Empirically, the covariance between stock returns varies with their volatility. We seek a robust theoretical explanation of this. With minimal assumptions, we model stochastic properties of equilibrium returns which result from the interaction between inter-temporal traders and noisy, price-sensitive short-term traders. The inter-temporal traders can have arbitrary investment rules, preferences and information. In all cases we find a set of restrictions between second moments of equilibrium returns. With two assets there is also a bound on the correlation between asset returns. Estimation with second moments of global stock returns supports our theoretical framework. Higher volatility in at least one market can increase comovement among markets. With globalization, covariances between two stock markets can also affect covariances between two other stock markets. We also find that the changes in trader behavior between normal and crisis periods lead to changes in the moment restrictions between asset returns.