| 5 Assets | |||||||||||||||||||||
| Returns: | 10.9176 | 13.6357 | 15.84892 | 8.69405 | 8.3573 | ||||||||||||||||
| Var - Cov Matrix | |||||||||||||||||||||
| 367.843 | 264.69 | 292.1499 | 59.9763 | 21.718 | |||||||||||||||||
| 264.69 | 349.275 | 345.3725 | 98.5251 | 45.6425 | |||||||||||||||||
| 292.15 | 345.373 | 651.2748 | 29.2018 | 1.56749 | |||||||||||||||||
| 59.9763 | 98.5251 | 29.20177 | 127.48 | 70.8837 | |||||||||||||||||
| 21.718 | 45.6425 | 1.567486 | 70.8837 | 44.7809 | |||||||||||||||||
| A=H= | mu1 | mu2 | mu3 | mu4 | mu5 | ||||||||||||||||
| 1 | 1 | 1 | 1 | 1 | |||||||||||||||||
| Target Return: | 9.1 | AT | mu1 | 1 | |||||||||||||||||
| mu2 | 1 | ||||||||||||||||||||
| mu3 | 1 | ||||||||||||||||||||
| mu4 | 1 | ||||||||||||||||||||
| mu5 | 1 | ||||||||||||||||||||
| Min: | h1+h2 | ||||||||||||||||||||
| ST | |||||||||||||||||||||
| Z | x1 | x2 | x3 | x4 | x5 | u1 | u2 | v1 | v2 | v3 | v4 | v5 | h1 | h2 | RHS | ||||||
| Row Zero | 1 | 1000 | 1000 | 0 | |||||||||||||||||
| n -equations | -367.84 | -264.69 | -292.15 | -59.976 | -21.72 | -10.918 | -1 | 1 | = | 0 | |||||||||||
| -264.69 | -349.27 | -345.37 | -98.525 | -45.64 | -13.636 | -1 | 1 | = | 0 | ||||||||||||
| -292.15 | -345.37 | -651.27 | -29.202 | -1.567 | -15.849 | -1 | 1 | = | 0 | ||||||||||||
| -59.976 | -98.525 | -29.202 | -127.48 | -70.88 | -8.6941 | -1 | 1 | = | 0 | ||||||||||||
| -21.718 | -45.643 | -1.5675 | -70.884 | -44.78 | -8.3573 | -1 | 1 | = | 0 | ||||||||||||
| 2-Equations | 10.918 | 13.636 | 15.849 | 8.694 | 8.357 | 1 | = | 9.1 | |||||||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | = | 1 | ||||||||||||||
| New Row Zero | 1 | -11918 | -14636 | -16849 | -9694.1 | -9357 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -10100 | |||||
| Z | x1 | x2 | x3 | x4 | x5 | u1 | u2 | v1 | v2 | v3 | v4 | v5 | h1 | h2 | RHS | ||||||
| Tableau 1 | Row zero | 1 | -11918 | -14636 | -16849 | -9694.1 | -9357 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -10100 | Ratio | |||
| x3 in; h1 out | v1 | 0 | -367.84 | -264.69 | -292.15 | -59.976 | -21.72 | -10.918 | -1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| ignore neg coeff | v2 | 0 | -264.69 | -349.27 | -345.37 | -98.525 | -45.64 | -13.636 | -1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| v3 | 0 | -292.15 | -345.37 | -651.27 | -29.202 | -1.567 | -15.849 | -1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |||||
| v4 | 0 | -59.976 | -98.525 | -29.202 | -127.48 | -70.88 | -8.6941 | -1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |||||
| v5 | 0 | -21.718 | -45.643 | -1.5675 | -70.884 | -44.78 | -8.3573 | -1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |||||
| h1 (x3) | 0 | 10.9176 | 13.6357 | 15.8489 | 8.6941 | 8.357 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 9.1 | 0.574172 | ||||
| h2 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | ||||
