Multi-stock portfolio optimization under prospect theory

We study how a behavioral agent allocates her portfolio. We consider a cumulative prospect theory investor in a single period setting with one riskless bond and multiple risky stocks, which follow a multivariate elliptical distribution. Our main result is a two-fund separation between the riskless bond and a mean–variance-portfolio, up to an exogenous benchmark portfolio. The mean–variance-portfolio, which we derive explicitly, is the same for all agents. Individual risk preferences are mirrored only in the participation in this portfolio. This dependence is illustrated by considering empirical returns. Furthermore we solve ill-posed optimization problems by imposing a regulatory risk constraint. Finally we address specific parameterizations of the value function by studying power, linear, and exponential utility.