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Posted on Sep 28, 2024

A B D E F. G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

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A B D E F. G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Nov 01 Dec 01 Jan 02 Feb 02 Mar 02 Apr 02 May 02 Jun 02 Jul 02 Aug 02 Sep 02 Oct 02 Nov 02 Dec 02 Jan 03 Feb 03 Mar 03 Apr 03 May 03 Jun 03 Jul 03 Aug 03 Sep 03 Oct 03 Nov 03 Dec 03 Jan 04 Feb 04 Mar 04 Apr 04 May 04 Jun 04 Jul 04 Aug 04 Portfolio A -4.50% 8.75% 1.03% -2.45% -1.87% -3.77% -7.43% 2.09% 5.94% 1.99% -1.18% -1.45% 4.95% -5.28% -0.68% -8.26% -7.03% 0.80% -10.07% 6.93% 4.13% -4.99% -2.11% -1.51% 1.66% 6.85% 5.13% 1.11% 1.96% 2.37% -0.23% 5.56% 1.48% 4.23% 2.24% 2.34% -0.86% -2.23% 1.88% 2.50% -3.94% -0.19% 1.42% 1.96% 5.21% 3.23% -2.72% Portfolio B -1.10% 1.38% -7.13% 3.68% 2.72% 13.44% -2.11% 2.51% 4.24% 10.09% 1.27% -0.56% -0.86% 3.56% -1.62% 7.47% -2.09% 3.40% -0.32% 2.82% 4.95% -5.70% 5.90% -6.23% 1.78% 3.24% 10.52% 1.09% -17.02% 1.77% 13.19% 12.80% 3.82% 4.50% 8.29% 7.74% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% S&P 500 -6.34% 7.77% 0.67% -2.43% -0.98% -6.26% -8.08% 1.91% 7.67% 0.88% -1.46% -1.93% 3.76% -6.06% -0.74% -7.12% -7.79% 0.66% -10.87% 8.80% 5.89% -5.87% -2.62% -1.50% 0.97% 8.24% 5.27% 1.28% 1.76% 1.95% -1.06% 5.66% 0.88% 5.24% 1.84% 1.39% -1.51% -1.57% 1.37% 1.94% -3.31% 0.40% 1.08% 1.53% 4.05% 3.40% -2.44% 90dBill 0.44% 0.38% 0.37% 0.32% 0.31% 0.30% 0.29% 0.26% 0.21% 0.18% 0.16% 0.13% 0.15% 0.14% 0.15% 0.14% 0.15% 0.14% 0.14% 0.14% 0.13% 0.12% 0.11% 0.09% 0.10% 0.10% 0.10% 0.09% 0.09% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.07% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% Sep 04 Oct 04 Nov 04 Dec 04 Jan 05 1 Portfolio A Portfolio B 90 dBill 38 Mar 04 39 Apr 04 40 May 04 41 Jun 04 42 Jul 04 43 Aug 04 44 Sep 04 45 Oct 04 46 Nov 04 47 Dec 04 48 Jan 05 49 Feb 05 50 Mar 05 51 Apr 05 52 May 05 53 Jun 05 54 Jul 05 55 Aug 05 56 Sep 05 57 Oct 05 58 Nov 05 59 Dec 05 60 Jan-06 61 Feb-06 62 Mar-06 Annualized 63 Return Annualized 64 Volatility 65 66 Monthly Vol 67 Avg Mthly Rtn 68 69 -0.86% -2.23% 1.88% 2.50% -3.94% -0.19% 1.42% 1.96% 5.21% 3.23% -2.72% 2.57% -0.58% -2.07% 3.84% 0.66% 4.16% -0.72% 1.96% -2.02% 4.75% 0.83% 4.15% 0.05% 1.00% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% 9.27% -1.09% -3.82% -0.06% 5.31% 2.78% -1.15% 7.09% 2.84% 5.94% -4.20% 1.17% 2.23% -5.05% S&P 500 -1.51% -1.57% 1.37% 1.94% -3.31% 0.40% 1.08% 1.53% 4.05% 3.40% -2.44% 2.10% -1.77% -1.90% 3.18% 0.14% 3.72% -0.91% 0.81% -1.67% 3.78% 0.03% 2.65% 0.27% 1.24% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% 0.18% 0.21% 0.22% 0.24% 0.24% 0.25% 0.27% 0.27% 0.29% 0.30% 0.32% 0.33% 0.32% 0.37% 5.86% 24.64% 2.57% 2. 