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.

Table of Contents:
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