CAPM & Beta

Diversifiable risk earns nothing — beta measures the risk that remains, and the CAPM line prices it.

The idea

The Capital Asset Pricing Model. An asset's fair expected return is

$\mathbb{E}[R_{i}] = r_{f} + \beta_{i}\left(\mathbb{E}[R_{m}] - r_{f}\right), \qquad \beta_{i} = \frac{\mathrm{Cov}(R_{i}, R_{m})}{\sigma_{m}^{2}},$

where $r_{f}$ is the risk-free rate, $R_{m}$ is the return on the market portfolio — the value-weighted mix of all assets — and $\mathbb{E}[R_{m}] - r_{f}$ is the market premium, the extra return the market as a whole pays over the safe rate.

The argument begins with diversification. An asset's return moves with market-wide events, which push on every asset at once, and with idiosyncratic events particular to one firm. Idiosyncratic shocks are largely independent across firms, so in a portfolio of many small positions they mostly cancel; a market-wide shock is the same shock in every holding, and no spreading cancels it. Risk an investor can shed for free earns no premium in a competitive market, so only the market-wide part is paid for.

Beta measures that part. It is the asset's covariance with the market divided by the market's variance: how far the asset moves per unit move of the market. Plot the asset's return against the market's, one point per period, and the points scatter about a line — $\beta_{i}$ is that line's slope. The CAPM line then pays $r_{f}$ for waiting plus $\beta_{i}$ times the market premium; the asset's own volatility appears nowhere in it. The CAPM is a model built on strong assumptions, not a law of nature.

Ways to work on it

• Walkthrough. Split risk into market and idiosyncratic, measure beta, and read required returns off the CAPM line.
• Practice. Compute required returns and betas from the CAPM line.
• Hardest. Find a portfolio's required return, or judge whether a stock is over- or under-priced.

Not sure where to start? Take the ten-question placement test.