Hedging shipping freight rates using conditional Value-at-Risk and Buffered Probability of Exceedance

Abstract

This paper investigates the performance of the minimum Conditional Value-at-Risk (CVaR) hedging technique in the dry bulk shipping freight market, where extreme volatility and asymmetric return distributions often limit the effectiveness of traditional minimum variance approaches. The CVaR-based framework is used to minimize the downside tail risk in both static and dynamic hedging settings using a dataset of Forward Freight Agreements (FFAs) for Capesize, Panamax and Supramax vessels over the period of January 2007 to December 2022. Our results suggest that the effectiveness of alternative hedging strategies is sensitive to the distributional shape of the underlying returns, underscoring the suitability of CVaR-based strategies under heavy-tailed and skewed returns. Furthermore, we introduce a probabilistic optimization framework that minimizes the Buffered Probability of Exceedance (bPOE), subject to a pre-specified CVaR constraint. This dual-risk formulation yields an efficient frontier, i.e., a set of optimal solutions between risk and return, that quantifies the trade-off between the likelihood and magnitude of extreme losses, ultimately enhancing hedging performance and offering insights into tail risk management.