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