Investments, tenth edition

 Table 7.4 

 Risk reduction of 

equally weighted 

portfolios in 

correlated and 

uncorrelated 

universes 

r

 5 0

r

 5 .40

Universe 

Size n

Portfolio 

Weights 

w 5 1/n (%)

Standard 

Deviation 

(%)

Reduction 

in s

Standard 

Deviation (%)

Reduction in s

1

100

50.00

14.64

50.00

8.17

2

50

35.36

41.83

5

20

22.36

 1.95

36.06

0.70

6

16.67

20.41

35.36

10

10

15.81

 0.73

33.91

0.20

11

9.09

15.08

33.71

20

5

11.18

 0.27

32.79

0.06

21

4.76

10.91

32.73

100

1

 5.00

 0.02

31.86

0.00

101

0.99

 4.98

31.86

 Suppose that the universe of available risky securities consists of a large number of stocks, identically dis-

tributed with  E ( r )  5  15%,  s   5  60%, and a common correlation coefficient of  r   5  .5. 

     a.   What are the expected return and standard deviation of an equally weighted risky portfolio of 25 stocks?  

    b.   What is the smallest number of stocks necessary to generate an efficient portfolio with a standard 

deviation equal to or smaller than 43%?  

    c.   What is the systematic risk in this security universe?  

    d.   If T-bills are available and yield 10%, what is the slope of the CML? (Because of the symmetry assumed 

for all securities in the investment universe, the market index in this economy will be an equally 

weighted portfolio of all stocks.)   

 CONCEPT CHECK 

7.5 

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bod61671_ch07_205-255.indd   228

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  C H A P T E R  

7

  Optimal Risky Portfolios 

229

  Asset Allocation and Security Selection 

 As we have seen, the theories of security selection and asset allocation are identical. Both 

activities call for the construction of an efficient frontier, and the choice of a particular 

portfolio from along that frontier. The determination of the optimal combination of secu-

rities proceeds in the same manner as the analysis of the optimal combination of asset 

classes. Why, then, do we (and the investment community) distinguish between asset allo-

cation and security selection? 

 Three factors are at work. First, as a result of greater need and ability to save (for col-

lege educations, recreation, longer life in retirement, health care needs, etc.), the demand 

for sophisticated investment management has increased enormously. Second, the widen-

ing spectrum of financial markets and financial instruments has put sophisticated invest-

ment beyond the capacity of many amateur investors. Finally, there are strong economies 

of scale in investment analysis. The end result is that the size of a competitive invest-

ment company has grown with the industry, and efficiency in organization has become an 

important issue. 

 A large investment company is likely to invest both in domestic and international mar-

kets and in a broad set of asset classes, each of which requires specialized expertise. Hence 

the management of each asset-class portfolio needs to be decentralized, and it becomes 

impossible to simultaneously optimize the entire organization’s risky portfolio in one 

stage, although this would be prescribed as optimal on  theoretical  grounds. In future chap-

ters we will see how optimization of decentralized portfolios can be mindful as well of the 

entire portfolio of which they are a part. 

 The practice is therefore to optimize the security selection of each asset-class portfo-

lio independently. At the same time, top management continually updates the asset allo-

cation of the organization, adjusting the investment budget allotted to each asset-class 

portfolio.