Kernel Trick for the Cross-Section

46 Pages Posted: 8 Jan 2019 Last revised: 24 Mar 2021

See all articles by Serhiy Kozak

Serhiy Kozak

University of Maryland - Robert H. Smith School of Business

Date Written: November 15, 2020


Characteristics-based asset pricing implicitly assumes that factor betas or risk prices are linear functions of pre-specified characteristics. Present-value identities, such as Campbell-Shiller or clean-surplus accounting, however, clearly predict that expected returns are highly non-linear functions of all characteristics. While basic non-linearities can be easily accommodated by adding non-linear functions to the set of characteristics, the problem quickly becomes infeasible once interactions of characteristics are considered. I propose a method which uses economically-driven regularization to construct a stochastic discount factor (SDF) when the set of characteristics is extended to an arbitrary — potentially infinitely-dimensional — set of non-linear functions of original characteristics. The method borrows ideas from a machine learning technique known as the “kernel trick” to circumvent the curse of dimensionality. I find that allowing for interactions and non-linearities of characteristics leads to substantially more efficient SDFs; out-of-sample Sharpe ratios for the implied MVE portfolio double.

Keywords: risk premia, kernel methods, non-linearities, characteristics, SDF, cross section, machine learning

JEL Classification: G12, G11

Suggested Citation

Kozak, Serhiy, Kernel Trick for the Cross-Section (November 15, 2020). Available at SSRN: or

Serhiy Kozak (Contact Author)

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

7621 Mowatt Ln
College Park, MD 20742
United States


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