Modèle d’évaluation des immobilisations (CAPM)
Le modèle d’évaluation des immobilisations (MEDAF) indique quel devrait être le taux de rendement attendu ou requis sur les actifs risqués comme les actions ordinaires de Nike.
Taux de rendement
Nike Inc., taux de rendement mensuels
| Nike Inc. (NKE) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixNKE,t1 | DividendeNKE,t1 | RNKE,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 30 juin 2017 | $59.00 | 2,423.41 | ||||
| 1. | 31 juil. 2017 | $59.05 | 0.08% | 2,470.30 | 1.93% | |
| 2. | 31 août 2017 | $52.81 | $0.18 | -10.26% | 2,471.65 | 0.05% |
| 3. | 30 sept. 2017 | $51.85 | -1.82% | 2,519.36 | 1.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 avr. 2023 | $126.72 | 3.33% | 4,169.48 | 1.46% | |
| 71. | 31 mai 2023 | $105.26 | -16.93% | 4,179.83 | 0.25% | |
| Moyenne (R): | 1.25% | 0.90% | ||||
| Écart type: | 8.33% | 5.03% | ||||
| Nike Inc. (NKE) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixNKE,t1 | DividendeNKE,t1 | RNKE,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 30 juin 2017 | $59.00 | 2,423.41 | ||||
