Risk-Adjusted Performance and
Informed Decision Making
www.mcubeit.com
Dr. Arun Muralidhar
Arun Muralidhar - Bio

Chairman of Mcube Investment Technologies, LLC and
Managing Director at FX Concepts, Inc.

Head of Investment Research and Member of Investment
Management Committee, World Bank Investment Department,
1995-1999

Derivatives and Liability Management, World Bank Funding
Department, 1992-1995

Managing Director and Head of Currency Research, JPMIM,
1999-2001

BA, Wabash College (1988); PhD, MIT Sloan (1992)
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Agenda
 Background
 Why the information ratio is wrong – M2
 Risk budgeting – connecting returns to risk – M3
 Confidence in skill: History matters - SHARAD
 Optimal portfolio construction using these measures
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Relative Risk – Tracking Error
 Most commonly used measure
 Ann. standard deviation of excess returns
 Depends on the standard deviation of the
benchmark, strategy and correlation
 Few test ex-ante forecast with ex-post outcomes
 Papers that recommend that managers stay within
tracking error ranges are WRONG
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Performance Measures
 Returns – Absolute and Relative
 Annualized versus
Cumulative
 Ratios – Risk-Adjusted
 Sharpe,
Information Ratio, Sortino Ratio
 Risk-Adjusted Returns
 M2,
M3, SHARAD
 Skill Measures
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How to Calculate Standard Measures?
 Unadjusted measures

Excess return = Portfolio return - Benchmark return
 Risk-adjusted ratio measures

Sharpe ratio = Excess over risk free rate/standard
deviation of portfolio
– higher the ratio, the better the investment opportunity

Information ratio = Excess over benchmark/standard
deviation of excess returns
– higher the ratio, better the manager
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Some Advanced Risk-Adjusted Measures
 Sortino ratio = Excess/Downside risk measure
 Risk-adjusted measures (in return terms)

M2 = extended Sharpe ratio (in basis points)

M3 = extended M2 ratio; corrects for correlation

SHARAD = Normalizes for different length of history
 Confidence in Skill – Tells how confident one can be that
there is skill (as opposed to noise) in a given track record
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Information Ratio is Wrong - M2
Need to normalize for different Std. deviations
Active portfolio A
Return
Active portfolio B
Benchmark
Riskless asset
Market
risk
Standard deviation
Standard
deviation of
unlevered
portfolio
B has a negative Information Ratio!
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Portfolio B has a Higher M2 Return
M2 Return for B
M2 Return for A
Benchmark Return
Benchmark
Riskless asset
Market risk
Standard deviation
Problem: Need to normalize for different correlations
i.e., have different tracking error
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Correlation-Adjustment: M3 Measure
Correcting for tracking error – different rankings
Standard
deviation
(%)

M2
(%)
Fund
Return
(%)
(1)
(2)
(3)
(4)
F
5.50
0.00
0.00
B
17.09
13.27
1.00
17.09
1
33.24
27.57
0.71
2
25.63
24.93
3
25.04
4
(6)
TE(basic)
(%)
TE(M2)
(%)
M3
(%)
(7)
(8)
(12)
18.85
20.45
10.14
18.43
0.77
16.21
17.02
9.04
17.43
25.02
0.73
15.86
17.74
9.68
17.41
24.08
21.33
0.80
17.06
13.34
8.38
17.65
5
21.95
21.75
0.59
15.53
17.52
11.97
17.68
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21.90
13.84
0.84
21.21
7.76
7.57
19.26
7
21.61
14.37
0.83
20.37
8.13
7.74
18.91
8
20.89
23.06
0.79
14.36
15.07
8.69
16.70
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20.77
14.00
0.89
19.97
6.53
6.32
18.83
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20.56
14.79
0.92
19.00
5.74
5.24
18.43
F = Risk-free asset; B = Benchmark (S&P500)
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Ranking Portfolios: Different Methods
M3 is the only one consistent with Skill
Ranking
Unadjusted
Skill using
raw returns
M2 or
Sharpe
Skill using
M2
M3
Skill using
M3
Information
ratio
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
First
Second
Third
Fourth
Fifth
Sixth
Seventh
Eighth
Ninth
Tenth
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10
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9
7
10
1
4
2
3
5
8
6
7
9
10
1
4
2
3
5
8
6
9
7
10
1
4
2
3
5
8
6
7
9
1
10
5
4
2
3
8
6
7
9
1
10
5
4
2
3
8
1
6
10
9
7
4
2
3
5
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Information ratio, Sharpe or M2 say little about Skill
Skill = Confidence in Skill Measure M3
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Which Measure Should you Use?
 Manage portfolio yourself – Sharpe, Information Ratio or M2
 External manager and with a tracking error budget – M3
(Previous papers ignore possible actions by client)
 Worried about skill – M3
 M2 provides valuable advice on leverage/ deleverage; M3
provides valuable advice on (a) active versus passive (“beta”)
and leverage/deleverage
Important to have a risk budget
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How Do You Compare 2 Strategies with
Different Data Histories?
 In the past – drop non-overlapping data

Lose valuable information on strategy with longer history
 SHARAD Measure – Normalizes for different risk and
different data history
 SHARAD = {M3 return}*{Confidence in skill (of M3 portfolio)}
 Confidence in skill acts as a probability measure and
explicitly captures the length of data history – more history,
greater the confidence in skill
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Risk Budgeting is only First Step
 Cannot force tracking error ranges on managers – client
needs to be evaluate how good manager is in dynamically
managing risk
 Risk-adjusted performance measures are the right way to go,
but many are paid on the basis of excess returns
 Measures can tell you how good manager is at managing risk
 Use creative measures along with risk budgets to achieve
optimal portfolio performance
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