The authors model trading by foreign and domestic investors in developed-country equity markets. The key assumptions are that (i) both the foreign and domestic investor populations contain investors of different sophistication, and (ii) investor sophistication matters for performance in both public equity and private off-market investments. A quantitative model with these assumptions delivers a unified explanation for three stylized facts about U.S. investors' international equity trades that have been documented in the literature: (i) trading by U.S. investors occurs in bursts of simultaneous buying and selling, (ii) Americans build and unwind foreign equity positions gradually, and (iii) U.S. investors increase their market share in a country when stock prices in that country have recently been rising.