Factor Models and Market Efficiency

The CAPM puzzles

When Eugene Fama and others tested CAPM empirically in the 1970s and 1980s, they found patterns the model couldn’t explain:

• Size: small-cap stocks earned higher returns than CAPM predicted.
• Value: stocks with high book-to-market (cheap on accounting metrics) earned higher returns than growth stocks at the same beta.
• Momentum (Jegadeesh-Titman, 1993): past 3-12 month winners continued to outperform; past losers continued to underperform.
• Profitability (Novy-Marx, 2013): firms with higher gross profitability outperformed.
• Investment: firms investing aggressively underperformed those investing conservatively.

Each pattern is statistically robust and economically meaningful (returns differences of 2-5% per year between portfolios sorted on these characteristics). CAPM treats them as anomalies.

Fama-French three-factor (1993)

Fama and French added two new “factors” to CAPM:

$$R_i - R_f = \alpha_i + \beta_M (R_m - R_f) + \beta_S \cdot \text{SMB} + \beta_V \cdot \text{HML} + \varepsilon_i.$$

• 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 stocks (value) minus low book-to-market stocks (growth).

Each factor has a positive long-run premium (small > big, value > growth). An asset’s expected return depends on its loadings on all three factors.

The three-factor model explains the cross-section of US stock returns substantially better than CAPM. Many practical applications (performance attribution, factor-based investing) use it.

Five-factor (2015)

Fama and French extended the model with two more factors:

• RMW (Robust Minus Weak): high-profitability stocks minus low- profitability stocks.
• CMA (Conservative Minus Aggressive): low-investment firms minus high-investment firms.

The five-factor model dominates the three-factor model in modern data. It still doesn’t fully explain momentum, leading to a separate Carhart MOM factor.

What this means for cost of capital

For most undergraduate work and most corporate-finance applications, CAPM is still the workhorse. Factor models are heavily used in:

• Hedge fund performance attribution (separating “alpha” from factor exposures).
• Smart-beta ETF construction (deliberately tilting toward value, small-cap, momentum factors).
• Academic asset-pricing research.

For computing a firm’s cost of equity for a DCF, factor models give slightly different answers than CAPM, but the practical effect is usually within the noise of input choices for beta and market premium. The exam answer is still CAPM; the research-grade answer adds factor adjustments.

The Efficient Markets Hypothesis (EMH)

The three patterns above (size, value, momentum) raised an old question: are markets “efficient” — meaning, do prices fully reflect all available information?

Three forms of EMH:

Weak form: prices reflect all past price and volume information. You can’t beat the market using only historical chart patterns. (Momentum slightly violates this — past returns predict future returns. But trading costs erode much of the gain.)

Semi-strong form: prices reflect all publicly available information — financial statements, news, analyst reports. Fundamental analysis of public data can’t yield consistent abnormal returns. (Mostly supported by event studies and mutual-fund performance data.)

Strong form: prices reflect all information, including private/inside information. (Empirically false — insider trading generates abnormal returns. That’s why it’s illegal.)

The mainstream consensus in 2026: markets are mostly efficient in the semi-strong sense. Most active managers don’t beat indexes after fees, consistent with semi-strong efficiency. Some persistent anomalies exist (small, value, momentum) but capturing them requires patience and discipline, and competition over time erodes them.

Why this matters for corporate finance

EMH implies three useful things:

1. Market prices are a fair estimate of value. If you’re trying to value a target firm, the market price is the consensus estimate of every analyst and investor. Significant disagreement with the market price requires a specific reason.

2. Issuing equity at market price doesn’t dilute existing shareholders. The new shares are sold at fair value; existing wealth per share is unchanged. (This is a textbook result; reality is messier when issuance signals private information.)

3. Buybacks at market price don’t enrich remaining shareholders. Same logic. Buybacks transfer value to exiting shareholders; remaining holders are left whole.

These results explain why basic corporate-finance theory is relatively benign about issuance and buyback decisions: in an efficient market, the price action mostly cancels out.

The honest takeaway

Markets are good but not perfect. Use CAPM for cost of capital unless you have a specific reason to do more. When you see an “anomaly” in the data, ask whether it survives after trading costs, whether it persists out-of-sample, and whether competing researchers have been able to replicate it. Most “free lunches” turn out to be either (a) compensation for some risk we hadn’t identified, or (b) statistical artifacts.

Now we’re done with Unit 4. Unit 5 takes everything we’ve covered (cash flows, discount rates, equity vs debt) and asks: how should the firm be financed?