Investments, tenth edition

  Investor Risk 

Aversion (  A  )  

  Utility Score of Portfolio   L  

 [  E  (  r  ) 5 .07;  s  5 .05]  

  Utility Score of Portfolio   M  

 [  E  (  r  ) 5 .09;  s  5 .10]  

  Utility Score of Portfolio   H 

  [  E  (  r  ) 5 .13;  s  5 .20]  

 2.0 

 .07  2  ½  3  2  3  .05 

2

  5 .0675  

.09  2  ½  3  2  3  .1 

2

  5 .0800 

  .13  2  ½  3  2  3  .2 

2

  5 .09  

 3.5 

 .07  2  ½  3  3.5  3  .05 

2

  5 .0656 

  .09  2  ½  3  3.5 3 .1 

2

  5 .0725  

 .13  2  ½  3  3.5  3  .2 

2

  5 .06 

 5.0 

 .07  2  ½  3  5  3  .05 

2

  5 .0638 

  .09  2  ½  3  5  3  .1 

2

  5 .0650  

 .13  2  ½  3  5  3  .2 

2

  5 .03 

 Table 6.2 

 Utility scores of alternative portfolios for investors with varying degrees of risk aversion 

 Consider three investors with different degrees of risk aversion:  A  

1

  5 2,  A  

2

  5 3.5, and 

 A  

3

  5 5, all of whom are evaluating the three portfolios in  Table 6.1 . Because the risk-free 

rate is assumed to be 5%, Equation 6.1 implies that all three investors would assign a 

utility score of .05 to the risk-free alternative.  Table 6.2  presents the utility scores that 

would be assigned by each investor to each portfolio. The portfolio with the highest util-

ity score for each investor appears in bold. Notice that the high-risk portfolio,  H,  would 

be chosen only by the investor with the lowest degree of risk aversion,  A  

1

  5 2, while 

the low-risk portfolio,  L,  would be passed over even by the most risk-averse of our three 

investors. All three portfolios beat the risk-free alternative for the investors with levels of 

risk aversion given in the table. 

 Example  6.1 

Evaluating Investments by Using Utility Scores 

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P A R T   I I

  Portfolio Theory and Practice

 A portfolio has an expected rate of return of 20% and standard deviation of 30%. T-bills offer a safe rate 

of return of 7%. Would an investor with risk-aversion parameter  A  5 4 prefer to invest in T-bills or the 

risky portfolio? What if  A  5 2? 

 CONCEPT CHECK