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 EMC.
Taux de rendement
EMC Corp., taux de rendement mensuels
| EMC Corp. (EMC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixEMC,t1 | DividendeEMC,t1 | REMC,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2011 | $24.89 | 1,286.12 | ||||
| 1. | 28 févr. 2011 | $27.21 | 9.32% | 1,327.22 | 3.20% | |
| 2. | 31 mars 2011 | $26.56 | -2.39% | 1,325.83 | -0.10% | |
| 3. | 30 avr. 2011 | $28.34 | 6.70% | 1,363.61 | 2.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2015 | $25.34 | -3.36% | 2,080.41 | 0.05% | |
| 59. | 31 déc. 2015 | $25.68 | $0.115 | 1.80% | 2,043.94 | -1.75% |
| Moyenne (R): | 0.39% | 0.84% | ||||
| Écart type: | 7.26% | 3.40% | ||||
| EMC Corp. (EMC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixEMC,t1 | DividendeEMC,t1 | REMC,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2011 | $24.89 | 1,286.12 | ||||
| 1. | 28 févr. 2011 | $27.21 | 9.32% | 1,327.22 | 3.20% | |
| 2. | 31 mars 2011 | $26.56 | -2.39% | 1,325.83 | -0.10% | |
| 3. | 30 avr. 2011 | $28.34 | 6.70% | 1,363.61 | 2.85% | |
| 4. | 31 mai 2011 | $28.47 | 0.46% | 1,345.20 | -1.35% | |
| 5. | 30 juin 2011 | $27.55 | -3.23% | 1,320.64 | -1.83% | |
| 6. | 31 juil. 2011 | $26.08 | -5.34% | 1,292.28 | -2.15% | |
| 7. | 31 août 2011 | $22.59 | -13.38% | 1,218.89 | -5.68% | |
| 8. | 30 sept. 2011 | $20.99 | -7.08% | 1,131.42 | -7.18% | |
| 9. | 31 oct. 2011 | $24.51 | 16.77% | 1,253.30 | 10.77% | |
| 10. | 30 nov. 2011 | $23.01 | -6.12% | 1,246.96 | -0.51% | |
| 11. | 31 déc. 2011 | $21.54 | -6.39% | 1,257.60 | 0.85% | |
| 12. | 31 janv. 2012 | $25.76 | 19.59% | 1,312.41 | 4.36% | |
| 13. | 29 févr. 2012 | $27.69 | 7.49% | 1,365.68 | 4.06% | |
| 14. | 31 mars 2012 | $29.88 | 7.91% | 1,408.47 | 3.13% | |
| 15. | 30 avr. 2012 | $28.21 | -5.59% | 1,397.91 | -0.75% | |
| 16. | 31 mai 2012 | $23.85 | -15.46% | 1,310.33 | -6.27% | |
| 17. | 30 juin 2012 | $25.63 | 7.46% | 1,362.16 | 3.96% | |
| 18. | 31 juil. 2012 | $26.21 | 2.26% | 1,379.32 | 1.26% | |
| 19. | 31 août 2012 | $26.29 | 0.31% | 1,406.58 | 1.98% | |
| 20. | 30 sept. 2012 | $27.27 | 3.73% | 1,440.67 | 2.42% | |
| 21. | 31 oct. 2012 | $24.42 | -10.45% | 1,412.16 | -1.98% | |
| 22. | 30 nov. 2012 | $24.82 | 1.64% | 1,416.18 | 0.28% | |
| 23. | 31 déc. 2012 | $25.30 | 1.93% | 1,426.19 | 0.71% | |
| 24. | 31 janv. 2013 | $24.61 | -2.73% | 1,498.11 | 5.04% | |
| 25. | 28 févr. 2013 | $23.01 | -6.50% | 1,514.68 | 1.11% | |
| 26. | 31 mars 2013 | $23.89 | 3.82% | 1,569.19 | 3.60% | |
| 27. | 30 avr. 2013 | $22.43 | -6.11% | 1,597.57 | 1.81% | |
| 28. | 31 mai 2013 | $24.76 | 10.39% | 1,630.74 | 2.08% | |
