Deep Learning in Characteristics-Sorted Factor Models

To study the characteristics-sorted factor model in asset pricing, we develop a bottom-up approach with state-of-the-art deep learning optimization. With an economic objective to minimize pricing errors, we train a non-reduced-form neural network using firm characteristics [inputs], and generate factors [intermediate features], to fit security returns [outputs]. Sorting securities on firm characteristics provides a nonlinear activation to create long-short portfolio weights, as a hidden layer, from lag characteristics to realized returns. Our model offers an alternative perspective for dimension reduction on firm characteristics [inputs], rather than factors [intermediate features], and allows for both nonlinearity and interactions on inputs. Our empirical findings are twofold. We find robust statistical and economic evidence in evaluating various portfolios and individual stock returns. Finally, we show highly significant results in factor investing, improvement in dissecting anomalies, as well as the volatility exposures in deep characteristics