19% 13.4% 19.0% 14.2% 0.3% 3.87% 0.55% 5.47% 2.00% 4.10% 0.30% 0.10% 0.18% A D E F G H 1 J K L M N o P Q RE Down/B] Down(B)^2 -1.54% 0.00023797 Down(S&P) -6.78% Down/S&P)^2 0.004591011 -7.50% 0.005622198 -2.76% -1.30% -6.56% -8.36% 0.000759113 0.00016848 0.004306872 0.006992639 -2.39% 0.000572433 -1.62% 2.06% 0.000260952 0.000425226 -0.69% 4.79832E-05 -1.01% 0.000101339 -1.77% 0.000312798 -6.21% -0.89% -7.27% -7.94% B Portfolio A 4.50% 8.75% 1.03% -2.45% -1,87% 3.77% -7.43% 2.09% 5.94% 1.99% -1.18% -1,45% 4.95% -5.28% -0.68% 8.26% -7.03% 0.80% -10.07% 6.93% 4.13% 4.99% 2.11% -1.51% 1.66% 6.85% 5.13% 1.11% 1.96% 2.37% -0.23% 5.56% 1.48% 0.003852685 7.85528E-05 0.005282092 0.006305948 -2.24% 0.000500225 -0.46% 2.10423E-05 -11.01% 0.012112983 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 -5.82% 0.003382902 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Nov 01 Dec 01 Jan 02 Feb 02 Mar 02 Apr 02 May 02 Jun 02 Jul 02 Aug 02 Sep 02 Oct 02 Nov 02 Dec 02 Jan 03 Feb 03 Mar 03 Apr 03 May 03 Jun 03 Jul 03 Aug 03 Sep 03 Oct 03 Nov 03 Dec 03 Jan 04 Feb 04 Mar 04 Apr 04 May 04 Jun 04 Jul 04 Aug 04 Sep 04 Oct 04 Nov 04 Dec 04 Jan 05 Portfolio B -1.10% 1.38% -7.13% 3.68% 2.72% 13.44% -2.11% 2.51% 4.24% 10.09% 1.27% -0.56% -0.86% 3.56% -1.62% 7.47% 2.09% 3.40% -0.32% 2.82% 4.95% -5.70% 5.90% -6.23% 1.78% 3.24% 10.52% 1.09% -17.02% 1.77% 13.19% 12.80% 3.82% 4.50% 8.29% 7.74% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% S&P 500 -6.34% 7.77% 0.67% -2.43% -0.98% -6.26% -8.08% 1.91% 7.67% 0.88% -1.46% -1.93% 3.76% -6.06% -0.74% -7.12% -7.79% 0.66% -10.87% 8.80% 5.89% -5.87% 2.62% -1.50% 0.97% 8.24% 5.27% 1.28% 1.76% 1.95% -1.06% 5.66% 0.88% 5.24% 1.84% 1.39% -1.51% -1.57% 1.37% 1.94% 3.31% 0.40% 1.08% 1.53% 4.05% 3.40% -2.44% 90dBill 0.44% 0.38% 0.37% 0.32% 0.31% 0.30% 0.29% 0.26% 0.21% 0.18% 0.16% 0.13% 0.15% 0.14% 0.15% 0.14% 0.15% 0.14% 0.14% 0.14% 0.13% 0.12% 0.11% 0.09% 0.10% 0.10% 0.10% 0.09% 0.09% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.07% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% Port A Down(A) Down(A)^2 4.94% 4.94% 0.00244074 8.37% 0.66% -2.77% -2.77% 0.00076907 -2.18% -2.18% 0.0004756 4.07% 4.07% 0.00165943 -7.72% -7.72% 0.00595768 1.83% 5.73% 1.81% -1.33% -1.33% 0.00017795 -1.58% -1.58% 0.00025 4.81% % -5.43% 5.43% 0.0029439 -0.83% 0.83% 6.8367E-05 8.41% 8.41% 0.0070655 -7.18% -7.18% 0.00515022 0.66% - 10.21% -10.21% 0.01042012 6.79% 4.00% -5.11% 5.11% 0.0026108 2.22% 2.22% 0.00049413 -1.60% -1.60% 0.00025581 1.56% 6.76% 5.04% 1.02% 1.87% 2.29% -0.30% % -0.30% 9.2355E-06 5.48% 1.40% 4.15% 2.16% 2.27% 0.94% 0.94% 8.7834E-05 -2.30% -2.30% 0.00052974 1.80% 2.42% 4.03% 4.03% 0.00162636 0.30% -0.30% 8.9653E-06 1.30% 1.82% 5.06% 3.07% -2.90% 2.90% 0.00083876 Port