Structural Deep Learning in Conditional Asset Pricing

Abstract

We develop a theoretical analysis of deep learning predictions in cross-sectional asset pricing. Our method is guided by economic theory and employs time-varying conditioning information on alphas and betas carried by firm-specific characteristics. We derive formal asymptotic theory for neural network estimators, and show that deep learning regressions of return on characteristics can be decomposed into mispricing (alpha) and risk related components -- thereby opening the ``black box'' of machine learning predictions. The analysis also shows that agnostic plugin estimators (pre-training a network and then plugging in new data) can only recover the sum of the mispricing and risk-related components.

Keywords: factor pricing model, neural network, double descent, alphas, characteristics, risk premium

JEL Classification: G11, G12, C14, C45, C58