# How does the Fama and French 3-factor model explain stock covariance?

Does it at all? If so, how?

It is understood that size and value play a role in determining returns and there are proposed explanation those these, but what about covariance?

• You should include more content in your question -like describe the model you are talking about, if not writing it out mathematically, provide a link to where it is presented-discussed more extensively etc. "Help us help you", it is called – Alecos Papadopoulos May 3 '15 at 15:55
• I was assuming that someone with relevant the finance knowledge would be rather familiar with the 3-factor model and could therefore put in there 2 sense. – user4574 May 5 '15 at 1:54
• That's a kind thought, but no model is so engraved in stone that by just saying "3-factor model" even those with the relevant financial knowledge would know exactly what you are referring to -in fact, those people will exactly be the ones that they will clearly know that under every "model label", many variants are hosted. – Alecos Papadopoulos May 5 '15 at 2:01

As in the CAPM model the covariance among assets is reduced to $\beta$, through the covariance with the market index.
$\beta_i=\sigma_{i,M}/\sigma_M^2$
Then, if CAPM is correct, we could explain the covariance relating the $\beta$s
$\sigma_{i,j}=\beta_i*\beta_j*\sigma_M^2$
In the context of multifactor models something similar occurs, since, in order to use those models, it is necessary to estimate $\beta$s, or sensitivities, related to each proposed factors.