Building a Better Fund of Hedge FundsA Fractal and α- Stable Distribution Appro

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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 α-stable distribution and a mean-CVaR portfolio optimization is performed. Results indicate that by using the α- 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  haracterized by higher risk-adjusted ratios. These findings open the door for the further study of econophysics tools in the analysis of hedge fund returns.

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