Parameter Uncertainty in Asset Allocation

Abstract

We revisit an investment experiment that compares the performance of an investor using Bayesian methods for determining portfolio weights with an investor that uses the Monte Carlo based resampling approach advocated in Michaud (1998). Markowitz and Usmen (2003) showed that the Michaud investor always won. However, in the original experiment, the Bayes investor was handicapped because the algorithm that was used to evaluate the predictive distribution of the portfolio provided only a rough approximation. We level the playing field by allowing the Bayes investor to use a more standard algorithm. Our results sharply contrast with those of the original experiment. The final part of our paper proposes a new investment experiment that is much more relevant for the average investor - a one-period ahead asset allocation. We examine in detail why this is the best comparison to make, and why the Bayes investor always wins.

Keywords: Bayesian decision problem, parameter uncertainty, optimal portfolios, utility function maximization, resampling