Deep Learning of Conditional Volatility and Negative Risk-Return Relation

Abstract

We originally use deep learning and likelihood-based estimation to forecast conditional volatility, demonstrating substantial economic benefits. The predicted conditional volatility and expected return can form double-sorted long-short portfolios. They achieve out-of-sample Sharpe ratios of approximately 3.0 under equal weights and 1.5 under value weights, which are 1.0 and 0.4 higher, respectively, than those from single sorting with predicted expected return alone. Additionally, we find significant and persistent negative risk-return relation in cross-sections, which remains persistent even when various alternative volatility measures are used. The negative risk-return relation helps explain the superior performance of the aforementioned portfolios.

Keywords: Conditional Volatility Prediction, Deep Learning, Double Sorting, Long-Short Portfolios, Risk-Return Relationship

JEL Classification: G12, G17