B -1.54% 1.00% -7.50% 3.36% 2.40% 13.14% -2.39% 2.25% 4.02% 9.91% 1.11% -0.69% -1.01% 3.41% % -1.77% 7.32% -2.24% 3.26% -0.46% 2.68% 4.82% 5.82% 5.79% 6.32% 1.68% % 3.15% 10.43% 1.00% -17.10% 1.69% 13.11% 12.72% 3.74% 4.43% 8.21% 7.67% 4.01% -9.30% 1.27% -2.04% 8.02% -2.97% 1.04% 0.48% 6.25% 0.28% 1.00% S&P 6.78% 7.39% 0.30% -2.76% -1.30% 6.56% 8.36% 1.65% 7.46% 0.70% -1.62% -2.06% 3.61% 6.21% 0.89% -7.27% -7.94% 0.51% -11.01% 8.66% 5.76% -5.99% 2.73% -1.59% 0.87% 8.14% 5.17% 1.18% 1.68% 1.87% -1.14% % 5.58% 0.80% 5.16% 1.76% 1.32% -1.59% -1.65% 1.29% 1.86% 3.40% 0.30% 0.96% 1.39% 3.90% 3.24% -2.62% -5.99% -2.73% -1.59% 0.003593163 0.000744799 0.000253542 -6.32% 0.003994531 -17.10% 0.029252393 -1.14% 0.000129459 4.23% -1.59% -1.65% 0.000251984 0.000271063 -9.30% 0.008641045 -2.04% 0.000416662 2.24% 2.34% -0.86% -2.23% 1.88% 2.50% 3.94% -0.19% 1.42% 1.96% 5.21% 3.23% -2.72% -3.40% 0.001159266 -2.97% 0.000882173 2.62% 0.000684607 A D F J N R P Down(S&P) Down(S&P) A2 -1.14% 0.000129459 -1.59% -1.65% 0.000251984 0.000271063 -3.40% 0.001159266 1 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Apr 03 May 03 Jun 03 Jul 03 Aug 03 Sep 03 Oct 03 Nov 03 Dec 03 Jan 04 Feb 04 Mar 04 Apr 04 May 04 Jun 04 Jul 04 Aug 04 Sep 04 Oct 04 Nov 04 Dec 04 Jan 05 Feb 05 Mar 05 Apr 05 May 05 Jun 05 Jul 05 Aug 05 Sep 05 Oct 05 Nov 05 Dec 05 Jan-06 Feb-06 Mar-06 Annualized Retum Annualized Volatility B Portfolio A 6.85% 5.13% 1.11% 1.96% 2.37% -0.23% 5.56% 1.48% 4.23% 2.24% 2.34% -0.86% -2.23% 1.88% 2.50% 3.94% -0.19% 1.42% 1.96% 5.21% 3.23% 2.72% 2.57% -0.58% 2.07% 3.84% 0.66% 4.16% 0.72% 1.96% -2.02% 4.75% 0.83% 4.15% 0.05% 1.00% Portfolio B 3.24% 10.52% 1.09% -17.02% 1.77% 13.19% 12.80% 3.82% 4.50% 8.29% 7.74% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% 9.27% -1.09% 3.82% -0.06% 5.31% 2.78% -1.15% 7.09% 2.84% 5.94% 4.20% 1.17% 2.23% -5.05% S&P 500 8.24% 5.27% 1.28% 1.76% 1.95% -1.06% 5.66% 0.88% 5.24% 1.84% 1.39% -1.51% -1.57% 1.37% 1.94% -3.31% 0.40% 1.08% 1.53% 4.05% 3.40% 2.44% 2.10% -1.77% -1.90% 3.18% 0.14% 3.72% -0.91% 0.81% -1.67% 3.78% 0.03% 2.65% 0.27% 1.24% E 90dBill 0.10% 0.10% 0.09% 0.09% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.07% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% 0.18% 0.21% 0.22% 0.24% 0.24% 0.25% 0.27% 0.27% 0.29% 0.30% 0.32% 0.33% 0.32% 0.37% G H Port A Down(A) Down(A) 2 6.76% 5.04% 1.02% 1.87% 2.29% -0.30% -0.30% 9.2355E-06 5.48% 1.40% 4.15% 2.16% 2.27% -0.94% -0.94% 8.7834E-05 -2.30% -2.30% 0.00052974 1.80% 2.42% 4.03% 4.03% 0.00162636 -0.30% -0.30% 8.9653E-06 1.30% 1.82% 5.06% 3.07% 2.90% -2.90% 0.00083876 2.40% -0.79% -0.79% 6.1665E-05 2.29% 2.29% 0.00052309 3.60% 0.42% 3.90% -0.99% -0.99% 9.7822E-05 1.69% -2.31% -2.31% 0.00053553 4.45% 0.51% 3.82% -0.27% -0.27% 