Mean-Modified Value-at-Risk Optimization with Hedge Funds

Based on the normal Value-at-Risk, we develop a new Value-at-Risk method called Modified Value-at-Risk. This Modified Value-at-Risk has the property to adjust the risk, measuring with the volatility only, with the skewness and the kurtosis of the distribution of returns. The Modified Value-at-Risk allows to measure first the risk of portfolio with assets non normally distributed like hedge funds or technology stocks and to compute optimal portfolio by minimizing the Modified Value-at-Risk at a given confidence level. A revisited version of this paper was published in the Autumn 2002 issue of the Journal of Alternative Investments.