single fund analysis (sfa) score as a risk adjusted performance measure
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By Peter Urbani, CIO, Infiniti Capital
Performance of the Infiniti Capital Single 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 common data set each using a different Risk Adjusted Performance Measure (RAPM) as the objective function to be maximised.
Performance is shown on an out-of-sample (ex post) basis and the data set used was a common sample universe of 36 anonymised hedge funds and the portfolios were rebalanced on a quarterly basis.
The RAPM’s used were the Sharpe, Sortino & Omega ratios and the Infiniti SFA Total Score.
The SFA Total score produces superior risk adjusted returns (CAGR/ABS(Drawdown)) for the following reasons:
It imposes a positively skewed distribution on the data during the in-sample optimisation and this shape is stable enough 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 it does not explicitly try to truncate the left tail as the SFA Score does.
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163.55
153.07
146.09
139.93141.18
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 Nov Dec
SFA Total
-4.00%
-2.00%
0.00%
2.00%
4.00%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Omega
-4.00%
-2.00%
0.00%
2.00%
4.00%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Sharpe
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
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 funds
0%10%20%30%40%50%60%70%80%90%
100%
1-Ja
n-06
1-A
pr-0
61-
Jul-0
61-
Oct
-06
1-Ja
n-07
1-A
pr-0
71-
Jul-0
71-
Oct
-07
1-Ja
n-08
1-A
pr-0
81-
Jul-0
81-
Oct
-08
1-Ja
n-09
1-A
pr-0
9
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-Ja
n-06
1-A
pr-0
61-
Jul-0
61-
Oct
-06
1-Ja
n-07
1-A
pr-0
71-
Jul-0
71-
Oct
-07
1-Ja
n-08
1-A
pr-0
81-
Jul-0
81-
Oct
-08
1-Ja
n-09
1-A
pr-0
9
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-Ja
n-06
1-A
pr-0
61-
Jul-0
61-
Oct
-06
1-Ja
n-07
1-A
pr-0
71-
Jul-0
71-
Oct
-07
1-Ja
n-08
1-A
pr-0
81-
Jul-0
81-
Oct
-08
1-Ja
n-09
1-A
pr-0
9
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-Ja
n-06
1-A
pr-0
61-
Jul-0
61-
Oct
-06
1-Ja
n-07
1-A
pr-0
71-
Jul-0
71-
Oct
-07
1-Ja
n-08
1-A
pr-0
81-
Jul-0
81-
Oct
-08
1-Ja
n-09
1-A
pr-0
9
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%
De
c-06
Jan-
07
Feb-0
7
Mar-
07
Ap
r-07
May
-07
Jun-0
7
Jul-0
7
Au
g-07
Sep-0
7
Oct-
07
No
v-07
De
c-07
Jan-
08
Feb-0
8
Mar-
08
Ap
r-08
May
-08
Jun-0
8
Jul-0
8
Au
g-08
Sep-0
8
Oct-
08
No
v-08
De
c-08
Jan-
09
Feb-0
9
Mar-
09
Ap
r-09
May
-09
Jun-0
9
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% 20.0%
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 built using 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 tail protection.
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 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 ( 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-sample portfolios 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-sample portfolios 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 the SFA 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)) for the following reasons:
It imposes a positively skewed distribution on the data during the in-sample optimisation and this shape is stable enough 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
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