This paper considers the role of foreign investors in developed country equity markets. It presents a quantitative model of trading that is built around two new assumptions about investor sophistication: (i) both the foreign and domestic populations contain investors with superior information sets; and (ii) these knowledgeable investors have access to both public equity markets and private investment opportunities. The model delivers a unified explanation for three stylized facts about U.S. investors' international equity trades: (i) trading by U.S. investors occurs in waves of simultaneous buying and selling; (ii) U.S. investors build and unwind foreign equity positions gradually; and (iii) U.S. investors increase their market share in a country when stock prices there have recently been rising. The results suggest that heterogeneity within the foreign investor population is much more important than heterogeneity of investors across countries.