# 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...

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.

• Hi, yes I know that it's not a 'real' factor mimicking portfolio. It was more sort of a quick and dirty try. I am not really interested whether the value factor in Europe comoves with the US -- I just downloaded the value factor etc for Europe (!) from the FF website. But that value factor is based on USD returns because I guess they just convert their raw data to USD and then do their sorting / calculate the factor return time series. My data is in € so it seems fishy to regress € returns on factors that are technically in USD (although they are, again, European factors). – marky2k Feb 15 '16 at 22:02
• Ok, so I understand the reason for conversion between currencies (which as I said, you're doing correctly). But given the way you have constructed your portfolio, I am not sure you should ex-ante expect it to have strong loading on FF's value factor! – Uditg_ucla Feb 16 '16 at 23:00