# Fama French model-small market beta (weird)

I am analyzing if good governance portfolios outperform bad governance portfolios. After dividing firms with good governance into one pf and bad ones into another for European companies I tried to run the regression of excess monthly returns on the Fama an French factors (from the official library). I have 3 portfolios and I obtain for each a market beta smaller than 0.5 which tells me that my sample is much less volatile than the market, which makes no sense. Any suggestions ? Please

• What is being used as "the market" in this calculation? Is it the CRSP MW index or something else? – Alex C Jun 13 '15 at 16:17
• Thanks a lot for your reply! Well that is the problem , I am not sure since I downloaded the Rmkt-Rf from the website.They do not really mention it. In the description they only mention the countries involved in constructing the factors. However, now I saw that the factors are in US dollars, but my returns are in Euros so maybe i should exchange my stock prices first and recalculate the returns. Do you think that the problem lies here? – Larisa Jun 13 '15 at 16:38
• I've added an answer, but of course you should convert everything in the same currency. The issue here is that the risk free return for Fama-French is a risk free for US investors, while you may be interested in a risk-free return for a European investor (e.g. something like German 3months bund). On the other hand, the safest thing to do is to run everything from the perspective of an american investor and convert your portfolios in dollars, even though there may issue too, if american investors are just a small fraction in your market. – fni Jun 13 '15 at 17:25
• @franic thanks a lot! I thought about downloading monthly exchange rates and convert my monthly prices and after calculate the returns and run the regression. what do you think? – Larisa Jun 13 '15 at 17:31
• Did you try to estimate betas on the basis of CAPM for comparison? I would be interested in the result. – vonjd Jun 14 '15 at 15:45

Market beta just tells your portfolio has low covariance, scaled by variance, with the market. Remember that $$\beta= \frac{Cov(x,y)}{Var(x)} = \rho\frac{\sigma_x \sigma_y}{\sigma_x^2}=\rho\frac{\sigma_y}{\sigma_x}$$ You can see that it well may be that $\sigma_x<\sigma_y$ but $\rho$ is small enough to have a beta of 0.5. By the way, you can directly check whether the sample variance of your portfolios is smaller than the sample variance of the market.

What in general happens with Fama-French factors, to be fair with many other factor models, is that market betas tend to be close to one. But i don't see any problem with the fact you have a beta of 0.5

• I replied above :) – Larisa Jun 13 '15 at 17:32

I am afraid you are missing something (as a lot of people) about beta computation and meaning:

The model you are fitting links the returns of a market factor $r_m$ with your returns $r_g$ thanks to a linear relationship:

$$r_g = \beta \;r_m + \epsilon_{m,g}.$$

As you can see, it does not say the volatility of $r_g$ can be deduced from the one of $r_m$ using $\beta$: you forgot the volatility of $\epsilon_{m,g}$, which is the idiosyncratic part of $r_g$ seen from your market factor $r_m$.