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...

This paper investigates whether multivariate crash risk (MCRASH), defined as exposure to extreme realizations of multiple systematic factors, is priced in the cross-section of expected stock returns. We derive an extended linear model with a positive premium for MCRASH and we empirically confirm...

Foster and Hart propose a measure of riskiness for discrete random variables. Their defining equation has no solution for many common continuous distributions. We show how to extend consistently the definition of riskiness to continuous random variables. For many continuous random variables, the...

This paper investigates whether multivariate crash risk is priced in the cross- section of expected stock returns. Motivated by a theoretical asset pricing model, we capture the multivariate crash risk of a stock by a combined measure based on its expected shortfall and its multivariate lower...

Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions. We show how to extend consistently the definition of riskiness to continuous random variables. For many...