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 Cummins.
Taux de rendement
Cummins Inc., taux de rendement mensuels
| Cummins Inc. (CMI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixCMI,t1 | DividendeCMI,t1 | RCMI,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2019 | $147.11 | 2,704.10 | ||||
| 1. | 28 févr. 2019 | $154.09 | $1.14 | 5.52% | 2,784.49 | 2.97% |
| 2. | 31 mars 2019 | $157.87 | 2.45% | 2,834.40 | 1.79% | |
| 3. | 30 avr. 2019 | $166.29 | 5.33% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $224.16 | $1.68 | 4.41% | 4,567.80 | 8.92% |
| 59. | 31 déc. 2023 | $239.57 | 6.87% | 4,769.83 | 4.42% | |
| Moyenne (R): | 1.36% | 1.11% | ||||
| Écart type: | 7.89% | 5.31% | ||||
| Cummins Inc. (CMI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixCMI,t1 | DividendeCMI,t1 | RCMI,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2019 | $147.11 | 2,704.10 | ||||
| 1. | 28 févr. 2019 | $154.09 | $1.14 | 5.52% | 2,784.49 | 2.97% |
| 2. | 31 mars 2019 | $157.87 | 2.45% | 2,834.40 | 1.79% | |
| 3. | 30 avr. 2019 | $166.29 | 5.33% | 2,945.83 | 3.93% | |
| 4. | 31 mai 2019 | $150.76 | $1.14 | -8.65% | 2,752.06 | -6.58% |
| 5. | 30 juin 2019 | $171.34 | 13.65% | 2,941.76 | 6.89% | |
| 6. | 31 juil. 2019 | $164.00 | -4.28% | 2,980.38 | 1.31% | |
| 7. | 31 août 2019 | $149.27 | $1.311 | -8.18% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $162.67 | 8.98% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $172.48 | 6.03% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $182.86 | $1.311 | 6.78% | 3,140.98 | 3.40% |
| 11. | 31 déc. 2019 | $178.96 | -2.13% | 3,230.78 | 2.86% | |
| 12. | 31 janv. 2020 | $159.97 | -10.61% | 3,225.52 | -0.16% | |
| 13. | 29 févr. 2020 | $151.29 | $1.311 | -4.61% | 2,954.22 | -8.41% |
| 14. | 31 mars 2020 | $135.32 | -10.56% | 2,584.59 | -12.51% | |
| 15. | 30 avr. 2020 | $163.50 | 20.82% | 2,912.43 | 12.68% | |
| 16. | 31 mai 2020 | $169.60 | $1.311 | 4.53% | 3,044.31 | 4.53% |
| 17. | 30 juin 2020 | $173.26 | 2.16% | 3,100.29 | 1.84% | |
| 18. | 31 juil. 2020 | $193.26 | 11.54% | 3,271.12 | 5.51% | |
| 19. | 31 août 2020 | $207.25 | $1.311 | 7.92% | 3,500.31 | 7.01% |
| 20. | 30 sept. 2020 | $211.16 | 1.89% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $219.89 | 4.13% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $231.17 | $1.35 | 5.74% | 3,621.63 | 10.75% |
| 23. | 31 déc. 2020 | $227.10 | -1.76% | 3,756.07 | 3.71% | |
| 24. | 31 janv. 2021 | $234.42 | 3.22% | 3,714.24 | -1.11% | |
| 25. | 28 févr. 2021 | $253.20 | $1.35 | 8.59% | 3,811.15 | 2.61% |
| 26. | 31 mars 2021 | $259.11 | 2.33% | 3,972.89 | 4.24% | |
| 27. | 30 avr. 2021 | $252.04 | -2.73% | 4,181.17 | 5.24% | |
