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 Parker.
Taux de rendement
Parker-Hannifin Corp., taux de rendement mensuels
| Parker-Hannifin Corp. (PH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixPH,t1 | DividendePH,t1 | RPH,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 juil. 2016 | $114.19 | 2,173.60 | ||||
| 1. | 31 août 2016 | $122.53 | $0.63 | 7.86% | 2,170.95 | -0.12% |
| 2. | 30 sept. 2016 | $125.53 | 2.45% | 2,168.27 | -0.12% | |
| 3. | 31 oct. 2016 | $122.75 | -2.21% | 2,126.15 | -1.94% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 mai 2022 | $272.17 | $1.33 | 0.99% | 4,132.15 | 0.01% |
| 71. | 30 juin 2022 | $246.05 | -9.60% | 3,785.38 | -8.39% | |
| Moyenne (R): | 1.61% | 0.89% | ||||
| Écart type: | 8.72% | 4.53% | ||||
| Parker-Hannifin Corp. (PH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixPH,t1 | DividendePH,t1 | RPH,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 juil. 2016 | $114.19 | 2,173.60 | ||||
| 1. | 31 août 2016 | $122.53 | $0.63 | 7.86% | 2,170.95 | -0.12% |
| 2. | 30 sept. 2016 | $125.53 | 2.45% | 2,168.27 | -0.12% | |
| 3. | 31 oct. 2016 | $122.75 | -2.21% | 2,126.15 | -1.94% | |
| 4. | 30 nov. 2016 | $138.93 | $0.63 | 13.69% | 2,198.81 | 3.42% |
| 5. | 31 déc. 2016 | $140.00 | 0.77% | 2,238.83 | 1.82% | |
| 6. | 31 janv. 2017 | $147.13 | 5.09% | 2,278.87 | 1.79% | |
| 7. | 28 févr. 2017 | $154.84 | $0.66 | 5.69% | 2,363.64 | 3.72% |
| 8. | 31 mars 2017 | $160.32 | 3.54% | 2,362.72 | -0.04% | |
| 9. | 30 avr. 2017 | $160.80 | 0.30% | 2,384.20 | 0.91% | |
| 10. | 31 mai 2017 | $157.47 | $0.66 | -1.66% | 2,411.80 | 1.16% |
| 11. | 30 juin 2017 | $159.82 | 1.49% | 2,423.41 | 0.48% | |
| 12. | 31 juil. 2017 | $165.98 | 3.85% | 2,470.30 | 1.93% | |
| 13. | 31 août 2017 | $160.89 | $0.66 | -2.67% | 2,471.65 | 0.05% |
| 14. | 30 sept. 2017 | $175.02 | 8.78% | 2,519.36 | 1.93% | |
| 15. | 31 oct. 2017 | $182.61 | 4.34% | 2,575.26 | 2.22% | |
| 16. | 30 nov. 2017 | $187.49 | $0.66 | 3.03% | 2,647.58 | 2.81% |
| 17. | 31 déc. 2017 | $199.58 | 6.45% | 2,673.61 | 0.98% | |
| 18. | 31 janv. 2018 | $201.42 | 0.92% | 2,823.81 | 5.62% | |
| 19. | 28 févr. 2018 | $178.47 | $0.66 | -11.07% | 2,713.83 | -3.89% |
| 20. | 31 mars 2018 | $171.03 | -4.17% | 2,640.87 | -2.69% | |
| 21. | 30 avr. 2018 | $164.62 | -3.75% | 2,648.05 | 0.27% | |
| 22. | 31 mai 2018 | $170.90 | $0.76 | 4.28% | 2,705.27 | 2.16% |
| 23. | 30 juin 2018 | $155.85 | -8.81% | 2,718.37 | 0.48% | |
