The empirical objective of this study is to account for the time-variation in the covariances between stock markets, and to assess the extent of capital market integration. Using data on sixteen national stock markets, we estimate a multivariate factor model in which the volatility of returns is induced by changing volatility in the factors. Unanticipated returns are assumed to depend both on innovations in "observable" economic variables and on "unobservable" factors. The risk premium on an asset is a linear combination of the risk premia associated with factors. We find that idiosyncratic risk is significantly priced, and that the "price of risk" is not common across countries. This either can be interpreted as evidence against the null of integrated capital markets or could reflect the failure of some other maintained assumptions. Another empirical finding is that only a small proportion of the covariances between national stock markets and their time-variation can be accounted for by "observable" economic variables. Changes in correlations between markets are driven primarily by movements in "unobservable" variables.