The Fama-French three-factor model uses RM-RF, SMB (small minus big), and HML (high minus low BE/ME) to price assets. Fama and French (1993) analyzed NYSE, Amex, and NASDAQ stocks from July 1963 to December 1991. The paper appeared in the Journal of Financial Economics under the title "Common Risk Factors in the Returns on Stocks and Bonds". Adding SMB and HML raised R² from 0.61–0.70 to 0.94–0.97 for the smallest-size quintile portfolios. The lowest three-factor R² across all 25 portfolios was 0.83.
What the Study Found
Average excess returns on the 25 size- and BE/ME-sorted stock portfolios ranged from 0.32% to 1.05% per month across the 29-year sample. SMB produced an average return of 0.27% per month (t = 1.73). HML produced an average return of 0.40% per month (t = 2.91). The average excess market return (RM-RF) was 0.43% per month. Bond portfolio excess returns were all less than 0.15% per month. Only one of seven exceeded 1.5 standard errors from 0.
Methodology
Fama and French drew stock data from CRSP and accounting data from COMPUSTAT for NYSE, Amex, and (after 1972) NASDAQ stocks. The sample covers July 1963 to December 1991, yielding 342 monthly observations across 25 size-BE/ME portfolios and 7 bond portfolios. The study used time-series regressions following Black, Jensen, and Scholes (1972), regressing excess portfolio returns on five mimicking-factor returns. Controls included the value-weighted market return, NYSE size median breakpoints, and COMPUSTAT book equity computed net of deferred taxes and preferred stock.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Three-factor R² — smallest-size portfolios | 0.94 to 0.97 | Up from 0.61–0.70 with market factor alone |
| Minimum three-factor R² (all 25 stock portfolios) | 0.83 | Largest-size, highest-BE/ME portfolio |
| Average HML monthly return | 0.40% per month (t = 2.91) | July 1963–December 1991 |
| Average SMB monthly return | 0.27% per month (t = 1.73) | July 1963–December 1991 |
| Average RM-RF monthly return | 0.43% per month | About 5% per year |
| SMB–HML correlation | −0.08 | Monthly, 1963–1991 |
| Average excess return range (25 stock portfolios) | 0.32% to 1.05% per month | July 1963–December 1991 |
| Average bond portfolio excess return | Less than 0.15% per month | All government and corporate bond portfolios |
| Three-factor model | R(t) − RF(t) = a + b[RM(t) − RF(t)] + s·SMB(t) + h·HML(t) + e(t) | Tests whether intercepts are indistinguishable from 0 |
| SMB construction | SMB = ⅓(S/L + S/M + S/H) − ⅓(B/L + B/M + B/H) | Mimicking portfolio for size risk factor |
| HML construction | HML = ½(S/H + B/H) − ½(S/L + B/L) | Mimicking portfolio for BE/ME risk factor |
Why This Matters
The three-factor model gives portfolio managers a framework to decompose return sources beyond market beta alone. Allocating to small-cap or high-BE/ME stocks loads on SMB and HML, which the model interprets as compensation for common risk factors. Institutional strategies that explicitly target size or value tilts rest on this decomposition. The bond-market results establish that stock and bond returns share variation through two term-structure factors, linking equity and fixed-income risk pricing in a single model.