"Ceny akcií za 70 dnů (denní, Kč):" Výnosy akcií (30-denní): Kovariance: datum CETV CEZ KOBA datum CETV CEZ KOBA ING konto CTV CEZ KOBA ING konto 0.002166667 1 "1,856.00" "1,059.00" "4,266.00" 31 0.1067 0.2077 -0.0063 0.0022 CTV 0.00673 -0.00095 0.00013 0 2 "1,913.00" "1,072.00" "4,108.00" 32 0.0784 0.1828 0.0326 0.0022 CEZ -0.00095 0.00926 -0.00232 0 3 "1,905.00" "1,094.00" "4,108.00" 33 0.0777 0.1572 0.0419 0.0022 KOBA 0.00013 -0.00232 0.00165 0 4 "1,868.00" "1,182.00" "4,072.00" 34 0.0958 0.0668 0.0548 0.0022 ING konto 0 0 0 0 5 "1,860.00" "1,186.00" "3,987.00" 35 0.0806 0.0497 0.0625 0.0022 6 "1,865.00" "1,192.00" "3,835.00" 36 0.0804 0.0545 0.1030 0.0022 7 "1,859.00" "1,200.00" "3,886.00" 37 0.1146 0.0583 0.1045 0.0022 8 "1,832.00" "1,293.00" "3,832.00" 38 0.1114 0.0062 0.0963 0.0022 9 "1,871.00" "1,302.00" "3,953.00" 39 0.1032 0.0315 0.0511 0.0022 10 "1,853.00" "1,307.00" "4,002.00" 40 0.1662 0.0589 0.0212 0.0022 11 "1,854.00" "1,399.00" "4,047.00" 41 0.1936 -0.0279 -0.0035 0.0022 12 "1,862.00" "1,302.00" "3,994.00" 42 0.1681 0.0323 -0.0018 0.0022 13 "1,870.00" "1,239.00" "4,030.00" 43 0.1834 0.1017 -0.0069 0.0022 14 "1,864.00" "1,214.00" "4,133.00" 44 0.1808 0.1326 -0.0242 0.0022 15 "1,834.00" "1,123.00" "4,271.00" 45 0.1903 0.2333 -0.0616 0.0022 16 "1,808.00" "1,140.00" "4,257.00" 46 0.1388 0.2377 -0.0472 0.0022 17 "1,814.00" "1,159.00" "4,261.00" 47 0.1279 0.1959 -0.0373 0.0022 18 "1,836.00" "1,203.00" "4,318.00" 48 0.0871 0.1571 -0.0252 0.0022 19 "1,807.00" "1,186.00" "4,239.00" 49 0.0564 0.1568 -0.0045 0.0022 20 "1,812.00" "1,224.00" "4,216.00" 50 0.0734 0.1168 -0.0036 0.0022 21 "1,843.00" "1,226.00" "4,274.00" 51 0.0461 0.1419 -0.0161 0.0022 22 "1,834.00" "1,219.00" "4,266.00" 52 0.0862 0.1682 0.0316 0.0022 23 "1,831.00" "1,238.00" "4,142.00" 53 0.0737 0.1551 0.0579 0.0022 24 "1,860.00" "1,246.00" "4,208.00" 54 0.0371 0.2239 0.0323 0.0022 25 "1,878.00" "1,273.00" "4,175.00" 55 0.0202 0.1925 0.0271 0.0022 26 "1,872.00" "1,255.00" "4,228.00" 56 0.0150 0.2231 0.0078 0.0022 27 "1,938.00" "1,243.00" "4,300.00" 57 -0.0351 0.2373 -0.0121 0.0022 28 "1,975.00" "1,265.00" "4,273.00" 58 -0.0420 0.2530 0.0012 0.0022 29 "1,954.00" "1,277.00" "4,316.00" 59 -0.0210 0.2451 -0.0199 0.0022 30 "2,010.00" "1,293.00" "4,294.00" 60 -0.0493 0.2212 -0.0282 0.0022 31 "2,054.00" "1,279.00" "4,239.00" 61 -0.0847 0.2166 -0.0281 0.0022 32 "2,063.00" "1,268.00" "4,242.00" 62 -0.0722 0.2027 -0.0200 0.0022 33 "2,053.00" "1,266.00" "4,280.00" 63 -0.0755 0.2085 -0.0150 0.0022 34 "2,047.00" "1,261.00" "4,295.00" 64 -0.0669 0.1301 -0.0377 0.0022 35 "2,010.00" "1,245.00" "4,236.00" 65 -0.0209 0.0924 0.0158 0.0022 36 "2,015.00" "1,257.00" "4,230.00" 66 0.0094 0.0613 0.0338 0.0022 37 "2,072.00" "1,270.00" "4,292.00" 67 -0.0193 0.0299 