When do flexible exchange rates prevent monetary and financial conditions from spilling over across currencies? We examine a model in which international investors strategically supply capital to a small inflation-targeting economy with flexible exchange rates. For some combination of parameters, the unique equilibrium exhibits the observed empirical feature of prolonged episodes of capital inflows and appreciation of the domestic currency, followed by reversals where capital outflows go hand-in-hand with currency depreciation, a rise in domestic interest rates, and inflationary pressure. Arbitrarily small shocks to global financial conditions suffice to trigger these dynamics.