We study an economic agent who has an exogenously determined initial amount of debt. The agent is equipped with a constant relative risk aversion utility function
and a deterministic terminal wealth (before debt interest payments) and faces a debt allocation problem: The choice between
fixed interest rate debt or floating
interest rate debt. The problem is thus related to the seminal Merton (1969,1971)
asset allocation problem. In order to model fixed and floating interest rates we use a simple term structure model based on a Heath-Jarrow-Morton formulation of the Vasicek model.
First, the static case is considered, where no rebalancing of debt is allowed after the initial point in time. Next, the dynamic case is treated where the debt portfolio can be rebalanced continuously at no cost. Numerical examples indicate a surprisingly low increase in welfare, measured by expected utility, in the dynamic case compared to the static case. The optimal debt portfolio in the dynamic case is sensitive to the shape of the initial forward rates and therefore may or may not resemble the static case.