Very roughly, three years ago the exchange rate was 1USD=0.9EUR while now it is 1USD=0.8EUR. Let us use those and imagine ABC corp was trading three years ago at 100USD and has risen to 150USD today. The annual return in dollars is the 1/3 power of 1.5, which is about 14.47%. In euros it has risen from 90 to 120, so the return is the 1/3 power of 120/90=4/3, about 10.06%. If you are a dollar denominated investor and bought it on the euro market you would have paid 100USD to buy the share, which was then converted to 90EUR and the share purchased. When it is sold three years later you would receive 120EUR which would convert to 150USD. Aside from exchange costs, you are the same place either way. Similarly, a euro denominated investor would realize the same appreciation either way. The higher return in dollars would be compensated by the lowered exchange rate at the end.
The reason we think of exchange rates changing the return on an investment is because we normally think of the return on a stock in its native currency. If we think a stock that appreciates 15% in a year in its native currency is doing well, you add to or subtract from that the change in exchange rate to your own currency. If instead of buying ABC corp, which returned 14.47% in its native dollars, you had bought DEF corp which returned 14.47% in its native euros any investor would be better off because the euro was gaining in value as well. Once you have decided what to buy it doesn't matter (up to exchange costs) what currency you use to buy it.
