Foreign Exchange Implied. Variance and the Forward Premium Puzzle

We explore the hypothesis that Jensen’s Inequality is related to the magnitude

of the commonly observed difference between forward rates and the

subsequent realizations of spot exchange rates. Compared to the standard

specification, it is shown that using the option-implied variance of the spot rate

as an additional regressor in the unbiased forward specification results in slope

coefficients that are closer to their theoretical value of unity. Furthermore,

implied variance is found to have a higher explanatory power over future spot

returns compared to that of the forward premium. Our empirical findings are

consistent with the hypothesis that the time-varying risk-premium documented

in previous studies contains a Jensen’s term of the future spot variance.