The Multiplicative Wedge Approach to Incomplete Markets and the Trifecta of Exchange Rate Puzzles

In international economies with incomplete markets, the multiplicative wedge approach of Backus, Foresi, and Telmer (2001) encapsulates the idea that log exchange rate growth deviates from log relative of the stochastic discount factors by a perturbation. We analyze the asset pricing implications of this approach in the context of the trifecta of exchange rate puzzles, with three results. First, we analytically show that the currency risk premium is detached from the multiplicative wedge perturbation. This key result is both distribution-free and preference-free and implies that the approach cannot resolve the forward premium puzzle. Moreover, it is not feasible to reproduce the low unconditional volatility of exchange rate growth with realistic parameterizations. Finally, the slope coefficient in the Backus and Smith regression is not affected by the perturbation.