Theoretical price of stock Stock-i Trading day Company 1 Company 2 Company 3 1 100 200 1000 daily return Var 2-dais return Var 2 110 210 1050 0.09531018 0.048790164 0.048790164 0.010072302 0.00133902 0.003796222 3 121 205 1080 0.09531018 -0.024097552 0.028170877 0.010072302 0.001317334 0.001680524 0.19062036 0.024692613 0.076961041 0.06062548 0.014541137 0.010758112 4 95 150 1020 -0.241913654 -0.312374685 -0.057158414 0.05610407 0.10534713 0.0019656 -0.146603474 -0.336472237 -0.028987537 0.008281257 0.057877876 4.96069E-06 5 98 210 950 0.031090587 0.336472237 -0.071095922 0.001306191 0.105154078 0.003395696 -0.210823067 0.024097552 -0.128254336 0.024093561 0.014397978 0.010301044 E(X) -0.005050677 0.012197541 -0.012823324 Manual 0.025851621 0.071052521 0.003612681 E(X) -0.055602061 -0.095894024 -0.026760277 D(X) 0.046500149 0.043408496 0.010532058 -0.005050677 fce 0.025851621 0.071052521 0.003612681 fce 0.046500149 0.043408496 0.010532058 std 0.160784394 0.266556787 0.06010558 std. 0.215638932 0.208347056 0.102625817 ##### Sheet/List 2 ##### Year 2014 2015 Company I. II. III. IV. I. II. III. IV. E(X¨) Var sigma^2 sigma (std.) A 1010 1055 1100 1031 988 1065 918 1060 0.043590436 0.041769413 -0.064780975 -0.042601786 0.07504738 -0.148532688 0.143826796 0.006902654 0.001345993 0.001215691 0.005138543 0.00245069 0.004643704 0.024160145 0.018748221 0.009617164 0.098067142 B 2650 3000 3848 3228 3638 4205 3979 4731 0.124052649 0.248941244 -0.175690782 0.11957133 0.144840213 -0.055243762 0.173106065 0.082796708 0.001702053 0.027604007 0.066815783 0.001352373 0.003849397 0.019055171 0.00815578 0.021422427 0.146364023 C 1505 2030 2190 2325 2250 2443 1700 1796 0.299242895 0.075865751 0.059818495 -0.032789823 0.082296576 -0.362598541 0.054933719 0.025252725 0.075070613 0.002561678 0.001194793 0.003368937 0.003254001 0.150428604 0.000880961 0.039459931 0.19864524 D 178 300 325 396 351 370 335 327 0.521998924 0.080042708 0.197589029 -0.120627988 0.052716782 -0.099372474 -0.024170361 0.086882374 0.189326412 4.6781E-05 0.012255963 0.04306055 0.001167288 0.034690868 0.01233271 0.048813429 0.220937613 E 281 372 358 494 460 539 443 468 0.280539185 -0.038360868 0.322002531 -0.071309028 0.158489081 -0.196145801 0.054898526 0.072873375 0.043125089 0.012373057 0.062065336 0.020788565 0.007330049 0.072371317 0.000323095 0.036396085 0.190777579 F 2645 3125 3400 3330 3400 3425 3475 4100 0.166763218 0.084341148 -0.020803128 0.020803128 0.00732604 0.014493007 0.165392495 0.062616558 0.010846527 0.000471958 0.006958844 0.001748363 0.003057041 0.002315876 0.010562893 0.005993584 0.077418239 G 547 800 803 1070 975 952 997 944 0.380162925 0.003742986 0.287059214 -0.092976456 -0.023872436 0.046185735 -0.054624604 0.077953909 0.091330289 0.005507261 0.043725028 0.02921719 0.010368605 0.001009217 0.017577062 0.033122442 0.18199572 2-years return 0.048318577 Cov_M 0.579576957 A B C D E F G 0.176769072 A 0.009617164 0.010344194 0.013408241 0.004913066 0.006367961 0.005068834 -0.003030327 0.608176621 B 0.010344194 0.021422427 0.011400388 -0.000978463 -0.006464734 0.006737595 -0.012350713 0.510113627 C 0.013408241 0.011400388 0.039459931 0.033622776 0.029489718 0.007956581 0.01646218 0.438315908 D 0.004913066 -0.000978463 0.033622776 0.048813429 0.032966067 0.00734128 0.035790339 0.545677364 E 0.006367961 -0.006464734 0.029489718 0.032966067 0.036396085 0.001803784 0.024994008 F 0.005068834 0.006737595 0.007956581 0.00734128 0.001803784 0.005993584 0.002183082 G -0.003030327 -0.012350713 