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. Our decomposition also reveals a large upward bias in standard quantifications of the FPP. Once we correct for this bias, the puzzle is significantly diminished—to the point that it does not require a systematic association between currency risk premia and expected depreciations. 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.