The betas of the following four stocks are: . Assume that the market is in equilibrium with available risk-free asset of 6 %. . What will bet he expected return of every of this stocks? beta_i rf 0.06 rm 0.14 1 1.235 2 0.268 3 1.997 4 2.45 ri rie=rf+beta*(rM-rf) 1 0.1588 2 0.08144 3 0.21976 4 0.256 ##### Sheet/List 2 ##### Year 1 10 9 22 0.899295065 2.208459215 2 32 24 48 0.749451926 1.501096148 3 20 14 30 0.698946312 1.501756147 4 18 -2 -20 -0.115448968 -1.11935304 5 17 16 29 0.940933255 1.708800945 6 3 4 -3 1.341296928 -1.04778157 7 12 8 21 0.664710813 1.754400671 8 -5 0 -15 0.013806706 2.972386588 9 18 12 28 0.66536531 1.557724484 10 21 15 36 0.713330148 1.71667463 ##### Sheet/List 3 ##### ri correlation i a M sigma i "cov_ri,M" "beta_i=cov_ri,M/var_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 ##### Sheet/List 4 ##### 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 rf=3% p. a. E(ri) 0.011410933 0.007698951 0.018531903 0.002479482 -0.002233347 0.009729884 OLS VRS rf for a trading day 0.00012 beta_i n sum_Xi Sum_Yi 1 year=250 TDs. cov_M 0.000267119 0.000122378 0.000257158 0.000190277 -0.000253024 -7.66363E-05 -0.246231127 sum_Xi sum_Xi^2 Sum_YiXi 0.000122378 0.001223278 -0.000106427 0.00016828 -1.35394E-05 -2.00636E-05 -0.064463954 0.000257158 -0.000106427 0.001071405 0.000203278 -0.001495229 -0.000143282 -0.460363256 19 0.184867802 0.216807733 0.146280066 0.352106161 0.04711016 -0.042433598 0.000190277 0.00016828 0.000203278 0.000329542 -0.000260157 -5.79076E-05 -0.186055958 0.184867802 0.007401015 0.00073006 0.001062143 0.000846872 -0.00058396 -0.006734779 -0.000253024 -1.35394E-05 -0.001495229 -0.000260157 0.017556896 -0.000351217 -1.128453695 0.000311237 Inv_M A B C D E VRS 0.069530193 -1.736774451 alfa 0.013806734 0.008326178 0.023011184 0.004289785 0.008746377 Min_var 0.000534238 0.000244757 0.000514316 0.000380554 -0.000506048 1 0 -1.736774451 178.4989822 beta -0.246231127 -0.064463954 -0.460363256 -0.186055958 -1.128453695 0.000244757 0.002446556 -0.000212854 0.00033656 -2.70788E-05 1 0 0.000514316 -0.000212854 0.002142809 0.000406556 -0.002990457 1 0 0.000380554 0.00033656 0.000406556 0.000659083 -0.000520315 1 0 -0.000506048 -2.70788E-05 -0.002990457 -0.000520315 0.035113793 1 0 1 1 1 1 1 0 1 Inv_M wi 3135.688208 -308.3583546 -723.9039686 -2041.711841 -61.71404383 0.518336137 1 0.518336137 -308.3583546 450.2517943 127.2654861 -269.300585 0.141659233 0.091635004 2 0.091635004 -723.9039686 127.2654861 713.6362945 -162.9241314 45.92631946 0.073795974 3 0.073795974 -2041.711841 -269.300585 -162.9241314 2488.708704 -14.77214575 0.285903523 4 0.285903523 -61.71404383 0.141659233 45.92631946 -14.77214575 30.41821088 0.030329362 5 0.030329362 0.518336137 0.091635004 0.073795974 0.285903523 0.030329362 -0.000430751 lambda1 -0.000430751 Proof 1 Tangency Portfolio CovM VRS E(ri) 0.000267119 0.000122378 0.000257158 0.000190277 -0.000253024 0.011290933 0.011410933 0.000122378 0.001223278 -0.000106427 0.00016828 -1.35394E-05 0.007578951 0.007698951 0.000257158 -0.000106427 0.001071405 0.000203278 -0.001495229 0.018411903 0.018531903 0.000190277 0.00016828 0.000203278 0.000329542 -0.000260157 0.002359482 0.002479482 -0.000253024 -1.35394E-05 -0.001495229 -0.000260157 0.017556896 -0.002353347 -0.002233347 Inv_M Zi Wi 7518.836014 -396.1822772 -1270.206012 -3395.350697 -50.43558186 50.61254302 1.281090309 -396.1822772 939.4911725 285.9286541 -416.9589258 13.18743242 6.896738729 0.174568291 -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 ##### Sheet/List 5 ##### VIG PX BRENT(USD) XR(CZC/USD) VIG PX BRENT(USD) XR(CZC/USD) 1 019.00 1 034.45 108.64 19.5985 0.003933142 -0.004282951 -0.002482189 0.002528898 alfa beta1 beta2 beta3 1 015.00 1 038.89 108.91 19.5490 0.01819407 0.010333409 -0.013769424 0.007857275 vrs 996.70 1 028.21 110.42 19.3960 -0.002004611 -0.000933226 0.001359373 -0.014612249 n sum_Xi1 sum_Xi2 sum_Xi3 sum_Yi 998.70 1 029.17 110.27 19.6815 0.029158362 0.011885702 -0.001359373 0.004940671 sum_Xi1 sum_Xi1^2 sum_Xi1Xi2 sum_Xi2Xi3 sum_YiXi1 970.00 1 017.01 110.42 19.5845 -0.001030397 0.01100417 0.004720415 -0.006818844 sum_Xi2 sum_Xi1Xi2 sum_Xi2^2 sum_Xi2Xi3 sum_YiXi2 971.00 1 005.88 109.9 19.7185 -0.017963333 -0.007152157 -0.002181422 0.000304329 sum_Xi3 sum_Xi2Xi3 sum_Xi2Xi3 sum_Xi3^2 sum_YiXi3 988.60 1 013.10 110.14 19.7125 -0.002929147 -0.00144994 -0.018530709 0.002972072 991.50 1 014.57 112.2 19.6540 0.00708505 0.018543182 -0.000356443 0.007353725 984.50 995.93 112.24 19.5100 0.010209379 0.003208177 -0.006394338 -0.003581482 1179 -0.204321797 -0.463262412 -0.098451579 -0.204321797 974.50 992.74 112.96 19.5800 -0.021421052 -0.020942808 -0.013977635 0.003453351 -0.204321797 0.433722108 0.210522699 -0.076578094 0.358295277 995.60 1 013.75 114.55 19.5125 0.017938155 0.013586329 0.007096267 0.007897858 -0.463262412 0.210522699 -0.098451579 0.188622459 0.19541719 977.90 1 000.07 113.74 19.3590 0.013590243 0.007034191 -0.003948586 0.002249545 -0.098451579 -0.076578094 0.188622459 0.141254575 -0.066531126 964.70 993.06 114.19 19.3155 0.000725878 -0.010677292 -0.017707259 0.011219547 964.00 1 003.72 116.23 19.1000 0.000518807 0.002813503 -0.00694477 0.008306656 0.000848328 0.000699837 -0.000178626 0.001209194 alfa -3.79395E-05 963.50 1 000.90 117.04 18.9420 -0.012787634 -0.002783613 -0.003071151 -0.004319661 0.000699837 1.489857578 1.329520707 -0.967176544 beta1 0.857824487 975.90 1 003.69 117.4 19.0240 0.021648782 0.004623651 -0.009157263 0.003580836 -0.000178626 1.329520707 -1.667283311 2.94703129 beta2 -0.045487642 955.00 999.06 118.48 18.9560 -0.014037142 -0.010732345 0.000422101 0.005501495 0.001209194 -0.967176544 2.94703129 2.620645901 beta3 0.054764197 968.50 1 009.84 118.43 18.8520 0.024669381 0.007424706 0.004570082 0.001459796 