| 24. | 31 juil. 2018 | $169.05 | 8.47% | 2,816.29 | 3.60% | |
| 25. | 31 août 2018 | $175.60 | $0.76 | 4.32% | 2,901.52 | 3.03% |
| 26. | 30 sept. 2018 | $183.93 | 4.74% | 2,913.98 | 0.43% | |
| 27. | 31 oct. 2018 | $151.63 | -17.56% | 2,711.74 | -6.94% | |
| 28. | 30 nov. 2018 | $172.04 | $0.76 | 13.96% | 2,760.17 | 1.79% |
| 29. | 31 déc. 2018 | $149.14 | -13.31% | 2,506.85 | -9.18% | |
| 30. | 31 janv. 2019 | $164.81 | 10.51% | 2,704.10 | 7.87% | |
| 31. | 28 févr. 2019 | $176.16 | $0.76 | 7.35% | 2,784.49 | 2.97% |
| 32. | 31 mars 2019 | $171.62 | -2.58% | 2,834.40 | 1.79% | |
| 33. | 30 avr. 2019 | $181.08 | 5.51% | 2,945.83 | 3.93% | |
| 34. | 31 mai 2019 | $152.32 | $0.88 | -15.40% | 2,752.06 | -6.58% |
| 35. | 30 juin 2019 | $170.01 | 11.61% | 2,941.76 | 6.89% | |
| 36. | 31 juil. 2019 | $175.08 | 2.98% | 2,980.38 | 1.31% | |
| 37. | 31 août 2019 | $165.77 | $0.88 | -4.81% | 2,926.46 | -1.81% |
| 38. | 30 sept. 2019 | $180.61 | 8.95% | 2,976.74 | 1.72% | |
| 39. | 31 oct. 2019 | $183.49 | 1.59% | 3,037.56 | 2.04% | |
| 40. | 30 nov. 2019 | $198.79 | $0.88 | 8.82% | 3,140.98 | 3.40% |
| 41. | 31 déc. 2019 | $205.82 | 3.54% | 3,230.78 | 2.86% | |
| 42. | 31 janv. 2020 | $195.69 | -4.92% | 3,225.52 | -0.16% | |
| 43. | 29 févr. 2020 | $184.77 | $0.88 | -5.13% | 2,954.22 | -8.41% |
| 44. | 31 mars 2020 | $129.73 | -29.79% | 2,584.59 | -12.51% | |
| 45. | 30 avr. 2020 | $158.12 | 21.88% | 2,912.43 | 12.68% | |
| 46. | 31 mai 2020 | $179.97 | $0.88 | 14.38% | 3,044.31 | 4.53% |
| 47. | 30 juin 2020 | $183.27 | 1.83% | 3,100.29 | 1.84% | |
| 48. | 31 juil. 2020 | $178.92 | -2.37% | 3,271.12 | 5.51% | |
| 49. | 31 août 2020 | $206.01 | $0.88 | 15.63% | 3,500.31 | 7.01% |
| 50. | 30 sept. 2020 | $202.34 | -1.78% | 3,363.00 | -3.92% | |
| 51. | 31 oct. 2020 | $208.36 | 2.98% | 3,269.96 | -2.77% | |
| 52. | 30 nov. 2020 | $267.26 | $0.88 | 28.69% | 3,621.63 | 10.75% |
| 53. | 31 déc. 2020 | $272.41 | 1.93% | 3,756.07 | 3.71% | |
| 54. | 31 janv. 2021 | $264.61 | -2.86% | 3,714.24 | -1.11% | |
| 55. | 28 févr. 2021 | $286.96 | $0.88 | 8.78% | 3,811.15 | 2.61% |
| 56. | 31 mars 2021 | $315.43 | 9.92% | 3,972.89 | 4.24% | |
| 57. | 30 avr. 2021 | $313.81 | -0.51% | 4,181.17 | 5.24% | |
| 58. | 31 mai 2021 | $308.15 | $1.03 | -1.48% | 4,204.11 | 0.55% |
| 59. | 30 juin 2021 | $307.11 | -0.34% | 4,297.50 | 2.22% | |
| 60. | 31 juil. 2021 | $312.03 | 1.60% | 4,395.26 | 2.27% | |
| 61. | 31 août 2021 | $296.67 | $1.03 | -4.59% | 4,522.68 | 2.90% |
| 62. | 30 sept. 2021 | $279.62 | -5.75% | 4,307.54 | -4.76% | |
| 63. | 31 oct. 2021 | $296.59 | 6.07% | 4,605.38 | 6.91% | |
| 64. | 30 nov. 2021 | $302.06 | $1.03 | 2.19% | 4,567.00 | -0.83% |
| 65. | 31 déc. 2021 | $318.12 | 5.32% | 4,766.18 | 4.36% | |
| 66. | 31 janv. 2022 | $310.01 | -2.55% | 4,515.55 | -5.26% | |
| 67. | 28 févr. 2022 | $296.39 | $1.03 | -4.06% | 4,373.94 | -3.14% |
| 68. | 31 mars 2022 | $283.76 | -4.26% | 4,530.41 | 3.58% | |
| 69. | 30 avr. 2022 | $270.82 | -4.56% | 4,131.93 | -8.80% | |
| 70. | 31 mai 2022 | $272.17 | $1.33 | 0.99% | 4,132.15 | 0.01% |
| 71. | 30 juin 2022 | $246.05 | -9.60% | 3,785.38 | -8.39% | |
| Moyenne (R): | 1.61% | 0.89% | ||||
| Écart type: | 8.72% | 4.53% | ||||
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 PH 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
Parker-Hannifin Corp., calcul de la variance et de la covariance des rendements
| t | Date | RPH,t | RS&P 500,t | (RPH,t–RPH)2 | (RS&P 500,t–RS&P 500)2 | (RPH,t–RPH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 août 2016 | 7.86% | -0.12% | 38.96 | 1.02 | -6.30 |
| 2. | 30 sept. 2016 | 2.45% | -0.12% | 0.70 | 1.02 | -0.84 |
| 3. | 31 oct. 2016 | -2.21% | -1.94% | 14.65 | 8.00 | 10.83 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 mai 2022 | 0.99% | 0.01% | 0.39 | 0.78 | 0.55 |
| 71. | 30 juin 2022 | -9.60% | -8.39% | 125.67 | 86.09 | 104.02 |
| Total (Σ): | 5,326.54 | 1,437.21 | 2,230.11 | |||
| t | Date | RPH,t | RS&P 500,t | (RPH,t–RPH)2 | (RS&P 500,t–RS&P 500)2 | (RPH,t–RPH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 août 2016 | 7.86% | -0.12% | 38.96 | 1.02 | -6.30 |
| 2. | 30 sept. 2016 | 2.45% | -0.12% | 0.70 | 1.02 | -0.84 |
| 3. | 31 oct. 2016 | -2.21% | -1.94% | 14.65 | 8.00 | 10.83 |
| 4. | 30 nov. 2016 | 13.69% | 3.42% | 145.96 | 6.40 | 30.57 |
| 5. | 31 déc. 2016 | 0.77% | 1.82% | 0.71 | 0.87 | -0.79 |
| 6. | 31 janv. 2017 | 5.09% | 1.79% | 12.11 | 0.81 | 3.14 |
| 7. | 28 févr. 2017 | 5.69% | 3.72% | 16.61 | 8.03 | 11.55 |
| 8. | 31 mars 2017 | 3.54% | -0.04% | 3.71 | 0.86 | -1.78 |
| 9. | 30 avr. 2017 | 0.30% | 0.91% | 1.73 | 0.00 | -0.03 |
| 10. | 31 mai 2017 | -1.66% | 1.16% | 10.72 | 0.07 | -0.89 |
| 11. | 30 juin 2017 | 1.49% | 0.48% | 0.01 | 0.16 | 0.05 |
| 12. | 31 juil. 2017 | 3.85% | 1.93% | 5.02 | 1.10 | 2.35 |
| 13. | 31 août 2017 | -2.67% | 0.05% | 18.34 | 0.69 | 3.56 |
| 14. | 30 sept. 2017 | 8.78% | 1.93% | 51.40 | 1.09 | 7.48 |
| 15. | 31 oct. 2017 | 4.34% | 2.22% | 7.42 | 1.77 | 3.63 |
| 16. | 30 nov. 2017 | 3.03% | 2.81% | 2.02 | 3.69 | 2.73 |
| 17. | 31 déc. 2017 | 6.45% | 0.98% | 23.38 | 0.01 | 0.47 |
| 18. | 31 janv. 2018 | 0.92% | 5.62% | 0.48 | 22.38 | -3.27 |
| 19. | 28 févr. 2018 | -11.07% | -3.89% | 160.77 | 22.86 | 60.63 |
| 20. | 31 mars 2018 | -4.17% | -2.69% | 33.43 | 12.78 | 20.67 |
| 21. | 30 avr. 2018 | -3.75% | 0.27% | 28.74 | 0.38 | 3.30 |
| 22. | 31 mai 2018 | 4.28% | 2.16% | 7.09 | 1.62 | 3.39 |
| 23. | 30 juin 2018 | -8.81% | 0.48% | 108.57 | 0.16 | 4.19 |
| 24. | 31 juil. 2018 | 8.47% | 3.60% | 47.01 | 7.37 | 18.62 |
| 25. | 31 août 2018 | 4.32% | 3.03% | 7.35 | 4.58 | 5.80 |
| 26. | 30 sept. 2018 | 4.74% | 0.43% | 9.80 | 0.21 | -1.43 |
| 27. | 31 oct. 2018 | -17.56% | -6.94% | 367.65 | 61.26 | 150.08 |
| 28. | 30 nov. 2018 | 13.96% | 1.79% | 152.48 | 0.81 | 11.10 |
| 29. | 31 déc. 2018 | -13.31% | -9.18% | 222.73 | 101.29 | 150.20 |
| 30. | 31 janv. 2019 | 10.51% | 7.87% | 79.10 | 48.74 | 62.09 |
| 31. | 28 févr. 2019 | 7.35% | 2.97% | 32.89 | 4.35 | 11.96 |
| 32. | 31 mars 2019 | -2.58% | 1.79% | 17.56 | 0.82 | -3.80 |
| 33. | 30 avr. 2019 | 5.51% | 3.93% | 15.20 | 9.27 | 11.87 |
| 34. | 31 mai 2019 | -15.40% | -6.58% | 289.33 | 55.72 | 126.97 |
| 35. | 30 juin 2019 | 11.61% | 6.89% | 100.01 | 36.08 | 60.07 |
| 36. | 31 juil. 2019 | 2.98% | 1.31% | 1.87 | 0.18 | 0.58 |
| 37. | 31 août 2019 | -4.81% | -1.81% | 41.32 | 7.27 | 17.33 |
| 38. | 30 sept. 2019 | 8.95% | 1.72% | 53.86 | 0.69 | 6.10 |
| 39. | 31 oct. 2019 | 1.59% | 2.04% | 0.00 | 1.34 | -0.02 |
| 40. | 30 nov. 2019 | 8.82% | 3.40% | 51.91 | 6.34 | 18.14 |
| 41. | 31 déc. 2019 | 3.54% | 2.86% | 3.70 | 3.89 | 3.79 |
| 42. | 31 janv. 2020 | -4.92% | -0.16% | 42.71 | 1.10 | 6.86 |
| 43. | 29 févr. 2020 | -5.13% | -8.41% | 45.48 | 86.45 | 62.70 |
| 44. | 31 mars 2020 | -29.79% | -12.51% | 986.06 | 179.52 | 420.74 |
| 45. | 30 avr. 2020 | 21.88% | 12.68% | 410.90 | 139.19 | 239.15 |
| 46. | 31 mai 2020 | 14.38% | 4.53% | 162.87 | 13.26 | 46.47 |
| 47. | 30 juin 2020 | 1.83% | 1.84% | 0.05 | 0.91 | 0.21 |
| 48. | 31 juil. 2020 | -2.37% | 5.51% | 15.89 | 21.38 | -18.43 |
| 49. | 31 août 2020 | 15.63% | 7.01% | 196.55 | 37.45 | 85.80 |
| 50. | 30 sept. 2020 | -1.78% | -3.92% | 11.52 | 23.13 | 16.33 |
| 51. | 31 oct. 2020 | 2.98% | -2.77% | 1.86 | 13.35 | -4.98 |
| 52. | 30 nov. 2020 | 28.69% | 10.75% | 733.19 | 97.38 | 267.20 |
