Modèle d’évaluation des immobilisations (CAPM)
Le modèle d’évaluation des actifs financiers (MEDAF) indique quel devrait être le taux de rendement attendu ou requis sur les actifs risqués comme les actions ordinaires de Motorola Solutions.
Taux de rendement
Motorola Solutions Inc., taux de rendement mensuels
| Motorola Solutions Inc. (MSI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMSI,t1 | DividendeMSI,t1 | RMSI,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2019 | $116.91 | 2,704.10 | ||||
| 1. | 28 févr. 2019 | $143.12 | 22.42% | 2,784.49 | 2.97% | |
| 2. | 31 mars 2019 | $140.42 | $0.57 | -1.49% | 2,834.40 | 1.79% |
| 3. | 30 avr. 2019 | $144.91 | 3.20% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $322.87 | 15.95% | 4,567.80 | 8.92% | |
| 59. | 31 déc. 2023 | $313.09 | $0.98 | -2.73% | 4,769.83 | 4.42% |
| Moyenne (R): | 2.08% | 1.11% | ||||
| Écart type: | 7.42% | 5.31% | ||||
| Motorola Solutions Inc. (MSI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMSI,t1 | DividendeMSI,t1 | RMSI,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2019 | $116.91 | 2,704.10 | ||||
| 1. | 28 févr. 2019 | $143.12 | 22.42% | 2,784.49 | 2.97% | |
| 2. | 31 mars 2019 | $140.42 | $0.57 | -1.49% | 2,834.40 | 1.79% |
| 3. | 30 avr. 2019 | $144.91 | 3.20% | 2,945.83 | 3.93% | |
| 4. | 31 mai 2019 | $149.95 | 3.48% | 2,752.06 | -6.58% | |
| 5. | 30 juin 2019 | $166.73 | $0.57 | 11.57% | 2,941.76 | 6.89% |
| 6. | 31 juil. 2019 | $165.96 | -0.46% | 2,980.38 | 1.31% | |
| 7. | 31 août 2019 | $180.91 | 9.01% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $170.41 | $0.57 | -5.49% | 2,976.74 | 1.72% |
| 9. | 31 oct. 2019 | $166.32 | -2.40% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $167.30 | 0.59% | 3,140.98 | 3.40% | |
| 11. | 31 déc. 2019 | $161.14 | $0.64 | -3.30% | 3,230.78 | 2.86% |
| 12. | 31 janv. 2020 | $177.00 | 9.84% | 3,225.52 | -0.16% | |
| 13. | 29 févr. 2020 | $165.68 | -6.40% | 2,954.22 | -8.41% | |
| 14. | 31 mars 2020 | $132.92 | $0.64 | -19.39% | 2,584.59 | -12.51% |
| 15. | 30 avr. 2020 | $143.81 | 8.19% | 2,912.43 | 12.68% | |
| 16. | 31 mai 2020 | $135.33 | -5.90% | 3,044.31 | 4.53% | |
| 17. | 30 juin 2020 | $140.13 | $0.64 | 4.02% | 3,100.29 | 1.84% |
| 18. | 31 juil. 2020 | $139.80 | -0.24% | 3,271.12 | 5.51% | |
| 19. | 31 août 2020 | $154.75 | 10.69% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $156.81 | $0.64 | 1.74% | 3,363.00 | -3.92% |
| 21. | 31 oct. 2020 | $158.06 | 0.80% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $171.53 | 8.52% | 3,621.63 | 10.75% | |
| 23. | 31 déc. 2020 | $170.06 | $0.71 | -0.44% | 3,756.07 | 3.71% |
| 24. | 31 janv. 2021 | $167.55 | -1.48% | 3,714.24 | -1.11% | |
