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Currency Choice for Regressing on Global Fama–French Factors

Article Quant Q&A · Author: T. Becker
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Summary

The discussion asks whether USD-denominated global Fama–French daily factor returns can be converted into euros by multiplying gross returns by the change in the exchange rate. The answer recommends converting the global portfolio returns into USD and running the regression against the published USD factors. It explains that the global factor portfolios and their sorting breakpoints are constructed using US-dollar measurements, so converting only the factor returns may mismatch the portfolio definitions and distort estimated exposures.

The response says this USD approach aligns the analysis with the perspective used to build the factors and supports comparison with US-based empirical studies. For a country-specific analysis, it describes a different approach: reproduce the Fama–French methodology using local-currency measurements and derive local factors. The discussion also notes that risk-free rates differ across currencies, reinforcing that currency conversion alone may not produce economically equivalent factors. It offers methodological guidance rather than data or an empirical comparison, and the preferred currency depends on the research question and portfolio being studied.

Key ideas

  • Global Fama–French factors are constructed using US-dollar measurements and breakpoints.
  • Converting only the factors to euros can mismatch their construction with the global portfolio being regressed.
  • The response recommends expressing global portfolio returns in USD when using the published global factors.
  • Country-specific research can instead replicate the factor methodology using local-currency data.
  • Risk-free rates vary by currency, so currency conversion alone does not make factor sets equivalent.

Tags

EquitiesFactor investingStatisticsForex
Full text
# Transform Fama French Returns to Euro


# Transform Fama French Returns to Euro












I constructed a global portfolio and calculate it's daily return in Euro.

Now i want to do the regression with the Fama-French daily factor-returns (HML, SMB). However, these returns can only be found in USD on their website.

Can I simply convert the daily Fama-French returns into Euro with the following formula:

$$(1+r_{\mathrm{EUR}}) = (1 + r_\mathrm{{USD}}) \cdot (1+ r_{\mathrm{currency}})$$

where $r_{\mathrm{currency}}$ equals EUR/USD in time $t$, divided by EUR/USD in $t-1$, minus 1.

## Answer by skoestlmeier (score 3)

https://quant.stackexchange.com/a/42830

#### I would recommend you to convert your global portfolio returns into US-$

Kenneth French provides several global factor-returns for the entire global stock market of developed countries. The description states, that

> all returns are in U.S. dollars, include dividends and capital gains, and are not continuously compounded.

Further:

> [...] The global portfolios use global size breaks, but we use the B/M breakpoints for the four regions to allocate the stocks of these regions to the global portfolios. [...]

So in fact, before calculating size- and book-to-market breakpoints, all these measures are converted into US-\$ instead of using local currencies. Therefore, i recommend you to convert your daily portfolio return into US-\$ (simple currency conversion) and apply your regression approach with US-$ portfolio returns. This is a common approach in international empirical research, as your results are based from the view of a US-investor and therefore your results are comparable to US-studies.

Furthermore, if you just convert the factor-returns from US-\$ into Euro, you would omit the fact, that the associated breakpoints and therefore the portfolio sort is based on variables measured in US-\$. This would bias your factor-exposure, so results are quite useless and not easily to interpret.

For local studies, it is often seen in some papers, that you use portfolio returns in local currency and replicate the Fama-French methodology for the specific country, i.e. you calculate your breakpoints in local currency and derive local factor-returns. However, for a global stock portfolio, this approach is quite inconvenient.

You may also take a look at this related question.

## Answer by ThePunisher (score 0)

https://quant.stackexchange.com/a/46773

Long story short...

Just think at the risk free rate (which is an essential part of Fama-French factors). It varies across currencies:

http://pages.stern.nyu.edu/~adamodar/pdfiles/DSV2/Ch6.pdf

You do not get the risk free of another currency just by converting the risk free of a currency. Hence, what are trying to do with converted Fama-French factors?

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