This paper investigates the estimation risk in covariance. It is known that covariance can be estimated accurately under the i.i.d. normality assumption. However, time varying volatility and non-normality of asset returns can lead to imprecise covariance estimates, which can incur economic loss to a mean variance investor. Applying the Fama French 3 factor model to 25 size, BE/ME sorted portfolios from 1963 to 2001, the loss from the covariance estimation error is 1.45% per annum, which is as large as the estimation risk in the expected return.