Forward and Spot Exchange Rates in a Multi-currency World

Separate literatures study violations of uncovered interest parity 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 anomalies, to test whether they are empirically distinct, and to estimate the joint restrictions they place on models of currency returns. We find that the forward premium puzzle (FPP) and the "dollar trade" anomaly are intimately linked. Both anomalies are almost exclusively driven by the cross-time component. By contrast, the "carry trade" anomaly is driven largely by the cross-currency component. The simplest model that the data do not reject features a highly persistent asymmetry that makes some currencies pay higher expected returns than others, and a more elastic expected return on the US dollar than on other currencies. In addition, we never reject the hypothesis that currencies with high interest rates are expected to depreciate rather than appreciate, so that none of our estimates require a systematic association between currency risk premia and predictable movements in exchange rates