Tbis paper investigates the sensitivity of meanvariance(MV)-efficientportfolios to changes in the means of individual assets. When only a budget constraint is imposed on the investment problem, the analytical results indicate that an MV-efficient portfolio's weights, mean, and variance can be extremely sensitive to cbanges in asset means. When nonnegativity constraints are also imposed on the problem, the computational results confirm that a positively weigbted MV-efficient portfolio's weigbts are extremely sensitive to cbanges in asset means, but the portfolio's returns are not. A surprisingly small increase in the mean of Just one asset drives balf the securities from the portfolio. Yet the portfolio's expected return and standard deviation are virtually uncbanged. This paper supersedes Should Investors Hold Well-Diversified Portfolios? Financial support from the Natural Science and Engineering Research Council of Canada is gratefully acknowledged. We also acknowledge the most capable assistance of Ruth Cornale, Simon Ng, Jean-Marc Potier, and Frederick Shen. The paper was presented at Simon Fraser University and the Western Finance Association meetings in San Diego. We thank the participants, especially Stephen Brown, John Herzog, John Heaney, Ray Koopman, and Bruce Lehmann, and the editors, Jon Ingersoll and Chester Spatt, for