An overlapping generations model of the forward discount bias

Many empirical studies have been undertaken to determine the validity of the uncovered interest rate parity hypothesis--the hypothesis that would lead one to expect a correlation between the forward discount and spot rate movements. The consensus of these studies has been that the forward discount is not a good indicator of foreign exchange spot rate movements. Not only this, but some prominent studies have actually found an inverse relationship between the forward discount and spot rate behavior. This empirical finding seems to contradict the straightforward implication of the joint UIP and CIP hypothesis. The joint parity hypothesis would seem to indicate that the expected future spot rate is equal to the forward rate. If agents, then, are rational, and markets are efficient, one might think that the expected future spot rate would be the actual future spot rate, and therefore, the forward rate would be an accurate predictor of future spot rates. The implication of the models presented here is that the theoretical unbiasedness of the forward discount is a special case, and an extremely restrictive one at that. When the extremely restrictive assumption is made that agents have perfect foresight, we find that the forward rate does indeed equal the expected future spot rate, and further that the expected future spot rate is an accurate predictor of future spot rates. When uncertainty is introduced into the model, however, this result no longer holds.