An Impossibility Theorem for the Stationarity of Exchange Rates

49 Pages Posted: 9 Aug 2023 Last revised: 15 Jan 2025

See all articles by Gurdip Bakshi

Gurdip Bakshi

Temple University

John Crosby

University of Maryland - Robert H. Smith School of Business

Date Written: August 8, 2022

Abstract

Can the exchange rate be stationary in levels? We answer this question in the negative by proving an impossibility theorem, built upon the absence of arbitrage in international economies. We establish the sufficient conditions for the exchange rate to not be a stationary process in levels, and we do so without making distributional or preference assumptions. The essence of the paper is to study the properties of an exchange rate whose dynamics are restricted by the domestic and foreign stochastic discount factors, and by (no-arbitrage) trade in domestic and foreign short-term (one-period) bonds and long-term (infinite-maturity) bonds.

Keywords: Exchange rates, impossibility theorem, stationarity

JEL Classification: G12, G13,

Suggested Citation

Bakshi, Gurdip and Crosby, John, An Impossibility Theorem for the Stationarity of Exchange Rates (August 8, 2022). Available at SSRN: https://ssrn.com/abstract=4534982 or http://dx.doi.org/10.2139/ssrn.4534982

Gurdip Bakshi (Contact Author)

Temple University ( email )

Philadelphia, PA 19122
United States

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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