7.393E-06 0.63% L M Port B Down(B) Down B)^2 3.15% 10.43% 1.00% -17.10% -17.10% 0.029252393 1.69% 13.11% 12.72% 3.74% 4.43% 8.21% 7.67% 4.01% -9.30% -9.30% 0.008641045 1.27% 2.04% 2.04% 0.000416662 8.02% -2.97% -2.97% 0.000882173 1.04% 0.48% 6.25% 0.28% 1.00% 9.10% -1.30% -1.30% 0.000168833 4.04% 4.04% 0.001630884 -0.29% -0.29% 8.68672E-06 5.07% 2.52% -1.42% -1.42% 0.00020206 6.82% 2.55% 5.64% 4.52% 4.52% 0.002040274 0.84% 1.92% -5.42% 5.42% 0.002932439 0 S&P 8.14% 5.17% 1.18% 1.68% 1.87% -1.14% 5.58% 0.80% 5.16% 1.76% 1.32% -1.59% -1.65% 1.29% 1.86% -3.40% 0.30% 0.96% 1.39% 3.90% 3.24% -2.62% 1.93% -1.98% -2.11% 2.94% -0.09% 3.47% -1.18% 0.54% -1.96% 3.48% -0.28% 2.31% -0.05% 0.87% 2.62% 0.000684607 -1.98% 2.11% 0.000392198 0.000447196 -0.09% 8.70489E-07 -1.18% 0.000139004 -1.96% 0.00038467 -0.28% 8.1168E-06 0.05% 2.07936E-07 63 5.86% 24.64% 2.57% 2.19% 9.42% 10.95% 10.27% 10.27% 13.4% 19.0% 14.2% 0.3% 64 65 66 t999 t.9995 t.50 0.50 1.00 t.75 0.25 0.50 t 80 0.20 0.40 t.85 0.15 0.30 t.90 0.10 0.20 t 95 0.05 0.10 t.975 0.025 0.05 t. 99 0.01 0.02 t.995 0.005 0.01 0.001 0.0005 0.002 0.001 cum. prob one-tail two-tails df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 80 100 1000 z 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.678 0.677 0.675 0.674 50% 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.848 0.846 0.845 0.842 0.842 60% 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.045 1.043 1.042 1.037 1.036 70% 3.078 6.314 12.71 1.886 2.920 4.303 1.638 2.353 3.182 1.533 2.132 2.776 1.476 2.015 2.571 1.440 1.943 2.447 1.415 1.895 2.365 1.397 1.860 2.306 1.383 1.833 2.262 1.372 1.812 2.228 1.363 1.796 2.201 1.356 1.782 2.179 1.350 1.771 2.160 1.345 1.761 2.145 1.341 1.753 2.131 1.337 1.746 2.120 1.333 1.740 2.110 1.330 1.734 2.101 1.328 1.729 2.093 1.325 1.725 2.086 1.323 1.721 2.080 1.321 1.717 2.074 1.319 1.714 2.069 1.318 1.711 2.064 1.316 1.708 2.060 1.315 1.706 2.056 1.314 1.703 2.052 1.313 1.701 2.048 1.311 1.699 2.045 1.310 1.697 2.042 1.303 1.684 2.021 1.296 1.671 2.000 1.292 1.664 1.990 1.290 1.660 1.984 1.282 1.646 1.962 1.282 1.645 1.960 80% 90% 95% Confidence Level 31.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.374 2.364 2.330 2.326 98% 63.66 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 318.31 22.327 10.215 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.232 3.195 3.174 3.098 3.090 99.8% 636.62 31.599 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.416 3.390 3.300 3.291 99.9% 0.000 2.771 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0% 2.763 2.756 2.750 2.704 2.660 2.639 2.626 2.581 2.576 99% 3. Calculate the Sortino Ratio for Portfolios A, B & the S&P 500 4. Calculate the Information Ratio for Portfolios A, B & the S&P 500. Note