rf 0.04 rm 0.1 sigma_m 0.09 rm rf x 0.09 0 y 0.1 0.04 "covar_i,m" 1 0.0108 2 -0.0027 3 0.0054 Beta_i 1 1.333333333 2 -0.333333333 3 0.666666667 r_ei 1 0.12 2 0.02 3 0.08 rf r1 r2 r3 x 0 1.333333333 -0.333333333 0.666666667 y 0.04 0.12 0.02 0.08 ##### Sheet/List 2 ##### ri correlation i a M sigma i "cov_i,m" beta_i r_ei Delta_i S1 15.5 0.9 20 216 1.5 15.5 0 S2 9.2 0.8 9 86.4 0.6 9.2 0 S3 11.2 0.5 15 90 0.625 9.375 1.825 MP 12 1 12 144 1 rf 5 0 0 rf s1 s2 s3 x 0 1.5 0.6 0.625 beta_i y 5 15.5 9.2 9.375 r_ei 15.5 9.2 11.2 r_i ##### Sheet/List 3 ##### Day A B C D E Market Index A B C D E Market Index 1 570 98.4 669.1 53.9 103.5 333.4 2 569 98.2 715 53.8 103 338.9 -0.001755927 -0.002034589 0.066349017 -0.001857011 -0.004842624 0.016362108 3 563.8 96.6 725 53.2 101.9 346.8 -0.009180855 -0.016427474 0.013889112 -0.011215071 -0.010737048 0.023043166 4 575.3 96.5 716 53.9 100 347.8 0.020192065 -0.001035733 -0.012491488 0.013072082 -0.018821754 0.002879357 5 595.1 97 725 55.6 101.6 350.9 0.033837815 0.00516797 0.012491488 0.031052723 0.015873349 0.008873681 6 602.8 98.4 727.5 57 101.2 348.1 0.012856008 0.014329826 0.003442344 0.024868067 -0.003944778 -0.008011488 7 601.8 99 716.6 54.7 102 349.4 -0.001660303 0.006079046 -0.015096194 -0.041187558 0.007874056 0.003727603 8 601.3 105.4 721.5 55.6 101.6 354.2 -0.000831186 0.062642786 0.006814573 0.016319492 -0.003929278 0.013644328 9 614.8 116.9 718.6 55.9 101.7 361.1 0.022203034 0.103556232 -0.004027504 0.005381179 0.000983768 0.019293203 10 628.1 119.6 717.8 56.5 100.5 372.7 0.021402378 0.022833973 -0.001113896 0.010676258 -0.011869576 0.031618878 11 629 113.2 729.5 56.4 103.4 371.6 0.001431867 -0.054996676 0.016168389 -0.00177148 0.028447235 -0.0029558 12 618.6 109.5 702.6 54.9 102.3 395.9 -0.016672396 -0.033231617 -0.037571628 -0.02695581 -0.010695289 0.063343647 13 638 105 750.8 55 102.8 397.6 0.030879423 -0.041964199 0.066351565 0.001819837 0.00487568 0.004284821 14 656 104.9 789.7 56.6 99.8 406.1 0.027822506 -0.000952835 0.050513822 0.0286758 -0.02961717 0.02115296 15 662 105.3 799.1 56.9 101.4 400.7 0.009104767 0.003805904 0.011832968 0.005286356 0.015904908 -0.013386417 16 669.4 105.7 805 56 100.9 396.6 0.011116233 0.003791474 0.007356183 -0.01594365 -0.004943164 -0.010284802 17 700.7 108.5 870 56.7 95.3 398.2 0.045698047 0.02614528 0.077650934 0.01242252 -0.057100117 0.004026176 18 709 110.3 937.6 57 65.7 400.9 0.011775691 0.016453753 0.074830207 0.005277057 -0.371930885 0.006757628 19 713 112.6 948.8 56.8 99.4 399.1 0.005625894 0.020637789 0.011874609 -0.003514942 0.414053188 -0.004500008 20 708 113.9 951.5 56.5 99.2 401.1 -0.007037327 0.011479155 0.002841658 -0.005295688 -0.002014099 0.004998761 E (R ) 0.011410933 0.007698951 0.018531903 0.002479482 -0.002233347 0.009729884 "Covar_i,m" -7.66363E-05 -2.00636E-05 -0.000143282 -5.79076E-05 -0.000351217 0.000311237 rf 0.03 p.a. Beta_i -0.246231127 -0.064463954 -0.460363256 -0.186055958 -1.128453695 1 0.000119048 p.d. assume 252day/year CovMatrix 0.000267119 0.000122378 0.000257158 0.000190277 -0.000253024 0.000122378 0.001223278 -0.000106427 0.00016828 -1.35394E-05 0.000257158 -0.000106427 0.001071405 0.000203278 -0.001495229 0.000190277 0.00016828 0.000203278 0.000329542 -0.000260157 -0.000253024 -1.35394E-05 -0.001495229 -0.000260157 0.017556896 wi 0.518336137 0.091635004 0.073795974 0.285903523 0.030329362 vrs 7.17675E-05 5.8127E-06 9.83657E-06 2.81979E-05 -3.97774E-06 MinVariance 0.000534238 0.000244757 0.000514316 0.000380554 -0.000506048 1 0 5.8127E-06 1.02718E-05 -7.1969E-07 4.40873E-06 -3.76292E-08 0.000244757 0.002446556 -0.000212854 0.00033656 -2.70788E-05 1 0 9.83657E-06 -7.1969E-07 5.8347E-06 4.28886E-06 -3.3466E-06 0.000514316 -0.000212854 0.002142809 0.000406556 -0.002990457 1 0 2.81979E-05 4.40873E-06 4.28886E-06 2.6937E-05 -2.25589E-06 0.000380554 0.00033656 0.000406556 0.000659083 -0.000520315 1 0 -3.97774E-06 -3.76292E-08 -3.3466E-06 -2.25589E-06 1.61501E-05 -0.000506048 -2.70788E-05 -0.002990457 -0.000520315 0.035113793 1 0 1 1 1 1 1 0 1 wi Rp VarP SigmaP ratio InvMatrix 3135.688208 -308.3583546 -723.9039686 -2041.711841 -61.71404383 0.518336137 0.518336137 0.008628929 0.000215376 0.01467568 0.587974718 -308.3583546 450.2517943 127.2654861 -269.300585 0.141659233 0.091635004 0.091635004 beta_P -0.254929935 -723.9039686 127.2654861 713.6362945 -162.9241314 45.92631946 0.073795974 0.073795974 SysVarP 2.02271E-05 -2041.711841 -269.300585 -162.9241314 2488.708704 -14.77214575 0.285903523 0.285903523 UnsVarP 0.000195149 -61.71404383 0.141659233 45.92631946 -14.77214575 30.41821088 0.030329362 0.030329362 0.518336137 0.091635004 0.073795974 0.285903523 0.030329362 -0.000430751 LAMBDA1 -0.000430751 1 Tangency Portfolio w_i 1.281004945 0.17455901 0.349049953 -0.837140901 0.032526993 CovarM vrs 0.000438335 2.73652E-05 0.000114984 -0.00020405 -1.05428E-05 ri 0.000267119 0.000122378 0.000257158 0.000190277 -0.000253024 0.011291886 2.73652E-05 3.72743E-05 -6.48458E-06 -2.45908E-05 -7.68752E-08 0.011410933 0.000122378 0.001223278 -0.000106427 0.00016828 -1.35394E-05 0.007579903 0.000114984 -6.48458E-06 0.000130536 -5.93986E-05 -1.69761E-05 0.007698951 0.000257158 -0.000106427 0.001071405 0.000203278 -0.001495229 0.018412856 -0.00020405 -2.45908E-05 -5.93986E-05 0.000230944 7.084E-06 0.018531903 0.000190277 0.00016828 0.000203278 0.000329542 -0.000260157 0.002360434 -1.05428E-05 -7.68752E-08 -1.69761E-05 7.084E-06 1.85753E-05 0.002479482 -0.000253024 -1.35394E-05 -0.001495229 -0.000260157 0.017556896 -0.002352395 -0.002233347 Z_i w_i Rp VarP SigmaP ratio InvM 7518.836014 -396.1822772 -1270.206012 -3395.350697 -50.43558186 1 50.61483508 1.281004945 0.020281623 0.000510292 0.02258965 0.897828146 -396.1822772 939.4911725 285.9286541 -416.9589258 13.18743242 2 6.897143934 0.17455901 beta_p -0.368315981 -1270.206012 285.9286541 1452.557932 -227.8867038 102.2446465 3 13.79159846 0.349049953 SysVarP 4.22214E-05 -3395.350697 -416.9589258 -227.8867038 5356.944275 10.71686928 4 -33.07695946 -0.837140901 UnsVarP 0.000468071 -50.43558186 13.18743242 102.2446465 10.71686928 65.10742655 5 1.285200636 0.032526993 sum_Z_i 39.51181865 1