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Modified Value-at-Risk (VaR) and Expected Shortfall (ES) are recently introduced downside risk estimators based on the Cornish-Fisher expansion for assets such as hedge funds whose returns are non-normally distributed. Modified VaR has been widely implemented as a portfolio selection criterion. We are the first to investigate hedge fund portfolio selection using modified ES as optimality criterion. We show that for the EDHEC hedge fund style indices, the optimal portfolios based on modified ES outperform out-of-sample the EDHEC Fund of Funds index and have better risk characteristics than the equal-weighted and Fund of Funds portfolios.
Boudt et al. (Tue,) studied this question.