| 28. | 31 mai 2021 | $257.28 | $1.35 | 2.61% | 4,204.11 | 0.55% |
| 29. | 30 juin 2021 | $243.81 | -5.24% | 4,297.50 | 2.22% | |
| 30. | 31 juil. 2021 | $232.10 | -4.80% | 4,395.26 | 2.27% | |
| 31. | 31 août 2021 | $235.98 | $1.45 | 2.30% | 4,522.68 | 2.90% |
| 32. | 30 sept. 2021 | $224.56 | -4.84% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $239.84 | 6.80% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $209.75 | $1.45 | -11.94% | 4,567.00 | -0.83% |
| 35. | 31 déc. 2021 | $218.14 | 4.00% | 4,766.18 | 4.36% | |
| 36. | 31 janv. 2022 | $220.88 | 1.26% | 4,515.55 | -5.26% | |
| 37. | 28 févr. 2022 | $204.12 | $1.45 | -6.93% | 4,373.94 | -3.14% |
| 38. | 31 mars 2022 | $205.11 | 0.49% | 4,530.41 | 3.58% | |
| 39. | 30 avr. 2022 | $189.19 | -7.76% | 4,131.93 | -8.80% | |
| 40. | 31 mai 2022 | $209.12 | $1.45 | 11.30% | 4,132.15 | 0.01% |
| 41. | 30 juin 2022 | $193.53 | -7.46% | 3,785.38 | -8.39% | |
| 42. | 31 juil. 2022 | $221.31 | 14.35% | 4,130.29 | 9.11% | |
| 43. | 31 août 2022 | $215.37 | $1.57 | -1.97% | 3,955.00 | -4.24% |
| 44. | 30 sept. 2022 | $203.51 | -5.51% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $244.51 | 20.15% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $251.16 | $1.57 | 3.36% | 4,080.11 | 5.38% |
| 47. | 31 déc. 2022 | $242.29 | -3.53% | 3,839.50 | -5.90% | |
| 48. | 31 janv. 2023 | $249.54 | 2.99% | 4,076.60 | 6.18% | |
| 49. | 28 févr. 2023 | $243.08 | $1.57 | -1.96% | 3,970.15 | -2.61% |
| 50. | 31 mars 2023 | $238.88 | -1.73% | 4,109.31 | 3.51% | |
| 51. | 30 avr. 2023 | $235.04 | -1.61% | 4,169.48 | 1.46% | |
| 52. | 31 mai 2023 | $204.41 | $1.57 | -12.36% | 4,179.83 | 0.25% |
| 53. | 30 juin 2023 | $245.16 | 19.94% | 4,376.86 | 4.71% | |
| 54. | 31 juil. 2023 | $260.80 | 6.38% | 4,588.96 | 4.85% | |
| 55. | 31 août 2023 | $230.04 | $1.68 | -11.15% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $228.46 | -0.69% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $216.30 | -5.32% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $224.16 | $1.68 | 4.41% | 4,567.80 | 8.92% |
| 59. | 31 déc. 2023 | $239.57 | 6.87% | 4,769.83 | 4.42% | |
| Moyenne (R): | 1.36% | 1.11% | ||||
| Écart type: | 7.89% | 5.31% | ||||
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 CMI 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
Cummins Inc., calcul de la variance et de la covariance des rendements
| t | Date | RCMI,t | RS&P 500,t | (RCMI,t–RCMI)2 | (RS&P 500,t–RS&P 500)2 | (RCMI,t–RCMI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2019 | 5.52% | 2.97% | 17.26 | 3.49 | 7.76 |
| 2. | 31 mars 2019 | 2.45% | 1.79% | 1.18 | 0.47 | 0.75 |
