Engel and West (EW, 2005) argue that as the discount factor gets closer to one, present-value asset pricing models place greater weight on future fundamentals. Consequently, current fundamentals have very weak forecasting power and exchange rates appear to follow approximately a random walk. We connect the Engel-West explanation to the studies of exchange rates with long-horizon regressions. We find that under EW's assumption that fundamentals are I(1) and observable to the econometrician, long-horizon regressions generally do not have significant forecasting power. However, when EW's assumptions are violated in a particular way, our analytical results show that there can be substantial power improvements for long-horizon regressions, even if the power of the corresponding short-horizon regression is low. We simulate population R squared for long-horizon regressions in the latter setting, using Monetary and Taylor Rule models of exchange rates calibrated to the data. Simulations show that long-horizon regression can have substantial forecasting power for exchange rates.