| 25. | 28 févr. 2021 | $175.48 | 4.73% | 3,811.15 | 2.61% | |
| 26. | 31 mars 2021 | $188.05 | $0.71 | 7.57% | 3,972.89 | 4.24% |
| 27. | 30 avr. 2021 | $188.30 | 0.13% | 4,181.17 | 5.24% | |
| 28. | 31 mai 2021 | $205.31 | 9.03% | 4,204.11 | 0.55% | |
| 29. | 30 juin 2021 | $216.85 | $0.71 | 5.97% | 4,297.50 | 2.22% |
| 30. | 31 juil. 2021 | $223.92 | 3.26% | 4,395.26 | 2.27% | |
| 31. | 31 août 2021 | $244.22 | 9.07% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $232.32 | $0.71 | -4.58% | 4,307.54 | -4.76% |
| 33. | 31 oct. 2021 | $248.59 | 7.00% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $253.18 | 1.85% | 4,567.00 | -0.83% | |
| 35. | 31 déc. 2021 | $271.70 | $0.79 | 7.63% | 4,766.18 | 4.36% |
| 36. | 31 janv. 2022 | $231.94 | -14.63% | 4,515.55 | -5.26% | |
| 37. | 28 févr. 2022 | $220.43 | -4.96% | 4,373.94 | -3.14% | |
| 38. | 31 mars 2022 | $242.20 | $0.79 | 10.23% | 4,530.41 | 3.58% |
| 39. | 30 avr. 2022 | $213.69 | -11.77% | 4,131.93 | -8.80% | |
| 40. | 31 mai 2022 | $219.74 | 2.83% | 4,132.15 | 0.01% | |
| 41. | 30 juin 2022 | $209.60 | $0.79 | -4.26% | 3,785.38 | -8.39% |
| 42. | 31 juil. 2022 | $238.59 | 13.83% | 4,130.29 | 9.11% | |
| 43. | 31 août 2022 | $243.41 | 2.02% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $223.97 | $0.79 | -7.66% | 3,585.62 | -9.34% |
| 45. | 31 oct. 2022 | $249.71 | 11.49% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $272.20 | 9.01% | 4,080.11 | 5.38% | |
| 47. | 31 déc. 2022 | $257.71 | $0.88 | -5.00% | 3,839.50 | -5.90% |
| 48. | 31 janv. 2023 | $257.01 | -0.27% | 4,076.60 | 6.18% | |
| 49. | 28 févr. 2023 | $262.81 | 2.26% | 3,970.15 | -2.61% | |
| 50. | 31 mars 2023 | $286.13 | $0.88 | 9.21% | 4,109.31 | 3.51% |
| 51. | 30 avr. 2023 | $291.40 | 1.84% | 4,169.48 | 1.46% | |
| 52. | 31 mai 2023 | $281.92 | -3.25% | 4,179.83 | 0.25% | |
| 53. | 30 juin 2023 | $293.28 | $0.88 | 4.34% | 4,376.86 | 4.71% |
| 54. | 31 juil. 2023 | $286.63 | -2.27% | 4,588.96 | 4.85% | |
| 55. | 31 août 2023 | $283.57 | -1.07% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $272.24 | $0.88 | -3.69% | 4,288.05 | -4.87% |
| 57. | 31 oct. 2023 | $278.46 | 2.28% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $322.87 | 15.95% | 4,567.80 | 8.92% | |
| 59. | 31 déc. 2023 | $313.09 | $0.98 | -2.73% | 4,769.83 | 4.42% |
| Moyenne (R): | 2.08% | 1.11% | ||||
| Écart type: | 7.42% | 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 MSI 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
Motorola Solutions Inc., calcul de la variance et de la covariance des rendements
| t | Date | RMSI,t | RS&P 500,t | (RMSI,t–RMSI)2 | (RS&P 500,t–RS&P 500)2 | (RMSI,t–RMSI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2019 | 22.42% | 2.97% | 413.82 | 3.49 | 37.98 |
