Modèle d’évaluation des immobilisations (CAPM)
Le modèle d’évaluation des immobilisations (MEDAF) indique quel devrait être le taux de rendement attendu ou requis pour les actifs risqués tels que les actions ordinaires de Monsanto.
Taux de rendement
Monsanto Co., taux de rendement mensuels
| Monsanto Co. (MON) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMON,t1 | DividendeMON,t1 | RMON,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 30 sept. 2011 | $60.04 | 1,131.42 | ||||
| 1. | 31 oct. 2011 | $72.75 | $0.30 | 21.67% | 1,253.30 | 10.77% |
| 2. | 30 nov. 2011 | $73.45 | 0.96% | 1,246.96 | -0.51% | |
| 3. | 31 déc. 2011 | $70.07 | -4.60% | 1,257.60 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 juil. 2017 | $116.82 | $0.54 | -0.84% | 2,470.30 | 1.93% |
| 71. | 31 août 2017 | $117.20 | 0.33% | 2,471.65 | 0.05% | |
| Moyenne (R): | 1.27% | 1.15% | ||||
| Écart type: | 6.07% | 3.01% | ||||
| Monsanto Co. (MON) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMON,t1 | DividendeMON,t1 | RMON,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 30 sept. 2011 | $60.04 | 1,131.42 | ||||
| 1. | 31 oct. 2011 | $72.75 | $0.30 | 21.67% | 1,253.30 | 10.77% |
| 2. | 30 nov. 2011 | $73.45 | 0.96% | 1,246.96 | -0.51% | |
| 3. | 31 déc. 2011 | $70.07 | -4.60% | 1,257.60 | 0.85% | |
| 4. | 31 janv. 2012 | $82.05 | $0.30 | 17.53% | 1,312.41 | 4.36% |
| 5. | 29 févr. 2012 | $77.38 | -5.69% | 1,365.68 | 4.06% | |
| 6. | 31 mars 2012 | $79.76 | 3.08% | 1,408.47 | 3.13% | |
| 7. | 30 avr. 2012 | $76.18 | $0.30 | -4.11% | 1,397.91 | -0.75% |
| 8. | 31 mai 2012 | $77.20 | 1.34% | 1,310.33 | -6.27% | |
| 9. | 30 juin 2012 | $82.78 | 7.23% | 1,362.16 | 3.96% | |
| 10. | 31 juil. 2012 | $85.62 | $0.30 | 3.79% | 1,379.32 | 1.26% |
| 11. | 31 août 2012 | $87.11 | 1.74% | 1,406.58 | 1.98% | |
| 12. | 30 sept. 2012 | $91.02 | 4.49% | 1,440.67 | 2.42% | |
| 13. | 31 oct. 2012 | $86.07 | $0.375 | -5.03% | 1,412.16 | -1.98% |
| 14. | 30 nov. 2012 | $91.59 | 6.41% | 1,416.18 | 0.28% | |
| 15. | 31 déc. 2012 | $94.65 | 3.34% | 1,426.19 | 0.71% | |
| 16. | 31 janv. 2013 | $101.35 | $0.375 | 7.47% | 1,498.11 | 5.04% |
| 17. | 28 févr. 2013 | $101.03 | -0.32% | 1,514.68 | 1.11% | |
| 18. | 31 mars 2013 | $105.63 | 4.55% | 1,569.19 | 3.60% | |
| 19. | 30 avr. 2013 | $106.82 | $0.375 | 1.48% | 1,597.57 | 1.81% |
| 20. | 31 mai 2013 | $100.64 | -5.79% | 1,630.74 | 2.08% | |
| 21. | 30 juin 2013 | $98.80 | -1.83% | 1,606.28 | -1.50% | |
| 22. | 31 juil. 2013 | $98.78 | $0.375 | 0.36% | 1,685.73 | 4.95% |
| 23. | 31 août 2013 | $97.89 | -0.90% | 1,632.97 | -3.13% | |
| 24. | 30 sept. 2013 | $104.37 | 6.62% | 1,681.55 | 2.97% | |
| 25. | 31 oct. 2013 | $104.88 | $0.43 | 0.90% | 1,756.54 | 4.46% |
| 26. | 30 nov. 2013 | $113.33 | 8.06% | 1,805.81 | 2.80% | |
| 27. | 31 déc. 2013 | $116.55 | 2.84% | 1,848.36 | 2.36% | |
| 28. | 31 janv. 2014 | $106.55 | $0.43 | -8.21% | 1,782.59 | -3.56% |
| 29. | 28 févr. 2014 | $110.02 | 3.26% | 1,859.45 | 4.31% | |
