# 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 = \$1.2, at the end of it it's £1 = \$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?

• £1 = \$1.2 to £1 = \$1 is a 16.67% fall of the pound, or 20% appreciation of the dollar. May 26, 2020 at 11:00
• @base64 Edited to fix the wrong expression. May 26, 2020 at 11:18
• So are you asking whether it would be 5 +16.67% or 5 +20%? May 26, 2020 at 11:19
• @base64 The specific question would be if the above calculation is correct, which I see now it's strongly wrong May 26, 2020 at 11:41

``````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`

• Under what circumstances is Linear Approximation / Fisher Equation acceptable? May 26, 2020 at 11:32
• Under the condition that both the FX rate change and the fund performance "are fairly small", as explained here: en.wikipedia.org/wiki/Fisher_equation#Derivation May 26, 2020 at 11:38