Tail Risk Hedging and Regime Switching

Abstract

In this paper, we analyze futures-based hedging strategies which minimize tail risk measured by Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR). In par- ticular, we first deduce general characterizations of VaR- and CVaR-minimal hedging policies from results on quantile derivatives. We then derive first-order conditions for tail-risk-minimal hedging in mixture and regime-switching (RS) models. Using cross hedging examples, we show that CVaR-minimal hedging can noticeably deviate from standard minimum-variance hedging if the return data exhibit nonelliptical features. In our examples, we find an increase in hedging amounts if RS models identify a joint crash scenario and we confirm a reduction in tail risk using empirical and EVT-based risk estimators. These results imply that switching from minimum-variance to CVaR- minimal hedging can cut losses during financial crises and reduce capital requirements for institutional investors