
the market risk remains, regardless of the number of firms combined into the portfolio. To understand these results, note that the excess rate of return on this equally weighted portfolio, for which each portfolio weight wi 1/n, is n 1 n 1 n RP wi Ri n Ri n ( i i RM ei) i 1 i 1 i 1 (10.6) 1 1 n bR 1 e i i 1 i M i 1 i i 1 Comparing equations 10.5 and 10.6, we see that the portfolio has a sensitivity to the market given by 1 n P i i 1 which is the average of the individual i s. It has a nonmarket return component of a con- stant (intercept) 1 n P i i 1 which is the average of the individual alphas, plus the zero mean variable 1 n eP ei i 1 which is the average of the firm-specific components. Hence the portfolios variance is 2 2 2 2 P P M (eP) (10.7) The systematic risk component of the portfolio variance, which we defined as the com- ponent that depends on marketwide movements, is 2 2 and depends on the sensitivity co- P M efficients of the individual securities. This part of the risk depends on portfolio beta and 2 and will persist regardless of the extent of portfolio diversification. No matter how many stocks are held, their common exposure to the market will be reflected in portfolio system- atic risk.7 In contrast, the nonsystematic component of the portfolio variance is 2(eP) and is at- tributable to firm-specific components, ei. Because these eis are