| 1. | 31 juil. 2017 | $59.05 | 0.08% | 2,470.30 | 1.93% | |
| 2. | 31 août 2017 | $52.81 | $0.18 | -10.26% | 2,471.65 | 0.05% |
| 3. | 30 sept. 2017 | $51.85 | -1.82% | 2,519.36 | 1.93% | |
| 4. | 31 oct. 2017 | $54.99 | 6.06% | 2,575.26 | 2.22% | |
| 5. | 30 nov. 2017 | $60.42 | 9.87% | 2,647.58 | 2.81% | |
| 6. | 31 déc. 2017 | $62.55 | $0.20 | 3.86% | 2,673.61 | 0.98% |
| 7. | 31 janv. 2018 | $68.22 | 9.06% | 2,823.81 | 5.62% | |
| 8. | 28 févr. 2018 | $67.03 | -1.74% | 2,713.83 | -3.89% | |
| 9. | 31 mars 2018 | $66.44 | $0.20 | -0.58% | 2,640.87 | -2.69% |
| 10. | 30 avr. 2018 | $68.39 | 2.93% | 2,648.05 | 0.27% | |
| 11. | 31 mai 2018 | $71.80 | 4.99% | 2,705.27 | 2.16% | |
| 12. | 30 juin 2018 | $79.68 | $0.20 | 11.25% | 2,718.37 | 0.48% |
| 13. | 31 juil. 2018 | $76.91 | -3.48% | 2,816.29 | 3.60% | |
| 14. | 31 août 2018 | $82.20 | $0.20 | 7.14% | 2,901.52 | 3.03% |
| 15. | 30 sept. 2018 | $84.72 | 3.07% | 2,913.98 | 0.43% | |
| 16. | 31 oct. 2018 | $75.04 | -11.43% | 2,711.74 | -6.94% | |
| 17. | 30 nov. 2018 | $75.12 | $0.22 | 0.40% | 2,760.17 | 1.79% |
| 18. | 31 déc. 2018 | $74.14 | -1.30% | 2,506.85 | -9.18% | |
| 19. | 31 janv. 2019 | $81.88 | 10.44% | 2,704.10 | 7.87% | |
| 20. | 28 févr. 2019 | $85.73 | 4.70% | 2,784.49 | 2.97% | |
| 21. | 31 mars 2019 | $84.21 | $0.22 | -1.52% | 2,834.40 | 1.79% |
| 22. | 30 avr. 2019 | $87.83 | 4.30% | 2,945.83 | 3.93% | |
| 23. | 31 mai 2019 | $77.14 | $0.22 | -11.92% | 2,752.06 | -6.58% |
| 24. | 30 juin 2019 | $83.95 | 8.83% | 2,941.76 | 6.89% | |
| 25. | 31 juil. 2019 | $86.03 | 2.48% | 2,980.38 | 1.31% | |
| 26. | 31 août 2019 | $84.50 | $0.22 | -1.52% | 2,926.46 | -1.81% |
| 27. | 30 sept. 2019 | $93.92 | 11.15% | 2,976.74 | 1.72% | |
| 28. | 31 oct. 2019 | $89.55 | -4.65% | 3,037.56 | 2.04% | |
| 29. | 30 nov. 2019 | $93.49 | $0.245 | 4.67% | 3,140.98 | 3.40% |
| 30. | 31 déc. 2019 | $101.31 | 8.36% | 3,230.78 | 2.86% | |
| 31. | 31 janv. 2020 | $96.30 | -4.95% | 3,225.52 | -0.16% | |
| 32. | 29 févr. 2020 | $89.38 | $0.245 | -6.93% | 2,954.22 | -8.41% |
| 33. | 31 mars 2020 | $82.74 | -7.43% | 2,584.59 | -12.51% | |
| 34. | 30 avr. 2020 | $87.18 | 5.37% | 2,912.43 | 12.68% | |
| 35. | 31 mai 2020 | $98.58 | $0.245 | 13.36% | 3,044.31 | 4.53% |
| 36. | 30 juin 2020 | $98.05 | -0.54% | 3,100.29 | 1.84% | |
| 37. | 31 juil. 2020 | $97.61 | -0.45% | 3,271.12 | 5.51% | |
| 38. | 31 août 2020 | $111.89 | $0.245 | 14.88% | 3,500.31 | 7.01% |
| 39. | 30 sept. 2020 | $125.54 | 12.20% | 3,363.00 | -3.92% | |
| 40. | 31 oct. 2020 | $120.08 | -4.35% | 3,269.96 | -2.77% | |
| 41. | 30 nov. 2020 | $134.70 | 12.18% | 3,621.63 | 10.75% | |
| 42. | 31 déc. 2020 | $141.47 | $0.275 | 5.23% | 3,756.07 | 3.71% |
| 43. | 31 janv. 2021 | $133.59 | -5.57% | 3,714.24 | -1.11% | |
| 44. | 28 févr. 2021 | $134.78 | $0.275 | 1.10% | 3,811.15 | 2.61% |
| 45. | 31 mars 2021 | $132.89 | -1.40% | 3,972.89 | 4.24% | |
