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 Salesforce.
Taux de rendement
Salesforce Inc., taux de rendement mensuels
| Salesforce Inc. (CRM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixCRM,t1 | DividendeCRM,t1 | RCRM,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 28 févr. 2017 | $81.35 | 2,363.64 | ||||
| 1. | 31 mars 2017 | $82.49 | 1.40% | 2,362.72 | -0.04% | |
| 2. | 30 avr. 2017 | $86.12 | 4.40% | 2,384.20 | 0.91% | |
| 3. | 31 mai 2017 | $89.64 | 4.09% | 2,411.80 | 1.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 déc. 2022 | $132.59 | -17.26% | 3,839.50 | -5.90% | |
| 71. | 31 janv. 2023 | $167.97 | 26.68% | 4,076.60 | 6.18% | |
| Moyenne (R): | 1.44% | 0.90% | ||||
| Écart type: | 9.39% | 5.01% | ||||
| Salesforce Inc. (CRM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixCRM,t1 | DividendeCRM,t1 | RCRM,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 28 févr. 2017 | $81.35 | 2,363.64 | ||||
| 1. | 31 mars 2017 | $82.49 | 1.40% | 2,362.72 | -0.04% | |
| 2. | 30 avr. 2017 | $86.12 | 4.40% | 2,384.20 | 0.91% | |
| 3. | 31 mai 2017 | $89.64 | 4.09% | 2,411.80 | 1.16% | |
| 4. | 30 juin 2017 | $86.60 | -3.39% | 2,423.41 | 0.48% | |
| 5. | 31 juil. 2017 | $90.80 | 4.85% | 2,470.30 | 1.93% | |
| 6. | 31 août 2017 | $95.49 | 5.17% | 2,471.65 | 0.05% | |
| 7. | 30 sept. 2017 | $93.42 | -2.17% | 2,519.36 | 1.93% | |
| 8. | 31 oct. 2017 | $102.34 | 9.55% | 2,575.26 | 2.22% | |
| 9. | 30 nov. 2017 | $104.32 | 1.93% | 2,647.58 | 2.81% | |
| 10. | 31 déc. 2017 | $102.23 | -2.00% | 2,673.61 | 0.98% | |
| 11. | 31 janv. 2018 | $113.91 | 11.43% | 2,823.81 | 5.62% | |
| 12. | 28 févr. 2018 | $116.25 | 2.05% | 2,713.83 | -3.89% | |
| 13. | 31 mars 2018 | $116.30 | 0.04% | 2,640.87 | -2.69% | |
| 14. | 30 avr. 2018 | $120.99 | 4.03% | 2,648.05 | 0.27% | |
| 15. | 31 mai 2018 | $129.33 | 6.89% | 2,705.27 | 2.16% | |
| 16. | 30 juin 2018 | $136.40 | 5.47% | 2,718.37 | 0.48% | |
| 17. | 31 juil. 2018 | $137.15 | 0.55% | 2,816.29 | 3.60% | |
| 18. | 31 août 2018 | $152.68 | 11.32% | 2,901.52 | 3.03% | |
| 19. | 30 sept. 2018 | $159.03 | 4.16% | 2,913.98 | 0.43% | |
| 20. | 31 oct. 2018 | $137.24 | -13.70% | 2,711.74 | -6.94% | |
| 21. | 30 nov. 2018 | $142.76 | 4.02% | 2,760.17 | 1.79% | |
| 22. | 31 déc. 2018 | $136.97 | -4.06% | 2,506.85 | -9.18% | |
| 23. | 31 janv. 2019 | $151.97 | 10.95% | 2,704.10 | 7.87% | |
| 24. | 28 févr. 2019 | $163.65 | 7.69% | 2,784.49 | 2.97% | |
