Příklad 1 Uvažujme s několika portfolii, tvořenými dvěma cennými papíry. 5% 20% 15% 40% Podíly (váhy) jednotlivých cenných papírů v portfoliích budou: 1 0.83 0.67 0.5 0.33 0.17 0 0 0.17 0.33 0.5 0.67 0.83 1 Vypočítat výnosnosti a rizika jednotlivých portfolií. Sestrojit spojnicový graf. 1 -1 0 0.5 -0.5 rp1 5.00% 20.00% 20.00% 20.00% 20.00% 20.00% 1 0 P1 rp2 5.10% 20.20% 19.40% 19.80% 20.00% 19.60% 0.99 0.01 P2 rp3 5.20% 20.40% 18.80% 19.62% 20.01% 19.21% 0.98 0.02 P3 rp4 5.30% 20.60% 18.20% 19.44% 20.03% 18.83% 0.97 0.03 P4 rp5 5.40% 20.80% 17.60% 19.27% 20.05% 18.45% 0.96 0.04 P5 rp6 5.50% 21.00% 17.00% 19.10% 20.07% 18.08% 0.95 0.05 P6 rp7 5.60% 21.20% 16.40% 18.95% 20.11% 17.72% 0.94 0.06 P7 rp8 5.70% 21.40% 15.80% 18.81% 20.15% 17.37% 0.93 0.07 P8 rp9 5.80% 21.60% 15.20% 18.68% 20.19% 17.03% 0.92 0.08 P9 rp10 5.90% 21.80% 14.60% 18.55% 20.24% 16.69% 0.91 0.09 P10 rp11 6.00% 22.00% 14.00% 18.44% 20.30% 16.37% 0.9 0.1 P11 rp12 6.10% 22.20% 13.40% 18.34% 20.36% 16.06% 0.89 0.11 P12 rp13 6.20% 22.40% 12.80% 18.24% 20.43% 15.76% 0.88 0.12 P13 rp14 6.30% 22.60% 12.20% 18.16% 20.50% 15.47% 0.87 0.13 P14 rp15 6.40% 22.80% 11.60% 18.09% 20.58% 15.19% 0.86 0.14 P15 rp16 6.50% 23.00% 11.00% 18.03% 20.66% 14.93% 0.85 0.15 P16 rp17 6.60% 23.20% 10.40% 17.98% 20.75% 14.69% 0.84 0.16 P17 rp18 6.70% 23.40% 9.80% 17.94% 20.85% 14.45% 0.83 0.17 P18 rp19 6.80% 23.60% 9.20% 17.91% 20.95% 14.24% 0.82 0.18 P19 rp20 6.90% 23.80% 8.60% 17.89% 21.06% 14.04% 0.81 0.19 P20 rp21 7.00% 24.00% 8.00% 17.89% 21.17% 13.86% 0.8 0.2 P21 rp22 7.10% 24.20% 7.40% 17.89% 21.28% 13.69% 0.79 0.21 P22 rp23 7.20% 24.40% 6.80% 17.91% 21.40% 13.55% 0.78 0.22 P23 rp24 7.30% 24.60% 6.20% 17.94% 21.53% 13.42% 0.77 0.23 P24 rp25 7.40% 24.80% 5.60% 17.98% 21.66% 13.31% 0.76 0.24 P25 rp26 7.50% 25.00% 5.00% 18.03% 21.79% 13.23% 0.75 0.25 P26 rp27 7.60% 25.20% 4.40% 18.09% 21.93% 13.16% 0.74 0.26 P27 rp28 7.70% 25.40% 3.80% 18.16% 22.08% 13.12% 0.73 0.27 P28 rp29 7.80% 25.60% 3.20% 18.24% 22.23% 13.10% 0.72 0.28 P29 rp30 7.90% 25.80% 2.60% 18.34% 22.38% 13.10% 0.71 0.29 P30 rp31 8.00% 26.00% 2.00% 18.44% 22.54% 13.11% 0.7 0.3 P31 rp32 8.10% 26.20% 1.40% 18.55% 22.70% 13.16% 0.69 0.31 P32 rp33 8.20% 26.40% 0.80% 18.68% 22.87% 13.22% 0.68 