| 29. | 30 juin 2013 | $23.62 | $0.10 | -4.20% | 1,606.28 | -1.50% |
| 30. | 31 juil. 2013 | $26.15 | 10.71% | 1,685.73 | 4.95% | |
| 31. | 31 août 2013 | $25.78 | -1.41% | 1,632.97 | -3.13% | |
| 32. | 30 sept. 2013 | $25.56 | $0.10 | -0.47% | 1,681.55 | 2.97% |
| 33. | 31 oct. 2013 | $24.07 | -5.83% | 1,756.54 | 4.46% | |
| 34. | 30 nov. 2013 | $23.85 | -0.91% | 1,805.81 | 2.80% | |
| 35. | 31 déc. 2013 | $25.15 | 5.45% | 1,848.36 | 2.36% | |
| 36. | 31 janv. 2014 | $24.24 | $0.10 | -3.22% | 1,782.59 | -3.56% |
| 37. | 28 févr. 2014 | $26.37 | 8.79% | 1,859.45 | 4.31% | |
| 38. | 31 mars 2014 | $27.41 | $0.10 | 4.32% | 1,872.34 | 0.69% |
| 39. | 30 avr. 2014 | $25.80 | -5.87% | 1,883.95 | 0.62% | |
| 40. | 31 mai 2014 | $26.56 | 2.95% | 1,923.57 | 2.10% | |
| 41. | 30 juin 2014 | $26.34 | $0.115 | -0.40% | 1,960.23 | 1.91% |
| 42. | 31 juil. 2014 | $29.30 | 11.24% | 1,930.67 | -1.51% | |
| 43. | 31 août 2014 | $29.53 | 0.78% | 2,003.37 | 3.77% | |
| 44. | 30 sept. 2014 | $29.26 | $0.115 | -0.52% | 1,972.29 | -1.55% |
| 45. | 31 oct. 2014 | $28.73 | -1.81% | 2,018.05 | 2.32% | |
| 46. | 30 nov. 2014 | $30.35 | 5.64% | 2,067.56 | 2.45% | |
| 47. | 31 déc. 2014 | $29.74 | $0.115 | -1.63% | 2,058.90 | -0.42% |
| 48. | 31 janv. 2015 | $25.93 | -12.81% | 1,994.99 | -3.10% | |
| 49. | 28 févr. 2015 | $28.94 | 11.61% | 2,104.50 | 5.49% | |
| 50. | 31 mars 2015 | $25.56 | $0.115 | -11.28% | 2,067.89 | -1.74% |
| 51. | 30 avr. 2015 | $26.91 | 5.28% | 2,085.51 | 0.85% | |
| 52. | 31 mai 2015 | $26.34 | -2.12% | 2,107.39 | 1.05% | |
| 53. | 30 juin 2015 | $26.39 | $0.115 | 0.63% | 2,063.11 | -2.10% |
| 54. | 31 juil. 2015 | $26.89 | 1.89% | 2,103.84 | 1.97% | |
| 55. | 31 août 2015 | $24.87 | -7.51% | 1,972.18 | -6.26% | |
| 56. | 30 sept. 2015 | $24.16 | $0.115 | -2.39% | 1,920.03 | -2.64% |
| 57. | 31 oct. 2015 | $26.22 | 8.53% | 2,079.36 | 8.30% | |
| 58. | 30 nov. 2015 | $25.34 | -3.36% | 2,080.41 | 0.05% | |
| 59. | 31 déc. 2015 | $25.68 | $0.115 | 1.80% | 2,043.94 | -1.75% |
| Moyenne (R): | 0.39% | 0.84% | ||||
| Écart type: | 7.26% | 3.40% | ||||
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 d’EMC 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
EMC Corp., calcul de la variance et de la covariance des rendements
| t | Date | REMC,t | RS&P 500,t | (REMC,t–REMC)2 | (RS&P 500,t–RS&P 500)2 | (REMC,t–REMC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2011 | 9.32% | 3.20% | 79.80 | 5.53 | 21.00 |
| 2. | 31 mars 2011 | -2.39% | -0.10% | 7.71 | 0.90 | 2.64 |
| 3. | 30 avr. 2011 | 6.70% | 2.85% | 39.87 | 4.02 | 12.66 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2015 | -3.36% | 0.05% | 14.02 | 0.63 | 2.97 |
