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This paper investigates the international asset allocation effects of time-variations in higher-order moments of stock returns such as skewness and kurtosis. In the context of a four-moment International Capital Asset Pricing Model (ICAPM) specification that relates stock returns in five regions to returns on a global market portfolio and allows for time-varying prices of covariance, co-skewness, and co-kurtosis risk, we find evidence of distinct bull and bear regimes. Ignoring such regimes, an unhedged US investor's optimal portfolio is strongly diversified internationally. The presence of regimes in the return distribution leads to a substantial increase in the investor's optimal holdings of US stocks, as does the introduction of skewness and kurtosis preferences.