Contrary to the classic framework of passive strategies, if investors exploit return predictability through active strategies then there is a tension between the mean-variance frontiers that drive empirical work and the mean-variance preferences that are used in finance theory. We show that standard preferences choose portfolios on a frontier that has not been studied in the literature, develop new betas and Sharpe ratios to construct portfolio efficiency tests, and highlight some concerns with current empirical work. An empirical application to active strategies on stock portfolios sorted by size and book-to-market confirms the relevance of our theoretical results.