| 25. | 31 mars 2019 | $158.37 | -3.23% | 2,834.40 | 1.79% | |
| 26. | 30 avr. 2019 | $165.35 | 4.41% | 2,945.83 | 3.93% | |
| 27. | 31 mai 2019 | $151.41 | -8.43% | 2,752.06 | -6.58% | |
| 28. | 30 juin 2019 | $151.73 | 0.21% | 2,941.76 | 6.89% | |
| 29. | 31 juil. 2019 | $154.50 | 1.83% | 2,980.38 | 1.31% | |
| 30. | 31 août 2019 | $156.07 | 1.02% | 2,926.46 | -1.81% | |
| 31. | 30 sept. 2019 | $148.44 | -4.89% | 2,976.74 | 1.72% | |
| 32. | 31 oct. 2019 | $156.49 | 5.42% | 3,037.56 | 2.04% | |
| 33. | 30 nov. 2019 | $162.89 | 4.09% | 3,140.98 | 3.40% | |
| 34. | 31 déc. 2019 | $162.64 | -0.15% | 3,230.78 | 2.86% | |
| 35. | 31 janv. 2020 | $182.31 | 12.09% | 3,225.52 | -0.16% | |
| 36. | 29 févr. 2020 | $170.40 | -6.53% | 2,954.22 | -8.41% | |
| 37. | 31 mars 2020 | $143.98 | -15.50% | 2,584.59 | -12.51% | |
| 38. | 30 avr. 2020 | $161.95 | 12.48% | 2,912.43 | 12.68% | |
| 39. | 31 mai 2020 | $174.79 | 7.93% | 3,044.31 | 4.53% | |
| 40. | 30 juin 2020 | $187.33 | 7.17% | 3,100.29 | 1.84% | |
| 41. | 31 juil. 2020 | $194.85 | 4.01% | 3,271.12 | 5.51% | |
| 42. | 31 août 2020 | $272.65 | 39.93% | 3,500.31 | 7.01% | |
| 43. | 30 sept. 2020 | $251.32 | -7.82% | 3,363.00 | -3.92% | |
| 44. | 31 oct. 2020 | $232.27 | -7.58% | 3,269.96 | -2.77% | |
| 45. | 30 nov. 2020 | $245.80 | 5.83% | 3,621.63 | 10.75% | |
| 46. | 31 déc. 2020 | $222.53 | -9.47% | 3,756.07 | 3.71% | |
| 47. | 31 janv. 2021 | $225.56 | 1.36% | 3,714.24 | -1.11% | |
| 48. | 28 févr. 2021 | $216.50 | -4.02% | 3,811.15 | 2.61% | |
| 49. | 31 mars 2021 | $211.87 | -2.14% | 3,972.89 | 4.24% | |
| 50. | 30 avr. 2021 | $230.32 | 8.71% | 4,181.17 | 5.24% | |
| 51. | 31 mai 2021 | $238.10 | 3.38% | 4,204.11 | 0.55% | |
| 52. | 30 juin 2021 | $244.27 | 2.59% | 4,297.50 | 2.22% | |
| 53. | 31 juil. 2021 | $241.93 | -0.96% | 4,395.26 | 2.27% | |
| 54. | 31 août 2021 | $265.27 | 9.65% | 4,522.68 | 2.90% | |
| 55. | 30 sept. 2021 | $271.22 | 2.24% | 4,307.54 | -4.76% | |
| 56. | 31 oct. 2021 | $299.69 | 10.50% | 4,605.38 | 6.91% | |
| 57. | 30 nov. 2021 | $284.96 | -4.92% | 4,567.00 | -0.83% | |
| 58. | 31 déc. 2021 | $254.13 | -10.82% | 4,766.18 | 4.36% | |
| 59. | 31 janv. 2022 | $232.63 | -8.46% | 4,515.55 | -5.26% | |
| 60. | 28 févr. 2022 | $210.53 | -9.50% | 4,373.94 | -3.14% | |
| 61. | 31 mars 2022 | $212.32 | 0.85% | 4,530.41 | 3.58% | |
| 62. | 30 avr. 2022 | $175.94 | -17.13% | 4,131.93 | -8.80% | |
