The Omega Measure: Hedge Fund Portfolio Optimization
Traditionally, asset allocation is performed via an optimization problem in the mean-variance framework. Mean-variance analysis assumes that either the investor's utility function is quadratic or the returns are normally distributed. However, it is well known that a quadratic utility function is inconsistent with the behavior of a rational investor. In addition, assets returns may not be normally distributed. This is typically the case for hedge fund returns which distributions usually exhibit negative skewness and excess kurtosis. Alternative methods capturing these statistical properties have been introduced but they still reduce the dimensionality to a few characteristics and do not take into account moments of higher order than skewness and kurtosis. Omega is a new measure that reflects all the statistical properties of a returns distribution. The measure incorporates all the moments of the distribution and requires no assumptions on its shape or on the investor's utility function. As a measure of attractiveness, omega can be used for performance measurement but also for optimal asset allocation. This paper sets first the theoretical foundations for using omega in the investment decision problem. Then, the measure is applied to optimal asset allocation for portfolios containing hedge fund indices. It shows that the portfolios derived in the omega framework can markedly depart from those obtained with other conventional techniques, which emphasizes the importance of including higher moments than skewness and kurtosis in the analysis. It further suggests that omega provides enhanced capabilities for risk diversification and performance enhancement when returns are not normally distributed. Finally, it shows that even if returns are normally distributed, omega still contributes to the analysis by considering investor?s specific perception of gain and loss.