Hong Life CalculatorsUnderstanding the currency-hedged vs unhedged return calculator — concept and principle
When you buy a foreign asset, your return in your own currency depends on two things: how the asset did in its local currency and how that currency moved against yours. A currency-hedged fund removes most of the second effect at a cost. This calculator compares the two choices for one period, which helps when deciding between hedged and unhedged share classes of the same ETF or fund.
How it is calculated
- Unhedged: R = (1 + a) × (1 + f) − 1, where a is the asset return in foreign currency and f the change of that currency against yours.
- Hedged: R ≈ a − h, where h is the yearly hedging cost.
- Currency effect: unhedged return − a, the part caused by the exchange rate.
All inputs are percentages for the same period. A negative f means the foreign currency weakened.
The principle
Unhedged returns multiply: each unit of foreign currency grows by (1 + a), then converts back at a rate that changed by (1 + f). The small cross term a × f is why the currency effect is not exactly f.
A hedge sells the foreign currency forward at a rate fixed today. By covered interest parity, the forward rate differs from the spot rate by roughly the interest-rate gap between the two currencies, so hedging a currency with higher interest rates than yours costs about that gap each year, and hedging a lower-rate currency can even add return. The model treats the hedge as perfect.
Worked example
- Inputs: asset return 8%, currency change −5%, hedging cost 1.5%.
- Unhedged: 1.08 × 0.95 − 1 = 0.026 = 2.6%.
- Hedged: 8% − 1.5% = 6.5%.
- Difference: 6.5% − 2.6% = 3.9 percentage points in favour of the hedge.
- Currency effect: 2.6% − 8% = −5.4% (−5% plus the cross term 0.08 × −0.05 = −0.4%).
How to read the result
Hedging pays off when the foreign currency falls by more than about the hedging cost, and costs you when it rises or stays flat. Here the break-even is a currency change of about −1.4%: 1.08 × (1 + f) − 1 = 6.5% gives f ≈ −1.39%. Over long periods currency moves partly cancel out, so the lasting difference is the hedging cost, and the real benefit of hedging is lower volatility, especially for bonds.
Common mistakes
- Adding instead of multiplying the two returns for the unhedged case.
- Assuming hedging is free. The cost follows the interest gap and changes when rates change.
- Judging a hedge by one year. It is a risk choice, not a forecast.
- Using the currency change in the wrong direction. Enter how the foreign currency moved against yours.
Frequently asked questions
Why does hedging US dollars cost money for many investors?
When US interest rates are higher than your home rates, the forward rate for selling dollars is lower than spot, and that gap is the cost.
Can the hedging cost be negative?
Yes. If the foreign currency has lower interest rates than yours, the forward is above spot and the hedge earns a small premium.
Sources: J. C. Hull, Options, Futures, and Other Derivatives, Pearson (forward exchange rates and interest rate parity) · CFA Institute, CFA Program Curriculum, currency management readings