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n 1 2 1 2(eP) a b 2(ei) - 2 (e) i 1 n n where - 2(e) is the average of the firm-specific variances. Because this average is indepen- dent of n, when n gets large, 2(eP) becomes negligible. To summarize, as diversification increases, the total variance of a portfolio approaches the systematic variance, defined as the variance of the market factor multiplied by the square of the portfolio sensitivity coefficient, 2 . This is shown in Figure 10.2. Figure 10.2 shows that as more and more securities are combined into a portfolio, the portfolio variance decreases because of the diversification of firm-specific risk. However, the power of diversification is limited. Even for very large n, part of the risk remains be- cause of the exposure of virtually all assets to the common, or market, factor. Therefore, this systematic risk is said to be nondiversifiable. This analysis is borne out by empirical evidence. We saw the effect of portfolio diversi- fication on portfolio standard deviations in Figure 8.2. These empirical results are similar to the theoretical graph presented here in Figure 10.2. CONCEPT C H E C K ☞ QUESTION 2 Reconsider the two stocks in Concept Check 1. Suppose we form an equally weighted portfolio of A and B. What will be the nonsystematic standard deviation of that portfolio? III. Equilibrium In Capital Markets 10. Single−Index and Multifactor Models The McGraw−Hill Companies, 2001 CHAPTER 10 Single-Index and Multifactor Models 301 10.2 THE CAPM AND THE INDEX MODEL Actual Returns versus Expected Returns The CAPM is an elegant model. The question is whether it has real-world value-whether its implications are borne out by experience. Chapter 13 provides a range of empirical ev- idence on this point, but for now we focus briefly on a more basic
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