Modèle d’évaluation des immobilisations (CAPM)
Le modèle d’évaluation des immobilisations (MEDAF) indique quel devrait être le taux de rendement prévu ou requis sur les actifs risqués comme les actions ordinaires de Apple.
Taux de rendement
Apple Inc., taux de rendement mensuels
| Apple Inc. (AAPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixAAPL,t1 | DividendeAAPL,t1 | RAAPL,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 oct. 2015 | $29.88 | 2,079.36 | ||||
| 1. | 30 nov. 2015 | $29.58 | $0.13 | -0.57% | 2,080.41 | 0.05% |
| 2. | 31 déc. 2015 | $26.32 | -11.02% | 2,043.94 | -1.75% | |
| 3. | 31 janv. 2016 | $24.34 | -7.52% | 1,940.24 | -5.07% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 août 2021 | $151.83 | $0.22 | 4.24% | 4,522.68 | 2.90% |
| 71. | 30 sept. 2021 | $141.50 | -6.80% | 4,307.54 | -4.76% | |
| Moyenne (R): | 2.69% | 1.12% | ||||
| Écart type: | 8.49% | 4.19% | ||||
| Apple Inc. (AAPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixAAPL,t1 | DividendeAAPL,t1 | RAAPL,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 oct. 2015 | $29.88 | 2,079.36 | ||||
| 1. | 30 nov. 2015 | $29.58 | $0.13 | -0.57% | 2,080.41 | 0.05% |
| 2. | 31 déc. 2015 | $26.32 | -11.02% | 2,043.94 | -1.75% | |
| 3. | 31 janv. 2016 | $24.34 | -7.52% | 1,940.24 | -5.07% | |
| 4. | 29 févr. 2016 | $24.17 | $0.13 | -0.16% | 1,932.23 | -0.41% |
| 5. | 31 mars 2016 | $27.25 | 12.74% | 2,059.74 | 6.60% | |
| 6. | 30 avr. 2016 | $23.44 | -13.98% | 2,065.30 | 0.27% | |
| 7. | 31 mai 2016 | $24.97 | $0.1425 | 7.14% | 2,096.95 | 1.53% |
| 8. | 30 juin 2016 | $23.90 | -4.29% | 2,098.86 | 0.09% | |
| 9. | 31 juil. 2016 | $26.05 | 9.00% | 2,173.60 | 3.56% | |
| 10. | 31 août 2016 | $26.53 | $0.1425 | 2.39% | 2,170.95 | -0.12% |
| 11. | 30 sept. 2016 | $28.26 | 6.52% | 2,168.27 | -0.12% | |
| 12. | 31 oct. 2016 | $28.39 | 0.46% | 2,126.15 | -1.94% | |
| 13. | 30 nov. 2016 | $27.63 | $0.1425 | -2.18% | 2,198.81 | 3.42% |
| 14. | 31 déc. 2016 | $28.96 | 4.81% | 2,238.83 | 1.82% | |
| 15. | 31 janv. 2017 | $30.34 | 4.77% | 2,278.87 | 1.79% | |
| 16. | 28 févr. 2017 | $34.25 | $0.1425 | 13.36% | 2,363.64 | 3.72% |
| 17. | 31 mars 2017 | $35.92 | 4.88% | 2,362.72 | -0.04% | |
| 18. | 30 avr. 2017 | $35.91 | -0.03% | 2,384.20 | 0.91% | |
| 19. | 31 mai 2017 | $38.19 | $0.1575 | 6.79% | 2,411.80 | 1.16% |
| 20. | 30 juin 2017 | $36.01 | -5.71% | 2,423.41 | 0.48% | |
| 21. | 31 juil. 2017 | $37.18 | 3.25% | 2,470.30 | 1.93% | |
| 22. | 31 août 2017 | $41.00 | $0.1575 | 10.70% | 2,471.65 | 0.05% |
| 23. | 30 sept. 2017 | $38.53 | -6.02% | 2,519.36 | 1.93% | |
| 24. | 31 oct. 2017 | $42.26 | 9.68% | 2,575.26 | 2.22% | |
| 25. | 30 nov. 2017 | $42.96 | $0.1575 | 2.03% | 2,647.58 | 2.81% |
| 26. | 31 déc. 2017 | $42.31 | -1.51% | 2,673.61 | 0.98% | |
| 27. | 31 janv. 2018 | $41.86 | -1.06% | 2,823.81 | 5.62% | |
| 28. | 28 févr. 2018 | $44.53 | $0.1575 | 6.75% | 2,713.83 | -3.89% |
