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We decompose violations of uncovered interest parity into a cross-currency, a between-time-and-currency, and a cross-time component. We show that most of the systematic violations are in the cross-currency dimension. By contrast, we find no statistically reliable evidence that currency risk premia respond to deviations of forward premia from their time- and currency-specific mean. These results imply that the forward premium puzzle (FPP) and the carry-trade anomaly are separate phenomena that may require separate explanations. The carry trade is driven by static differences in interest rates across currencies, whereas the FPP appears to be driven primarily by cross-time variation in all currency risk premia against the US dollar. Models that feature two symmetric countries thus cannot explain either of the two phenomena. Once we make the appropriate econometric adjustments we also cannot reject the hypothesis that the elasticity of risk premia with respect to forward premia in all three dimensions is smaller than one. As a result, currency risk premia need not be correlated with expected changes in exchange rates.
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Separate literatures study violations of uncovered interest parity (UIP) using regression-based and portfolio-based methods. We propose a decomposition of these violations into a cross-currency, a between-time-and-currency, and a cross-time component that allows us to analytically relate regression-based and portfolio-based facts, and to estimate the joint restrictions they place on models of currency returns. Subject to standard assumptions on investors' information sets, we find that the forward premium puzzle (FPP) and the "dollar trade" anomaly are intimately linked: both are driven almost exclusively by the cross-time component. By contrast, the "carry trade" anomaly is driven largely by cross-sectional violations of UIP. The simplest model the data do not reject features a cross-sectional asymmetry that makes some currencies pay permanently higher expected returns than others, and larger time series variation in expected returns on the US dollar than on other currencies. Importantly, conventional estimates of the FPP are not directly informative about expected returns, because they do not correct for uncertainty about future mean interest rates. Once we correct for this uncertainty, we never reject the null that investors expect high-interest-rate currencies to depreciate, not appreciate.
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