0.32 P33 rp34 8.30% 26.60% 0.20% 18.81% 23.04% 13.30% 0.67 0.33 P34 rp35 8.40% 26.80% 0.40% 18.95% 23.21% 13.40% 0.66 0.34 P35 rp36 8.50% 27.00% 1.00% 19.10% 23.39% 13.53% 0.65 0.35 P36 rp37 8.60% 27.20% 1.60% 19.27% 23.57% 13.67% 0.64 0.36 P37 rp38 8.70% 27.40% 2.20% 19.44% 23.75% 13.83% 0.63 0.37 P38 rp39 8.80% 27.60% 2.80% 19.62% 23.94% 14.01% 0.62 0.38 P39 rp40 8.90% 27.80% 3.40% 19.80% 24.14% 14.21% 0.61 0.39 P40 rp41 9.00% 28.00% 4.00% 20.00% 24.33% 14.42% 0.6 0.4 P41 rp42 9.10% 28.20% 4.60% 20.20% 24.53% 14.65% 0.59 0.41 P42 rp43 9.20% 28.40% 5.20% 20.42% 24.73% 14.90% 0.58 0.42 P43 rp44 9.30% 28.60% 5.80% 20.63% 24.94% 15.16% 0.57 0.43 P44 rp45 9.40% 28.80% 6.40% 20.86% 25.15% 15.43% 0.56 0.44 P45 rp46 9.50% 29.00% 7.00% 21.10% 25.36% 15.72% 0.55 0.45 P46 rp47 9.60% 29.20% 7.60% 21.34% 25.57% 16.01% 0.54 0.46 P47 rp48 9.70% 29.40% 8.20% 21.58% 25.79% 16.33% 0.53 0.47 P48 rp49 9.80% 29.60% 8.80% 21.84% 26.01% 16.65% 0.52 0.48 P49 rp50 9.90% 29.80% 9.40% 22.10% 26.23% 16.98% 0.51 0.49 P50 rp51 10.00% 30.00% 10.00% 22.36% 26.46% 17.32% 0.5 0.5 P51 rp52 10.10% 30.20% 10.60% 22.63% 26.69% 17.67% 0.49 0.51 P52 rp53 10.20% 30.40% 11.20% 22.91% 26.92% 18.03% 0.48 0.52 P53 rp54 10.30% 30.60% 11.80% 23.19% 27.15% 18.40% 0.47 0.53 P54 rp55 10.40% 30.80% 12.40% 23.48% 27.38% 18.77% 0.46 0.54 P55 rp56 10.50% 31.00% 13.00% 23.77% 27.62% 19.16% 0.45 0.55 P56 rp57 10.60% 31.20% 13.60% 24.07% 27.86% 19.55% 0.44 0.56 P57 rp58 10.70% 31.40% 14.20% 24.37% 28.10% 19.94% 0.43 0.57 P58 rp59 10.80% 31.60% 14.80% 24.67% 28.35% 20.35% 0.42 0.58 P59 rp60 10.90% 31.80% 15.40% 24.98% 28.60% 20.75% 0.41 0.59 P60 rp61 11.00% 32.00% 16.00% 25.30% 28.84% 21.17% 0.4 0.6 P61 rp62 11.10% 32.20% 16.60% 25.62% 29.10% 21.58% 0.39 0.61 P62 rp63 11.20% 32.40% 17.20% 25.94% 29.35% 22.01% 0.38 0.62 P63 rp64 11.30% 32.60% 17.80% 26.26% 29.60% 22.43% 0.37 0.63 P64 rp65 11.40% 32.80% 18.40% 26.59% 29.86% 22.87% 0.36 0.64 P65 rp66 11.50% 33.00% 19.00% 26.93% 30.12% 23.30% 0.35 0.65 P66 rp67 11.60% 33.20% 19.60% 27.26% 30.38% 23.74% 0.34 0.66 P67 rp68 11.70% 33.40% 20.20% 27.60% 30.64% 24.19% 0.33 0.67 P68 rp69 11.80% 33.60% 20.80% 27.94% 30.90% 24.63% 0.32 0.68 P69 rp70 11.90% 33.80% 21.40% 28.29% 31.17% 25.08% 0.31 0.69 P70 rp71 12.00% 34.00% 22.00% 28.64% 31.43% 25.53% 0.3 0.7 P71 rp72 12.10% 34.20% 22.60% 28.99% 31.70% 25.99% 0.29 0.71 P72 rp73 12.20% 34.40% 23.20% 29.34% 31.97% 26.45% 0.28 0.72 P73 rp74 12.30% 34.60% 23.80% 29.70% 32.24% 26.91% 0.27 0.73 P74 rp75 12.40% 34.80% 24.40% 30.05% 32.51% 27.37% 0.26 0.74 P75 rp76 12.50% 35.00% 25.00% 30.41% 32.79% 27.84% 0.25 0.75 P76 rp77 12.60% 35.20% 25.60% 30.78% 33.06% 28.31% 0.24 0.76 P77 rp78 12.70% 35.40% 26.20% 31.14% 33.34% 28.78% 0.23 0.77 P78 rp79 12.80% 35.60% 26.80% 31.51% 33.62% 29.25% 0.22 0.78 P79 rp80 12.90% 35.80% 27.40% 31.88% 33.90% 29.72% 0.21 0.79 P80 rp81 13.00% 36.00% 28.00% 32.25% 34.18% 30.20% 0.2 0.8 P81 rp82 13.10% 36.20% 28.60% 32.62% 34.46% 30.68% 0.19 0.81 P82 rp83 13.20% 36.40% 29.20% 33.00% 34.74% 31.16% 0.18 0.82 P83 rp84 13.30% 36.60% 29.80% 33.37% 35.02% 31.64% 0.17 0.83 P84 rp85 13.40% 36.80% 30.40% 33.75% 35.31% 32.12% 0.16 0.84 P85 rp86 13.50% 37.00% 31.00% 34.13% 35.59% 32.60% 0.15 0.85 P86 rp87 13.60% 37.20% 31.60% 34.51% 35.88% 33.09% 0.14 0.86 P87 rp88 13.70% 37.40% 32.20% 34.90% 36.17% 33.58% 0.13 0.87 P88 rp89 13.80% 37.60% 32.80% 35.28% 36.46% 34.06% 0.12 0.88 P89 rp90 13.90% 37.80% 33.40% 35.67% 36.75% 34.55% 0.11 0.89 P90 rp91 14.00% 38.00% 34.00% 36.06% 37.04% 35.04% 0.1 0.9 P91 rp92 14.10% 38.20% 34.60% 36.44% 37.33% 35.53% 0.09 0.91 P92 rp93 14.20% 38.40% 35.20% 36.83% 37.63% 36.03% 0.08 0.92 P93 rp94 14.30% 38.60% 35.80% 37.23% 37.92% 36.52% 0.07 0.93 P94 rp95 14.40% 38.80% 36.40% 37.62% 38.21% 37.01% 0.06 0.94 P95 rp96 14.50% 39.00% 37.00% 38.01% 38.51% 37.51% 0.05 0.95 P96 rp97 14.60% 39.20% 37.60% 38.41% 38.81% 38.01% 0.04 0.96 P97 rp98 14.70% 39.40% 38.20% 38.80% 39.10% 38.50% 0.03 0.97 P98 rp99 14.80% 39.60% 38.80% 39.20% 39.40% 39.00% 0.02 0.98 P99 rp100 14.90% 39.80% 39.40% 39.60% 39.70% 39.50% 0.01 0.99 P100 rp101 15.00% 40.00% 40.00% 40.00% 40.00% 40.00% 0 1 P101 ##### Sheet 2 ##### Příklad 2 Vypočítejte a graficky zobrazte vytvořená portfolia jestliže známe matici výnosnosti a kovarianční matici. 