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$$ x $$ 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.