the benchmark for Port A is the S&P 500. The benchmark for Port B is 90d T-bills. A B D E F. G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Nov 01 Dec 01 Jan 02 Feb 02 Mar 02 Apr 02 May 02 Jun 02 Jul 02 Aug 02 Sep 02 Oct 02 Nov 02 Dec 02 Jan 03 Feb 03 Mar 03 Apr 03 May 03 Jun 03 Jul 03 Aug 03 Sep 03 Oct 03 Nov 03 Dec 03 Jan 04 Feb 04 Mar 04 Apr 04 May 04 Jun 04 Jul 04 Aug 04 Portfolio A -4.50% 8.75% 1.03% -2.45% -1.87% -3.77% -7.43% 2.09% 5.94% 1.99% -1.18% -1.45% 4.95% -5.28% -0.68% -8.26% -7.03% 0.80% -10.07% 6.93% 4.13% -4.99% -2.11% -1.51% 1.66% 6.85% 5.13% 1.11% 1.96% 2.37% -0.23% 5.56% 1.48% 4.23% 2.24% 2.34% -0.86% -2.23% 1.88% 2.50% -3.94% -0.19% 1.42% 1.96% 5.21% 3.23% -2.72% Portfolio B -1.10% 1.38% -7.13% 3.68% 2.72% 13.44% -2.11% 2.51% 4.24% 10.09% 1.27% -0.56% -0.86% 3.56% -1.62% 7.47% -2.09% 3.40% -0.32% 2.82% 4.95% -5.70% 5.90% -6.23% 1.78% 3.24% 10.52% 1.09% -17.02% 1.77% 13.19% 12.80% 3.82% 4.50% 8.29% 7.74% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% S&P 500 -6.34% 7.77% 0.67% -2.43% -0.98% -6.26% -8.08% 1.91% 7.67% 0.88% -1.46% -1.93% 3.76% -6.06% -0.74% -7.12% -7.79% 0.66% -10.87% 8.80% 5.89% -5.87% -2.62% -1.50% 0.97% 8.24% 5.27% 1.28% 1.76% 1.95% -1.06% 5.66% 0.88% 5.24% 1.84% 1.39% -1.51% -1.57% 1.37% 1.94% -3.31% 0.40% 1.08% 1.53% 4.05% 3.40% -2.44% 90dBill 0.44% 0.38% 0.37% 0.32% 0.31% 0.30% 0.29% 0.26% 0.21% 0.18% 0.16% 0.13% 0.15% 0.14% 0.15% 0.14% 0.15% 0.14% 0.14% 0.14% 0.13% 0.12% 0.11% 0.09% 0.10% 0.10% 0.10% 0.09% 0.09% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.07% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% Sep 04 Oct 04 Nov 04 Dec 04 Jan 05 1 Portfolio A Portfolio B 90 dBill 38 Mar 04 39 Apr 04 40 May 04 41 Jun 04 42 Jul 04 43 Aug 04 44 Sep 04 45 Oct 04 46 Nov 04 47 Dec 04 48 Jan 05 49 Feb 05 50 Mar 05 51 Apr 05 52 May 05 53 Jun 05 54 Jul 05 55 Aug 05 56 Sep 05 57 Oct 05 58 Nov 05 59 Dec 05 60 Jan-06 61 Feb-06 62 Mar-06 Annualized 63 Return Annualized 64 Volatility 65 66 Monthly Vol 67 Avg Mthly Rtn 68 69 -0.86% -2.23% 1.88% 2.50% -3.94% -0.19% 1.42% 1.96% 5.21% 3.23% -2.72% 2.57% -0.58% -2.07% 3.84% 0.66% 4.16% -0.72% 1.96% -2.02% 4.75% 0.83% 4.15% 0.05% 1.00% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% 9.27% -1.09% -3.82% -0.06% 5.31% 2.78% -1.15% 7.09% 2.84% 5.94% -4.20% 1.17% 2.23% -5.05% S&P 500 -1.51% -1.57% 1.37% 1.94% -3.31% 0.40% 1.08% 1.53% 4.05% 3.40% -2.44% 2.10% -1.77% -1.90% 3.18% 0.14% 3.72% -0.91% 0.81% -1.67% 3.78% 0.03% 2.65% 0.27% 1.24% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% 0.18% 0.21% 0.22% 0.24% 0.24% 0.25% 0.27% 0.27% 0.29% 0.30% 0.32% 0.33% 0.32% 0.37% 5.86% 24.64% 2.57% 2. 