Standard macro models cannot explain why real exchange rates are volatile and disconnected from macro aggregates. Recent research argues that models with persistent growth rate shocks and recursive preferences can solve that puzzle. I show that this result is highly sensitive to the structure of financial markets. When just a bond is traded internationally, then long-run risk generates insufficient exchange rate volatility. A long-run risk model with recursive-preferences can generate realistic exchange rate volatility, if all agents efficiently share their consumption risk by trading in complete financial markets; however, this entails massive international wealth transfers, and excessive swings in net foreign asset positions. By contrast, a long-run risk, recursivepreferences model in which only a fraction of households trades in complete markets, while the remaining households lead hand-to-mouth lives, can generate realistic exchange rate and external balance volatility.