Currency 1: Portfolio consists of a bond Formula: H1 = I1 (Interest Rate)

Currency 2: Currency 1 is held in this portfolio.

Asset 3: Currency 1 is held in this portfolio.

Here is a simple case when a bond is held in the Currency 1 portfolio. Currency 2 and Currency 3 portfolios both consist of Currency 1. Please compare this diagram with the one in the "PAT In a Two-Currency Environment" section. You will see that this case is just an extension of the two-currency case. It is easy to see that, since in each of these cases only Currency 1 is involved, the payoffs must be financially equivalent and are therefore interchangeable.