Estimation and selection bias in mean-variance portfolio selection

Much research has focused on the problem of selecting portfolios without the benefit of parametric measures of risk and return. In this paper, a Monte Carlo technique is used to isolate the extent and nature of the problems introduced by this practice. The technique is employed in the context of classical statistical methodology without permitting short sales. It is shown that using estimators of expected return and risk not only obscures parametric values, but also affects portfolio composition in the Markowitz framework. In this study, these two components of bias are isolated and measured.