Hedge Fund Allocation with Survival Uncertainty and Investment Constraints

Abstract

In this paper, we propose to study a hedge funds allocation problem. A typical feature of those alternative investments vehicles is their propensity to cease their activity after experiencing a distressing situation. We use an expected utility framework to integrate the hedge funds survival uncertainty and rely on the class of isoelastic functions to model the investor's preferences. The addition of investment constraints complicates the resolution of the optimal allocation problem. It is solved using a genetic algorithm that mimics the mechanism of natural evolution and is specifically designed to handle a set of non-linear investment constraints. We finally apply the genetic algorithm to analyze the impact of the survival uncertainty and of the investments constraints on the optimal allocation and on the certainty equivalent of hedge funds' portfolios. One observes in particular that the optimal portfolio weights are significantly affected when the survival uncertainty is taken into account. An out-of-sample analysis shows that when the survival uncertainty is introduced into an expected utility model, the use of tight investment constraints provides an interesting complement to the due diligence process in the absence of any a priori skills for detecting persistence in the hedge funds' performance.