Is the mean-variance efficient portfolio really that sensitive to estimation errors?

In order to give a complete and accurate description about the sensitivity of efficient portfolios to changes in assets' expected returns, variances and covariances, the simultaneous effect of estimation errors in means, variances and covariances on efficient portfolios' weights is investigated in this paper. It is proved that the efficient portfolios' weights are a Lipschitz continuous mapping of these parameters under suitable conditions. We further derive the change speed of efficient portfolios' weights with respect to variations about risk-return estimates by estimating the Lipschitz constant. The implications of these general results for the authentic sensitivity of the efficient portfolios' weights to estimation errors and the practical application of the MV model are then discussed in detail. Some numerical results are finally provided as a support to our theoretical results.