Building a Better Fund of Hedge Funds: A Fractal and Alpha-Stable Distribution Approach

Abstract

Markowitz's (1952) portfolio theory has permeated financial institutions over the past 50 years. Assuming that returns are normally distributed, Markowitz suggests that portfolio optimization should be performed in a mean-variance framework. With the emergence of hedge funds and their non-normally distributed returns, mean-variance portfolio optimization is no longer adequate. Here, hedge fund returns are modeled with the alpha-stable distribution and a mean-CVaR portfolio optimization is performed. Results indicate that by using the alpha-stable distribution, a more efficient fund of hedge funds portfolio can be created than would be by assuming a normal distribution. To further increase efficiency, the Hurst exponent is considered as a filtering tool and it is found that combining hedge fund strategies within a range of Hurst exponents leads to the creation of more efficient portfolios as characterized by higher risk-adjusted ratios. These findings open the door for the further study of econophysics tools in the analysis of hedge fund returns.