| 3. | 30 avr. 2019 | 5.33% | 3.93% | 15.75 | 7.98 | 11.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 4.41% | 8.92% | 9.28 | 61.03 | 23.79 |
| 59. | 31 déc. 2023 | 6.87% | 4.42% | 30.36 | 11.00 | 18.28 |
| Total (Σ): | 3,606.22 | 1,634.30 | 1,651.43 | |||
| t | Date | RCMI,t | RS&P 500,t | (RCMI,t–RCMI)2 | (RS&P 500,t–RS&P 500)2 | (RCMI,t–RCMI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2019 | 5.52% | 2.97% | 17.26 | 3.49 | 7.76 |
| 2. | 31 mars 2019 | 2.45% | 1.79% | 1.18 | 0.47 | 0.75 |
| 3. | 30 avr. 2019 | 5.33% | 3.93% | 15.75 | 7.98 | 11.21 |
| 4. | 31 mai 2019 | -8.65% | -6.58% | 100.37 | 59.04 | 76.98 |
| 5. | 30 juin 2019 | 13.65% | 6.89% | 150.95 | 33.49 | 71.10 |
| 6. | 31 juil. 2019 | -4.28% | 1.31% | 31.91 | 0.04 | -1.17 |
| 7. | 31 août 2019 | -8.18% | -1.81% | 91.15 | 8.50 | 27.83 |
| 8. | 30 sept. 2019 | 8.98% | 1.72% | 57.95 | 0.37 | 4.66 |
| 9. | 31 oct. 2019 | 6.03% | 2.04% | 21.77 | 0.88 | 4.37 |
| 10. | 30 nov. 2019 | 6.78% | 3.40% | 29.30 | 5.28 | 12.44 |
| 11. | 31 déc. 2019 | -2.13% | 2.86% | 12.23 | 3.07 | -6.13 |
| 12. | 31 janv. 2020 | -10.61% | -0.16% | 143.43 | 1.61 | 15.19 |
| 13. | 29 févr. 2020 | -4.61% | -8.41% | 35.66 | 90.57 | 56.83 |
| 14. | 31 mars 2020 | -10.56% | -12.51% | 142.10 | 185.44 | 162.33 |
| 15. | 30 avr. 2020 | 20.82% | 12.68% | 378.69 | 134.06 | 225.32 |
| 16. | 31 mai 2020 | 4.53% | 4.53% | 10.04 | 11.71 | 10.84 |
| 17. | 30 juin 2020 | 2.16% | 1.84% | 0.63 | 0.54 | 0.58 |
| 18. | 31 juil. 2020 | 11.54% | 5.51% | 103.60 | 19.40 | 44.83 |
| 19. | 31 août 2020 | 7.92% | 7.01% | 42.93 | 34.82 | 38.66 |
| 20. | 30 sept. 2020 | 1.89% | -3.92% | 0.27 | 25.29 | -2.62 |
| 21. | 31 oct. 2020 | 4.13% | -2.77% | 7.67 | 15.00 | -10.72 |
| 22. | 30 nov. 2020 | 5.74% | 10.75% | 19.17 | 93.10 | 42.25 |
| 23. | 31 déc. 2020 | -1.76% | 3.71% | 9.77 | 6.79 | -8.15 |
| 24. | 31 janv. 2021 | 3.22% | -1.11% | 3.45 | 4.93 | -4.12 |
| 25. | 28 févr. 2021 | 8.59% | 2.61% | 52.16 | 2.26 | 10.86 |
| 26. | 31 mars 2021 | 2.33% | 4.24% | 0.94 | 9.85 | 3.04 |
| 27. | 30 avr. 2021 | -2.73% | 5.24% | 16.76 | 17.11 | -16.93 |
| 28. | 31 mai 2021 | 2.61% | 0.55% | 1.56 | 0.31 | -0.70 |
| 29. | 30 juin 2021 | -5.24% | 2.22% | 43.57 | 1.24 | -7.36 |
| 30. | 31 juil. 2021 | -4.80% | 2.27% | 38.04 | 1.37 | -7.21 |
| 31. | 31 août 2021 | 2.30% | 2.90% | 0.87 | 3.22 | 1.67 |
| 32. | 30 sept. 2021 | -4.84% | -4.76% | 38.49 | 34.37 | 36.37 |
| 33. | 31 oct. 2021 | 6.80% | 6.91% | 29.59 | 33.74 | 31.60 |
| 34. | 30 nov. 2021 | -11.94% | -0.83% | 177.05 | 3.76 | 25.80 |
| 35. | 31 déc. 2021 | 4.00% | 4.36% | 6.94 | 10.60 | 8.58 |
| 36. | 31 janv. 2022 | 1.26% | -5.26% | 0.01 | 40.51 | 0.69 |
