Elements of Quantitative Investing

GIUSEPPE A. PALEOLOGO, PhD, is the Head of Quantitative Research at Balyasny Asset Management. Previously, he held senior positions in quantitative research and risk at Citadel, Millennium, and Hudson River Trading. He has extensive experience in equities quantitative risk management, portfolio construction, and alpha signal research. He holds a doctorate in Management Science and Engineering from Stanford University.

• Acknowledgments xvIntroduction xviiNotation xxiiiChapter 1 The Map and the Territory 11.1 The Securities 31.2 Modes of Exchange 51.3 Who Are the Market Participants? 61.3.1 The Sell Side 61.3.2 The Buy Side 91.4 Where Do Excess Returns Come From? 121.5 The Elements of Quantitative Investing 15Chapter 2 Univariate Returns 202.1 Returns 212.1.1 Definitions 212.1.2 Excess Returns 232.1.3 Log Returns 232.1.4 Estimating Prices and Returns 242.1.5 Stylized Facts 262.2 Conditional Heteroskedastic Models 302.2.1 GARCH(1, 1) and Return Stylized Facts 322.2.2 GARCH as Random Recursive Equations 342.2.3 ⋆GARCH(1, 1) Estimation 362.2.4 Realized Volatility 372.3 State-Space Estimation of Variance 402.3.1 Muth’s Original Model: EWMA 402.3.2 ⋆The Harvey–Shephard Model 442.4 ⋆Appendix 462.4.1 The Kalman Filter 462.4.2 Kalman Filter Examples 492.5 Exercises 51Chapter 3 Interlude: What Is Performance? 533.1 Expected Return 543.2 Volatility 543.3 Sharpe Ratio 553.4 Capacity 58Chapter 4 Linear Models of Returns 614.1 Factor Models 624.2 Interpretations of Factor Models 654.2.1 Graphical Model 664.2.2 Superposition of Effects 664.2.3 Single-Asset Product 674.3 Alpha Spanned and Alpha Orthogonal 684.4 Transformations 714.4.1 Rotations 714.4.2 Projections 734.4.3 Push-Outs 744.5 Applications 754.5.1 Performance Attribution 754.5.2 Risk Management: Forecast and Decomposition 764.5.3 Portfolio Management 804.5.4 Alpha Research 804.6 Factor Models Types 814.7 ⋆Appendix 824.7.1 Linear Regression 824.7.2 Linear Regression Decomposition 864.7.3 The Frisch–Waugh–Lovell Theorem 874.7.4 The Singular Value Decomposition 894.8 Exercises 92Chapter 5 Evaluating Risk 945.1 Evaluating the Covariance Matrix 955.1.1 Robust Loss Functions for Volatility Estimation 955.1.2 Application to Multivariate Returns 975.2 Evaluating the Precision Matrix 1005.2.1 Minimum-Variance Portfolios 1005.2.2 Mahalanobis Distance 1015.3 Ancillary Tests 1025.3.1 Model Turnover 1035.3.2 Testing Betas 1035.3.3 Coefficient of Determination? 1045.4 ⋆Appendix 1075.4.1 Proof for Minimum-Variance Portfolios 107Chapter 6 Fundamental Factor Models 1106.1 The Inputs and the Process 1116.1.1 The Inputs 1116.1.2 The Process 1146.2 Cross-Sectional Regression 1156.2.1 Rank-Deficient Loadings Matrices 1186.3 Estimating the Factor Covariance Matrix 1206.3.1 Factor Covariance Matrix Shrinkage 1216.3.2 Dynamic Conditional Correlation 1226.3.3 Short-Term Volatility Updating 1226.3.4 Correcting for Autocorrelation in Factor Returns 1246.4 Estimating the Idiosyncratic Covariance Matrix 1256.4.1 Exponential Weighting 1256.4.2 Visual Inspection 1256.4.3 Short-Term Idio Update 1266.4.4 Off-Diagonal Clustering 1276.4.5 Idiosyncratic Covariance Matrix Shrinkage 1316.5 Winsorization of Returns 1316.6 ⋆Advanced Model Topics 1336.6.1 Linking Models 1336.6.2 Currency Rebasing 1396.7 A Tour of Factors 141Chapter 7 Statistical Factor Models 1477.1 Statistical Models: The Basics 1497.1.1 Best Low-Rank Approximation and PCA 1497.1.2 Maximum Likelihood Estimation and PCA 1527.1.3 Cross-Sectional and Time-Series Regressions via SVD 1557.2 Beyond the