Investments, tenth edition

   SOLUTIONS TO CONCEPT CHECKS 

 

 

 

 

1. We can characterize the entire population by two representative investors. One is the 

“uninformed” investor, who does not engage in security analysis and holds the market portfolio, 

whereas the other optimizes using the Markowitz algorithm with input from security analysis. 

The uninformed investor does not know what input the informed investor uses to make portfolio 

purchases. The uninformed investor knows, however, that if the other investor is informed, the 

market portfolio proportions will be optimal. Therefore, to depart from these proportions would 

constitute an uninformed bet, which will, on average, reduce the efficiency of diversification with 

no compensating improvement in expected returns.  

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bod61671_ch09_291-323.indd   322

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  C H A P T E R  

9

  The Capital Asset Pricing Model 

323

   2.      a.    Substituting the historical mean and standard deviation in Equation 9.2 yields a coefficient of 

risk aversion of   

A

5

E(r

M

)

2 r

f

s

M

2

5

.079

.232

2

5 1.47   

   b.    This relationship also tells us that for the historical standard deviation and a coefficient of risk 

aversion of 3.5 the risk premium would be   

E(r

M

)

2 r

f

5 As

M

2

5 3.5 3 .232

2

5 .188 5 18.8%      

   3.  For these investment proportions,  w  

Ford

 ,  w  

Toyota

 , the portfolio  b   is   

b

P

 5 w

Ford

b

Ford

 1 w

Toyota

b

Toyota

5 (.75 3 1.25) 1 (.25 3 1.10) 5 1.2125  

     As the market risk premium,  E ( r  

 M 

 )  2   r  

 f 

  , is 8%, the portfolio risk premium will be   

E(r

P

)

2 r

f

5 b

P

3E(r

M

)

2 r

f

4

5 1.2125 3 8 5  9.7%   

   4.  The alpha of a stock is its expected return in excess of that required by the CAPM.   

a

5 E(r) 2 5r

f

1 b3E(r

M

)

2 r

f

46

a

XYZ

5 12 2 35 1 1.0(11 2 5)4 5 1%

a

ABC

5 13 2 35 1 1.5(11 2 5)4 5 21%  

  ABC  plots below the SML, while  XYZ   plots  above.      

 

E(r), Percent

b

 .5 

1 

1.5

14

α

XYZ

⬎ 0

XYZ

Market

SML

0

α

ABC

⬍ 0

E(r

M

) ⫽ 11

r

f

⫽ 5

ABC

12

   5.  The project-specific required return is determined by the project beta coupled with the market 

risk premium and the risk-free rate. The CAPM tells us that an acceptable expected rate of return 

for the project is   

r

f

1 b3E(r

M

)

2 r

f

4 5 8 1 1.3(16 2 8) 5 18.4% 

    which becomes the project’s hurdle rate. If the IRR of the project is 19%, then it is desirable. Any 

project with an IRR equal to or less than 18.4% should be rejected.              

bod61671_ch09_291-323.indd   323

bod61671_ch09_291-323.indd   323

6/21/13   3:39 PM

6/21/13   3:39 PM

Final PDF to printer

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