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Say you you invest x euros at t0 in a mutual fund through a European exchange. After ten years, at t1, the investment doubles to 2x euros.

Would you end up with the same amount of euros at t1 if you converted x euros into dollars at t0, purchased shares in the same mutual fund through an American exchange at t0, sold them for dollars at t1, and then exchanged them to euros at t1?

These two sources claim that indeed you would end up with exactly the same amount of 2x euros either way, but I don't understand why that is:

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You can think of the ETFs as a currency of its own. So EUR>ETF then ETF>EUR is the same as EUR>USD>ETF, then ETF>USD>EUR.

In both cases, the money only spends the time between t0 and t1 while in this "ETF currency", and (almost) no time in EUR or USD.

This is of course a simplification and reality is a little more complicated, but the general idea holds.

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In both scenarios, the amount of the ETF that you hold at t0 is the same. Once you've bought the ETF, the currency that you bought it in isn't going to change its movement. So in both scenarios, you end up with the same value of ETF.

  • I could see that being true until before the last step in the process: exchanging USD for euros again. If the exchange rate is not favorable, it would discourage you from changing to euros. But I think both articles there would be no unfavorable exchange rate at the end due to some mechanism I don't yet understand. – weltschmerz Apr 30 at 21:23
  • @weltschmerz The value of the ETF is the same in both cases, so the amount of Euros that you get for selling it is the same. Can you be more clear as to what you're confused about? – Acccumulation Apr 30 at 21:27
  • For example, does this mean for a European mutual fund that when its value is determined at the end of the day, the same fund's value in USD traded at an American exchange is calculated by taking that value times that day's exchange rate? – weltschmerz May 2 at 4:32
  • At the end of each day, that is. – weltschmerz May 2 at 4:40
  • I'm basically trying to find variables that I could change that would break this :) Another is this: would it still work if you invested not in a European fund, but an Asian one, all else being equal? – weltschmerz May 2 at 4:40

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