Correspondence: P. van Rensburg, School of Management Studies, University of Cape Town, Private Bag, Rondebosch 7701, South Africa. Tel: +27 21 6502481; Fax: +27 21 6897570; E-mail: pvanrens@commerce.uct.ac.za

¹Greg Bergh is a director and fund manager with Praesidium Capital Management, a specialist hedge fund firm in South Africa.

²Paul van Rensburg is the Frank Robb Professor of Finance at the University of Cape Town and Principal of Salient Quantitative Asset Management.

Received 22 November 2007; Revised 22 November 2007.

Abstract

Notwithstanding the central limit theorem, the returns of several hedge fund indices are found to exhibit distributional characteristics inconsistent with normality. Using world hedge fund index and asset class data from 1994 to 2004, this study empirically compares the results of the Markowitz mean–variance optimisation technique with a higher moment methodology recently proposed by Davies et al. This comparison is conducted both when constructing fund-of-hedge-fund portfolios and when determining an appropriate weighting to apply when adding hedge funds to the traditional asset classes of equities, bonds and cash. The descriptive statistics show that, in particular, the hedge fund strategies of Fixed Income Arbitrage and Event-driven Opportunities, despite displaying low volatility, exhibit latent higher moment risk in the form of negative skewness and high kurtosis. These two higher moments collectively suggest an increase in the probability of extreme adverse returns to the investor that is not revealed in traditional mean–variance analysis. Confirming the findings of Amin and Kat and Lo, Jarque-Bera tests find that only two out of the 14 hedge fund indices used in this study are normal at the 5 per cent level. Applying Markowitz mean–variance portfolio selection to an array of published hedge fund indices produces fund-of-fund portfolios with higher ex post returns but naïve exposure to undesirable higher moment risks. When the higher moments of hedge fund index return distribution are accounted for in the portfolio optimisation algorithm, the resultant portfolios have improved diversification and higher moment statistics. This study confirms the findings of Davies et al. and Feldman et al. that Global Macro and Equity Market Neutral strategies are crucial constituents in a fund-of-hedge-funds portfolio. When constructing multi-asset class portfolios that include an allocation to hedge funds, the results show that mean–variance optimisation significantly over-allocates to the hedge fund class in comparison to when skewness and kurtosis are also taken into account. The higher moment-optimised portfolios all outperform the mean–variance comparatives when evaluated on an Omega function basis.