0.0084 0.0022 38 "2,036.00" "1,301.00" "4,201.00" 68 0.0000 -0.0361 0.0464 0.0022 39 "2,064.00" "1,343.00" "4,155.00" 69 -0.0208 -0.0856 0.0452 0.0022 40 "2,161.00" "1,384.00" "4,087.00" 70 -0.0740 -0.1272 0.0700 0.0022 41 "2,213.00" "1,360.00" "4,033.00" Průměry: 0.0530 0.1241 0.0137 0.0022 42 "2,175.00" "1,344.00" "3,987.00" Rozptyly: 0.0067 0.0093 0.0017 0.0000 43 "2,213.00" "1,365.00" "4,002.00" Sm.odchylky: 0.0821 0.0962 0.0406 0.0000 44 "2,201.00" "1,375.00" "4,033.00" CETV CEZ KOBA ING konto 45 "2,183.00" "1,385.00" "4,008.00" 46 "2,059.00" "1,411.00" "4,056.00" 47 "2,046.00" "1,386.00" "4,102.00" 48 "1,996.00" "1,392.00" "4,209.00" 49 "1,909.00" "1,372.00" "4,220.00" 50 "1,945.00" "1,367.00" "4,201.00" 51 "1,928.00" "1,400.00" "4,205.00" 52 "1,992.00" "1,424.00" "4,401.00" 53 "1,966.00" "1,430.00" "4,382.00" 54 "1,929.00" "1,525.00" "4,344.00" 55 "1,916.00" "1,518.00" "4,288.00" 56 "1,900.00" "1,535.00" "4,261.00" 57 "1,870.00" "1,538.00" "4,248.00" 58 "1,892.00" "1,585.00" "4,278.00" 59 "1,913.00" "1,590.00" "4,230.00" 60 "1,911.00" "1,579.00" "4,173.00" 61 "1,880.00" "1,556.00" "4,120.00" 62 "1,914.00" "1,525.00" "4,157.00" 63 "1,898.00" "1,530.00" "4,216.00" 64 "1,910.00" "1,425.00" "4,133.00" 65 "1,968.00" "1,360.00" "4,303.00" 66 "2,034.00" "1,334.00" "4,373.00" 67 "2,032.00" "1,308.00" "4,328.00" 68 "2,036.00" "1,254.00" "4,396.00" 69 "2,021.00" "1,228.00" "4,343.00" 70 "2,001.00" "1,208.00" "4,373.00" ##### Sheet/List 2 ##### Markowitzův model Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.0530 0.1241 0.0137 Výnos: 0.05 Zadaný výnos: 0.05 Průměrné riziko tj Si: 0.082067031 0.096204843 0.040645918 "Kovarianční matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.024550181 CETV 0.0067 -0.0010 0.0001 CEZ -0.0010 0.0093 -0.0023 KOBA 0.0001 -0.0023 0.0017 Zi: 0.1216 0.2857 0.5927 suma: 1 = 1 krátký prodej: 0 0 0 Zi*Kov.mat.: 0.0006 0.0012 0.0003 ##### Sheet/List 3 ##### Sharpeův model Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.0530 0.1241 0.0137 Výnos: 0.060713523 Průměrné riziko tj Si: 0.0821 0.0962 0.0406 "Kovarianční matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.030000816 Zadané riziko: 0.03 CETV 0.0067 -0.0010 0.0001 CEZ -0.0010 0.0093 -0.0023 KOBA 0.0001 -0.0023 0.0017 Zi: 0.1536 0.3713 0.4750 suma: 1 = 1 krátký prodej: 0 0 0 Zi*Kov.mat.: 0.0007 0.0022 -0.0001 ##### Sheet/List 4 ##### Blackův model (s bezrizikovým aktivem) Minimalizace rizika při zadaném výnosu Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.0530 0.1241 0.0137 0.0022 Výnos: 0.05 Zadaný výnos: 0.05 Průměrné riziko tj Si: 0.0821 0.0962 0.0406 0.0000 "Kovarianční matice, tj. Sij:" CETV CEZ KOBA ING konto Riziko: 0.024075162 CETV 0.0067 -0.0010 0.0001 0.0000 CEZ -0.0010 0.0093 -0.0023 0.0000 