Comparison of different estimation techniques for portfolio selection

The main problem in applying the mean-variance portfolio selection consists of the fact that the first two moments of the asset returns are unknown. In practice the optimal portfolio weights have to be estimated. This is usually done by replacing the moments by the classical unbiased sample estimators. We provide a comparison of the exact and the asymptotic distributions of the estimated portfolio weights as well as a sensitivity analysis to shifts in the moments of the asset returns. Furthermore we consider several types of shrinkage estimators for the moments. The corresponding estimators of the portfolio weights are compared with each other and with the portfolio weights based on the sample estimators of the moments. We show how the uncertainty about the portfolio weights can be introduced into the performance measurement of trading strategies. The methodology explains the bad out-of-sample performance of the classical Markowitz procedures.