19% 13.4% 19.0% 14.2% 0.3% 3.87% 0.55% 5.47% 2.00% 4.10% 0.30% 0.10% 0.18% A D E F G H 1 J K L M N o P Q RE Down/B] Down(B)^2 -1.54% 0.00023797 Down(S&P) -6.78% Down/S&P)^2 0.004591011 -7.50% 0.005622198 -2.76% -1.30% -6.56% -8.36% 0.000759113 0.00016848 0.004306872 0.006992639 -2.39% 0.000572433 -1.62% 2.06% 0.000260952 0.000425226 -0.69% 4.79832E-05 -1.01% 0.000101339 -1.77% 0.000312798 -6.21% -0.89% -7.27% -7.94% B Portfolio A 4.50% 8.75% 1.03% -2.45% -1,87% 3.77% -7.43% 2.09% 5.94% 1.99% -1.18% -1,45% 4.95% -5.28% -0.68% 8.26% -7.03% 0.80% -10.07% 6.93% 4.13% 4.99% 2.11% -1.51% 1.66% 6.85% 5.13% 1.11% 1.96% 2.37% -0.23% 5.56% 1.48% 0.003852685 7.85528E-05 0.005282092 0.006305948 -2.24% 0.000500225 -0.46% 2.10423E-05 -11.01% 0.012112983 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 -5.82% 0.003382902 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Nov 01 Dec 01 Jan 02 Feb 02 Mar 02 Apr 02 May 02 Jun 02 Jul 02 Aug 02 Sep 02 Oct 02 Nov 02 Dec 02 Jan 03 Feb 03 Mar 03 Apr 03 May 03 Jun 03 Jul 03 Aug 03 Sep 03 Oct 03 Nov 03 Dec 03 Jan 04 Feb 04 Mar 04 Apr 04 May 04 Jun 04 Jul 04 Aug 04 Sep 04 Oct 04 Nov 04 Dec 04 Jan 05 Portfolio B -1.10% 1.38% -7.13% 3.68% 2.72% 13.44% -2.11% 2.51% 4.24% 10.09% 1.27% -0.56% -0.86% 3.56% -1.62% 7.47% 2.09% 3.40% -0.32% 2.82% 4.95% -5.70% 5.90% -6.23% 1.78% 3.24% 10.52% 1.09% -17.02% 1.77% 13.19% 12.80% 3.82% 4.50% 8.29% 7.74% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% S&P 500 -6.34% 7.77% 0.67% -2.43% -0.98% -6.26% -8.08% 1.91% 7.67% 0.88% -1.46% -1.93% 3.76% -6.06% -0.74% -7.12% -7.79% 0.66% -10.87% 8.80% 5.89% -5.87% 2.62% -1.50% 0.97% 8.24% 5.27% 1.28% 1.76% 1.95% -1.06% 5.66% 0.88% 5.24% 1.84% 1.39% -1.51% -1.57% 1.37% 1.94% 3.31% 0.40% 1.08% 1.53% 4.05% 3.40% -2.44% 90dBill 0.44% 0.38% 0.37% 0.32% 0.31% 0.30% 0.29% 0.26% 0.21% 0.18% 0.16% 0.13% 0.15% 0.14% 0.15% 0.14% 0.15% 0.14% 0.14% 0.14% 0.13% 0.12% 0.11% 0.09% 0.10% 0.10% 0.10% 0.09% 0.09% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.07% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% Port A Down(A) Down(A)^2 4.94% 4.94% 0.00244074 8.37% 0.66% -2.77% -2.77% 0.00076907 -2.18% -2.18% 0.0004756 4.07% 4.07% 0.00165943 -7.72% -7.72% 0.00595768 1.83% 5.73% 1.81% -1.33% -1.33% 0.00017795 -1.58% -1.58% 0.00025 4.81% % -5.43% 5.43% 0.0029439 -0.83% 0.83% 6.8367E-05 8.41% 8.41% 0.0070655 -7.18% -7.18% 0.00515022 0.66% - 10.21% -10.21% 0.01042012 6.79% 4.00% -5.11% 5.11% 0.0026108 2.22% 2.22% 0.00049413 -1.60% -1.60% 0.00025581 1.56% 6.76% 5.04% 1.02% 1.87% 2.29% -0.30% % -0.30% 9.2355E-06 5.48% 1.40% 4.15% 2.16% 2.27% 0.94% 0.94% 8.7834E-05 -2.30% -2.30% 0.00052974 1.80% 2.42% 4.03% 4.03% 0.00162636 0.30% -0.30% 8.9653E-06 1.30% 1.82% 5.06% 3.07% -2.90% 2.90% 0.00083876 Port B -1.54% 1.00% -7.50% 3.36% 2.40% 13.14% -2.39% 2.25% 4.02% 9.91% 1.11% -0.69% -1.01% 3.41% % -1.77% 7.32% -2.24% 