Questions: Factor Models and Multifactor Pricing (Fama-French)

Question 1

A small-cap stock with a high book-to-market ratio has CAPM beta = 0.9 — below the market average. CAPM predicts it should earn slightly below-market returns. What does the Fama-French 3-factor model predict for this stock's expected return compared to CAPM's prediction?

• A. The same as CAPM — beta is the only relevant risk measure
• B. Lower than CAPM — small-cap and value stocks are safer, so their required return is lower
• C. Higher than CAPM — positive SMB and HML loadings add expected return beyond the market factor
• D. Indeterminate — factor loadings only affect volatility, not expected returns

Answer: (C)

This stock has positive exposure to both the SMB (small minus big) and HML (high minus low book-to-market) factors. In the Fama-French model, expected return includes compensation for these factor exposures: E[Rᵢ] = Rf + βmkt(Rm−Rf) + βSMB·E[SMB] + βHML·E[HML]. Since both additional factor premiums are positive and this stock loads positively on both, its expected return is *higher* than CAPM alone would predict — despite its below-average market beta. CAPM systematically underpredicts returns for small-cap value stocks, which is exactly the empirical anomaly Fama-French was designed to explain.

Question 2

A fund manager claims her portfolio generates positive alpha in the Fama-French 3-factor model, proving she has superior stock-picking skill. What is the key challenge to this interpretation?

• A. Fama-French alpha is always zero by construction, so positive alpha is impossible
• B. The positive alpha could reflect exposure to additional systematic risk factors (e.g., momentum, profitability) not included in the 3-factor model, rather than genuine skill
• C. Alpha in the Fama-French model only measures trading costs, not skill
• D. Factor models cannot be applied to managed portfolios, only to individual stocks

Answer: (B)

Alpha is measured relative to the factors included in the model. If the portfolio systematically loads on factors outside the model — like momentum (WML) or profitability (RMW) — those factor premiums appear as 'alpha' in the 3-factor regression but represent compensation for bearing systematic risk, not managerial skill. A manager who tilts toward past winners earns momentum premium but appears to have positive alpha in a model that doesn't include momentum. True alpha requires a model that fully controls for all priced risk factors, which remains an open empirical challenge.

Question 3

The Fama-French 3-factor model explains a higher proportion of cross-sectional return variation than single-factor CAPM.

• T. True
• F. False

Answer: True

Empirically, the Fama-French 3-factor model explains roughly 90% of cross-sectional return variation across diversified portfolios, compared to about 70% for CAPM. The addition of SMB and HML factors captures systematic return patterns — the size premium and value premium — that CAPM's single market factor cannot explain. This improvement motivated the entire multifactor empirical asset pricing research program.

Question 4

SMB and HML are long-short portfolios with zero expected return under the null hypothesis that CAPM fully describes expected returns.

• T. True
• F. False

Answer: False

Under CAPM, any portfolio's expected return is fully explained by its market beta. SMB and HML are constructed precisely to capture returns that CAPM *cannot* explain — their historical average returns (approximately 2–3% annually for SMB and 4–5% for HML) represent the size and value premiums that CAPM leaves unexplained. If CAPM fully described returns, these portfolios would have zero expected return after adjusting for market beta — but they don't, which is the empirical foundation of the Fama-French model.

Question 5

Why does the interpretation of factor premiums — whether they represent compensation for risk or correction of mispricing — matter for whether the premiums will persist in the future?

Model answer: If factor premiums (like the value premium) compensate for genuine systematic risk that investors cannot diversify away, they should persist as long as that risk exists — earning the premium is 'payment' for bearing unavoidable exposure. If instead premiums reflect behavioral mispricing (investors systematically undervaluing certain stocks), they are vulnerable to erosion as informed investors recognize and arbitrage the pattern, capital flows into strategies that exploit it, and prices correct. Risk-based premiums are equilibrium; behavioral premiums are potential arbitrage opportunities that smart money may eventually eliminate.

This debate is central to asset pricing. The risk-based view (Fama-French's preferred interpretation) predicts durable premiums. The behavioral view (e.g., Lakonishok, Shleifer, Vishny) predicts premiums may decay as awareness spreads. Empirically, value and size premiums have weakened since Fama-French published their 1993 paper, which some interpret as consistent with the behavioral story (publication led to trading that arbitraged the mispricing), though risk advocates dispute this.