The Elements of Quantitative Investing

Practical and relevant insights into the intricacies of quantitative trading at every stage of the investing process The Elements of Quantitative Investing is an in insightful and practical roadmap to every part of the quantitative investing process, from strategy formulation to post-trade analysis. Written by Dr. Giuseppe Paleologo, the author of the widely read Advanced Portfolio Management: A Quant's Guide for Fundamental Investors, the book walks you through every step of quantitative modeling. You'll learn about the statistical properties of returns, factor models, and portfolio management as you discover critical quantitative investing concepts grounded in key financial context. Everything that's been included in the book is highly relevant to quantitative investing in contemporary markets, and the author has focused exclusively on those subjects that can advance a quantitative investor's success in an increasingly competitive financial marketplace. Perfect for financial practitioners looking for applicable insights from one of the industry's leading lights, The Elements of Quantitative Investing makes accessible information, techniques, strategies, and knowledge typically available only to a select few. It's an essential and hands-on guide to quantitative investing.

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
9. 7. 2 Some Portfolio Optimization Problems  320
9. 7. 3 Optimality of FMPs  321
9. 7. 4 Single-Factor Covariance Matrix Updating  324
10 Beyond Simple Mean-Variance  327
10. 1 Shortcomings of Naive MVO  328
10. 2 Constraints and Modified Objectives  335
10. 2. 1 Types of Constraints  336
10. 2. 2 Do Constraints Improve or Worsen Performance?   341
10. 2. 3 Constraints as Penalties  342
10. 3 How Does Estimation Error Affect the Sharpe Ratio?   349
10. 3. 1 The Impact of Alpha Error  351
10. 3. 2 The Impact of Risk Error  352
10. 4 Appendix  354
10. 4. 1 Theorems on Sharpe Efficiency Loss  354
11 Market-Impact-Aware Portfolio Management  361
11. 1 Market Impact  362
11. 1. 1 Temporary Market Impact  364
11. 2 Finite-Horizon Optimization  372
11. 3 Infinite-Horizon Optimization  376
11. 3. 1 Comparison to Single-Period Optimization  379
11. 3. 2 The No-Market-Impact Limit  380
11. 3. 3 Optimal Liquidation  381
11. 3. 4 Deterministic Alpha  381
11. 3. 5 AR(1) Signal  382
11. 4 Appendix  384
11. 4. 1 Proof of the Infinite-Horizon Quadratic Problem  384
12 Hedging  389
12. 1 Toy Story  390
12. 2 Factor Hedging  393
12. 2. 1 The General Case  393
12. 3 Hedging Tradable Factors with Time-Series Betas  397
12. 4 Factor-Mimicking Portfolios of Time Series  402
12. 5 Appendix    404
13 Dynamic Risk Allocation 407
13. 1 The Kelly Criterion  409
13. 2 Mathematical Properties  419
13. 3 The Fractional Kelly Strategy  421
13. 4 Fractional Kelly and Drawdown Control  427
14 Ex Post Performance Attribution  433
14. 1 Performance Attribution: The Basics  435
14. 2 Performance Attribution with Errors  437
14. 2. 1 Two Paradoxes  37
14. 2. 2 Estimating Attribution Errors  439
14. 2. 3 Paradox Resolution  440
14. 3 Maximal Performance Attribution  442
14. 4 Selection vs. Sizing Attribution  451
14. 4. 1 Connection to the Fundamental Law of Active Management
14. 4. 2 Long-Short Performance Attribution  456
14. 5 Appendix?   458
14. 5. 1 Proof of the Selection vs. Sizing Decomposition  458
15 A Coda about Leitmotifs  465
About the Author
Index 495