Empirical moments of asset prices and exchange rates imply that pricing kernels are almost perfectly correlated across countries. Otherwise, observed real exchange rates would be too smooth for high Sharpe ratios. However, the cross-country correlation among macro fundamentals is weak. We reconcile these facts in a two-country stochastic growth model with heterogeneous households and a home bias in consumption. In our model, only a small fraction of households trade domestic and foreign equities. We show that this mechanism can quantitatively account for the smoothness of exchange rates in the presence of volatile pricing kernels and weakly correlated macro fundamentals.