Complexity in Factor Pricing Models

Abstract

We theoretically characterize the behavior of machine learning asset pricing models. We prove that expected out-of-sample model performance—in terms of SDF Sharpe ratio and test asset pricing errors—is improving in model parameterization (or “complexity”). Our empirical findings verify the theoretically predicted “virtue of complexity” in the cross-section of stock returns. Models with an extremely large number of factors (more than the number of training observations or base assets) outperform simpler alternatives by a large margin.

Keywords: Stochastic discount factor (SDF), asset pricing test, pricing error, alpha, cross section of returns, portfolio choice

JEL Classification: C3, C58, C61, G11, G12, G14