Shrinking the cross-section

We construct a robust stochastic discount factor (SDF) summarizing 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 contributions of low-variance principal components of the candidate characteristics-based factors. We find that characteristics-sparse SDFs formed from a few such factors—e.g., the four- or five-factor models in the recent literature—cannot adequately summarize the cross-section of expected stock returns. However, an SDF formed from a small number of principal components performs well.