# Fama-French 5 factor model interpretation of coefficients

I run a regression of the excess return of a company on the 5 Fama-French factors, I obtained the beta coefficients, but I am struggling to understand the meaning of my results. For example, what does a negative beta coefficient for the SMB factor mean? Or what does a big positive beta for the HML factor mean? etc. Thank you.

## 3 Answers

The coefficients of a linear model like this indicate the extent to which the excess return is explained by the corresponding variables. A negative coefficient for the SMB factor would indicate that the excess return is in part, due to the size of the company. In particular, it would indicate that the excess return was achieved because the company was large. Similarly, a large, positive coefficient for the HML factor would indicate that the excess return is due to the company’s high book-to-market equity value. The same kind of interpretation holds for the rest of the variables in the model.

• This isn't technically true, your first sentence in particular. Aside from R-squared, the coefficient of determination, regression models don't attempt to assess the degree to which dependent variables are explained by independent variables. As a simple example, consider the FF 5-factor versus a regression of only three of its factors. Coefficients will obviously vary between the two sets of shared factors, despite model inputs being otherwise identical...that doesn't mean a given factor explains more or less in one model to the other, just that their relationship in each model changed. – Chris Apr 9 '19 at 18:39
• I’m happy to look at a proof, but I don’t read comments that start with telling me that something isn’t “technically true”, then follows up with a hand-waving, intuitive explanation. – vrume21 Apr 11 '19 at 21:34

Classically, a regression model tells us, for a one unit change in an independent variable, how much will our dependent variable will change. This is obviously dependent on model specification (ie, 3- v. 5-factor model will give different coefficients).

This is no different in your case--a negative SMB coefficient indicates, given your specified model, that your portfolio is negatively exposed to the FF Size factor (eg, for a 1% return by the Size factor, you can expect your portfolio to return beta(SMB)*1%). A big positive beta means something similar. For a large beta, your portfolio is highly positively exposed to it--for a 1% return to the FF Value factor, your portfolio is expected to return beta(HML)*1%.

I suppose a negative beta coefficient for the SMB factor means that we have more of large cap stocks and hence if size factor works our portfolio will lose. Correct me if I am wrong please.