated EGARCH-X models for Daily Baltic Exchange Indices157 A1 Macroeconomic Variables........................... 160 A2 Results of Estimated EGARCH Model for the MSCI World Index.... 160 List of Figures Value Added of Rebalancing I Performance of a $100-Investment and its Portfolio Weights of Stocks. 25 (A) Performance of a $100-Investment ........................ 25 (B) Portfolio Weights of Stocks ........................... 25 Optimal Rebalancing I Sharpe Ratios of a 10-Year Rolling Window................ 66 (A) 15 bps Transaction Costs ............................ 66 (B) 100 bps Transaction Costs ........................... 66 Rebalancing Across Asset Allocations I Sharpe Ratio Across Different Asset Allocations.............. 86 (A) Average Sharpe Ratio (United States) ....................... 86 (B) 10%-Quantiles of the Average Sharpe Ratio .................... 86 (C) Average Sharpe Ratio (United Kingdom) .....................