0.01646218 0.035790339 0.024994008 0.002183082 0.033122442 Corr_M 0.098067142 0.146364023 0.19864524 0.220937613 0.190777579 0.077418239 0.18199572 A B C D E F G 0.098067142 A 1 0.720673878 0.688287867 0.226756317 0.340368617 0.667638298 -0.169787138 0.146364023 B 0.720673878 1 0.392109307 -0.030258016 -0.231520241 0.594603268 -0.463656671 0.19864524 C 0.688287867 0.392109307 1 0.76610051 0.778153237 0.51737455 0.455352787 0.220937613 D 0.226756317 -0.030258016 0.76610051 1 0.782114164 0.429199152 0.890092167 0.190777579 E 0.340368617 -0.231520241 0.778153237 0.782114164 1 0.122127651 0.719858925 0.077418239 F 0.667638298 0.594603268 0.51737455 0.429199152 0.122127651 1 0.154940723 0.18199572 G -0.169787138 -0.463656671 0.455352787 0.890092167 0.719858925 0.154940723 1 1 0.720673878 0.688287867 0.226756317 0.340368617 0.667638298 -0.169787138 0.720673878 1 0.392109307 -0.030258016 -0.231520241 0.594603268 -0.463656671 0.688287867 0.392109307 1 0.76610051 0.778153237 0.51737455 0.455352787 0.226756317 -0.030258016 0.76610051 1 0.782114164 0.429199152 0.890092167 0.340368617 -0.231520241 0.778153237 0.782114164 1 0.122127651 0.719858925 0.667638298 0.594603268 0.51737455 0.429199152 0.122127651 1 0.154940723 -0.169787138 -0.463656671 0.455352787 0.890092167 0.719858925 0.154940723 1 ##### Sheet/List 3 ##### Appl AIG ExxonMobile Var Appl AIG ExxonMobile Appl-Appl Appl-AIG Appl-Exxon AIG-AIG AIG-Exxon Exxon-Exxon 135.720001 62.5 81.760002 0.122435743 -0.046730872 -0.038510114 0.01489599 0.002788134 0.00138019 0.12204913 -0.052802782 -0.037150913 0.01489599 -0.006444534 -0.004534237 0.002788134 0.001961672 0.00138019 135.350006 62.27 82.300003 0.120372318 -0.066323517 -0.042696252 0.014396569 0.005241098 0.001708752 0.119985705 -0.072395426 -0.041337051 0.014396569 -0.008686416 -0.004959855 0.005241098 0.002992613 0.001708752 135.509995 60.849998 83.160004 0.123388683 -0.085627285 -0.018703255 0.015129509 0.008408742 0.000300816 0.12300207 -0.091699194 -0.017344054 0.015129509 -0.011279191 -0.002133355 0.008408742 0.001590436 0.000300816 135.020004 66.889999 82.82 0.118014556 0.009764984 -0.040928232 0.013836333 1.36388E-05 0.001565708 0.117627943 0.003693075 -0.039569031 0.013836333 0.000434409 -0.004654424 1.36388E-05 -0.000146131 0.001565708 133.289993 66.139999 83 0.10503541 0.001210303 -0.051196916 0.010951371 2.36352E-05 0.002483798 0.104648797 -0.004861607 -0.049837715 0.010951371 -0.000508761 -0.005215457 2.36352E-05 0.000242291 0.002483798 132.119995 65.610001 82.519997 0.104250983 -0.011215592 -0.04536813 0.010787807 0.000298858 0.001936786 0.10386437 -0.017287502 -0.044008929 0.010787807 -0.001795555 -0.00457096 0.000298858 0.000760804 0.001936786 132.419998 65.32 81.839996 0.104756545 -0.014137197 -0.053526871 0.010893083 0.000408408 0.002721466 0.104369932 -0.020209106 -0.05216767 0.010893083 -0.002109223 -0.005444736 0.000408408 0.001054262 0.002721466 132.039993 64.910004 81.480003 0.097698618 -0.030944271 -0.063364171 0.009469626 0.001370198 0.003844616 0.097312005 -0.03701618 -0.06200497 0.009469626 -0.003602119 -0.006033828 0.001370198 0.002295187 0.003844616 131.529999 64.879997 82.769997 0.099187511 -0.035133839 -0.037467371 0.009761617 0.001697914 0.0013038 0.098800898 -0.041205749 -0.03610817 0.009761617 -0.004071165 -0.00356752 0.001697914 0.001487864 0.0013038 130.289993 64.900002 83.309998 0.090723242 -0.022548107 -0.043799229 0.008160707 0.000819105 0.001801156 0.090336629 -0.028620016 -0.042440028 0.008160707 -0.002585436 -0.003833889 0.000819105 0.001214634 0.001801156 129.080002 64.940002 83.540001 0.090510727 -0.028388943 -0.057676981 0.008122356 0.00118755 0.003171692 0.090124114 -0.034460852 -0.05631778 0.008122356 -0.003105754 -0.00507559 0.00118755 0.001940759 0.003171692 128.529999 64.120003 83.449997 0.09732729 -0.022819291 -0.059319784 0.009397495 0.000834701 0.003359429 0.096940677 -0.028891201 -0.057960583 0.009397495 -0.002800733 -0.005618738 0.000834701 0.001674551 0.003359429 128.75 64.269997 82.940002 0.104109975 -0.026107196 -0.080469211 0.010758536 0.001035495 0.006258394 0.103723362 -0.032179105 -0.07911001 0.010758536 -0.003337725 -0.008205556 0.001035495 0.002545689 0.006258394 121.349998 64.260002 83.889999 0.043796439 -0.013294383 -0.080143568 0.001884413 0.000375053 0.006206977 0.043409826 -0.019366293 -0.078784367 0.001884413 -0.000840687 -0.003420016 0.000375053 0.001525761 0.006206977 121.629997 64.889999 84.860001 0.048946363 -0.00645162 -0.061691565 0.002358049 0.000156839 0.003639994 0.04855975 -0.01252353 -0.060332364 0.002358049 -0.000608139 -0.002929725 0.000156839 0.000755574 0.003639994 121.949997 65.209999 85.510002 0.043747499 -0.004437327 -0.055057643 0.001880166 0.000110444 0.002883523 0.043360886 -0.010509236 -0.053698443 0.001880166 -0.00045569 -0.002328412 0.000110444 0.00056433 0.002883523 121.940002 66.019997 85.599998 0.043408574 0.002122821 -0.053452234 0.001850889 1.55953E-05 0.002713684 0.043021961 -0.003949088 -0.052093033 0.001850889 -0.000169898 -0.002241144 1.55953E-05 0.00020572 0.002713684 121.879997 65.720001 85.339996 0.038643221 -0.0148016 -0.061465242 0.001463568 0.000435703 0.003612736 0.038256608 -0.020873509 -0.060106041 0.001463568 -0.00079855 -0.002299453 0.000435703 0.001254624 0.003612736 119.970001 65.5 85.089996 0.029178814 -0.013797565 -0.063958121 0.000828991 0.000394796 0.003918625 0.028792201 -0.019869475 -0.06259892 0.000828991 -0.000572086 -0.001802361 0.000394796 0.001243808 0.003918625 120.080002 65.489998 84.970001 0.032071124 -0.011236149 -0.067131682 0.001003908 0.000299569 0.004326019 0.031684511 -0.017308059 -0.065772481 0.001003908 -0.000548397 -0.002083969 0.000299569 0.001138394 0.004326019 120 66.540001 85.889999 0.024805136 -0.001801847 -0.049848545 0.000596264 6.1996E-05 0.002351216 0.024418523 -0.007873757 -0.048489344 0.000596264 -0.000192266 -0.001184038 6.1996E-05 0.000381793 0.002351216 119.779999 66.290001 84.730003 0.023910251 -0.004665476 -0.065106305 0.000553362 0.000115291 0.004063693 0.023523638 -0.010737386 -0.063747104 0.000553362 -0.000252582 -0.001499564 0.000115291 0.000684477 0.004063693 119.989998 66.239998 86.279999 0.02831613 -0.004518806 -0.04686765 0.000780058 0.000112163 0.002071019 0.027929517 -0.010590715 -0.045508449 0.000780058 -0.000295794 -0.001271029 0.000112163 0.000481967 0.002071019 120 66.059998 87.360001 0.034160197 -0.003626553 -0.042798051 0.001140655 9.40602E-05 0.001717178 0.033773584 -0.009698462 -0.041438851 0.001140655 -0.000327552 -0.001399539 9.40602E-05 0.000401893 0.001717178 119.040001 66.349998 86.349998 0.027422318 0.002414306 -0.051241192 0.000730929 1.33781E-05 0.002488213 0.027035705 -0.003657603 -0.049881991 0.000730929 -9.88859E-05 -0.001348595 1.33781E-05 0.000182449 0.002488213 119.25 66.25 86.339996 0.034639173 0.003629189 -0.047940516 0.001173238 5.96688E-06 0.002169819 0.034252561 -0.002442721 -0.046581316 0.001173238 -8.36694E-05 -0.001595529 5.96688E-06 0.000113785 0.002169819 119.75 66.949997 86.809998 0.03882328 0.009605342 -0.064351358 0.001477377 1.24851E-05 0.003968012 0.038436667 0.003533432 -0.062992157 0.001477377 0.000135813 -0.002421209 1.24851E-05 -0.000222579 0.003968012 119.110001 67.199997 85.93 0.05000825 0.02379263 -0.057106724 0.002462307 0.000314024 0.003107786 0.049621637 0.01772072 -0.055747523 0.002462307 0.000879331 -0.002766283 0.000314024 -0.000987886 0.003107786 118.989998 66.379997 87.040001 0.04327971 0.008320069 -0.022268575 0.001839818 5.05422E-06 0.000437202 0.042893097 0.00224816 -0.020909374 0.001839818 9.64305E-05 -0.000896868 5.05422E-06 -4.70076E-05 0.000437202 117.910004 66.809998 88.5 0.050351902 0.014928996 0.002035969 0.00249653 7.8448E-05 1.15272E-05 0.04996529 0.008857087 0.00339517 0.00249653 0.000442547 0.000169641 7.8448E-05 3.00713E-05 1.15272E-05 116.610001 65.599998 88.550003 0.049034616 0.010419954 0.005435445 0.002366628 1.89055E-05 4.61672E-05 0.048648003 0.004348044 0.006794646 0.002366628 0.000211524 0.000330546 1.89055E-05 2.95434E-05 4.61672E-05 116.019997 65.970001 89.889999 0.053736874 0.027196944 0.02626244 0.00284625 0.000446267 0.000762955 0.053350262 0.021125035 0.02762164 0.00284625 0.001127026 0.001473622 0.000446267 0.000583508 0.000762955 116.150002 65.120003 90.889999 0.06252592 0.013917064 0.038239743 0.003861293 6.15464E-05 0.001568076 0.062139307 0.007845154 0.039598944 0.003861293 0.000487492 0.002460651 6.15464E-05 0.00031066 0.001568076 115.82 65.309998 90.260002 0.052466382 0.024175949 0.036326622 0.002712302 0.000327756 0.001420221 0.052079769 0.01810404 0.037685823 0.002712302 0.000942854 0.001962669 0.000327756 0.000682266 0.001420221 116.730003 65.5 90.349998 0.064030399 0.021449769 0.035028076 0.004050531 0.000236479 0.001324034 0.063643786 0.015377859 0.036387277 0.004050531 0.000978705 0.002315824 0.000236479 0.000559558 0.001324034 116.760002 65.879997 90.300003 0.05492409 0.039475678 0.033786996 0.002974336 0.001115812 0.001235255 0.054537477 0.033403768 0.035146197 0.002974336 0.001821757 0.001916785 0.001115812 0.001174015 0.001235255 117.260002 66.699997 90.75 0.050727935 0.0526356 0.054924621 0.002534249 0.002168177 0.003167869 0.050341323 0.046563691 0.056283822 0.002534249 0.002344078 0.002833402 0.002168177 0.002620782 0.003167869 116.519997 66.410004 90.709999 0.04341071 0.047804397 0.047870049 0.001851073 0.001741601 0.002423519 0.043024097 0.041732488 0.04922925 0.001851073 0.001795503 0.002118044 0.001741601 0.002054459 0.002423519 116.290001 66.230003 90.870003 0.03946496 0.027398988 0.042143434 0.001527117 0.000454844 0.001892479 0.039078347 0.021327079 0.043502634 0.001527117 0.000833427 0.001700011 0.000454844 0.000927784 0.001892479 117.059998 66.660004 90.279999 0.05108645 0.035579016 0.037927808 0.002570474 0.000870669 0.001543469 0.050699837 0.029507107 0.039287009 0.002570474 0.001496006 0.001991845 0.000870669 0.001159246 0.001543469 116.949997 66.599998 90.43 0.04503488 0.039821464 0.042352894 0.001993468 0.001139032 0.001910747 0.044648267 0.033749555 0.043712095 0.001993468 0.001506859 0.001951669 0.001139032 0.001475264 0.001910747 116.639999 66.540001 90.419998 0.043006986 0.040171015 0.044436683 0.001816496 0.001162749 0.002097263 0.042620373 0.034099106 0.045795883 0.001816496 0.001453317 0.001951838 0.001162749 0.001561599 0.002097263 115.970001 66.300003 91.18 0.052305892 0.036714099 0.066895626 0.002695612 0.000938944 0.004658721 0.051919279 0.030642189 0.068254827 0.002695612 0.00159092 0.003543741 0.000938944 0.002091477 0.004658721 115.82 66.190002 90.889999 0.052011572 0.030058986 0.064296453 0.002665136 0.00057538 0.004310665 0.051624959 0.023987077 0.065655654 0.002665136 0.001238332 0.00338947 0.00057538 0.001574887 0.004310665 115.190002 66.010002 90.580002 0.046193522 0.029361943 0.054797374 0.002098273 0.000542426 0.003153561 0.045806909 0.023290034 0.056156575 0.002098273 0.001066844 0.002572359 0.000542426 0.001307889 0.003153561 115.190002 66.309998 92.580002 0.072726603 0.026126305 0.064236147 0.005233074 0.000402179 0.00430275 0.07233999 0.020054396 0.065595348 0.005233074 0.001450735 0.004745167 0.000402179 0.001315475 0.00430275 113.300003 65.620003 90.980003 0.069339708 0.01799089 0.064699786 0.004754529 0.000142062 0.00436379 0.068953095 0.011918981 0.066058987 0.004754529 0.000821851 0.004554972 0.000142062 0.000787356 0.00436379 113.949997 65.830002 89 0.049654926 0.038874457 0.038133687 0.002427367 0.001076007 0.001559688 0.049268313 0.032802547 0.039492888 0.002427367 0.001616126 0.001945748 0.001076007 0.001295467 0.001559688 112.120003 65.82 88.32 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83.580002 -0.046294992 -0.029542684 -0.051986987 0.002179172 0.001268399 0.002563173 -0.046681604 -0.035614594 -0.050627786 0.002179172 0.001662546 0.002363386 0.001268399 0.001803088 0.002563173 124.239998 54.169998 84.32 -0.033402464 -0.02118808 -0.048835354 0.001141702 0.000743107 0.002253985 -0.033789076 -0.02725999 -0.047476153 0.001141702 0.00092109 0.001604175 0.000743107 0.001294199 0.002253985 123.379997 54.52 84.860001 -0.055490997 -0.007492041 -0.043693204 0.003122307 0.000183981 0.001792168 -0.05587761 -0.01356395 -0.042334003 0.003122307 0.000757921 0.002365523 0.000183981 0.000574216 0.001792168 126.690002 55.369999 84.519997 -0.016439943 0.010347737 -0.05836714 0.000283133 1.82827E-05 0.003249905 -0.016826556 0.004275827 -0.05700794 0.000283133 -7.19475E-05 0.000959247 1.82827E-05 -0.000243756 0.003249905 127.209999 55.830002 85.43 -0.038249701 0.014251183 -0.045647021 0.001492765 6.69005E-05 0.001961411 -0.038636314 0.008179274 -0.04428782 0.001492765 -0.000316017 0.001711118 6.69005E-05 -0.000362242 0.001961411 125.900002 55.939999 84.540001 -0.054861171 0.024795389 -0.051523938 0.003052318 0.000350569 0.002516501 -0.055247784 0.018723479 -0.050164738 0.003052318 -0.001034431 0.002771491 0.000350569 -0.000939258 0.002516501 127.5 55.650002 84.410004 128.470001 56.419998 86.07 127.040001 55.799999 84.080002 124.949997 55.93 84.760002 123.589996 55.299999 83.870003 124.449997 55.599998 84.220001 122.239998 54.720001 84.019997 124.510002 54.419998 84.260002 127.139999 56.110001 85.160004 126.599998 56 85.629997 126.410004 55.610001 86.739998 128.539993 55.380001 87.18 129.360001 55.580002 87.620003 129.089996 55.650002 88.040001 128.460007 55.330002 88.540001 130.419998 54.93 88.650002 128.789993 54.799999 89.599998 132.169998 55.040001 89.419998 133 54.57 89.010002 app-aig app-exxon aig-exxon E(X) 0.000386613 0.00607191 -0.001359201 0.004408587 0.002451518 0.002245751 "covar(X,Y)" 0.004408587 0.001245092 0.000208487 0.002451518 0.000392351 0.002245751 484 risk 0.066397193 0.049512805 0.04738935 Cov_M Apple AIG Exxon Apple 0.004408587 0.001245092 0.000208487 AIG 0.001245092 0.002451518 0.000392351 Exxon 0.000208487 0.000392351 0.002245751 fce Cov_M 0.004408587 0.001245092 0.000208487 0.001245092 0.002451518 0.000392351 0.000208487 0.000392351 0.002245751 corr_M 0.066397193 1 0.378734003 0.066259696 0.049512805 0.378734003 1 0.167215505 0.04738935 0.066259696 0.167215505 1