"Our results are disturbing in that, like Fama and French (1992), they suggest that traditional measures of risk do not determine expected returns. In equilibrium asset pricing models the covariance structure of returns determines expected returns. Yet we find that variables that reliably predict the future covariance structure do not predict future returns. Our results indicate that high book-to-market stocks and stocks with low capitalizations have high average returns whether or not they have the return patterns (i.e., covariances) of other small and high book-to-market stocks. Similarly, after controlling for size and book-to-market ratios, a common share that ‘act like’ a bond (i.e., has a low market beta) has the same expected return as other common shares with high market betas."