NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Shrinking the Cross Section

Serhiy Kozak, Stefan Nagel, Shrihari Santosh

NBER Working Paper No. 24070
Issued in November 2017
NBER Program(s):Asset Pricing

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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Document Object Identifier (DOI): 10.3386/w24070

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