| 59. | 31 déc. 2015 | 1.80% | -1.75% | 1.98 | 6.75 | -3.66 |
| Total (Σ): | 3,054.66 | 670.89 | 1,007.60 | |||
| t | Date | REMC,t | RS&P 500,t | (REMC,t–REMC)2 | (RS&P 500,t–RS&P 500)2 | (REMC,t–REMC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2011 | 9.32% | 3.20% | 79.80 | 5.53 | 21.00 |
| 2. | 31 mars 2011 | -2.39% | -0.10% | 7.71 | 0.90 | 2.64 |
| 3. | 30 avr. 2011 | 6.70% | 2.85% | 39.87 | 4.02 | 12.66 |
| 4. | 31 mai 2011 | 0.46% | -1.35% | 0.01 | 4.82 | -0.16 |
| 5. | 30 juin 2011 | -3.23% | -1.83% | 13.10 | 7.13 | 9.67 |
| 6. | 31 juil. 2011 | -5.34% | -2.15% | 32.76 | 8.95 | 17.13 |
| 7. | 31 août 2011 | -13.38% | -5.68% | 189.61 | 42.56 | 89.83 |
| 8. | 30 sept. 2011 | -7.08% | -7.18% | 55.81 | 64.34 | 59.92 |
| 9. | 31 oct. 2011 | 16.77% | 10.77% | 268.37 | 98.56 | 162.63 |
| 10. | 30 nov. 2011 | -6.12% | -0.51% | 42.35 | 1.82 | 8.79 |
| 11. | 31 déc. 2011 | -6.39% | 0.85% | 45.92 | 0.00 | -0.06 |
| 12. | 31 janv. 2012 | 19.59% | 4.36% | 368.78 | 12.35 | 67.47 |
| 13. | 29 févr. 2012 | 7.49% | 4.06% | 50.47 | 10.33 | 22.84 |
| 14. | 31 mars 2012 | 7.91% | 3.13% | 56.57 | 5.24 | 17.21 |
| 15. | 30 avr. 2012 | -5.59% | -0.75% | 35.72 | 2.54 | 9.53 |
| 16. | 31 mai 2012 | -15.46% | -6.27% | 251.01 | 50.55 | 112.64 |
| 17. | 30 juin 2012 | 7.46% | 3.96% | 50.06 | 9.68 | 22.01 |
| 18. | 31 juil. 2012 | 2.26% | 1.26% | 3.52 | 0.17 | 0.78 |
| 19. | 31 août 2012 | 0.31% | 1.98% | 0.01 | 1.28 | -0.09 |
| 20. | 30 sept. 2012 | 3.73% | 2.42% | 11.15 | 2.49 | 5.27 |
| 21. | 31 oct. 2012 | -10.45% | -1.98% | 117.48 | 7.97 | 30.61 |
| 22. | 30 nov. 2012 | 1.64% | 0.28% | 1.56 | 0.31 | -0.70 |
| 23. | 31 déc. 2012 | 1.93% | 0.71% | 2.39 | 0.02 | -0.21 |
| 24. | 31 janv. 2013 | -2.73% | 5.04% | 9.70 | 17.62 | -13.08 |
| 25. | 28 févr. 2013 | -6.50% | 1.11% | 47.46 | 0.07 | -1.80 |
| 26. | 31 mars 2013 | 3.82% | 3.60% | 11.81 | 7.58 | 9.46 |
| 27. | 30 avr. 2013 | -6.11% | 1.81% | 42.24 | 0.93 | -6.26 |
| 28. | 31 mai 2013 | 10.39% | 2.08% | 100.00 | 1.52 | 12.32 |
| 29. | 30 juin 2013 | -4.20% | -1.50% | 21.05 | 5.50 | 10.76 |
| 30. | 31 juil. 2013 | 10.71% | 4.95% | 106.57 | 16.82 | 42.34 |
| 31. | 31 août 2013 | -1.41% | -3.13% | 3.25 | 15.80 | 7.17 |
| 32. | 30 sept. 2013 | -0.47% | 2.97% | 0.73 | 4.54 | -1.82 |
| 33. | 31 oct. 2013 | -5.83% | 4.46% | 38.65 | 13.07 | -22.47 |
| 34. | 30 nov. 2013 | -0.91% | 2.80% | 1.69 | 3.84 | -2.55 |
| 35. | 31 déc. 2013 | 5.45% | 2.36% | 25.63 | 2.28 | 7.65 |
| 36. | 31 janv. 2014 | -3.22% | -3.56% | 13.02 | 19.39 | 15.89 |
| 37. | 28 févr. 2014 | 8.79% | 4.31% | 70.55 | 12.02 | 29.12 |
