# Fama-French 3-factor model: factors implying risk

The Fama-French three-factor risk model is given by $$r=R_f+\beta_m(K_m-R_f) + \beta_s\cdot\mathit{SMB}+\beta_v\cdot\mathit{HML}+\alpha$$ where $r$ is the return, $R_f$ is the risk-free rate, $K_m$ is the market return, $SMB$ is the Small Minus Big factor and $HML$ is the High Minus Low factor. $\alpha$ and the $\beta$'s are estimated from the data and $\alpha$ can be interpreted as excess return not explained by the model.

Both $\beta_s$ and $\beta_v$ are highly significant and thus the CAPM (where $\beta_s = \beta_v = 0$) does not hold. This result can be explained in the two ways: the first is that this is a stock pricing anomaly and $\alpha$ can be obtained. This does not seem to be the case as the anomaly has persisted.

The second is that investing in small cap or value stocks carries extra risk and that the FF 3-factor model just explains risk better than the CAPM does. This interpretation is in line with semi-strong EMH but does not satisfy me. Why should small cap or value stocks be more risky? Economists can come up with all kinds of interesting narratives but have these narratives been tested quantitatively? And what were the results?

• This question is part of this weeks topic challenge, see meta.quant.stackexchange.com/q/1369/35?cb=1 for more info. – Bob Jansen Oct 20 '13 at 11:33
• I think small cap indices get raped the most during crises. – user2763361 Oct 23 '13 at 13:31
• That would be quite easy to show statistically and I guess that result would be well known in that case. – Bob Jansen Oct 23 '13 at 19:01
• This holds for Australia (just knowledge from my work); but would be interesting to see for other countries. – user2763361 Oct 24 '13 at 1:07