The Elements of Quantitative Investing

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Expert real-world insight on the intricacies of quantitative trading before, during, and after the trade The Elements of Quantitative Investing is a comprehensive guide to quantitative investing, covering everything readers need to know from inception of a strategy, to execution, to post-trade analysis, with insight into all the quantitative methods used throughout the investment process. This book describes all the steps of quantitative modeling, including statistical properties of returns, factor model, portfolio management, and more. The inclusion of each topic is determined by real-world applicability. Divided into three parts, each corresponding to a phase of the investment process, this book focuses on well-known factor models, such as PCA, but with essential grounding in financial context. This book encourages the reader to think deeply about simple things. The author, Giuseppe Paleologo, has held senior quantitative research and risk management positions at three of the four biggest hedge fund platforms in the world, and at one of the top three proprietary trading firms. Currently, he serves as the Head of Quantitative Research at Balyasny Asset Management with $21 billion in assets under management. He has held teaching positions at Cornell University and New York University and holds a Ph.D. and two M.S. from Stanford University. This book answers questions that every quantitative investor has asked at some point in their career, including:

• How do I model multivariate returns?
• How do I test these models, either developed by me or by commercial vendors?
• How do I incorporate asset-specific data in my model?
• How do I convert risk appetite and expected returns into a portfolio?
• How do I account for transaction costs in portfolio management? The Elements of Quantitative Investing earns a well-deserved spot on the bookshelves of financial practitioners seeking expert insight from a leading financial executive on quantitative investment topics-knowledge which is usually accessible to few and transmitted by one-on-one apprenticeship.

