Currency Alignment and Construction of Fama-French Value Factors
Summary
The discussion examines whether European stock portfolio returns should be converted to euros before regression against Fama-French factors reported in dollars. It first points out that a portfolio of ten high book-to-market stocks is not constructed like the standard HML factor, which uses long and short value and growth portfolios, size groups, and data-based breakpoints. A concentrated long-only portfolio may also retain substantial stock-specific risk.
For comparisons between European and US factors, the answers distinguish studying how the factors co-move from estimating a European portfolio’s exposure to US factors. Currency conversion can put return series in the same unit, but does not guarantee a one-to-one factor relationship; exchange rates may have independent drivers. The conversion formula is described as correct for that purpose, while a separate answer cautions that risk-free rates differ across currencies and questions converting the whole factor set. The discussion is an informal exchange rather than a tested empirical analysis, and it does not resolve which currency convention fits every research hypothesis.
Key ideas
- A value-mimicking portfolio should reflect both long value and short growth exposure.
- Fama-French portfolio construction uses size groups and breakpoints derived from the relevant stock universe.
- A small, concentrated portfolio can show substantial stock-specific variation.
- Currency conversion aligns return units but does not imply that factors across markets move in lockstep.
- Risk-free rates vary by currency, complicating the interpretation of converted factor returns.
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Full text
# Fama-French Factors in € # Fama-French Factors in € I am having a bit of a problem with currency conversion issues. What I do: I sort European stocks based on their book-to-market ratio, each year I form a portfolio (equal-weight) with the 10 stocks that have the highest book-to-market ratio. I calculate the return on that porfolio in Euros. So basically I am constructing a factor-mimicking portfolio. Then I download the Fama-French Factors from Kenneth French's website. I am planning to run a time-series regression of my portfolio returns on the factors to see whether my portfolio indeed has a exposure to the value factor (I hope so) and/or whether it has exposure to other factors as well. However, the FF factors are generally calculated in USD as far as I understand, so I converted the returns of the factors into € using: return in € = (1+return in $)*(1+currency_return) - 1 where currency return is E/USD in t divided by E/USD in t-1, minus 1. If I then run the time-series regression, I get no (significant) exposure to the value factor but significant exposures to the market (positiv), size (negativ, but that's because I filtered out a lot of small stocks I guess), momentum (negativ). So that's weird?! If I run the time-series regressions with the original factor returns calculated in USD, everything works -- significant positive exposure to HML. No exposure to WML or SMB. But I am pretty sure it's technically incorrect because of the currency issue... ## Answer by Uditg_ucla (score 2) https://quant.stackexchange.com/a/24310 There are a couple of things that I'd like to highlight in your approach to forming a factor-mimicking portfolio: (a) Fama-French (FF) construct a long-short portfolio of stocks, and not just a long portfolio, as you have indicated. Here is the formula from Kenneth French's website HML = 1/2 (Small Value + Big Value) - 1/2 (Small Growth + Big Growth) (b) To put stocks into 'small' 'big' / 'value' 'growth' ' neutral' buckets - they use yearly breakpoints calculated from the data itself (again, you can read up more on this on their website). (c) Including just '10' stocks may not be the right approach, since you're aiming for a diversified portfolio, which serves as a proxy for value factor. However, with such a small number of stocks, you're likely to pick up (in your return series), stock specific idiosyncrasies. Once you've followed these steps, you'll essentially have a value factor mimicking portfolio for Europe (constructed in was similar to FF's). Next, if you are interested in learning whether the value factor in Europe covaries/ moves together with that in the US - you could plot/ regress/ calculate correlation/ calculate moving correlation etc. on the two return time series, to get better insights. Its not obviously clear to me why you'd want to convert return series to another currency for this sort of analysis. However, if you want to check whether European portfolio has exposure to US factors, you should be mindful that you might implicitly be assuming a much stricter relationship - a certain lock-step between the two economies and common underlying risk factors (that investors get compensation for). Also, this might imply that exchange rate is just a by-product of these two equity markets (while in reality, it has independent drivers of its own). Whatever your hypothesis, if you need to convert both time series to the same currency, your formula is correct. I'm just trying to highlight that going into your analysis, you should not expect a one-to-one relationship. Hope it helps. ## Answer by ThePunisher (score 0) https://quant.stackexchange.com/a/46772 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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