. rf 0.06 beta_1 beta_2 beta_3 beta_4 r_M 0.14 1.235 0.268 1.997 2.45 ri_e 0.1588 0.08144 0.21976 0.256 ##### Sheet/List 2 ##### Year 1 10 9 22 0.666666667 5 defensive agressive 2 32 24 48 0.68 1.64 defensive agressive 3 20 14 30 0.538461538 1.769230769 defensive agressive 4 18 -2 -20 -0.818181818 -2.454545455 defensive agressive 5 17 16 29 0.9 2.2 defensive agressive 6 3 4 -3 0.75 2.5 defensive agressive 7 12 8 21 0.2 2.8 defensive agressive 8 -5 0 -15 0.583333333 1.833333333 defensive agressive 9 18 12 28 0.454545455 1.909090909 defensive agressive 10 21 15 36 0.571428571 2.071428571 defensive agressive 14.6 10 17.6 beta over last 10 years? "what about the expected return of i, j security?" rf 7 "cov_i,M" 105.3777778 61.44444444 166.3777778 Beta_i 1 0.583087305 1.578869675 r_ie 14.6 11.43146352 18.99940953 delta_i=ri-rie -1.431463518 -1.399409532 ##### Sheet/List 3 ##### "= 0,04, " ", " "= 0,10 a " ", " "= 0,09 " "cov_i,M" rf 0.04 1 0.0108 r_M 0.1 2 -0.0027 sigma_M 0.09 3 0.0054 sigma return rf 0 0.04 Market 0.09 0.1 SML "covar_i,M" return rf 0 0.04 r1 0.0108 0.12 r2 -0.0027 0.02 r3 0.0054 0.08 beta_i return rf 0 0.04 r1 1.333333333 0.12 r2 -0.333333333 0.02 r3 0.666666667 0.08 ##### Sheet/List 4 ##### ri correlation i a M sigma i "cov_i,M" "beta_i,M" rie 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 12 rf 5 0 0 0 5 ##### Sheet/List 5 ##### Day 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 (ri) 0.011410933 0.007698951 0.018531903 0.002479482 -0.002233347 0.009729884 Minimum Variance rf 0.03 p.a. 0.000267119 0.000122378 0.000257158 0.000190277 -0.000253024 days in one year 250 0.00012 p.d. 0.000122378 0.001223278 -0.000106427 0.00016828 -1.35394E-05 0.000257158 -0.000106427 0.001071405 0.000203278 -0.001495229 ri 0.000190277 0.00016828 0.000203278 0.000329542 -0.000260157 0.011410933 -0.000253024 -1.35394E-05 -0.001495229 -0.000260157 0.017556896 0.518336137 0.091635004 0.073795974 0.285903523 0.030329362 0.007698951 vrs 0.018531903 0.000534238 0.000244757 0.000514316 0.000380554 -0.000506048 1 0 7.17675E-05 5.8127E-06 9.83657E-06 2.81979E-05 -3.97774E-06 0.002479482 0.000244757 0.002446556 -0.000212854 0.00033656 -2.70788E-05 1 0 5.8127E-06 1.02718E-05 -7.1969E-07 4.40873E-06 -3.76292E-08 -0.002233347 0.000514316 -0.000212854 0.002142809 0.000406556 -0.002990457 1 0 9.83657E-06 -7.1969E-07 5.8347E-06 4.28886E-06 -3.3466E-06 0.000380554 0.00033656 0.000406556 0.000659083 -0.000520315 1 0 2.81979E-05 4.40873E-06 4.28886E-06 2.6937E-05 -2.25589E-06 -0.000506048 -2.70788E-05 -0.002990457 -0.000520315 0.035113793 1 0 -3.97774E-06 -3.76292E-08 -3.3466E-06 -2.25589E-06 1.61501E-05 1 1 1 1 1 0 1 Inv_M wi 3135.688208 -308.3583546 -723.9039686 -2041.711841 -61.71404383 0.518336137 0.518336137 Rp Var_P Sigma_P -308.3583546 450.2517943 127.2654861 -269.300585 0.141659233 0.091635004 0.091635004 0.008628929 0.000215376 0.01467568 -723.9039686 127.2654861 713.6362945 -162.9241314 45.92631946 0.073795974 0.073795974 0.587974718 -2041.711841 -269.300585 -162.9241314 2488.708704 -14.77214575 0.285903523 0.285903523 -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 -0.000430751 proof 1 Tangency Portfolio Covariance Matrix vrs 1.281090309 0.174568291 0.349080762 -0.8372666 0.032527239 0.000267119 0.000122378 0.000257158 0.000190277 -0.000253024 0.011290933 0.000122378 0.001223278 -0.000106427 0.00016828 -1.35394E-05 0.007578951 0.000438394 2.73684E-05 0.000115002 -0.000204094 -1.05436E-05 0.000257158 -0.000106427 0.001071405 0.000203278 -0.001495229 0.018411903 2.73684E-05 3.72783E-05 -6.48549E-06 -2.45958E-05 -7.68798E-08 0.000190277 0.00016828 0.000203278 0.000329542 -0.000260157 0.002359482 0.000115002 -6.48549E-06 0.000130559 -5.94128E-05 -1.69778E-05 -0.000253024 -1.35394E-05 -0.001495229 -0.000260157 0.017556896 -0.002353347 -0.000204094 -2.45958E-05 -5.94128E-05 0.000231014 7.08512E-06 -1.05436E-05 -7.68798E-08 -1.69778E-05 7.08512E-06 1.85756E-05 Inv_M Zi wi Rp Var_P Sigma_P 7518.836014 -396.1822772 -1270.206012 -3395.350697 -50.43558186 50.61254302 1.281090309 0.020282927 0.000510358 0.022591111 -396.1822772 939.4911725 285.9286541 -416.9589258 13.18743242 6.896738729 0.174568291 0.897827804 -1270.206012 285.9286541 1452.557932 -227.8867038 102.2446465 13.79127214 0.349080762 -3395.350697 -416.9589258 -227.8867038 5356.944275 10.71686928 -33.07822372 -0.8372666 -50.43558186 13.18743242 102.2446465 10.71686928 65.10742655 1.285066521 0.032527239 sum_Zi 39.50739669 1