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



Publishing details

Social Sciences Research Network

Authors / Editors

Bryzgalova S; Pelger M; Zhu J


Publication Year



We show how to build a cross-section of asset returns, that is, a small set of basis or test assets that capture complex information contained in a given set of stock characteristics and span the Stochastic Discount Factor (SDF). We use decision trees to generalize the concept of conventional sorting and introduce a new approach to the robust recovery of the SDF, which endogenously yields optimal portfolio splits. These low-dimensional value-weighted long-only investment strategies are well diversified, easily interpretable, and reflect many characteristics at the same time. Empirically, we show that traditionally used cross-sections of portfolios and their combinations, especially deciles and long-short anomaly factors, present too low a hurdle for model evaluation and serve as the wrong building blocks for the SDF. Constructed from the same pricing signals as conventional double or triple sorts, our cross-sections have significantly higher (up to a factor of three) out-of-sample Sharpe ratios and pricing errors relative to the leading reduced-form asset pricing models.


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


Social Sciences Research Network