Quantitative Equity Investing

FRANK J. FABOZZI is Professor in the Practice of Finance and Becton Fellow at the Yale School of Management and Editor of the Journal of Portfolio Management. He is a Chartered Financial Analyst and earned a doctorate in economics from the City University of New York. SERGIO M. FOCARDI is Professor of Finance at EDHEC Business School in Nice and a founding partner of the Paris-based consulting firm The Intertek Group. He is also a member of the Editorial Board of the Journal of Portfolio Management. Sergio holds a degree in electronic engineering from the University of Genoa and a PhD in mathematical finance from the University of Karlsruhe as well as a postgraduate degree in communications from the Galileo Ferraris Electrotechnical Institute (Turin). PETTER N. KOLM is the Deputy Director of the Mathematics in Finance Master's Program and Clinical Associate Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University; and a founding Partner of the New York–based financial consulting firm the Heimdall Group, LLC. Previously, Petter worked in the Quantitative Strategies Group at Goldman Sachs Asset Management. He received an MS in mathematics from ETH in Zurich; an MPhil in applied mathematics from the Royal Institute of Technology in Stockholm; and a PhD in applied mathematics from Yale University.

• Preface xiAbout the Authors xvChapter 1 Introduction 1In Praise of Mathematical Finance 3Studies of the Use of Quantitative Equity Management 9Looking Ahead for Quantitative Equity Investing 45Chapter 2 Financial Econometrics I: Linear Regressions 47Historical Notes 47Covariance and Correlation 49Regressions, Linear Regressions, and Projections 61Multivariate Regression 76Quantile Regressions 78Regression Diagnostic 80Robust Estimation of Regressions 83Classification and Regression Trees 96Summary 99Chapter 3 Financial Econometrics II: Time Series 101Stochastic Processes 101Time Series 102Stable Vector Autoregressive Processes 110Integrated and Cointegrated Variables 114Estimation of Stable Vector Autoregressive (VAR) Models 120Estimating the Number of Lags 137Autocorrelation and Distributional Properties of Residuals 139Stationary Autoregressive Distributed Lag Models 140Estimation of Nonstationary VAR Models 141Estimation with Canonical Correlations 151Estimation with Principal Component Analysis 153Estimation with the Eigenvalues of the Companion Matrix 154Nonlinear Models in Finance 155Causality 156Summary 157Chapter 4 Common Pitfalls in Financial Modeling 159Theory and Engineering 159Engineering and Theoretical Science 161Engineering and Product Design in Finance 163Learning, Theoretical, and Hybrid Approaches to Portfolio Management 164Sample Biases 165The Bias in Averages 167Pitfalls in Choosing from Large Data Sets 170Time Aggregation of Models and Pitfalls in the Selection of Data Frequency 173Model Risk and its Mitigation 174Summary 193Chapter 5 Factor Models and Their Estimation 195The Notion of Factors 195Static Factor Models 196Factor Analysis and Principal Components Analysis 205Why Factor Models of Returns 219Approximate Factor Models of Returns 221Dynamic Factor Models 222Summary 239Chapter 6 Factor-Based Trading Strategies I: Factor Construction and Analysis 243Factor-Based Trading 245Developing Factor-Based Trading Strategies 247Risk to Trading Strategies 249Desirable Properties of Factors 251Sources for Factors 251Building Factors from Company Characteristics 253Working with Data 253Analysis of Factor Data 261Summary 266Chapter 7 Factor-Based Trading Strategies II: Cross-Sectional Models and Trading Strategies 269Cross-Sectional Methods for Evaluation of Factor Premiums 270Factor Models 278Performance Evaluation of Factors 288Model Construction Methodologies for a Factor-Based Trading Strategy 295Backtesting 306Backtesting Our Factor Trading Strategy 308Summary 309Chapter 8 Portfolio Optimization: Basic Theory and Practice 313Mean-Variance Analysis: Overview 314Classical Framework for Mean-Variance Optimization 317Mean-Variance Optimization with a Risk-Free Asset 321Portfolio Constraints Commonly Used in Practice 327Estimating the Inputs Used in Mean-Variance Optimization: Expected Return and Risk 333Portfolio Optimization with Other Risk Measures 342Summary 357Chapter 9 Portfolio Optimization: Bayesian Techniques and the Black-Litterman Model 361Practical Problems Encountered in Mean-Variance Optimization 362Shrinkage Estimation 369The Black-Litterman Model 373Summary 394Chapter 10 Robust Portfolio Optimization 395Robust Mean-Variance Formulations 396Using Robust Mean-Variance Portfolio Optimization in Practice 411Some Practical Remarks on Robust Portfolio Optimization Models 416Summary 418Chapter 11 Transaction Costs and Trade Execution 419A Taxonomy of Transaction Costs 420Liquidity and Transaction Costs 427Market Impact Measurements and Empirical Findings 430Forecasting and Modeling Market Impact 433Incorporating Transaction Costs in Asset-Allocation Models 439Integrated Portfolio Management: Beyond Expected Return and Portfolio Risk 444Summary 446Chapter 12 Investment Management and Algorithmic Trading 449Market Impact and the Order Book 450Optimal Execution 452Impact Models 455Popular Algorithmic Trading Strategies 457What Is Next? 465Some Comments about the High-Frequency Arms Race 467Summary 470Appendix A Data Descriptions and Factor Definitions 473The MSCI World Index 473One-Month LIBOR 482The Compustat Point-in-Time, IBES Consensus Databases and Factor Definitions 483Appendix B Summary of Well-Known Factors and Their Underlying Economic Rationale 487Appendix C Review of Eigenvalues and Eigenvectors 493The SWEEP Operator 494Index 497