a - single fund analysis score as a rapm
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8/7/2019 a - Single Fund Analysis Score as a RAPM
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By Peter Urbani, CIO, Infiniti Capital
Performance of the Infiniti CapitalSingle Fund Analysis Score (SFA)as a Risk Adjusted Performance
Measure ( RAPM)
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The Infiniti SFA Total Score as a RAPMThis presentation shows the realised performance of 4 portfolios built from a commondata set each using a different Risk Adjusted Performance Measure (RAPM) as theobjective function to be maximised.
Performance is shown on an out-of-sample (ex post) basis and the data set used was acommon sample universe of 36 anonymised hedge funds and the portfolios wererebalanced on a quarterly basis.
The RAPM’s used were the Sharpe, Sortino & Omega ratios and the Infiniti SFA TotalScore.
The SFA Total score produces superior risk adjusted returns (CAGR/ABS(Drawdown)) forthe following reasons:
It imposes a positively skewed distribution on the data during the in-sample optimisation and this shape is stableenough to persist out-of sample (predictive)
The Sharpe ratio does not differentiate between upside and downside risk
The Sortino ratio can too easily generate zero downside portfolios in the in-sample period but these do not persist aswell out of sample (over-fitting)
The Omega ratio has the advantage of being distribution independent but still has the downside area of the distribution
as its denominator, therefore it does not explicitly try to truncate the left tail as the SFA Score does.
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80
90
100
110
120
130
140
150
160
170
180
SFA Total CAGR : 15.1%
Omega CAGR : 12.9%
Sharpe CAGR : 11.4%
Sortino CAGR : 10.1%
Equally Weighted Fund CAGR : 10.4%
Out-of-Sample Returns
Note: All returns shown are Gross of any fees
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Table of Statistics
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Out-of-Sample Returns 2008
-4.00%
-2.00%
0.00%
2.00%
4.00%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct N
SFA Total
-4.00%
-2.00%
0.00%
2.00%
4.00%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct N
Omega
-4.00%
-2.00%
0.00%
2.00%
4.00%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct N
Sharpe
-4.00%
-2.00%
0.00%
2.00%
4.00%6.00%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct N
Sortino
+4.98%
+2.58%
-0.86%
+4.40%
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Weights through time (Quarterly)
The Charts to the Left
show the weights
through time of each of portfolios (SFA Total,
Omega, Sharpe,
Sortino ) with quarterly
rebalancing of the
common universe of 36
funds0%
10%
20%
30%
40%
50%
60%70%
80%
90%
100%
1-Jan
-06
1-Apr
-06
1-Jul
-06
1-Oct
-06
1-Jan
-07
1-Apr
-07
1-Jul
-07
1-Oct
-07
1-Jan
-08
1-Apr
-08
1-Jul
-08
1-Oct
-08
1-Jan
-09
1-Apr
-09
Example Fund 50
Example Fund 17
Example Fund 7
Example Fund 30
Example Fund 10
Example Fund 9
Example Fund 5
Example Fund 19
Example Fund 49
Example Fund 39
0%
10%
20%
30%
40%
50%
60%70%
80%
90%
100%
1-Jan
-06
1-Apr
-06
1-Jul
-06
1-Oct
-06
1-Jan
-07
1-Apr
-07
1-Jul
-07
1-Oct
-07
1-Jan
-08
1-Apr
-08
1-Jul
-08
1-Oct
-08
1-Jan
-09
1-Apr
-09
Example Fund 50
Example Fund 17
Example Fund 7
Example Fund 30
Example Fund 10
Example Fund 9
Example Fund 5
Example Fund 19
Example Fund 49
Example Fund 39
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1-Jan
-06
1-Apr
-06
1-Jul-06
1-Oct
-06
1-Jan
-07
1-Apr
-07
1-Jul-07
1-Oct
-07
1-Jan
-08
1-Apr
-08
1-Jul-08
1-Oct
-08
1-Jan
-09
1-Apr
-09
Example Fund 50
Example Fund 17
Example Fund 7
Example Fund 30
Example Fund 10
Example Fund 9
Example Fund 5
Example Fund 19
Example Fund 49
Example Fund 39
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1-Jan
-06
1-Apr
-06
1-Jul-06
1-Oct
-06
1-Jan
-07
1-Apr
-07
1-Jul-07
1-Oct
-07
1-Jan
-08
1-Apr
-08
1-Jul-08
1-Oct
-08
1-Jan
-09
1-Apr
-09
Example Fund 50
Example Fund 17
Example Fund 7
Example Fund 30
Example Fund 10
Example Fund 9
Example Fund 5
Example Fund 19
Example Fund 49
Example Fund 39
SFA Total Omega
Sharpe Sortino
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Realised Best-Fit Value at Risk 95%
12 Month rolling Best-Fit Infiniti VaR
-5.00%
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
Dec-06
Jan-07
Feb-07
Mar
-07
Apr-07
May
-07Jun-07
Jul-07
Aug-07
Sep-07
Oct-07
Nov-07
Dec-07
Jan-08
Feb-08
Mar
-08
Apr-08
May
-08Jun-08
Jul-08
Aug-08
Sep-08
Oct-08
Nov-08
Dec-08
Jan-09
SFA Total ( Avg -1.2%)
Omega ( Avg -0.8%)
Sharpe ( Avg -0.7%)
Sortino ( Avg -1.5%)
Equally Weighted Fund ( Avg -1.7%)
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0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.04
-10.0% -5.0% 0.0% 5.0% 10.0% 15.0%
SFA Total (Gumbel (Max) )
Omega (Johnson (Lognormal) )
Sharpe (Mixture of Normals )
Sortino (Modified Normal )
Portfolio Best-Fit Distributions
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Best-Fit DistributionsThe Charts to the Left
show the best-fitting
distribution for each of
the portfolios builtusing the SFA Total
Score, Sharpe, Sortino
or Omega ratio’s. Also
shown in grey is the
best fitting distribution
of the Equally
Weighted (Benchmark)
portfolio.
