Hedge Fund Replication Beyond Alphas and Betas

Abstract

The concept of the gamma of a financed return as the highest level of stress that a return distribution can withstand is introduced. The various stress levels passed describe convex cones of acceptable cash flows that start with positive expectation and finish with arbitrage at infinity. Stress is measured by positive expectation under a concave distortion. Four distortions are employed. It is shown that the skewness, peakedness and tailweightedness of the centered and scaled random variable accessed by investment significantly affects the Sharpe ratio required to enter a target cone of acceptability. Results are illustrated on data for hedge fund returns and we raise the question of whether the gamma or acceptability levels of hedge fund returns can be replicated by portfolios seeking to access just the alphas and betas.

Keywords: Concave Distortions, Acceptable Cash Flows, Skewness and Kurtosis

JEL Classification: G10, G12, G13