WHEN WILL MEAN-VARIANCE EFFICIENT PORTFOLIOS BE WELL DIVERSIFIED

We characterize the conditions under which efficient portfolios put small weights on individual assets. These conditions bound mean returns with measures of average absolute covariability between assets. The bounds clarify the relationship between linear asset pricing models and well-diversified efficient portfolios. We argue that the extreme weightings in sample efficient portfolios are due to the dominance of a single factor in equity returns. This makes it easy to diversify on subsets to reduce residual risk, while weighting the subsets to reduce factor risk simultaneously. The latter involves taking extreme positions. This behavior seems unlikely to be attributable to sampling error.