Linear Regression for Trading: OLS, Applications, and Model Checks
Summary
The document explains simple and multiple linear regression as ways to estimate a target from one or more predictors. It presents Ordinary Least Squares as the method for fitting coefficients by minimizing squared residuals, with coefficients describing the direction and magnitude of modeled relationships. Trading uses include estimating market sensitivity, building factor models, calculating hedge ratios, and identifying relative value or pairs trading opportunities.
It outlines assumptions such as linear relationships, independent errors, constant error variance, normally distributed residuals, and limited multicollinearity. Suggested evaluation measures include R², adjusted R², coefficient significance, RMSE, and out-of-sample testing. The guide also discusses Python implementation, although the supplied text omits substantial sections. Regression is interpretable and computationally efficient, but outliers, nonlinear relationships, correlated predictors, and changing market regimes can undermine conclusions; rolling windows and regularized variants are mentioned as possible extensions.
Key ideas
- Simple regression uses one predictor, while multiple regression models a target using several predictors.
- Ordinary Least Squares estimates coefficients by minimizing the sum of squared residuals.
- Trading applications include market beta estimation, factor modeling, hedge ratios, and pairs trading.
- Residual assumptions and out-of-sample performance should be checked before trusting a model.
- Outliers, nonlinear effects, and shifting market regimes can make linear regression unreliable.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.