KOBA 0.0001 -0.0023 0.0017 0.0000 ING konto 0.0000 0.0000 0.0000 0.0000 Zi: 0.1236 0.2947 0.4882 0.0935 suma: 1.0000 = 1 krátký prodej: 0 0 0 0 Zi*Kov.mat.: 0.0006 0.0015 0.0001 0.0000 ##### Sheet/List 5 ##### Tobinův model s krátkým prodejem (a bezrizikovým aktivem) Maximalizace výnosu při zadaném riziku a krátkém prodeji 100% Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.0530 0.1241 0.0137 0.0022 Výnos: 0.0840 Průměrné riziko tj Si: 0.0821 0.0962 0.0406 0.0000 "Kovarianční matice, tj. Sij:" CETV CEZ KOBA ING konto Riziko: 0.0500 Zadané riziko: 0.05 CETV 0.0067 -0.0010 0.0001 0.0000 CEZ -0.0010 0.0093 -0.0023 0.0000 KOBA 0.0001 -0.0023 0.0017 0.0000 ING konto 0.0000 0.0000 0.0000 0.0000 Zi: 0.2233 0.5575 0.2192 0.0000 suma: 1.0000 = 1 krátký prodej: -1 -1 -1 0 Zi*Kov.mat.: 0.0010 0.0044 -0.0009 0.0000 ##### Sheet/List 6 ##### Ceny akcií (denní): Výnosy akcií (30-denní): datum CETV CEZ KOBA PX CETV CEZ KOBA PX ING konto 1 "1,856.00" "1,059.00" "4,266.00" "1,798.60" 0.1067 0.2077 -0.0063 0.0488 0.0022 2 "1,913.00" "1,072.00" "4,108.00" "1,812.10" 0.0784 0.1828 0.0326 0.0442 0.0022 3 "1,905.00" "1,094.00" "4,108.00" "1,806.30" 0.0777 0.1572 0.0419 0.0441 0.0022 4 "1,868.00" "1,182.00" "4,072.00" "1,776.20" 0.0958 0.0668 0.0548 0.0562 0.0022 5 "1,860.00" "1,186.00" "3,987.00" "1,762.40" 0.0806 0.0497 0.0625 0.0488 0.0022 6 "1,865.00" "1,192.00" "3,835.00" "1,757.50" 0.0804 0.0545 0.1030 0.0626 0.0022 7 "1,859.00" "1,200.00" "3,886.00" "1,765.00" 0.1146 0.0583 0.1045 0.0610 0.0022 8 "1,832.00" "1,293.00" "3,832.00" "1,755.70" 0.1114 0.0062 0.0963 0.0734 0.0022 9 "1,871.00" "1,302.00" "3,953.00" "1,770.20" 0.1032 0.0315 0.0511 0.0790 0.0022 10 "1,853.00" "1,307.00" "4,002.00" "1,761.90" 0.1662 0.0589 0.0212 0.0989 0.0022 11 "1,854.00" "1,399.00" "4,047.00" "1,747.80" 0.1936 -0.0279 -0.0035 0.0947 0.0022 12 "1,862.00" "1,302.00" "3,994.00" "1,750.80" 0.1681 0.0323 -0.0018 0.0900 0.0022 13 "1,870.00" "1,239.00" "4,030.00" "1,780.70" 0.1834 0.1017 -0.0069 0.0813 0.0022 14 "1,864.00" "1,214.00" "4,133.00" "1,790.90" 0.1808 0.1326 -0.0242 0.0656 0.0022 15 "1,834.00" "1,123.00" "4,271.00" "1,793.80" 0.1903 0.2333 -0.0616 0.0528 0.0022 16 "1,808.00" "1,140.00" "4,257.00" "1,792.10" 0.1388 0.2377 -0.0472 0.0621 0.0022 17 "1,814.00" "1,159.00" "4,261.00" "1,802.90" 0.1279 0.1959 -0.0373 0.0380 0.0022 18 "1,836.00" "1,203.00" "4,318.00" "1,825.30" 0.0871 0.1571 -0.0252 0.0195 0.0022 19 "1,807.00" "1,186.00" "4,239.00" "1,816.30" 0.0564 0.1568 -0.0045 0.0087 0.0022 20 "1,812.00" "1,224.00" "4,216.00" "1,828.80" 0.0734 0.1168 -0.0036 -0.0045 0.0022 21 "1,843.00" "1,226.00" "4,274.00" "1,845.50" 0.0461 0.1419 -0.0161 -0.0186 0.0022 22 "1,834.00" "1,219.00" "4,266.00" "1,835.10" 0.0862 0.1682 0.0316 -0.0037 0.0022 23 "1,831.00" "1,238.00" "4,142.00" "1,862.70" 0.0737 0.1551 0.0579 -0.0351 0.0022 24 "1,860.00" "1,246.00" "4,208.00" "1,881.50" 0.0371 0.2239 0.0323 -0.0466 0.0022 25 "1,878.00" "1,273.00" "4,175.00" "1,896.10" 0.0202 0.1925 0.0271 -0.0662 0.0022 26 "1,872.00" "1,255.00" "4,228.00" "1,883.40" 0.0150 0.2231 0.0078 -0.0618 0.0022 27 "1,938.00" "1,243.00" "4,300.00" "1,881.00" -0.0351 0.2373 -0.0121 -0.0812 0.0022 28 "1,975.00" "1,265.00" "4,273.00" "1,900.70" -0.0420 0.2530 0.0012 -0.0835 0.0022 29 "1,954.00" "1,277.00" "4,316.00" "1,898.80" -0.0210 0.2451 -0.0199 -0.0689 0.0022 30 "2,010.00" "1,293.00" "4,294.00" "1,908.30" -0.0493 0.2212 -0.0282 -0.0719 0.0022 31 "2,054.00" "1,279.00" "4,239.00" "1,886.30" -0.0847 0.2166 -0.0281 -0.0788 0.0022 32 "2,063.00" "1,268.00" "4,242.00" "1,892.20" -0.0722 0.2027 -0.0200 -0.0762 0.0022 33 "2,053.00" "1,266.00" "4,280.00" "1,886.00" -0.0755 0.2085 -0.0150 -0.0681 0.0022 34 "2,047.00" "1,261.00" "4,295.00" "1,876.10" -0.0669 0.1301 -0.0377 -0.0544 0.0022 35 "2,010.00" "1,245.00" "4,236.00" "1,848.40" -0.0209 0.0924 0.0158 -0.0441 0.0022 36 "2,015.00" "1,257.00" "4,230.00" "1,867.60" 0.0094 0.0613 0.0338 -0.0594 0.0022 37 "2,072.00" "1,270.00" "4,292.00" "1,872.60" -0.0193 0.0299 0.0084 -0.0501 0.0022 38 "2,036.00" "1,301.00" "4,201.00" "1,884.60" 0.0000 -0.0361 0.0464 -0.0381 0.0022 39 "2,064.00" "1,343.00" "4,155.00" "1,910.10" -0.0208 -0.0856 0.0452 -0.0353 0.0022 40 "2,161.00" "1,384.00" "4,087.00" "1,936.10" "Cov(Xi,PX)" 0.0045 -0.0022 0.0006 0.0037 0.0000 41 "2,213.00" "1,360.00" "4,033.00" "1,913.40" Var(Xi) 0.0065 0.0078 0.0016 0.0037 0.0000 42 "2,175.00" "1,344.00" "3,987.00" "1,908.30" BETAi 0.6872 -0.2802 0.3555 1.0000 0.0000 43 "2,213.00" "1,365.00" "4,002.00" "1,925.50" E(Xi) 0.0563 0.1305 0.0122 0.0021 0.0022 44 "2,201.00" "1,375.00" "4,033.00" "1,908.30" ALFAi 0.0548 0.1311 0.0115 0.0000 0.0022 45 "2,183.00" "1,385.00" "4,008.00" "1,888.60" Var(ei) 0.0048 0.0075 0.0011 0.0000 0.0000 46 "2,059.00" "1,411.00" "4,056.00" "1,903.30" 47 "2,046.00" "1,386.00" "4,102.00" "1,871.40" 48 "1,996.00" "1,392.00" "4,209.00" "1,860.90" 49 "1,909.00" "1,372.00" "4,220.00" "1,832.10" 50 "1,945.00" "1,367.00" "4,201.00" "1,820.50" 51 "1,928.00" "1,400.00" "4,205.00" "1,811.10" 52 "1,992.00" "1,424.00" "4,401.00" "1,828.30" 53 "1,966.00" "1,430.00" "4,382.00" "1,797.40" 54 "1,929.00" "1,525.00" "4,344.00" "1,793.80" 55 "1,916.00" "1,518.00" "4,288.00" "1,770.60" 56 "1,900.00" "1,535.00" "4,261.00" "1,767.10" 57 "1,870.00" "1,538.00" "4,248.00" "1,728.20" 58 "1,892.00" "1,585.00" "4,278.00" "1,742.00" 59 "1,913.00" "1,590.00" "4,230.00" "1,767.90" 60 "1,911.00" "1,579.00" "4,173.00" "1,771.10" 61 "1,880.00" "1,556.00" "4,120.00" "1,737.70" 62 "1,914.00" "1,525.00" "4,157.00" "1,748.10" 