The Fama-French 3-Factor Asset Pricing Model

The Fama-French 3-Factor Asset Pricing Model

The Fama-French 3-factor asset pricing model was developed in 1992 by Eugene Fama and Kenneth French. This model is an extended version of the Capital Asset Pricing Model (CAPM), published in 1964. The CAPM was a single-factor model based only on market risk. However, when this model was tested empirically, it could explain 70% of the change in the rate of return. Fama-French extended this model by adding two more factors. First, they noticed that small firms performed higher returns than larger firms. Second, they found that companies with a low book value-to-market ratio (value stocks) yield better returns than companies with a high book value-to-market ratio. Of course, they made these observations by looking at historical data in the US capital markets.

The Fama-French model

You can see the Fama-French 3-factor asset pricing model in the image below. The left side of the equation shows the expected excess return of the portfolio relative to the risk-free asset. This model explains the excess return in question with three factors:

  1. The market factor
  2. The scale factor (SMB)
  3. The value factor (HML)

The epsilon at the end represents the part of the change in our dependent variable that these factors cannot explain. Fama and French subjected this model to regression analysis using historical data. Accordingly, they concluded that these three variables explain the change in the rate of excess return obtained from the portfolio by 90%. If we remove SMB and HML from the model, CAPM remains. CAPM, on the other hand, explains the change in the variable in question by around 70%, as I mentioned above. Also, the parameters (b1, b2, and b3) estimated by regression within the model are positive. Let’s also note that Fama and French randomly created thousands of portfolios and tested the model. You can access the dataset on Kenneth French’s website.

The Fama French 3 factor model
The Fama-French 3 factor model

Scale factor

The SMB factor implies smaller companies provide higher returns than those with large market capitalization. According to the Fama-French model, if more small-scale companies are in your portfolio, your expected return rate will be higher in the long run. Technically speaking, the predicted beta2 coefficient of SMB is positive. In other words, such a portfolio is expected to earn higher returns than the market’s average return in the long run.

Value factor

The HML variable, also called the value premium, shows the difference in the rate of return between value stocks and growth stocks. According to the Fama-French model, the return performance of value stocks is expected to be higher than the return performance of growth stocks. Again, value stocks mean companies with a lower book value than market value. It is usually measured by the ratio of book value to market value. The stock becomes cheaper than its intrinsic value if this ratio is large. On the contrary, if the book value to market value is small, it is called a growth share. That is, market players see the company’s future as bright and pay an additional premium for the extra profits they anticipate. Therefore, the company’s market value is more significant than its book value.


There are differing opinions on why portfolios with small market caps and value stocks outperform. Those close to the efficient market hypothesis believe that such firms offer higher returns due to higher cost of capital and higher operational risk. Others argue that the market is mispricing these companies while it will correct that in the long run.

Factor wars

In fact, there is more than you see. Behind the scenes, there was a desire to correct CAPM, which was very elegant in theory. At the same time, it was not very useful in practice. Fama-French’s concern was to explain the observed anomalies (small companies and value stocks) within the scope of the efficient market hypothesis. This is why they developed the 3-factor model. Later, some researchers tried to use this model to measure the performance of portfolio managers. The result was that the performance of good portfolio managers continued to be good. In contrast, the bad ones continued to be wrong. Unfortunately, these empirical results were inconsistent with the efficient market hypothesis.

Carhart’s momentum factor

Then, in 1997, Mark Carhart added the momentum variable and created a 4-factor model. Momentum was a variable that reflected the upward trend in the prices of successful stocks in the recent past. The explanatory power of this model was higher than the 3-factor model. He was also quite good at explaining the performance of securities fund managers with stock returns. But this model ignited factor wars because the investment strategy based on past prices (momentum) weakened the efficient market hypothesis.

Neoclassical q-factors

In the following years, a new model emerged from the field of business finance, combining theory and empirical studies. In 2007, Lu Zheng and Long Chen introduced the model that includes two additional factors: return on investment and return on equity. They also refined their approach, which they called neoclassical q-factors, with new papers. Although, this team seems to have had some difficulty expressing their ideas and publishing their articles. 🙂 Nevertheless, Fama-French could not remain indifferent to these developments and published their 3-factor models in 2014 by converting their 3-factor models to 5-factor, including very ‘similars’ of these two variables.

Return of value factor

The debate is not over here, of course. The investment and profitability factors added by Fama-French made the value factor in the 3-factor model unnecessary. The other team in the competition for the new asset pricing model suggested that both the value factor and the momentum factor can be explained by q-factors. So these two variables were not needed.

Cliff Asness of Applied Quantitative Research Capital Management had no reason to let these teams down the value factor. First, he repeated Fama-French’s 5-factor model study with his team. Later, he added Carhart’s momentum variable to this model and developed a new model with 6 factors. The explanatory power of the new model was better, but the value factor still seemed unnecessary.

At this point, Cliff Asness did not give up. Instead, he questioned what constitutes the concept of ‘value.’ Fama and French created the HML variable using book value and price information. However, they used the data with a 6-month delay due to the lack of accounting records. According to Asness, this didn’t make sense because they had up-to-date pricing information. Asness reworked its 6-factor model, recreating the HML variable to reflect current price data. This time the value factor was not in vain! Moreover, the momentum variable also seemed much more effective. By the way, let me point out that Cliff Asness is Eugene Fama’s former Ph.D. student.

In conclusion

I was interested in factor models for a while. I did some research and read whenever I got the chance. So I tried to increase my knowledge. I also shared with you what I learned. Because the more I write, the better I understood the subject. Besides, there is a concept called factor investment. With the influence of these theoretical and empirical studies, new investment styles are created. As an investor, I think it wouldn’t hurt to know what these guys mean. By the way, I hope I didn’t bore you.

See you in the following article.


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