A global equity fund returned 14.2% on international holdings in local currency. After translating to dollars, the return was 3.8%. Over 10 percentage points vanished in currency translation. The hedge ratio had been set to zero.
The domestic currency return on a foreign asset:
R(DC) = (1 + R(FC)) x (1 + R(FX)) - 1
Where R(DC) = domestic currency return, R(FC) = foreign asset return, R(FX) = percentage change in the exchange rate (domestic per foreign). The approximation R(DC) ~ R(FC) + R(FX) works when both returns are small. The cross-product can be material when either is large.
HIGH-FREQUENCY: Return decomposition appears in nearly every currency management item set. The key trap: exchange rate convention. If the rate is domestic per foreign (e.g., USD/EUR = 1.0850 = $1.085 per euro), an increase means the foreign currency appreciated, positive R(FX) for the US investor.
Arguments for hedging: currency adds volatility without compensating return. Most institutions have domestic liabilities. Short-term currency moves are noise.
Common mistakes
- Reversing the exchange rate convention. If USD/EUR = 1.08, an increase to 1.12 means the EUR appreciated (positive R(FX) for the US investor). An increase in the rate means the foreign currency strengthened. Candidates who reverse this get the sign of the currency return wrong.
- Assuming hedging is always beneficial. Hedging has costs: roll yield (which can be significantly negative for carry currencies), bid-ask spreads, and transaction costs. For long-horizon investors with domestic-foreign currency correlation, partial hedging may be optimal.
- Forgetting roll yield sign depends on the rate differential. Positive roll yield when domestic rates > foreign rates. Negative when domestic rates < foreign. Candidates who compute roll yield without checking the rate differential may get the sign wrong.
Bottom line
- Domestic return ; the approximation only holds when both returns are small.
- Forward hedge: sell foreign currency forward to lock in the domestic-currency value of foreign assets.
- Roll yield = (Forward - Spot) / Spot, positive when domestic rates exceed foreign rates, negative when they are lower.
- Hedging high-yield currencies carries negative roll yield, which is why carry trades exist.
Exam shortcut
For return decomposition, set up the exact formula first: (1 + RFC)(1 + RFX) - 1. Check the exchange rate convention, domestic per foreign means "rate up = foreign currency stronger." For roll yield, remember: domestic rate > foreign rate = positive roll yield = hedging is cheap. The reverse = negative roll yield = hedging costs money.
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Learning objectives
- currency management
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