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
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