We show that currencies with a steeper yield curve tend to depreciate at business cycle horizons, in violation of uncovered interest parity (UIP), but the yield curve adds no explanatory power over and above interest differentials in explaining the exchange rate at longer horizons. We argue that exchange rate risk premia reallocate returns intertemporally to investors who value them relatively highly, reflecting transitory innovations to their stochastic discount factor consistent with business cycle risk. Using holding period returns, we identify a tent-shape relationship, across horizons, between dollar-bond excess returns for long maturity bonds and the relative slope. In addition, we find that short-horizon UIP deviations switch sign following yield curve inversions, consistent with the interpretation of inversions as indicators of changes in growth and inflation expectations. We show that accounting for liquidity yields does not alter our results, but rather contributes to explaining cross-sectional differences across currencies, consistent with permanent innovations to agents' stochastic discount factor.