| 29. | 31 mars 2018 | $41.95 | -5.79% | 2,640.87 | -2.69% | |
| 30. | 30 avr. 2018 | $41.32 | -1.50% | 2,648.05 | 0.27% | |
| 31. | 31 mai 2018 | $46.72 | $0.1825 | 13.51% | 2,705.27 | 2.16% |
| 32. | 30 juin 2018 | $46.28 | -0.94% | 2,718.37 | 0.48% | |
| 33. | 31 juil. 2018 | $47.57 | 2.79% | 2,816.29 | 3.60% | |
| 34. | 31 août 2018 | $56.91 | $0.1825 | 20.02% | 2,901.52 | 3.03% |
| 35. | 30 sept. 2018 | $56.44 | -0.83% | 2,913.98 | 0.43% | |
| 36. | 31 oct. 2018 | $54.72 | -3.05% | 2,711.74 | -6.94% | |
| 37. | 30 nov. 2018 | $44.65 | $0.1825 | -18.07% | 2,760.17 | 1.79% |
| 38. | 31 déc. 2018 | $39.44 | -11.67% | 2,506.85 | -9.18% | |
| 39. | 31 janv. 2019 | $41.61 | 5.50% | 2,704.10 | 7.87% | |
| 40. | 28 févr. 2019 | $43.29 | $0.1825 | 4.48% | 2,784.49 | 2.97% |
| 41. | 31 mars 2019 | $47.49 | 9.70% | 2,834.40 | 1.79% | |
| 42. | 30 avr. 2019 | $50.17 | 5.64% | 2,945.83 | 3.93% | |
| 43. | 31 mai 2019 | $43.77 | $0.1925 | -12.37% | 2,752.06 | -6.58% |
| 44. | 30 juin 2019 | $49.48 | 13.05% | 2,941.76 | 6.89% | |
| 45. | 31 juil. 2019 | $53.26 | 7.64% | 2,980.38 | 1.31% | |
| 46. | 31 août 2019 | $52.19 | $0.1925 | -1.65% | 2,926.46 | -1.81% |
| 47. | 30 sept. 2019 | $55.99 | 7.28% | 2,976.74 | 1.72% | |
| 48. | 31 oct. 2019 | $62.19 | 11.07% | 3,037.56 | 2.04% | |
| 49. | 30 nov. 2019 | $66.81 | $0.1925 | 7.74% | 3,140.98 | 3.40% |
| 50. | 31 déc. 2019 | $73.41 | 9.88% | 3,230.78 | 2.86% | |
| 51. | 31 janv. 2020 | $77.38 | 5.41% | 3,225.52 | -0.16% | |
| 52. | 29 févr. 2020 | $68.34 | $0.1925 | -11.43% | 2,954.22 | -8.41% |
| 53. | 31 mars 2020 | $63.57 | -6.98% | 2,584.59 | -12.51% | |
| 54. | 30 avr. 2020 | $73.45 | 15.54% | 2,912.43 | 12.68% | |
| 55. | 31 mai 2020 | $79.49 | $0.205 | 8.50% | 3,044.31 | 4.53% |
| 56. | 30 juin 2020 | $91.20 | 14.73% | 3,100.29 | 1.84% | |
| 57. | 31 juil. 2020 | $106.26 | 16.51% | 3,271.12 | 5.51% | |
| 58. | 31 août 2020 | $129.04 | $0.205 | 21.63% | 3,500.31 | 7.01% |
| 59. | 30 sept. 2020 | $115.81 | -10.25% | 3,363.00 | -3.92% | |
| 60. | 31 oct. 2020 | $108.86 | -6.00% | 3,269.96 | -2.77% | |
| 61. | 30 nov. 2020 | $119.05 | $0.205 | 9.55% | 3,621.63 | 10.75% |
| 62. | 31 déc. 2020 | $132.69 | 11.46% | 3,756.07 | 3.71% | |
| 63. | 31 janv. 2021 | $131.96 | -0.55% | 3,714.24 | -1.11% | |
| 64. | 28 févr. 2021 | $121.26 | $0.205 | -7.95% | 3,811.15 | 2.61% |
| 65. | 31 mars 2021 | $122.15 | 0.73% | 3,972.89 | 4.24% | |
| 66. | 30 avr. 2021 | $131.46 | 7.62% | 4,181.17 | 5.24% | |
| 67. | 31 mai 2021 | $124.61 | $0.22 | -5.04% | 4,204.11 | 0.55% |
| 68. | 30 juin 2021 | $136.96 | 9.91% | 4,297.50 | 2.22% | |
| 69. | 31 juil. 2021 | $145.86 | 6.50% | 4,395.26 | 2.27% | |
| 70. | 31 août 2021 | $151.83 | $0.22 | 4.24% | 4,522.68 | 2.90% |
| 71. | 30 sept. 2021 | $141.50 | -6.80% | 4,307.54 | -4.76% | |
| Moyenne (R): | 2.69% | 1.12% | ||||
| Écart type: | 8.49% | 4.19% | ||||
Afficher tout
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’AAPL au cours de la période t.
