Calculate investment return taking into account the currency change
Lets suppose an investor invests £10000 in a mutual fund denominated in pounds sterling, but whose underlying assets are all US stocks, therefore the underlying currency is US dollars.
Lets suppose now that, over the next year, the stocks in the fund have a performance of 5%, and that the pound sterling falls from 1.2 to 1.0 with respect to the US dollar (that is, if at the beginning of the year £1 = .2, at the end of it it's £1 = ).
Then, by the end of the year, the mutual fund gross return would be 5 + 2 = 7%, in other words, £700 (without taking into account fees, taxes etc.).
Is the above correct?
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gbp = 10000
usd = 1.2 gbp = 12000
future value
fv = 1.05 usd = 12600
FX is now on parity so the Sterling gain is £2600
Sterling rate of return is 12600/10000 - 1 = 26%
So not 0.05 + 0.2 = 0.25
but (1 + 0.05)*(1 + 0.2) - 1 = 0.26
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