Why One Factor Is Not Enough

The Capital Asset Pricing Model (CAPM) was a revolution when Sharpe, Lintner, and Mossin published it in the mid-1960s. The idea: in a market where all investors hold the efficient tangency portfolio, the only risk that earns a return premium is market risk — correlation with the overall market portfolio. All other risk can be diversified away and therefore earns no premium.

The CAPM pricing equation is:

$$E(r_i) = R_f + \beta_i \left(E[R_M] - R_f\right)$$

where $\beta_i = \frac{\text{Cov}(r_i, r_M)}{\text{Var}(r_M)}$ is the stock's sensitivity to market returns, and $E[R_M] - R_f$ is the market risk premium — the extra return the market earns above the risk-free rate.

CAPM is elegant. It is also empirically incomplete.

The first problem: stocks with the same beta do not earn the same return. In the decades after CAPM's publication, researchers found systematic patterns — small-cap stocks earn more than large-cap stocks at the same beta; cheap stocks (low P/B, low P/E) earn more than expensive stocks; recent winners continue to outperform for months.

The second problem: CAPM says the market portfolio is mean-variance efficient. But in practice, the cap-weighted market index leaves systematic return premiums on the table — it under-weights cheap stocks and over-weights expensive ones simply because expensive stocks have higher market capitalisation.

These anomalies are not noise. They persist across markets, across time periods, and even out-of-sample (they were largely known before being published). The explanation: there are multiple priced risk factors beyond just market beta. A stock's expected return depends on its exposure to several systematic risks, each of which commands a risk premium.