What explains house price variation in global cities like London and New York? A widely-held and politically contentious view is that foreign demand is partly responsible especially during crises, but there is little rigorous empirical evidence on the subject given the obstacles confounding identification. We propose a new approach, based on the insight that foreigners exhibit "home bias abroad," concentrating demand in particular areas within global cities. Employing the approach on large databases of housing transactions over the past two decades, we find that foreign risk strongly affects London house prices. The effects are long-lasting but temporary, and are associated with both safe-haven effects and immigration.