On the Cross-sectional Relation between Expected Returns and Betas

There is an exact linear relation between expected returns and true "betas" when the market portfolio is on the ex ante mean‐variance efficient frontier, but empirical research has found little relation between sample mean returns and estimated betas. A possible explanation is that market portfolio proxies are mean‐variance inefficient. We categorize proxies that produce particular relations between expected returns and true betas. For the special case of a zero relation, a market portfolio proxy must lie inside the efficient frontier, but it may be close to the frontier.