3 Taux de rendement du S&P 500 (l’indicateur du portefeuille de marché) au cours de la période t.
Variance et covariance
Apple Inc., calcul de variance et covariance des rendements
| t | Date | RAAPL,t | RS&P 500,t | (RAAPL,t–RAAPL)2 | (RS&P 500,t–RS&P 500)2 | (RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 nov. 2015 | -0.57% | 0.05% | 10.62 | 1.14 | 3.48 |
| 2. | 31 déc. 2015 | -11.02% | -1.75% | 187.98 | 8.24 | 39.36 |
| 3. | 31 janv. 2016 | -7.52% | -5.07% | 104.29 | 38.33 | 63.23 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 août 2021 | 4.24% | 2.90% | 2.42 | 3.17 | 2.77 |
| 71. | 30 sept. 2021 | -6.80% | -4.76% | 90.12 | 34.51 | 55.77 |
| Total (Σ): | 5,051.17 | 1,226.33 | 1,589.97 | |||
| t | Date | RAAPL,t | RS&P 500,t | (RAAPL,t–RAAPL)2 | (RS&P 500,t–RS&P 500)2 | (RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 nov. 2015 | -0.57% | 0.05% | 10.62 | 1.14 | 3.48 |
| 2. | 31 déc. 2015 | -11.02% | -1.75% | 187.98 | 8.24 | 39.36 |
| 3. | 31 janv. 2016 | -7.52% | -5.07% | 104.29 | 38.33 | 63.23 |
| 4. | 29 févr. 2016 | -0.16% | -0.41% | 8.14 | 2.34 | 4.37 |
| 5. | 31 mars 2016 | 12.74% | 6.60% | 101.08 | 30.04 | 55.11 |
| 6. | 30 avr. 2016 | -13.98% | 0.27% | 277.93 | 0.72 | 14.14 |
| 7. | 31 mai 2016 | 7.14% | 1.53% | 19.77 | 0.17 | 1.84 |
| 8. | 30 juin 2016 | -4.29% | 0.09% | 48.64 | 1.05 | 7.16 |
| 9. | 31 juil. 2016 | 9.00% | 3.56% | 39.77 | 5.97 | 15.41 |
| 10. | 31 août 2016 | 2.39% | -0.12% | 0.09 | 1.54 | 0.37 |
| 11. | 30 sept. 2016 | 6.52% | -0.12% | 14.68 | 1.54 | -4.76 |
| 12. | 31 oct. 2016 | 0.46% | -1.94% | 4.97 | 9.37 | 6.82 |
| 13. | 30 nov. 2016 | -2.18% | 3.42% | 23.66 | 5.29 | -11.19 |
| 14. | 31 déc. 2016 | 4.81% | 1.82% | 4.51 | 0.49 | 1.49 |
| 15. | 31 janv. 2017 | 4.77% | 1.79% | 4.31 | 0.45 | 1.39 |
| 16. | 28 févr. 2017 | 13.36% | 3.72% | 113.80 | 6.77 | 27.76 |
| 17. | 31 mars 2017 | 4.88% | -0.04% | 4.78 | 1.34 | -2.53 |
| 18. | 30 avr. 2017 | -0.03% | 0.91% | 7.38 | 0.04 | 0.57 |
| 19. | 31 mai 2017 | 6.79% | 1.16% | 16.80 | 0.00 | 0.16 |
| 20. | 30 juin 2017 | -5.71% | 0.48% | 70.52 | 0.41 | 5.35 |
| 21. | 31 juil. 2017 | 3.25% | 1.93% | 0.31 | 0.67 | 0.46 |
| 22. | 31 août 2017 | 10.70% | 0.05% | 64.14 | 1.13 | -8.52 |
| 23. | 30 sept. 2017 | -6.02% | 1.93% | 75.93 | 0.66 | -7.08 |
