Deep Learning in Characteristics-Sorted Factor Models

Abstract

To study the characteristics-sorted factor model in empirical asset pricing, we design a non-reduced-form feedforward neural network with the non-arbitrage objective to minimize pricing errors. Our model starts from firm characteristics [inputs], generates risk factors [intermediate features], and fits the cross-sectional returns [outputs]. A nonlinear activation in deep learning approximates the traditional security sorting on characteristics to create long-short portfolio weights, like a hidden layer, from lag characteristics to realized returns. Our model offers an alternative approach for dimension reduction in empirical asset pricing on characteristics [inputs], rather than factors [intermediate features], and allows for both nonlinearity and interactions directly through [inputs]. Our empirical findings are threefold. First, we find substantial and robust asset pricing improvements of multiple performance measures, such as Cross-Sectional R^2, in both in-sample and out-of-sample analysis. Second, the deep learning augmented models produce all positive improvements regarding return prediction over the benchmark factor models. Finally, we show significant increases in factor investing, nonlinear relationships in deep characteristics, and their importance on raw characteristics.

Keywords: Alpha, Characteristics-Sorted Factor Models, Cross-Sectional Returns, Deep Learning, Firm Characteristics, Non-Arbitrage, Pricing Errors.

JEL Classification: C1, G1