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

78 Pages Posted: 23 Oct 2018 Last revised: 22 May 2019

See all articles by Gurdip Bakshi

Gurdip Bakshi

Fox School of Business

John Crosby

University of Maryland - Robert H. Smith School of Business

Date Written: May 20, 2019

Abstract

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

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). Available at SSRN: https://ssrn.com/abstract=3257604 or http://dx.doi.org/10.2139/ssrn.3257604

Gurdip S. Bakshi (Contact Author)

Fox School of Business ( email )

Department of Finance
Philadelphia, PA 19022
United States
215-204-6117 (Phone)
tuk40718@temple.edu (Fax)

HOME PAGE: http://https://sites.google.com/view/gurdipbakshi1

John Crosby

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
+447979901892 (Phone)

HOME PAGE: http://www.john-crosby.co.uk/

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