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1- Calculer la rentabilité et la volatilité annuelles pour chaque action BRVM C

1- Calculer la rentabilité et la volatilité annuelles pour chaque action BRVM Composite SERVAIR ABIDJAN BERNABE BICICI BOA BENIN BOA CÔTE D'IVOIRE BOA BF BOA NIGER BOA SENEGAL CFAO CI RA -13.82% -71.58% -36.78% -1.59% 22.55% 2.92% 49.96% -1.17% 9.01% -46.93% ECT 12.99% 52.76% 32.60% 26.02% 34.85% 36.96% 35.87% 41.32% 40.91% 37.90% CIE CI ECOB ANK (ETI) FILTIS AC NEI- CEDA NEST LE CI PALM CI TRACTAFRIC MOTORS CI SAFCA BOLLORE AFRICA LOGISTICS CI SAPH RA -18.10% - 59.71% -42.60% -95.01% 18.93% 38.13% -107.00% -4.17% -33.72% 14.27% ECT 40.31% 52.26% 52.21% 32.90% 42.87% 52.20% 37.25% 39.79% 40.41% 43.88% SETAO SGBCI VIVO ENERGY CI SICABLE SICOR CROWN SIEM SITAB AIR LIQUIDE CI MOVIS SMB RA -72.71% 8.09% 6.75% -44.03% -7.65% -45.92% -52.00% -122.96% -31.20% -54.21% ECT 29.41% 38.57% 66.25% 33.65% 46.93% 44.95% 33.03% 42.94% 31.15% 45.06% SODE CI SOG B SOLIBR A SONATE L TOTAL SN TOTAL CI TRITURA F UNIWA X UNILEVE R ONATE L RA -28.28% 38.94 % -20.80% -0.22% -2.13% -0.42% 0.00% -0.06% -2.51% -1.04% ECT 43.50% 42.17 % 40.85% 21.45% 36.84% 48.57% 0.00% 45.08% 33.32% 41.79% X 2- Effectuer un premier tri en sélectionnant uniquement les actions dont la rentabilité est supérieure ou égale à 8% et dont la volatilité n’excède pas 45% BOA BENIN BOA BF BOA SENEGAL NESTLE CI SAPH SGBCI SOGB RA 22,55% 49,96% 9,01% 18,93% 14,27% 8,09% 38,94% ECT 34,85% 35,87% 40,91% 42,87% 43,88% 38,57% 42,17% 3- Classez les titres selon le coefficient de variation. BOA BENIN BOA BF BOA SENEGAL NESTLE CI SAPH SGBCI SOGB CV 1,545565 0,71802573 4,54004918 2,2642873 3,07523871 4,76985693 1,08310917 Rang 3 1 6 4 5 7 2 4- En prenant les deux meilleurs, déterminez les pondérations du portefeuille de risque minimal. BOA BF SOGB VAR 0,000510658 0,00070571 COV 1,89537E-05 Pond PF 58,28% 41,72% 5- En considérant un pas de progression de 20%, Tracez la frontière efficiente. Commentez. Pond BOA BF 0% 20% 40% 58,28% 60% 80% 100% Pond SOGB 100% 80% 60% 41,72% 40% 20% 0% ECT port 42,17% 34,71% 29,48% 27,75% 27,76% 30,17% 35,87% Rent port 38,94% 41,14% 43,35% 45,36% 45,55% 47,76% 49,96% 26.00% 28.00% 30.00% 32.00% 34.00% 36.00% 38.00% 40.00% 42.00% 44.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 38.94% 41.14% 43.35% 45.36% 45.55% 47.76% 49.96% Frontière éfficiente 6- Soit A, le meilleur portefeuille selon le coefficient de variation, précisez ses caractéristiques. Portefeuille A RA 45.55% ECT 27.76% 7- Déterminez les pondérations du portefeuille B qui permettent de minimiser le risque et précisez ce risque.  Avant optimisation BOA BENIN BOA BF BOA SENEGAL NESTLE CI SAPH SGBCI SOGB RA 22.55% 49.96% 9.01% 18.93% 14.27% 8.09% 38.94% Pond 14.29% 14.29% 14.29% 14.29% 14.29% 14.29 % 14.29% Portefeuille B Rent pf 23% ECT pf 16.47%  Apres optimisation BOA BENIN BOA BF BOA SENEGAL NESTLE CI SAPH SGBCI SOGB RA 22.55% 49.96% 9.01% 18.93% 14.27% 8.09% 38.94% Pond 17.55% 8.30% 17.13% 7.97% 16.27% 20.23% 12.56% Portefeuille B Rent pf 20.00% ECT pf 16.53% 8- Calculez la rentabilité et