Polynomial Goal Programming and the Implicit Higher Moment Preferences of U.S. Institutional Investors in Hedge Funds

Abstract

Polynomial goal programming (PGP) has been successfully introduced in the hedge fund allocation literature. The method is intuitive, and flexible enough to incorporate investor preferences in higher moments of the return distribution. However, until now, PGP could not be used to its full effectiveness because it requires quantification of real preference parameters toward those moments. Previously, those parameters were chosen without elaborate research. Our goal in this paper is to identify implied sets of preference parameters by using investors' choice of and the importance they attribute to risk and performance measures. We use three groups of institutional investors, pension funds, insurance companies, and endowments, and we derive implied sets of preference parameters in the context of a hedge fund portfolio optimization. To extract implied investor preference parameters, we determine optimal hedge fund portfolios according to the criteria set by those fund of hedge fund sponsors. We then fit implied preference parameters so that the PGP optimal portfolio is identical to the desired hedge fund portfolio. We can thus determine real preferences for the higher moments of the portfolio return distribution. With the obtained economically justified sets of preference parameters, we can use the well established PGP framework more efficiently to derive allocations that satisfy institutional investor expectations for hedge fund investments. Furthermore, the implied preference parameters enable fund of hedge fund managers and other managers to combine different hedge fund strategies optimally according to investor expectations. Finally, we can assess the importance of individual moments, as well as their marginal rates of substitution.