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 3M.
Taux de rendement
3M Co., taux de rendement mensuels
| 3M Co. (MMM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMMM,t1 | DividendeMMM,t1 | RMMM,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2017 | $174.82 | 2,278.87 | ||||
| 1. | 28 févr. 2017 | $186.35 | $1.175 | 7.27% | 2,363.64 | 3.72% |
| 2. | 31 mars 2017 | $191.33 | 2.67% | 2,362.72 | -0.04% | |
| 3. | 30 avr. 2017 | $195.83 | 2.35% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $170.04 | $1.48 | -4.01% | 4,567.00 | -0.83% |
| 59. | 31 déc. 2021 | $177.63 | 4.46% | 4,766.18 | 4.36% | |
| Moyenne (R): | 0.46% | 1.36% | ||||
| Écart type: | 6.03% | 4.48% | ||||
| 3M Co. (MMM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMMM,t1 | DividendeMMM,t1 | RMMM,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2017 | $174.82 | 2,278.87 | ||||
| 1. | 28 févr. 2017 | $186.35 | $1.175 | 7.27% | 2,363.64 | 3.72% |
| 2. | 31 mars 2017 | $191.33 | 2.67% | 2,362.72 | -0.04% | |
| 3. | 30 avr. 2017 | $195.83 | 2.35% | 2,384.20 | 0.91% | |
| 4. | 31 mai 2017 | $204.47 | $1.175 | 5.01% | 2,411.80 | 1.16% |
| 5. | 30 juin 2017 | $208.19 | 1.82% | 2,423.41 | 0.48% | |
| 6. | 31 juil. 2017 | $201.17 | -3.37% | 2,470.30 | 1.93% | |
| 7. | 31 août 2017 | $204.32 | $1.175 | 2.15% | 2,471.65 | 0.05% |
| 8. | 30 sept. 2017 | $209.90 | 2.73% | 2,519.36 | 1.93% | |
| 9. | 31 oct. 2017 | $230.19 | 9.67% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $243.14 | $1.175 | 6.14% | 2,647.58 | 2.81% |
| 11. | 31 déc. 2017 | $235.37 | -3.20% | 2,673.61 | 0.98% | |
| 12. | 31 janv. 2018 | $250.50 | 6.43% | 2,823.81 | 5.62% | |
| 13. | 28 févr. 2018 | $235.51 | $1.36 | -5.44% | 2,713.83 | -3.89% |
| 14. | 31 mars 2018 | $219.52 | -6.79% | 2,640.87 | -2.69% | |
| 15. | 30 avr. 2018 | $194.39 | -11.45% | 2,648.05 | 0.27% | |
| 16. | 31 mai 2018 | $197.23 | $1.36 | 2.16% | 2,705.27 | 2.16% |
| 17. | 30 juin 2018 | $196.72 | -0.26% | 2,718.37 | 0.48% | |
| 18. | 31 juil. 2018 | $212.32 | 7.93% | 2,816.29 | 3.60% | |
| 19. | 31 août 2018 | $210.92 | $1.36 | -0.02% | 2,901.52 | 3.03% |
| 20. | 30 sept. 2018 | $210.71 | -0.10% | 2,913.98 | 0.43% | |
| 21. | 31 oct. 2018 | $190.26 | -9.71% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $207.92 | $1.36 | 10.00% | 2,760.17 | 1.79% |
| 23. | 31 déc. 2018 | $190.54 | -8.36% | 2,506.85 | -9.18% | |
| 24. | 31 janv. 2019 | $200.30 | 5.12% | 2,704.10 | 7.87% | |
| 25. | 28 févr. 2019 | $207.39 | $1.44 | 4.26% | 2,784.49 | 2.97% |
