Currency Risk and Pricing Kernel Volatility

Abstract
A basic tenet of lognormal asset pricing models is that a risky currency is associated with low pricing kernel volatility. Empirical evidence indicates that a risky currency is associated with a relatively high interest rate. Taken together, these two statements associate high-interest-rate currencies with low pricing kernel volatility. We document evidence suggesting that the opposite is true, thus contradicting a fundamental empirical restriction of lognormal models. Our identification strategy revolves around using interest rate volatility differentials to make inferences about pricing kernel volatility differentials. In most lognormal models the two are monotonic functions of one another. A risky currency, therefore, is one with relatively low pricing kernel volatility and relatively low interest rate volatility. In the data, however, we see the opposite. High interest rates are associated with high interest rate volatility. This indicates that lognormal models of currency risk are inadequate and that future work should emphasize distributions in which higher moments play an important role. Our results apply to a fairly
broad class of models, including Gaussian affine term structure models and many recent consumption-based models.