Robust Portfolio Optimization and Management

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.

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