Investments, tenth edition

  SOLUTIONS TO CONCEPT CHECKS 

    1.       a.     1  1 rn 5 (1 1 rr)(1 1 i ) 5 (1.03)(1.08) 5  1.1124   

rn 5  11.24%   

       b.     1  1 rn 5 (1.03)(1.10) 5  1.133   

rn 5  13.3%      

   2.       a.     EAR  5  (1  1  .01) 

12

   2  1  5  .1268  5  12.68%  

   b.  EAR  

5   e  

.12

   2  1  5  .1275  5  12.75%    

 Choose the continuously compounded rate for its higher EAR.  

   3.  Number of bonds bought is 27,000/900  5  30  

Interest Rates

Probability

Year-end Bond Price

HPR

End-of-Year Value

High

.2

$850

(75 1 850)/900 2 1 5 .0278

(75 1 850)30 5 $27,750

Unchanged

.5

  915

.1000

$29,700

Low

.3

  985

.1778

$31,800

Expected rate of return

.1089

Expected end-of-year 

 dollar 

value

$29,940

Risk premium

.0589

   4.  (1   1  Required rate)(1  2  .40)  5   1 

     Required rate  5  .667, or 66.7%  

   5.       a.    Arithmetic  return  5  (1/3)(.2869)  1  (1/3)(.1088)  1  (1/3)(0.0491)  5  .1483  5  14.83%  

   b.  Geometric average 5   

3

"1.2869 3 1.1088 3 1.0491 2 1 5 .1439 5 14.39%   

   c.  Standard deviation  

5  12.37%  

   d.  Sharpe ratio  

5  (14.83  2  6.0)/12.37  5  .71     

 

 

 

6. The probability of a more extreme bad month, with return below  

2 

15%, is much lower: 

NORMDIST( 2 15,1,6,TRUE)   5 

  .00383. Alternatively, we can note that  

2 

15% is 16/6 

standard deviations below the mean return, and use the standard normal function to compute 

NORMSDIST( 2 16/6)  5  .00383.  

   7.  If the probabilities in  Spreadsheet  5.2  represented the true return distribution, we would use 

Equations 5.19 and 5.20 to obtain: Skew  5  0.0931; Kurtosis  5   2 1.2081. However, in this case, 

the data in the table represent a (short) historical sample, and correction for degrees-of-freedom 

bias is required (in a similar manner to our calculations for standard deviation). You can use 

Excel functions to obtain: SKEW(C5:C9)  5  0.1387; KURT(C5:C9)  5   2 0.2832.                           

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bod61671_ch05_117-167.indd   167

6/18/13   8:04 PM

6/18/13   8:04 PM

Final PDF to printer

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