Day O2 ČEZ Erste Bank CETV Fortuna PX O2 ČEZ Erste Bank CETV Fortuna PX Fce 20 570 98.4 669.1 53.9 103.5 333.4 0.001755927 0.002034589 -0.066349017 0.001857011 0.004842624 -0.016362108 Fortuna 19 569 98.2 715 53.8 103 338.9 0.009180855 0.016427474 -0.013889112 0.011215071 0.010737048 -0.023043166 beta alfa 18 563.8 96.6 725 53.2 101.9 346.8 -0.020192065 0.001035733 0.012491488 -0.013072082 0.018821754 -0.002879357 -1.128453695 -0.008746377 17 575.3 96.5 716 53.9 100 347.8 -0.033837815 -0.00516797 -0.012491488 -0.031052723 -0.015873349 -0.008873681 1.800924248 0.035543836 16 595.1 97 725 55.6 101.6 350.9 -0.012856008 -0.014329826 -0.003442344 -0.024868067 0.003944778 0.008011488 0.022574154 0.134796177 15 602.8 98.4 727.5 57 101.2 348.1 0.001660303 -0.006079046 0.015096194 0.041187558 -0.007874056 -0.003727603 0.392623776 17 14 601.8 99 716.6 54.7 102 349.4 0.000831186 -0.062642786 -0.006814573 -0.016319492 0.003929278 -0.013644328 0.007133978 0.308890156 13 601.3 105.4 721.5 55.6 101.6 354.2 -0.022203034 -0.103556232 0.004027504 -0.005381179 -0.000983768 -0.019293203 12 614.8 116.9 718.6 55.9 101.7 361.1 -0.021402378 -0.022833973 0.001113896 -0.010676258 0.011869576 -0.031618878 11 628.1 119.6 717.8 56.5 100.5 372.7 -0.001431867 0.054996676 -0.016168389 0.00177148 -0.028447235 0.0029558 10 629 113.2 729.5 56.4 103.4 371.6 0.016672396 0.033231617 0.037571628 0.02695581 0.010695289 -0.063343647 9 618.6 109.5 702.6 54.9 102.3 395.9 -0.030879423 0.041964199 -0.066351565 -0.001819837 -0.00487568 -0.004284821 8 638 105 750.8 55 102.8 397.6 -0.027822506 0.000952835 -0.050513822 -0.0286758 0.02961717 -0.02115296 7 656 104.9 789.7 56.6 99.8 406.1 -0.009104767 -0.003805904 -0.011832968 -0.005286356 -0.015904908 0.013386417 6 662 105.3 799.1 56.9 101.4 400.7 -0.011116233 -0.003791474 -0.007356183 0.01594365 0.004943164 0.010284802 5 669.4 105.7 805 56 100.9 396.6 -0.045698047 -0.02614528 -0.077650934 -0.01242252 0.057100117 -0.004026176 4 700.7 108.5 870 56.7 95.3 398.2 -0.011775691 -0.016453753 -0.074830207 -0.005277057 0.371930885 -0.006757628 3 709 110.3 937.6 57 65.7 400.9 -0.005625894 -0.020637789 -0.011874609 0.003514942 -0.414053188 0.004500008 2 713 112.6 948.8 56.8 99.4 399.1 0.007037327 -0.011479155 -0.002841658 0.005295688 0.002014099 -0.004998761 1 708 113.9 951.5 56.5 99.2 401.1 E(ri) -0.011410933 -0.007698951 -0.018531903 -0.002479482 0.002233347 -0.009729884 p.a. p.d.(250 trading days) O2 ČEZ Erste Bank CETV Fortuna rf 0.005 0.00002 19 -0.184867802 -0.216807733 -0.146280066 -0.352106161 -0.04711016 0.042433598 -0.184867802 0.007401015 0.00073006 0.001062143 0.000846872 -0.00058396 -0.006734779 Inv.Matrice O2 ČEZ Erste Bank CETV Fortuna -0.013806734 0.069530193 1.736774451 0.069530193 1.736774451 alfa -0.013806734 -0.008326178 -0.023011184 -0.004289785 -0.008746377 -0.246231127 1.736774451 178.4989822 1.736774451 178.4989822 beta -0.246231127 -0.064463954 -0.460363256 -0.186055958 -1.128453695 E(ri) 0.002420725 0.000648516 0.004508489 0.001834024 0.011022293 Cov_M O2 ČEZ Erste Bank CETV Fortuna PX O2 0.000267119 0.000122378 0.000257158 0.000190277 -0.000253024 -7.66363E-05 ČEZ 2.61634E-05 0.001223278 -0.000106427 0.00016828 -1.35394E-05 -2.00636E-05 Erste Bank 0.000257158 -0.000106427 0.001071405 0.000203278 -0.001495229 -0.000143282 CETV 0.000190277 0.00016828 0.000203278 0.000329542 -0.000260157 -5.79076E-05 Fortuna -0.000253024 -1.35394E-05 -0.001495229 -0.000260157 0.017556896 -0.000351217 PX -7.66363E-05 -2.00636E-05 -0.000143282 -5.79076E-05 -0.000351217 0.000311237 sigma_M^2 O2 ČEZ Erste Bank CETV Fortuna beta_i -0.246231127 -0.064463954 -0.460363256 -0.186055958 -1.128453695 beta_i O2 -0.246231127 ČEZ -0.064463954 Erste Bank -0.460363256 CETV -0.186055958 Fortuna -1.128453695 Global Minimum VRS 0.000534238 0.000244757 0.000514316 0.000380554 -0.000506048 1 0 5.23268E-05 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_matrice wi 0.489302196 0.134029134 0.085778846 0.260547124 0.0303427 2960.046611 -291.0860525 -683.3554062 -1927.347943 -58.25720995 0.489302196 w1 0.489302196 -51.89394209 425.0315112 68.05819449 -436.2899006 -4.905863015 0.134029134 w2 0.134029134 6.39527E-05 8.02567E-06 1.07934E-05 2.42577E-05 -3.75658E-06 -651.4132678 120.1368713 696.9011147 -210.1243351 44.49961693 0.085778846 w3 0.085778846 1.71581E-06 2.19747E-05 -1.22358E-06 5.87649E-06 -5.50622E-08 -2195.106047 -254.2160544 -127.5115946 2588.586863 -11.75316678 0.260547124 w4 0.260547124 1.07934E-05 -1.22358E-06 7.88341E-06 4.54314E-06 -3.89172E-06 -61.63335442 0.13372437 45.90769153 -14.8246843 30.41662282 0.0303427 w5 0.0303427 2.42577E-05 5.87649E-06 4.54314E-06 2.23709E-05 -2.05673E-06 0.570531637 0.086502186 0.061746138 0.251917947 0.029302093 -0.000422123 lambda1 -0.000422123 -3.75658E-06 -5.50622E-08 -3.89172E-06 -2.05673E-06 1.61643E-05 1 Rp -0.00878318 Rp_matrixCalc -0.00878318 Var_P 0.000211062 Sigma_P 0.014527958 ##### Sheet/List 2 ##### Date K L M Index K L M Index 2/22/2016 176.39999 82.39 15.86121 112.48 0.062514754 0.107669284 0.270884299 0.118005322 2/19/2016 182.01 82.5 25.05275 110.49 0.135220261 0.074592938 0.106669501 0.126201483 2/18/2016 186.21001 82.45 9.439176 111.34 0.143051327 0.106776517 -0.454981316 0.112229954 2/17/2016 182.61 82 28.95428 108.98 0.159999854 0.113797088 0.478850743 0.115114092 2/16/2016 175.49001 81.22 18.83143 106.03 0.112483404 0.061178826 -0.504480151 0.092522407 2/12/2016 177.75 81.03 3.040745 107.33 0.145050162 0.043509794 -1.131680602 0.103364517 2/11/2016 180.05 79.6 8.759708 107.23 0.171659422 0.006048406 -0.415503023 0.107507741 2/10/2016 182.95 79.35 30.16247 108.61 0.153859204 0.047751007 0.315374636 0.068493174 2/9/2016 182.47 80.08 3.064378 108.03 0.188511553 0.062874904 -2.147233775 0.082854519 2/8/2016 181.62 81.16 12.43475 106.82 0.162046173 0.09655541 