Shrinking the Cross Section

69 Pages Posted: 5 Apr 2017 Last revised: 1 Aug 2018

See all articles by Serhiy Kozak

Serhiy Kozak

University of Michigan, Stephen M. Ross School of Business

Stefan Nagel

University of Chicago - Booth School of Business; National Bureau of Economic Research (NBER); Centre for Economic Policy Research; CESifo (Center for Economic Studies and Ifo Institute)

Shrihari Santosh

University of Maryland - R.H. Smith School of Business; University of Colorado at Boulder - Department of Finance

Multiple version iconThere are 4 versions of this paper

Date Written: July 22, 2018

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

Suggested Citation

Kozak, Serhiy and Nagel, Stefan and Santosh, Shrihari, Shrinking the Cross Section (July 22, 2018). Available at SSRN: https://ssrn.com/abstract=2945663 or http://dx.doi.org/10.2139/ssrn.2945663

Serhiy Kozak (Contact Author)

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Stefan Nagel

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Centre for Economic Policy Research ( email )

London
United Kingdom

CESifo (Center for Economic Studies and Ifo Institute) ( email )

Poschinger Str. 5
Munich, DE-81679
Germany

Shrihari Santosh

University of Maryland - R.H. Smith School of Business ( email )

Robert H. Smith School of Business
Van Munching Hall
College Park, MD 20742
United States

University of Colorado at Boulder - Department of Finance ( email )

Campus Box 419
Boulder, CO 80309
United States

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