Datum CETV denní třídenní ERSTE denní třídenní PM denní třídenní KB denní třídenní 3/10/20081,307.00 0.77% -5.84% 902.7 -1.73% -3.76% 6,751.00 -1.45% -5.59% 3,786.00 -2.12% -3.76% 1 3/7/20081,297.00 -5.40% -6.69% 918.6 -0.85% 2.00% 6,850.00 -3.00% -4.54% 3,868.00 -0.15% 0.36% 2 3/6/20081,371.00 -1.22% -8.96% 926.5 -1.23% 0.35% 7,062.00 -1.24% -1.09% 3,874.00 -1.53% -4.06% 3 3/5/20081,388.00 -0.14% -13.30% 938 4.15% -3.50% 7,151.00 -0.35% -0.76% 3,934.00 2.08% -3.32% 4 3/4/20081,390.00 -7.70% -14.72% 900.6 -2.46% -9.20% 7,176.00 0.50% -1.36% 3,854.00 -4.56% -2.87% 5 3/3/20081,506.00 -5.93% -6.23% 923.3 -5.01% -7.31% 7,140.00 -0.92% -1.52% 4,038.00 -0.76% 2.33% 6 2/29/20081,601.00 -1.78% -2.02% 972 -2.01% -2.90% 7,206.00 -0.95% 0.85% 4,069.00 2.55% 3.56% 7 2/28/20081,630.00 1.49% 1.94% 991.9 -0.42% 2.84% 7,275.00 0.34% 0.96% 3,968.00 0.56% 0.79% 8 2/27/20081,606.00 -1.71% 2.62% 996.1 -0.49% 4.47% 7,250.00 1.47% 1.38% 3,946.00 0.43% 1.96% 9 2/26/20081,634.00 2.19% 2.13% 1,001.00 3.78% 3.57% 7,145.00 -0.85% 0.27% 3,929.00 -0.20% 1.03% 10 2/25/20081,599.00 2.17% -1.96% 964.5 1.15% -0.92% 7,206.00 0.77% 0.78% 3,937.00 1.73% 1.89% 11 2/22/20081,565.00 -2.19% -5.55% 953.5 -1.35% -3.93% 7,151.00 0.35% -0.90% 3,870.00 -0.49% 1.12% 12 2/21/20081,600.00 -1.90% -4.82% 966.5 -0.72% -0.10% 7,126.00 -0.34% -0.70% 3,889.00 0.65% 1.99% 13 2/20/20081,631.00 -1.57% -0.12% 973.5 -1.91% 2.74% 7,150.00 -0.91% -0.04% 3,864.00 0.97% 3.51% 14 2/19/20081,657.00 -1.43% -0.30% 992.5 2.58% 2.15% 7,216.00 0.56% 0.63% 3,827.00 0.37% -0.39% 15 2/18/20081,681.00 2.94% 0.78% 967.5 2.11% -0.69% 7,176.00 0.32% 0.14% 3,813.00 2.14% -0.78% 16 2/15/20081,633.00 -1.74% -1.98% 947.5 -2.48% 2.32% 7,153.00 -0.25% -0.46% 3,733.00 -2.84% 1.30% 17 2/14/20081,662.00 -0.36% 1.47% 971.6 -0.27% 8.92% 7,171.00 0.07% -1.17% 3,842.00 -0.03% 4.52% 18 2/13/20081,668.00 0.12% 974.2 5.21% 7,166.00 -0.28% 3,843.00 4.29% 19 2/12/20081,666.00 1.71% 926 3.81% 7,186.00 -0.96% 3,685.00 0.24% 20 2/11/20081,638.00 892 7,256.00 3,676.00 21 očekávaný výnos -1.08% -3.53% 0.09% -0.16% -0.36% -0.73% 0.17% 0.51% riziko 2.79% 5.15% 2.70% 4.41% 0.98% 1.81% 1.98% 2.58% kovarianční matice CETV ERSTE PM KB CETV 0.0007770.0004780.0000530.0002782 ERSTE 0.0004780.0007290.0000360.0003094 PM 0.0000530.0000360.0000960.0000163 KB 0.0002780.0003090.0000160.0003935 korelační matice CETV ERSTE PM KB CETV 1.0000 0.6350 0.1956 0.5029 ERSTE 0.6350 1.0000 0.1387 0.5776 PM 0.1956 