Factor InvestingMarket EfficiencyMomentum

How the Three-Factor Model Explains Stock Market Anomalies

Summary by Robert Gorak · Published June 19, 2026 · Last reviewed June 19, 2026

Eugene F. Fama and Kenneth R. French·1996·Journal of Finance
Sample: 366 monthly observations (July 1963–December 1993)Data: CRSP and COMPUSTAT data for NYSE, AMEX, and NASDAQ stocksPeriod: July 1963–December 1993

Asset pricing anomalies are patterns in average stock returns—from size and value to past-return effects—that the Capital Asset Pricing Model fails to explain. In "Multifactor Explanations of Asset Pricing Anomalies," Fama and French (1996) showed a three-factor model absorbs most of them. Using CRSP and COMPUSTAT data over 366 months from July 1963 to December 1993, the model left tiny pricing errors. Its average absolute intercept on the 25 size-BE/ME portfolios was just 0.093 percent per month.

What the Study Found

The three-factor model explained the 25 size-BE/ME portfolios with an average R-squared of 0.93. Its average absolute intercept on those portfolios was just 0.093 percent per month. The average HML (value) return was 0.46 percent per month, or 6.33 percent per year. Under the CAPM, the high-book-to-market portfolio H was mispriced by 0.46 percent per month (t = 4.08). The model failed on momentum: returns ranged from −0.00 percent to 1.31 percent across the worst and best 12-2 deciles.

Methodology

The study drew on CRSP returns and COMPUSTAT accounting data for NYSE, AMEX, and NASDAQ stocks. The main tests covered 366 monthly observations from July 1963 to December 1993. Test portfolios were formed on size, book-to-market, E/P, C/P, five-year sales rank, and past returns. Each portfolio's excess return was regressed on the market return, SMB, and HML, with Gibbons-Ross-Shanken F-tests of the intercepts.

Key Statistics

Metric Finding Context
Three-factor model E(Ri) − Rf = bi[E(RM) − Rf] + si·E(SMB) + hi·E(HML) Equation (1), expected excess return
Avg absolute intercept 0.093 percent/month 25 size-BE/ME portfolios, R² = 0.93
Average HML return 0.46 percent/month (6.33 percent/year) Value premium, 7/63–12/93
CAPM mispricing of H 0.46 percent/month (t = 4.08) High-book-to-market portfolio under CAPM
Short-term momentum (12-2) −0.00 to 1.31 percent/month Worst to best past-return decile, unexplained
Annual premiums RM−Rf 5.94%, SMB 4.92%, HML 6.33% 1964–1993, N = 30

Why This Matters

The work established that a few systematic factors, not dozens of separate anomalies, can describe the cross-section of equity returns. It became the empirical foundation of modern factor investing. By treating value, size, and reversal effects as shared risk, it reframed those characteristics as proxies rather than independent mispricings. The lone holdout, short-term continuation, remained unexplained and motivated later momentum research.

Frequently Asked Questions

Three factors drive the model: the market excess return, SMB (small minus big, size), and HML (high minus low book-to-market, value). They explain a portfolio's expected excess return. Fama and French (1996) showed the model absorbs most CAPM anomalies from July 1963 to December 1993.

Monthly returns after formation ranged from −0.00 percent for the worst 12-2 past-return decile to 1.31 percent for the best. The three-factor model cannot capture this continuation. Past short-term winners load negatively on HML, so the model wrongly predicts reversal instead of continuation.

0.46 percent per month, or 6.33 percent per year, was the average HML return over July 1963 to December 1993. The premium was not riskless. HML had an annual standard deviation of 13.11 percent and was negative in 10 of the 30 years from 1964 to 1993.

The CAPM mispriced the high-book-to-market portfolio by 0.46 percent per month (t = 4.08). The three-factor model cut pricing errors to 5 to 10 basis points. On the 25 size-BE/ME portfolios, it reached an average absolute intercept of 0.093 percent per month and an R-squared of 0.93.

Source

Eugene F. Fama and Kenneth R. French (1996). Multifactor Explanations of Asset Pricing Anomalies. Journal of Finance.

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