Why CAPM isn't enough — the factor zoo preview

The empirical failure of pure CAPM

Quick refresher: CAPM (the Capital Asset Pricing Model) says a stock's expected return depends on exactly one thing — its beta, its sensitivity to the overall market. Same beta, same expected return. Fama & French (1992) ran the obvious test: do stocks with the same beta actually have the same average returns?

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

1. Size effect: Small-cap stocks — companies with a small total stock-market value — earned higher average returns than large-caps, even after controlling for beta.
2. Value effect: High book-to-market stocks earned higher returns than low book-to-market stocks, regardless of beta. Book-to-market is the company's accounting ("book") value divided by its stock-market value. A high ratio means the market prices the company cheaply relative to its books — a "value" stock. A low ratio means the market pays a rich price for expected growth — a "growth" stock.

These weren't small effects. The book-to-market premium — the extra average return the cheap stocks earned over the expensive ones — was ~5% per year. CAPM's single-factor model couldn't see it. Something was missing.

Fama-French 3-Factor

The fix — same regression idea as CAPM, but with three explanatory series instead of one:

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

Read the symbols: $r_i$ ("r sub i") is the return of stock $i$ — the subscript $i$ labels which stock. $r_f$ is the risk-free rate. Each $\beta$ carries a word subscript naming which factor it belongs to: $\beta_\text{MKT}$ reads "beta MKT," the stock's sensitivity to the MKT factor. The $\cdot$ dot means "times," and $\varepsilon$ (epsilon) is leftover noise.

In words: a stock's return above the risk-free rate equals its alpha, plus its market beta times the market factor's return, plus its size beta times the size factor's return, plus its value beta times the value factor's return, plus noise.

The three factors:

• MKT = market excess return (the original CAPM factor).
• SMB ("Small Minus Big") = return of a portfolio that is long (owns) small-caps and short (bets against) large-caps.
• HML ("High Minus Low") = return of a portfolio long high book-to-market stocks, short low book-to-market stocks.

Each factor is a tradable long-short portfolio with zero net market exposure — the longs and shorts cancel out the overall market move. Loadings — the fitted beta values — are interpretable: $\beta_\text{HML} > 0$ (a positive beta on HML) means "this stock behaves like value stocks."

Does the fix work? In time-series regressions on diversified portfolios, the FF 3-factor model achieves an R² of ~90%+, versus ~70–80% for the market factor alone. (R², read "R squared," is the fraction of the return variation the model explains — 100% would be a perfect fit.) More importantly, it eliminates most of the cross-sectional pricing errors CAPM leaves behind — the errors you see when comparing many stocks against each other at the same time, rather than one stock over time (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:

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

In words: the same regression as the 3-factor model, with a fourth term added — a momentum beta times the momentum factor's return. MOM = the return of a portfolio long past winners, short 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 — traded on by professionals until the profit disappears? 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 problem: if researchers test hundreds of candidate factors, some will look great by pure luck. Honest statistics must raise the bar to account for all those tries.
• The t-statistic — a score for how statistically convincing an effect is; bigger means harder to explain as luck — should clear ~3.0 before declaring a new factor "real," not the traditional 2.0.
• A significant chunk of published "anomalies" — patterns that appear to beat what CAPM predicts — 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 — tests on fresh data that the researcher didn't use when finding the pattern. 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 the historical record, because of crowding: once everyone knows a trade, everyone doing it shrinks the reward.

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 (markets behaving differently than in the study period), and possibly survivorship/publication bias in the original research — journals mostly publish the tests that worked, so the published record looks rosier than reality.

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 — the alpha left over after the factors have claimed their share. If your strategy's "edge" disappears after controlling for these factors, you're not generating alpha. You're just earning factor premia — rewards you could have collected 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.