[Quant Lecture] Alpha and factor decomposition (PART I)
Statistics for algorithmic traders
Alpha & Factor Decomposition
This chapter frames factor analysis as a decision tool: use regression to separate true edge (Ξ±) from systematic risk premia (Ξ²), diagnose hidden exposures, and turn findings into concrete hedges and portfolio rules. The workflow runs from simple/ multiple regression foundations to multi-factor models, statistical significance of Ξ±, rolling diagnostics, and implementation.
Whatβs inside:
Regression bedrock. Simple OLS, estimator properties, and how to form CIs for slope/intercept, mean response, and prediction intervals.
From one factor to many. Build multi-factor regressions to explain returns with partial betas.
Isolating true alpha. Regress excess returns on factors; the intercept (Ξ±) is the skill component.
Hidden risk exposures. Find βbeta leaks,β factor crowding, sector concentration, liquidity sensitivity, and style drift via rolling betas and CIs.
Actionable applications. Neutralize unintended betas with minimum-variance hedges; construct factor-neutral, residual-Sharpe-oriented blends and keep betas in check over time.
Model adequacy & transforms. Residual checks, R2 and transformations (log/Box-Cox) to stabilize variance and linearize relations.
Multiple Linear Regression (MLR). Extend to many predictors; diagnostics for influential points, polynomial terms, and the dummy-variable trap.
Risk-aware inference. Use mean-response CIs vs. wider prediction intervals for trading decisions (stops/targets/position sizing) and report robust stats alongside fit.
Again, I have decided to devide this chapter in several parts because itβs pretty long.
Check a sample of what you will find inside:
