Interpreting Fama–French Five-Factor Regression Betas
Summary
The document explains how to interpret coefficients from a regression of a company’s or portfolio’s excess return on the five Fama–French factors. Each beta describes exposure to its corresponding factor within the specified regression: a negative SMB coefficient indicates negative exposure to the size factor, while a positive HML coefficient indicates positive exposure to the value factor.
The answers illustrate this interpretation by relating a one-percent factor return to an expected portfolio return scaled by the estimated beta. A negative SMB loading is associated with larger-company exposure, and a positive HML loading with higher book-to-market exposure. These are conditional regression interpretations, not proof that a factor caused realized excess returns. Coefficients may change with model specification, such as using a three-factor rather than five-factor model, and the document does not address statistical significance or estimation uncertainty.
Key ideas
- A factor regression beta measures the modeled return exposure to its associated factor.
- A negative SMB beta indicates negative exposure to the size factor and is consistent with large-cap exposure.
- A positive HML beta indicates positive exposure to the value factor and higher book-to-market exposure.
- The expected return contribution for a factor move scales with its estimated beta.
- Factor beta interpretations depend on the regression specification and do not establish causation.
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# Fama-French 5 factor model interpretation of coefficients # 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. ## Answer by vrume21 (score 1) https://quant.stackexchange.com/a/44487 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. ## Answer by Chris (score 1) https://quant.stackexchange.com/a/45018 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%. ## Answer by Harsh Surana (score 0) https://quant.stackexchange.com/a/45085 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.
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