Factor models: CAPM, Fama–French and statistical factors

A factor model says that most of the variation in returns comes from a handful of common drivers, and that what is left is idiosyncratic. It matters twice over: as a risk model, telling you what you are exposed to, and as a benchmark, telling you whether your alpha is anything more than a known premium.

Equation 4.1

CAPM

Only market risk is compensated; idiosyncratic risk is diversifiable and earns nothing.

\mathbb{E}[r_i] - r_f = \beta_i\left(\mathbb{E}[r_m] - r_f\right), \qquad \beta_i = \frac{\mathrm{Cov}(r_i, r_m)}{\mathrm{Var}(r_m)}

$\beta$: The regression slope on the market — exactly the one from the regression chapter.
$\alpha$: The intercept, which CAPM says should be zero for every asset.

Figure 4.2 · What CAPM predicts, and what is observed. The predicted line goes through the origin; the fitted one is flatter and starts above it. Low-beta stocks earn more than they should and high-beta ones less — the observation that launched betting-against-beta, and the first evidence that one factor was not enough.

Proposition 4.3

What the evidence says

The core insight — that only undiversifiable risk should be paid — is sound and survives. The specific prediction does not: empirically the relationship between beta and return is much flatter than CAPM implies, and low-beta stocks have historically earned more than their beta justifies. That flatness is the *betting against beta* anomaly, and it is one of the better-documented effects in the field.

Holds when

A common explanation is leverage aversion: investors who want more return but cannot borrow buy high-beta stocks instead, bidding them up.
The residual from a CAPM regression is what every other factor model set out to explain.

Factor	Long / short	The story
Market	The index over cash	Compensation for undiversifiable risk
Size (SMB)	Small over large	Illiquidity and distress risk; weak in recent decades
Value (HML)	Cheap over expensive	Risk premium, or over-extrapolation of growth
Momentum (UMD)	Recent winners over losers	Underreaction; crashes violently on reversals
Profitability (RMW)	Profitable over not	Quality, and a valuation identity
Investment (CMA)	Conservative over aggressive	Over-investment destroys value

Table 4.4 · The standard factors. Momentum is the awkward one: it has the strongest evidence and the least comfortable story, and its returns are strongly negatively skewed — long quiet gains and occasional violent crashes.

Factor models: CAPM, Fama–French and statistical factors

After this lesson you should be able to

CAPM

What the evidence says

The rest of this lesson is in Premium