Can someone explain the Fama-French 3-factor model with a worked example showing SMB and HML?

The Fama-French 3-factor model is one of the most important asset pricing models in finance and a key topic for CFA Level II.

The Model:

E(Ri) - Rf = bi_mkt x (Rm - Rf) + bi_smb x SMB + bi_hml x HML

Where:

• (Rm - Rf) = Market risk premium (same as CAPM)
• SMB (Small Minus Big) = Return of small-cap stocks minus return of large-cap stocks
• HML (High Minus Low) = Return of high book-to-market (value) stocks minus low book-to-market (growth) stocks

How SMB and HML Are Constructed:

Fama and French sort all NYSE/AMEX/NASDAQ stocks into groups:

1. Size sort: Split into Small and Big at the NYSE median market cap
2. Value sort: Split into three groups based on book-to-market ratio (top 30% = High, middle 40% = Neutral, bottom 30% = Low)

This creates 6 portfolios (2 x 3). Then:

• SMB = average return of 3 small portfolios minus average return of 3 big portfolios
• HML = average return of 2 high B/M portfolios minus average return of 2 low B/M portfolios

Worked Example: Stonegate Analytics runs a regression for Apex Manufacturing and finds:

Factor	Factor Loading (b)	Risk Premium	Contribution
Market (Rm - Rf)	1.15	6.0%	6.90%
SMB	0.45	2.5%	1.13%
HML	0.70	3.0%	2.10%

Rf = 4.0%

E(R_Apex) = 4.0% + 6.90% + 1.13% + 2.10% = 14.13%

Interpreting the Loadings:

• SMB loading = 0.45 (positive): Apex behaves somewhat like a small-cap stock, earning a size premium
• HML loading = 0.70 (positive): Apex behaves like a value stock (high book-to-market), earning a value premium
• If HML loading were negative, the stock would behave like a growth stock

Contrast with CAPM: Using CAPM alone: E(R) = 4.0% + 1.15 x 6.0% = 10.90% Fama-French adds 3.23% from size and value factors. A fund manager who generates 12% return might appear to have 1.10% alpha under CAPM but only -2.13% under Fama-French — meaning the returns were fully explained by factor exposures, not skill.

Exam tip: The CFA Level II exam often tests whether apparent alpha disappears once you account for size and value exposures. Be prepared to calculate expected returns under both CAPM and Fama-French and compare the implied alphas.

Explore more factor models in our CFA Level II portfolio course on AcadiFi.