The Use of Risk Budgets in Portfolio Optimization (eBook)

Albina Unger holds a doctoral degree from the Faculty of Finance at the University of Bremen, Germany. She now works as a risk manager.

Foreword 5
Preface 7
Contents 9
List of Figures 12
List of Tables 14
1 Introduction 24
1.1 Motivation and Problem Statement 24
1.2 Outline of Thesis 30
2 Theoretical Background 33
2.1 Modern Portfolio Theory 33
2.1.1 Mean Variance Framework 33
2.1.2 Separation Theorem 43
2.1.3 Utility Theoretic Foundation 46
2.1.4 Weaknesses of the Classical Portfolio Theory 56
2.2 Asset Pricing Theory 58
2.2.1 Capital Asset Pricing Model - CAPM 58
2.2.2 Empirical Evidence - Critique and Anomalies 63
2.2.3 Factor Models 66
2.2.4 Methodology for Empirical Testing 69
2.3 Summary 73
3 Alternative Approaches in Portfolio Management 75
3.1 Risk Measures and Risk Contributions 75
3.1.1 What Is Risk? 75
3.1.2 Risk Measures 77
3.1.3 Risk Contributions 85
3.2 Portfolio Models 96
3.2.1 Equally Weighted Portfolio (1/n) 96
3.2.2 Minimum Risk Portfolios 97
3.2.3 Equally Risk Contribution Portfolios 99
3.3 Utility Theoretic Foundations 102
3.3.1 Expected Utility Theory 102
3.3.2 Other Approaches 107
3.3.3 Summary 127
4 Literature Review 129
4.1 Minimum Risk Portfolios 129
4.1.1 MV/Low Risk Anomaly 129
4.1.2 Minimum-CVaR Portfolio 141
4.1.3 Maximum Drawdown and Drawdown Measures 145
4.1.4 Minimum-CDaR Portfolio 148
4.2 Risk Budgeting Portfolios 150
4.2.1 Volatility Risk Budgets 150
4.2.2 CVaR Risk Budgets 159
4.2.3 Summary of the Risk Budgeting Studies 162
5 Robustness 168
5.1 Definition of Robustness 168
5.2 Approaches to Robust Portfolios: A Short Review 170
5.3 Review of the Robustness of the Markowitz Approach 173
5.4 Robustness of the Volatility Risk Budgeting Portfolio 176
5.5 Summary 179
6 Empirical Studies 180
6.1 Organization of Studies 180
6.2 Performance Study 182
6.2.1 Methodology 183
6.2.2 European Fund 194
6.2.3 Global Portfolio 213
6.2.4 German Market 236
6.2.5 Summary of the Performance Studies 261
6.3 Exploring Risk-Based Pricing Anomalies 262
6.3.1 Methodology 263
6.3.2 Global Portfolio 267
6.3.3 Germany 1973 271
6.3.4 Rolling Regressions 278
6.3.5 US Industry Indices 283
6.3.6 US MSCI 285
6.3.7 German Industry Indices 287
6.3.8 German MSCI 291
6.3.9 Four-Factor Model 295
6.3.10 Summary of the Factor Regressions 296
6.4 Robustness Study 297
6.4.1 Methodology 298
6.4.2 Simulation Study 301
6.4.3 Empirical Study 325
6.4.4 Results of the Robustness Study 339
7 Extensions of Empirical Studies 342
7.1 Fat Tailed Distributions 342
7.2 Binary Stability Portfolio 356
7.3 Hierarchical Clustering 369
7.3.1 Global Portfolio 373
7.3.2 German Market 376
7.3.3 Different Clustering Algorithm 380
7.3.4 Summary 382
8 Conclusion 384
A Appendix 391
A.1 Germany1973 Dataset 391
A.2 Regressions 392
A.2.1 Global Dataset 392
A.2.2 Germany 1973 Dataset 397
A.2.3 US Industry Dataset 403
A.2.4 US MSCI Dataset 404
A.2.5 German Industry Dataset 405
A.2.6 German MSCI Dataset 407
A.3 Robustness Study 408
Bibliography 410