Hedge funds and higher moment portfolio selection

Bergh, Gregory

Hedge funds and higher moment portfolio selection

Thesis / Dissertation

2005

Abstract

Recent studies by Amin and Kat (2001) and Lo (2001) show that, notwithstanding the central limit theorem, the returns of several hedge fund indices exhibit distributional characteristics inconsistent with normality. In this context, this study empirically compares the Markowitz (1952) mean-variance optimisation technique with a higher moment methodology recently proposed by Davies, Kat and Lu (2005). It extends the methodology to optimise portfolios without a unity-variance constraint. In addition, this study augments the application of Davies et al (2005) beyond that of fund of hedge fund portfolio construction to also incorporate the traditional asset classes of equities, bonds and cash. The descriptive statistics show that hedge fund strategies of Fixed Income Arbitrage and EventDriven while displaying low volatility, also exhibit latent higher moment risk in their 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 (2001) and Lo (2002), Jarque-Bera tests find that only two out of the fourteen hedge fund indices used in this study are normal at the 5% level. Applying Markowitz (1952) mean-variance portfolio selection to an array of published hedge fund indices produces portfolios with higher ex-post returns but nai've 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, Kat and Lu (2003) and Feldman, Chen and Goda (2002) that Global Macro and Equity Market-Neutral strategies are crucial constituents in a fund of hedge funds portfolio. When comparing optimised multi-asset class portfolios including an allocation to hedge funds, the results show that mean-variance optimisation overallocates to the hedge fund class on the basis of its high reward to volatility ratio. The higher moment optimised portfolios all outperform the mean-variance comparatives when evaluated on an Omega function basis. More generally, the results suggest that when assembling portfolios that include hedge funds, higher-order optimisation makes a meaningful difference to portfolio composition.

Keywords

Management Studies

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