Portfolio Choice under Parameter Uncertainty: Bayesian Analysis and Robust Optimization Comparison

Parameter uncertainty has been a recurrent subject treated in the financial literature. The normative portfolio selection approach considers two main kinds of decision rules: expected expected utility maximization and mean-variance criterion. Assuming that the mean-variance criterion is a good approximation to the expected utility maximization paradigm, a major factor of concern is parameter uncertainty which, when it is not taken into account, can lead to meaningless portfolios. A statistical approach, based on a Bayesian analysis, can be applied to parameter uncertainty. This can be compared with a robust optimization approach where it is assumed that the value of the unknown parameters can change within a given region. Comparisons over these two approaches are performed in this paper. We consider two measures to quantify the effects of the estimation risk, one of the measures is new and extends an existing one. The results allows us to distinguish the approaches and select the one that implies lower mean losses.