We propose a tractable small-open-economy model in which uncovered interest parity premia on foreign exchange (FX) markets arise from the endogenous lack of insurability of exchange rate risks. Asymmetric information about monetary policy can make the tails of the exchange rate distribution uninsurable in FX hedging markets, which in turn generates premia in FX spot markets because of the risk aversion of lenders holding the external debt. There is a role for government intervention because of an information sensitivity externality: agents do not internalize that their actions can reduce the insurability of exchange rates. The model predicts that premia may be amplified by weaknesses in monetary, fiscal, and financial policy frameworks, and can be reduced through reforms which reduce the sensitivity of exchange rates to private information. The constrained efficient policy depends on the composition of external lenders and may include delegation of monetary policy to an “aloof central banker”, constraints on fiscal policy, more active use of macroprudential tools, and institutions which limit asymmetric information.