This article examines the link between several well-known asset pricing "anomalies" and the covariance structure of returns. I find size, book-to-market, and momentum strategies exhibit a strong, weak, and negligible relation to covariance risk, respectively. A size factor helps predict future volatility and covariation, improving the efficiency of investment strategies. Moreover, its premium rises following increases in both its volatility and covariation with other assets. These effects are amplified in recessions. No such relations exist for book-to-market or momentum. These findings may shed light on explanations for these premia and present a challenging set of facts for future theory. Copyright 2003, Oxford University Press.