A euro-based investor converts €10,000 into dollars and buys a U.S. stock. The stock later trades 10% higher in dollar terms. If the dollar has fallen 8% against the euro over the same period, converting the position back into euros leaves about €10,120—not €11,000.
The stock return is quoted in dollars
The 10% gain describes what happened to the stock in its trading currency. It does not yet answer what happened to the investor's euros. To get that answer, the dollar value of the position must be converted at the new exchange rate.
The starting EUR/USD rate does not need to be specified when only the percentage return is required. The combined calculation is:
With the stock up 10% and the dollar down 8% against the euro:
Applied to the original investment:
The same U.S. stock gain can therefore produce very different euro returns as the dollar moves.
| Dollar move<br>against the euro | Return in euros | Ending value of €10,000 |
|---|---|---|
| +8% | +18.8% | €11,880 |
| 0% | +10.0% | €11,000 |
| -5% | +4.5% | €10,450 |
| -8% | +1.2% | €10,120 |
| -10% | -1.0% | €9,900 |
Even though the U.S. stock is up 10%, a 10% dollar decline turns the euro return into a 1% loss.
Why 10% minus 8% is not the final answer
Subtracting the dollar's 8% decline from the stock's 10% gain gives a quick 2% estimate. It misses the fact that the new exchange rate applies to a position that has already changed in value. Expanding the formula shows the missing term:
The cross term subtracts another 0.8 percentage points. If the stock rises 10% and the dollar also gains 8% against the euro, the cross term adds 0.8 points instead. The euro return is then 18.8%, not 18%.
The shortcut is less reliable as either the stock or the exchange rate makes a larger move.
A stronger dollar can offset a stock loss
Now reverse the directions. Suppose the U.S. stock falls 5%, while the dollar gains 10% against the euro. The euro return is:
The stock is down in dollars, but the original €10,000 position is worth about €10,450 in euro terms. A U.S. stock chart and a euro-based account can therefore show returns with different signs.
Isolate the 10% stock move before currency effects
ReturnLab's public calculator does not currently combine stock and currency returns. The link uses $10,000 to isolate the stock-only move from $10,000 to $11,000. It does not reproduce the €10,120 currency-adjusted result.
What the calculation leaves out
This scenario compares one starting stock price and exchange rate with one ending price and exchange rate. It excludes dividends, taxes, trading fees, conversion fees, bid-ask spreads, and any purchases or sales made during the holding period.
The investor does not need to sell the shares or convert the dollars immediately for the euro valuation to move with the exchange rate. The cash ultimately received can still differ because of the rate and costs at the time of sale and conversion. This is an educational calculation, not investment advice or a forecast for the dollar or euro.