The most common approach for controlling currency risk in an international portfolio uses mean–variance optimization to find a hedge ratio that maximizes the portfolio's risk-adjusted return. To calculate the optimal hedge ratio, an investor needs estimates of expected returns, variances, and covariances. These parameter estimates contain errors, which then become embedded in the optimal hedge ratio. This article examines the size of the estimation error of the optimal hedge ratio for a U.S. investor holding an internationally diversified portfolio. The results indicate that the estimation error is so large that the estimates of the optimal hedge ratio are of little practical use to an investor with moderate or low aversion to risk.