63 "1,898.00" "1,530.00" "4,216.00" "1,757.60" 64 "1,910.00" "1,425.00" "4,133.00" "1,774.10" 65 "1,968.00" "1,360.00" "4,303.00" "1,766.90" 66 "2,034.00" "1,334.00" "4,373.00" "1,756.60" 67 "2,032.00" "1,308.00" "4,328.00" "1,778.80" 68 "2,036.00" "1,254.00" "4,396.00" "1,812.80" 69 "2,021.00" "1,228.00" "4,343.00" "1,842.70" ##### Sheet/List 7 ##### Sharpeův Indexový model RPF = å E(Xi) Zi s2PF = Var(F) åå bibj Zi Zj + å Var(ei)Zi2 Model používá 30-tidenní výnosy Var(Xi) - bi2 Var(F) = Var(ei) "Průměrné výnosy, tj Ri:" 0.0530 0.1241 0.0137 0.0022 Výnos: 0.088797282 Kovariance s PX: CETV CEZ KOBA ING konto PX Riziko: 0.050000987 PX50 0.0045 0.0040 0.0021 0.0000 0.003665837 Koeficient BETAi: BETA 0.6872 0.8066 1.1853 0.0000 Zadané riziko: 0.05 Koeficient ALFAi: ALFA 0.0548 0.1267 0.0337 0.0000 Individ.riziko: Var(ei) 0.0048 0.0026 -0.0034 0.0000 Zi: 0.0113 0.7058 0.0000 0.2829 suma: 1.0000 = 1 krátký prodej: 0 0 0 0 Zi^2.: 0.0001 0.4981 0.0000 0.0800 (suma BETAi*Zi)^2 = 0.3330 ##### Sheet/List 8 ##### Markowitzův Indexový model RPF = å (ai + bi E(F)) Zi s2PF = Var(F) åå bibj Zi Zj + å Var(ei)Zi2 Model používá 30-tidenní výnosy Var(Xi) - bi2 Var(F) = Var(ei) "Průměrné výnosy, tj Ri:" 0.0530 0.1241 0.0137 0.0022 Výnos: 0.096594535 Kovariance s PX: CETV CEZ KOBA ING konto PX Riziko: 0.054501334 PX50 0.0045 0.0040 0.0021 0.0000 0.003665837 Koeficient BETAi: BETA 0.6872 0.8066 1.1853 0.0000 Zadaný výnos: 0.10 Koeficient ALFAi: ALFA 0.0548 0.1267 0.0337 0.0000 Individ.riziko: Var(ei) 0.0048 0.0026 -0.0034 0.0000 Zi: 0.0123 0.7693 0.0000 0.2184 suma: 1.0000 = 1 krátký prodej: 0 0 0 0 Zi^2.: 0.0002 0.5918 0.0000 0.0477 (suma BETAi*Zi)^2 = 0.3956 ##### Sheet/List 9 ##### Kataokův model Model používá 30-tidenní výnosy 1-alpha = 0.95 k_alpha = 1.644853627 "Průměrné výnosy, tj Ri:" 0.0322 0.1046 0.0137 Výnos: 0.104588995 Účel.fce: 0.250 Průměrné riziko tj Si: 0.08051776 0.088500586 0.040137602 "Kovarianční matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.088500586 CETV 0.0065 -0.0018 0.0003 CEZ -0.0018 0.0078 -0.0020 KOBA 0.0003 -0.0020 0.0016 Zi: 0.0000 1.0000 0.0000 suma: 0.999999993 = 1 krátký prodej: 0 0 0 Zi*Kov.mat.: -0.0018 0.0078 -0.0020 ##### Sheet/List 10 ##### Min-Risk model Model používá 30-tidenní výnosy maximalizuje se pravděpodobnost dosažení zadané hodnoty výnosu PF "Průměrné výnosy, tj Ri:" 0.0322 0.1046 0.0137 Výnos: 0.055067436 Zadaný výnos: 0.02 Průměrné riziko tj Si: 0.08051776 0.088500586 0.040137602 "Kovarianční matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.030896717 Účel. fce: 1.134989088 CETV 0.0065 -0.0018 0.0003 CEZ -0.0018 0.0078 -0.0020 KOBA 0.0003 -0.0020 0.0016 Zi: 0.2035 0.4139 0.3826 suma: 1.000000004 = 1 krátký prodej: 0 0 0 Zi*Kov.mat.: 0.0007 0.0021 -0.0001