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. In this paper we investigate to what extent incomplete information processing can explain this puzzle. We consider two types of incompleteness: 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 show that incomplete information processing is consistent both with evidence that little capital is devoted to actively managing short-term currency positions and with a small welfare gain from active portfolio management. The gain is small because exchange rate changes are very hard to predict. The welfare gain is easily outweighed by a small cost of active portfolio management.