Ceny akcií (denní): Výnosy akcií (30-denní): Kovariance: datum CETV CEZ KOBA CETV CEZ KOBA CETV CEZ KOBA ING konto 0.002166667 1 "1,916.00" "1,089.00" "4,206.00" 0.1200 0.1800 -0.0043 CETV 0.001854907 0.001525094 -0.00060437 0 2 "1,827.00" "1,072.00" "4,498.00" 0.0985 0.0177 0.0189 CEZ 0.001525094 0.007243274 -0.00095029 0 3 "1,843.00" "1,074.00" "4,478.00" 0.1763 0.2076 -0.0670 KOBA -0.000604 -0.000950 0.00118019 0 4 "1,849.00" "1,082.00" "4,458.00" 0.2353 0.3983 -0.0864 ING konto 0 0 0 0 5 "1,860.00" "1,086.00" "4,438.00" 0.1774 0.2053 -0.0455 6 "1,871.00" "1,092.00" "4,418.00" 0.1764 0.2042 -0.0426 7 "1,777.00" "1,200.00" "4,698.00" 0.1322 0.1008 -0.1009 8 "1,893.00" "1,093.00" "4,378.00" 0.1743 0.2141 -0.0822 9 "1,904.00" "1,102.00" "4,358.00" 0.1707 0.2096 -0.0335 10 "1,915.00" "1,107.00" "4,338.00" 0.1723 0.2096 -0.0304 11 "1,926.00" "1,099.00" "4,298.00" 0.1713 0.2238 -0.0228 12 "2,237.00" "1,202.00" "4,008.00" 0.0581 0.0408 0.0464 13 "1,953.00" "1,009.00" "4,278.00" 0.1664 0.3449 -0.0210 14 "1,959.00" "1,114.00" "4,273.00" 0.1710 0.2235 -0.0213 15 "1,970.00" "1,123.00" "4,268.00" 0.1675 0.2191 -0.0216 16 "1,981.00" "1,140.00" "4,263.00" 0.1666 0.2061 0.0298 17 "1,892.00" "1,159.00" "4,258.00" 0.0687 0.1657 -0.0221 18 "2,003.00" "1,303.00" "4,253.00" 0.1648 0.0645 -0.0223 19 "2,009.00" "1,186.00" "4,548.00" 0.1643 0.1745 -0.0871 20 "2,025.00" "1,224.00" "4,243.00" 0.1630 0.1430 -0.0229 21 "2,036.00" "1,226.00" "4,238.00" 0.1621 0.1460 -0.0231 22 "2,147.00" "1,219.00" "4,233.00" 0.1537 0.1575 0.0239 23 "2,058.00" "1,018.00" "4,228.00" 0.1603 0.3919 -0.0237 24 "2,074.00" "1,246.00" "4,023.00" 0.1543 0.1421 0.0246 25 "2,080.00" "1,273.00" "4,218.00" 0.1587 0.2011 -0.0242 26 "2,091.00" "1,255.00" "4,213.00" 0.1578 0.1434 -0.0244 27 "2,002.00" "1,261.00" "4,208.00" 0.0649 0.1427 -0.0485 28 "2,113.00" "1,267.00" "4,203.00" 0.1562 0.1421 -0.0250 29 "2,119.00" "1,273.00" "4,198.00" 0.1581 0.1414 -0.0253 30 "2,135.00" "1,279.00" "4,193.00" 0.1569 0.1407 -0.0255 31 "2,146.00" "1,285.00" "4,188.00" 0.1538 0.1401 0.0220 32 "2,007.00" "1,091.00" "4,583.00" 0.2392 0.1925 -0.1111 33 "2,168.00" "1,297.00" "4,178.00" 0.2445 0.1388 -0.0263 34 "2,284.00" "1,513.00" "4,073.00" 0.0985 -0.0198 -0.0027 35 "2,190.00" "1,309.00" "4,236.00" 0.1507 0.1375 -0.0425 36 "2,201.00" "1,315.00" "4,230.00" 0.1499 