  This paper presents an augmented deep factor model that generates latent
factors for cross-sectional asset pricing. The conventional security sorting on
firm characteristics for constructing long-short factor portfolio weights is
nonlinear modeling, while factors are treated as inputs in linear models. We
provide a structural deep learning framework to generalize the complete
mechanism for fitting cross-sectional returns by firm characteristics through
generating risk factors -- hidden layers. Our model has an economic-guided
objective function that minimizes aggregated realized pricing errors. Empirical
results on high-dimensional characteristics demonstrate robust asset pricing
performance and strong investment improvements by identifying important raw
characteristic sources.
