CHAPTER 1
Introduction 1
Quantitative Techniques in the Investment Management Industry 1
Central Themes of This Book 9
Overview of This Book 12
PART ONE
Portfolio Allocation: Classical Theory and Extensions 15
CHAPTER 2
Mean-Variance Analysis and Modern Portfolio Theory 17
The Benefits of Diversification 18
Mean-Variance Analysis: Overview 21
Classical Framework for Mean-Variance Optimization 24
The Capital Market Line 35
Selection of the Optimal Portfolio When There Is a Risk-Free Asset 41
More on Utility Functions: A General Framework for Portfolio Choice 45
Summary 50
CHAPTER 3
Advances in the Theory of Portfolio Risk Measures 53
Dispersion and Downside Measures 54
Portfolio Selection with Higher Moments through Expansions of Utility 70
Polynomial Goal Programming for Portfolio
Optimization with Higher Moments 78
Some Remarks on the Estimation of Higher Moments 80
The Approach of Malevergne and Sornette 81
Summary 86
CHAPTER 4
Portfolio Selection in Practice 87
Portfolio Constraints Commonly Used in Practice 88
Incorporating Transaction Costs in Asset-Allocation Models 101
Multiaccount Optimization 106
Summary 111
PART TWO
Robust Parameter Estimation 113
CHAPTER 5
Classical Asset Pricing 115
Definitions 115
Theoretical and Econometric Models 117
Random Walk Models 118
General Equilibrium Theories 131
Capital Asset Pricing Model (CAPM) 132
Arbitrage Pricing Theory (APT) 136
Summary 137
CHAPTER 6
Forecasting Expected Return and Risk 139
Dividend Discount and Residual Income Valuation Models 140
The Sample Mean and Covariance Estimators 146
Random Matrices 157
Arbitrage Pricing Theory and Factor Models 160
Factor Models in Practice 168
Other Approaches to Volatility Estimation 172
Application to Investment Strategies and Proprietary Trading 176
Summary 177
CHAPTER 7
Robust Estimation 179
The Intuition behind Robust Statistics 179
Robust Statistics 181
Robust Estimators of Regressions 192
Confidence Intervals 200
Summary 206
CHAPTER 8
Robust Frameworks for Estimation: Shrinkage,
Bayesian Approaches, and the Black-Litterman Model 207
Practical Problems Encountered in Mean-Variance Optimization 208
Shrinkage Estimation 215
Bayesian Approaches 229
Summary 253
PART THREE
Optimization Techniques 255
CHAPTER 9
Mathematical and Numerical Optimization 257
Mathematical Programming 258
Necessary Conditions for Optimality for Continuous
Optimization Problems 267
Optimization Duality Theory 269
How Do Optimization Algorithms Work? 272
Summary 288
CHAPTER 10
Optimization under Uncertainty 291
Stochastic Programming 293
Dynamic Programming 308
Robust Optimization 312
Summary 332
CHAPTER 11
Implementing and Solving Optimization Problems in Practice 333
Optimization Software 333
Practical Considerations When Using Optimization Software 340
Implementation Examples 346
Specialized Software for Optimization Under Uncertainty 358
Summary 360
PART FOUR
Robust Portfolio Optimization 361
CHAPTER 12
Robust Modeling of Uncertain Parameters in Classical
Mean-Variance Portfolio Optimization 363
Portfolio Resampling Techniques 364
Robust Portfolio Allocation 367
Some Practical Remarks on Robust Portfolio Allocation Models 392
Summary 393
CHAPTER 13
The Practice of Robust Portfolio Management: Recent Trends and
New Directions 395
Some Issues in Robust Asset Allocation 396
Portfolio Rebalancing 410
Understanding and Modeling Transaction Costs 413
Rebalancing Using an Optimizer 422
Summary 435
CHAPTER 14
Quantitative Investment Management Today and Tomorrow 439
Using Derivatives in Portfolio Management 440
Currency Management 442
Benchmarks 445
Quantitative Return-Forecasting Techniques and Model-Based
Trading Strategies 447
Trade Execution and Algorithmic Trading 456
Summary 460
APPENDIX A
Data Description: The MSCI World Index 463
INDEX 473
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