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

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

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Robust Portfolio Optimization and Management

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Table of Contents

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