0.3346 -0.0426 37 "2,012.00" "1,321.00" "4,224.00" 0.2634 0.1363 -0.0426 38 "2,223.00" "1,327.00" "4,018.00" 0.1484 0.1356 -0.0199 39 "2,229.00" "1,333.00" "4,212.00" 0.1054 0.1350 -0.0427 40 "2,245.00" "1,339.00" "4,206.00" Průměry: 0.1572 0.1752 -0.0287 0.0022 41 "2,256.00" "1,345.00" "4,200.00" Rozptyly: 0.001854907 0.007243274 0.00118019 0 42 "2,367.00" "1,251.00" "4,194.00" Sm.Odch.: 0.043068632 0.085107427 0.034353895 0 43 "2,278.00" "1,357.00" "4,188.00" 44 "2,294.00" "1,363.00" "4,182.00" 45 "2,300.00" "1,369.00" "4,176.00" 46 "2,311.00" "1,375.00" "4,390.00" 47 "2,022.00" "1,351.00" "4,164.00" 48 "2,333.00" "1,387.00" "4,158.00" 49 "2,339.00" "1,393.00" "4,152.00" 50 "2,355.00" "1,399.00" "4,146.00" 51 "2,366.00" "1,405.00" "4,140.00" 52 "2,477.00" "1,411.00" "4,334.00" 53 "2,388.00" "1,417.00" "4,128.00" 54 "2,394.00" "1,423.00" "4,122.00" 55 "2,410.00" "1,529.00" "4,116.00" 56 "2,421.00" "1,435.00" "4,110.00" 57 "2,132.00" "1,441.00" "4,004.00" 58 "2,443.00" "1,447.00" "4,098.00" 59 "2,454.00" "1,453.00" "4,092.00" 60 "2,470.00" "1,459.00" "4,086.00" 61 "2,476.00" "1,465.00" "4,280.00" 62 "2,487.00" "1,301.00" "4,074.00" 63 "2,698.00" "1,477.00" "4,068.00" 64 "2,509.00" "1,483.00" "4,062.00" 65 "2,520.00" "1,489.00" "4,056.00" 66 "2,531.00" "1,755.00" "4,050.00" 67 "2,542.00" "1,501.00" "4,044.00" 68 "2,553.00" "1,507.00" "3,938.00" 69 "2,464.00" "1,513.00" "4,032.00" ##### Sheet/List 2 ##### Markowitzův model Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.1572 0.1752 -0.0287 Výnos: 0.1 Zadaný výnos: 0.10 "Kov. matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.026649519 CETV 0.0019 0.0015 -0.0006 CEZ 0.0015 0.0072 -0.0010 KOBA -0.0006 -0.0010 0.0012 Zi: 0.6117 0.0733 0.3149 suma: 1 = 1 krátký prodej: 0 0 0 "(Krátký prodej představuje ""vypůjčení"" akcií (tzv. krátkých pozic) za účelem jejich okamžitého prodeje" a za získané prostředky zakoupení jiných akcií (tzv. dlouhých pozic)) Zi*Kov.mat.: 0.0011 0.0012 -0.0001 ##### Sheet/List 3 ##### Sharpeův model Model používá 30-tidenní výnosy "Průměry, tj Ri:" 0.1572 0.1752 -0.0287 Výnos: 0.164160256 "Kovar. matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.049999037 CETV 0.0019 0.0015 -0.0006 CEZ 0.0015 0.0072 -0.0010 Zadané riziko: 0.05 KOBA -0.0006 -0.0010 0.0012 Zi: 0.6144 0.3856 0.0000 suma: 1 = 1 krátký prodej: 