Fama–French Three-Factor Model

The Fama–French Three-Factor Model extends the Capital Asset Pricing Model (CAPM) by adding two systematic risk factors—size and value—alongside market risk. It was developed to better explain cross‑sectional differences in stock and portfolio returns that CAPM could not account for.

Key takeaways
* Improves on CAPM by including size (small vs. big) and value (high vs. low book‑to‑market) factors in addition to market risk.
* Uses three factors—market excess return, SMB (small minus big), and HML (high minus low)—to explain expected excess returns.
* Factor loadings (betas) measure a portfolio’s sensitivity to each risk factor; the model often explains a large portion of return variation in diversified portfolios.
* The approach was later expanded into a five‑factor model that adds profitability and investment factors; other factors (momentum, quality, low volatility) are also used in the literature.

How the model works
The model is a linear regression that decomposes a stock’s or portfolio’s excess return into exposure to common risk factors plus an idiosyncratic error. In compact form:

Ri − Rf = α + βM (Rm − Rf) + βSMB SMB + βHML HML + ε

Where:
* Ri = total return of asset or portfolio i
* Rf = risk‑free rate
* Rm = return of the market portfolio (index)
* Rm − Rf = market excess return
* SMB (small minus big) = return premium of small‑cap stocks over large‑cap stocks
* HML (high minus low) = return premium of high book‑to‑market (value) stocks over low book‑to‑market (growth) stocks
* βM, βSMB, βHML = factor loadings (sensitivities)
* α = intercept (often interpreted as abnormal return)
* ε = idiosyncratic error term

Interpretation
* βM captures exposure to systematic market risk (the CAPM beta).
* βSMB measures sensitivity to firm size: positive βSMB implies tilt toward small‑cap stocks.
* βHML measures sensitivity to value: positive βHML implies tilt toward high book‑to‑market (value) stocks.
* A portfolio’s expected excess return is driven by its exposures to these systematic factors; remaining variation is idiosyncratic risk.

Why the factors matter
Empirical research found that small‑cap and value stocks have historically delivered higher average returns than large‑cap and growth stocks. Two broad explanations exist:
* Risk‑based (efficient markets) view: higher returns compensate investors for bearing additional systematic risk associated with small or value firms.
* Behavioral/mispricing view: persistent mispricing or investor biases cause predictable excess returns that decay slowly.

Practical implications for investors
* Factor exposure informs expected returns and risk: investors can design portfolios with deliberate size and value tilts to achieve desired expected returns.
* Long horizon: factors can be volatile and may underperform in the short term; many proponents recommend multi‑year to multi‑decade horizons to capture premiums.
* Performance attribution: the model is widely used to attribute portfolio returns to market, size, and value exposures rather than to manager skill.

Extensions and other factors
* Five‑Factor Model: Fama and French later added profitability and investment factors (profitability premium and investment‑related premium) to capture additional cross‑sectional return patterns.
* Additional factors used by researchers and practitioners include momentum, quality, and low volatility. No single model captures all anomalies; choice of factors depends on research goals and investment design.

Selected sources
* Eugene F. Fama and Kenneth R. French — foundational papers on multifactor explanations of asset pricing and value vs. growth evidence.
* Journal of Financial Economics — papers presenting the five‑factor extension and related empirical results.