Social Sciences and Humanities Open (Jan 2023)
Currency attribution for bilateral exchange rates: A decomposition of the moments
Abstract
A bilateral exchange rate is the price of a base currency in terms of a quote currency. In this situation, how do international investors decide the contributions of both the base currency and the quote currency to the mean, variance, skewness, and kurtosis of the movements in each bilateral exchange rate? For a group of currencies, each bilateral exchange rate can be decomposed into a difference between two multilateral exchange rates: a base-currency multilateral exchange rate minus a quote-currency multilateral exchange rate. In this paper, the decomposition of bilateral exchange rates is used to decompose the moments of the movements in bilateral exchange rates. The result is a quantitative methodology to perform currency attribution, where the mean, variance, skewness, and kurtosis of the movements in each bilateral exchange rate can be attributed to the base currency and the quote currency.