3.26% -0.46% 2.68% 4.82% 5.82% 5.79% 6.32% 1.68% % 3.15% 10.43% 1.00% -17.10% 1.69% 13.11% 12.72% 3.74% 4.43% 8.21% 7.67% 4.01% -9.30% 1.27% -2.04% 8.02% -2.97% 1.04% 0.48% 6.25% 0.28% 1.00% S&P 6.78% 7.39% 0.30% -2.76% -1.30% 6.56% 8.36% 1.65% 7.46% 0.70% -1.62% -2.06% 3.61% 6.21% 0.89% -7.27% -7.94% 0.51% -11.01% 8.66% 5.76% -5.99% 2.73% -1.59% 0.87% 8.14% 5.17% 1.18% 1.68% 1.87% -1.14% % 5.58% 0.80% 5.16% 1.76% 1.32% -1.59% -1.65% 1.29% 1.86% 3.40% 0.30% 0.96% 1.39% 3.90% 3.24% -2.62% -5.99% -2.73% -1.59% 0.003593163 0.000744799 0.000253542 -6.32% 0.003994531 -17.10% 0.029252393 -1.14% 0.000129459 4.23% -1.59% -1.65% 0.000251984 0.000271063 -9.30% 0.008641045 -2.04% 0.000416662 2.24% 2.34% -0.86% -2.23% 1.88% 2.50% 3.94% -0.19% 1.42% 1.96% 5.21% 3.23% -2.72% -3.40% 0.001159266 -2.97% 0.000882173 2.62% 0.000684607 A D F J N R P Down(S&P) Down(S&P) A2 -1.14% 0.000129459 -1.59% -1.65% 0.000251984 0.000271063 -3.40% 0.001159266 1 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Apr 03 May 03 Jun 03 Jul 03 Aug 03 Sep 03 Oct 03 Nov 03 Dec 03 Jan 04 Feb 04 Mar 04 Apr 04 May 04 Jun 04 Jul 04 Aug 04 Sep 04 Oct 04 Nov 04 Dec 04 Jan 05 Feb 05 Mar 05 Apr 05 May 05 Jun 05 Jul 05 Aug 05 Sep 05 Oct 05 Nov 05 Dec 05 Jan-06 Feb-06 Mar-06 Annualized Retum Annualized Volatility B Portfolio A 6.85% 5.13% 1.11% 1.96% 2.37% -0.23% 5.56% 1.48% 4.23% 2.24% 2.34% -0.86% -2.23% 1.88% 2.50% 3.94% -0.19% 1.42% 1.96% 5.21% 3.23% 2.72% 2.57% -0.58% 2.07% 3.84% 0.66% 4.16% 0.72% 1.96% -2.02% 4.75% 0.83% 4.15% 0.05% 1.00% Portfolio B 3.24% 10.52% 1.09% -17.02% 1.77% 13.19% 12.80% 3.82% 4.50% 8.29% 7.74% 4.09% -9.22% 1.35% -1.96% 8.12% -2.86% 1.15% 0.62% 6.39% 0.44% 1.18% 9.27% -1.09% 3.82% -0.06% 5.31% 2.78% -1.15% 7.09% 2.84% 5.94% 4.20% 1.17% 2.23% -5.05% S&P 500 8.24% 5.27% 1.28% 1.76% 1.95% -1.06% 5.66% 0.88% 5.24% 1.84% 1.39% -1.51% -1.57% 1.37% 1.94% -3.31% 0.40% 1.08% 1.53% 4.05% 3.40% 2.44% 2.10% -1.77% -1.90% 3.18% 0.14% 3.72% -0.91% 0.81% -1.67% 3.78% 0.03% 2.65% 0.27% 1.24% E 90dBill 0.10% 0.10% 0.09% 0.09% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.07% 0.08% 0.08% 0.08% 0.08% 0.10% 0.11% 0.12% 0.13% 0.14% 0.16% 0.18% 0.18% 0.21% 0.22% 0.24% 0.24% 0.25% 0.27% 0.27% 0.29% 0.30% 0.32% 0.33% 0.32% 0.37% G H Port A Down(A) Down(A) 2 6.76% 5.04% 1.02% 1.87% 2.29% -0.30% -0.30% 9.2355E-06 5.48% 1.40% 4.15% 2.16% 2.27% -0.94% -0.94% 8.7834E-05 -2.30% -2.30% 0.00052974 1.80% 2.42% 4.03% 4.03% 0.00162636 -0.30% -0.30% 8.9653E-06 1.30% 1.82% 5.06% 3.07% 2.90% -2.90% 0.00083876 2.40% -0.79% -0.79% 6.1665E-05 2.29% 2.29% 0.00052309 3.60% 0.42% 3.90% -0.99% -0.99% 9.7822E-05 1.69% -2.31% -2.31% 0.00053553 4.45% 0.51% 3.82% -0.27% -0.27% 7.393E-06 0.63% L M Port B Down(B) Down B)^2 3.15% 10.43% 1.00% -17.10% -17.10% 