| 30. | 31 mars 2014 | $113.77 | 3.41% | 1,872.34 | 0.69% | |
| 31. | 30 avr. 2014 | $110.70 | $0.43 | -2.32% | 1,883.95 | 0.62% |
| 32. | 31 mai 2014 | $121.85 | 10.07% | 1,923.57 | 2.10% | |
| 33. | 30 juin 2014 | $124.74 | 2.37% | 1,960.23 | 1.91% | |
| 34. | 31 juil. 2014 | $113.09 | $0.43 | -8.99% | 1,930.67 | -1.51% |
| 35. | 31 août 2014 | $115.65 | 2.26% | 2,003.37 | 3.77% | |
| 36. | 30 sept. 2014 | $112.51 | -2.72% | 1,972.29 | -1.55% | |
| 37. | 31 oct. 2014 | $115.04 | $0.49 | 2.68% | 2,018.05 | 2.32% |
| 38. | 30 nov. 2014 | $119.91 | 4.23% | 2,067.56 | 2.45% | |
| 39. | 31 déc. 2014 | $119.47 | -0.37% | 2,058.90 | -0.42% | |
| 40. | 31 janv. 2015 | $117.98 | $0.49 | -0.84% | 1,994.99 | -3.10% |
| 41. | 28 févr. 2015 | $120.43 | 2.08% | 2,104.50 | 5.49% | |
| 42. | 31 mars 2015 | $112.54 | $0.49 | -6.14% | 2,067.89 | -1.74% |
| 43. | 30 avr. 2015 | $113.96 | 1.26% | 2,085.51 | 0.85% | |
| 44. | 31 mai 2015 | $116.98 | 2.65% | 2,107.39 | 1.05% | |
| 45. | 30 juin 2015 | $106.59 | $0.49 | -8.46% | 2,063.11 | -2.10% |
| 46. | 31 juil. 2015 | $101.89 | -4.41% | 2,103.84 | 1.97% | |
| 47. | 31 août 2015 | $97.65 | -4.16% | 1,972.18 | -6.26% | |
| 48. | 30 sept. 2015 | $85.34 | -12.61% | 1,920.03 | -2.64% | |
| 49. | 31 oct. 2015 | $93.22 | $0.54 | 9.87% | 2,079.36 | 8.30% |
| 50. | 30 nov. 2015 | $95.16 | 2.08% | 2,080.41 | 0.05% | |
| 51. | 31 déc. 2015 | $98.52 | 3.53% | 2,043.94 | -1.75% | |
| 52. | 31 janv. 2016 | $90.60 | $0.54 | -7.49% | 1,940.24 | -5.07% |
| 53. | 29 févr. 2016 | $89.99 | -0.67% | 1,932.23 | -0.41% | |
| 54. | 31 mars 2016 | $87.74 | -2.50% | 2,059.74 | 6.60% | |
| 55. | 30 avr. 2016 | $93.68 | $0.54 | 7.39% | 2,065.30 | 0.27% |
| 56. | 31 mai 2016 | $112.47 | 20.06% | 2,096.95 | 1.53% | |
| 57. | 30 juin 2016 | $103.41 | -8.06% | 2,098.86 | 0.09% | |
| 58. | 31 juil. 2016 | $106.77 | $0.54 | 3.77% | 2,173.60 | 3.56% |
| 59. | 31 août 2016 | $106.50 | -0.25% | 2,170.95 | -0.12% | |
| 60. | 30 sept. 2016 | $102.20 | -4.04% | 2,168.27 | -0.12% | |
| 61. | 31 oct. 2016 | $100.77 | $0.54 | -0.87% | 2,126.15 | -1.94% |
| 62. | 30 nov. 2016 | $102.71 | 1.93% | 2,198.81 | 3.42% | |
| 63. | 31 déc. 2016 | $105.21 | 2.43% | 2,238.83 | 1.82% | |
| 64. | 31 janv. 2017 | $108.31 | $0.54 | 3.46% | 2,278.87 | 1.79% |
| 65. | 28 févr. 2017 | $113.83 | 5.10% | 2,363.64 | 3.72% | |
| 66. | 31 mars 2017 | $113.20 | -0.55% | 2,362.72 | -0.04% | |
| 67. | 30 avr. 2017 | $116.61 | $0.54 | 3.49% | 2,384.20 | 0.91% |
| 68. | 31 mai 2017 | $117.42 | 0.69% | 2,411.80 | 1.16% | |
| 69. | 30 juin 2017 | $118.36 | 0.80% | 2,423.41 | 0.48% | |
| 70. | 31 juil. 2017 | $116.82 | $0.54 | -0.84% | 2,470.30 | 1.93% |
| 71. | 31 août 2017 | $117.20 | 0.33% | 2,471.65 | 0.05% | |
| Moyenne (R): | 1.27% | 1.15% | ||||
| Écart type: | 6.07% | 3.01% | ||||
Tout afficher
1 Données en dollars américains par action ordinaire, ajustées pour tenir compte des fractionnements et des dividendes en actions.
