Quantitative Equity Investing: Techniques and Strategies

Preface xi

About the Authors xv

Chapter 1 Introduction 1

In Praise of Mathematical Finance 3

Studies of the Use of Quantitative Equity Management 9

Looking Ahead for Quantitative Equity Investing 45

Chapter 2 Financial Econometrics I: Linear Regressions 47

Historical Notes 47

Covariance and Correlation 49

Regressions, Linear Regressions, and Projections 61

Multivariate Regression 76

Quantile Regressions 78

Regression Diagnostic 80

Robust Estimation of Regressions 83

Classification and Regression Trees 96

Summary 99

Chapter 3 Financial Econometrics II: Time Series 101

Stochastic Processes 101

Time Series 102

Stable Vector Autoregressive Processes 110

Integrated and Cointegrated Variables 114

Estimation of Stable Vector Autoregressive (VAR) Models 120

Estimating the Number of Lags 137

Autocorrelation and Distributional Properties of Residuals 139

Stationary Autoregressive Distributed Lag Models 140

Estimation of Nonstationary VAR Models 141

Estimation with Canonical Correlations 151

Estimation with Principal Component Analysis 153

Estimation with the Eigenvalues of the Companion Matrix 154

Nonlinear Models in Finance 155

Causality 156

Summary 157

Chapter 4 Common Pitfalls in Financial Modeling 159

Theory and Engineering 159

Engineering and Theoretical Science 161

Engineering and Product Design in Finance 163

Learning, Theoretical, and Hybrid Approaches to Portfolio Management 164

Sample Biases 165

The Bias in Averages 167

Pitfalls in Choosing from Large Data Sets 170

Time Aggregation of Models and Pitfalls in the Selection of Data Frequency 173

Model Risk and its Mitigation 174

Summary 193

Chapter 5 Factor Models and Their Estimation 195

The Notion of Factors 195

Static Factor Models 196

Factor Analysis and Principal Components Analysis 205

Why Factor Models of Returns 219

Approximate Factor Models of Returns 221

Dynamic Factor Models 222

Summary 239

Chapter 6 Factor-Based Trading Strategies I: Factor Construction and Analysis 243

Factor-Based Trading 245

Developing Factor-Based Trading Strategies 247

Risk to Trading Strategies 249

Desirable Properties of Factors 251

Sources for Factors 251

Building Factors from Company Characteristics 253

Working with Data 253

Analysis of Factor Data 261

Summary 266

Chapter 7 Factor-Based Trading Strategies II: Cross-Sectional Models and Trading Strategies 269

Cross-Sectional Methods for Evaluation of Factor Premiums 270

Factor Models 278

Performance Evaluation of Factors 288

Model Construction Methodologies for a Factor-Based Trading Strategy 295

Backtesting 306

Backtesting Our Factor Trading Strategy 308

Summary 309

Chapter 8 Portfolio Optimization: Basic Theory and Practice 313

Mean-Variance Analysis: Overview 314

Classical Framework for Mean-Variance Optimization 317

Mean-Variance Optimization with a Risk-Free Asset 321

Portfolio Constraints Commonly Used in Practice 327

Estimating the Inputs Used in Mean-Variance Optimization: Expected Return and Risk 333

Portfolio Optimization with Other Risk Measures 342

Summary 357

Chapter 9 Portfolio Optimization: Bayesian Techniques and the Black-Litterman Model 361

Practical Problems Encountered in Mean-Variance Optimization 362

Shrinkage Estimation 369

The Black-Litterman Model 373

Summary 394

Chapter 10 Robust Portfolio Optimization 395

Robust Mean-Variance Formulations 396

Using Robust Mean-Variance Portfolio Optimization in Practice 411

Some Practical Remarks on Robust Portfolio Optimization Models 416

Summary 418

Chapter 11 Transaction Costs and Trade Execution 419

A Taxonomy of Transaction Costs 420

Liquidity and Transaction Costs 427

Market Impact Measurements and Empirical Findings 430

Forecasting and Modeling Market Impact 433

Incorporating Transaction Costs in Asset-Allocation Models 439

Integrated Portfolio Management: Beyond Expected Return and Portfolio Risk 444

Summary 446

Chapter 12 Investment Management and Algorithmic Trading 449

Market Impact and the Order Book 450

Optimal Execution 452

Impact Models 455

Popular Algorithmic Trading Strategies 457

What Is Next? 465

Some Comments about the High-Frequency Arms Race 467

Summary 470

Appendix A Data Descriptions and Factor Definitions 473

The MSCI World Index 473

One-Month LIBOR 482

The Compustat Point-in-Time, IBES Consensus Databases and Factor Definitions 483

Appendix B Summary of Well-Known Factors and Their Underlying Economic Rationale 487

Appendix C Review of Eigenvalues and Eigenvectors 493

The SWEEP Operator 494

Index 497