0.029252393 1.69% 13.11% 12.72% 3.74% 4.43% 8.21% 7.67% 4.01% -9.30% -9.30% 0.008641045 1.27% 2.04% 2.04% 0.000416662 8.02% -2.97% -2.97% 0.000882173 1.04% 0.48% 6.25% 0.28% 1.00% 9.10% -1.30% -1.30% 0.000168833 4.04% 4.04% 0.001630884 -0.29% -0.29% 8.68672E-06 5.07% 2.52% -1.42% -1.42% 0.00020206 6.82% 2.55% 5.64% 4.52% 4.52% 0.002040274 0.84% 1.92% -5.42% 5.42% 0.002932439 0 S&P 8.14% 5.17% 1.18% 1.68% 1.87% -1.14% 5.58% 0.80% 5.16% 1.76% 1.32% -1.59% -1.65% 1.29% 1.86% -3.40% 0.30% 0.96% 1.39% 3.90% 3.24% -2.62% 1.93% -1.98% -2.11% 2.94% -0.09% 3.47% -1.18% 0.54% -1.96% 3.48% -0.28% 2.31% -0.05% 0.87% 2.62% 0.000684607 -1.98% 2.11% 0.000392198 0.000447196 -0.09% 8.70489E-07 -1.18% 0.000139004 -1.96% 0.00038467 -0.28% 8.1168E-06 0.05% 2.07936E-07 63 5.86% 24.64% 2.57% 2.19% 9.42% 10.95% 10.27% 10.27% 13.4% 19.0% 14.2% 0.3% 64 65 66 t999 t.9995 t.50 0.50 1.00 t.75 0.25 0.50 t 80 0.20 0.40 t.85 0.15 0.30 t.90 0.10 0.20 t 95 0.05 0.10 t.975 0.025 0.05 t. 99 0.01 0.02 t.995 0.005 0.01 0.001 0.0005 0.002 0.001 cum. prob one-tail two-tails df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 80 100 1000 z 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.678 0.677 0.675 0.674 50% 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.848 0.846 0.845 0.842 0.842 60% 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.045 1.043 1.042 1.037 1.036 70% 3.078 6.314 12.71 1.886 2.920 4.303 1.638 2.353 3.182 1.533 2.132 2.776 1.476 2.015 2.571 1.440 1.943 2.447 1.415 1.895 2.365 1.397 1.860 2.306 1.383 1.833 2.262 1.372 1.812 2.228 1.363 1.796 2.201 1.356 1.782 2.179 1.350 1.771 2.160 1.345 1.761 2.145 1.341 1.753 2.131 1.337 1.746 2.120 1.333 1.740 2.110 1.330 1.734 2.101 1.328 1.729 2.093 1.325 1.725 2.086 1.323 1.721 2.080 1.321 1.717 2.074 1.319 1.714 2.069 1.318 1.711 2.064 1.316 1.708 2.060 1.315 1.706 2.056 1.314 1.703 2.052 1.313 1.701 2.048 1.311 1.699 2.045 1.310 1.697 2.042 1.303 1.684 2.021 1.296 1.671 2.000 1.292 1.664 1.990 1.290 1.660 1.984 1.282 1.646 1.962 1.282 1.645 1.960 80% 90% 95% Confidence Level 31.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.374 2.364 2.330 2.326 98% 63.66 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 318.31 22.327 10.215 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.232 3.195 3.174 3.098 3.090 99.8% 636.62 31.599 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.416 3.390 3.300 3.291 99.9% 0.000 2.771 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0% 2.763 2.756 2.750 2.704 2.660 2.639 2.626 2.581 2.576 99% 3. Calculate the Sortino Ratio for Portfolios A, B & the S&P 500 4. Calculate the Information Ratio for Portfolios A, B & the S&P 500. Note the benchmark for Port A is the S&P 500. The benchmark for Port B is 90d T-bills