Hedging Cross-Currency Assets in a Return Regression

Summary

The document addresses a hedge regression in which the target asset is quoted in US dollars while candidate hedge assets are quoted in euros. Its suggested approach is to express returns in the investor’s local currency and hedge the foreign-exchange exposure of the euro positions. This makes the currency treatment explicit rather than leaving FX effects embedded ambiguously in the regression inputs.

The answer notes that hedging the currency exposure adds a drift component related to the difference between the currencies’ short-term interest rates. It summarizes the resulting portfolio as the dollar asset, euro-denominated hedges, and an FX hedge for those positions. This is a concise industry-practice suggestion, not a full implementation guide: it does not specify hedge instruments, rebalancing frequency, estimation choices, or evidence comparing alternative regression conventions. The appropriate setup still depends on the hedger’s local currency and intended FX exposure.

Key ideas

• Expressing all asset returns in the local currency makes the currency basis of the regression consistent.
• Foreign-currency hedge positions generally require a corresponding FX hedge if currency exposure is not intended.
• An FX hedge adds a drift related to the difference in short-term rates between the currencies.
• The suggested portfolio combines the target asset, foreign-currency hedges, and an FX hedge.

Tags

# Currency conversion in return regression model


# Currency conversion in return regression model












If I want to hedge a position (in the sense of replicating the returns as best as possible), but the asset is quoted in USD and my basket of possible hedges are all in EUR, do I need to convert my hedges to USD before calculating the returns or am I introducing currency risk/effects when doing that? Alternatively, I could do my regression of returns in USD on the returns in EUR of my hedges and then rescale the final betas by the fx rate? Or I could just ignore all fx conversion and regress returns of the asset in USD on those in EUR and leave it at that - what is the approach in the industry for this problem? Thanks

## Answer by Chris Taylor (score 3, accepted)

https://quant.stackexchange.com/a/82064

Generally you assume that you are going to hedge all FX exposures into your local currency. This allows you to use local currency returns for all assets, remembering that you will pick up a drift term from the FX hedge which is equal to the difference in short rates between the currency being hedged and the currency being hedged into.

So your final portfolio would look like "USD Asset" + "EUR hedges" + "FX hedge for EUR hedges".

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.