2 Taux de rendement des actions ordinaires de MON au cours de la période t.
3 Taux de rendement de l’indice S&P 500 (l’indicateur du portefeuille de marché) au cours de la période t.
Variance et covariance
Monsanto Co., calcul de la variance et de la covariance des rendements
| t | Date | RMON,t | RS&P 500,t | (RMON,t–RMON)2 | (RS&P 500,t–RS&P 500)2 | (RMON,t–RMON)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 oct. 2011 | 21.67% | 10.77% | 416.05 | 92.57 | 196.25 |
| 2. | 30 nov. 2011 | 0.96% | -0.51% | 0.10 | 2.74 | 0.51 |
| 3. | 31 déc. 2011 | -4.60% | 0.85% | 34.50 | 0.09 | 1.75 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 juil. 2017 | -0.84% | 1.93% | 4.48 | 0.61 | -1.66 |
| 71. | 31 août 2017 | 0.33% | 0.05% | 0.90 | 1.20 | 1.04 |
| Total (Σ): | 2,577.67 | 633.66 | 743.38 | |||
| t | Date | RMON,t | RS&P 500,t | (RMON,t–RMON)2 | (RS&P 500,t–RS&P 500)2 | (RMON,t–RMON)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 oct. 2011 | 21.67% | 10.77% | 416.05 | 92.57 | 196.25 |
| 2. | 30 nov. 2011 | 0.96% | -0.51% | 0.10 | 2.74 | 0.51 |
| 3. | 31 déc. 2011 | -4.60% | 0.85% | 34.50 | 0.09 | 1.75 |
| 4. | 31 janv. 2012 | 17.53% | 4.36% | 264.18 | 10.29 | 52.13 |
| 5. | 29 févr. 2012 | -5.69% | 4.06% | 48.49 | 8.46 | -20.25 |
| 6. | 31 mars 2012 | 3.08% | 3.13% | 3.25 | 3.93 | 3.58 |
| 7. | 30 avr. 2012 | -4.11% | -0.75% | 28.99 | 3.61 | 10.23 |
| 8. | 31 mai 2012 | 1.34% | -6.27% | 0.00 | 54.99 | -0.50 |
| 9. | 30 juin 2012 | 7.23% | 3.96% | 35.48 | 7.87 | 16.71 |
| 10. | 31 juil. 2012 | 3.79% | 1.26% | 6.36 | 0.01 | 0.27 |
| 11. | 31 août 2012 | 1.74% | 1.98% | 0.22 | 0.68 | 0.39 |
| 12. | 30 sept. 2012 | 4.49% | 2.42% | 10.35 | 1.62 | 4.09 |
| 13. | 31 oct. 2012 | -5.03% | -1.98% | 39.67 | 9.79 | 19.71 |
| 14. | 30 nov. 2012 | 6.41% | 0.28% | 26.44 | 0.75 | -4.45 |
| 15. | 31 déc. 2012 | 3.34% | 0.71% | 4.28 | 0.20 | -0.92 |
| 16. | 31 janv. 2013 | 7.47% | 5.04% | 38.48 | 15.15 | 24.14 |
| 17. | 28 févr. 2013 | -0.32% | 1.11% | 2.52 | 0.00 | 0.07 |
| 18. | 31 mars 2013 | 4.55% | 3.60% | 10.77 | 5.99 | 8.03 |
| 19. | 30 avr. 2013 | 1.48% | 1.81% | 0.04 | 0.43 | 0.14 |
| 20. | 31 mai 2013 | -5.79% | 2.08% | 49.80 | 0.86 | -6.53 |
| 21. | 30 juin 2013 | -1.83% | -1.50% | 9.61 | 7.03 | 8.22 |
