Robust Portfolio Optimization and Management

Praise for Robust Portfolio Optimization and Management "In the half century since Harry Markowitz introduced his elegant theory for selecting portfolios, investors and scholars have extended and refined its application to a wide range of real-world problems, culminating in the contents of this masterful book. Fabozzi, Kolm, Pachamanova, and Focardi deserve high praise for producing a technically rigorous yet remarkably accessible guide to the latest advances in portfolio construction." --Mark Kritzman, President and CEO, Windham Capital Management, LLC "The topic of robust optimization (RO) has become 'hot' over the past several years, especially in real-world financial applications. This interest has been sparked, in part, by practitioners who implemented classical portfolio models for asset allocation without considering estimation and model robustness a part of their overall allocation methodology, and experienced poor performance. Anyone interested in these developments ought to own a copy of this book. The authors cover the recent developments of the RO area in an intuitive, easy-to-read manner, provide numerous examples, and discuss practical considerations. I highly recommend this book to finance professionals and students alike." --John M. Mulvey, Professor of Operations Research and Financial Engineering, Princeton University

Table of Contents:
Preface xi About the Authors xv 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

About the Author :
Frank J. Fabozzi, PhD, CFA, is Professor in the Practice of Finance at Yale University's School of Management and the Editor of the Journal of Portfolio Management. Petter N. Kolm, PhD, is a graduate student in finance at the Yale School of Management and a financial consultant in New York City. He previously worked at Goldman Sachs asset management where he developed quantitative investment models and strategies. Dessislava A. Pachamanova, PhD, is an Assistant Professor of Operations Research at?Babson College. Her experience also includes work for Goldman Sachs and WestLB, and teaching management science, probability, statistics, and financial mathematics at MIT and Princeton University. Sergio M. Focardi is a founding partner of the Paris-based consulting firm, The Intertek Group.