Estimation of Non-Gaussian Returns: The Hedge Funds Case

Purpose – The purpose of this chapter is to estimate non-Gaussian distributions by means of Johnson distributions. An empirical illustration on hedge fund returns is detailed. Methodology/approach – To fit non-Gaussian distributions, the chapter introduces the family of Johnson distributions and its general extensions. We use both parametric and non-parametric approaches. In a first step, we analyze the serial correlation of our sample of hedge fund returns and unsmooth the series to correct the correlations. Then, we estimate the distribution by the standard Johnson system of laws. Finally, we search for a more general distribution of Johnson type, using a non-parametric approach. Findings – We use data from the indexes Credit Suisse/Tremont Hedge Fund (CSFB/Tremont) provided by Credit Suisse. For the parametric approach, we find that the SU Johnson distribution is the most appropriate, except for the Managed Futures. For the non-parametric approach, we determine the best polynomial approximation of the function characterizing the transformation from the initial Gaussian law to the generalized Johnson distribution. Originality/value of chapter – These findings are novel since we use an extension of the Johnson distributions to better fit non-Gaussian distributions, in particular in the case of hedge fund returns. We illustrate the power of this methodology that can be further developed in the multidimensional case.