Asset currency and account currency: translating a return
Why an asset gain of 10% and a 5% fall in its currency produce 4.5%, not 5%.
A return in the quoted currency may differ from a return in the account currency. Adding percentages is insufficient: the final asset value is multiplied by the final exchange rate. First define that rate’s units unambiguously.
Define the exchange direction
Let F be the asset-price currency and H the reporting currency. Define q as H per 1 F. The value in H is the price in F multiplied by q. A fall in q means one unit of F buys fewer H: that is F weakening relative to H under this definition.
Use one completed period and a fixed asset quantity. There are no deposits, withdrawals, dividends, interest, fees or taxes. Currency hedging is excluded. All prices and exchange rates are invented, not current quotations.
Translate both endpoint values
The asset rises from 100 F to 110 F, a 10% return in F. The exchange rate falls from 2 H/F to 1.9 H/F, a−5% currency return. Initial value is 100 × 2=200 H; final value 110 × 1.9=209 H. The account-currency return is 209/200−1=4.5%.
Under these assumptions use (1+asset return)×(1+currency return)−1. The product includes the cross-term 0.10 ×(−0.05)=−0.005. Simply subtracting 5% from 10% omits it. If a quotation is in F/H, invert it first; its percentage change is not converted merely by reversing the sign.
Our own teaching example; all figures are hypothetical.
(1 + 0.10) × (1 − 0.05) − 1 = 0.045 = 4.5%; (110 × 1.9) / (100 × 2) − 1 = 4.5%
| Measure | Start | End | Change |
|---|---|---|---|
| Asset price,F | 100 | 110 | +10% |
| Rate,H per 1 F | 2 | 1.9 | −5% |
| Value,H | 200 | 209 | +4.5% |
What a real account adds
The listing currency alone does not describe every economic currency exposure of a company or fund. Hedged products need their own method. Flows, distributions and costs belong to their actual dates; this two-endpoint formula is not a substitute for a complex account calculation.
Record the instrument, both currencies, exchange units, dates, source and valuation times. A foreign-price chart and an account-currency chart are different series. Elliott does not translate a brokerage portfolio: next, separate nominal results from purchasing power.
An asset loses 10% while q in H/F rises 10%. Is the H result zero?
No.0.9 × 1.1−1=−1%. Equal opposite percentage changes do not cancel when multiplied.
Sources
Sources checked: 2026-10-21
This material and its translations were prepared with AI assistance. Educational calculations were checked programmatically. Sources explain concepts; examples and files were created for this article.
Related reading
Next step
After currency translation, distinguish the nominal result from the change in purchasing power.
Nominal and real returns: what inflation changes →