The uncovered interest rate parity equation is the cornerstone of most models in international macro. However, this equation does not hold empirically since the forward discount, or interest rate differential, is negatively related to the subsequent change in the exchange rate. This forward discount puzzle implies that excess returns on foreign currency investments are predictable. Motivated by the fact that even today only a tiny fraction of foreign currency holdings are actively managed, we investigate to what extent incomplete information processing can explain this puzzle. Two types of incompleteness are considered: infrequent and partial information processing. We calibrate a two-country general equilibrium model to the data and show that incomplete information processing can fully match the empirical evidence. It can also account for several related empirical phenomena, including that of "delayed overshooting". We also show that incomplete information processing is optimal. Predictability is largely overshadowed by uncertainty about future exchange rates, so that the welfare gain from actively managing foreign exchange positions is small and easily outweighed by a small cost of active portfolio management.