| Tableau 2 | Row zero | 1 | -311.15 | -139.65 | 0 | -451.44 | -472.7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1063.1 | 0 | -425.8 | Ratio | |||
| x5 in; h2 out | v1 | 0 | -166.59 | -13.338 | 0 | 100.28 | 132.3 | -10.918 | -1 | 1 | 0 | 0 | 0 | 0 | 18.433 | 0 | 167.7 | 1.672677 | |||
| ignore neg coeff | v2 | 0 | -26.78 | -52.132 | 0 | 90.932 | 136.5 | -13.636 | -1 | 0 | 1 | 0 | 0 | 0 | 21.792 | 0 | 198.3 | 2.180788 | |||
| v3 | 0 | 156.482 | 214.954 | 0 | 328.06 | 341.9 | -15.849 | -1 | 0 | 0 | 1 | 0 | 0 | 41.093 | 0 | 373.9 | 1.139862 | ||||
| v4 | 0 | -39.861 | -73.401 | 0 | -111.46 | -55.49 | -8.6941 | -1 | 0 | 0 | 0 | 1 | 0 | 1.8425 | 0 | 16.77 | |||||
| v5 | 0 | -20.638 | -44.294 | 0 | -70.024 | -43.95 | -8.3573 | -1 | 0 | 0 | 0 | 0 | 1 | 0.0989 | 0 | 0.9 | |||||
| x3 | 0 | 0.68885 | 0.86035 | 1 | 0.5486 | 0.527 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.0631 | 0 | 0.574 | 1.046692 | ||||
| h2 (x5) | 0 | 0.31115 | 0.13965 | 0 | 0.4514 | 0.473 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -0.0631 | 1 | 0.426 | 0.943263 | ||||
| Z | x1 | x2 | x3 | x4 | x5 | u1 | u2 | v1 | v2 | v3 | v4 | v5 | h1 | h2 | RHS | ||||||
| Tableau 3* | Row zero | 1 | -2E-12 | -1E-12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1000 | 1000 | -2E-12 | Ratio | |||
| u1 in; v3 out | v1 | 0 | -253.7 | -52.434 | 0 | -26.102 | 0 | -10.918 | -1 | 1 | 0 | 0 | 0 | 0 | 36.098 | -280 | 48.53 | ||||
| Remove complementary Slackness | v2 | 0 | -116.61 | -92.451 | 0 | -39.409 | 0 | -13.636 | -1 | 0 | 1 | 0 | 0 | 0 | 40.009 | -288.7 | 75.36 | ||||
| (Others nearly zero) | v3 (u1) | 0 | -68.544 | 113.96 | 0 | 1.5708 | 0 | -15.849 | -1 | 0 | 0 | 1 | 0 | 0 | 86.725 | -723.2 | 65.98 | ||||
| v4 | 0 | -3.3375 | -57.009 | 0 | -58.47 | 0 | -8.6941 | -1 | 0 | 0 | 0 | 1 | 0 | -5.5638 | 117.38 | 66.75 | -20.0007 | ||||
| v5 | 0 | 8.29469 | -31.309 | 0 | -28.045 | 0 | -8.3573 | -1 | 0 | 0 | 0 | 0 | 1 | -5.7682 | 92.988 | 40.5 | 4.882266 | ||||
| x3 | 0 | 0.34175 | 0.70457 | 1 | 0.045 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1335 | -1.116 | 0.099 | 0.290088 | ||||
| x5 | 0 | 0.65825 | 0.29543 | 0 | 0.955 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -0.1335 | 2.1156 | 0.901 | 1.368574 | ||||
| Tableau 4* | Row zero | 1 | -2E-12 | -1E-12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1000 | 1000 | -2E-12 | ||||
| u2 in; v4 out | v1 | 0 | -206.49 | -130.94 | 0 | -27.184 | 0 | 0 | -0.31 | 1 | 0 | -0.69 | 0 | 0 | -23.643 | 218.23 | 3.079 | ||||
| Remove complementary Slackness | v2 | 0 | -57.642 | -190.5 | 0 | -40.761 | 0 | 0 | -0.14 | 0 | 1 | -0.86 | 0 | 0 | -34.605 | 333.5 | 18.59 | ||||
| (Others nearly zero) | u1 | 0 | 4.32485 | -7.1904 | 0 | -0.0991 | 0 | 1 | 0.063 | 0 | 0 | -0.06 | 0 | 0 | -5.472 | 45.632 | -4.163 | ||||
| v4 | 0 | 34.263 | -119.52 | 0 | -59.331 | 0 | 0 | -0.45 | 0 | 0 | -0.55 | 1 | 0 | -53.137 | 514.11 | 30.56 | |||||