| 2. | 31 mars 2019 | -1.49% | 1.79% | 12.71 | 0.47 | -2.45 |
| 3. | 30 avr. 2019 | 3.20% | 3.93% | 1.26 | 7.98 | 3.17 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 15.95% | 8.92% | 192.44 | 61.03 | 108.37 |
| 59. | 31 déc. 2023 | -2.73% | 4.42% | 23.06 | 11.00 | -15.93 |
| Total (Σ): | 3,191.39 | 1,634.30 | 1,502.06 | |||
| t | Date | RMSI,t | RS&P 500,t | (RMSI,t–RMSI)2 | (RS&P 500,t–RS&P 500)2 | (RMSI,t–RMSI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2019 | 22.42% | 2.97% | 413.82 | 3.49 | 37.98 |
| 2. | 31 mars 2019 | -1.49% | 1.79% | 12.71 | 0.47 | -2.45 |
| 3. | 30 avr. 2019 | 3.20% | 3.93% | 1.26 | 7.98 | 3.17 |
| 4. | 31 mai 2019 | 3.48% | -6.58% | 1.96 | 59.04 | -10.77 |
| 5. | 30 juin 2019 | 11.57% | 6.89% | 90.14 | 33.49 | 54.94 |
| 6. | 31 juil. 2019 | -0.46% | 1.31% | 6.44 | 0.04 | -0.53 |
| 7. | 31 août 2019 | 9.01% | -1.81% | 48.05 | 8.50 | -20.21 |
| 8. | 30 sept. 2019 | -5.49% | 1.72% | 57.23 | 0.37 | -4.63 |
| 9. | 31 oct. 2019 | -2.40% | 2.04% | 20.04 | 0.88 | -4.20 |
| 10. | 30 nov. 2019 | 0.59% | 3.40% | 2.21 | 5.28 | -3.42 |
| 11. | 31 déc. 2019 | -3.30% | 2.86% | 28.90 | 3.07 | -9.42 |
| 12. | 31 janv. 2020 | 9.84% | -0.16% | 60.31 | 1.61 | -9.85 |
| 13. | 29 févr. 2020 | -6.40% | -8.41% | 71.77 | 90.57 | 80.62 |
| 14. | 31 mars 2020 | -19.39% | -12.51% | 460.66 | 185.44 | 292.28 |
| 15. | 30 avr. 2020 | 8.19% | 12.68% | 37.41 | 134.06 | 70.82 |
| 16. | 31 mai 2020 | -5.90% | 4.53% | 63.57 | 11.71 | -27.29 |
| 17. | 30 juin 2020 | 4.02% | 1.84% | 3.78 | 0.54 | 1.42 |
| 18. | 31 juil. 2020 | -0.24% | 5.51% | 5.34 | 19.40 | -10.18 |
| 19. | 31 août 2020 | 10.69% | 7.01% | 74.26 | 34.82 | 50.85 |
| 20. | 30 sept. 2020 | 1.74% | -3.92% | 0.11 | 25.29 | 1.67 |
| 21. | 31 oct. 2020 | 0.80% | -2.77% | 1.64 | 15.00 | 4.95 |
| 22. | 30 nov. 2020 | 8.52% | 10.75% | 41.55 | 93.10 | 62.19 |
| 23. | 31 déc. 2020 | -0.44% | 3.71% | 6.35 | 6.79 | -6.57 |
| 24. | 31 janv. 2021 | -1.48% | -1.11% | 12.62 | 4.93 | 7.88 |
| 25. | 28 févr. 2021 | 4.73% | 2.61% | 7.06 | 2.26 | 3.99 |
| 26. | 31 mars 2021 | 7.57% | 4.24% | 30.16 | 9.85 | 17.23 |
| 27. | 30 avr. 2021 | 0.13% | 5.24% | 3.78 | 17.11 | -8.04 |
| 28. | 31 mai 2021 | 9.03% | 0.55% | 48.40 | 0.31 | -3.88 |
| 29. | 30 juin 2021 | 5.97% | 2.22% | 15.13 | 1.24 | 4.34 |
| 30. | 31 juil. 2021 | 3.26% | 2.27% | 1.40 | 1.37 | 1.38 |
| 31. | 31 août 2021 | 9.07% | 2.90% | 48.85 | 3.22 | 12.53 |
| 32. | 30 sept. 2021 | -4.58% | -4.76% | 44.33 | 34.37 | 39.04 |
| 33. | 31 oct. 2021 | 7.00% | 6.91% | 24.28 | 33.74 | 28.62 |
| 34. | 30 nov. 2021 | 1.85% | -0.83% | 0.05 | 3.76 | 0.45 |
| 35. | 31 déc. 2021 | 7.63% | 4.36% | 30.81 | 10.60 | 18.07 |
