Investments, tenth edition

A: No manipulation: Sharpe vs. MRAR

MRAR

Sharpe Ratio

Average Sharpe Ratio               .32

SD                                               .66

Average MRAR                          .077%

SD                                               .13 

Slope of Sharpe on MRAR        .19

R-Square                                    .90

Correlation between Halves     .14

B: Manipulation: Sharpe vs. MRAR

–1.5

–1

–0.5

0.5

1

1.5

2

2.5

3

–0.5

–0.4

–0.3

0.1

0.3

–0.2

–0.1

0

0.2

0.4

MRAR

Sharpe Ratio

Average Sharpe Ratio                .40

SD                                                .66

Average MRAR                       –2.74%

SD                                                .18

Slope of Sharpe on MRAR         .25

R-Square                                     .84

Correlation between Halves    –.06

0

(they move upward). Some Sharpe ratios move from negative to positive values, while oth-

ers do not look worse (because the increased SD in the second period reduced the absolute 

value of the negative Sharpe ratios). 

bod61671_ch24_835-881.indd   849

bod61671_ch24_835-881.indd   849

7/31/13   6:26 PM

7/31/13   6:26 PM

Final PDF to printer

---

850 

P A R T   V I I

  Applied Portfolio Management

 The statistics in the box of panel B quantify the improvement of measured Sharpe 

ratios; in contrast, MRARs clearly deteriorated from a slight positive value to a certainty-

equivalent of  2 2.74% per year! As predicted, the correlation between average returns in 

the first and second legs of the period changes from positive to negative. All this happened 

because of an average increase in leverage from 1.0 to 1.39.  

18

    

 Morningstar introduced the MRAR in 2002. It is particularly relevant to hedge funds, 

where managers have great latitude and incentive to manipulate. See Chapter 26 for further 

discussion. Given its immunity to manipulation, we would expect the MRAR measure to 

become a standard performance statistic sometime in the future, required especially of 

managers who have the most discretion over investment policy.