| v5 (u2) | 0 | 44.4387 | -91.401 | 0 | -28.874 | 0 | 0 | -0.47 | 0 | 0 | -0.53 | 0 | 1 | -51.499 | 474.35 | 5.706 | |||||
| x3 | 0 | 0.34175 | 0.70457 | 1 | 0.045 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1335 | -1.116 | 0.099 | |||||
| x5 | 0 | 0.65825 | 0.29543 | 0 | 0.955 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -0.1335 | 2.1156 | 0.901 | |||||
| Z | x1 | x2 | x3 | x4 | x5 | u1 | u2 | v1 | v2 | v3 | v4 | v5 | h1 | h2 | RHS | ||||||
| Tableau 5* | Row zero | 1 | -2E-12 | -1E-12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1000 | 1000 | -2E-12 | ||||
| v1 | 0 | -235.74 | -70.771 | 0 | -8.1782 | 0 | 0 | 0 | 1 | 0 | -0.34 | 0 | -0.66 | 10.257 | -94.01 | -0.677 | |||||
| v2 | 0 | -70.771 | -163.49 | 0 | -32.231 | 0 | 0 | 0 | 0 | 1 | -0.7 | 0 | -0.3 | -19.391 | 193.36 | 16.91 | |||||
| u1 | 0 | 10.2566 | -19.391 | 0 | -3.9532 | 0 | 1 | 0 | 0 | 0 | -0.13 | 0 | 0.133 | -12.346 | 108.95 | -3.401 | |||||
| v4 | 0 | -8.1782 | -32.231 | 0 | -31.756 | 0 | 0 | 0 | 0 | 0 | -0.04 | 1 | -0.96 | -3.9532 | 61.084 | 25.11 | |||||
| u2 | 0 | -94.012 | 193.363 | 0 | 61.084 | 0 | 0 | 1 | 0 | 0 | 1.116 | 0 | -2.12 | 108.95 | -1004 | -12.07 | |||||
| x3 | 0 | 0.34175 | 0.70457 | 1 | 0.045 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1335 | -1.116 | 0.099 | |||||
| x5 | 0 | 0.65825 | 0.29543 | 0 | 0.955 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -0.1335 | 2.1156 | 0.901 | |||||
| Z | x1 | x2 | x3 | x4 | x5 | u1 | u2 | v1 | v2 | v3 | v4 | v5 | h1 | h2 | s | RHS | |||||
| Tableau 6 | Row zero | 1 | -2E-12 | -1E-12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1000 | 1000 | -2E-12 | ||||
| Introduce s | v1 (s) | 0 | -235.74 | -70.771 | 0 | -8.1782 | 0 | 0 | 0 | 1 | 0 | -0.34 | 0 | -0.66 | 10.257 | -94.01 | -0.68 | -0.677 | |||
| s in; v1 out | v2 | 0 | -70.771 | -163.49 | 0 | -32.231 | 0 | 0 | 0 | 0 | 1 | -0.7 | 0 | -0.3 | -19.391 | 193.36 | 16.91 | ||||
| IGNORE u's | u1 | 0 | 10.2566 | -19.391 | 0 | -3.9532 | 0 | 1 | 0 | 0 | 0 | -0.13 | 0 | 0.133 | -12.346 | 108.95 | -3.401 | ||||
| Iterations here (!) | v4 | 0 | -8.1782 | -32.231 | 0 | -31.756 | 0 | 0 | 0 | 0 | 0 | -0.04 | 1 | -0.96 | -3.9532 | 61.084 | 25.11 | ||||
| u2 | 0 | -94.012 | 193.363 | 0 | 61.084 | 0 | 0 | 1 | 0 | 0 | 1.116 | 0 | -2.12 | 108.95 | -1004 | -12.07 | |||||
| x3 | 0 | 0.34175 | 0.70457 | 1 | 0.045 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1335 | -1.116 | 0.099 | |||||
| x5 | 0 | 0.65825 | 0.29543 | 0 | 0.955 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -0.1335 | 2.1156 | 0.901 | |||||
| Tableau 7 | Row zero | 1 | -2E-12 | -1E-12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1000 | 1000 | 2000 | -2E-12 | |||
| Add Big M to s | s | 0 | 348.183 | 104.528 | 0 | 12.079 | 0 | 0 | 0 | -1.48 | 0 | 0.505 | 0 | 0.972 | -15.149 | 138.85 | 1 | 1 | |||
| v2 | 0 | -70.771 | -163.49 | 0 | -32.231 | 0 | 0 | 0 | 0 | 1 | -0.7 | 0 | -0.3 | -19.391 | 193.36 | 0 | 16.91 | ||||