| 26. | 31 mars 2019 | $207.78 | 0.19% | 2,834.40 | 1.79% | |
| 27. | 30 avr. 2019 | $189.51 | -8.79% | 2,945.83 | 3.93% | |
| 28. | 31 mai 2019 | $159.75 | $1.44 | -14.94% | 2,752.06 | -6.58% |
| 29. | 30 juin 2019 | $173.34 | 8.51% | 2,941.76 | 6.89% | |
| 30. | 31 juil. 2019 | $174.72 | 0.80% | 2,980.38 | 1.31% | |
| 31. | 31 août 2019 | $161.72 | $1.44 | -6.62% | 2,926.46 | -1.81% |
| 32. | 30 sept. 2019 | $164.40 | 1.66% | 2,976.74 | 1.72% | |
| 33. | 31 oct. 2019 | $164.99 | 0.36% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $169.77 | $1.44 | 3.77% | 3,140.98 | 3.40% |
| 35. | 31 déc. 2019 | $176.42 | 3.92% | 3,230.78 | 2.86% | |
| 36. | 31 janv. 2020 | $158.66 | -10.07% | 3,225.52 | -0.16% | |
| 37. | 29 févr. 2020 | $149.24 | $1.47 | -5.01% | 2,954.22 | -8.41% |
| 38. | 31 mars 2020 | $136.51 | -8.53% | 2,584.59 | -12.51% | |
| 39. | 30 avr. 2020 | $151.92 | 11.29% | 2,912.43 | 12.68% | |
| 40. | 31 mai 2020 | $156.44 | $1.47 | 3.94% | 3,044.31 | 4.53% |
| 41. | 30 juin 2020 | $155.99 | -0.29% | 3,100.29 | 1.84% | |
| 42. | 31 juil. 2020 | $150.47 | -3.54% | 3,271.12 | 5.51% | |
| 43. | 31 août 2020 | $163.02 | $1.47 | 9.32% | 3,500.31 | 7.01% |
| 44. | 30 sept. 2020 | $160.18 | -1.74% | 3,363.00 | -3.92% | |
| 45. | 31 oct. 2020 | $159.96 | -0.14% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $172.73 | $1.47 | 8.90% | 3,621.63 | 10.75% |
| 47. | 31 déc. 2020 | $174.79 | 1.19% | 3,756.07 | 3.71% | |
| 48. | 31 janv. 2021 | $175.66 | 0.50% | 3,714.24 | -1.11% | |
| 49. | 28 févr. 2021 | $175.06 | $1.48 | 0.50% | 3,811.15 | 2.61% |
| 50. | 31 mars 2021 | $192.68 | 10.07% | 3,972.89 | 4.24% | |
| 51. | 30 avr. 2021 | $197.14 | 2.31% | 4,181.17 | 5.24% | |
| 52. | 31 mai 2021 | $203.04 | $1.48 | 3.74% | 4,204.11 | 0.55% |
| 53. | 30 juin 2021 | $198.63 | -2.17% | 4,297.50 | 2.22% | |
| 54. | 31 juil. 2021 | $197.94 | -0.35% | 4,395.26 | 2.27% | |
| 55. | 31 août 2021 | $194.74 | $1.48 | -0.87% | 4,522.68 | 2.90% |
| 56. | 30 sept. 2021 | $175.42 | -9.92% | 4,307.54 | -4.76% | |
| 57. | 31 oct. 2021 | $178.68 | 1.86% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $170.04 | $1.48 | -4.01% | 4,567.00 | -0.83% |
| 59. | 31 déc. 2021 | $177.63 | 4.46% | 4,766.18 | 4.36% | |
| Moyenne (R): | 0.46% | 1.36% | ||||
| Écart type: | 6.03% | 4.48% | ||||
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 MMM 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
3M Co., calcul de la variance et de la covariance des rendements
