4 CAPM: Pricing Market Risk
4.1 The basic question
If investors hold diversified portfolios, what compensation should an asset earn for its exposure to the broad market? In the simplest Capital Asset Pricing Model, expected excess return is proportional to market beta:
\[E[R_i]=R_f+\beta_i(E[R_m]-R_f), \qquad \beta_i=\frac{\operatorname{Cov}(R_i,R_m)}{\operatorname{Var}(R_m)}.\]
Here \(R_f\) is the risk-free rate for the relevant horizon. Beta reflects systematic exposure, not an asset’s total volatility.
4.2 What the model assumes
The textbook model uses strong simplifications, including common expectations, frictionless trading, mean-variance preferences, and the availability of a risk-free investment. Real investors face different taxes, borrowing rates, information, constraints, and horizons.
4.3 Alpha, beta, and misunderstanding
A positive historical regression intercept is not automatically persistent manager skill. Choice of benchmark, sampling noise, survivorship, and changing exposures can all create apparent alpha.
Working example: Suppose \(R_f=3\%\), \(E[R_m]=8\%\), and \(\beta=1.2\). The model implies \(E[R_i]=9\%\). That is a model-implied expectation, not a guaranteed or forecast realized return.
Living chapter. This is an initial working treatment. Derivations, examples, and references will be expanded in future editions.