  Deep learning searches for nonlinear factors for predicting asset returns.
Predictability is achieved via multiple layers of composite factors as opposed
to additive ones. Viewed in this way, asset pricing studies can be revisited
using multi-layer deep learners, such as rectified linear units (ReLU) or
long-short-term-memory (LSTM) for time-series effects. State-of-the-art
algorithms including stochastic gradient descent (SGD), TensorFlow and dropout
design provide imple- mentation and efficient factor exploration. To illustrate
our methodology, we revisit the equity market risk premium dataset of Welch and
Goyal (2008). We find the existence of nonlinear factors which explain
predictability of returns, in particular at the extremes of the characteristic
space. Finally, we conclude with directions for future research.