944.90 1 002.37 117.89 18.8245 0.005199227 0.003407737 -0.00338725 -0.000663808 940.00 998.96 118.29 18.8370 -0.000425441 0.004846755 -0.005143567 -0.002200688 940.40 994.13 118.9 18.8785 -0.023748095 0.008039229 0.014656932 0.001855682 963.00 986.17 117.17 18.8435 -0.009405268 -0.012665731 0.001195559 -0.001060811 972.10 998.74 117.03 18.8635 -0.027496279 -0.008762586 0.008323013 -0.006683687 999.20 1 007.53 116.06 18.9900 -0.003795829 -0.009168485 0.004403962 0.008408077 1 003.00 1 016.81 115.55 18.8310 0.000997506 -0.004543121 0 -0.003710383 1 002.00 1 021.44 115.55 18.9010 0.007010544 0.003511012 0.001125687 0.00111167 995.00 1 017.86 115.42 18.8800 0 -0.002070831 0.001734305 -0.007414184 995.00 1 019.97 115.22 19.0205 -0.008008051 0.007281562 0.011346897 -0.004275697 1 003.00 1 012.57 113.92 19.1020 0.002995509 -0.011508036 0.000351185 0.0062492 1 000.00 1 024.29 113.88 18.9830 -0.017839918 0.002375194 -0.006215278 -0.007086458 1 018.00 1 021.86 114.59 19.1180 0.021948346 -0.004842152 0.007973057 -0.005477179 995.90 1 026.82 113.68 19.2230 0.01100521 0.001520409 0.008480616 -0.001481501 985.00 1 025.26 112.72 19.2515 -0.010000588 -0.01669462 0.00900064 0.000857444 994.90 1 042.52 111.71 19.2350 0.006049015 0.000249427 0.00628594 0.0071741 988.90 1 042.26 111.01 19.0975 0.004053101 0.002834401 0.000360393 -0.006602062 984.90 1 039.31 110.97 19.2240 -0.002028604 -0.002911154 -0.006735847 -0.000883921 986.90 1 042.34 111.72 19.2410 -0.003136226 -0.004871359 0.003586804 0.006831661 990.00 1 047.43 111.32 19.1100 -0.014042357 -0.005968235 0.00920501 -0.005479466 1 004.00 1 053.70 110.3 19.2150 0.019105659 0.005347861 -0.02391837 -0.004828294 985.00 1 048.08 112.97 19.3080 -0.022089252 -0.01708473 -0.000884799 -0.015494625 1 007.00 1 066.14 113.07 19.6095 -0.022583189 0.004644306 0.000353826 0.004702644 1 030.00 1 061.20 113.03 19.5175 -0.00869991 0.006238795 0.004788941 0.001794872 1 039.00 1 054.60 112.49 19.4825 0.005791522 -0.007434838 -0.000799751 0.003805512 1 033.00 1 062.47 112.58 19.4085 0.003879733 -0.000536342 -0.00398919 0.002502033 1 029.00 1 063.04 113.03 19.3600 -0.00581397 -0.002789979 0.000442458 0.012709558 1 035.00 1 066.01 112.98 19.1155 0.034401427 0.025952775 0.026276004 0.006007915 1 000.00 1 038.70 110.05 19.0010 0.002002003 0.002651051 9.08719E-05 0.002344729 998.00 1 035.95 110.04 18.9565 -0.017875352 -0.000414992 0.008304104 -0.005812211 1 016.00 1 036.38 109.13 19.0670 0.021891421 0.002502211 -0.013108972 0.002520613 994.00 1 033.79 110.57 19.0190 0.005953299 -0.007228668 0.005623088 -0.000630749 988.10 1 041.29 109.95 19.0310 0.011297255 0.009921425 -9.09463E-05 -5.25445E-05 977.00 1 031.01 109.96 19.0320 0 0.019242945 0.005562916 -0.007615944 977.00 1 011.36 109.35 19.1775 0.01443324 0.003307949 0.000640351 0.00075638 963.00 1 008.02 109.28 19.1630 0.00938974 0.005810383 -0.008201996 -0.00790066 