Investments, tenth edition

 Figure 24.1 

Universe comparison, periods ending 

December 31, 2010  

  

4

 Jack L. Treynor, “How to Rate Management Investment Funds,”  Harvard Business Review  43 (January– February 

1966). 

  

5

 William F. Sharpe, “Mutual Fund Performance,”  Journal of Business  39 (January 1966). 

  

6

 

Michael C. Jensen, “The Performance of Mutual Funds in the Period 1945–1964,”  

Journal of Finance,  

May  1968; and “Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios,”  Journal of 

Business,   April  1969. 

bod61671_ch24_835-881.indd   839

bod61671_ch24_835-881.indd   839

7/25/13   3:13 AM

7/25/13   3:13 AM

Final PDF to printer

---

840 

P A R T   V I I

  Applied Portfolio Management

 But while widely used, risk-adjusted performance measures each have their own limita-

tions. Moreover, their reliability requires quite a long history of consistent management 

with a steady level of performance and a representative sample of investment environ-

ments: bull as well as bear markets. 

 We start by cataloging some possible risk-adjusted performance measures for a portfo-

lio,  P,  and examine the circumstances in which each measure might be most relevant. 

    1.   Sharpe ratio:     (r

P

2 r

f

)/s

P

  

        Sharpe’s  ratio    divides average portfolio excess return over the sample period by 

the standard deviation of returns over that period. It measures the reward to (total) 

volatility trade-off.  

7

     

   2.   Treynor measure:     (r

P

2 r

f

)/b

P

  

     Like the Sharpe ratio,    Treynor’s  measure    gives excess return per unit of risk, but it 

uses systematic risk instead of total risk.  

   3.   Jensen’s alpha:     a

P

5 r

P

2 3r

f

1 b

P 

(r

M

2 r

f

)

4  

        Jensen’s  alpha    is the average return on the portfolio over and above that predicted 

by the CAPM, given the portfolio’s beta and the average market return.  

8

    

   4.   Information ratio:    a  

 P 

 / s ( e  

 P 

 ) 

    

The