Asset allocation and risk management models assume at least short–term stability of the covariance structure of asset returns, but actual covariance and correlation relationships fluctuate dramatically. Moreover, correlations tend to increase in volatile periods, which reduces the power of diversification when it might most be desired. We propose a framework to both explain these phenomena and to predict changes in correlation structure. We model correlations between assets as resulting from the common dependence of returns on a marketwide factor. Through this link, an increase in market volatility increases the relative importance of systematic risk compared with the unsystematic component of returns. The increase in the importance of systematic risk results, in turn, in an increase in asset correlations. We report that a large portion of the variation in correlation structures can be attributed to variation in market volatility. Moreover, market volatility contains enough predictability to construct useful forecasts of covariance.