0 0 0 Zi*Kov.mat.: 0.0017 0.0037 -0.0007 ##### Sheet/List 4 ##### Markowitzův CAPM model Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.1572 0.1752 -0.0287 0.0022 Výnos: 0.099999997 Zadaný výnos: 0.10 "Kovar. matice, tj. Sij:" CETV CEZ KOBA ING konto Riziko: 0.026266413 CETV 0.0019 0.0015 -0.0006 0.0000 CEZ 0.0015 0.0072 -0.0010 0.0000 KOBA -0.0006 -0.0010 0.0012 0.0000 ING konto 0.0000 0.0000 0.0000 0.0000 Zi: 0.591 0.067 0.172 0.171 suma: 1.000 = 1 krátký prodej: 0 0 0 0 Zi*Kov.mat.: 0.0011 0.0012 -0.0002 0.0000 ##### Sheet/List 5 ##### Sharpeův CAPM model Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.1572 0.1752 -0.0287 0.0022 Výnos: 0.16416105 "Kovar. matice, tj. Sij:" CETV CEZ KOBA ING konto Riziko: 0.050000808 Zadané riziko: 0.05 CETV 0.0019 0.0015 -0.0006 0.0000 CEZ 0.0015 0.0072 -0.0010 0.0000 KOBA -0.0006 -0.0010 0.0012 0.0000 ING konto 0.0000 0.0000 0.0000 0.0000 Zi: 0.614 0.386 0.000 0.000 suma: 1.000 = 1 krátký prodej: 0 0 0 0 Zi*Kov.mat.: 0.0017 0.0037 -0.0007 0.0000 ##### Sheet/List 6 ##### Ceny akcií (denní): Výnosy akcií (30-denní): datum CETV CEZ KOBA PX CETV CEZ KOBA PX ING konto 1 "1,916.00" "1,089.00" "4,206.00" "1,798.60" 0.1200 0.1800 -0.0043 0.0488 0.0022 2 "1,827.00" "1,072.00" "4,498.00" "1,812.10" 0.0985 0.0177 0.0189 0.0442 0.0022 3 "1,843.00" "1,074.00" "4,478.00" "1,806.30" 0.1763 0.2076 -0.0670 0.0441 0.0022 4 "1,849.00" "1,082.00" "4,458.00" "1,776.20" 0.2353 0.3983 -0.0864 0.0562 0.0022 5 "1,860.00" "1,086.00" "4,438.00" "1,762.40" 0.1774 0.2053 -0.0455 0.0488 0.0022 6 "1,871.00" "1,092.00" "4,418.00" "1,757.50" 0.1764 0.2042 -0.0426 0.0626 0.0022 7 "1,777.00" "1,200.00" "4,698.00" "1,765.00" 0.1322 0.1008 -0.1009 0.0610 0.0022 8 "1,893.00" "1,093.00" "4,378.00" "1,755.70" 0.1743 0.2141 -0.0822 0.0734 0.0022 9 "1,904.00" "1,102.00" "4,358.00" "1,770.20" 0.1707 0.2096 -0.0335 0.0790 0.0022 10 "1,915.00" "1,107.00" "4,338.00" "1,761.90" 0.1723 0.2096 -0.0304 0.0989 0.0022 11 "1,926.00" "1,099.00" "4,298.00" "1,747.80" 0.1713 0.2238 -0.0228 0.0947 0.0022 12 "2,237.00" "1,202.00" "4,008.00" "1,750.80" 0.0581 0.0408 0.0464 0.0900 0.0022 13 "1,953.00" "1,009.00" "4,278.00" "1,780.70" 0.1664 0.3449 -0.0210 0.0813 0.0022 14 "1,959.00" "1,114.00" "4,273.00" "1,790.90" 0.1710 0.2235 -0.0213 0.0656 0.0022 15 "1,970.00" "1,123.00" "4,268.00" "1,793.80" 