954.00 1 002.18 110.18 19.3150 -0.001047669 0.00058889 9.07647E-05 -0.00018119 955.00 1 001.59 110.17 19.3185 0.001991511 0.008996104 0.02360398 -0.004854002 953.10 992.62 107.6 19.4125 0.005365328 0.006853842 -0.006022719 -0.005855329 948.00 985.84 108.25 19.5265 -0.010493276 -0.007760123 0.010120322 0.001537555 958.00 993.52 107.16 19.4965 0.008701633 -0.00606099 -0.007900771 0.002876443 949.70 999.56 108.01 19.4405 0.007079863 0.001832484 -0.008757027 0.007616183 943.00 997.73 108.96 19.2930 0.011733468 0.003443727 -0.00940861 0.000907476 932.00 994.30 109.99 19.2755 0.005918769 -3.01715E-05 -0.011570228 -0.002331849 926.50 994.33 111.27 19.3205 0.003243246 -0.002992511 0.00387196 -0.006423259 923.50 997.31 110.84 19.4450 0.01253081 0.005197428 0.003343729 0.001235013 912.00 992.14 110.47 19.4210 0.029939357 0.01679106 0.02020825 -0.004315888 885.10 975.62 108.26 19.5050 -0.011123085 -0.019780117 -0.00983509 -0.003991 895.00 995.11 109.33 19.5830 0.002685166 0.011989872 -0.007744561 0.004555117 892.60 983.25 110.18 19.4940 0.003141834 0.006479119 0.000363108 -0.001819417 889.80 976.90 110.14 19.5295 0.025957742 0.014704783 -0.006064739 -0.016454171 867.00 962.64 110.81 19.8535 0.006828335 -0.007781496 0.007245752 0.003633157 861.10 970.16 110.01 19.7815 -0.002204049 -0.004463513 -0.000454401 0.000126389 863.00 974.50 110.06 19.7790 0.014002563 0.004422283 0.029974117 -0.013683195 851.00 970.20 106.81 20.0515 -0.008308514 0.000876492 -0.030064972 0.004273137 858.10 969.35 110.07 19.9660 -0.010894869 -0.005093521 0.003731857 -0.000650895 867.50 974.30 109.66 19.9790 0.022616958 0.008369112 0.007689529 -0.004370036 848.10 966.18 108.82 20.0665 -0.010789362 -0.011791352 -0.012873951 0.004995889 857.30 977.64 110.23 19.9665 -0.000349875 -0.002227377 0.014805608 0 857.60 979.82 108.61 19.9665 -0.009169584 -0.005678769 0.012787424 0.001077384 865.50 985.40 107.23 19.9450 -0.000577534 -0.004020727 -0.009097723 0.002887092 866.00 989.37 108.21 19.8875 0.005674267 -0.006196837 -0.0097481 0.008914538 861.10 995.52 109.27 19.7110 0.023024628 0.007380107 0.034258214 0.001497747 841.50 988.20 105.59 19.6815 0.009672295 0.007384005 -0.011300619 0.000533638 833.40 980.93 106.79 19.6710 0.005896882 0.005284447 -0.019014625 0.010270651 828.50 975.76 108.84 19.4700 0.003991056 0.005013778 -0.009600952 0.005614086 825.20 970.88 109.89 19.3610 -0.004594374 0.001412087 0.004468975 0.004192444 829.00 969.51 109.4 19.2800 0.000603318 0.010941425 0.000640059 -0.006075903 828.50 958.96 109.33 19.3975 0.012632258 -0.005407892 0.003940802 0.006231516 818.10 964.16 108.9 19.2770 -0.002685548 -0.012983716 0.011637704 -0.001140606 820.30 976.76 107.64 19.2990 0.002685548 0.000542758 -0.000185787 0.001348128 818.10 976.23 107.66 19.2730 0.003673773 0.003992677 0.001208235 0.004524306 815.10 972.34 107.53 19.1860 -0.012678458 -0.018009507 -0.019249961 