Optimal allocation to hedge funds: an empirical analysis

Abstract

What percentage of their portfolio should investors allocate to hedge funds? The only available answers to the above question are set in a static mean-variance framework, with no explicit accounting for uncertainty on the active manager's ability to generate abnormal return, and usually generate unreasonably high allocations to hedge funds. In this paper, we apply the model introduced in Cvitanić, Lazrak, Martellini and Zapatero (2002b) for optimal investment strategies in the presence of uncertain abnormal returns to a database of hedge funds. We find that the presence of model risk significantly decreases an investor's optimal allocation to hedge funds. Another finding of this paper is that low beta hedge funds may serve as natural substitutes for a significant portion of an investor risk-free asset holdings. * Jaksa Cvitanic is with the Departments of Mathematics and Economics at the University of Southern California. His research is supported in part by NSF grant DMS-00-99549. Ali Lazrak is with the Finance Department at the University of British Columbia. Lionel Martellini and Fernando Zapatero are with the Marshall School of Business at the University of Southern California. The author for correspondence is Lionel Martellini. He can be reached at University of Southern California, Marshall School of Business, Business and Economics, Hoffman Hall 710, Los Angeles, CA 90089-1427. Phone: (213) 740 5796. Email address: martelli@usc.edu. We would like to express our gratitude to Noël Amenc, Avi Bick, Marc Cassano, Nicole El Karoui, Robert Grauer, Alan Kraus, Gordon Sick as well as seminar participants at Calgary, SFU and UBC for very useful comments and suggestions. All errors are, of course, the authors' sole responsibility.

Dynamic Hedge Fund Portfolio Construction

“…However, the optimal portfolio allocation across individual hedge funds is complicated by the fact that owing to the strategies that hedge fund managers typically adopt, hedge fund returns are far from normally distributed, usually exhibiting very significant negative skewness and excess kurtosis (see, for example, Amin and Kat, 2001;Lo, 2001;Brooks and Kat, 2002;Hsieh, 1997a, 2001;Agarwal and Naik, 2001). Portfolio optimisation in the presence of such nonnormality in hedge fund returns generally leads to very different portfolio allocations than those implied by mean-variance analysis (see, for example, McFall and Lamm, 2003;Fung and Hsieh, 1997b;Cvitanic et al, 2003;Terhaar et al, 2003;Popova et al,. 2003).…”

Hedge funds and higher moment portfolio selection

“…The conventional mean-variance approach above is also criticised by numerous other investigations, including Cvitani'c et al, 1 Agarwal and Naik, 2 Amenc and Martellini 3 and Amin and Kat. 4 These studies observe that mean-variance portfolio optimisation makes the key assumption of normal asset return distributions.…”

“…It is well documented (see Cvitani'c et al, 1 Agarwal and Naik, 2 Amenc and Martellini 3 and Amin and Kat 4 ) that hedge funds are marked by their heterogeneity and unusual statistical properties. This makes the use of conventional methods of portfolio construction subject to question and necessitates the investigation of a more sophisticated approach to inform the construction of appropriate and efficient portfolios.…”

Dynamic Hedge Fund Portfolio Construction: A Semi-Parametric Approach

“…However, the optimal portfolio allocation across individual hedge funds is complicated by the fact that owing to the strategies that hedge fund managers typically adopt, hedge fund returns are far from normally distributed, often exhibiting very significant negative skewness and excess kurtosis (see, for example, Amin & Kat, 2001;Lo, 2001;Brooks & Kat, 2002;Fung & Hsieh, 1997a, 2001Agarwal & Naik, 2004, Hudson et al, 2006Wegener et al, 2010). Portfolio optimization in the presence of such non-normality generally leads to very different portfolio allocations than those implied by mean-variance analysis (see, for example, McFall Lamm, 2003;Fung & Hsieh, 1997b;Cvitanic et al, 2003;Terhaar et al, 2003;Popova et al,. 2003;Glaffig, 2006;Wong et al, 2008).…”