0.1675 0.2191 -0.0216 0.0528 0.0022 16 "1,981.00" "1,140.00" "4,263.00" "1,792.10" 0.1666 0.2061 0.0298 0.0621 0.0022 17 "1,892.00" "1,159.00" "4,258.00" "1,802.90" 0.0687 0.1657 -0.0221 0.0380 0.0022 18 "2,003.00" "1,303.00" "4,253.00" "1,825.30" 0.1648 0.0645 -0.0223 0.0195 0.0022 19 "2,009.00" "1,186.00" "4,548.00" "1,816.30" 0.1643 0.1745 -0.0871 0.0087 0.0022 20 "2,025.00" "1,224.00" "4,243.00" "1,828.80" 0.1630 0.1430 -0.0229 -0.0045 0.0022 21 "2,036.00" "1,226.00" "4,238.00" "1,845.50" 0.1621 0.1460 -0.0231 -0.0186 0.0022 22 "2,147.00" "1,219.00" "4,233.00" "1,835.10" 0.1537 0.1575 0.0239 -0.0037 0.0022 23 "2,058.00" "1,018.00" "4,228.00" "1,862.70" 0.1603 0.3919 -0.0237 -0.0351 0.0022 24 "2,074.00" "1,246.00" "4,023.00" "1,881.50" 0.1543 0.1421 0.0246 -0.0466 0.0022 25 "2,080.00" "1,273.00" "4,218.00" "1,896.10" 0.1587 0.2011 -0.0242 -0.0662 0.0022 26 "2,091.00" "1,255.00" "4,213.00" "1,883.40" 0.1578 0.1434 -0.0244 -0.0618 0.0022 27 "2,002.00" "1,261.00" "4,208.00" "1,881.00" 0.0649 0.1427 -0.0485 -0.0812 0.0022 28 "2,113.00" "1,267.00" "4,203.00" "1,900.70" 0.1562 0.1421 -0.0250 -0.0835 0.0022 29 "2,119.00" "1,273.00" "4,198.00" "1,898.80" 0.1581 0.1414 -0.0253 -0.0689 0.0022 30 "2,135.00" "1,279.00" "4,193.00" "1,908.30" 0.1569 0.1407 -0.0255 -0.0719 0.0022 31 "2,146.00" "1,285.00" "4,188.00" "1,886.30" 0.1538 0.1401 0.0220 -0.0788 0.0022 32 "2,007.00" "1,091.00" "4,583.00" "1,892.20" 0.2392 0.1925 -0.1111 -0.0762 0.0022 33 "2,168.00" "1,297.00" "4,178.00" "1,886.00" 0.2445 0.1388 -0.0263 -0.0681 0.0022 34 "2,284.00" "1,513.00" "4,073.00" "1,876.10" 0.0985 -0.0198 -0.0027 -0.0544 0.0022 35 "2,190.00" "1,309.00" "4,236.00" "1,848.40" 0.1507 0.1375 -0.0425 -0.0441 0.0022 36 "2,201.00" "1,315.00" "4,230.00" "1,867.60" 0.1499 0.3346 -0.0426 -0.0594 0.0022 37 "2,012.00" "1,321.00" "4,224.00" "1,872.60" 0.2634 0.1363 -0.0426 -0.0501 0.0022 38 "2,223.00" "1,327.00" "4,018.00" "1,884.60" 0.1484 0.1356 -0.0199 -0.0381 0.0022 39 "2,229.00" "1,333.00" "4,212.00" "1,910.10" 0.1054 0.1350 -0.0427 -0.0353 0.0022 40 "2,245.00" "1,339.00" "4,206.00" "1,936.10" E(Xi) 0.1572 0.1752 -0.0287 0.0021 0.0022 41 "2,256.00" "1,345.00" "4,200.00" "1,913.40" "Cov(Xi,PX)" -0.0002 0.0011 0.0000 0.0037 0.0000 42 "2,367.00" "1,251.00" "4,194.00" "1,908.30" Var(Xi) 0.0019 0.0072 0.0012 0.0037 0.0000 43 "2,278.00" "1,357.00" "4,188.00" "1,925.50" BETAi -0.0894 0.1520 0.0079 1.0000 0.0000 44 "2,294.00" "1,363.00" "4,182.00" "1,908.30" ALFAi 0.1574 0.1749 -0.0287 0.0000 0.0022 45 "2,300.00" "1,369.00" "4,176.00" "1,888.60" Var(ei) 0.0018 0.0072 0.0012 0.0000 0.0000 46 "2,311.00" "1,375.00" "4,390.00" "1,903.30" 47 "2,022.00" "1,351.00" "4,164.00" "1,871.40" 48 "2,333.00" "1,387.00" "4,158.00" "1,860.90" 49 "2,339.00" "1,393.00" "4,152.00" "1,832.10" 50 "2,355.00" "1,399.00" "4,146.00" "1,820.50" 51 "2,366.00" "1,405.00" "4,140.00" "1,811.10" 52 "2,477.00" "1,411.00" "4,334.00" "1,828.30" 53 "2,388.00" "1,417.00" "4,128.00" "1,797.40" 54 "2,394.00" "1,423.00" "4,122.00" "1,793.80" 55 "2,410.00" "1,529.00" "4,116.00" "1,770.60" 56 "2,421.00" "1,435.00" "4,110.00" "1,767.10" 57 "2,132.00" "1,441.00" "4,004.00" "1,728.20" 58 "2,443.00" "1,447.00" "4,098.00" "1,742.00" 59 "2,454.00" "1,453.00" "4,092.00" "1,767.90" 60 "2,470.00" "1,459.00" "4,086.00" "1,771.10" 61 "2,476.00" "1,465.00" "4,280.00" "1,737.70" 62 "2,487.00" "1,301.00" "4,074.00" "1,748.10" 63 "2,698.00" "1,477.00" "4,068.00" "1,757.60" 64 "2,509.00" "1,483.00" "4,062.00" "1,774.10" 65 "2,520.00" "1,489.00" "4,056.00" "1,766.90" 66 "2,531.00" "1,755.00" "4,050.00" "1,756.60" 67 "2,542.00" "1,501.00" "4,044.00" "1,778.80" 68 "2,553.00" "1,507.00" "3,938.00" "1,812.80" 69 "2,464.00" "1,513.00" "4,032.00" "1,842.70" ##### Sheet/List 7 ##### 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:" 0.1572 0.1752 -0.0287 0.0022 Výnos: 0.1 Kovariance s PX: CETV CEZ KOBA ING konto PX Riziko: 0.023924827 PX -0.0002 0.0011 0.0000 0.0037 0.000 Koeficient BETAi: BETA -0.0894 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: 0.1909 0.3943 0.0000 0.4148 suma: 1.0000 = 1 krátký prodej: 0 0 0 0 Zi^2.: 0.0364 0.1555 0.0000 0.1720 (suma BETAi*Zi)^2 = 0.0906 ##### Sheet/List 8 ##### 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:" 0.1572 0.1752 -0.0287 0.0022 Výnos: 0.168571041 CETV CEZ KOBA ING konto PX Riziko: 0.050000477 Kovariance s PX: PX -0.0002 0.0011 0.0000 0.0037 0.003665837 Koeficient BETAi: BETA -0.0894 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: 0.3689 0.6311 0.0000 0.0000 suma: 1.0000 = 1 krátký prodej: 0 0 0 0 Zi^2.: 0.1361 0.3983 0.0000 0.0000 (suma BETAi*Zi)^2 = 0.2266 ##### Sheet/List 9 ##### Den PX BCPP close 7/17/2013 "1,798.60" 7/18/2013 "1,812.10" 7/19/2013 "1,806.30" 7/22/2013 "1,776.20" 7/23/2013 "1,762.40" 7/24/2013 "1,757.50" 7/25/2013 "1,765.00" 7/26/2013 "1,755.70" 7/29/2013 "1,770.20" 7/30/2013 "1,761.90" 7/31/2013 "1,747.80" 8/1/2013 "1,750.80" 8/2/2013 "1,780.70" 8/5/2013 "1,790.90" 8/6/2013 "1,793.80" 8/7/2013 "1,792.10" 8/8/2013 "1,802.90" 8/9/2013 "1,825.30" 8/12/2013 "1,816.30" 8/13/2013 "1,828.80" 8/14/2013 "1,845.50" 8/15/2013 "1,835.10" 8/16/2013 "1,862.70" 8/19/2013 "1,881.50" 8/20/2013 "1,896.10" 8/21/2013 "1,883.40" 8/22/2013 "1,881.00" 8/23/2013 "1,900.70" 8/26/2013 "1,898.80" 8/27/2013 "1,908.30" 8/28/2013 "1,886.30" 8/29/2013 "1,892.20" 8/30/2013 "1,886.00" 9/2/2013 "1,876.10" 9/3/2013 "1,848.40" 9/4/2013 "1,867.60" 9/5/2013 "1,872.60" 9/6/2013 "1,884.60" 9/9/2013 "1,910.10" 9/10/2013 "1,936.10" 9/11/2013 "1,913.40" 9/12/2013 "1,908.30" 9/13/2013 "1,925.50" 9/16/2013 "1,908.30" 9/17/2013 "1,888.60" 9/18/2013 "1,903.30" 9/19/2013 "1,871.40" 9/20/2013 "1,860.90" 9/23/2013 "1,832.10" 9/24/2013 "1,820.50" 9/25/2013 "1,811.10" 9/26/2013 "1,828.30" 9/27/2013 "1,797.40" 9/30/2013 "1,793.80" 10/1/2013 "1,770.60" 10/2/2013 "1,767.10" 10/3/2013 "1,728.20" 10/4/2013 "1,742.00" 10/7/2013 "1,767.90" 10/8/2013 "1,771.10" 10/9/2013 "1,737.70" 10/10/2013 "1,748.10" 10/11/2013 "1,757.60" 10/14/2013 "1,774.10" 10/15/2013 "1,766.90" 10/16/2013 "1,756.60" 10/17/2013 "1,778.80" 10/18/2013 "1,812.80" 10/21/2013 "1,842.70" ##### Sheet/List 10 ##### Kataokův / VaR model Model používá 30-tidenní výnosy Alfa 1-Alfa K_Alfa 0.05 0.95 -1.644853627 "Průměrné výnosy, tj Ri:" 0.1572 0.1752 -0.0287 Výnos: 0.159616332 Výnos R_Alfa: 0.0884 "Kov. matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.043288433 CETV 0.0019 0.0015 -0.0006 CEZ 0.0015 0.0072 -0.0010 KOBA -0.0006 -0.0010 0.0012 Zi: 0.8673 0.1327 0.0000 suma: 1 = 1 krátký prodej: 0 0 0 Zi*Kov.mat.: 0.0018 0.0023 -0.0007 ##### Sheet/List 11 ##### Min-Risk model Model používá 30-tidenní výnosy "Průměrné výnosy, tj Ri:" 0.1572 0.1752 -0.0287 Výnos: 0.160776997 Zadaný výnos: 0.12 "Kov. matice, tj. Sij:" CETV CEZ KOBA Riziko: 0.044274763 Učel.fce: 0.9210 CETV 0.0019 0.0015 -0.0006 CEZ 0.0015 0.0072 -0.0010 Pravd.Zad.Výnosu: #NÁZEV? KOBA -0.0006 -0.0010 0.0012 Zi: 0.8027 0.1973 0.0000 suma: 0.999997 = 1 krátký prodej: 0 0 0 Zi*Kov.mat.: 0.0018 0.0027 -0.0007