In this paper, we test a partially segmented ICAPM for two developed markets, two emerging markets and World market, using an asymmetric extension of the multivariate GARCH process of De Santis and Gerard (1997,1998). We find that this asymmetric process provides a significantly better fit of the data than a standard symmetric process. The evidence obtained from the whole period and sub-periods analysis supports the financial integration hypothesis and suggests that domestic risk is not a priced factor.