The Fama-French 3-factor model attempts to explain the returns of a diversified stock or bond portfolio versus the returns of the market. It was introduced by Eugene Fama and Kenneth French in 1992 as an expansion of the traditional Capital Asset Pricing Model (CAPM), which uses only one factor of market exposure.
Let’s learn how the Fama-French 3-factor model can be used to build portfolios, evaluate mutual funds and alpha, the value added by a fund manager.
Definition and Examples of the Fama-French 3-Factor Model
The Fama-French 3-factor model, an expansion of the traditional Capital Asset Pricing Model (CAPM), attempts to explain the returns of a diversified stock or bond portfolio versus the returns of the market. Instead of the single factor of market risk used by CAPM, the Fama-French 3-factor model uses three factors: market risk, size risk, and value risk.
- Alternate names: Fama French 3-factor model, Fama and French 3-factor model
In their research, Fama and French found that small companies tend to outperform large companies over the long term, and value companies tend to outperform growth companies.
The Morningstar mutual fund rating system style box is based in part on the Fama-French 3-factor model. The style box shows investors at a glance how the mutual fund portfolio is constructed based on value and size. The box has three categories of value, blend and growth and three categories of company size of small, medium, and large. Funds are then classed in one of the nine styles of value and size.
Since 1992, Fama And French have expanded the model to include two additional factors: profitability, and investment factors like conservative versus aggressive.
How the Fama-French 3-Factor Model Works
In their 1992 study, Fama and French found that beta on its own did not explain average portfolio returns.
The CAPM uses beta to determine the risk and expected return of a portfolio. Beta compares the total price changes of the individual components of a portfolio to the price changes of a benchmark like the S&P 500. An S&P 500 index fund, for example, has a beta of 1 because the fund will go up or down at the same rate the stock market as measured by the S&P 500 goes up and down. If the XYZ fund has a beta of 1.1 it will rise or fall 10% more than the benchmark.
A higher beta means greater price variation, risk, and potentially higher returns.
Fama and French introduced the 3-factor model to explain portfolio performance. The model includes beta and two additional factors:
- Size of the companies: a company can be considered large or small based on its market capitalization
- Book value to market value: a company’s book value compared to its market value establishes whether it is a value company or a growth company
The traditional CAPM formula for expected returns is:
Expected Returns = Risk-Free Rate + (Market Risk Premium x Beta)
The U.S. Treasury six-month note or 10-year bond rate is typically used as the “risk-free” rate because there is virtually no risk of default, or the issuer not providing the expected return.
Market Risk Premium
Market risk premium is the return investors receive above the risk-free rate, or essentially compensation for taking the risk.
The market risk premium is calculated by subtracting the risk-free rate from the expected market return of a broad index like the S&P 500. Market risk premium is then adjusted by the portfolio beta.
The Fama-French 3-factor model adds SMB (small minus large), which is size, and HML (high minus low), which is value versus growth. So, its formula is:
Expected Returns = Risk-Free Rate + (Market Risk Premium x beta) + SMB + HML
Small Minus Large (Size)
SMB is the effect of size on portfolio returns. SMB measures the historical excess returns of small cap companies versus large cap companies. Current SMB factors are maintained by the Dartmouth Tuck School of Business.
High Minus Low (Value)
HML is the value premium or the difference between the book value and market value. High book-to-market companies are considered value companies, and low book-to-market companies are considered growth companies. The Dartmouth Tuck School of Business provides current HML factors.
What It Means to the Average Investor
Investors can use the Fama-French 3-factor model as they analyze which assets to buy and sell. However, this model is not used by average investors. Instead, it's more often used by professional analysts.
You can however incorporate the premise of the model into your investment strategy. According to the Fama-French model, over the long term, value companies will outperform growth companies, and small companies will outperform large companies.
- The Fama-French 3-factor model is an expansion of the Capital Asset Pricing Model (CAPM).
- The model includes a company’s size and value in addition to its market risk premium in the Fama-French 3-factor model.
- Average investors typically don’t use the Fama-French 3-factor model, which is more often used by professional analysts.