Risk Sensitive Dynamic Asset Allocation

This paper develops a continuous time portfolio optimization model where the mean returns of individual securities or asset categories are explicitly affected by underlying economic factors such as dividend yields, a firm's ROE, interest rates, and unemployment rates. The factors are Gaussian processes, and the drift coefficients for the securities are aEne hnctions of these factors. We employ methods of risk sensitive control theory, thereby using an infinite horizon objective that is natural and features the long run growth rate, the asymptotic variance, and a single risk aversion parameter. Even with constraints on the admissible trading strategies, it is shown that the optimal trading strategy has a simple characterization in terms of the factor levels. For particular factor levels, the optimal trading positions can be obtained by solving a quadratic program. The optimal objective value, as a hnction of the risk aversion parameter, is shown to be the solution of a partial differential equation. A simple asset allocation example, featuring a Vasicek-type interest rate which affects a stock index and also serves as a second investment opportunity, illustrates how factors which are commonly used for forecasting returns can be explicitly incorporated in a portfolio optimization model.