Alternative risk measures for alternative investments

This paper deals with portfolio optimization under different risk constraints. We use a set of hedge funds where departure from normality are significant. We optimizethe expected return under standard deviation, semi-variance, VaR and expected shortfall (or CVaR) constraints. As far as the VaR is concerned, we compare different estimators. While the optimization with respect to VaR constraints appears to be difficult and lengthy, very fast optimization algorithms exists for the other risk constraints. We find that the choice of VaR estimator is less discriminant than the choice of riskconstraint. We provide financial interpretations of the optimal portfolios associated with a decomposition of risk measures.