Je zadaná tabulka s portfolii CP A a B na třech trzích. Trh CP ri sigmai "korelaceA,B" kovariance I A 0.22 0.3 B 0.31 0.32 0.15 0.0144 II A 0.26 0.29 B 0.34 0.33 -0.06 -0.005742 III A 0.18 0.2 B 0.41 0.38 0.09 0.00684 a) Pro každý trh určete portfolio s minimálním rizikem (tedy vypočítat xi=podíly CP v portf.) b) Vypočítejte pro tato portfolia očekávaný výnos rp. "c) Určete, na kterém trhu máme nejvýhodněji investovat." I. 0.18 0.0288 1 0 3.056234719 -3.056234719 0.537897311 0.0288 0.2048 1 0 -3.056234719 3.056234719 0.462102689 1 1 0 1 0.537897311 0.462102689 -0.110130073 Xa 53.79% rp 26.16% Xb 46.21% riziko 23.47% 0.897 1.115 -0.110130073 0.234659406 II. 0.1682 -0.011484 1 0 2.445179085 -2.445179085 0.560640441 -0.011484 0.2178 1 0 -2.445179085 2.445179085 0.439359559 1 1 0 1 0.560640441 0.439359559 -0.089254117 Xa 56.06% rp 29.51% Xb 43.94% riziko 21.13% 0.716 1.397 -0.089254117 0.211251174 III. 0.08 0.01368 1 0 2.928772259 -2.928772259 0.805763824 0.01368 0.2888 1 0 -2.928772259 2.928772259 0.194236176 1 1 0 1 0.805763824 0.194236176 -0.067118257 Xa 80.58% rp 22.47% Xb 19.42% riziko 18.32% 0.815 1.226 -0.067118257 0.183191507 ##### Sheet/List 2 ##### Je zadaná tabulka investičních možností Firma 1 (A) Firma 2(B) Firma 3 (C) Kovariance 0.8 0.3 0.6 "s1,2" -0.1 0.8 1.2 0.8 1.1 "s1,3" -0.5 0.3 "s2,3" 0.3 0.6 a) Formulujte a řešte zadanou úlohu s prodejem CP nakrátko Lagrangeovou metodou b) Řešte předchozí model s předem určenou výnosností 15% c) Vždy spočítejte výnosnost a riziko sestaveného portfolia 2.88 -0.2 -1 1 0 0.219575604 -0.230115233 0.010539629 0.332138842 -0.2 1.28 0.6 1 0 -0.230115233 0.641160764 -0.411045531 0.379918494 -1 0.6 2.42 1 0 0.010539629 -0.411045531 0.400505902 0.287942664 1 1 1 0 1 0.332138842 0.379918494 0.287942664 -0.592633502 0.332138842 rp 0.55245222 0.379918494 0.287942664 sigmap 0.544349842 -0.592633502 2.88 -0.2 -1 1 0.8 0 0.08400224 0.056001493 -0.140003733 -0.330968826 1.200298675 -0.2 1.28 0.6 1 0.3 0 0.056001493 0.037334329 -0.093335822 1.779354116 -2.533134217 -1 0.6 2.42 1 0.6 0 -0.140003733 -0.093335822 0.233339556 -0.44838529 1.332835542 1 1 1 0 0 1 -0.330968826 1.779354116 -0.44838529 -3.835982826 5.870823222 0.8 0.3 0.6 0 0 0.15 1.200298675 -2.533134217 1.332835542 5.870823222 -10.62684338 -0.150924025 rp 0.15 1.399383984 -0.248459959 sigmap 1.075602119 -2.955359343 4.276796715 ##### Sheet/List 3 ##### Emise CP1 CP2 CP3 CP4 CP5 CP6 CP7 ri % CP1 80.5 82.7 85.3 85.1 123.9 22 3.5 1.9 CP2 184.7 131.5 69.4 49.5 58 -9.9 6.1 CP3 374.2 384.5 366.5 103.8 343.5 2.9 CP4 684.8 599.1 51.6 502.7 4 CP5 871.4 -21.2 520.4 5.7 CP6 89.7 74.4 3.4 CP7 574.6 4.9 "a) Vypočítejte podíly cenných papírů v portfoliu, je-li povolen sell short, při minimalizaci rizika" b) Očekávaná výnosnost portfolia nechť je 5% 161 165.4 170.6 170.2 247.8 44 7 1 1.9 0 165.4 369.4 263 138.8 99 116 -19.8 1 6.1 0 170.6 263 748.4 769 733 207.6 687 1 2.9 0 170.2 138.8 769 1369.6 1198.2 103.2 1005.4 1 4 0 247.8 99 733 1198.2 1742.8 -42.4 1040.8 1 5.7 0 44 116 207.6 103.2 -42.4 179.4 148.8 1 3.4 0 7 -19.8 687 1005.4 1040.8 148.8 1149.2 1 4.9 0 1 1 1 1 1 1 1 0 0 1 1.9 6.1 2.9 4 5.7 3.4 4.9 0 0 5 0.077541972 -0.006186729 0.008788437 -0.009709852 -0.037687458 -0.077748274 0.045001904 