| 22. | 31 juil. 2013 | 0.36% | 4.95% | 0.83 | 14.41 | -3.46 |
| 23. | 31 août 2013 | -0.90% | -3.13% | 4.72 | 18.32 | 9.30 |
| 24. | 30 sept. 2013 | 6.62% | 2.97% | 28.60 | 3.33 | 9.76 |
| 25. | 31 oct. 2013 | 0.90% | 4.46% | 0.14 | 10.95 | -1.23 |
| 26. | 30 nov. 2013 | 8.06% | 2.80% | 46.04 | 2.74 | 11.22 |
| 27. | 31 déc. 2013 | 2.84% | 2.36% | 2.46 | 1.45 | 1.89 |
| 28. | 31 janv. 2014 | -8.21% | -3.56% | 89.92 | 22.17 | 44.65 |
| 29. | 28 févr. 2014 | 3.26% | 4.31% | 3.94 | 9.99 | 6.27 |
| 30. | 31 mars 2014 | 3.41% | 0.69% | 4.57 | 0.21 | -0.98 |
| 31. | 30 avr. 2014 | -2.32% | 0.62% | 12.90 | 0.28 | 1.91 |
| 32. | 31 mai 2014 | 10.07% | 2.10% | 77.45 | 0.91 | 8.38 |
| 33. | 30 juin 2014 | 2.37% | 1.91% | 1.21 | 0.57 | 0.83 |
| 34. | 31 juil. 2014 | -8.99% | -1.51% | 105.40 | 7.07 | 27.30 |
| 35. | 31 août 2014 | 2.26% | 3.77% | 0.98 | 6.84 | 2.59 |
| 36. | 30 sept. 2014 | -2.72% | -1.55% | 15.89 | 7.30 | 10.77 |
| 37. | 31 oct. 2014 | 2.68% | 2.32% | 2.00 | 1.37 | 1.65 |
| 38. | 30 nov. 2014 | 4.23% | 2.45% | 8.77 | 1.70 | 3.86 |
| 39. | 31 déc. 2014 | -0.37% | -0.42% | 2.69 | 2.46 | 2.57 |
| 40. | 31 janv. 2015 | -0.84% | -3.10% | 4.45 | 18.10 | 8.97 |
| 41. | 28 févr. 2015 | 2.08% | 5.49% | 0.65 | 18.82 | 3.49 |
| 42. | 31 mars 2015 | -6.14% | -1.74% | 55.00 | 8.35 | 21.44 |
| 43. | 30 avr. 2015 | 1.26% | 0.85% | 0.00 | 0.09 | 0.00 |
| 44. | 31 mai 2015 | 2.65% | 1.05% | 1.90 | 0.01 | -0.14 |
| 45. | 30 juin 2015 | -8.46% | -2.10% | 94.76 | 10.57 | 31.66 |
| 46. | 31 juil. 2015 | -4.41% | 1.97% | 32.27 | 0.68 | -4.68 |
| 47. | 31 août 2015 | -4.16% | -6.26% | 29.52 | 54.89 | 40.25 |
| 48. | 30 sept. 2015 | -12.61% | -2.64% | 192.60 | 14.40 | 52.67 |
| 49. | 31 oct. 2015 | 9.87% | 8.30% | 73.87 | 51.09 | 61.43 |
| 50. | 30 nov. 2015 | 2.08% | 0.05% | 0.66 | 1.21 | -0.89 |
| 51. | 31 déc. 2015 | 3.53% | -1.75% | 5.10 | 8.43 | -6.56 |
| 52. | 31 janv. 2016 | -7.49% | -5.07% | 76.78 | 38.74 | 54.54 |
| 53. | 29 févr. 2016 | -0.67% | -0.41% | 3.78 | 2.44 | 3.04 |
| 54. | 31 mars 2016 | -2.50% | 6.60% | 14.23 | 29.68 | -20.55 |
| 55. | 30 avr. 2016 | 7.39% | 0.27% | 37.38 | 0.78 | -5.38 |
| 56. | 31 mai 2016 | 20.06% | 1.53% | 352.91 | 0.15 | 7.17 |
| 57. | 30 juin 2016 | -8.06% | 0.09% | 87.00 | 1.12 | 9.88 |
