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I have a series of log returns calculated on an index that is priced in Euro terms, and I'd like to convert those returns into USD terms. Would it be mathematically correct to calculate log returns on a USD/EUR exchange rate and just add the returns from the exchange rate to my Euro-denominated returns in order to successfully convert them into USD?

So something like this?

Return(Euro Index) + Return(USD/EUR exchange rate) = Return(USD terms)

Thank you

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    $\begingroup$ Yes, you have the right idea, as you can prove by writing the dollar equivalent of the Eurostoxx value on day t, on day t+1, and then computing what is the log return from one to the other. You end up with the sum of two log returns, on the Eurostoxx and on the exchange rate. $\endgroup$ – noob2 Mar 6 at 2:54
  • $\begingroup$ That is the unhedged return. If you had a hedged return then the usd return would be similar to the eur return, adjusted for cross currency basis at inception. Usually the unhedged return is the one referenced $\endgroup$ – Attack68 Mar 6 at 17:57

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