OPTIMAL PORTFOLIO CONSTRUCTION UNDER PARTIAL INFORMATION FOR A BALANCED FUND

Abstract

The model parameters in optimal asset allocation problems are often assumed to be deterministic. This is not a realistic assumption since most parameters are not known exactly and therefore have to be estimated. We consider investment opportunities which are modeled as local geometric Brownian motions whose drift terms may be stochastic and not necessarily measurable. The drift terms of the risky assets are assumed to be affine functions of some arbitrary factors. These factors themselves may be stochastic processes. They are modeled to have a mean-reverting behavior. We consider two types of factors, namely observable and unobservable ones. The closed-form solution of the general problem is derived. The investor is assumed to have either constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA). The optimal asset allocation under partial information is derived by transforming the problem into a full-information problem, where the solution is well known. The analytical result is empirically tested in a real-world application. In our case, we consider the optimal management of a balanced fund mandate. The unobservable risk factors are estimated with a Kalman filter. We compare the results of the partial-information strategy with the corresponding full-information strategy. We find that using a partial-information approach yields much better results in terms of Sharpe ratios than the full-information approach.