Beta and expected returns in the CAPM

Question

Explain the Capital Asset Pricing Model.

Short answer

CAPM says an asset's expected excess return is proportional to its beta with the market: $\mathbb{E}[R_i]-r_f=\beta_i(\mathbb{E}[R_m]-r_f)$ , with $\beta_i=\operatorname{Cov}(R_i,R_m)/\operatorname{Var}(R_m)$ . If all investors hold mean-variance efficient portfolios, everyone holds the market portfolio, so only systematic risk is rewarded; idiosyncratic risk can be diversified away and earns nothing. Beta is estimated by regressing asset returns on market returns.

Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 10, p.54; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Mean-Variance Optimisation

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