| 24. | 31 oct. 2017 | 9.68% | 2.22% | 48.88 | 1.21 | 7.70 |
| 25. | 30 nov. 2017 | 2.03% | 2.81% | 0.44 | 2.86 | -1.12 |
| 26. | 31 déc. 2017 | -1.51% | 0.98% | 17.66 | 0.02 | 0.57 |
| 27. | 31 janv. 2018 | -1.06% | 5.62% | 14.09 | 20.25 | -16.89 |
| 28. | 28 févr. 2018 | 6.75% | -3.89% | 16.53 | 25.13 | -20.38 |
| 29. | 31 mars 2018 | -5.79% | -2.69% | 71.97 | 14.49 | 32.29 |
| 30. | 30 avr. 2018 | -1.50% | 0.27% | 17.57 | 0.72 | 3.55 |
| 31. | 31 mai 2018 | 13.51% | 2.16% | 117.09 | 1.09 | 11.28 |
| 32. | 30 juin 2018 | -0.94% | 0.48% | 13.19 | 0.40 | 2.30 |
| 33. | 31 juil. 2018 | 2.79% | 3.60% | 0.01 | 6.17 | 0.24 |
| 34. | 31 août 2018 | 20.02% | 3.03% | 300.27 | 3.64 | 33.07 |
| 35. | 30 sept. 2018 | -0.83% | 0.43% | 12.36 | 0.47 | 2.42 |
| 36. | 31 oct. 2018 | -3.05% | -6.94% | 32.91 | 64.94 | 46.23 |
| 37. | 30 nov. 2018 | -18.07% | 1.79% | 430.92 | 0.45 | -13.87 |
| 38. | 31 déc. 2018 | -11.67% | -9.18% | 206.15 | 106.00 | 147.83 |
| 39. | 31 janv. 2019 | 5.50% | 7.87% | 7.91 | 45.57 | 18.99 |
| 40. | 28 févr. 2019 | 4.48% | 2.97% | 3.19 | 3.44 | 3.31 |
| 41. | 31 mars 2019 | 9.70% | 1.79% | 49.18 | 0.45 | 4.73 |
| 42. | 30 avr. 2019 | 5.64% | 3.93% | 8.73 | 7.92 | 8.31 |
| 43. | 31 mai 2019 | -12.37% | -6.58% | 226.88 | 59.22 | 115.92 |
| 44. | 30 juin 2019 | 13.05% | 6.89% | 107.25 | 33.35 | 59.81 |
| 45. | 31 juil. 2019 | 7.64% | 1.31% | 24.50 | 0.04 | 0.96 |
| 46. | 31 août 2019 | -1.65% | -1.81% | 18.81 | 8.57 | 12.70 |
| 47. | 30 sept. 2019 | 7.28% | 1.72% | 21.08 | 0.36 | 2.76 |
| 48. | 31 oct. 2019 | 11.07% | 2.04% | 70.29 | 0.86 | 7.76 |
| 49. | 30 nov. 2019 | 7.74% | 3.40% | 25.49 | 5.23 | 11.55 |
| 50. | 31 déc. 2019 | 9.88% | 2.86% | 51.69 | 3.03 | 12.52 |
| 51. | 31 janv. 2020 | 5.41% | -0.16% | 7.39 | 1.64 | -3.48 |
| 52. | 29 févr. 2020 | -11.43% | -8.41% | 199.47 | 90.80 | 134.58 |
| 53. | 31 mars 2020 | -6.98% | -12.51% | 93.49 | 185.77 | 131.79 |
| 54. | 30 avr. 2020 | 15.54% | 12.68% | 165.19 | 133.78 | 148.66 |
| 55. | 31 mai 2020 | 8.50% | 4.53% | 33.79 | 11.63 | 19.82 |
| 56. | 30 juin 2020 | 14.73% | 1.84% | 145.01 | 0.52 | 8.68 |
| 57. | 31 juil. 2020 | 16.51% | 5.51% | 191.09 | 19.29 | 60.72 |
| 58. | 31 août 2020 | 21.63% | 7.01% | 358.78 | 34.67 | 111.54 |
| 59. | 30 sept. 2020 | -10.25% | -3.92% | 167.50 | 25.41 | 65.24 |
| 60. | 31 oct. 2020 | -6.00% | -2.77% | 75.53 | 15.09 | 33.76 |
| 61. | 30 nov. 2020 | 9.55% | 10.75% | 47.05 | 92.86 | 66.10 |
| 62. | 31 déc. 2020 | 11.46% | 3.71% | 76.88 | 6.73 | 22.75 |
| 63. | 31 janv. 2021 | -0.55% | -1.11% | 10.50 | 4.98 | 7.23 |
| 64. | 28 févr. 2021 | -7.95% | 2.61% | 113.27 | 2.22 | -15.87 |
| 65. | 31 mars 2021 | 0.73% | 4.24% | 3.82 | 9.77 | -6.11 |
| 66. | 30 avr. 2021 | 7.62% | 5.24% | 24.33 | 17.01 | 20.34 |
| 67. | 31 mai 2021 | -5.04% | 0.55% | 59.80 | 0.32 | 4.40 |
| 68. | 30 juin 2021 | 9.91% | 2.22% | 52.15 | 1.22 | 7.97 |
| 69. | 31 juil. 2021 | 6.50% | 2.27% | 14.51 | 1.34 | 4.41 |
| 70. | 31 août 2021 | 4.24% | 2.90% | 2.42 | 3.17 | 2.77 |
| 71. | 30 sept. 2021 | -6.80% | -4.76% | 90.12 | 34.51 | 55.77 |
| Total (Σ): | 5,051.17 | 1,226.33 | 1,589.97 | |||
Afficher tout
VarianceAAPL = Σ(RAAPL,t–RAAPL)2 ÷ (71 – 1)
= 5,051.17 ÷ (71 – 1)
= 72.16
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,226.33 ÷ (71 – 1)
= 17.52
CovarianceAAPL, S&P 500 = Σ(RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,589.97 ÷ (71 – 1)
= 22.71
Estimation systématique des risques (β)
| VarianceAAPL | 72.16 |
| VarianceS&P 500 | 17.52 |
| CovarianceAAPL, S&P 500 | 22.71 |
| Coefficient de corrélationAAPL, S&P 5001 | 0.64 |
| βAAPL2 | 1.30 |
| αAAPL3 | 1.24% |
Calculs
1 Coefficient de corrélationAAPL, S&P 500
= CovarianceAAPL, S&P 500 ÷ (Écart typeAAPL × Écart typeS&P 500)
= 22.71 ÷ (8.49% × 4.19%)
= 0.64
2 βAAPL
= CovarianceAAPL, S&P 500 ÷ VarianceS&P 500
= 22.71 ÷ 17.52
= 1.30
3 αAAPL
= MoyenneAAPL – βAAPL × MoyenneS&P 500
= 2.69% – 1.30 × 1.12%
= 1.24%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 3.26% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 12.75% |
| Risque systématique de Apple actions ordinaires | βAAPL | 1.30 |
| Taux de rendement attendu des actions ordinaires d’Apple3 | E(RAAPL) | 15.57% |
1 Moyenne non pondérée des rendements des offres sur toutes les obligations du Trésor américain à coupon fixe en circulation, ni exigibles ni exigibles depuis moins de 10 ans (indicateur de taux de rendement sans risque).
3 E(RAAPL) = RF + βAAPL [E(RM) – RF]
= 3.26% + 1.30 [12.75% – 3.26%]
= 15.57%