Investments, tenth edition

 Example  24.1 

 M  

2

  Measure 

12

  M  

2

  is positive when the portfolio’s Sharpe ratio exceeds the market’s. Letting  R  denote excess returns and 

S  denote Sharpe measures, the geometry of  Figure 24.2  implies that  R  

 P *

   5   S  

 P 

  s  

 M 

 , and therefore that

   M

2

5 r

p*

2 r

M

5 R

p*

2 R

M

5 S

P

s

M

2 S

M

s

M

5 (S

P

2 S

M

)s

M

  

M  

2

  and the Sharpe ratio will therefore rank order portfolios identically. 

 Figure 24.2 

 M  

2

  of portfolio  P   

E(r)

CAL(P)

CML

P*

P

M

F

M

2

σ

M

σ

P

σ 

bod61671_ch24_835-881.indd   842

bod61671_ch24_835-881.indd   842

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  C H A P T E R  

2 4

  Portfolio Performance Evaluation

843

  Appropriate Performance Measures in Two Scenarios 

 To evaluate Jane’s portfolio choice, we first ask whether this portfolio is her exclusive 

investment vehicle. If the answer is no, we need to know her “complementary” port-

folio. The appropriate measure of portfolio performance depends critically on whether 

the portfolio is the entire investment fund or only a portion of the investor’s overall 

wealth. 

  Jane’s Portfolio Represents Her Entire Risky Investment Fund   

In this 

simplest case we need to ascertain only whether Jane’s portfolio has the highest Sharpe 

measure. We can proceed in three steps:

    1.  Assume that past security performance is representative of expected performance, 

meaning that realized security returns over Jane’s holding period exhibit averages 

and covariances similar to those that Jane had anticipated.  

   2.  Determine the benchmark (alternative) portfolio that Jane would have held if she 

had chosen a passive strategy, such as the S&P 500.  

   3.  Compare Jane’s Sharpe measure or  M  

2

  to that of the best portfolio.    

 In sum, when Jane’s portfolio represents her entire investment fund, the benchmark is 

the market index or another specific portfolio. The performance criterion is the Sharpe 

measure of the actual portfolio versus the benchmark.