Why does the neural network with random Fourier features perform so well in asset return prediction?

Abstract

We answer the question by applying Fourier series expansion to the average asset return function. In the single-factor case, the market return explains only sine components of the neural network with random Fourier features (thereafter the model). The piecemeal addition of one factor at a time cannot capture cosine components of the model. In the multi-factor case with covariance between the market return and hedge-asset return, the Fourier series expansion captures both sine and cosine components of the model. Alpha encodes the longer-run historical path-dependence of this covariance risk. We adapt this analysis to further illuminate the equity premium puzzle.

Keywords: macrofinance, asset return prediction, alpha, Fourier series expansion, cross covariance, equity premium puzzle, neural networks, random Fourier features, machine-learning algorithms

JEL Classification: G11, G12