The Numeraire Problem and Foreign Exchange Risk

Abstract

TRADITIONAL EXPLANATIONS of foreign exchange exposure have generally suffered from two deficiencies: the failure to place the foreign exchange problem within the context of the firm trying to maximize shareholder wealth, and the attempt to deal with exposure management on a transaction by transaction basis. The first deficiency manifests itself in the assumption or belief that assets denominated in a home or numeraire currency are void of foreign exchange risk. Invoking that assumption ignores the impact of exchange rate changes on the home currency's purchasing power over imported goods. The second weakness is evidenced by the attempt to deal with foreign exchange decisions using a hedge or no-hedge decision rule, thus ignoring portfolio considerations. In a recent article, Makin [7] discusses the hedge-no-hedge strategy and offers an alternative way to analyze foreign currency problems using portfolio theory. Although Makin's approach is a significant improvement on the hedge-no-hedge analysis it still suffers from the first deficiency. Makin's model is dependent upon his assumption that the home currency is a risk-free asset, an assumption that will likely bring about the inclusion in the resulting portfolio of more assets denominated in the home currency than would be the case if risk were correctly specified. The purpose of this paper is to show that the assumption is not generally correct and to suggest an index that more accurately measures exchange risk. The index that is used is one that was developed by Kouri and Braga de Macedo [3]. It is similar in concept to a trade-weighted exchange rate and reflects the impact of exchange rate variation on the purchasing power of a unit of currency. Section I presents a verbal description of exchange risk. The differences between the traditional view and the global view espoused here are highlighted. Section II discusses the Kouri and Braga de Macedo index of value and its applicability to the foreign exchange exposure problem. Section III demonstrates the use of the index in adjusting returns and analytically shows the error in confusing the nominal riskless asset with a real riskless asset. In section IV the characteristics of a real riskless asset are investigated.