| u1 | 0 | 10.2566 | -19.391 | 0 | -3.9532 | 0 | 1 | 0 | 0 | 0 | -0.13 | 0 | 0.133 | -12.346 | 108.95 | 0 | -3.401 | ||||
| v4 | 0 | -8.1782 | -32.231 | 0 | -31.756 | 0 | 0 | 0 | 0 | 0 | -0.04 | 1 | -0.96 | -3.9532 | 61.084 | 0 | 25.11 | ||||
| u2 | 0 | -94.012 | 193.363 | 0 | 61.084 | 0 | 0 | 1 | 0 | 0 | 1.116 | 0 | -2.12 | 108.95 | -1004 | 0 | -12.07 | ||||
| x3 | 0 | 0.34175 | 0.70457 | 1 | 0.045 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1335 | -1.116 | 0 | 0.099 | ||||
| x5 | 0 | 0.65825 | 0.29543 | 0 | 0.955 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -0.1335 | 2.1156 | 0 | 0.901 | ||||
| Tableau 8 | New Row Zero | 1 | -696367 | -209055 | 0 | -24158 | 0 | 0 | 0 | 2954 | 0 | -1010 | 0 | -1944 | 31298 | -3E+05 | 0 | -2000 | Ratio | ||
| x1 in; s out | s (x1) | 0 | 348.183 | 104.528 | 0 | 12.079 | 0 | 0 | 0 | -1.48 | 0 | 0.505 | 0 | 0.972 | -15.149 | 138.85 | 1 | 1 | 0.009567 | ||
| v2 | 0 | -70.771 | -163.49 | 0 | -32.231 | 0 | 0 | 0 | 0 | 1 | -0.7 | 0 | -0.3 | -19.391 | 193.36 | 0 | 16.91 | -0.10341 | |||
| u1 | 0 | 10.2566 | -19.391 | 0 | -3.9532 | 0 | 1 | 0 | 0 | 0 | -0.13 | 0 | 0.133 | -12.346 | 108.95 | 0 | -3.401 | ||||
| v4 | 0 | -8.1782 | -32.231 | 0 | -31.756 | 0 | 0 | 0 | 0 | 0 | -0.04 | 1 | -0.96 | -3.9532 | 61.084 | 0 | 25.11 | -0.77905 | |||
| u2 | 0 | -94.012 | 193.363 | 0 | 61.084 | 0 | 0 | 1 | 0 | 0 | 1.116 | 0 | -2.12 | 108.95 | -1004 | 0 | -12.07 | -0.06243 | |||
| x3 | 0 | 0.34175 | 0.70457 | 1 | 0.045 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1335 | -1.116 | 0 | 0.099 | 0.140707 | |||
| x5 | 0 | 0.65825 | 0.29543 | 0 | 0.955 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -0.1335 | 2.1156 | 0 | 0.901 | 3.049334 | |||
| Z | x1 | x2 | x3 | x4 | x5 | u1 | u2 | v1 | v2 | v3 | v4 | v5 | h1 | h2 | s | RHS | |||||
| Tableau 9 | Row Zero | 1 | -487311 | -146295 | 0 | -16906 | 0 | 0 | 0 | 2067 | 0 | -706 | 0 | -1361 | 22202 | -2E+05 | 600.4 | -1400 | |||
| DONE! | x1 | 0 | 1 | 0.30021 | 0 | 0.0347 | 0 | 0 | 0 | -0 | 0 | 0.001 | 0 | 0.003 | -0.0435 | 0.3988 | 0.003 | 0.003 | |||
| v2 | 0 | 0 | -142.25 | 0 | -29.776 | 0 | 0 | 0 | -0.3 | 1 | -0.6 | 0 | -0.1 | -22.47 | 221.59 | 0.203 | 17.11 | ||||
| u1 | 0 | 0 | -22.47 | 0 | -4.309 | 0 | 1 | 0 | 0.04 | 0 | -0.15 | 0 | 0.105 | -11.9 | 104.86 | -0.03 | -3.431 | ||||
| v4 | 0 | 0 | -29.776 | 0 | -31.472 | 0 | 0 | 0 | -0.03 | 0 | -0.03 | 1 | -0.93 | -4.309 | 64.345 | 0.023 | 25.13 | ||||
| u2 | 0 | 0 | 221.586 | 0 | 64.345 | 0 | 0 | 1 | -0.4 | 0 | 1.252 | 0 | -1.85 | 104.86 | -966 | 0.27 | -11.8 | ||||
| x3 | 0 | 0 | 0.60197 | 1 | 0.0331 | 0 | 0 | 0 | 0 | 0 | -0 | 0 | -0 | 0.1484 | -1.252 | -0 | 0.098 | ||||
| x5 | 0 | 0 | 0.09782 | 0 | 0.9322 | 1 | 0 | 0 | 0 | 0 | -0 | 0 | -0 | -0.1048 | 1.853 | -0 | 0.899 | ||||
| DONE! | 0.5521 | ||||||||||||||||||||
| x1 | 0.002872 | 0.4478 | |||||||||||||||||||
| x3 | 0.098156 | 0.9999 | |||||||||||||||||||
| x5 | 0.898972 | ||||||||||||||||||||