rf]   where i Cov(Ri , RM)/ 2 . This is a statement about the mean of expected excess returns of assets relative to the mean excess return of the (theoretical) market portfolio. If the index M in equation 10.9 represents the true market portfolio, we can take the ex- pectation of each side of the equation to show that the index model specification is   E(ri) rf i i[E(rM) rf] A comparison of the index model relationship to the CAPM expected return-beta rela- tionship (equation 10.8) shows that the CAPM predicts that i should be zero for all assets. The alpha of a stock is its expected return in excess of (or below) the fair expected return as predicted by the CAPM. If the stock is fairly priced, its alpha must be zero. We emphasize again that this is a statement about expected returns on a security. After the fact, of course, some securities will do better or worse than expected and will have re- turns higher or lower than predicted by the CAPM; that is, they will exhibit positive or neg- ative alphas over a sample period. But this superior or inferior performance could not have been forecast in advance. Therefore, if we estimate the index model for several firms, using equation 10.9 as a regression equation, we should find that the ex post or realized alphas (the regression III. Equilibrium In Capital Markets 10. Single−Index and Multifactor Models The McGraw−Hill Companies, 2001           CHAPTER 10 Single-Index and Multifactor Models 303     Figure 10.3 Frequency distribution of alphas.   Frequency 32   29 28   24 24   20 20