Optimal Portfolio Choice Under Incomplete Information

Abstract

Models of asset pricing generally assume that the variables which characterize the state of the economy are observable. However, the distributional properties of asset prices that are relevant for portfolio decisions are in general not observable, and therefore must be estimated. The estimation of expected returns is a particularly difficult problem and estimation errors are likely to be substantial. In this light, it is reasonable to examine whether the assumption of observability of expected returns and other relevant state variables causes significant mis‐specification in equilibrium models of asset prices. This paper has three main objectives: first, to derive optimal estimators for the unobservable expected instantaneous returns using observations of past realized returns; second, to establish that estimation and portfolio choice can be solved in two separate steps; third, to analyze the impact of estimation error on investment choices. The estimators of expected returns are in general not consistent, i.e., the estimation error does not tend to disappear asymptotically. The effects of the estimation error, therefore, cannot be ignored even if realized returns are observed continuously over an infinite time period.