Forward Exchange Rate

Forecasting Future Spot Exchange Rate

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.

F_t = E_t(S_{t + k})

where

F_t is the forward exchange rate at time t

E_t(S_{t + k}) 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 being equal to a future spot rate and a risk premium (not to be confused with a forward premium):

F_t = E_t(S_{t + 1}) + P_t

The current spot rate can be introduced so that the equation solves for the forward-spot differential (the difference between the forward rate and the current spot rate):

F_t - S_t = E_t(S_{t + 1} - S_t) + P_t

Eugene Fama concluded that large positive correlations of the difference between the forward exchange rate and the current spot exchange rate signal variations over time in the premium component of the forward-spot differential F_t - S_t or in the forecast of the expected change in the spot exchange rate. Fama suggested that slope coefficients in the regressions of the difference between the forward rate and the future spot rate F_t - S_{t + 1}, and the expected change in the spot rate E_t(S_{t + 1} - S_t), on the forward-spot differential F_t - S_t which are different from zero imply variations over time in both components of the forward-spot differential: the premium and the expected change in the spot rate.[12] Fama's findings were sought to be empirically validated by a significant body of research, ultimately finding that large variance in expected changes in the spot rate could only be accounted for by risk aversion coefficients that were deemed "unacceptably high." Other researchers have found that the unbiasedness hypothesis has been rejected in both cases where there is evidence of risk premia varying over time and cases where risk premia are constant.

Other rationales for the failure of the forward rate unbiasedness hypothesis include considering the conditional bias to be an exogenous variable explained by a policy aimed at smoothing interest rates and stabilizing exchange rates, or considering that an economy allowing for discrete changes could facilitate excess returns in the forward market. Some researchers have contested empirical failures of the hypothesis and have sought to explain conflicting evidence as resulting from contaminated data and even inappropriate selections of the time length of forward contracts. Economists demonstrated that the forward rate could serve as a useful proxy for future spot exchange rates between currencies with liquidity premia that average out to zero during the onset of floating exchange rate regimes in the 1970s. Research examining the introduction of endogenous breaks to test the structural stability of cointegrated spot and forward exchange rate time series have found some evidence to support forward rate unbiased in both the short and long term.