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.