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Partial derivatives zoom on the left skew
0,05 0 0
5
10
15
20
-0,05 -0,1 -0,15 -0,2 -0,25 -0,3 Kernel VaR Granger VaR
DSR
ES
STDV
7! H 3 ! $ !
.N80 -$ 8 .80 .83N0 . 0 "
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Æ Efficient frontiers in an expected return - Granger VaR diagram
1,8% 1,8%
1,7% 1,7%
1,6% 1,6%
1,5% 1,5%
1,4% 1,4%
1,3% 1,3%
1,2% 1,2%
1,1% 1,1%
1,0% 1,0%
0,9% 0,9% 0,0% 0,0%
0,2% 0,2%
0,4% 0,4%
0,6% 0,6%
M VaR M ean ean // Kernel Granger VaR
0,8% 0,8%
1,0% 1,0%
M M ean ean // ES ES (Uryasev) (Uryasev)
1,2% 1,2%
1,4% 1,4%
1,6% 1,6%
M M ean ean // St Standard andard deviation deviation
1,8% 1,8%
2,0% 2,0%
M M ean ean // DSR DSR
Return
Return 1.8% 1.8%
1.7% 1.7% 1.6% 1.6% 1.5% 1.5% 1.4% 1.4% 1.3% 1.3% 1.2% 1.2% 1.1% 1.1% 1.0% 1.0% 0.9% 0.9% 0.8% 0.8% 0.0% 0.0%
Expected Expected Shortfall Shortfall
0.5% 0.5%
1.0% 1.0%
M M ean ean // S&M S&M VaR VaR (GA) (GA)
1.5% 1.5%
2.0% 2.0%
M Mean ean // Gaussian Gaussian VaR VaR
2.5% 2.5%
3.0% 3.0%
M M ean ean // ES ES (Uryasev) (Uryasev)
3.5% 3.5%
4.0% 4.0%
M Mean ean // DSR DSR
7! C , Æ , $ ! .$$ $ 0
, 8 ! . $ 0"
H
C
0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2
0.6 0.6
0.5 0.5
0.4 0.4
0.3 0.3
0.2 0.2
0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1
0.4 0.4
0.3 0.3
0.2 0.2
0.1 0.1
Discovery Discovery MasterFund MasterFund Ltd Ltd Calamos Calamos Convertible Convertible Hedge Hedge Fund Fund LP LP RXR RXR Secured Secured Participating Participating Note Note Dean Dean Witter Witter Cornerstone Cornerstone Fund Fund IV IV LP LP Bay Bay Capital Capital Management Management
Aetos Aetos Corporation Corporation Sage Sage Capital Capital Limited Limited Partnership Partnership Arrowsmith Arrowsmith Fund Fund Ltd Ltd GAMut GAMut Investments Investments Inc Inc Blenheim Blenheim Investments Investments LP LP (Composite) (Composite)
0.86% 0.86% 0.94% 0.94% 1.01% 1.01% 1.09% 1.09% 1.17% 1.17% 1.24% 1.24% 1.32% 1.32% 1.40% 1.40% 1.47% 1.47% 1.55% 1.55% 1.63% 1.63% 1.70% 1.70% 1.78% 1.78% Return Return
Efficient Efficient portfolio portfolio according according to to ES ES (Uryasev) (Uryasev)
7! 2 3 !$ $ $ $ -$ 5
"
AXA AXA Rosenberg Rosenberg Market Market Neutral Neutral Strategy Strategy LP LP Bennett Bennett Restructuring Restructuring Fund Fund LP LP Genesis Genesis Emerging Emerging Markets Markets Fund Fund Ltd Ltd Blue Blue Rock Rock Capital Capital Fund Fund LP LP Aquila Aquila International International Fund Fund Ltd Ltd Red Red Oak Oak Commodity Commodity Advisors Advisors Inc Inc
0.86% 1.32% 0.86% 0.94% 0.94% 1.01% 1.01% 1.09% 1.09% 1.17% 1.17% 1.24% 1.24% 1.32% 1.40% 1.40% 1.47% 1.47% 1.55% 1.55% 1.63% 1.63% 1.70% 1.70% 1.78% 1.78% Return Return
00
0.6 0.6
0.5 0.5
00
0.7 0.7
0.6 0.6
0.8 0.8
0.7 0.7
0.9 0.9
11
0.8 0.8
Efficient Efficient portfolios portfolios according according to to sem semi-variance i-variance
Efficient Efficient portfolios portfolios according according to to Granger Granger VaR VaR (GA) (GA)
00 0.86% 0.86% 0.94% 0.94% 1.01% 1.01% 1.09% 1.09% 1.17% 1.17% 1.24% 1.24% 1.32% 1.32% 1.40% 1.40% 1.47% 1.47% 1.55% 1.55% 1.63% 1.63% 1.70% 1.70% 1.78% 1.78% Return Return
0.9 0.9
11
0.88% 0.88% 0.96% 0.96% 1.03% 1.03% 1.11% 1.11% 1.19% 1.19% 1.26% 1.26% 1.34% 1.34% 1.42% 1.42% 1.49% 1.49% 1.57% 1.57% 1.65% 1.65% 1.72% 1.72% 1.80% 1.80% Return Return
00
0.1 0.1
0.8 0.8
0.7 0.7
0.1 0.1
0.9 0.9
11
0.8 0.8
Efficient Efficient portfolios portfolios according according to to standard standard deviation deviation
0.9 0.9
11
Æ
Participation Participation ratio ratio 88 77 66 55
44 33 22 11 00 0,8% 0,8%
1,0% 1,0% Kernel VaR Granger VaR
1,2% 1,2%
1,4% 1,4% Expected Expected return return ES Semi-variance ES (Uryassev) (Uryassev) semi variance
7! '
2
1,6% 1,6% Variance VaR Gaussian
1,8% 1,8%
2,0% 2,0%