Computing currency invariant indices with an application to minimum variance currency baskets

Abstract

This paper provides an exact and computable invariant currency value index ( ICVI) which is independent of base currency choice. Thus, given a fixed set of currencies, the index of a currency will have the same value, regardless of base currency choice. This currency index can be used as an indicator to assess movements of an individual currency's value in world currency markets. The methodological and mathematical reasoning behind ICVI is formulated in terms of a simple exchange model (SIMEX). To demonstrate one possible application we employ ICVI to construct a currency basket of minimum variance. Utilizing a quadratic optimization framework, we compute optimal weights for currencies and construct a stable aggregate currency ( SAC). Comparative empirical analyses of a five-currency SAC and the IMF's Special Drawing Rights ( SDR) demonstrates that the SAC has lower volatility and lower correlations with its components than the SDR. In a similar way it is shown that a three-currency SAC has a smaller variance than the world money basket proposed by R. Mundell. Numerous academic and business implications are possible for further study with the use of the indices ICVI and SAC.