The widely used mean-variance approach to decisions under uncertainty requires estimates df the parameters of the j?int distribution of returns. When optimal behavior is determined using estimates, rather than the true values, the decision is a random variable. We examine the usefulness of mean-variance analysis by deriving the bias and variance-covariance matrix for the decision.vector. The latter shows that decisions based on estimated parameters can have a large variance around the true optimum. The results show that optimal decisions can differ substantially from those based on mean-variance analysis.