le risque de C. Portefeuille C Portefeuille B ASR Rent 20.00% 6% ECT 16.53% 0% Pond 70% 30% Renta pf C 15.80% ECT pf C 11.57% 9- Déterminez les primes calls et put selon le modèle de COX-ROSS-RUBINSTEIN sur 5 sous périodes. k 16750 S0 16750 U 1.1488345389 t 0.5 d 0.8704473674 v 43.88% p 0.4869860486 r 6% 1-p 0.5130139514 n 5 t/n 0.1 0 1 2 3 4 5 33519.86267 29177.27622 25397.2832 7 25397.28327 22106.9984 22106.99836 19242.97853 19242.9785 3 19242.97853 16750 16750 16750 14579.9934 14579.9934 14579.9934 12691.1169 12691.11688 11046.9492 7 11046.94927 9615.787914 8370.037275 16769.86267 12527.47532 8847.08208 8647.283271 5943.56164 5457.197465 3833.037926 3257.07451 2492.978527 Prime call 2391.7407 1874.5566 1206.783297 1051.624984 584.17107 0 282.781371 0 0.00000 0 0 0 Prime put 1896.703387 10- Tracez les graphiques d’évolution des P&L, acheteur et vendeur du call, acheteur et vendeur du put et acheteur et vendeur du straddle. S 8000 9000 1000 0 1100 0 1200 0 1300 0 1400 0 1500 0 1600 0 1700 0 1800 0 1900 0 2000 0 2100 0 2200 0 2300 0 2400 0 2500 0 2600 0 2700 0 28000 29000 P&L Vte Call 6853 .297 5853 .297 4853 .297 3853 .297 2853 .297 1853 .297 853. 2966 - 146. 7034 - 1146 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896 .703 - 1896. 70339 - 1896. 70339 P&L VTE Put - 6853 .297 - 5853 .297 - 4853 .297 - 3853 .297 - 2853 .297 - 1853 .297 - 853. 2966 146. 7034 1146 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896 .703 1896. 70338 7 1896. 70338 7 S 8000 9000 1000 0 1100 0 1200 0 1300 0 1400 0 1500 0 1600 0 1700 0 1800 0 1900 0 2000 0 2100 0 2200 0 2300 0 2400 0 2500 0 2600 0 2700 0 2800 0 2900 0 P&L Ach Call - 2391 .741 - 2391 .741 - 2391 .741 - 2391 .741 - 2391 .741 - 2391 .741 - 2391 .741 - 2391 .741 - 2391 .741 - 2141 .741 - 1141 .741 - 141. 7407 858. 2593 1858 .259 2858 .259 3858 .259 4858 .259 5858 .259 6858 .259 7858 .259 8858 .259 9858 .259 P&L Ach put 2391 .741 2391 .741 2391 .741 2391 .741 2391 .741 2391 .741 2391 .741 2391 .741 2391 .741 2141 .741 1141 .741 141. 7407 - 858. 2593 - 1858 .259 - 2858 .259 - 3858 .259 - 4858 .259 - 5858 .259 - 6858 .259 - 7858 .259 - 8858 .259 - 9858 .259 0 5 10 15 20 25 -15000 -10000 -5000 0 5000 10000 15000 P&L Ach Call P&L Ach put 0 5 10 15 20 25 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 Chart Title P&L Vte Call P&L VTE Put S 8000 9000 1000 0 1100 0 1200 0 1300 0 1400 0 1500 0 1600 0 1700 0 1800 0 1900 0 2000 0 2100 0 2200 0 2300 0 2400 0 2500 0 2600 0 2700 0 2800 0 2900 0 P&L Ach Stra 4461 .556 3461 .556 2461 .556 1461 .556 461. 5559 - 538. 444 - 1538 .44 - 2538 .44 - 3538 .44 - 4038 .44 - 3038 .44 - 2038 .44 - 1038 .44 - 38.4 441 961. 5559 1961 .556 2961 .556 3961 .556 4961 .556 5961 .556 6961 .556 7961 .556 P&L Vte Stra - 4461 .56 - 3461 .56 - 2461 .56 - 1461 .56 - 461. 556 538. 4441 1538 .444 2538 .444 3538 .444 4038 .444 3038 .444 2038 .444 1038 .444 38.4 4409 - 961. 556 - 1961 .56 - 2961 .56 - 3961 .56 - 4961 .56 - 5961 .56 - 6961 .56 - 7961 .56 0 5 10 15 20 25 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 Chart Title P&L Ach Stra P&L Vte Stra uploads/Finance/ examen-final-eaf.pdf