1.35460791 0.066074994 2/5/2016 183.53 80.08 28.47809 108.74 0.177245376 0.069679921 2.192253508 0.151854257 2/4/2016 182.01 79.83 19.2481 107.32 0.147433733 0.046144288 0.400789102 0.131563255 2/3/2016 180.23 78.48 31.10395 105.26 0.109357222 0.012953051 0.261565682 0.078223476 2/2/2016 177.14 74.59 29.55045 105.35 0.103956524 -0.046239656 0.328692745 0.088470784 2/1/2016 174.09 76.29 25.21651 102.71 0.137667521 -0.015219806 0.329506294 0.083521311 1/29/2016 169.84 77.85 29.17203 100.7 0.106512655 -0.001283697 0.122115211 0.044158405 1/28/2016 164.62 76.99 12.35519 96.45 0.050647613 -0.014442546 -0.421034122 -0.001554002 1/27/2016 163.94 75.29 2.982268 96.96 0.046636209 -0.050123797 -1.642031416 0.030790997 1/26/2016 165.73 76.7 31.57403 98.53 0.104737206 -0.026249577 1.432876983 0.036378921 1/25/2016 165.71001 73.98 12.09742 99.96 0.111339295 -0.069821581 0.052965252 0.050998483 1/22/2016 158.99001 76.57 22.51798 97.39 0.07684538 -0.046193464 1.067645524 0.032560531 1/21/2016 161.39 74.1 14.8775 99.52 0.137264908 -0.046796017 0.000355634 0.06026044 1/20/2016 155.61 73.18 17.93703 97.13 0.062856172 -0.054254198 -0.359909652 0.032861894 1/19/2016 156.82001 76.4 31.18719 96.66 0.051018189 -0.011452494 0.546629643 0.000206932 1/15/2016 153.75 77.58 9.428935 96.79 0.0184455 -0.004886213 -1.395122136 -0.013647536 1/14/2016 151.64999 79.12 13.27212 96.3 0.026188885 -0.000379099 -1.09071153 0.000415455 1/13/2016 156.86 75.65 22.00399 101.42 0.065533533 -0.04875869 -0.342271025 0.054505539 1/12/2016 151.12 75.2 26.23458 99.44 0.015538375 -0.010976768 1.952594256 0.026081348 1/11/2016 154.45 73.69 3.208768 99.99 1/8/2016 153.72 74.69 3.180001 93.42 1/7/2016 157.06 76.23 12.89221 94.09 1/6/2016 161.56 77.47 23.94523 97.34 1/5/2016 159.64999 78.12 21.27231 96.43 1/4/2016 151.7 77.46 18.1377 94.48 12/31/2015 152.67999 77.95 25.8186 96.35 12/30/2015 156.49001 78.11 18.82358 96.6 12/29/2015 156.47 79.16 15.40536 94.02 12/28/2015 149.25 78.74 7.53424 95.01 12/24/2015 148.25 79.33 11.47335 94.99 12/23/2015 147.23 80.19 7.742066 94.27 12/22/2015 140.69 77.65 14.87221 93.7 12/21/2015 146.13001 77.26 25.70735 93.99 12/18/2015 149.02 77.28 18.05419 96.64 12/17/2015 150.94 77.96 38.05016 98.12 12/16/2015 147.73 79.15 39.50302 96.26 12/15/2015 146.91 79.43 30.98474 96.04 12/14/2015 148.78999 76.03 3.72283 96.88 Rf "1,5 p.a." 0.00125 E(ri) 0.106557872 0.014373351 0.046764935 0.067143525 E(Rp) 10% OLS VRS K L M 28 1.880018691 2.983620408 0.402453829 1.309418173 2.983620408 0.402453829 1.309418173 1.880018691 0.180147628 0.247331706 0.07009375 0.321300751 0.247331706 0.07009375 0.321300751 Inv_M 0.119329672 -1.24532316 alfa 0.048026543 -0.039264687 -0.243870825 -1.24532316 18.54718182 beta 0.871734528 0.79885646 4.328574669 Function K L M 0.048026543 -0.039264687 -0.243870825 beta alfa beta alfa beta alfa 0.871734528 0.79885646 4.328574669 0.871734528 0.048026543 0.79885646 -0.039264687 4.328574669 -0.243870825 0.144246739 0.011570211 0.189374077 0.015189931 4.350523983 0.348960946 0.584147464 0.033494002 0.406324064 0.043972541 0.036677933 1.010188924 36.52216291 26 17.79493661 26 0.989935031 26 0.040972321 0.029168052 0.034408011 0.050273194 1.010210546 26.53252321 CAPM - SML K L M Ri 0.058691661 0.053889468 0.286475042 Cov_M K L M Index K 0.002597792 0.001444339 0.005267849 0.001740775 L 0.001444339 0.003136341 0.004451999 0.001595244 M 0.005267849 0.004451999 1.02010125 0.00864377 Index 0.001740775 0.001595244 0.00864377 0.001996909 Market_var beta_i 0.871734528 0.79885646 4.328574669 Min.Var.Port VRS Sys_Eq 0.005195583 0.002888678 0.010535698 1 0 0.002888678 0.006272682 0.008903999 1 0 0.010535698 0.008903999 2.0402025 1 0 1 1 1 0 1 wi 0.597077512 0.405695777 -0.002773289 Inv_M 176.1025758 -175.6671776 -0.435398285 0.597077512 w1 0.597077512 -175.6671776 175.7257902 -0.058612677 0.405695777 w2 0.405695777 0.000926117 0.000349865 -8.72287E-06 -0.435398285 -0.058612677 0.494010963 -0.002773289 w3 -0.002773289 0.000349865 0.000516207 -5.009E-06 0.597077512 0.405695777 -0.002773289 -0.004244872 lambda1 -0.004244872 -8.72287E-06 -5.009E-06 7.84573E-06 MinVarP TgP Given10% Proof 1 Ratio(Rp/sigmaP) 1.504774729 2.291897078 2.025578767 Rp_matrice 0.069324824 0.069324824 Rp_sumproduct 0.069324824 VarP 0.002122436 Sigma_p 0.046069902 Tg_portfolio VRS Sys_Eq(CM) 0.002597792 0.001444339 0.005267849 0.105307872 0.001444339 0.003136341 0.004451999 0.013123351 0.005267849 0.004451999 1.02010125 0.045514935 Inv_M Zi wi 1.608480644 -0.604202382 -0.004278262 520.1732692 -237.2051932 -1.650970219 Z1 51.59026909 w1 1.608480644 -237.2051932 428.9988304 -0.647329317 Z2 -19.37913496 w2 -0.604202382 0.006721032 -0.001403678 -3.62507E-05 -1.650970219 -0.647329317 0.991645654 Z3 -0.137220603 w3 -0.004278262 -0.001403678 0.001144954 1.15081E-05 -3.62507E-05 1.15081E-05 1.86714E-05 sum_Zi 32.07391352 Proof 1 Rp_matrice 0.162511789 Rp_sumproduct 0.162511789 VarP 0.005027818 Sigma_p 0.070907106 Given return of 10 % in Rp VRS Sys_Eq 0.005195583 0.002888678 0.010535698 1 0.106557872 0 0.002888678 0.006272682 0.008903999 1 0.014373351 0 0.010535698 0.008903999 2.0402025 1 0.046764935 0 1 1 1 0 0 1 0.106557872 0.014373351 0.046764935 0 0 0.1 wi 0.930010012 0.073258683 -0.003268694 Inv_M 0.06094557 0.112501898 -0.173447468 -0.155338285 10.85348297 w1 0.930010012 0.112501898 0.207671812 -0.32017371 1.156991976 -10.83733293 w2 0.073258683 0.002246878 9.84047E-05 -1.60138E-05 -0.173447468 -0.32017371 0.493621178 -0.001653691 -0.016150036 w3 -0.003268694 9.84047E-05 1.68322E-05 -1.06608E-06 -0.155338285 1.156991976 -0.001653691 -0.007460756 0.046388641 lambda1 -0.002821892 -1.60138E-05 -1.06608E-06 1.08991E-05 10.85348297 -10.83733293 -0.016150036 0.046388641 -0.669149067 lambda2 -0.020526265 Proof 1 Rp_matrice 0.1 Rp_sumproduct 0.1 VarP 0.002437259 Sigma_p 0.049368606