Investments, tenth edition

  The  M  

2

  Measure of Performance 

 While the Sharpe ratio can be used to rank portfolio performance, its numerical value is 

not easy to interpret. Comparing the ratios for portfolios  M  and  P  in Concept Check 2, 

you should have found that  S  

 P 

   5  .69 and  S  

 M 

   5  .73. This suggests that portfolio  P   under-

performed the market index. But is a difference of .04 in the Sharpe ratio economically 

meaningful? We often compare rates of return, but these pure numbers are difficult to 

interpret. 

 An equivalent representation of Sharpe’s ratio was proposed by Graham and Harvey, 

and later popularized by Leah Modigliani of Morgan Stanley and her grandfather Franco 

Modigliani, past winner of the Nobel Prize in Economics.  

11

   Their approach has been 

dubbed the  M  

2

  measure (for Modigliani-squared). Like the Sharpe ratio,  M  

2

  focuses on 

total volatility as a measure of risk, but its risk adjustment leads to an easy-to-interpret dif-

ferential return relative to the benchmark index.  

 To  compute   M  

2

 , we imagine that a managed portfolio,  P,  is mixed with a position in 

T-bills so that the complete, or “adjusted,” portfolio matches the volatility of a market 

index such as the S&P 500. If the managed portfolio has 1.5 times the standard deviation 

of the index, the adjusted portfolio would be two-thirds invested in the managed portfolio 

and one-third in bills. The adjusted portfolio, which we call  P *, would then have the same 

standard deviation as the index. (If the managed portfolio had  lower  standard deviation 

than the index, it would be leveraged by borrowing money and investing the proceeds in 

the portfolio.) Because the market index and portfolio  P * have the same standard devia-

tion, we may compare their performance simply by comparing returns. This is the  M  

2

  

measure for portfolio  P: 

 

   M

P

2

5 r

P

*

2 r

M

 

 (24.1)      

 Consider the following data for a particular sample period: