2999 495598 503342 758600 0017442 25 537295 505129 522404 463700

2999 495598 503342 758600 0017442 25 537295 505129

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52.2999 49.5598 50.3342 758600 -0.017442
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Nov-97 50.5725 53.7295 50.5129 52.2404 463700 0.037871 Dec-97 52.4191 55.7986 52.4191 55.7388 1090300 0.066967 Jan-98 55.6191 55.6191 49.1003 50.4759 617800 -0.094421 Feb-98 51.4328 54.2436 51.0739 53.7054 969000 0.063981 Mar-98 53.825 60.3752 53.4661 59.475 838100 0.107431 Apr-98 57.8546 58.9348 54.6137 56.1141 889200 -0.056509 May-98 55.694 56.5942 49.7525 49.8125 912900 -0.1123 Jun-98 49.9326 51.112 49.4524 50.9613 1002700 0.023062 Jul-98 50.9914 51.0517 38.2737 38.7559 1536500 -0.239503 Aug-98 38.7559 40.6244 31.282 31.8244 1436100 -0.17885 Sep-98 32.7285 34.4765 29.1939 29.3759 1457700 -0.076938 Oct-98 29.3759 35.0812 28.1621 34.5956 1365700 0.177686 Nov-98 35.4453 36.7806 33.139 33.928 1362600 -0.019297 Dec-98 33.139 33.6245 30.4994 32.1496 1237700 -0.052417 Jan-99 33.7388 35.0834 31.1106 31.844 1369300 -0.009506 Feb-99 32.2719 32.3941 31.2939 31.9663 1159800 0.003841 Mar-99 31.844 39.1627 31.6607 37.9945 1457900 0.18858 Apr-99 37.8716 42.4211 37.5027 42.0522 2965600 0.106797 May-99 41.8063 41.9907 36.9494 37.5642 1088000 -0.106724 Jun-99 37.3183 39.689 36.3346 38.7617 1472100 0.031879 Jul-99 39.1945 39.3799 37.5871 37.7108 920600 -0.027112 Aug-99 37.8962 38.8235 37.8344 38.4526 642600 0.019671 Sep-99 38.5763 39.7509 38.1734 38.4842 781500 0.000822 Oct-99 37.8004 38.1734 35.6865 36.0596 878200 -0.063002 Nov-99 35.8109 43.458 35.1891 42.7119 1021400 0.184481 Dec-99 41.7793 43.5 41.4063 43.375 703900 0.015525 0.013388 Mean retur 0.081454 Std Dev of
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rn per month f return
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IBM MSFT DE -0.069857 -0.002053 -0.005222 -0.101853 -0.161786 0.111693 0.045818 0.120254 0.011878 -0.03943 0.082861 0.12676 0.020524 -0.124003 -0.063172 0.027934 0.033012 0.060406 0.018479 0.073119 0.065398 -0.067238 0.165931 -0.049979 -0.082378 0.193399 -0.079667 -0.026185 0.064206 0.095675 -0.03585 0 0.031535 0.047808 0.063229 0.069106 0.053229 0.067564 0.074144 0.021664 0.121546 0.039139 0.02709 0.047393 0.02916 0.100917 0.258643 -0.013336 -0.020835 0.041079 -0.003176 -0.051064 -0.125006 -0.006825 -0.086321 -0.075195 -0.219929 0.044171 0.02441 -0.158844 -0.008227 0.011886 -0.153439 0.077015 0.13333 0.118748 -0.0055 0.041557 0.058937 0.121681 0.303976 0.165331 0.01578 0.057306 -0.05492 -0.115533 0.022902 -0.046146 -0.0955 -0.067133 0.010254 0.030341 0.108582 0.134514 -0.084807 -0.068917 -0.060712 0.042473 0.078915 -0.007209 -0.04321 0.159869 0.004841 0.069676 0.043974 0.038462 -0.05187 0.054796 0.060895 -0.058522 0.035945 -0.145696 -0.03784 0.14395 0.003521 0.011237 0.080899 0.04427 -0.034723 0.027024 0.017459 -0.038848 -0.04048 0.012111 0.086825 -0.06961 -0.029337 0 0.097501 -0.075567 0.078512 -0.132237 -0.059582 -0.031926 0.039291 -0.014666 -0.085752 0.024038 -0.074404 -0.067822 0.080538 0.136127 -0.171824 0.1025 -0.094558 0.020558 0.049289 -0.009486 -0.261906 -0.083226 0.131562 0.022332 0.013175 0.06 0.055831 -0.036125 0.121291 -0.064372 0.109444 0.031292 -0.044225 -0.075659 0.134121 0.084837 0.08333 0.047716 -0.063979 -0.049939 0.059573
