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

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