21.42429 17.66352 13.37909 459 -211 112 16.2 -211 312 215 24.6 112 215 179 22.8 A B C D E 0.2 0.25 0.5 0.3 0.1 0.2 0.25 0.1 0.4 0.2 0.6 0.5 0.4 0.3 0.7 rPa rPb rPc rPd rPe sigmaPa sigmaPb sigmaPc sigmaPd sigmaPe rPa 21.84% 12.53%tmave modra rPb 21.60% 12.18%ruzova rPc 19.68% 13.69%zluta rPd 21.54% 11.33%svetle modra rPe 22.50% 13.12%fialova ##### Sheet 3 ##### Příklad 3 Je zadané portfolio, které se skládá ze dvou cenných papírů následovně: Cenný papír Oček. vRiziko Podíl v 0.15 0.28 0.6 0.21 0.42 0.4 1.      úloha: Vypočítejte očekávaný výnos portfolia 2.      úloha: Vypočítejte celkové riziko portfolia, kdy koeficient korelace mezi složkami portfolia je z intervalu . Krok h = 0,2. Určete nejmenší a největší riziko portfolia. 1. 17.40% 2. 0.00% -1 3.36% -0.98 4.75% -0.96 5.82% -0.94 6.72% -0.92 7.51% -0.9 8.23% -0.88 8.89% -0.86 9.50% -0.84 10.08% -0.82 10.63% -0.8 11.14% -0.78 11.64% -0.76 12.11% -0.74 12.57% -0.72 13.01% -0.7 13.44% -0.68 13.85% -0.66 14.26% -0.64 14.65% -0.62 15.03% -0.6 15.40% -0.58 15.76% -0.56 16.11% -0.54 16.46% -0.52 16.80% -0.5 17.13% -0.48 17.46% -0.46 17.78% -0.44 18.09% -0.42 18.40% -0.4 18.71% -0.38 19.01% -0.36 19.30% -0.34 19.59% -0.32 19.88% -0.3 20.16% -0.28 20.44% -0.26 20.71% -0.24 20.98% -0.22 21.25% -0.2 21.51% -0.18 21.78% -0.16 22.03% -0.14 22.29% -0.12 22.54% -0.1 22.79% -0.08 23.03% -0.06 23.28% -0.04 23.52% -0.02 23.76% 0 24.00% 0.02 24.23% 0.04 24.46% 0.06 24.69% 0.08 24.92% 0.1 25.14% 0.12 25.37% 0.14 25.59% 0.16 25.81% 0.18 26.03% 0.2 26.24% 0.22 26.46% 0.24 26.67% 0.26 26.88% 0.28 27.09% 0.3 27.30% 0.32 27.50% 0.34 27.71% 0.36 27.91% 0.38 28.11% 0.4 28.31% 0.42 28.51% 0.44 28.71% 0.46 28.90% 0.48 29.10% 0.5 29.29% 0.52 29.48% 0.54 29.67% 0.56 29.86% 0.58 30.05% 0.6 30.24% 0.62 30.43% 0.64 30.61% 0.66 30.79% 0.68 30.98% 0.7 31.16% 0.72 31.34% 0.74 31.52% 0.76 31.70% 0.78 31.88% 0.8 32.05% 0.82 32.23% 0.84 32.40% 0.86 32.58% 0.88 32.75% 0.9 32.92% 0.92 33.09% 0.94 33.26% 0.96 33.43% 0.98 33.60% 1 ##### Sheet 4 ##### Příklad 4 Mějme vícesložkové portfolio a matici korelačních koeficientů: Cenný papír Oček. výRiziko Podíl v portfoliu 0.13 0.28 0.2 0.25 0.42 0.4 0.21 0.35 0.1 0.41 0.48 0.2 0.3 0.39 0.1 1. úloha: Vypočítejte očekávaný výnos portfolia 2.      úloha: Vypočítejte riziko portfolia vyjádřené rozptylem a směrodatnou odchylkou 1 0.3 0.41 -0.23 0.13 0.3 1 0.25 -0.09 0 0.41 0.25 1 -0.22 0.33 -0.23 -0.09 -0.22 1 0.14 0.13 0 0.33 0.14 1 1. 25.90% 2. 22.18%