Fama-French Three Factor Model: Size and Value Added

Key Takeaways

• The Fama-French three factor model adds SMB (small minus big) and HML (high minus low book-to-market) to CAPM's single market factor to explain more return variation.
• A small-cap value fund with positive SMB and HML loadings of 0.55 and 0.40 can have most of its return explained by factor harvesting rather than manager skill.
• The most common mistake is assuming value always wins; HML had a brutal decade-long drawdown from roughly 2010 to 2020 before recovering sharply in 2021–2022.
• A three-factor alpha only means returns are unexplained by market, size, and value, adding momentum removes the alpha of many seemingly skilled funds.

What It Is

In 1992 and 1993, Eugene Fama and Kenneth French published work showing that CAPM's single market-beta did a poor job of explaining the cross-section of U.S. stock returns. Small-cap stocks earned more than their CAPM betas predicted. High book-to-market (cheap) stocks earned more than low book-to-market (expensive) stocks, even after adjusting for beta. These were not small effects.

Their response was to widen the model. Alongside the market factor, they added two portfolio-based factors: SMB (Small Minus Big) for the size premium and HML (High Minus Low) for the value premium. Together, these three variables explained a far larger share of return variation than CAPM alone.

The Intuition

CAPM assumes the only risk that matters for expected returns is exposure to the overall market. If that were true, you could take any diversified stock portfolio, measure its beta, and predict its return. In the data, you cannot. Portfolios built from small firms or cheap firms systematically beat the CAPM prediction, and portfolios of large growth firms systematically fell short.

One interpretation is that small and value stocks carry extra risk that beta does not pick up, for example distress risk or sensitivity to business-cycle downturns. Another is that investors persistently misprice these groups. Fama and French leaned toward the risk story. Either way, if a portfolio loads on those characteristics, you should expect returns above or below the market beta prediction over the long run.

The three-factor model turns that observation into a testable equation.

How It Works

For any asset or portfolio, the expected excess return is modeled as:

E[R_i] - R_f = alpha_i
             + beta_i  * (E[R_m] - R_f)
             + s_i     * SMB
             + h_i     * HML

Where:

R_i     = return on asset i
R_f     = risk-free rate
R_m     = return on the broad market
SMB     = small minus big (size factor return)
HML     = high minus low book-to-market (value factor return)
beta, s, h = the asset's sensitivities to each factor
alpha   = unexplained excess return

Kenneth French's data library at Dartmouth publishes the factor returns monthly. SMB is constructed as the average return of small-cap portfolios minus the average return of large-cap portfolios. HML is the return of high book-to-market portfolios minus low book-to-market portfolios. Both are built from NYSE, AMEX, and Nasdaq stocks using NYSE breakpoints for size and book-to-market quantiles.

You estimate the betas by regressing the asset's excess returns on the three factor returns. A positive s_i means the portfolio behaves like a small-cap. A positive h_i means it behaves like a value stock.

Worked Example

Imagine you run a regression for a diversified small-cap value fund over 10 years of monthly returns and get: beta = 1.05, s = 0.55, h = 0.40, alpha = 0.05 percent per month.

Over the same window, suppose the market risk premium averaged 0.60 percent per month, SMB averaged 0.20 percent, and HML averaged 0.15 percent.

The model's predicted excess return per month is:

1.05 * 0.60 + 0.55 * 0.20 + 0.40 * 0.15 = 0.630 + 0.110 + 0.060 = 0.80%

Plus the alpha of 0.05 percent gives 0.85 percent per month actual average. Almost all of the fund's return is explained by its three factor loadings. The manager is not generating meaningful skill beyond harvesting size and value exposures.

Common Mistakes

1. Assuming value always wins. HML has had multi-year stretches of negative returns. The period from roughly 2010 to 2020 was particularly brutal for U.S. value investors. The model describes a long-run premium, not a monthly guarantee. Investors who abandon it after a drawdown often exit near the bottom.

2. Treating the three-factor alpha as true skill. A positive alpha here only means returns are unexplained by market, size, and value. Momentum, quality, profitability, and low-volatility factors may still absorb that alpha if you add them. Carhart's four-factor extension, which adds momentum (UMD), removed the alphas of many funds that looked skilled under Fama-French.

3. Applying it blindly to non-equity assets. The factors were built from the cross-section of U.S. stocks. Using them to explain commodity, currency, or fixed-income returns without adapting the factor construction rarely produces clean results.

4. Using lagged or mismatched factor data. French's data library publishes factors with specific return conventions (monthly, in percent, arithmetic). Mixing those with daily log returns or misaligned date windows is a common regression error that produces meaningless loadings.

5. Ignoring construction details. SMB and HML use NYSE breakpoints and specific portfolio formation dates. Rebuilding factors on your own universe without replicating those rules can change estimated loadings materially and quietly break comparisons to published research.

Frequently Asked Questions

Q: What is the Fama-French three factor model in simple terms? It is a model that explains a stock or fund's expected return using three risk factors: market beta, size (small firms earn more than large), and value (cheap firms earn more than expensive). Any return above what these three factors predict is the manager's true alpha.

Q: How does the Fama-French three factor model affect investment decisions? It reveals how much of a fund's return comes from deliberate factor exposures versus stock-picking skill. A fund that looks like a winner can be fully explained by loading on small-cap and value risk, which you can replicate cheaply with an index ETF.

Q: What is a real-world example of the Fama-French three factor model? A small-cap value fund posting 12% annual returns sounds impressive, but if the model predicts 11.5% based on its SMB and HML loadings, the manager added only 50 basis points of alpha. Much of the outperformance was earned by taking on systematic factor risk, not skill.

Q: How can investors use the Fama-French three factor model? Run a factor regression on any active fund you own. If the alpha disappears once you control for market, size, and value exposures, you are paying active fees for factor exposure available much more cheaply. Only pay active fees when genuine alpha remains after the regression.

Q: How is the Fama-French three factor model different from the five-factor model? The three-factor model uses market, size, and value. The five-factor model adds operating profitability (RMW) and investment aggressiveness (CMA). The 2015 update showed HML actually becomes redundant once RMW and CMA are included, though it is still widely used in practice.

Sources

1. Fama, E.F. and French, K.R. (1993). "Common risk factors in the returns on stocks and bonds." Journal of Financial Economics, 33(1), 3-56. Hosted copy: https://www.bauer.uh.edu/rsusmel/phd/Fama-French_JFE93.pdf
2. Fama, E.F. and French, K.R. (1993). "Common risk factors in the returns on stocks and bonds." ScienceDirect entry. https://www.sciencedirect.com/science/article/abs/pii/0304405X93900235
3. French, K.R. "Description of Fama/French Factors." Data Library, Tuck School of Business, Dartmouth College. https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_factors.html
4. Corporate Finance Institute. "Fama-French Three-Factor Model: Components, Formula & Uses." https://corporatefinanceinstitute.com/resources/valuation/fama-french-three-factor-model/

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.