0.1387 1.0000 0.0837 KB 0.5029 0.5776 0.0837 1.0000 ##### Sheet 2 ##### 2. Máme portfolio sestavené ze tří cenných papírů s následujícími charakteristikami: CP1 CP2 CP3 očekávaná výnosnost -1.08% 0.09% -0.36% riziko očekávané výnosnosti 2.79% 2.70% 0.98% Dále známe korelační matici: CP1 CP2 CP3 CP1 CP2 CP3 CP1 1 0.635 0.1956 CP2 0.635 1 0.1387 CP3 0.1956 0.1387 1 Vypočítejte výnosnost portfolia a riziko výnosnosti portfolia, pokud váhy cenných papírů v portfoliu jsou následující: C výnos portolia -0.35% riziko portfolia 2.03% bezrizikové aktivum 3.5% nové portfolio podíly 0.5 0.5 výnos portolia 1.57% riziko portfolia 1.02% ##### Sheet 3 ##### CP1 CP2 CP3 CP4 očekávaná výnosnost -1.08% 0.09% -0.36% 0.17% riziko očekávané výnosnosti 2.79% 2.70% 0.98% 1.98% a kovarianční matice CP1 CP2 CP3 CP4 CP1 0.0007777 0.0004781 0.0000537 0.0002782 CP2 0.0004781 0.000729 0.0000368 0.0003094 CP3 0.0000537 0.0000368 0.0000968 0.0000163 CP4 0.0002782 0.0003094 0.0000163 0.0003935 0.0007777 0.0004781 0.0000537 0.0002782 0.0004781 0.000729 0.0000368 0.0003094 0.0000537 0.0000368 0.0000968 0.0000163 0.0002782 0.0003094 0.0000163 0.0003935 matice A matice pravých stran 0.0015554 0.0009562 0.0001074 0.0005564 1- 0.01080 0 0.0009562 0.001458 0.0000736 0.0006188 1 0.00090 0 0.0001074 0.0000736 0.0001936 0.0000326 1- 0.00360 0 0.0005564 0.0006188 0.0000326 0.000787 1 0.00170 0 1 1 1 1 0 0 1 - 0.0108 0.00- 0.00 0. 0 0 0.01 inverzní matice 210.4910971 -77.29264109 -484.7744529 351.5759969-0.20327-74.6505988 1 0 0 0 0 0 -77.29264109 1064.542231 21.60834504 -1008.8579350.10732841.29761155 0 1 0 0 0 0 -484.7744529 21.60834504 1140.074337 -676.9082290.783963 -18.850114 0 0 1 0 0 0 351.5759969 -1008.857935 -676.908229 1334.1901670.31197952.20310125 0 0 0 1 0 0 -0.203269205 0.107327716 0.783962808 0.31197868 -0.0002-0.01441243 0 0 0 0 1 0 -74.65059881 41.29761155 -18.85011399 52.20310125-0.01441-5.92721262 0 0 0 0 0 1 řešení podíly CP1 -95% CP2 52% výpočet podílů pro minimální riziko CP3 60% 1150.682087-597.417636-247.3656763-305.8987754-0.021751023 CP4 83% -597.4176361352.281651-109.7290533-645.1349618 0.006909669 -0.000344023 -247.365676-109.729053 1200.022717-842.9279877 0.829798186 -0.073684561 -305.898775-645.134962-842.9279877 1793.961725 0.185043168 -0.021751020.006909669 0.829798186 0.185043168-0.000164854 riziko 0.12% -0.00066649 -2% 0.05% 1% 2.32% 83% 19% - 0.00 0.01% 1.89726E-06 0.01% riziko 0.90% výnos -0.24%