A Practitioner's Guide to Asset Allocation

Foreword by Harry Markowitz xi Preface xiii SECTION ONE Basics of Asset Allocation CHAPTER 1 What Is an Asset Class? 3 Stable Aggregation 3 Investable 4 Internally Homogeneous 4 Externally Heterogeneous 5 Expected Utility 5 Selection Skill 6 Cost-Effective Access 6 Potential Asset Classes 7 References 8 Notes 8 CHAPTER 2 Fundamentals of Asset Allocation 9 The Foundation: Portfolio Theory 9 Practical Implementation 12 References 23 Notes 23 SECTION TWO Fallacies of Asset Allocation CHAPTER 3 The Importance of Asset Allocation 27 Fallacy: Asset Allocation Determines More Than 90 Percent of Performance 27 The Determinants of Portfolio Performance 27 The Behavioral Bias of Positive Economics 30 The Samuelson Dictum 34 References 34 Notes 35 CHAPTER 4 Time Diversification 36 Fallacy: Time Diversifies Risk 36 Samuelson's Bet 36 Time, Volatility, and Probability of Loss 36 Time and Expected Utility 37 Within-Horizon Risk 40 A Preference-Free Contradiction to Time Diversification 41 The Bottom Line 41 References 42 Notes 42 CHAPTER 5 Error Maximization 43 Fallacy: Optimized Portfolios Are Hypersensitive to Input Errors 43 The Intuitive Argument 43 The Empirical Argument 44 The Analytical Argument 48 The Bottom Line 52 References 53 Notes 53 CHAPTER 6 Factors 54 Fallacy: Factors Offer Superior Diversification and Noise Reduction 54 What Is a Factor? 54 Equivalence of Asset Class and Factor Diversification 55 Noise Reduction 57 Where Does This Leave Us? 59 References 59 Notes 59 CHAPTER 7 1/N 60 Fallacy: Equally Weighted Portfolios Are Superior to Optimized Portfolios 60 The Case for 1/N 60 Setting the Record Straight 61 Empirical Evidence in Defense of Optimization 61 Practical Problems with 1/N 62 Broken Clock 63 The Bottom Line 64 References 64 Note 64 SECTION THREE Challenges to Asset Allocation CHAPTER 8 Necessary Conditions for Mean-Variance Analysis 67 The Challenge 67 Departures from Elliptical Distributions 68 Departures from Quadratic Utility 71 Full-Scale Optimization 73 The Curse of Dimensionality 75 Applying Full-Scale Optimization 77 Summary 78 References 79 Notes 79 CHAPTER 9 Constraints 80 The Challenge 80 Wrong and Alone 80 Mean-Variance-Tracking Error Optimization 81 References 85 Note 85 CHAPTER 10 Currency Risk 86 The Challenge 86 Why Hedge? 86 Why Not Hedge Everything? 87 Linear Hedging Strategies 90 Nonlinear Hedging Strategies 96 Economic Intuition 100 References 101 Notes 102 CHAPTER 11 Illiquidity 103 The Challenge 103 Shadow Assets and Liabilities 103 Expected Return and Risk of Shadow Allocations 105 Other Considerations 107 Case Study 108 The Bottom Line 118 Appendix 119 References 120 Notes 120 CHAPTER 12 Risk in the Real World 121 The Challenge 121 End-of-Horizon Exposure to Loss 121 Within-Horizon Exposure to Loss 123 Regimes 124 The Bottom Line 127 References 127 Notes 127 CHAPTER 13 Estimation Error 128 The Challenge 128 Traditional Approaches to Estimation Error 129 Stability-Adjusted Optimization 131 Building a Stability-Adjusted Return Distribution 140 Determining the Optimal Allocation 142 Empirical Analysis 143 The Bottom Line 146 References 146 Notes 147 CHAPTER 14 Leverage versus Concentration 148 The Challenge 148 Leverage in Theory 148 Leverage in Practice 150 The Bottom Line 156 References 157 Notes 157 CHAPTER 15 Rebalancing 158 The Challenge 158 The Dynamic Programming Solution 159 The Markowitz-van Dijk Heuristic 163 The Bottom Line 166 References 167 Notes 167 CHAPTER 16 Regime Shifts 168 The Challenge 168 Predictability of Return and Risk 169 Regime-Sensitive Allocation 169 Tactical Asset Allocation 174 The Bottom Line 179 Appendix: Baum-Welch Algorithm 180 References 181 Notes 182 SECTION FOUR Addendum CHAPTER 17 Key Takeaways 185 CHAPTER 18 Statistical and Theoretical Concepts 192 Discrete and Continuous Returns 192 Arithmetic and Geometric Average Returns 193 Standard Deviation 194 Correlation 195 Covariance 196 Covariance Invertibility 196 Maximum Likelihood Estimation 198 Mapping High-Frequency Statistics onto Low-Frequency Statistics 198 Portfolios 199 Probability Distributions 200 The Central Limit Theorem 201 The Normal Distribution 201 Higher Moments 201 The Lognormal Distribution 202 Elliptical Distributions 202 Probability of Loss 203 Value at Risk 203 Utility Theory 204 Sample Utility Functions 204 Alternative Utility Functions 204 Expected Utility 206 Certainty Equivalents 206 Mean-Variance Analysis for More Than Two Assets 207 Equivalence of Mean-Variance Analysis and Expected Utility Maximization 208 Monte Carlo Simulation 208 Bootstrap Simulation 209 References 210 Note 210 CHAPTER 19 Glossary of Terms 211 Index 233