Sensitivity to Estimation Errors in Mean-variance Models

In order to give a complex and accurate description about the sensitivity of efficient portfolios to changes in asset's expected returns, variances and covariances, the joint effect of estimation errors in means, variances and covariances on the efficient portfolio's weights is investigated in this paper. It is proved that the efficient portfolio's composition is a Lipschitz continuous, differentiable mapping of these parameters under suitable conditions. The change rate of the efficient portfolio's weights with respect to variations about risk-return estimations is derived by estimating the Lipschitz constant. Our general quantitative results show that the efficient portfolio's weights are normally not so sensitive to estimation errors about means and variances. Moreover, we point out those extreme cases which might cause stability problems and how to avoid them in practice. Preliminary numerical results are also provided as an illustration to our theoretical results.