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Converting Euro-Denominated Index Returns to USD Returns

Article Quant Q&A · Author: sa90210
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Summary

The document asks whether an index’s Euro-denominated log returns can be converted to USD-denominated log returns by adding the log returns of a USD/EUR exchange rate. It identifies the key operation to examine: combining the asset’s price change with the currency conversion over the same period. The exchange-rate quote convention matters, because the rate must express the number of USD per EUR for the proposed addition to represent conversion into USD terms.

The text provides no answer, derivation, data, or worked example, so it does not establish that the suggested calculation is correct. Any application would need consistent return intervals and a clearly defined exchange-rate direction; reversing the quote changes the sign of its log return. The document is therefore a focused question about currency-adjusted return measurement rather than a complete conversion method.

Key ideas

  • The question concerns converting index returns from euros into US dollars.
  • The proposed approach is to add the currency exchange rate’s log return to the index’s log return.
  • The exchange rate must be quoted in the direction needed to convert euros into dollars.
  • The document does not provide a derivation or answer.

Tags

ForexStatistics
Full text
# Converting Euro returns into USD terms


# Converting Euro returns into USD terms












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