The Forward Premium Anomaly is Not as Bad as You Think

The forward premium anomaly refers to the widespread empirical finding that the slope coefficient in the regression of the change in the logarithm of the spot exchange rate on theforward premium is invariably less than unity, and often negative. This “anomaly” impliesthe apparent predictability of excess returns over uncovered interest rate parity (UIP), and isconventionally viewed as evidence of a biased forward rate and/or of evidence of a timevaryingrisk premium. This paper presents a stylized model that imposes UIP and allows the daily spot exchange rate to possess very persistent volatility. The model is calibrated around realistic parameter values for daily returns and the slope coefficient estimates in the anomalousregressions with monthly data are found to be centered around unity, but are very widelydispersed, and converge to the true value of unity at a very slow rate. This theoretical evidenceis shown to be consistent with the empirical findings for the monthly sample sizes typically employed in the literature. Hence, the celebrated unbiasedness regression does not appear toprovide as much evidence as previously supposed concerning the possible bias of the forwardrate.