Skewness in energy returns: Estimation, testing and implications for tail risk

In this paper we estimate the skewness of the unconditional distribution of energy returns and test its statistical significance. We compare the performance of traditional and robust tests for skewness with those based on the implied unconditional skewness in a TGARCH model with Gram-Charlier (TGARCH-GC) innovations. We also analyze the implications of TGARCH-GC skewness for tail risk through evaluation of Value-at-Risk (VaR) and expected shortfall (ES) accuracy. Our results show that crude oil (Brent and WTI) and Gasoline returns are negatively skewed, while we do not find evidence of skewed distribution for other energy returns such as Heating oil, Kerosene and Natural gas. This indicates that the returns of the former are likely to encapsulate more largely the effect of negative shocks and so present higher tail risk than those of the latter. These results differ from traditional and robust tests for skewness providing important information on how to improve mean-variance risk management measures. Indeed, we find that the threemoment VaR and ES measures based on the third-order Cornish Fisher (CF3) expansion for the unconditional distribution of returns considerably improve their corresponding two-moment ones. We adopt CF3 to disentangle skewness effects from kurtosis in tail risk. & COPY; 2023 The Author(s). Published by Elsevier Inc. on behalf of Board of Trustees of the University of Illinois. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

In this study, we estimate the skewness of energy returns and test its statistical significance. Traditional and robust tests for skewness are compared with tests based on the implied skewness in a TGARCH-GC model. The study also examines the impact of skewness on tail risk through the evaluation of VaR and ES accuracy. The results suggest that crude oil and gasoline returns have negative skewness, indicating higher tail risk compared to other energy returns.