Synthetic money: Addressing the budget‐constraint issue

A synthetic currency attempts to mimic a target currency with an optimal portfolio of other currencies, without having a position in the target currency. The original construction methodology of a synthetic currency imposed a budget constraint such that the portfolio weights sum to a non‐zero value, x say. However, a synthetic currency is a portfolio of invariant currency indexes, rather than a portfolio of currency positions. In this article, we show that invariant currency indexes are tradable multilateral exchange rates. Consequently, the sum‐to‐x budget constraint unintentionally creates a non‐zero position in the target currency. We address this budget‐constraint issue by replacing the sum‐to‐x budget constraint with a sum‐to‐zero budget constraint, which correctly enforces a zero position in the target currency. Once the budget‐constraint issue is addressed, investors are faced with the fact that synthetic money is unable to mimic significant currency‐specific movements in target currencies.