We analyze hedging strategies that minimize tail risk measured by Value-at-Risk (VaR) or Conditional-Value-at-Risk (CVaR). In particular, we derive first-order conditions characterizing VaR- and CVaR-minimal hedging with futures in regime-switching models. Using cross-hedging examples, we theoretically and empirically demonstrate that tail-risk-minimal strategies can noticeably deviate from standard minimum-variance
policies in the presence of crash regimes. In such examples, VaR- and CVaR-minimal strategies based on regime-switching models are able to attain additional tail risk reductions, which can be confirmed by nonparametric and extreme-value-theory-based meth-
ods. These results imply that the proposed methodology for tail risk management can cut losses during financial crises and reduce capital requirements for institutional investors.
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