Forest Through the Trees: Building Cross-Sections of Stock Returns
79 Pages Posted: 19 Dec 2019 Last revised: 28 Sep 2020
Date Written: September 25, 2020
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.
Keywords: Asset Pricing, Sorting, Portfolios, Cross-Section of Expected Returns, Decision Trees, Elastic Net, Stock Characteristics, Machine Learning
JEL Classification: G11, G12, C55, C58
Suggested Citation: Suggested Citation