The Fama-French 3-Factor Model is the most influential extension of the Capital Asset Pricing Model (CAPM) in modern finance. Where CAPM explains stock returns with one factor (market beta), Fama and French (1993) added two more — size and value — that together capture a much larger fraction of the cross-sectional variation in equity returns. This article covers what the three factors are, why they work, and how QuanterLab uses them in factor-based strategies.
The Three Factors
MKT — Market Excess Return
The return of a broad market portfolio (e.g., total US equity) minus the risk-free rate. The same factor as CAPM's β. Captures the systematic equity-risk premium that all stocks share to varying degrees.
SMB — Small Minus Big
The return of small-cap stocks minus the return of large-cap stocks. Captures the historical tendency of smaller companies to outperform larger ones over long horizons. Loadings on SMB are positive for small-cap exposure, negative for large-cap.
HML — High Minus Low
The return of high book-to-market (value) stocks minus low book-to-market (growth) stocks. Captures the historical value premium — stocks trading at lower multiples to fundamentals have outperformed growth stocks over multi-decade periods. Loadings on HML are positive for value tilt, negative for growth.
The 3-factor model explains roughly 90–95% of the cross-sectional variation in diversified equity portfolio returns — far better than CAPM's ~70%. The remaining 5–10% is alpha plus other systematic effects (momentum, profitability, investment) that subsequent research has formalized.
The Regression
For any portfolio with returns r_p, the 3-factor decomposition is:
The estimated coefficients tell you the portfolio's exposure to each factor. The intercept α is the unexplained return — what's left after accounting for systematic risk. A statistically significant positive α is evidence of skill or an unidentified factor; a significant negative α suggests the strategy is paying for an exposure rather than being compensated for it.
Why It Matters for Strategy Research
- Performance attribution. Is your strategy outperforming because of skill (α) or because it's loading on a factor (β)? A momentum strategy that earns 8% per year but has β_HML = -0.5 may simply be a growth bet — not a momentum edge.
- Risk decomposition. Decompose your strategy's variance into factor-attributable variance and residual variance. The residual is the part you can't explain with public factors.
- Hedging factor exposures. If your strategy has unwanted factor tilts, you can hedge them by shorting factor-replicating portfolios.
- Backtest sanity check. A backtest with α = 0.03 (3% annualized after factor exposure) is much more defensible than a backtest with raw return = 0.15 but no factor analysis.
The Standard Factor Construction
QuanterLab uses Kenneth French's data library convention:
- SMB: average return of small-cap portfolios minus large-cap portfolios, where the cutoff is the NYSE median market cap.
- HML: average return of high-BE/ME portfolios (top 30% value) minus low-BE/ME portfolios (bottom 30% growth).
- Rebalancing: annually at the end of June, using prior fiscal-year-end book values and June market cap.
This standard convention means your factor loadings are directly comparable to academic research and to other practitioners using the same definitions.
Where the 3-Factor Model Falls Short
- Doesn't capture momentum. The Carhart 4-factor model adds the UMD (up-minus-down) momentum factor. See the Carhart 4-Factor article.
- Misses profitability and investment effects. Fama-French's own 5-factor model (2015) adds RMW (robust-minus-weak profitability) and CMA (conservative-minus-aggressive investment) factors. Useful for finer attribution.
- US-centric calibration. The size and value premia documented in US data are weaker (or different) in international markets. Use international factor data for international strategies.
- Time-varying premia. The size premium has been weak or absent for stretches (especially post-2000). Factor exposure today doesn't guarantee factor reward going forward.
How QuanterLab Uses It
The factor module computes 3-factor regressions on any saved strategy or portfolio: it reports α, the three β values with t-statistics, and the R² (how much of the variance is explained by the factors). Use this to:
- Verify strategies have meaningful α before deploying capital.
- Identify hidden factor tilts that you may want to hedge or accept consciously.
- Compare strategies on apples-to-apples factor-adjusted metrics.
- Decompose portfolio risk into factor exposures and idiosyncratic residual.
The Bottom Line
Fama-French 3-factor is the baseline for honest performance attribution. Reporting raw returns without factor adjustment in a research context is roughly equivalent to reporting Sharpe without specifying the risk-free rate — incomplete, often misleading, and inconsistent with how the rest of the field communicates. Run it on every meaningful strategy.
Further Reading
Foundational papers
- Fama, E. F. & French, K. R. (1992). The Cross-Section of Expected Stock Returns. Journal of Finance, 47(2), 427–465.
- Fama, E. F. & French, K. R. (1993). Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33(1), 3–56.
Textbook references
- Campbell, J. Y., Lo, A. W. & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press.
- López de Prado, M. (2018). Advances in Financial Machine Learning. Wiley.
Related QuanterLab articles
Try it in QuanterLab
Run any saved strategy through the factor module to get its Fama-French 3-factor regression. The α tells you what's left after market, size, and value — that's the part of your return you can claim as edge.