| 46. | 30 avr. 2021 | $132.62 | -0.20% | 4,181.17 | 5.24% | |
| 47. | 31 mai 2021 | $136.46 | $0.275 | 3.10% | 4,204.11 | 0.55% |
| 48. | 30 juin 2021 | $154.49 | 13.21% | 4,297.50 | 2.22% | |
| 49. | 31 juil. 2021 | $167.51 | 8.43% | 4,395.26 | 2.27% | |
| 50. | 31 août 2021 | $164.74 | $0.275 | -1.49% | 4,522.68 | 2.90% |
| 51. | 30 sept. 2021 | $145.23 | -11.84% | 4,307.54 | -4.76% | |
| 52. | 31 oct. 2021 | $167.29 | 15.19% | 4,605.38 | 6.91% | |
| 53. | 30 nov. 2021 | $169.24 | 1.17% | 4,567.00 | -0.83% | |
| 54. | 31 déc. 2021 | $166.67 | $0.305 | -1.34% | 4,766.18 | 4.36% |
| 55. | 31 janv. 2022 | $148.07 | -11.16% | 4,515.55 | -5.26% | |
| 56. | 28 févr. 2022 | $136.55 | -7.78% | 4,373.94 | -3.14% | |
| 57. | 31 mars 2022 | $134.56 | $0.305 | -1.23% | 4,530.41 | 3.58% |
| 58. | 30 avr. 2022 | $124.70 | -7.33% | 4,131.93 | -8.80% | |
| 59. | 31 mai 2022 | $118.85 | -4.69% | 4,132.15 | 0.01% | |
| 60. | 30 juin 2022 | $102.20 | $0.305 | -13.75% | 3,785.38 | -8.39% |
| 61. | 31 juil. 2022 | $114.92 | 12.45% | 4,130.29 | 9.11% | |
| 62. | 31 août 2022 | $106.45 | -7.37% | 3,955.00 | -4.24% | |
| 63. | 30 sept. 2022 | $83.12 | $0.305 | -21.63% | 3,585.62 | -9.34% |
| 64. | 31 oct. 2022 | $92.68 | 11.50% | 3,871.98 | 7.99% | |
| 65. | 30 nov. 2022 | $109.69 | 18.35% | 4,080.11 | 5.38% | |
| 66. | 31 déc. 2022 | $117.01 | $0.34 | 6.98% | 3,839.50 | -5.90% |
| 67. | 31 janv. 2023 | $127.33 | 8.82% | 4,076.60 | 6.18% | |
| 68. | 28 févr. 2023 | $118.79 | -6.71% | 3,970.15 | -2.61% | |
| 69. | 31 mars 2023 | $122.64 | $0.34 | 3.53% | 4,109.31 | 3.51% |
| 70. | 30 avr. 2023 | $126.72 | 3.33% | 4,169.48 | 1.46% | |
| 71. | 31 mai 2023 | $105.26 | -16.93% | 4,179.83 | 0.25% | |
| Moyenne (R): | 1.25% | 0.90% | ||||
| Écart type: | 8.33% | 5.03% | ||||
Afficher tout
1 Données en $ US par action ordinaire, ajustées pour tenir compte des fractionnements et des dividendes en actions.
2 Taux de rendement des actions ordinaires de NKE 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
Nike Inc., calcul de la variance et de la covariance des rendements
| t | Date | RNKE,t | RS&P 500,t | (RNKE,t–RNKE)2 | (RS&P 500,t–RS&P 500)2 | (RNKE,t–RNKE)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 juil. 2017 | 0.08% | 1.93% | 1.36 | 1.08 | -1.21 |
| 2. | 31 août 2017 | -10.26% | 0.05% | 132.52 | 0.71 | 9.69 |
| 3. | 30 sept. 2017 | -1.82% | 1.93% | 9.41 | 1.07 | -3.17 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 avr. 2023 | 3.33% | 1.46% | 4.32 | 0.32 | 1.18 |
| 71. | 31 mai 2023 | -16.93% | 0.25% | 330.67 | 0.42 | 11.79 |
| Total (Σ): | 4,860.93 | 1,772.87 | 1,983.24 | |||
| t | Date | RNKE,t | RS&P 500,t | (RNKE,t–RNKE)2 | (RS&P 500,t–RS&P 500)2 | (RNKE,t–RNKE)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 juil. 2017 | 0.08% | 1.93% | 1.36 | 1.08 | -1.21 |
| 2. | 31 août 2017 | -10.26% | 0.05% | 132.52 | 0.71 | 9.69 |
| 3. | 30 sept. 2017 | -1.82% | 1.93% | 9.41 | 1.07 | -3.17 |
