Forward-premium puzzle: is it time to abandon the usual regression?

The forward premium puzzle is usually evidenced by the rejection of the null hypothesis in the uncovered interest parity (UIP) regression. Because this parity need only hold in a risk-neutral world, a risk adjustment term is missing from the equation if speculation in foreign exchange markets is risky. We deal with this issue following the literature which assumes that discounted returns on foreign government bonds are log-normal, so we can linearize the Euler pricing equations (in level) and obtain a modified UIP system for which the risk adjustment term is obtained by applying to the pricing kernel-based relations a generalized autoregressive conditional heteroscedasticity-in-mean model. However, here we innovate by adopting a methodology which differs from all these related works. We construct and use a stochastic discount factor that does not depend on a specific model, by residing in the space of returns which we extract from the data by simply imposing the orthogonality restrictions represented by the Euler equations. So, we devise a purely statistical pricing kernel that performs well in in-sample level equations. Somewhat disappointingly, the risk premium inclusion in the conventional regression changes neither the significance nor the magnitude of the forecasting power of the forward premium for most currencies we study. The contrasting performance of the tests in level and in logs suggests that linearization may be to blame.