| 63. | 31 mai 2022 | $160.24 | -8.92% | 4,132.15 | 0.01% | |
| 64. | 30 juin 2022 | $165.04 | 3.00% | 3,785.38 | -8.39% | |
| 65. | 31 juil. 2022 | $184.02 | 11.50% | 4,130.29 | 9.11% | |
| 66. | 31 août 2022 | $156.12 | -15.16% | 3,955.00 | -4.24% | |
| 67. | 30 sept. 2022 | $143.84 | -7.87% | 3,585.62 | -9.34% | |
| 68. | 31 oct. 2022 | $162.59 | 13.04% | 3,871.98 | 7.99% | |
| 69. | 30 nov. 2022 | $160.25 | -1.44% | 4,080.11 | 5.38% | |
| 70. | 31 déc. 2022 | $132.59 | -17.26% | 3,839.50 | -5.90% | |
| 71. | 31 janv. 2023 | $167.97 | 26.68% | 4,076.60 | 6.18% | |
| Moyenne (R): | 1.44% | 0.90% | ||||
| Écart type: | 9.39% | 5.01% | ||||
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 CRM 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
Salesforce Inc., calcul de la variance et de la covariance des rendements
| t | Date | RCRM,t | RS&P 500,t | (RCRM,t–RCRM)2 | (RS&P 500,t–RS&P 500)2 | (RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mars 2017 | 1.40% | -0.04% | 0.00 | 0.87 | 0.04 |
| 2. | 30 avr. 2017 | 4.40% | 0.91% | 8.75 | 0.00 | 0.04 |
| 3. | 31 mai 2017 | 4.09% | 1.16% | 7.00 | 0.07 | 0.69 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 déc. 2022 | -17.26% | -5.90% | 349.79 | 46.14 | 127.04 |
| 71. | 31 janv. 2023 | 26.68% | 6.18% | 637.15 | 27.88 | 133.28 |
| Total (Σ): | 6,174.35 | 1,754.14 | 2,112.55 | |||
| t | Date | RCRM,t | RS&P 500,t | (RCRM,t–RCRM)2 | (RS&P 500,t–RS&P 500)2 | (RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mars 2017 | 1.40% | -0.04% | 0.00 | 0.87 | 0.04 |
| 2. | 30 avr. 2017 | 4.40% | 0.91% | 8.75 | 0.00 | 0.04 |
| 3. | 31 mai 2017 | 4.09% | 1.16% | 7.00 | 0.07 | 0.69 |
| 4. | 30 juin 2017 | -3.39% | 0.48% | 23.36 | 0.17 | 2.00 |
| 5. | 31 juil. 2017 | 4.85% | 1.93% | 11.61 | 1.08 | 3.54 |
| 6. | 31 août 2017 | 5.17% | 0.05% | 13.86 | 0.71 | -3.13 |
| 7. | 30 sept. 2017 | -2.17% | 1.93% | 13.03 | 1.07 | -3.74 |
| 8. | 31 oct. 2017 | 9.55% | 2.22% | 65.71 | 1.75 | 10.73 |
| 9. | 30 nov. 2017 | 1.93% | 2.81% | 0.24 | 3.66 | 0.94 |
| 10. | 31 déc. 2017 | -2.00% | 0.98% | 11.87 | 0.01 | -0.30 |
| 11. | 31 janv. 2018 | 11.43% | 5.62% | 99.66 | 22.30 | 47.15 |
| 12. | 28 févr. 2018 | 2.05% | -3.89% | 0.37 | 22.94 | -2.93 |
| 13. | 31 mars 2018 | 0.04% | -2.69% | 1.96 | 12.84 | 5.01 |
| 14. | 30 avr. 2018 | 4.03% | 0.27% | 6.71 | 0.39 | -1.61 |
| 15. | 31 mai 2018 | 6.89% | 2.16% | 29.71 | 1.60 | 6.90 |
