Risk sensitive asset allocation

Abstract

Abstract This paper develops a continuous time modeling approach for making optimal asset allocation decisions. Macroeconomic and financial factors are explicitly modeled as Gaussian stochastic processes which directly affect the mean returns of the assets. We employ methods of risk sensitive control theory, thereby using an infinite horizon objective that is natural and features the long run expected growth rate and the asymptotic variance as two measures of performance, analogous to the mean return and variance, respectively, in the single period Markowitz model. The optimal strategy is a simple function of the factor levels, and, even with constraints on the portfolio proportions, it can be computed by solving a quadratic program. Explicit formulas can be obtained, as is illustrated by an example where the only factor is a Vasicek-type interest rate and where there are two assets: cash and a stock index. The methods are further illustrated by studies of two data sets: U.S. data with two assets and up to three factors, and Australian data with three assets and three factors.