0.007008763 825.50 990.01 109.62 19.0520 -0.002419844 0.001738867 -0.020496406 -0.001756802 827.50 988.29 111.89 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0.003097656 0.001645478 1 225.00 1 675.90 128.93 16.0915 0.020619287 0.018731538 7.75645E-05 0.002520029 1 200.00 1 644.80 128.92 16.0510 -0.019802627 -0.01598297 -0.006186224 0.009137628 1 224.00 1 671.30 129.72 15.9050 0.012330612 -0.003643209 0.005255848 -0.004203664 1 209.00 1 677.40 129.04 15.9720 0.00165563 0.005080249 0.01373305 0.001817328 1 207.00 1 668.90 127.28 15.9430 -0.026973438 -0.020285393 0.025140544 -0.00319379 1 240.00 1 703.10 124.12 15.9940 0 -0.004510978 0.015671629 -0.007257581 1 240.00 1 710.80 122.19 16.1105 0.00809721 0.005685997 -0.00644453 0.002454828 1 230.00 1 701.10 122.98 16.0710 -0.002436055 0.019410017 0.001790511 -0.010676423 1 233.00 1 668.40 122.76 16.2435 0.002436055 0.007943236 0.012954186 0.001910279 1 230.00 1 655.20 121.18 16.2125 0.013093477 0.00806774 -0.015801221 0.005690796 1 214.00 1 641.90 123.11 16.1205 -0.025214837 0.000609236 0.001788618 0.007159341 1 245.00 1 640.90 122.89 16.0055 0.021104679 0.002501756 -0.005275344 -0.0108744 1 219.00 1 636.80 123.54 16.1805 -0.037041272 -0.016300921 0.026825775 -0.009778676 1 265.00 1 663.70 120.27 16.3395 0.011928571 0.011911741 0.003247973 0.006754915 1 250.00 1 644.00 119.88 16.2295 ##### Sheet/List 6 ##### Security ri beta_i var_eps (ri-rf)/beta_i (ri-rf)*beta_I/var_esp_i cum Ci "if_(long,short)" Zi wi with short Zi wi 1 19 1 20 16 0.8 0.05 0.8 0.05 5.333333333 long 0.32345679 0.337411462 0.454271357 0.468066378 3 11 0.5 10 16 0.4 0.025 1.2 0.075 6.857142857 long 0.32345679 0.337411462 0.454271357 0.468066378 2 23 1.5 30 13.33333333 1 0.075 2.2 0.15 8.8 long 0.190123457 0.198325821 0.320938023 0.330684064 6 9 0.5 50 12 0.06 0.005 2.26 0.155 8.862745098 long 0.024691358 0.0257566 0.050854271 0.052398581 4 25 2 40 11 1.1 0.1 3.36 0.255 9.464788732 long 0.07345679 0.076625885 0.204271357 0.210474539 5 13 1 20 10 0.5 0.05 3.86 0.305 9.530864198 long C* 0.02345679 0.02446877 0.154271357 0.158956171 7 14 1.5 30 7.333333333 0.55 0.075 4.41 0.38 9.1875 short 0.020938023 0.021573856 8 10 1 50 7 0.14 0.02 4.55 0.4 9.1 short sum_zi 0.958641975 1 0.001708543 0.001760427 9 9.5 1 50 6.5 0.13 0.02 4.68 0.42 9 short -0.008291457 -0.008543247 11 11 1.5 30 5.333333333 0.4 0.075 5.08 0.495 8.537815126 short -0.079061977 -0.08146288 10 13 2 20 5 1 0.2 6.08 0.695 7.647798742 short -0.191457286 -0.197271339 12 8 1 20 5 0.25 0.05 6.33 0.745 7.49112426 short -0.095728643 -0.098635669 14 7 1 20 4 0.2 0.05 6.53 0.795 7.296089385 short -0.145728643 -0.150154037 13 10 2 40 3.5 0.35 0.1 6.88 0.895 6.914572864 short -0.170728643 -0.175913221 rf 3 sum_Zi 0.970527638 var_m 10 short allowed - C*= 6.914572864 beta_portf 0.994204765 sys_var_p 9.884431147 uns_var_p 4.875394362 Var_p 14.75982551 Sigma_p 3.841851833