Under rational expectations and risk neutrality the linear projection of exchange rate change on the forward premium has a unit coefficient. However, empirical estimates of this coefficient are significantly less than one and often negative. We investigate whether replacing rational expectations by discounted least squares (or "perpetual") learning can explain the result. We calculate the asymptotic bias under perpetual learning and show that there is a negative bias that becomes strongest when the fundamentals are strongly persistent, i.e. close to a random walk. Simulations confirm that perpetual learning is potentially able to explain the forward premium puzzle.JEL classifications: D83, D84, F31, G12, G15

Abstract:The Forward Premium Puzzle is one of the most prominent empirical anomalies in international finance. The forward premium predicts exchange rate depreciation but typically with the opposite sign and smaller magnitude than specified by rational expectations, a result also considered to indicate inefficiency in the foreign exchange market. This paper proposes a resolution of the puzzle based on recursive least squares learning applied to a simple model of exchange rate determination. The key assumption is that risk neutral agents are not blessed with rational expectations and do not have perfect knowledge about the market. Agents learn about the parameters underlying the stochastic process generating the exchange rate using constant gain recursive least squares. When exchange rate data are generated from the model and the empirical tests are performed, for plausible parameter values the results replicate the anomaly along with other observed empirical features of the forward and spot exchange rate data.