| 4. | 31 oct. 2017 | 6.06% | 2.22% | 23.10 | 1.75 | 6.36 |
| 5. | 30 nov. 2017 | 9.87% | 2.81% | 74.39 | 3.65 | 16.49 |
| 6. | 31 déc. 2017 | 3.86% | 0.98% | 6.80 | 0.01 | 0.23 |
| 7. | 31 janv. 2018 | 9.06% | 5.62% | 61.08 | 22.29 | 36.90 |
| 8. | 28 févr. 2018 | -1.74% | -3.89% | 8.96 | 22.96 | 14.34 |
| 9. | 31 mars 2018 | -0.58% | -2.69% | 3.35 | 12.85 | 6.57 |
| 10. | 30 avr. 2018 | 2.93% | 0.27% | 2.84 | 0.39 | -1.05 |
| 11. | 31 mai 2018 | 4.99% | 2.16% | 13.96 | 1.60 | 4.72 |
| 12. | 30 juin 2018 | 11.25% | 0.48% | 100.08 | 0.17 | -4.13 |
| 13. | 31 juil. 2018 | -3.48% | 3.60% | 22.33 | 7.32 | -12.79 |
| 14. | 31 août 2018 | 7.14% | 3.03% | 34.68 | 4.54 | 12.54 |
| 15. | 30 sept. 2018 | 3.07% | 0.43% | 3.30 | 0.22 | -0.85 |
| 16. | 31 oct. 2018 | -11.43% | -6.94% | 160.66 | 61.42 | 99.34 |
| 17. | 30 nov. 2018 | 0.40% | 1.79% | 0.72 | 0.79 | -0.76 |
| 18. | 31 déc. 2018 | -1.30% | -9.18% | 6.52 | 101.49 | 25.73 |
| 19. | 31 janv. 2019 | 10.44% | 7.87% | 84.46 | 48.61 | 64.07 |
| 20. | 28 févr. 2019 | 4.70% | 2.97% | 11.92 | 4.31 | 7.17 |
| 21. | 31 mars 2019 | -1.52% | 1.79% | 7.65 | 0.80 | -2.48 |
| 22. | 30 avr. 2019 | 4.30% | 3.93% | 9.30 | 9.21 | 9.25 |
| 23. | 31 mai 2019 | -11.92% | -6.58% | 173.45 | 55.87 | 98.44 |
| 24. | 30 juin 2019 | 8.83% | 6.89% | 57.44 | 35.96 | 45.44 |
| 25. | 31 juil. 2019 | 2.48% | 1.31% | 1.51 | 0.17 | 0.51 |
| 26. | 31 août 2019 | -1.52% | -1.81% | 7.68 | 7.32 | 7.50 |
| 27. | 30 sept. 2019 | 11.15% | 1.72% | 97.98 | 0.67 | 8.13 |
| 28. | 31 oct. 2019 | -4.65% | 2.04% | 34.84 | 1.31 | -6.77 |
| 29. | 30 nov. 2019 | 4.67% | 3.40% | 11.72 | 6.29 | 8.59 |
| 30. | 31 déc. 2019 | 8.36% | 2.86% | 50.62 | 3.85 | 13.96 |
| 31. | 31 janv. 2020 | -4.95% | -0.16% | 38.37 | 1.12 | 6.56 |
| 32. | 29 févr. 2020 | -6.93% | -8.41% | 66.93 | 86.63 | 76.15 |
| 33. | 31 mars 2020 | -7.43% | -12.51% | 75.31 | 179.79 | 116.36 |
| 34. | 30 avr. 2020 | 5.37% | 12.68% | 16.95 | 138.95 | 48.53 |
| 35. | 31 mai 2020 | 13.36% | 4.53% | 146.60 | 13.19 | 43.97 |
| 36. | 30 juin 2020 | -0.54% | 1.84% | 3.19 | 0.89 | -1.68 |
| 37. | 31 juil. 2020 | -0.45% | 5.51% | 2.88 | 21.28 | -7.83 |
| 38. | 31 août 2020 | 14.88% | 7.01% | 185.81 | 37.33 | 83.28 |
| 39. | 30 sept. 2020 | 12.20% | -3.92% | 119.90 | 23.23 | -52.77 |
| 40. | 31 oct. 2020 | -4.35% | -2.77% | 31.34 | 13.42 | 20.51 |
| 41. | 30 nov. 2020 | 12.18% | 10.75% | 119.37 | 97.18 | 107.71 |
| 42. | 31 déc. 2020 | 5.23% | 3.71% | 15.85 | 7.93 | 11.21 |
| 43. | 31 janv. 2021 | -5.57% | -1.11% | 46.51 | 4.04 | 13.71 |
| 44. | 28 févr. 2021 | 1.10% | 2.61% | 0.02 | 2.93 | -0.26 |
| 45. | 31 mars 2021 | -1.40% | 4.24% | 7.03 | 11.20 | -8.88 |
| 46. | 30 avr. 2021 | -0.20% | 5.24% | 2.11 | 18.89 | -6.31 |
| 47. | 31 mai 2021 | 3.10% | 0.55% | 3.44 | 0.12 | -0.64 |
| 48. | 30 juin 2021 | 13.21% | 2.22% | 143.12 | 1.75 | 15.85 |
| 49. | 31 juil. 2021 | 8.43% | 2.27% | 51.53 | 1.90 | 9.89 |