2.137199771 1 0 0 0 0 0 0 0 -0.006186729 0.007803096 -0.003616667 0.000167497 0.001056212 -0.000477668 0.001254258 0.04443472 0 1 0 0 0 0 0 0 0.008788437 -0.003616667 0.007543944 -0.002286279 -0.004259006 -0.008793788 0.00262336 -0.290668798 0 0 1 0 0 0 0 0 -0.009709852 0.000167497 -0.002286279 0.004278044 0.004071768 0.010660407 -0.007181586 -0.230272848 0 0 0 1 0 0 0 0 -0.037687458 0.001056212 -0.004259006 0.004071768 0.02058011 0.040174616 -0.023936242 -0.773325871 0 0 0 0 1 0 0 0 -0.077748274 -0.000477668 -0.008793788 0.010660407 0.040174616 0.086382111 -0.050197403 -1.12240341 0 0 0 0 0 1 0 0 0.045001904 0.001254258 0.00262336 -0.007181586 -0.023936242 -0.050197403 0.032435709 1.235036437 0 0 0 0 0 0 1 0 2.137199771 0.04443472 -0.290668798 -0.230272848 -0.773325871 -1.12240341 1.235036437 -30.28748412 0 0 0 0 0 0 0 1 váhy v portfoliu CP1 2.137199771 výnosnost 0.395249927 CP2 0.04443472 riziko 3.891496121 1946.560763 -670.6568763 CP3 -0.290668798 -15.09089916 CP4 -0.230272848 -1245.669245 CP5 -0.773325871 CP6 -1.12240341 CP7 1.235036437 -30.28748412 0.016039416 0.007660609 -0.004068331 -0.00315134 -0.009140957 -0.023510276 0.01617088 2.286870663 -0.378674055 1 0 0 0 0 0 0 0 0 0.007660609 0.00468536 -0.000721958 -0.001309155 -0.00537105 -0.012689387 0.007745581 0.010736227 0.085258694 0 1 0 0 0 0 0 0 0 -0.004068331 -0.000721958 0.004856308 -0.000915259 0.001708481 0.002544365 -0.003403606 -0.259380927 -0.079159711 0 0 1 0 0 0 0 0 0 -0.00315134 -0.001309155 -0.000915259 0.003578658 0.001027626 0.004876574 -0.004107102 -0.246233458 0.040381057 0 0 0 1 0 0 0 0 0 -0.009140957 -0.00537105 0.001708481 0.001027626 0.00733021 0.01499997 -0.01055428 -0.842795834 0.175762112 0 0 0 0 1 0 0 0 0 -0.023510276 -0.012689387 0.002544365 0.004876574 0.01499997 0.038550595 -0.024771841 -1.254395478 0.333945838 0 0 0 0 0 1 0 0 0 0.01617088 0.007745581 -0.003403606 -0.004107102 -0.01055428 -0.024771841 0.018920369 1.305198807 -0.177513935 0 0 0 0 0 0 1 0 0 2.286870663 0.010736227 -0.259380927 -0.246233458 -0.842795834 -1.254395478 1.305198807 -30.65171899 0.921530536 0 0 0 0 0 0 0 1 0 -0.378674055 0.085258694 -0.079159711 0.040381057 0.175762112 0.333945838 -0.177513935 0.921530536 -2.331513485 0 0 0 0 0 0 0 0 1 váhy v portfoliu CP1 0.393500391 výnosnost 5 CP2 0.437029695 riziko 6.313645966 326.5384 -6.654495518 CP3 -0.655179483 -58.99456978 CP4 -0.044328174 -221.0272093 CP5 0.036014728 CP6 0.415333712 CP7 0.417629131 -26.04406632 -10.73603689 ##### Sheet/List 4 ##### Mějme bezrizikové aktivum s výnosností " a portfolia umístněná na efektivní množině. Sestrojte graf umístnění jednotlivých portfolií, jestliže budeme měnit podíly investování do bezrizikového aktiva a rizikového portfolia." Riziková portfolia A B C D 0.0620 0.0400 0.0750 0.0840 rf 0.035 0.1450 0.0970 0.1700 0.2000 sigmaf 0 U všech portfolií budeme volit podíly (váhy) takto: 1. 2. 3. 4. 5. 0.2 0.4 0.5 0.6 0.8 Portfolio 0.8 0.6 0.5 0.4 0.2 výnosnosti A 0.0566 0.0512 0.0485 0.0458 0.0404 B 0.039 0.038 0.0375 0.037 0.036 C 0.067 0.059 0.055 0.051 0.043 D 0.0742 0.0644 0.0595 0.0546 0.0448 rizika A 0.116 0.087 0.0725 0.058 0.029 B 0.0776 0.0582 0.0485 0.0388 0.0194 C 0.136 0.102 0.085 0.068 0.034 D 0.16 0.12 0.1 0.08 0.04