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In the context of a three-moment Intertemporal Capital Asset Pricing Model specification,we characterize conditional co-skewness between stock and bond excess returns using a bivariate regime-switching model.We find that both conditional U.S.stock co-skewness (the relation between stock return and bond volatility) and bond co-skewness (the relation between bond return and stock volatility) command statistically and economically significant negative ex ante risk premiums.The impacts of stock and bond co-skewness on the conditional stock and bond premium are quite robust to various model specifications and various sample periods.They also hold in another country (U.K.).Portfolio implications of these findings are discussed.