"Předpokládejme, že kapitálový trh je v rovnováze. Je dáno" "= 0,04," "= 0,10 a" 0.09 a)      Popište a nakreslete přímku kapitálového trhu (CML) b)      Mějme tři CP mající následující kovariance s výnosem tržního portfolia: ", " ", " . Popište a nakreslete přímku SML. Zaneste CP na přímku SML CML 0 0.09 0.04 0.1 kovar výnosnosti kovar verze 0.0108 0.12 0 0.0081 -0.0027 0.02 0.04 0.1 0.0054 0.08 beta verze beta 0 1 1.333333333 0.12 0.04 0.1 -0.333333333 0.02 0.666666667 0.08 ##### Sheet/List 2 ##### "Mějme tři cenné papíry, tržní portfolio a bezrizikovou investici." ri korelace i a M sigma i kovariance beta delta C1 15.5 0.9 20 216 1.5 15.5 15.5 0 C2 9.2 0.8 9 86.4 0.6 9.2 9.2 0 C3 11.2 0.5 15 90 0.625 9.375 9.375 1.825 TP 12 1 12 144 1 rf 5 0 0 "Nakreslete SML, zobrazte cenné papíry na této přímce a určete beta cenných papírů." 0 144 5 12 0 1 5 12 ##### Sheet/List 3 ##### den Český Telecom ČEZ Komerční banka UNIPETROL IPB PX50 Český Telecom ČEZ Komerční banka UNIPETROL IPB PX50 1 570 98.4 669.1 53.9 103.5 333.4 portfolio s minimálním rizikem 2 569 98.2 715 53.8 103 338.9 -0.001754386 -0.00203252 0.068599611 -0.001855288 -0.004830918 0.016496701 Český Telecom ČEZ Komerční banka UNIPETROL IPB PX50 váhy výnosnost riziko 3 563.8 96.6 725 53.2 101.9 346.8 -0.00913884 -0.016293279 0.013986014 -0.011152416 -0.010679612 0.023310711 Český Telecom 0.000274593 0.000124726 0.000267938 0.00019227 -0.000286021 -7.93865E-05 Český Telecom 0.517979494 0.008814295 0.01486732 -0.243933092 4 575.3 96.5 716 53.9 100 347.8 0.020397304 -0.001035197 -0.012413793 0.013157895 -0.018645731 0.002883506 ČEZ 0.000124726 0.001280067 -0.000119099 0.000169014 8.75264E-05 -1.99036E-05 ČEZ 0.084323627 -0.061158425 5 595.1 97 725 55.6 101.6 350.9 0.034416826 0.005181347 0.012569832 0.031539889 0.016 0.008913168 Komerční banka 0.000267938 -0.000119099 0.001134006 0.000202789 -0.001398667 -0.000148542 Komerční banka 0.05757765 beta portfolia -0.45642826 6 602.8 98.4 727.5 57 101.2 348.1 0.012939002 0.01443299 0.003448276 0.025179856 -0.003937008 -0.007979481 UNIPETROL 0.00019227 0.000169014 0.000202789 0.000327972 -0.000283732 -6.01183E-05 UNIPETROL 0.313910523 -0.251491502 -0.184727167 7 601.8 99 716.6 54.7 102 349.4 -0.001658925 0.006097561 -0.014982818 -0.040350877 0.007905138 0.003734559 IPB -0.000286021 8.75264E-05 -0.001398667 -0.000283732 0.020276011 -0.000443477 IPB 0.026208705 -1.362684405 8 601.3 105.4 721.5 55.6 101.6 354.2 -0.000830841 0.064646465 0.006837845 0.016453382 -0.003921569 0.013737836 PX50 -7.93865E-05 -1.99036E-05 -0.000148542 -6.01183E-05 -0.000443477 0.000325444 -0.000442074 systematické riziko (rozptyl) nesystematické riziko (rozptyl) 9 614.8 116.9 718.6 55.9 101.7 361.1 0.022451355 0.109108159 -0.004019404 0.005395683 0.000984252 0.019480519 0.00002 0.00020 10 628.1 119.6 717.8 56.5 100.5 372.7 0.021633051 0.023096664 -0.001113276 0.010733453 -0.01179941 0.032124065 11 629 113.2 729.5 56.4 103.4 371.6 0.001432893 -0.053511706 0.016299805 -0.001769912 0.028855721 -0.002951435 Český Telecom 0.000549185 0.000249452 0.000535876 0.00038454 -0.000572041 1 0 3052.801274 -287.0530503 -665.1159821 -2057.489995 -43.14224628 0.517979494 12 618.6 109.5 702.6 54.9 102.3 395.9 -0.016534181 -0.032685512 -0.036874572 -0.026595745 -0.010638298 0.065392896 ČEZ 0.000249452 0.002560135 -0.000238198 0.000338028 0.000175053 1 0 -287.0530503 430.920765 117.7807745 -258.1716019 -3.476887393 0.084323627 13 638 105 750.8 55 102.8 397.6 0.031361138 -0.04109589 0.068602334 0.001821494 0.004887586 0.004294014 Komerční banka 0.000535876 -0.000238198 0.002268012 0.000405577 -0.002797334 1 0 -665.1159821 117.7807745 647.449589 -131.6238145 31.50943303 0.05757765 14 656 104.9 789.7 56.6 99.8 406.1 0.028213166 -0.000952381 0.051811401 0.029090909 -0.029182879 0.02137827 UNIPETROL 0.00038454 0.000338028 0.000405577 0.000655943 -0.000567465 1 0 -2057.489995 -258.1716019 -131.6238145 2457.624409 -10.3389969 0.313910523 15 662 105.3 799.1 56.9 101.4 400.7 0.009146341 0.003813155 0.011903254 0.005300353 0.016032064 -0.013297217 IPB -0.000572041 0.000175053 -0.002797334 -0.000567465 0.040552023 1 0 -43.14224628 -3.476887393 31.50943303 -10.3389969 25.44869753 0.026208705 16 669.4 105.7 805 56 100.9 396.6 0.011178248 0.00379867 0.007383306 -0.015817223 -0.004930966 -0.010232094 1 1 1 1 1 0 1 0.517979494 0.084323627 0.05757765 0.313910523 0.026208705 -0.000442074 17 700.7 108.5 870 56.7 95.3 398.2 0.046758291 0.026490066 0.080745342 0.0125 -0.055500496 0.004034291 18 709 110.3 937.6 57 65.7 400.9 0.011845298 0.016589862 0.077701149 0.005291005 -0.310598111 0.006780512 19 713 112.6 948.8 56.8 99.4 399.1 0.005641749 0.020852221 0.011945392 -0.003508772 0.512937595 -0.004489898 20 708 113.9 951.5 56.5 99.2 401.1 -0.007012623 0.011545293 0.0028457 -0.00528169 -0.002012072 0.005011275 výnosnost 0.011604467 0.008318209 0.019225021 0.002638526 0.006364489 0.009927484 "Odhadněte beta a výnosnosti jednotlivých akcií. Vypočítejte výnosnost a riziko optimálního portfolia složeného z těchto akcií (sell short povolen), systematické a nesystematické riziko tohoto portfolia." Bezriziková investice má výnosnost 3% p.a. 0.03 250 kovar -7.93865E-05 -1.99036E-05 -0.000148542 -6.01183E-05 -0.000443477 0.000325444 0.517979494 0.084323627 0.05757765 0.313910523 0.026208705 0.00012 Český Telecom ČEZ Komerční banka UNIPETROL IPB 0.517979494 7.3674E-05 5.44777E-06 7.991E-06 3.12629E-05 -3.88289E-06 ri 0.011604467 0.008318209 0.019225021 0.002638526 0.006364489 beta -0.243933092 -0.061158425 -0.45642826 -0.184727167 -1.362684405 1 0.084323627 5.44777E-06 9.10189E-06 -5.78244E-07 4.47381E-06 1.93434E-07 rie -0.00227237 -0.00047981 -0.004356413 -0.001691709 -0.013244506 0.05757765 7.991E-06 -5.78244E-07 3.75944E-06 3.66525E-06 -2.11064E-06 delta 0.013876837 0.008798019 0.023581434 0.004330235 0.019608994 matice soustavy 0.313910523 3.12629E-05 4.47381E-06 3.66525E-06 3.23183E-05 -2.33432E-06 19 0.188622199 0.026208705 -3.88289E-06 1.93434E-07 -2.11064E-06 -2.33432E-06 1.39275E-05 0.188622199 0.007730528 0.000221037 inverzní 0.069455615 -1.694692808 -1.694692808 170.7071784 vektory pravých stran Český Telecom ČEZ Komerční banka UNIPETROL IPB 0.220484867 0.158045968 0.365275401 0.050131996 0.120925286 0.000759904 0.001210734 0.000952516 -0.000584444 -0.0067821 výsledek odhad alfa 0.014026109 0.008925358 0.023756205 0.004472402 0.019892517 odhad beta -0.243933092 -0.061158425 -0.45642826 -0.184727167 -1.362684405 tangenciální portfolio - s využitím bezrizikové investice matice soustavy vektor prav stran vektor výnosností 0.000274593 0.000124726 0.000267938 0.00019227 -0.000286021 0.011484467 0.011604467 0.000124726 0.001280067 -0.000119099 0.000169014 8.75264E-05 0.008198209 0.008318209 0.000267938 -0.000119099 0.001134006 0.000202789 -0.001398667 0.019105021 0.019225021 0.00019227 0.000169014 0.000202789 0.000327972 -0.000283732 0.002518526 0.002638526 -0.000286021 8.75264E-05 -0.001398667 -0.000283732 0.020276011 0.006244489 0.006364489 1.257703207 0.176579921 0.340380232 -0.811595261 0.036931902 inverzni matice Zi váhy výnosnost riziko bety 7319.437777 -376.5017727 -1195.304267 -3379.360807 -24.86690682 49.4705961 Český Telecom 1.257703207 0.020701258 0.022874493 -0.243933092 0.000434355 2.76998E-05 0.000114704 -0.000196259 -1.32855E-05 -376.5017727 894.0102046 257.5268836 -396.5892776 3.04460099 6.945608386 ČEZ 0.176579921 -0.061158425 2.76998E-05 3.99131E-05 -7.15836E-06 -2.42216E-05 5.70797E-07 -1195.304267 257.5268836 1309.897493 -181.4775504 69.8459322 13.3885426 Komerční banka 0.340380232 beta portfolia -0.45642826 0.000114704 -7.15836E-06 0.000131384 -5.60205E-05 -1.75825E-05 -3379.360807 -396.5892776 -181.4775504 5361.055274 16.54283585 -31.92335135 UNIPETROL -0.811595261 -0.373356772 -0.184727167 -0.000196259 -2.42216E-05 -5.60205E-05 0.000216031 8.50452E-06 -24.86690682 3.04460099 69.8459322 16.54283585 54.00499958 1.452682298 IPB 0.036931902 -1.362684405 -1.32855E-05 5.70797E-07 -1.75825E-05 8.50452E-06 2.76558E-05 suma Zi 39.33407804 systematické riziko (rozptyl) nesystematické riziko (rozptyl) rozptyl 0.00005 0.00048 zrychlená varianta 0.000523242 ještě rychlejší varianta 0.000523242