This article investigates the estimation risk in covariance. Although previous research has shown that the covariance can be estimated accurately by assuming independently and identically distributed normal returns, time-varying volatility and non-normality can lead to imprecise covariance estimates, which can cause economic loss to a mean variance investor. Applying the Fama-French three-factor model to 25 portfolios sorted by size and book-to-market ratio from 1963 to 2008, we find that the estimation risk in covariance is as large as two-thirds of that in the expected return.