Kernel Trick for the Cross-Section

Abstract

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.