Confident Risk Premia: Economics and Econometrics of Machine Learning Uncertainties

Abstract

This paper derives ex-ante standard errors of risk premium predictions from neural networks (NNs). Considering standard errors, I provide improved investment strategies and ex-post out-of-sample (OOS) statistical inferences relative to existing literature. The equal-weighted (value-weighted) confident high-low strategy that takes long-short positions exclusively on stocks that have precise risk premia earns an OOS average monthly return of 3.61% (2.21%). In contrast, the conventional high-low portfolio yields 2.52% (1.48%). Existing OOS inferences do not account for ex-ante estimation uncertainty and thus are not adequate to statistically compare the OOS returns, Sharpe ratios and mean squared errors of competing trading strategies and return prediction models (e.g., linear, NN, and random forest). I develop a bootstrap procedure that delivers robust OOS inferences. The bootstrap tests reveal that large OOS return and Sharpe ratio differences between NN and benchmark linear models' traditional high-low portfolios are statistically insignificant. However, the NN-based confident high-low portfolios significantly outperform all competing strategies. Economically, standard errors reflect time-varying market uncertainty and spike after financial shocks. In the cross-section, the level and precision of risk premia are correlated, thus NN-based investments deliver more gains in the long positions.

Keywords: Machine Learning, Neural Networks, Standard Errors, Risk Premium, Novel Investment Strategies, Robust Out-of-Sample Inferences, Average Return Comparisons, Sharpe Ratio Comparisons, Machine Learning Uncertainties

JEL Classification: G10, G11, G12, C53, C58