Beta, the security market line and the CAPM

In short

• The CAPM adds that investors share the same views, hold mean-variance efficient portfolios, act as price takers, and markets clear.
• Beta measures systematic risk: $\beta_i = \sigma_{im}/\sigma_m^2 = \rho_{im}\sigma_i/\sigma_m$. The market's beta is 1.
• The security market line prices every asset: $E(r_i) = r_f + \frac{E(r_m) - r_f}{\sigma_m^2}\sigma_{im}$, which is the CAPM.
• For efficient portfolios on the CML ($\rho = 1$), $\beta = \sigma_p/\sigma_m$, so the CML and CAPM give the same expected return.
• Beta is estimated by regressing the asset's excess returns on the market's excess returns; the choice of period, frequency and index matters.
• Limitations: non-normal returns, unstable correlations, imperfect markets, estimation error, stale history, plus transaction costs and taxes.