| 16. | 30 juin 2018 | 5.47% | 0.48% | 16.20 | 0.17 | -1.65 |
| 17. | 31 juil. 2018 | 0.55% | 3.60% | 0.80 | 7.33 | -2.42 |
| 18. | 31 août 2018 | 11.32% | 3.03% | 97.64 | 4.54 | 21.06 |
| 19. | 30 sept. 2018 | 4.16% | 0.43% | 7.38 | 0.22 | -1.27 |
| 20. | 31 oct. 2018 | -13.70% | -6.94% | 229.34 | 61.40 | 118.66 |
| 21. | 30 nov. 2018 | 4.02% | 1.79% | 6.66 | 0.79 | 2.30 |
| 22. | 31 déc. 2018 | -4.06% | -9.18% | 30.23 | 101.46 | 55.38 |
| 23. | 31 janv. 2019 | 10.95% | 7.87% | 90.43 | 48.63 | 66.31 |
| 24. | 28 févr. 2019 | 7.69% | 2.97% | 38.98 | 4.32 | 12.97 |
| 25. | 31 mars 2019 | -3.23% | 1.79% | 21.79 | 0.80 | -4.19 |
| 26. | 30 avr. 2019 | 4.41% | 3.93% | 8.79 | 9.22 | 9.00 |
| 27. | 31 mai 2019 | -8.43% | -6.58% | 97.47 | 55.85 | 73.78 |
| 28. | 30 juin 2019 | 0.21% | 6.89% | 1.51 | 35.97 | -7.38 |
| 29. | 31 juil. 2019 | 1.83% | 1.31% | 0.15 | 0.17 | 0.16 |
| 30. | 31 août 2019 | 1.02% | -1.81% | 0.18 | 7.31 | 1.15 |
| 31. | 30 sept. 2019 | -4.89% | 1.72% | 40.08 | 0.68 | -5.21 |
| 32. | 31 oct. 2019 | 5.42% | 2.04% | 15.85 | 1.32 | 4.57 |
| 33. | 30 nov. 2019 | 4.09% | 3.40% | 7.01 | 6.30 | 6.64 |
| 34. | 31 déc. 2019 | -0.15% | 2.86% | 2.55 | 3.86 | -3.13 |
| 35. | 31 janv. 2020 | 12.09% | -0.16% | 113.47 | 1.12 | -11.27 |
| 36. | 29 févr. 2020 | -6.53% | -8.41% | 63.60 | 86.61 | 74.22 |
| 37. | 31 mars 2020 | -15.50% | -12.51% | 287.19 | 179.75 | 227.21 |
| 38. | 30 avr. 2020 | 12.48% | 12.68% | 121.86 | 138.98 | 130.14 |
| 39. | 31 mai 2020 | 7.93% | 4.53% | 42.07 | 13.20 | 23.56 |
| 40. | 30 juin 2020 | 7.17% | 1.84% | 32.86 | 0.89 | 5.41 |
| 41. | 31 juil. 2020 | 4.01% | 5.51% | 6.62 | 21.30 | 11.87 |
| 42. | 31 août 2020 | 39.93% | 7.01% | 1,481.18 | 37.35 | 235.20 |
| 43. | 30 sept. 2020 | -7.82% | -3.92% | 85.84 | 23.21 | 44.64 |
| 44. | 31 oct. 2020 | -7.58% | -2.77% | 81.40 | 13.41 | 33.04 |
| 45. | 30 nov. 2020 | 5.83% | 10.75% | 19.21 | 97.21 | 43.21 |
| 46. | 31 déc. 2020 | -9.47% | 3.71% | 119.01 | 7.93 | -30.73 |
| 47. | 31 janv. 2021 | 1.36% | -1.11% | 0.01 | 4.04 | 0.16 |
| 48. | 28 févr. 2021 | -4.02% | 2.61% | 29.80 | 2.94 | -9.36 |
| 49. | 31 mars 2021 | -2.14% | 4.24% | 12.82 | 11.21 | -11.99 |
| 50. | 30 avr. 2021 | 8.71% | 5.24% | 52.80 | 18.90 | 31.59 |
| 51. | 31 mai 2021 | 3.38% | 0.55% | 3.75 | 0.12 | -0.67 |
| 52. | 30 juin 2021 | 2.59% | 2.22% | 1.32 | 1.76 | 1.52 |
| 53. | 31 juil. 2021 | -0.96% | 2.27% | 5.76 | 1.90 | -3.31 |
| 54. | 31 août 2021 | 9.65% | 2.90% | 67.33 | 4.02 | 16.44 |
