The Elements of Quantitative Investing

Contents
	Preface
Before the Trade
	The Map and the Territory
		The Securities
		Modes of Exchange
		Who Are the Market Participants?
			The Sell Side
			The Buy Side
		Where Do Excess Return Come From?
		The Elements of Quantitative Investing
	Returns: Properties and Models
		Returns
			Definitions
			Excess Returns
			Log Returns
			Estimating Prices and Returns
			Stylized Facts
		Conditional Heteroscedastic Models (CHM)
			GARCH(1, 1) and Return Stylized Facts
			GARCH as random recursive equations
			GARCH(1, 1) Estimation
			Realized Volatility
			Combining CHM and Realized Volatility
		State-Space Estimation of Variance
			Muth\'s Original Model: EWMA
			The Harvey-Shephard Model
		Appendix
			The Kalman Filter
			Kalman Filter Examples
		Exercises
	Linear Models of Returns: The Basics
		Factor Models
		Interpretations of Factor Models
			Graphical Model
			Superposition of Effects
			Single-Asset Product
		Alpha Spanned and Alpha Orthogonal
		Transformations
			Rotations
			Projections
			Push-Outs
		Applications
			Performance Attribution
			Risk Management: Forecast and Decomposition
			Portfolio Management
			Alpha Research
		Factor Models Types
		Appendix
			Linear Regression
			Linear Regression Decomposition
			The Frisch-Waugh-Lovell Theorem
			The Singular Value Decomposition
		Exercises
	Evaluating Excess Returns
		Backtesting Best Practices
		The Backtesting Protocol
			Cross-Validation and Walk Forward
		The Rademacher Anti-Serum
			Setup
			Main result and Interpretation
		Appendix
			Proofs for RAS
	Evaluating Risk
		Evaluating The Covariance Matrix
			Robust Loss Functions for Volatility Estimation
			Application to Multivariate Returns
		Evaluating the Precision Matrix
			Minimum-Variance Portfolios
			Mahalanobis Distance
		Ancillary Tests
			Model Turnover
			Testing Betas
			Coefficient of Determination?
	Fundamental Factor Models
		The Inputs and the Process
			The Inputs
			The Process
		Cross-Sectional Regression
			Rank-Deficient Loadings Matrices
			Conditions for Constrained Identification
		Estimating The Factor Covariance Matrix
			Factor Covariance Shrinkage
			Dynamic Conditional Correlation
			Short-Term Factor Updating
			Correcting for Autocorrelation in Factor Returns
		Estimating the Idiosyncratic Covariance Matrix
			Exponential Weighting
			Visual Inspection
			Short-Term Idio Update
			Off-Diagonal Clustering
			Shrinking of Variances
		Winsorization of Returns
		Selecting Factors: the Large Number of Predictor Case
		Advanced Model Topics
			Linking Models
			Currency Rebasing
		A Tour of Factors
		Further Reading
	Statistical Factor Models
		Statistical Models: The Basics
			Best Low-Rank Approximation and PCA
			Maximum Likelihood Estimation and PCA
			Cross-Sectional and Time-Series Regressions via SVD
		Beyond the Basics
			The Spiked Covariance Model
			Spectral Limit Behavior of the Spiked Covariance Model
			Optimal Shrinkage of Eigenvalues
			Eigenvalues: Experiments Vs. Theory
			Choosing the Number of Factors
		Real-Life Stylized Behavior of PCA
			Concentration of Eigenvalues
			Controlling the Turnover of Eigenvectors
		Interpreting Principal Components
			The Clustering View
			The Regression View
		Statistical Model Estimation in Practice
			Weighted and Two-Stage PCA
			Implementing Statistical Models in Production
		Further Reading
		Exercises
During The Trade
	Portfolio Management: The Basics
		Why Mean-Variance Optimization?
		Mean-Variance Optimal Portfolios
		Trading in Factor Space
		Trading in Idio Space
		Drivers of Information Ratio: Information Coefficient and Diversification
		Investment Performance Metrics
			Expected Return
			Volatility
			Sharpe Ratio
			Capacity
		Appendix
			Convex Optimization
			Duality
			Local Analysis
			Solutions to Specific Optimization Problems
	MVO and Its Discontents
		Shortcomings of Naïve MVO
		Constraints and Modified Objectives
			Types of Constraints
			Do Constraints Improve or Worsen Performance?
			Constraints as Penalties
		How Does Estimation Error Affect Sharpe Ratio?
			The Impact of Alpha Error
			The Impact of Risk Error
		Trading Sharpe For Capacity
		Appendix
			Theorems on Sharpe Efficiency Loss
	Market-Impact-Aware Portfolio Management
		Market Impact
			Temporary Market Impact
		Multiperiod Optimization
		Baldacci-Benveniste-Ritter
			Comparison to Single-Period Optimization
			The No-Market-Impact Limit
			Optimal Liquidation
			Deterministic Alpha
			AR(1) Signal
			Mixing Signals
			Essential Statistics for AR(1) Processes
		Further Reading
	Hedging
		Toy Story
		Factor Hedging
			The General Case
		Hedging Tradable Factors with Time-Series Betas
		Factor-Mimicking Portfolios of Time Series
		Appendix
After the Trade
	Dynamic Risk Allocation
		The Kelly Criterion
			Kelly Portfolios: Mathematical properties
		Log-Return Mean-Variance Optimization
		Fractional Kelly and Drawdown Control
		Variants of Fractional Kelly: Finite Horizon, Transaction Costs, and Heuristics
		Further Reading*
	Ex Post Performance Attribution
		Performance Attribution: The Basics
		Performance Attribution with Errors
			Two Paradoxes
			Estimating Attribution Errors
			Paradox Resolution
		Maximal Performance Attribution
		Selection vs. Sizing Attribution
			Connection to the Fundamental Law of Active Management
			Long-Short Performance Attribution
		Time-Series Performance Attribution
		Appendix
			Proof of the Selection vs. Sizing Decomposition
		Exercises
	Appendix
		Realized Variance of Minimum Variance Portfolios
		Asymptotic Properties of Principal Component Analysis
		The Linear-Quadratic Regulator
		The Discounted Linear-Quadratic Regulator
		Spiked Covariance Matrix: Basic Results
			Some Useful Results from Linear Algebra
		Optimal Trading: The Single-Signal Case
		Conditioning
		Three Papers on Backtesting Tests
			White (2000)
			Romano and Wolf (2005)
			Hansen, Lunde and Nason (2011)
	Bibliography
	Index