Optimal Investment in Alternative Portfolio Strategies Preliminary and Incomplete

What percentage of their portfolio should investors allocate to alternative investment vehicles? The only available answers to the above question are set in a static meanvariance framework, with no explicit accounting for uncertainty on the active manager’s ability to generate abnormal return. In this paper we consider the problem of an investor who can choose between the riskfree security and two risky securities: a passive fund that tracks the market and a hedge fund. The hedge fund might o¤er a positive abnormal expected return or alpha (excess risk-adjusted expected return). The investor has power utility and is uncertain about both the expected return of the index and the alpha of the hedge fund, but upgrades beliefs in a Bayesian way. We derive analytic expressions for the optimal investment policy of the investor and calibrate our model to a database of hedge funds. Our results have important implications for investors who consider including alternative investment vehicles in their portfolios. In particular, they suggest that low beta hedge funds may serve as natural substitutes for a signi...cant portion of an investor risk-free asset holdings. ¤Jaksa Cvitanic ([email protected]) is with the Departments of Economics and Mathematics at the University of Southern California. Ali Lazrak ([email protected]) is with the Département de Mathématiques, Université d’Evry Val d’Essonne, and is currently visiting the Finance Department at the University of British Columbia. Lionel Martellini ([email protected]) and Fernando Zapatero ([email protected]) are with the Marshall School of Business at the University of Southern California.