2 2(eP) Variance( wiei) w i (ei) Note that in deriving the nonsystematic variance of the portfolio, we depend on the fact that the firm-specific eis are uncorrelated and hence that the variance of the "portfolio" of non- systematic eis is the weighted sum of the individual nonsystematic variances with the square of the investment proportions as weights. If the portfolio were equally weighted, wi 1/n, then the nonsystematic variance would be   2aeP, wi     1 1 2 nb anb     1 2(e ) n     2(ei) 1 n n   -     - 2(ei) In this case, we divide the average nonsystematic variance, 2(ei), by n, so that when the portfolio gets large in the sense that n is large and the portfolio remains equally weighted across all n stocks, the nonsystematic variance approaches zero.     CONCEPT C H E C K ☞ QUESTION 2 What will be the nonsystematic standard deviation of the equally weighted portfolio if the aver- age value of (ei) equals 30%, and (a) n 10, (b) n 100, (c) n 1,000, and (d) n 10,000? What do you conclude about the nonsystematic risk of large, diversified portfolios?     The set of portfolios for which the nonsystematic variance approaches zero as n gets