Investments, tenth edition

principle,    because of the notion that an insurance company depends on the risk reduction 

achieved through diversification when it writes many policies insuring against many inde-

pendent sources of risk, each policy being a small part of the company’s overall portfolio. 

(See Section 7.5 for a discussion of the insurance principle.) 

 

  

  When common sources of risk affect all firms, however, even extensive diversifica-

tion cannot eliminate risk. In  Figure 7.1 , panel B, portfolio standard deviation falls as the 

number of securities increases, but it cannot be reduced to zero. The risk that remains even 

after extensive diversification is called    market  risk,    risk that is attributable to marketwide 

risk sources. Such risk is also called    systematic  risk,    or    nondiversifiable  risk   . In contrast, 

the risk that  can  be eliminated by diversification is called    unique  risk   ,    firm-specific  risk   , 

   nonsystematic  risk   , or    diversifiable  risk   . 

 This analysis is borne out by empirical studies.  Figure 7.2  shows the effect of portfolio 

diversification, using data on NYSE stocks.  

1

   The figure shows the average standard devia-

tion of equally weighted portfolios constructed by selecting stocks at random as a function 

of the number of stocks in the portfolio. On average, portfolio risk does fall with diversifi-

cation, but the power of diversification to reduce risk is limited by systematic or common 

sources of risk.

      

  

1

 

Meir Statman, “How Many Stocks Make a Diversified Portfolio?”  

Journal of Financial and Quantitative 

 Analysis  22 (September 1987). 

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  C H A P T E R  

7

  Optimal Risky Portfolios 

207

A

verage Portfolio Standard Deviation (%)

50

0

2

4

6

8

10

12

14

16

18

20

100 200 300 400 500 600 700 800 900 1,000

0

100

75

50

40

Risk Compared to a One-Stock Portfolio (%)

Number of Stocks in Portfolio

40

45

35

30

25

20

15

10

5

0

 Figure 7.2 

Portfolio diversification. The average standard deviation of returns of portfolios composed 

of only one stock was 49.2%. The average portfolio risk fell rapidly as the number of stocks included in 

the portfolio increased. In the limit, portfolio risk could be reduced to only 19.2%. 

  Source: From Meir Statman, “How Many Stocks Make a Diversified Portfolio?”  Journal of Financial and Quantitative Analysis  22 

(September 1987). Reprinted by permission.