Shrinking the Cross Section

Abstract

We construct a robust stochastic discount factor (SDF) that summarizes the joint explanatory power of a large number of cross-sectional stock return predictors. Our method achieves robust out-of-sample performance in this high-dimensional setting by imposing an economically motivated prior on SDF coefficients that shrinks the contributions of low-variance principal components of the candidate factors. While empirical asset pricing research has focused on SDFs with a small number of characteristics-based factors --- e.g., the four- or five-factor models discussed in the recent literature --- we find that such a characteristics-sparse SDF cannot adequately summarize the cross-section of expected stock returns. However, a relatively small number of principal components of the universe of potential characteristics-based factors can approximate the SDF quite well.

Keywords: Factor Models, SDF, Cross Section, Shrinkage, Machine Learning

JEL Classification: G12, G11