Currency Consistency in Fama–French Factor Regressions

Summary

The document raises a currency alignment issue in testing whether portfolio returns earned by a Danish investor are explained by European Fama–French three-factor returns supplied in US dollars. It reports two attempted specifications: regressing Danish-krone portfolio returns directly on the dollar factor series, and converting portfolio prices to dollars before calculating returns and regressing those returns on the same factors. The reported alpha differs substantially between the two approaches, while the first regression also shows exposure to size and value factors.

No answer or definitive recommendation is included, so the examples should be read as an unresolved research question rather than guidance. The comparison illustrates that currency conversion changes the return series and may affect estimated alpha and factor loadings. A valid interpretation would need to ensure the portfolio and factor returns use compatible currency conventions and timing, and to state any currency exposure assumptions. The document does not provide a tested solution or resolve whether either specification is appropriate.

Key ideas

• The question concerns explaining Danish-krone portfolio returns with factor returns denominated in US dollars.
• The author compares regressions using local-currency returns and returns converted into dollars.
• The two attempted specifications report different alpha estimates and significance levels.
• Currency conversion changes the return series and can affect regression results.
• The document does not resolve which specification is appropriate.

Tags

# Regressing non-USD returns on FF 3-factor returns


# Regressing non-USD returns on FF 3-factor returns












I am analysing some portfolio returns from the perspective of a Danish investor, i.e. in the local currency, DKK.

I want to regress portfolio returns in DKK on the returns of a 3 factor Fama & French model.

The only factor returns I can find on Ken French's website are all denominated in USD, even the European factors he has at: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#Developed

What is the right approach to see if portfolio returns in other currencies than USD are explained by FF factors?

Some ideas and the result of attempting them:

- Regress portfolio returns in DKK on the European 3 factor returns (which is denominated in USD). Result: Positive alpha with p=0.057 (so significant on a 10% level), but also significantly exposed to SMB and HML

- Convert daily portfolio prices to USD (using the fx rate of a given day) and recalculate returns. Then regress these returns (now on a USD base) with European 3 factor returns (still denominated in USD). Result: No alpha (p=0.82)

Please help me understand if either of these are the correct approach, or if there is another, better way. Also, do I make any assumptions unknowingly when calculating to USD?

Cheers

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