Forest Through the Trees: Building Cross-Sections of Stock Returns

Abstract

We show how to build a cross-section of asset returns, that is, a small set of basis assets that capture complex information contained in a given set of stock characteristics. We use decision trees to generalize the concept of conventional sorting and introduce a new approach to the robust recovery of a low-dimensional set of portfolios that span the stochastic discount factor (SDF). Constructed from the same pricing signals as conventional double- or triple-sorted portfolios, our cross-sections have on average 30% higher Sharpe ratios and pricing errors relative to the leading reduced-form asset pricing models. They include long-only investment strategies that are well diversified, easily interpretable, and that could be built to reflect many characteristics at the same time. Empirically, we show that traditionally used cross-sections of portfolios and their combinations often present too low a hurdle for candidate asset pricing models, as they miss a lot of the underlying information from the original returns.

Keywords: Asset Pricing, Sorting, Portfolios, Cross-Section of Expected Returns, Decision Trees, Elastic Net, Stock Characteristics, Machine Learning

JEL Classification: G11, G12, C55, C58