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

Abstract

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, measured by volatility alone, with the skewness and the kurtosis of the distribution of returns. The modified value-at-risk allows us to measure the risk of a portfolio with non-normally distributed assets like hedge funds or technology stocks and to solve for optimal portfolio by minimizing the modified value-at-risk at a given confidence level.