| 53. | 31 déc. 2020 | 1.93% | 3.71% | 0.10 | 7.98 | 0.89 |
| 54. | 31 janv. 2021 | -2.86% | -1.11% | 20.04 | 4.00 | 8.95 |
| 55. | 28 févr. 2021 | 8.78% | 2.61% | 51.35 | 2.97 | 12.34 |
| 56. | 31 mars 2021 | 9.92% | 4.24% | 69.02 | 11.27 | 27.89 |
| 57. | 30 avr. 2021 | -0.51% | 5.24% | 4.52 | 18.97 | -9.26 |
| 58. | 31 mai 2021 | -1.48% | 0.55% | 9.54 | 0.11 | 1.04 |
| 59. | 30 juin 2021 | -0.34% | 2.22% | 3.81 | 1.78 | -2.60 |
| 60. | 31 juil. 2021 | 1.60% | 2.27% | 0.00 | 1.93 | -0.02 |
| 61. | 31 août 2021 | -4.59% | 2.90% | 38.51 | 4.05 | -12.49 |
| 62. | 30 sept. 2021 | -5.75% | -4.76% | 54.17 | 31.85 | 41.54 |
| 63. | 31 oct. 2021 | 6.07% | 6.91% | 19.85 | 36.33 | 26.86 |
| 64. | 30 nov. 2021 | 2.19% | -0.83% | 0.33 | 2.96 | -0.99 |
| 65. | 31 déc. 2021 | 5.32% | 4.36% | 13.72 | 12.07 | 12.87 |
| 66. | 31 janv. 2022 | -2.55% | -5.26% | 17.33 | 37.76 | 25.58 |
| 67. | 28 févr. 2022 | -4.06% | -3.14% | 32.20 | 16.18 | 22.83 |
| 68. | 31 mars 2022 | -4.26% | 3.58% | 34.51 | 7.24 | -15.81 |
| 69. | 30 avr. 2022 | -4.56% | -8.80% | 38.11 | 93.75 | 59.77 |
| 70. | 31 mai 2022 | 0.99% | 0.01% | 0.39 | 0.78 | 0.55 |
| 71. | 30 juin 2022 | -9.60% | -8.39% | 125.67 | 86.09 | 104.02 |
| Total (Σ): | 5,326.54 | 1,437.21 | 2,230.11 | |||
Tout afficher
VariancePH = Σ(RPH,t–RPH)2 ÷ (71 – 1)
= 5,326.54 ÷ (71 – 1)
= 76.09
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,437.21 ÷ (71 – 1)
= 20.53
CovariancePH, S&P 500 = Σ(RPH,t–RPH)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,230.11 ÷ (71 – 1)
= 31.86
Estimation systématique des risques (β)
| VariancePH | 76.09 |
| VarianceS&P 500 | 20.53 |
| CovariancePH, S&P 500 | 31.86 |
| Coefficient de corrélationPH, S&P 5001 | 0.81 |
| βPH2 | 1.55 |
| αPH3 | 0.24% |
Calculs
1 Coefficient de corrélationPH, S&P 500
= CovariancePH, S&P 500 ÷ (Écart typePH × Écart typeS&P 500)
= 31.86 ÷ (8.72% × 4.53%)
= 0.81
2 βPH
= CovariancePH, S&P 500 ÷ VarianceS&P 500
= 31.86 ÷ 20.53
= 1.55
3 αPH
= MoyennePH – βPH × MoyenneS&P 500
= 1.61% – 1.55 × 0.89%
= 0.24%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.91% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 14.84% |
| Risque systématique lié à Parker actions ordinaires | βPH | 1.55 |
| Taux de rendement attendu des actions ordinaires de Parker3 | E(RPH) | 20.32% |
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(RPH) = RF + βPH [E(RM) – RF]
= 4.91% + 1.55 [14.84% – 4.91%]
= 20.32%