Contenu

Introduction xvii

Prerequisites xxi

Organization xxii

Acknowledgments xxv

1 The Map and the Territory 5

1.1 The Securities 7

1.2 Modes of Exchange 9

1.3 Who Are the Market Participants? 11

1.3.1 The Sell Side 11

1.3.2 The Buy Side 15

1.4 Where Do Excess Returns Come From? 19

1.5 The Elements of Quantitative Investing 24

2 Univariate Returns 29

2.1 Returns 30

2.1.1 Definitions 30

2.1.2 Excess Returns 32

2.1.3 Log Returns 33

2.1.4 Estimating Prices and Returns 34

2.1.5 Stylized Facts 37

2.2 Conditional Heteroscedastic Models (CHM) 42

2.2.1 GARCH(1, 1) and Return Stylized Facts 44

2.2.2 GARCH as Random Recursive Equations 47

2.2.3 ?GARCH(1, 1) Estimation 49

2.2.4 Realized Volatility 50

2.3 State-Space Estimation of Variance 55

2.3.1 Muth's Original Model: EWMA 55

2.3.2 The Harvey-Shephard Model 60

2.4 Appendix 62

2.4.1 The Kalman Filter 62

2.4.2 Kalman Filter Examples 66

2.5 Exercises 70

3 Interlude: What is Performance? 73

3.1 Expected Return 74

3.2 Volatility 74

3.3 Sharpe Ratio 76

3.4 Capacity 78

4 Linear Models of Returns 83

4.1 Factor Models 84

4.2 Interpretations of Factor Models 87

4.2.1 Graphical Model 88

4.2.2 Superposition of E_ects 89

4.2.3 Single-Asset Product 90

4.3 Alpha Spanned and Alpha Orthogonal 91

4.4 Transformations 95

4.4.1 Rotations 95

4.4.2 Projections 98

4.4.3 Push-Outs 99

4.5 Applications 101

4.5.1 Performance Attribution 101

4.5.2 Risk Management: Forecast and Decomposition 102

4.5.3 Portfolio Management 105

4.5.4 Alpha Research 107

4.6 Factor Models Types 108

4.7 Appendix 109

4.7.1 Linear Regression 109

4.7.2 Linear Regression Decomposition 116

4.7.3 The Frisch-Waugh-Lovell Theorem 116

4.7.4 The Singular Value Decomposition 120

4.8 Exercises 123

5 Evaluating Risk 127

5.1 Evaluating the Covariance Matrix 128

5.1.1 Robust Loss Functions for Volatility Estimation 128

5.1.2 Application to Multivariate Returns 130

5.2 Evaluating the Precision Matrix 134

5.2.1 Minimum-Variance Portfolios 134

5.2.2 Mahalanobis Distance 135

5.3 Ancillary Tests 137

5.3.1 Model Turnover 138

5.3.2 Testing Betas 139

5.3.3 Coefficient of Determination? 140

5.4 Appendix 143

5.4.1 Proof for Minimum-Variance Portfolios 143

6 Fundamental Factor Models 147

6.1 The Inputs and the Process 148

6.1.1 The Inputs 148

6.1.2 The Process 152

6.2 Cross-Sectional Regression 153

6.2.1 Rank-Deficient Loadings Matrices 158

6.3 Estimating The Factor Covariance Matrix 160

6.3.1 Factor Covariance Matrix Shrinkage 161

6.3.2 Dynamic Conditional Correlation 162

6.3.3 Short-Term Volatility Updating 163

6.3.4 Correcting for Autocorrelation in Factor Returns 166

6.4 Estimating the Idiosyncratic Covariance Matrix 167

6.4.1 Exponential Weighting 167

6.4.2 Visual Inspection 167

6.4.3 Short-Term Idio Update 168

6.4.4 O_-Diagonal Clustering 169

6.4.5 Idiosyncratic Covariance Matrix Shrinkage 173

6.5 Winsorization of Returns 174

6.6 ?Advanced Model Topics 176

6.6.1 Linking Models 176

6.6.2 Currency Rebasing 184

6.7 A Tour of Factors 188

7 Statistical Factor Models 195

7.1 Statistical Models: The Basics 197

7.1.1 Best Low-Rank Approximation and PCA 197

7.1.2 Maximum Likelihood Estimation and PCA 202

7.1.3 Cross-Sectional and Time-Series Regressions via SVD 205

7.2 Beyond the Basics 207

7.2.1 The Spiked Covariance Model 208

7.2.2 Spectral Limit Behavior of the Spiked Covariance

Model 210

7.2.3 Optimal Shrinkage of Eigenvalues 213

7.2.4 Eigenvalues: Experiments vs. Theory 216

7.2.5 Choosing the Number of Factors 218

7.3 Real-Life Stylized Behavior of PCA 220

7.3.1 Concentration of Eigenvalues 221

7.3.2 Controlling the Turnover of Eigenvectors 223

7.4 Interpreting Principal Components 230

7.4.1 The Clustering View 230

7.4.2 The Regression View 232

7.5 Statistical Model Estimation in Practice 234

7.5.1 Weighted and Two-Stage PCA 234

7.5.2 Implementing Statistical Models in Production 238

7.6 Appendix 241

7.6.1 Exercises and Extensions to PCA 241

7.6.2 Asymptotic Properties of PCA 246

8 Evaluating Excess Returns 249

8.1 Backtesting Best Practices 251

8.1.1 Data Sourcing 251

8.1.2 Research Process 253

8.2 The Backtesting Protocol 259

8.2.1 Cross-Validation and Walk-Forward 259

8.3 The Rademacher Anti-Serum (RAS) 265

8.3.1 Setup 265

8.3.2 Main result and Interpretation 269

8.4 Some Empirical Results 275

8.4.1 Simulations 275

8.4.2 Historical Anomalies 279

8.5 ?Appendix 282

8.5.1 Proofs for RAS 282

9 Portfolio Management: The Basics 289

9.1 Why Mean-Variance Optimization? 290

9.2 Mean-Variance Optimal Portfolios 293

9.3 Trading in Factor Space 301

9.3.1 Factor-Mimicking Portfolios 301

9.3.2 Adding, Estimating, and Trading a New Factor 304

9.3.3 Factor Portfolios from Sorts? 308

9.4 Trading in Idio Space 310

9.5 Drivers of Information Ratio: Information Coefficient and Diversification 311

9.6 Aggregation: Signals vs. Portfolios 315

9.7 Appendix 320

**9.7.1 Some Useful Results from Linear Algebra 320…