Why CAPM isn't enough — the factor zoo preview

The empirical failure of pure CAPM

Fama & French (1992) ran the obvious test: do stocks with the same beta have the same average returns?

Answer: no. They found two strong patterns CAPM didn't explain:

1. Size effect: Small-cap stocks earned higher average returns than large-caps, even after controlling for beta.
2. Value effect: High book-to-market ("value") stocks earned higher returns than low book-to-market ("growth") stocks, regardless of beta.

These weren't small effects. The book-to-market premium was ~5% per year. CAPM's single-factor model couldn't see them. Something was missing.

Fama-French 3-Factor

The fix:

$r_i - r_f = \alpha_i + \beta_\text{MKT} \cdot \text{MKT}_t + \beta_\text{SMB} \cdot \text{SMB}_t + \beta_\text{HML} \cdot \text{HML}_t + \varepsilon$

Where:

• MKT = market excess return (the original CAPM factor)
• SMB ("Small Minus Big") = return of a portfolio long small-caps, short large-caps
• HML ("High Minus Low") = return of a portfolio long high-BM, short low-BM

Each factor is a tradable long-short portfolio with zero net market exposure. Loadings on these factors are interpretable: $\beta_\text{HML} > 0$ means "this stock behaves like value stocks."

In time-series regressions on diversified portfolios, the FF 3-factor model achieves R² of ~90%+ vs. ~70–80% for the market factor alone — and, more importantly, it eliminates most of the cross-sectional pricing errors that CAPM leaves behind (Fama-French 1993). A huge improvement.

Momentum (Carhart 4-Factor)

Jegadeesh & Titman (1993) found that stocks with high returns over the past 6–12 months continue to outperform over the next 3–12 months. Momentum doesn't fit cleanly into the Fama-French story but earns its own risk premium.

Mark Carhart (1997) added it:

$r_i - r_f = \alpha + \beta_\text{MKT} \text{MKT} + \beta_\text{SMB} \text{SMB} + \beta_\text{HML} \text{HML} + \beta_\text{MOM} \text{MOM} + \varepsilon$

Where MOM = past-winners minus past-losers. The momentum premium has been a remarkably persistent ~8% per year globally, despite being well-known for 30+ years.

(Why doesn't this get arbed away? Hypothesis: it requires tolerance for occasional catastrophic reversals — in the 2009 momentum crash, the winners-minus-losers portfolio lost on the order of 70%+ in three months (Daniel & Moskowitz, "Momentum Crashes"). The exact figure depends on portfolio construction, but the tail risk is severe. Behavioral and institutional constraints prevent most players from running it at full scale.)

The 5-Factor model (Fama-French 2015)

Fama & French added two more factors:

• RMW ("Robust Minus Weak") = profitable companies minus unprofitable ones (profitability premium).
• CMA ("Conservative Minus Aggressive") = companies with low investment vs. high investment (investment premium).

With these, the HML (value) factor became redundant for explaining returns. The 5-factor model is the current academic gold standard.

The factor zoo (and the multiple-testing crisis)

Hundreds of "factors" have been published since 2000 — momentum, low-vol, quality, profitability, accruals, asset growth, share issuance, beta arbitrage, idiosyncratic volatility, etc. Harvey, Liu & Zhu (2016) examined this factor zoo and concluded:

• Many published factors don't survive proper multiple-testing corrections.
• The right t-statistic threshold for declaring a new factor "real" is ~3.0, not 2.0.
• A significant chunk of published "anomalies" are likely false positives.

This is a major warning for retail traders: most factors you read about on blogs or in popular books haven't survived rigorous out-of-sample tests. The reliable ones (size, value, momentum, low-vol, quality) have decades of evidence; the rest are noisier.

What this means for you as a learner

Three practical points:

1. The reliable factor exposures

For long-only retail investors, a tilt toward:

• Small/mid-cap (size)
• Value (high book-to-market, or any value composite)
• Momentum (recent winners)
• Quality (high profitability, low debt)
• Low volatility

has decades of academic support and reasonable forward expectations of modest excess returns (probably 1–3% per factor, lower than historical due to crowding).

2. The factor strategies that "should work" but disappoint

Many factor strategies have produced poor live performance vs. their academic backtests since ~2010. Reasons include crowding (everyone trying them), high implementation costs, regime change, and possibly survivorship/publication bias in the original research.

This is why honest factor implementation requires expecting lower returns than the historical record. Robert Carver's "Systematic Trading" is a good treatment of practical expectation calibration.

3. Where to focus

For Phase 1 of this curriculum, the most important takeaway is:

When evaluating any strategy, regress its returns on the established factors (MKT, SMB, HML, MOM) and report the residual alpha. If your strategy's "edge" disappears after controlling for these factors, you're not generating alpha — you're just earning factor premia, which you could have done passively much cheaper.

We'll do exactly this regression in Track D2 lessons that come later, on real strategies.

Predict before the next lesson

This is the end of the opening sequence (Weeks 1–5). In subsequent batches we'll dive into:

• Time series analysis (D1): stationarity, autocorrelation, ARIMA, cointegration
• Portfolio theory (D3): mean-variance optimization, risk parity
• Backtesting methodology (D4): the corrections to all the failure modes from D4-01
• Strategy archetypes (D5): trend, mean-reversion, factor strategies, pairs trading

Before then: review what you've learned. The 21 lessons covered here are the foundation for everything that follows.