The Fama-French Three Factor model is a formula for calculating the rate of return on a given asset. Like many (if not most) such models, it offers an estimated value based on market factors at large. In this case, investors can predict their return on investment based on overall market risk, market size and market value. What follows is a description of how it works. Meanwhile, consider using the services of a financial advisor to make sure you’re taking full advantage of the most appropriate analytical tools.
The Fama-French Three Factor model is a formula to describe the rate of return on a stock investment. Developed in 1992 by then-University of Chicago professors Eugene Fama and Kenneth French, it is based on the observation that value shares tend to outperform growth shares and small-cap shares tend to outperform large-cap shares. Jumping on those observations the two economists developed their three-factor model as an expansion of the Capital Asset Pricing Model (CAPM). Rather than just gauge market risk as the CAPM does, the Fama-French Three Factor model adds value risk and size risk to the calculation.
The Fama-French Three Factor model calculates an investment’s likely rate of return based on three elements: overall market risk, the degree to which small companies outperform large companies and the degree to which high-value companies outperform low-value companies.
The model uses market capitalization to calculate a company’s size, comparing small-cap firms to large cap-firms. It uses book-to-market to calculate a company’s value, comparing high book-to-market value companies against low book-to-market value companies. Book-to-market is simply the inverse of the price-to-book ratio. This third element is used to distinguish value stocks from growth stocks.
The model is known as a three-factor model, in distinction to the CAPM, which only uses the single factor of market risk to calculate the likely return on investment.
In shorthand this model is expressed as:
Expressed as a complete formula the Fama-French Three Factor model is:
R = Rf + B1(Rm – Rf) + B2(SMB) + B3(HML) + a
In this expanded model we have added a few elements:
The market coefficients (B1, B2 and B3) set the Fama-French Three Factor model apart from its predecessor. In the CAPM, the return on investment is calculated using only one element and only one coefficient of risk. In fact, that formula is used as the basis for the Fama-French Three Factor model. The CAPM model is:
The Fama-French Three Factor model expands on this concept. Under the CAPM model, the return on your investment is estimated based entirely on overall market risk. The Fama-French Three Factor model estimates an investment’s return based on market risk, market size and investment value.
The CAPM makes up the first factor of the Fama-French Three Factor. Its central element, (Rm – Rf), is known as the “market risk premium.” It measures the returns you get by investing in the market (which carries the potential for loss) compared to the returns you would get by investing in a risk-free asset. This difference is your compensation for accepting the market’s risk of loss.
Typically when calculating formulas such as the CAPM and the Fama-French Three Factor model you will use the return on U.S. Treasury bills or bonds as the risk-free rate.
In the CAPM the beta variable, “B1” in the formula above, is calculated based on the volatility of the investment being measured. This represents the risks involved with that investment.
One of the two key observations of the Fama-French Three Factor model is that small firms tend – over the long term – to outperform large firms when it comes to stock market returns. This element of the model captures that observation.
The SMB factor of the Fama-French Three Factor model measures the degree to which small-cap companies have historically posted excess returns over large-cap companies. It helps to weight the model in favor of small-cap companies, as the Fama-French Three Factor model predicts that investment portfolios with smaller companies will have higher rates of return than portfolios with larger companies.
The SMB beta, “B2” in the formula above, is calculated based on assets in the portfolio being measured compared against small-cap/large-cap returns in the market at large. Generally speaking, a B2 value above zero indicates that return in the investment portfolio being measured is weighted toward small-cap stocks. (For more information on interpreting SMB beta values, see this paper.)
The second key observation in the Fama-French model is that firms with high book-to-market values tend to post stronger returns than those with low book-to-market values. This factor of the model captures that observation.
The HML factor of the Fama-French Three Factor model measures the average return on value portfolios (those with companies that have a high book-to-market value) against the average return on growth portfolios (those with companies that have a low book-to-market value). It helps to weight the model in favor of value stocks, as the Fama-French Three Factor model predicts that investment portfolios with value stocks will have higher rates of return than portfolios with growth stocks.
The HML beta, “B3” in the formula above, is calculated based on assets in the portfolio being measured compared against the value/growth stock returns in the market at large. Generally, a B3 value above zero indicates that the portfolio being measured is weighted toward high book-to-market stocks.
The SMB and the HML are historic market constants. In other words, at any given time you will use the same values for SMB and HML in any given Fama-French Three Factor calculation. At the time of writing, French posted a running calculation of the SMB and HML values on his website here and explained the formula for calculating them here.
The final variable of the Fama-French Three Factor model, “a,” represents the investment’s risk. This is more formally known as the investment’s alpha. This is a relatively rarely applied variable.
Alpha measures an investment’s ability to beat the market. If a given investment or portfolio manages to post stronger returns than comparable investments in the market at large, this investment has some value that an investor’s market analysis hasn’t captured. The same holds true in reverse for unexpectedly weak returns. This is expressed as the investment’s “alpha.”
In this case, if an investment performs more highly than the Fama-French model suggests, that means it posted returns stronger than an investor would expect based on the investment’s composition as compared to the market’s overall risk, size and value. (Again, the same would hold true in reverse.)
We would express this as the investment’s “alpha,” generally calculated as the percent by which the investment beat expectations. Absent specific reasons to believe that an investment will outperform or underperform the market, the alpha is generally not used in predictive Fama-French Three Factor models.
The Fama-French model is, in essence, a form of modified market constant. When running a Fama-French analysis, you take four constants into account:
The Fama-French Three Factor model is a formula for calculating the likely return on a stock market investment. It measures this return based on a comparison of the investment to the overall risk in the market, the size of the companies involved and their book-to-market values (the inverse of the price-to-book ratio). Its prediction that investments with smaller and more value-oriented stocks will generally post stronger returns over time has proven highly reliable over time.
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Eric ReedEric Reed is a freelance journalist who specializes in economics, policy and global issues, with substantial coverage of finance and personal finance. He has contributed to outlets including The Street, CNBC, Glassdoor and Consumer Reports. Eric’s work focuses on the human impact of abstract issues, emphasizing analytical journalism that helps readers more fully understand their world and their money. He has reported from more than a dozen countries, with datelines that include Sao Paolo, Brazil; Phnom Penh, Cambodia; and Athens, Greece. A former attorney, before becoming a journalist Eric worked in securities litigation and white collar criminal defense with a pro bono specialty in human trafficking issues. He graduated from the University of Michigan Law School and can be found any given Saturday in the fall cheering on his Wolverines.
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