The bias of tests for a risk premium in forward exchange rates

The pure expectations theory of unbiased forward exchange rates predicts that the slope coefficient in a regression of the change in the spot rate on the difference between the current forward and spot rates should equal unity. In the recent empirical work by Fama, the estimates of this coefficient turn out to be negative in all regressions for nine major industrialized nations. This paper demonstrates that under the expectations theory, the sampling distribution of the regression estimator of this coefficient is upward-biased relative to unity and strongly skewed to the right. The likelihood of negative values is essentially zero. Thus, the estimator is biased in a direction opposite to what is observed. Since the observed estimates lie far out in the thin left-hand tail of the estimator's sampling distribution, the evidence against the hypothesis of unbiased forward rates is much stronger than previously believed.