Optimal Policies for Investment with Time-Varying Return Distributions

We develop a model in which investors must learn the distribution of asset returns over time. The process of learning is made more difficult by the fact that the distributions are not constant through time. We consider risk-neutral investors who have quadratic utility and are selecting between two risky assets. We determine the time at which it is optimal to update the distribution estimate and hence, alter portfolio weights. Our results deliver an optimal policy for asset allocation, that is, the sequence of time intervals at which it is optimal to switch between assets, based on stochastic optimal control theory. In addition, we determine the time intervals in which asset switching leads to a loss with high probability. We provide estimates of the effectiveness of the optimal policy.