Convert USD Investment Returns into EUR Using Historical Exchange Rates

Summary

The document describes how to express an unhedged US investment’s performance in euros. First, turn the dollar return series into a total-return price index, using an arbitrary starting value such as 100. Next, convert each index value into euros using the corresponding historical EUR/USD exchange rate, with the quote convention applied consistently. Finally, calculate ordinary period returns from the euro-denominated index. This approach incorporates the exchange-rate movement into the investor’s euro return rather than removing currency exposure through a hedge.

An algebraic expression for the resulting return is also given, combining the dollar gross return with the ratio of exchange rates across adjacent dates. The index procedure is offered as the more intuitive way to perform the conversion. No performance data or worked series are supplied, so the explanation is conceptual. Accurate results depend on aligning dates and using exchange rates whose quotation direction matches the conversion.

Key ideas

• Build a total-return index from the investment’s dollar returns before converting currencies.
• Convert each index observation into euros using the matching historical exchange rate.
• Calculate euro returns from successive values of the converted index.
• The resulting euro return includes currency movements and does not represent a hedged return.
• The exchange-rate quote direction and date alignment must be handled consistently.

Tags

# translating performance from EUR to USD


# translating performance from EUR to USD












can someone please let me know how to translate a performance return from USD to EUR. For instance, I have a time series (return) over 7 years from an US hedge fund and would like to translate it into EUR return. I am not interested in any form of hedging, I just need the return to be denominated in EUR

Thank you very much!

## Answer by nbbo2 (score 1, accepted)

https://quant.stackexchange.com/a/29799

First you build a total return index for the HF starting at say 100 so it might look like {100,105,...} if the first period return is 5% etc. These are the dollar amounts owned by an US investor who started with 100 USD.

Then you translate these numbers into EUR by dividing by the time series of historical EURUSD exchange rates which might look like {1.3125,1.2745,...).

Then you compute the EUR returns from these EUR prices by the usual formula $\frac{P_{t+1}-P_t}{P_t}$

P.S. If you do the algebra on the above procedure you will see that the EUR returns are $-1+\frac{e_{t-1}}{e_t}(1+r_t)$ for t = 1 to n, which however may be more difficult to remember than the straightforward steps above.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.