Two well-known, but seemingly contradictory, features of exchange rates are that they are close to a random walk (RW) while at the same time exchange rate changes are predictable by interest rate di¤erentials. The RW hypothesis received strong support from the work of Richard A. Meese and Kenneth Rogo ¤ (1983) who were the …rst to show that macro models of exchange rate determination could not beat the RW in predicting exchange rates. On the other hand, Eugene F. Fama (1984) showed that high interest rate currencies tend to subsequently appreciate. This is known as the forward discount puzzle and stands in contrast to Uncovered Interest Parity (UIP), which says that a positive interest di¤erential should lead to an expected depreciation of equal magnitude. The RW hypothesis and the forward discount puzzle are not as contradictory as it seems since the predictability of exchange rate changes by interest di¤erentials is limited. For example, Fama (1984) reports an average R2 of 0.01 when regressing monthly exchange rate changes on beginning-of-period interest di¤erentials. Instead of opposing these two features of the data, in this paper we investigate whether in fact they may be related to each other.