Currency: two returns in one

When a fund holds foreign assets, its return in the base currency has two parts: the asset's return in its local currency, and the change in the exchange rate. They compound together, so there's also a small cross term.

1 + R_base = (1 + R_local) × (1 + R_FX) so R_base = R_local + R_FX + R_local × R_FX

A US investor holds a European share that rises 10% in euros, while the euro rises 5% against the dollar. The dollar return is 1.10 × 1.05 − 1 = 15.5%. The extra 0.5% is the cross term: the currency move applied to the local gain.

Hedging with forwards

An FX forward locks in an exchange rate today for a future date. The forward rate differs from today's spot rate by the interest rate difference between the two currencies. So a hedge doesn't make currency returns zero; it replaces the uncertain spot move with a known return close to the interest rate differential.

R_hedged ≈ R_local + (i_base − i_foreign)

In plain termsBuying a foreign share is really two bets: one on the company and one on its currency. Hedging lets you keep the first bet and swap the second for a small, predictable interest payment or cost.

Local return, currency and hedging

One year holding a foreign asset. A positive currency move means the foreign currency strengthened against your base currency.

Local return

Currency move

Hedge ratio

Interest rate differential (base − foreign)

Unhedged return

Return at this hedge ratio

Fully hedged return

Currency in attribution

Multi-currency attribution adds currency decisions to the allocation and selection effects: did the manager over- or underweight currencies that moved, and did hedging help? The Karnosky-Singer model is the standard framework. It splits each market's return into a local return above local cash and a currency return that includes the forward premium, so market and currency bets are measured separately and cleanly.

For practitionersThe FX rate source is one of the most common causes of return breaks. Major index providers generally value at the WM/Reuters 4pm London closing spot rates; a portfolio valued at a different fix, or at local market close, will show a return difference against the benchmark (and against third-party analytics) even with identical holdings. Match the fix and the timestamp, or feed the analytics system the same rates the accounting system used. Hedged share classes hold class-specific forwards whose P&L is allocated only to that class, so they differ from the unhedged class by roughly the interest differential plus hedge slippage (the cross term on gains, rebalancing lags and forward roll costs). In Karnosky-Singer, currency allocation uses the forward premium, and forward contracts appear as pure currency exposure.

All numbers are illustrative. The models are simplified for teaching: annual coupons, Black-Scholes options, simplified fee mechanics and no intra-period trading. Real systems add transaction-based returns, daily valuation, tax and corporate action processing, and reconciliation to the official TWR.