| 50. | 31 août 2021 | -1.49% | 2.90% | 7.50 | 4.01 | -5.48 |
| 51. | 30 sept. 2021 | -11.84% | -4.76% | 171.41 | 31.96 | 74.02 |
| 52. | 31 oct. 2021 | 15.19% | 6.91% | 194.33 | 36.21 | 83.89 |
| 53. | 30 nov. 2021 | 1.17% | -0.83% | 0.01 | 2.99 | 0.14 |
| 54. | 31 déc. 2021 | -1.34% | 4.36% | 6.70 | 12.00 | -8.97 |
| 55. | 31 janv. 2022 | -11.16% | -5.26% | 153.99 | 37.89 | 76.38 |
| 56. | 28 févr. 2022 | -7.78% | -3.14% | 81.53 | 16.26 | 36.41 |
| 57. | 31 mars 2022 | -1.23% | 3.58% | 6.17 | 7.19 | -6.66 |
| 58. | 30 avr. 2022 | -7.33% | -8.80% | 73.56 | 93.94 | 83.13 |
| 59. | 31 mai 2022 | -4.69% | 0.01% | 35.29 | 0.79 | 5.30 |
| 60. | 30 juin 2022 | -13.75% | -8.39% | 225.06 | 86.28 | 139.35 |
| 61. | 31 juil. 2022 | 12.45% | 9.11% | 125.37 | 67.49 | 91.98 |
| 62. | 31 août 2022 | -7.37% | -4.24% | 74.30 | 26.43 | 44.31 |
| 63. | 30 sept. 2022 | -21.63% | -9.34% | 523.46 | 104.78 | 234.20 |
| 64. | 31 oct. 2022 | 11.50% | 7.99% | 105.10 | 50.26 | 72.68 |
| 65. | 30 nov. 2022 | 18.35% | 5.38% | 292.55 | 20.06 | 76.60 |
| 66. | 31 déc. 2022 | 6.98% | -5.90% | 32.88 | 46.16 | -38.95 |
| 67. | 31 janv. 2023 | 8.82% | 6.18% | 57.31 | 27.86 | 39.96 |
| 68. | 28 févr. 2023 | -6.71% | -2.61% | 63.30 | 12.31 | 27.91 |
| 69. | 31 mars 2023 | 3.53% | 3.51% | 5.19 | 6.80 | 5.94 |
| 70. | 30 avr. 2023 | 3.33% | 1.46% | 4.32 | 0.32 | 1.18 |
| 71. | 31 mai 2023 | -16.93% | 0.25% | 330.67 | 0.42 | 11.79 |
| Total (Σ): | 4,860.93 | 1,772.87 | 1,983.24 | |||
Afficher tout
VarianceNKE = Σ(RNKE,t–RNKE)2 ÷ (71 – 1)
= 4,860.93 ÷ (71 – 1)
= 69.44
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,772.87 ÷ (71 – 1)
= 25.33
CovarianceNKE, S&P 500 = Σ(RNKE,t–RNKE)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,983.24 ÷ (71 – 1)
= 28.33
Estimation systématique des risques (β)
| VarianceNKE | 69.44 |
| VarianceS&P 500 | 25.33 |
| CovarianceNKE, S&P 500 | 28.33 |
| Coefficient de corrélationNKE, S&P 5001 | 0.68 |
| βNKE2 | 1.12 |
| αNKE3 | 0.25% |
Calculs
1 Coefficient de corrélationNKE, S&P 500
= CovarianceNKE, S&P 500 ÷ (Écart typeNKE × Écart typeS&P 500)
= 28.33 ÷ (8.33% × 5.03%)
= 0.68
2 βNKE
= CovarianceNKE, S&P 500 ÷ VarianceS&P 500
= 28.33 ÷ 25.33
= 1.12
3 αNKE
= MoyenneNKE – βNKE × MoyenneS&P 500
= 1.25% – 1.12 × 0.90%
= 0.25%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de l’indice composé LT Treasury1 | RF | 4.66% |
| Taux de rendement attendu sur le portefeuille de marché2 | E(RM) | 13.57% |
| Risque systématique d’ Nike actions ordinaires | βNKE | 1.12 |
| Taux de rendement attendu sur les actions ordinaires de Nike3 | E(RNKE) | 14.63% |
1 Moyenne non pondérée des rendements acheteurs de toutes les obligations du Trésor américain à coupon fixe en circulation qui ne sont ni exigibles ni exigibles depuis moins de 10 ans (approximation du taux de rendement sans risque).
3 E(RNKE) = RF + βNKE [E(RM) – RF]
= 4.66% + 1.12 [13.57% – 4.66%]
= 14.63%