Forward and Spot Exchange Rates in a Multi-Currency World*

TLDR

Separate literatures study violations of uncovered interest parity (UIP) using regression‑based and portfolio‑based methods. The study aims to decompose UIP violations into cross‑currency, between‑time‑and‑currency, and cross‑time components to relate regression‑based and portfolio‑based findings and estimate joint restrictions on currency‑return models. The authors analytically decompose violations into these three components. The analysis shows that the forward premium puzzle and dollar‑trade anomaly are driven almost exclusively by cross‑time violations, while the carry trade anomaly stems mainly from cross‑sectional UIP violations; the simplest model consistent with the data features cross‑sectional asymmetry with some currencies earning permanently higher expected returns and greater time‑series variation in U.S.

Abstract

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 put 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 that 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 U.S. 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.