Sparse Signals in the Cross-Section of Returns

Abstract

How do arbitrageurs find variables that predict returns? If a predictor lasts 30 days or more, then a clever arbitrageur can use his intuition to get the job done. But, what’s an arbitrageur supposed to do if a predictor lasts 30 minutes or less? An arbitrageur’s intuition is useless if the predictor decays before he can finish his morning coffee. Motivated by this observation, we show how arbitrageurs can find these sorts of rare, short-lived, “sparse” predictors by replacing intuition with a statistical procedure known as the LASSO. Using the LASSO boosts out-of-sample predictability in 1-minute returns by 23% relative to standard OLS-regression models. This out-of-sample predictive power comes from quickly identifying the right predictors at the right time, not from better estimating the effects of some new factor. What’s more, the predictors chosen by the LASSO correspond to real-world events: the lagged returns of stocks with announcements are 18.3% more likely to be used by the LASSO as predictors.

Keywords: Return Predictability, Out-of-Sample Fit, Sparsity, The LASSO

JEL Classification: C55, C58, G12, G14