Deep Learning Factor Alpha

Abstract

Does a factor model exist to absorb all existing anomalies? We provide a deep learning automated solution to generate long-short factors using a high-dimensional firm characteristic. Sorting securities on firm characteristics is a common practice in finance and a nonlinear activation function built into deep learning. Our algorithm performs a nonlinear search and finds the optimal transformation of characteristics used for security sorting, with one asset pricing objective: minimizing alphas. Our deep factors, hidden neurons in the neural network, are trained greedily with the backward propagation feedback from the loss function that considers both time series and cross-sectional variations. Our conditional forecast generalizes a benchmark, such as CAPM, and includes Fama-French type models as special cases. We have designed a train-validation-test study for monthly U.S. equity returns from 1975 to 2017 and 57 published firm characteristics. In an out-of-sample evaluation, the conditional deep factor model shows a forecasting improvement over the benchmark with factors that offer significant alphas. The conclusion is the improvement of insignificant alphas for some anomalies as well as sorted portfolios.

Keywords: Characteristic-based Anomalies, Cross-Sectional Returns, Deep Learning, Long- Short Factors, Security Sorting, Mispricing Alpha, Neural Network