11.3 Fama-French Three-Factor Model and Extensions
4 min read•Last Updated on July 30, 2024
The Fama-French Three-Factor Model builds on the CAPM by adding size and value factors to explain stock returns. It suggests that small-cap and value stocks tend to outperform the market over time, offering investors a more nuanced approach to understanding risk and return.
This model has significant implications for portfolio management and performance evaluation. By considering size and value characteristics alongside market risk, investors can potentially construct more effective portfolios and better assess fund manager performance.
Fama-French Three-Factor Model
Model Overview
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Extends the capital asset pricing model (CAPM) by adding size risk and value risk factors to the market risk factor
The three factors used are:
The excess return on the market (market factor)
The difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks (size factor)
The difference between the return on a portfolio of high book-to-market stocks and the return on a portfolio of low book-to-market stocks (value factor)
States that the expected return on a portfolio in excess of the risk-free rate is explained by the sensitivity of its return to the three factors
Model Extensions
Extensions to the model have been proposed, such as the Carhart four-factor model which includes a momentum factor
The Fama-French five-factor model adds profitability and investment factors to the original three factors
The five-factor model includes the market factor, size factor, value factor, profitability factor (measured by operating profitability), and investment factor (measured by change in total assets)
Size and Value Factors
Size Factor (SMB)
Represents the additional return investors have historically received by investing in stocks of companies with relatively small market capitalization (referred to as the "size premium")
Positive SMB in the model indicates that small-cap stocks outperformed large-cap stocks in a given period
Negative SMB indicates that large-cap stocks outperformed small-cap stocks
The coefficient (factor loading) for SMB in the regression indicates the portfolio's exposure to the size factor
A positive coefficient indicates a portfolio is exposed to small-cap stocks
A negative coefficient indicates the portfolio is exposed to large-cap stocks
Value Factor (HML)
Represents the additional return provided to investors for investing in companies with high book-to-market values (value stocks), often referred to as the "value premium"
Positive HML in the model indicates that value stocks outperformed growth stocks in a given period
Negative HML indicates that growth stocks outperformed value stocks
The coefficient (factor loading) for HML in the regression indicates the portfolio's exposure to the value factor
A positive coefficient indicates a portfolio is exposed to value stocks
A negative coefficient indicates the portfolio is exposed to growth stocks
The model predicts that portfolios consisting of small-cap and value stocks tend to outperform the market over the long term
Fama-French vs CAPM
Superior Explanatory Power
The Fama-French model has been shown to explain a greater proportion of the cross-sectional variation in average stock returns compared to the CAPM
The CAPM only takes into account the market factor (beta), while the Fama-French model incorporates additional factors (size and value) that have been shown to historically affect stock returns
Empirical studies have shown that the Fama-French model provides a better fit to actual stock returns data compared to the CAPM, as evidenced by higher R-squared values in regressions
Criticisms and Limitations
The Fama-French model has been criticized for its empirical nature and lack of strong theoretical foundation
Some argue that the size and value factors are simply proxies for other, more fundamental risk factors
Despite its limitations, the Fama-French model is widely used in practice for portfolio management and performance evaluation due to its superior explanatory power compared to the CAPM
Implications for Portfolio Management
Factor-Tilted Portfolios
The Fama-French model suggests that investors should consider a stock's size and value characteristics in addition to its beta (market risk) when constructing portfolios
Investors may be able to achieve higher risk-adjusted returns by tilting their portfolios towards small-cap and value stocks, which have historically outperformed the market according to the model
Multifactor models like the Fama-French model can be used to construct factor-tilted portfolios or "smart beta" strategies that systematically exploit the size and value premiums
Performance Evaluation
The model can be used to evaluate the performance of portfolio managers by comparing their returns to what would be expected given the portfolio's exposures to the size and value factors
The Fama-French model also has implications for the debate between active and passive investing
Some argue that the model's success in explaining stock returns suggests that markets are not perfectly efficient
Skilled active managers may be able to exploit mispricing related to size and value factors
Risk Considerations
Investors should be aware that the size and value premiums are not guaranteed to persist in the future
Factor-tilted portfolios may underperform the market for extended periods of time