Modeling hedge fund leverage via power utility with subsistence

We use a power utility function with subsistence to model leverage. We prove that as the value of the subsistence level grows the allocation in the risky asset increases. The implication of this result is that if a hedge fund uses leverage, or a high water mark, it tends to have a more aggressive investment strategy. In addition, we prove that the total risk of a portfolio held by an investor with preferences described by a power utility with subsistence is a weighted sum of the covariances between the portfolio's return and higher order powers of that return, shifted by the subsistence level.