or discount is calculated. The forward exchange rate differs by a premium or discount of the spot exchange rate: where P is the premium (if positive) or discount (if negative) The equation can be rearranged as follows to solve for the forward premium/discount: In practice, forward premiums and discounts are quoted as annualized percentage deviations from the spot exchange rate, in which case it is necessary to account for the number of days to delivery as in the following example. where N represents the maturity of a given forward exchange rate quote d represents the number of days to delivery For example, to calculate the 6-month forward premium or discount for the euro versus the dollar deliverable in 30 days, given a spot rate quote of 1.2238 $/€ and a 6-month forward rate quote of 1.2260 $/€: The resulting 0.021572 is positive, so one would say that the euro is trading at a 0.021572 or 2.16% premium against the dollar for delivery in 30 days. Conversely, if one were to work this example in euro terms rather than dollar terms, the perspective would be reversed and one would say that the dollar is trading at a discount against the Euro. Forecasting future spot exchange rates Unbiasedness hypothesis The unbiasedness hypothesis states that given conditions of rational expectations and risk neutrality, the forward exchange rate is an unbiased predictor of the future spot exchange rate. Without introducing a foreign exchange risk premium (due to the assumption of risk neutrality), the following equation illustrates the unbiasedness hypothesis. where is the forward exchange rate at time t is the expected future spot exchange rate at time t + k k is the number of periods into the future from time t The empirical rejection of the unbiasedness hypothesis is a well-recognized puzzle among finance researchers. Empirical evidence for cointegration between the forward rate and the future spot rate is mixed. Researchers have published papers demonstrating empirical failure of the hypothesis by conducting regression analyses of the realized changes in spot exchange rates on forward premiums and finding negative slope coefficients. These researchers offer numerous rationales for such failure. One rationale centers around the relaxation of risk neutrality, while still assuming rational expectations, such that a foreign exchange risk premium may exist that can account for differences between the forward rate and the future spot rate. The following equation represents the forward rate as