Fama French Models Beta

Can someone clarify on the meanings of the 3 Betas for the Fama - French model? How can the betas be used to determine if it is a large cap, growth value etc

The Fama-French model is:

E® = R_f_ + α + β_mkt_(R_mkt_ – R_f_) + β_sml_(SML) + β_hml_(HML)


  • β_sml_ > 0, then the portfolio has higher expected returns if small-cap stocks outperform large-cap stocks, suggesting that the portfolio is predominantly small-cap stocks
  • 0 > β_sml_, then the portfolio has higher expected returns if large-cap stocks outperform small-cap stocks, suggesting that the portfolio is predominantly large-cap stocks
  • β_hml_ > 0, then the portfolio has higher expected returns if high book-to-market (i.e., value) stocks outperform low book-to-market (i.e., growth) stocks, suggesting that the portfolio is predominantly value stocks
  • 0 > β_hml_, then the portfolio has higher expected returns if low book-to-market (i.e., growth) stocks outperform high book-to-market (i.e., value) stocks, suggesting that the portfolio is predominantly growth stocks

Thank you S2000 !

My pleasure.

S2000 magician with all due respect,is alpha included in the formula ? I didn’t find the same in curriculum----

I don’t have a copy of the curriculum, but every other formulation I’ve seen has alpha in it; I don’t see how you can have a proper formulation _ without _ alpha. Nevertheless, if alpha isn’t in the curriculum’s formula, then cross it out from what I typed. The answer to the original question’s still the same.

You are actually a magician. Trust me. I was trying to cram up this formula for consecutive days, but I didn’t understand anything. Now that I read it again with a different perspective, I get it. Fama-French boils down to including small cap/ large cap and value/growth funda, in addition to the basic CAPM approach. Wonderful! I guess that nails it into my head for sometime.

What is the logic behind baseline value of Beta SML and Beta HML being equal to zero? Also, why would an investor demand a risk premium for value stocks over growth stocks? Beta SML should then be mostly negative because growth stocks are more rosky comapared to value stocks. Also, isn’t this an anomaly that growth stocks are more risky as compared to value stocks? Will you really factor in an anomaly into a model? What am I missing?

Think of the betas as sensitivities to factors. The factors are empirical - historically, value stocks have outperformed growth stocks (i.e. HML is positive) and small stocks have outperformed large stocks (SML is positive). A positive beta on HML means that your portfolio has a positive relationship with the value premium. In other words, your portfolio behaves like one with exposure to value stocks. If the beta were zero, it’s “Value vs growth stock neutral”, and if it were negative, it behaves more like a growth stock portfolio.

The empirical fact that value stocks have historically outperformed growth stocks (and small stocks have outperfomed large ones) has been pretty robust - it’s been found internationally as well as domestically. The “why” behind that is something pointy-headed academic nerds like myself have written a lot of papers on. And the jury is still out.

The key is that the FF model is an empirical one, and that we’re still trying to determine what theories best fit the pretty robust empirical fact.

So, you are saying HML is always positive? (Empirically speaking?)

HML and SML have been positive (i.e. the value and size premiums held) in most periods, but not all.

Cool. You have my respect. Thank you so much busprof.