Portfolio choice and estimation risk - A comparison of Bayesian approaches to resampled efficiency

Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios,which is one of the primary reasons to make standard Markowitz optimization unfeasible inpractice. Several approaches to incorporate estimation risk into portfolio selection are suggestedin the earlier literature. These papers regularly discuss heuristic approaches (e.g., placingrestrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class ofestimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985,1986), which is probably the most popular estimator. We will show that optimal portfolios basedon the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficientfrontier with a higher risk aversion. We quantify this increase in risk aversion.Furthermore, we review a relatively new approach introduced by Michaud (1998), resamplingefficiency. Michaud argues that the limitations of MV efficiency in practice generally derivefrom a lack of statistical understanding of MV optimization. He advocates a statistical view ofMV optimization that leads to new procedures that can reduce estimation risk. Resamplingefficiency has been contrasted to standard Markowitz portfolios until now, but not to otherapproaches which explicitly incorporate estimation risk. This paper attempts to fill this gap.Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are comparedin an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochasticdominance.