In this note, I conduct an empirical investigation of the affine stochastic discount factor model proposed by Backus, Foresi and Telmer (2001), who showed that such a model might be able to explain the forward premium anomaly. Evidence presented here suggests that the model can reproduce the forward premium anomaly only by placing restrictions on the behavior of spot and forward exchange rates that are not consistent with the data. The model assumes that an increase in the forward premium must be accompanied by an increase in volatilities of the forward premium and of the exchange rate depreciation. I find that this assumption is not supported by the data. When I relax the model by allowing the forward premium to vary without necessarily affecting conditional second moments, the model no longer reproduces the forward premium anomaly. Thus, I conclude that the model can reproduce the anomaly only by forcing a linear heteroskedastic process that is not supported by the data.