We demonstrate that the mean–variance optimal portfolio does not outperform (out of sample) the naive 1/N diversification strategy even if securities are grouped into indexes or broad asset classes. This finding is due to insufficient data on past returns, which limit investors' ability to accurately estimate the means and covariance structure of securities. The resulting high estimation errors eliminate the benefits of using the means and covariance matrix as compared to the naive strategy in portfolio optimization. Using value-weighted indexes, characteristic-sorted portfolios, or portfolios defined by principal components as underlying assets in mean–variance optimization does not help. At the same time, increasing data frequency or adding data on past earnings may in some cases make mean–variance optimization useful.