| 36. | 31 janv. 2022 | -14.63% | -5.26% | 279.23 | 40.51 | 106.35 |
| 37. | 28 févr. 2022 | -4.96% | -3.14% | 49.54 | 17.99 | 29.86 |
| 38. | 31 mars 2022 | 10.23% | 3.58% | 66.56 | 6.11 | 20.16 |
| 39. | 30 avr. 2022 | -11.77% | -8.80% | 191.75 | 98.04 | 137.11 |
| 40. | 31 mai 2022 | 2.83% | 0.01% | 0.57 | 1.21 | -0.83 |
| 41. | 30 juin 2022 | -4.26% | -8.39% | 40.09 | 90.21 | 60.13 |
| 42. | 31 juil. 2022 | 13.83% | 9.11% | 138.18 | 64.09 | 94.11 |
| 43. | 31 août 2022 | 2.02% | -4.24% | 0.00 | 28.62 | 0.30 |
| 44. | 30 sept. 2022 | -7.66% | -9.34% | 94.83 | 109.11 | 101.72 |
| 45. | 31 oct. 2022 | 11.49% | 7.99% | 88.67 | 47.34 | 64.79 |
| 46. | 30 nov. 2022 | 9.01% | 5.38% | 48.03 | 18.23 | 29.59 |
| 47. | 31 déc. 2022 | -5.00% | -5.90% | 50.07 | 49.04 | 49.56 |
| 48. | 31 janv. 2023 | -0.27% | 6.18% | 5.51 | 25.70 | -11.90 |
| 49. | 28 févr. 2023 | 2.26% | -2.61% | 0.03 | 13.82 | -0.67 |
| 50. | 31 mars 2023 | 9.21% | 3.51% | 50.86 | 5.76 | 17.11 |
| 51. | 30 avr. 2023 | 1.84% | 1.46% | 0.05 | 0.13 | -0.08 |
| 52. | 31 mai 2023 | -3.25% | 0.25% | 28.40 | 0.74 | 4.57 |
| 53. | 30 juin 2023 | 4.34% | 4.71% | 5.13 | 13.02 | 8.17 |
| 54. | 31 juil. 2023 | -2.27% | 4.85% | 18.87 | 13.99 | -16.25 |
| 55. | 31 août 2023 | -1.07% | -1.77% | 9.88 | 8.28 | 9.05 |
| 56. | 30 sept. 2023 | -3.69% | -4.87% | 33.19 | 35.73 | 34.44 |
| 57. | 31 oct. 2023 | 2.28% | -2.20% | 0.04 | 10.92 | -0.69 |
| 58. | 30 nov. 2023 | 15.95% | 8.92% | 192.44 | 61.03 | 108.37 |
| 59. | 31 déc. 2023 | -2.73% | 4.42% | 23.06 | 11.00 | -15.93 |
| Total (Σ): | 3,191.39 | 1,634.30 | 1,502.06 | |||
Tout afficher
VarianceMSI = Σ(RMSI,t–RMSI)2 ÷ (59 – 1)
= 3,191.39 ÷ (59 – 1)
= 55.02
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceMSI, S&P 500 = Σ(RMSI,t–RMSI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,502.06 ÷ (59 – 1)
= 25.90
Estimation systématique des risques (β)
| VarianceMSI | 55.02 |
| VarianceS&P 500 | 28.18 |
| CovarianceMSI, S&P 500 | 25.90 |
| Coefficient de corrélationMSI, S&P 5001 | 0.66 |
| βMSI2 | 0.92 |
| αMSI3 | 1.06% |
Calculs
1 Coefficient de corrélationMSI, S&P 500
= CovarianceMSI, S&P 500 ÷ (Écart typeMSI × Écart typeS&P 500)
= 25.90 ÷ (7.42% × 5.31%)
= 0.66
2 βMSI
= CovarianceMSI, S&P 500 ÷ VarianceS&P 500
= 25.90 ÷ 28.18
= 0.92
3 αMSI
= MoyenneMSI – βMSI × MoyenneS&P 500
= 2.08% – 0.92 × 1.11%
= 1.06%
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) | 14.72% |
| Risque systématique des actions Motorola Solutions ordinaires | βMSI | 0.92 |
| Taux de rendement attendu sur les actions ordinaires de Motorola Solutions3 | E(RMSI) | 13.92% |
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(RMSI) = RF + βMSI [E(RM) – RF]
= 4.91% + 0.92 [14.72% – 4.91%]
= 13.92%