Highlighting some of the issues with multicurrency numéraires

• Multicurrency numéraires are weighted baskets of currencies, in which the weights are positive and sum to one. • Highlight some of the issues that arise when using multicurrency numéraires by utilising two conditions, namely, a consistency condition and a no-arbitrage condition. • Both the consistency condition and the no-arbitrage condition are satisfied by common equally-weighted multicurrency numéraires. Multicurrency numéraires are weighted baskets of currencies, in which the weights are positive and sum to one. Some popular multicurrency numéraires are: trade-weighted, the IMF's Special Drawing Right (SDR), equally-weighted, risk-weighted, and GDP-weighted. But which multicurrency numéraire should be used to model systems of currencies? This paper highlights some of the issues that arise when using multicurrency numéraires by utilising two conditions, namely, a consistency condition and a no-arbitrage condition. It is shown that both the consistency condition and the no-arbitrage condition are satisfied by common equally-weighted multicurrency numéraires. As a consequence, it is recommended that common equally-weighted multicurrency numéraires be used to model systems of currencies.