Fama and French Three Factor Model


What is Fama and the French three-factor model?

The Fama and French Three-Factor Model (or Fama French Model for short) is an asset pricing model developed in 1992 which broadens the asset price capitalization (CAPM) model by adding significant risks and value risk to the market risk factor in CAPM. This model recognizes that value and small cap stocks regularly outperform the markets. By including these two additional factors, the model adjusts to this trend of outperformance, which is considered a better tool to assess the performance of managers.

Key points to remember

  • The French Fama 3-factor model is an asset pricing model which extends the fixed asset pricing model by adding size and value risk factors to market risk factors.
  • The model was developed by Nobel laureates Eugene Fama and his colleague Kenneth French in the 1990s.
  • The model is essentially the result of an econometric regression of historical stock prices.

The formula of the French Fama model is:


RItRFt=αIt+β1(RMtRFt)+β2SMBt+β3HMThet+εItor:RIt=total return of a stock or portfolio I at the time tRFt=risk-free rate of return at the time tRMt=total market portfolio return at time tRItRFt=expected excess returnRMtRFt=excess return from the market portfolio (index)SMBt=premium size (small less large)HMThet=value premium (high less low)β1,2,3=factor coefficients begin {aligned} & R_ {it} – R_ {ft} = alpha_ {it} + beta_1 (R_ {Mt} – R_ {ft}) + beta_2SMB_t + beta_3HML_t + epsilon_ {it} \ & textbf {where:} \ & R_ {it} = text {total return of a stock or portfolio} i text {at the moment} t \ & R_ {ft} = text {rate of risk-free return at time} t \ & R_ {Mt} = text {total return on the market portfolio at time} t \ & R_ {it} – R_ {ft} = text {expected excess return} \ & R_ {Mt} – R_ {ft} = text {excess return of the market portfolio (index)} \ & SMB_t = text {size premium (small minus big)} \ & HML_t = text {value premium (high minus low)} \ & beta_ {1, 2,3} = text {factor coefficients} \ end {aligned}

TheRItTheRFtThe=αItThe+β1The(RMtTheRFtThe)+β2TheSMBtThe+β3TheHMThetThe+εItTheor:RItThe=total return of a stock or portfolio I at the time tRFtThe=risk-free rate of return at the time tRMtThe=total market portfolio return at time tRItTheRFtThe=expected excess returnRMtTheRFtThe=excess return from the market portfolio (index)SMBtThe=premium size (small less large)HMThetThe=value premium (high less low)β1,2,3The=factor coefficientsTheThe


Fama and the French three-factor model

How the French Fama model works

Nobel Prize winner Eugene Fama and researcher Kenneth French, former professors at the University of Chicago’s Booth School of Business, have attempted to better measure market returns and, through research, have found that valuable stocks outperform growth stocks. Likewise, small cap stocks tend to outperform large cap stocks. As a valuation tool, the performance of portfolios with a large number of small cap or value securities would be less than CAPM As a result, the three-factor model adjusts downward for the observed performance of small caps and value stocks.

The Fama and French model has three factors: the size of the companies, the market values ​​and the excess return on the market. In other words, the three factors used are SMB (small less big), HML (high less) and the portfolio return minus the risk-free rate of return. SMB represents publicly traded companies with small market capitalizations that generate higher returns, while HML represents value stocks with high book-to-market ratios that generate higher returns relative to the market.

There is much debate as to whether the trend of outperformance is due to the efficiency or ineffectiveness of the market. In support of market efficiency, outperformance is generally explained by the excessive risk that securities and small caps run due to their rise cost of capital and greater commercial risk. In support of market inefficiency, the outperformance is explained by the fact that market participants incorrectly assess the value of these companies, which provides long-term excess return as the value adjusts. Investors who subscribe to all of the evidence provided by the Hypothesis of efficient markets (EMH) are more likely to agree with the efficiency aspect.

What the French Fama model means for investors

Fama and French stressed that investors must be able to overcome the additional short-term volatility and periodic underperformance that could occur in a short time. Investors with a long-term horizon of 15 years or more will be compensated for short-term losses. Using thousands of random stock portfolios, Fama and French conducted studies to test their model and found that when the size and value factors were combined with the beta factor, they could then explain up 95% of the return of a diversified equity portfolio.

Given the ability to explain 95% of a portfolio’s return relative to the market as a whole, investors can build a portfolio in which they receive an expected average return based on the relative risks they assume in their portfolios. The main factors behind expected returns are market sensitivity, size sensitivity and sensitivity to value stocks, as measured by the book to market ratio. Any expected average additional return can be attributed to an unassessed or unsystematic risk.

Fama and the French five-factor model

Researchers have expanded the three-factor model in recent years to include other factors. These include “momentum”, “quality” and “low volatility”. In 2020, Fama and French adapted their model to include five factors. Along with the three original factors, the new model adds the concept that companies that report higher future profits have higher returns on the stock market, a factor called profitability. The fifth factor, called investment, relates to the concept of internal investment and return, which suggests that companies that direct their profits towards major growth projects may suffer losses on the stock market.

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