As you can see the
SFA portfolio had the
most positive
skewness and good tailprotection.
0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.04
-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Portfolio Best Fit
Distribution ( SFA Total
Benchmark Best Fit
Distribution
0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.04
-0.2 -0.1 0 0.1 0.2
Portfolio Best Fit
Distribution ( Omega )
Benchmark Best FitDistribution
0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.04
-0.2 -0.1 0 0.1 0.2
Portfolio Best Fit
Distribution ( Sharpe
Benchmark Best Fit
Distribution
0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.04
-0.2 -0.1 0 0.1 0.2
Portfolio Best Fit
Distribution ( Sortino
Benchmark Best Fit
Distribution
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Piecewise Non-Linear RegressionThe Charts to the Left
show the piecewise
regressions of each of
the out-of-sampleportfolios constructed
using either the SFA
Total Score, Sharpe,
Sortino or Omega
ratio’s against an
Equally Weighted
(Benchmark) portfolio.
As you can see the
SFA portfolio had the
best upside capture to
downside capture.
-0.04
-0.02
0.00
0.02
0.04
0.06
-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05
SFA Total versus Equally Weighted Fund
-0.04
-0.02
0.00
0.02
0.04
0.06
-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05
Omega versus Equally Weighted Fund
-0.04
-0.02
0.00
0.02
0.04
0.06
-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05
Sharpe versus Equally Weighted Fund
-0.04
-0.02
0.00
0.02
0.04
0.06
-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05
Sortino versus Equally Weighted Fund
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-0.04
-0.02
0
0.02
0.04
0.06
0.08
-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05
SFA Total
-0.04
-0.02
0
0.02
0.04
0.06
0.08
-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05
Omega
-0.04
-0.02
0
0.02
0.04
0.06
0.08
-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05
Sharpe
-0.04
-0.02
0
0.02
0.04
0.06
0.08
-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05
Sortino
Bi-Variate Best Fit CopulaThe Charts to the Left
depict the best-fit bi-
variate Copula of each
of the out-of-sampleportfolios constructed
using either the SFA
Total Score, Sharpe,
Sortino or Omega
ratio’s as the objective
function or risk
adjusted performance
measure (RAPM) to
maximize. Shown here
against the common
benchmark.
As you can see theSFA portfolio had the
best zone 2 (upside) to
zone 4 ( downside )
dependence.
Zone 4
Zone 2
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Conclusions
The SFA Total score produces superior risk adjusted returns (CAGR/ABS(Drawdown)) forthe following reasons:
It imposes a positively skewed distribution on the data during the in-sample optimisation and this shape is stableenough to persist out-of sample (predictive)
The Sharpe ratio does not differentiate between upside and downside risk
The Sortino ratio can too easily generate zero downside portfolios in the in-sample period but these do not persist as
well out of sample (over-fitting)
The Omega ratio has the advantage of being distribution independent but still has the downside area of the distribution
as its denominator, therefore does not explicitly try to truncate the left tail as the SFA Score does.
For further information or to download a free trial of the Infiniti Analytics Suite
which was used to generate these results please go to:
www.infiniti-analytics.com
i l i
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DisclaimerThe information and opinions in this presentation were prepared by the Infiniti Group (collectively “Infiniti”). This presentation is provided for informationpurposes only. It is not an offer or solicitation to enter into any agreement or contract with Infiniti. Whilst all reasonable care has been taken to ensure thatthe facts stated herein are accurate and that the opinions and expectations contained herein are fair and reasonable, Infiniti makes no representation orwarranty, express or implied, with respect to the fairness, correctness, accuracy reasonableness or completeness of the information and opinions herein buthas obtained the information from sources believed to be reliable.
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