International portfolio diversification has long been advocated as a way of enhancing average returns while reducing portfolio risk for the investor who considers diversifying into foreign securities. This proposition, however, relies on the assumption that the required inputs to the classical mean-variance analysis are known with certainty. Typically, expected returns, variances, and covariances are simply replaced by their ex post sample values and the optimal portfolio is derived without mentioning the uncertainty inherent in these parameter values. But the rational investor should take this uncertainty into account when forming expectations, and probably will consider estimators that are less subject to estimation error than the classical sample mean. This paper investigates alternative estimators of expected returns and their implications for the alleged gains from diversification. An important observation is the crucial influence that errors in estimating expected returns have on portfolio analysis. A closer examiPrevious studies of international portfolio diversification have relied on ex post meanvariance analysis without considering the problem of estimation risk. Typically, past averages are substituted for expected returns and no allowance is made for the uncertainty inherent in these parameter values. First I demonstrate the shortcomings of such an approach, and second I investigate another method of estimating expected returns initially proposed by Stein. By shrinking the sample averages toward a common mean, I find that the out-of-sample performance of the optimal portfolio is substantially increased. One of the implications of this method is that the classical conclusions vastly overestimate the possible gains in average returns; instead, benefits from diversification are more likely to accrue from a reduction in risk. * This paper draws on part of my dissertation at the University of Chicago. I am grateful to Arnold Zellner, Michael Mussa, George Constantinides, and especially John Bilson, for useful discussions and comments. Numerous improvements were also suggested by the referee. This research received the generous financial support of the College Interuniversitaire d'Etudes Doctorales dans les Sciences du Management.