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One thing to note is that the CAPM can be rewritten as $$r_i=r_f(1-\beta_i)+\beta_i r_m$$ Thus, one can identify $\alpha_i$ with $(1-\beta_i)r_f$. Then, we we have, for the CAPM, \beta_i=\frac {r_i-...
Is this right? No. $\beta_{i,M} = \frac{\sigma_i \rho_{i,M}}{\sigma_M}$ (note the correlation $\rho_{i,M}$ that is missing from your formula.) The first formula (CML) is only for portfolios on the ...