| 38. | 31 mars 2014 | 4.32% | 0.69% | 15.49 | 0.02 | -0.60 |
| 39. | 30 avr. 2014 | -5.87% | 0.62% | 39.21 | 0.05 | 1.41 |
| 40. | 31 mai 2014 | 2.95% | 2.10% | 6.54 | 1.58 | 3.22 |
| 41. | 30 juin 2014 | -0.40% | 1.91% | 0.61 | 1.13 | -0.83 |
| 42. | 31 juil. 2014 | 11.24% | -1.51% | 117.72 | 5.54 | -25.53 |
| 43. | 31 août 2014 | 0.78% | 3.77% | 0.16 | 8.53 | 1.16 |
| 44. | 30 sept. 2014 | -0.52% | -1.55% | 0.83 | 5.74 | 2.19 |
| 45. | 31 oct. 2014 | -1.81% | 2.32% | 4.84 | 2.18 | -3.24 |
| 46. | 30 nov. 2014 | 5.64% | 2.45% | 27.57 | 2.59 | 8.45 |
| 47. | 31 déc. 2014 | -1.63% | -0.42% | 4.08 | 1.60 | 2.55 |
| 48. | 31 janv. 2015 | -12.81% | -3.10% | 174.21 | 15.59 | 52.12 |
| 49. | 28 févr. 2015 | 11.61% | 5.49% | 125.90 | 21.57 | 52.11 |
| 50. | 31 mars 2015 | -11.28% | -1.74% | 136.18 | 6.68 | 30.16 |
| 51. | 30 avr. 2015 | 5.28% | 0.85% | 23.95 | 0.00 | 0.04 |
| 52. | 31 mai 2015 | -2.12% | 1.05% | 6.28 | 0.04 | -0.51 |
| 53. | 30 juin 2015 | 0.63% | -2.10% | 0.06 | 8.68 | -0.70 |
| 54. | 31 juil. 2015 | 1.89% | 1.97% | 2.27 | 1.28 | 1.70 |
| 55. | 31 août 2015 | -7.51% | -6.26% | 62.41 | 50.45 | 56.11 |
| 56. | 30 sept. 2015 | -2.39% | -2.64% | 7.73 | 12.17 | 9.70 |
| 57. | 31 oct. 2015 | 8.53% | 8.30% | 66.24 | 55.56 | 60.66 |
| 58. | 30 nov. 2015 | -3.36% | 0.05% | 14.02 | 0.63 | 2.97 |
| 59. | 31 déc. 2015 | 1.80% | -1.75% | 1.98 | 6.75 | -3.66 |
| Total (Σ): | 3,054.66 | 670.89 | 1,007.60 | |||
Tout afficher
VarianceEMC = Σ(REMC,t–REMC)2 ÷ (59 – 1)
= 3,054.66 ÷ (59 – 1)
= 52.67
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 670.89 ÷ (59 – 1)
= 11.57
CovarianceEMC, S&P 500 = Σ(REMC,t–REMC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,007.60 ÷ (59 – 1)
= 17.37
Estimation systématique des risques (β)
| VarianceEMC | 52.67 |
| VarianceS&P 500 | 11.57 |
| CovarianceEMC, S&P 500 | 17.37 |
| Coefficient de corrélationEMC, S&P 5001 | 0.70 |
| βEMC2 | 1.50 |
| αEMC3 | -0.88% |
Calculs
1 Coefficient de corrélationEMC, S&P 500
= CovarianceEMC, S&P 500 ÷ (Écart typeEMC × Écart typeS&P 500)
= 17.37 ÷ (7.26% × 3.40%)
= 0.70
2 βEMC
= CovarianceEMC, S&P 500 ÷ VarianceS&P 500
= 17.37 ÷ 11.57
= 1.50
3 αEMC
= MoyenneEMC – βEMC × MoyenneS&P 500
= 0.39% – 1.50 × 0.84%
= -0.88%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.54% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 17.37% |
| Risque systématique lié à EMC actions ordinaires | βEMC | 1.50 |
| Taux de rendement attendu des actions ordinaires d’EMC3 | E(REMC) | 23.80% |
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(REMC) = RF + βEMC [E(RM) – RF]
= 4.54% + 1.50 [17.37% – 4.54%]
= 23.80%