In this paper we estimate and test a conditional version of the international CAPM. By using a parsimonious parameterization recently proposed by Ding and Engle (1994), we allow risk premia, betas, and correlations to very through time and test the cross-section restrictions of the model using a relatively large number of assets. One advantage of our test is is that it does not require the market weights to be observed in each period. In support of the international CAPM, we find that world-wide risk is priced whereas country-specific risk is not. Further, we find that the price of world risk is time-varying and has a strong January seasonal. When the price of risk is allowed to vary, a January dummy and the world dividend yield are driven out as independently priced factors. However, contrary to the prediction of the model, differences in risk premia across countries are explained not only by world-wide risk, but also by a constant country-specific factor. The estimated correlations reveal three main facts, cross-country correlations vary through time; they have been affected only to a limited extent by the process of liberalization of the last decade; they tend to increase during severe bear markets in the U.S. However, international correlations are smaller than correlations among U.S. assets. Therefore, investors gain from global diversification, even with contagious bear markets.