Suppose you regress the realized rate of appreciation of a foreign currency on a constant and the forward premium on the foreign currency

What interpretation can you give to the estimated slope coefficient? If the slope coefficient is negative, is it true that the forward premium is predicting the wrong sign for the rate of appreciation?


The slope coefficient is the covariance of the rate of appreciation with the forward premium divided by the variance of the forward premium. The slope coefficient indicates how much the expected rate of appreciation moves with the forward premium. If the slope coefficient is negative, some people interpret the regression as saying that the forward premium is predicting the wrong direction for the rate of appreciation. To get a correct interpretation of the regression, one must remember to include the constant term in the forecast. The correct interpretation is that the forecast of the expected rate of appreciation is the constant plus the slope coefficient multiplied by the forward premium. A negative coefficient certainly does predict that the expected rate of appreciation predicted by an increase in the forward premium is smaller than before the increase in the forward premium.

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