| 37. | 28 févr. 2022 | -6.93% | -3.14% | 68.83 | 17.99 | 35.19 |
| 38. | 31 mars 2022 | 0.49% | 3.58% | 0.77 | 6.11 | -2.17 |
| 39. | 30 avr. 2022 | -7.76% | -8.80% | 83.29 | 98.04 | 90.37 |
| 40. | 31 mai 2022 | 11.30% | 0.01% | 98.72 | 1.21 | -10.93 |
| 41. | 30 juin 2022 | -7.46% | -8.39% | 77.79 | 90.21 | 83.77 |
| 42. | 31 juil. 2022 | 14.35% | 9.11% | 168.73 | 64.09 | 103.99 |
| 43. | 31 août 2022 | -1.97% | -4.24% | 11.15 | 28.62 | 17.87 |
| 44. | 30 sept. 2022 | -5.51% | -9.34% | 47.22 | 109.11 | 71.78 |
| 45. | 31 oct. 2022 | 20.15% | 7.99% | 352.75 | 47.34 | 129.23 |
| 46. | 30 nov. 2022 | 3.36% | 5.38% | 3.99 | 18.23 | 8.53 |
| 47. | 31 déc. 2022 | -3.53% | -5.90% | 23.98 | 49.04 | 34.29 |
| 48. | 31 janv. 2023 | 2.99% | 6.18% | 2.65 | 25.70 | 8.25 |
| 49. | 28 févr. 2023 | -1.96% | -2.61% | 11.05 | 13.82 | 12.36 |
| 50. | 31 mars 2023 | -1.73% | 3.51% | 9.56 | 5.76 | -7.42 |
| 51. | 30 avr. 2023 | -1.61% | 1.46% | 8.83 | 0.13 | -1.07 |
| 52. | 31 mai 2023 | -12.36% | 0.25% | 188.48 | 0.74 | 11.77 |
| 53. | 30 juin 2023 | 19.94% | 4.71% | 344.87 | 13.02 | 67.00 |
| 54. | 31 juil. 2023 | 6.38% | 4.85% | 25.15 | 13.99 | 18.76 |
| 55. | 31 août 2023 | -11.15% | -1.77% | 156.63 | 8.28 | 36.01 |
| 56. | 30 sept. 2023 | -0.69% | -4.87% | 4.21 | 35.73 | 12.26 |
| 57. | 31 oct. 2023 | -5.32% | -2.20% | 44.72 | 10.92 | 22.09 |
| 58. | 30 nov. 2023 | 4.41% | 8.92% | 9.28 | 61.03 | 23.79 |
| 59. | 31 déc. 2023 | 6.87% | 4.42% | 30.36 | 11.00 | 18.28 |
| Total (Σ): | 3,606.22 | 1,634.30 | 1,651.43 | |||
Tout afficher
VarianceCMI = Σ(RCMI,t–RCMI)2 ÷ (59 – 1)
= 3,606.22 ÷ (59 – 1)
= 62.18
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceCMI, S&P 500 = Σ(RCMI,t–RCMI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,651.43 ÷ (59 – 1)
= 28.47
Estimation systématique des risques (β)
| VarianceCMI | 62.18 |
| VarianceS&P 500 | 28.18 |
| CovarianceCMI, S&P 500 | 28.47 |
| Coefficient de corrélationCMI, S&P 5001 | 0.68 |
| βCMI2 | 1.01 |
| αCMI3 | 0.25% |
Calculs
1 Coefficient de corrélationCMI, S&P 500
= CovarianceCMI, S&P 500 ÷ (Écart typeCMI × Écart typeS&P 500)
= 28.47 ÷ (7.89% × 5.31%)
= 0.68
2 βCMI
= CovarianceCMI, S&P 500 ÷ VarianceS&P 500
= 28.47 ÷ 28.18
= 1.01
3 αCMI
= MoyenneCMI – βCMI × MoyenneS&P 500
= 1.36% – 1.01 × 1.11%
= 0.25%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.68% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 13.79% |
| Risque systématique lié à Cummins actions ordinaires | βCMI | 1.01 |
| Taux de rendement prévu des actions ordinaires de Cummins3 | E(RCMI) | 13.88% |
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(RCMI) = RF + βCMI [E(RM) – RF]
= 4.68% + 1.01 [13.79% – 4.68%]
= 13.88%