Transcript Outline
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
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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
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21.61
14.37
0.83
20.37
8.13
7.74
18.91
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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
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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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