Time-varying risk is the primary force driving nominal interest rate differentials on currency-denominated bonds. This finding is an immediate implication of the fact that exchange rates are roughly random walks. We show that a general equilibrium monetary model with an endogenous source of risk variation—a variable degree of asset market segmentation—can produce key features of actual interest rates and exchange rates. The endogenous segmentation arises from a fixed cost for agents to exchange money for assets. As inflation varies, the benefit of asset market participation varies, and that changes the fraction of agents participating. These effects lead the risk premium to vary systematically with the level of inflation. Our model produces variation in the risk premium even though the fundamental shocks have constant conditional variances.