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-0.098734 -0.159091 -0.041429 0.028087 0.0152 0.145383 -0.081968 0.098162 0.000483 0.095235 -0.028781 0.067357 0.171201 -0.001558 -0.082524 0.048725 0.00782 0.05138 0 0.055804 0.087835 -0.064162 -0.030844 0.048139 0.033095 0.027288 0.005763 0.05263 0.091431 -0.091852 0.095659 0.162181 -0.089722 -0.067461 -0.039546 -0.023467 0.053186 -0.002417 0.036968 0.107077 0.128637 0.058824 0.016423 -0.034409 -0.06833 0.070018 0.122498 0.043715 -0.050336 -0.001981 -0.102965 0.038869 -0.027839 0.03984 -0.01871 -0.028623 0.075475 0.043329 0.061049 0.073684 0.091364 0.128965 0.069442 0.152207 0.149394 0.009232 -0.017173 0.035924 0.054877 0.032256 0.067165 -0.00376 0.134116 0.001381 0.049632 -0.050516 0.022099 -0.047285 -0.085855 -0.021622 -0.042545 0.0291 0.104972 0.098312 -0.006426 -0.128752 0.107693 -0.054331 0.007181 0.074297 0.187412 0.054126 0.063831 0.130185 0.066889 0.043333 -0.092763 0.044966 0.0689 -0.031459 0.09818 -0.066066 -0.009281 0.048572 0.070739 -0.072599 0.011574 -0.034212 0.085856 -0.018727 -0.106248 0.063955 0.039235 0.111885 0.088523 0.076532 0.061676 0.036147 0.040754 -0.002977 0.235463 0.142992 0.065673 -0.049411 0.053383 -0.088096 0.035479 0.234496 0.055556 -0.083665 -0.044118 -0.002924 -0.045218 -0.059614 0.025228 0.169397 0.325152 0.057472 0.077882 0.020576 0.111413 0.043353 0.019155 0.077326 0.171745 0.118694 0.036447 -0.041371 -0.064987 -0.015385 0.045623 0.000944 -0.036644 -0.070756 -0.017477 -0.017442 0.111677 0.088462 0.037871 -0.044521 -0.086572 0.066967
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-0.056154 0.154256 -0.094421 0.057595 0.136153 0.063981 -0.005386 0.056047 0.107431 0.115523 0.006983 -0.056509 0.014024 -0.058947 -0.1123 -0.022873 0.27782 0.023062 0.154056 0.014418 -0.239503 -0.15 -0.127345 -0.17885 0.140954 0.147229 -0.076938 0.155643 -0.038046 0.177686 0.113597 0.152302 -0.019297 0.116577 0.136784 -0.052417 -0.006101 0.261829 -0.009506 -0.072441 -0.142143 0.003841 0.044183 0.194005 0.18858 0.180181 -0.092748 0.106797 0.11031 -0.007686 -0.106724 0.114228 0.117738 0.031879 -0.027566 -0.04851 -0.027112 -0.007983 0.07866 0.019671 -0.0286 -0.021607 0.000822 -0.188016 0.022084 -0.063002 0.050377 -0.016374 0.184481 0.0467 0.282306 0.015525
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Portfolio Optimization with Solver Variance-Covariance Matrix, Sigma IBM MSFT DE 0.003 IBM 0.007004 0.002638 0.001109 MSFT 0.002638 0.009141 0.000878 DE 0.001109 0.000878 0.006534 Expected Returns (R) IBM 0.0127 MSFT 0.0428 DE 0.0134 Global Minimum Variance Portfolio (Minimize variance without restriction on expected return) Minimum Variance Frontier (Minimize variance such that portfolio expected return equals the Target Exp. Return) Weights MVP IBM 0.5508 0.4850 0.3975 0.3291 0.2662 0.1787 0.0694 -0.0619 -0.2150 -0.4118 MSFT -0.1024 -0.0020 0.1319 0.2365 0.3327 0.4667 0.6340 0.8348 1.0691 1.3704 DE 0.5516 0.5170 0.4706 0.4344 0.4010 0.3546 0.2967 0.2271 0.1459 0.0415 Sum of weights 1 1.000001 1 1 1 1 1 1 1 1 Target Expected return 0.01 0.013 0.017 0.02012 0.023 0.027 0.032 0.038 0.045 0.054 Variance 0.00449 0.00394 0.00351 0.00341 0.00350 0.00391 0.00489 0.00676 0.00990 0.01545 Standard Deviation 0.06698 0.06280 0.05927 0.05840 0.05914 0.06251 0.06993 0.08224 0.09951 0.12429 Exp return 0.010 0.013 0.017 0.02012 0.023 0.027 0.032 0.038 0.045 0.054 Weights (w) Tangency IBM -0.0863 MSFT 0.8722 DE 0.2141 Sum of weights 1 0.00720 Standard Deviation 0.084824 Exp Return (w'R) 0.03912 Sharpe Ratio 0.42578 R f Variance (w' S w) 0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000 0.000 0.010 0.020 0.030 0.040 0.050 0.060 Portfolio Frontier Standard Deviation Expected return A B C D E F G H I J K 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 49 50 51 52 53 54 55 56 57 58 59
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