Cross-Currency Consistency, Three-Part SDF Factorizations, and an Impossibility Theorem for the Stationarity of Exchange Rates in International Economies

We consider an incomplete markets international economy in discrete-time. The first result is an impossibility theorem showing that if cross-currency no-arbitrage is to hold, the exchange rate cannot be a stationary process in levels. The second result is a system of stochastic discount factor (SDF) factorizations that enforce no-arbitrage in international economies. For example, the domestic SDF admits a new three-part multiplicative factorization: the inverse of (gross) exchange rate growth, a martingale, and a non-martingale component which is the reciprocal of the gross return of the foreign long-term bond. Examples and empirical work showcase our theoretical characterizations and economic insights.

Keywords: Three-Part Decomposition, Stationarity of Exchange Rates, Incomplete Markets, SDFs

JEL Classification: G12, G15, E44, F31, F36

Suggested Citation: Suggested Citation

Bakshi, Gurdip S. and Bakshi, Gurdip S. and Crosby, John, Cross-Currency Consistency, Three-Part SDF Factorizations, and an Impossibility Theorem for the Stationarity of Exchange Rates in International Economies (May 20, 2019). Proceedings of Paris December 2019 Finance Meeting EUROFIDAI - ESSEC, Available at SSRN: https://ssrn.com/abstract=3257604 or http://dx.doi.org/10.2139/ssrn.3257604