Exchange Rate Accounting in a Multi-Currency World

I develop an accounting framework that attributes FX movements in incomplete markets to SDF and non-SDF shocks. This framework allows a general characterization of FX dynamics and SDF-FX pass-through. Under this framework, Triangular arbitrage imposes a tight relation between SDF correlations and FX correlations, which produces counterfactual implications if the SDF-FX pass-through is symmetric across countries. This result suggests that asymmetry is an inherent feature of equilibrium FX dynamics in incomplete markets, which generates novel implications about international spill-over, Backus-Smith coefficients, and FX comovements.