Fama French Three Factor Model: How It Works, Formula, and Impact

What Is the Fama and French Three Factor Model?

The Fama and French Three-Factor Model, introduced in 1992 by Nobel Laureate Eugene Fama and researcher Kenneth French, enhances the traditional capital asset pricing model (CAPM) by incorporating size and value risk factors alongside market risk. This model acknowledges that small-cap and value stocks consistently outperform the broader market. By integrating these additional factors, the Three-Factor Model offers a more refined evaluation tool for portfolio performance, adjusting for the typical outperformance of these stock categories.

Breaking Down the Fama and French Three Factor Model

Eugene Fama and Kenneth French, former University of Chicago professors, found that value stocks often outperform growth stocks. Small-cap stocks also often outperform large-cap stocks. Portfolios heavy in small-cap or value stocks may show lower performance than CAPM suggests, as the Three-Factor Model accounts for their outperformance.

The Fama and French model has three factors: the size of firms, book-to-market values, and excess return on the market. In other words, the three factors used are small minus big (SMB), high minus low (HML), and the portfolio's return minus the risk-free rate of return. SMB accounts for publicly traded companies with small market caps that generate higher returns, while HML accounts for value stocks with high book-to-market ratios that generate higher returns in comparison to the market.

There is a lot of debate about whether the outperformance tendency is due to market efficiency or market inefficiency. Supporters of market efficiency explain stock outperformance by the extra risk and higher cost of capital that small and value stocks face. For market inefficiency, the outperformance is due to incorrect pricing by market participants, leading to excess returns over time. Investors who subscribe to the body of evidence provided by the Efficient Markets Hypothesis (EMH) are more likely to agree with the efficiency side.

The formula is:

$\begin{aligned} &R_{it} - R_{ft} = \alpha_{it} + \beta_1 ( R_{Mt} - R_{ft} ) + \beta_2SMB_t + \beta_3HML_t + \epsilon_{it} \\ &\textbf{where:} \\ &R_{it} = \text{total return of a stock or portfolio } i \text{ at time } t \\ &R_{ft} = \text{risk free rate of return at time } t \\ &R_{Mt} = \text{total market portfolio return at time } t \\ &R_{it} - R_{ft} = \text{expected excess return} \\ &R_{Mt} - R_{ft} = \text{excess return on the market portfolio (index)} \\ &SMB_t = \text{size premium (small minus big)} \\ &HML_t = \text{value premium (high minus low)} \\ &\beta_{1,2,3} = \text{factor coefficients} \\ \end{aligned}$​Rit​−Rft​=αit​+β1​(RMt​−Rft​)+β2​SMBt​+β3​HMLt​+ϵit​where:Rit​=total return of a stock or portfolio i at time tRft​=risk free rate of return at time tRMt​=total market portfolio return at time tRit​−Rft​=expected excess returnRMt​−Rft​=excess return on the market portfolio (index)SMBt​=size premium (small minus big)HMLt​=value premium (high minus low)β1,2,3​=factor coefficients​

Fama and French highlighted that investors must be able to ride out the extra volatility and periodic underperformance that could occur in a short time. Investors with a long-term time horizon of 15 years or more will be rewarded for losses suffered in the short term. Fama and French tested their model and found that combining size and value factors with the beta factor explains up to 95% of returns in diversified portfolios.

Since the model explains 95% of portfolio returns, investors can construct portfolios to receive expected returns based on their assumed risks. The main factors driving expected returns are sensitivity to the market, sensitivity to size, and sensitivity to value stocks, as measured by the book-to-market ratio. Any additional average expected return may be attributed to unpriced or unsystematic risk.

Exploring the Expansion: Fama and French's Five Factor Model

Researchers have expanded the Three-Factor model in recent years to include other factors. These include "momentum," "quality," and "low volatility," among others. In 2014, Fama and French adapted their model to include five factors. Along with the original three factors, the new model adds the concept that companies reporting higher future earnings have higher returns in the stock market, a factor referred to as profitability.

The fifth factor, "investment," proposes that companies investing heavily in growth projects may face stock market losses.