Basics 1557.2.1 The Spiked Covariance Model 1567.2.2 Spectral Limit Behavior of the Spiked Covariance Model 1587.2.3 Optimal Shrinkage of Eigenvalues 1607.2.4 Eigenvalues: Experiments versus Theory 1627.2.5 Choosing the Number of Factors 1627.3 Real-Life Stylized Behavior of PCA 1657.3.1 Concentration of Eigenvalues 1667.3.2 Controlling the Turnover of Eigenvectors 1687.4 Interpreting Principal Components 1737.4.1 The Clustering View 1737.4.2 The Regression View 1747.5 Statistical Model Estimation in Practice 1767.5.1 Weighted and Two-Stage PCA 1767.5.2 Implementing Statistical Models in Production 1797.6 ⋆Appendix 1817.6.1 Exercises and Extensions to PCA 1817.6.2 Asymptotic Properties of PCA 185Chapter 8 Evaluating Excess Returns 1888.1 Backtesting Best Practices 1908.1.1 Data Sourcing 1908.1.2 Research Process 1918.2 The Backtesting Protocol 1958.2.1 Cross-Validation and Walk-Forward 1958.3 The Rademacher Anti-Serum (RAS) 2008.3.1 Setup 2008.3.2 Main Result and Interpretation 2038.4 Some Empirical Results 2088.4.1 Simulations 2088.4.2 Historical Anomalies 2108.5 ⋆Appendix 2148.5.1 Proofs for RAS 214Chapter 9 Portfolio Management: The Basics 2209.1 Why Mean-Variance Optimization? 2219.2 Mean-Variance Optimal Portfolios 2239.3 Trading in Factor Space 2299.3.1 Factor-Mimicking Portfolios 2299.3.2 Adding, Estimating, and Trading a New Factor 2329.3.3 Factor Portfolios from Sorts? 2359.4 Trading in Idio Space 2369.5 Drivers of Information Ratio: Information Coefficient and Diversification 2379.6 Aggregation: Signals versus Portfolios 2409.7 ⋆Appendix 2449.7.1 Some Useful Results from Linear Algebra 2449.7.2 Some Portfolio Optimization Problems 2459.7.3 Optimality of FMPs 2459.7.4 Single-Factor Covariance Matrix Updating 247Chapter 10 Beyond Simple Mean-Variance 25010.1 Shortcomings of Naïve MVO 25110.2 Constraints and Modified Objectives 25410.2.1 Types of Constraints 25710.2.2 Do Constraints Improve or Worsen Performance? 26110.2.3 Constraints as Penalties 26110.3 How Does Estimation Error Affect the Sharpe Ratio? 26710.3.1 The Impact of Alpha Error 26810.3.2 The Impact of Risk Error 26910.4 ⋆Appendix 27010.4.1 Theorems on Sharpe Efficiency Loss 270Chapter 11 Market-Impact-Aware Portfolio Management 27611.1 Market Impact 27711.1.1 Temporary Market Impact 27811.2 Finite-Horizon Optimization 28411.3 Infinite-Horizon Optimization 28611.3.1 Comparison to Single-Period Optimization 28911.3.2 The No-Market-Impact Limit 29011.3.3 Optimal Liquidation 29011.3.4 Deterministic Alpha 29111.3.5 AR(1) Signal 29111.4 ⋆Appendix 29311.4.1 Proof of the Infinite-Horizon Quadratic Problem 293Chapter 12 Hedging 29712.1 Toy Story 29812.2 Factor Hedging 30112.2.1 The General Case 30112.3 Hedging Tradeable Factors with Time-Series Betas 30412.4 Factor-Mimicking Portfolios of Time Series 30712.5 ⋆Appendix 309Chapter 13 Dynamic Risk Allocation 31213.1 The Kelly Criterion 31413.2 Mathematical Properties 32113.3 The Fractional Kelly Strategy 32313.4 Fractional Kelly and Drawdown Control 327Chapter 14 Ex-Post Performance Attribution 33314.1 Performance Attribution: The Basics 33514.2 Performance Attribution with Errors 33614.2.1 Two Paradoxes 33614.2.2 Estimating Attribution Errors 33714.2.3 Paradox Resolution 33914.3 Maximal Performance Attribution 34014.4 Selection versus Sizing Attribution 34714.4.1 Connection to the Fundamental Law of Active Management 35114.4.2 Long–Short Performance Attribution 35114.5 Appendix⋆ 35214.5.1 Proof of the Selection versus Sizing Decomposition 352Chapter 15 A Coda about Leitmotifs 357References 359Index 373