This paper empirically investigates the importance of asymmetric conditional covariance when computing the risk premium of international assets. Conditional second moment asymmetry of equity indices is significant and varies over time. The risk premia estimated allowing for asymmetry are statistically and economically different from risk premia estimated without allowing for asymmetry. In particular, an international investor who ignores covariance asymmetry overestimates required returns for equities of the G4 countries and for the world market, on average.