| 55. | 30 sept. 2021 | 2.24% | -4.76% | 0.64 | 31.95 | -4.53 |
| 56. | 31 oct. 2021 | 10.50% | 6.91% | 81.99 | 36.23 | 54.50 |
| 57. | 30 nov. 2021 | -4.92% | -0.83% | 40.41 | 2.99 | 10.99 |
| 58. | 31 déc. 2021 | -10.82% | 4.36% | 150.33 | 12.01 | -42.50 |
| 59. | 31 janv. 2022 | -8.46% | -5.26% | 98.05 | 37.87 | 60.94 |
| 60. | 28 févr. 2022 | -9.50% | -3.14% | 119.73 | 16.25 | 44.11 |
| 61. | 31 mars 2022 | 0.85% | 3.58% | 0.35 | 7.19 | -1.59 |
| 62. | 30 avr. 2022 | -17.13% | -8.80% | 345.09 | 93.91 | 180.02 |
| 63. | 31 mai 2022 | -8.92% | 0.01% | 107.44 | 0.79 | 9.22 |
| 64. | 30 juin 2022 | 3.00% | -8.39% | 2.41 | 86.25 | -14.43 |
| 65. | 31 juil. 2022 | 11.50% | 9.11% | 101.17 | 67.51 | 82.64 |
| 66. | 31 août 2022 | -15.16% | -4.24% | 275.67 | 26.41 | 85.33 |
| 67. | 30 sept. 2022 | -7.87% | -9.34% | 86.63 | 104.75 | 95.26 |
| 68. | 31 oct. 2022 | 13.04% | 7.99% | 134.40 | 50.28 | 82.21 |
| 69. | 30 nov. 2022 | -1.44% | 5.38% | 8.30 | 20.07 | -12.91 |
| 70. | 31 déc. 2022 | -17.26% | -5.90% | 349.79 | 46.14 | 127.04 |
| 71. | 31 janv. 2023 | 26.68% | 6.18% | 637.15 | 27.88 | 133.28 |
| Total (Σ): | 6,174.35 | 1,754.14 | 2,112.55 | |||
Afficher tout
VarianceCRM = Σ(RCRM,t–RCRM)2 ÷ (71 – 1)
= 6,174.35 ÷ (71 – 1)
= 88.21
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,754.14 ÷ (71 – 1)
= 25.06
CovarianceCRM, S&P 500 = Σ(RCRM,t–RCRM)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,112.55 ÷ (71 – 1)
= 30.18
Estimation systématique des risques (β)
| VarianceCRM | 88.21 |
| VarianceS&P 500 | 25.06 |
| CovarianceCRM, S&P 500 | 30.18 |
| Coefficient de corrélationCRM, S&P 5001 | 0.64 |
| βCRM2 | 1.20 |
| αCRM3 | 0.36% |
Calculs
1 Coefficient de corrélationCRM, S&P 500
= CovarianceCRM, S&P 500 ÷ (Écart typeCRM × Écart typeS&P 500)
= 30.18 ÷ (9.39% × 5.01%)
= 0.64
2 βCRM
= CovarianceCRM, S&P 500 ÷ VarianceS&P 500
= 30.18 ÷ 25.06
= 1.20
3 αCRM
= MoyenneCRM – βCRM × MoyenneS&P 500
= 1.44% – 1.20 × 0.90%
= 0.36%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de l’indice composé LT Treasury1 | RF | 4.54% |
| Taux de rendement attendu sur le portefeuille de marché2 | E(RM) | 13.24% |
| Risque systématique d’ Salesforce actions ordinaires | βCRM | 1.20 |
| Taux de rendement attendu des actions ordinaires Salesforce3 | E(RCRM) | 15.02% |
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(RCRM) = RF + βCRM [E(RM) – RF]
= 4.54% + 1.20 [13.24% – 4.54%]
= 15.02%