| 58. | 31 juil. 2016 | 3.77% | 3.56% | 6.25 | 5.81 | 6.03 |
| 59. | 31 août 2016 | -0.25% | -0.12% | 2.32 | 1.62 | 1.94 |
| 60. | 30 sept. 2016 | -4.04% | -0.12% | 28.19 | 1.62 | 6.76 |
| 61. | 31 oct. 2016 | -0.87% | -1.94% | 4.59 | 9.57 | 6.63 |
| 62. | 30 nov. 2016 | 1.93% | 3.42% | 0.43 | 5.14 | 1.48 |
| 63. | 31 déc. 2016 | 2.43% | 1.82% | 1.35 | 0.45 | 0.78 |
| 64. | 31 janv. 2017 | 3.46% | 1.79% | 4.79 | 0.41 | 1.40 |
| 65. | 28 févr. 2017 | 5.10% | 3.72% | 14.63 | 6.60 | 9.83 |
| 66. | 31 mars 2017 | -0.55% | -0.04% | 3.33 | 1.42 | 2.17 |
| 67. | 30 avr. 2017 | 3.49% | 0.91% | 4.92 | 0.06 | -0.54 |
| 68. | 31 mai 2017 | 0.69% | 1.16% | 0.33 | 0.00 | 0.00 |
| 69. | 30 juin 2017 | 0.80% | 0.48% | 0.22 | 0.45 | 0.32 |
| 70. | 31 juil. 2017 | -0.84% | 1.93% | 4.48 | 0.61 | -1.66 |
| 71. | 31 août 2017 | 0.33% | 0.05% | 0.90 | 1.20 | 1.04 |
| Total (Σ): | 2,577.67 | 633.66 | 743.38 | |||
Tout afficher
VarianceMON = Σ(RMON,t–RMON)2 ÷ (71 – 1)
= 2,577.67 ÷ (71 – 1)
= 36.82
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 633.66 ÷ (71 – 1)
= 9.05
CovarianceMON, S&P 500 = Σ(RMON,t–RMON)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 743.38 ÷ (71 – 1)
= 10.62
Estimation systématique des risques (β)
| VarianceMON | 36.82 |
| VarianceS&P 500 | 9.05 |
| CovarianceMON, S&P 500 | 10.62 |
| Coefficient de corrélationMON, S&P 5001 | 0.58 |
| βMON2 | 1.17 |
| αMON3 | -0.08% |
Calculs
1 Coefficient de corrélationMON, S&P 500
= CovarianceMON, S&P 500 ÷ (Écart typeMON × Écart typeS&P 500)
= 10.62 ÷ (6.07% × 3.01%)
= 0.58
2 βMON
= CovarianceMON, S&P 500 ÷ VarianceS&P 500
= 10.62 ÷ 9.05
= 1.17
3 αMON
= MoyenneMON – βMON × MoyenneS&P 500
= 1.27% – 1.17 × 1.15%
= -0.08%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.76% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 14.73% |
| Risque systématique lié à Monsanto actions ordinaires | βMON | 1.17 |
| Taux de rendement attendu des actions ordinaires de Monsanto3 | E(RMON) | 16.45% |
1 Moyenne non pondérée des rendements des offres sur tous les bons du Trésor américain à coupon fixe en circulation qui ne sont ni échus ni remboursables par anticipation dans moins de 10 ans (indicateur du taux de rendement sans risque).
3 E(RMON) = RF + βMON [E(RM) – RF]
= 4.76% + 1.17 [14.73% – 4.76%]
= 16.45%