| t | Date | RMMM,t | RS&P 500,t | (RMMM,t–RMMM)2 | (RS&P 500,t–RS&P 500)2 | (RMMM,t–RMMM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2017 | 7.27% | 3.72% | 46.30 | 5.58 | 16.07 |
| 2. | 31 mars 2017 | 2.67% | -0.04% | 4.88 | 1.95 | -3.09 |
| 3. | 30 avr. 2017 | 2.35% | 0.91% | 3.57 | 0.20 | -0.85 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -4.01% | -0.83% | 19.98 | 4.80 | 9.80 |
| 59. | 31 déc. 2021 | 4.46% | 4.36% | 16.01 | 9.02 | 12.02 |
| Total (Σ): | 2,109.95 | 1,164.17 | 1,113.30 | |||
| t | Date | RMMM,t | RS&P 500,t | (RMMM,t–RMMM)2 | (RS&P 500,t–RS&P 500)2 | (RMMM,t–RMMM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2017 | 7.27% | 3.72% | 46.30 | 5.58 | 16.07 |
| 2. | 31 mars 2017 | 2.67% | -0.04% | 4.88 | 1.95 | -3.09 |
| 3. | 30 avr. 2017 | 2.35% | 0.91% | 3.57 | 0.20 | -0.85 |
| 4. | 31 mai 2017 | 5.01% | 1.16% | 20.69 | 0.04 | -0.91 |
| 5. | 30 juin 2017 | 1.82% | 0.48% | 1.84 | 0.77 | -1.19 |
| 6. | 31 juil. 2017 | -3.37% | 1.93% | 14.71 | 0.33 | -2.21 |
| 7. | 31 août 2017 | 2.15% | 0.05% | 2.85 | 1.70 | -2.20 |
| 8. | 30 sept. 2017 | 2.73% | 1.93% | 5.14 | 0.33 | 1.30 |
| 9. | 31 oct. 2017 | 9.67% | 2.22% | 84.70 | 0.74 | 7.92 |
| 10. | 30 nov. 2017 | 6.14% | 2.81% | 32.19 | 2.10 | 8.23 |
| 11. | 31 déc. 2017 | -3.20% | 0.98% | 13.39 | 0.14 | 1.37 |
| 12. | 31 janv. 2018 | 6.43% | 5.62% | 35.58 | 18.15 | 25.41 |
| 13. | 28 févr. 2018 | -5.44% | -3.89% | 34.86 | 27.59 | 31.01 |
| 14. | 31 mars 2018 | -6.79% | -2.69% | 52.60 | 16.37 | 29.35 |
| 15. | 30 avr. 2018 | -11.45% | 0.27% | 141.86 | 1.18 | 12.94 |
| 16. | 31 mai 2018 | 2.16% | 2.16% | 2.88 | 0.64 | 1.36 |
| 17. | 30 juin 2018 | -0.26% | 0.48% | 0.52 | 0.76 | 0.63 |
| 18. | 31 juil. 2018 | 7.93% | 3.60% | 55.76 | 5.04 | 16.76 |
| 19. | 31 août 2018 | -0.02% | 3.03% | 0.23 | 2.78 | -0.80 |
| 20. | 30 sept. 2018 | -0.10% | 0.43% | 0.32 | 0.86 | 0.52 |
| 21. | 31 oct. 2018 | -9.71% | -6.94% | 103.39 | 68.86 | 84.38 |
| 22. | 30 nov. 2018 | 10.00% | 1.79% | 90.89 | 0.18 | 4.08 |
| 23. | 31 déc. 2018 | -8.36% | -9.18% | 77.83 | 111.00 | 92.94 |
| 24. | 31 janv. 2019 | 5.12% | 7.87% | 21.71 | 42.39 | 30.33 |
| 25. | 28 févr. 2019 | 4.26% | 2.97% | 14.41 | 2.61 | 6.13 |
| 26. | 31 mars 2019 | 0.19% | 1.79% | 0.08 | 0.19 | -0.12 |
| 27. | 30 avr. 2019 | -8.79% | 3.93% | 85.67 | 6.62 | -23.82 |
| 28. | 31 mai 2019 | -14.94% | -6.58% | 237.37 | 62.97 | 122.26 |
| 29. | 30 juin 2019 | 8.51% | 6.89% | 64.71 | 30.64 | 44.52 |
| 30. | 31 juil. 2019 | 0.80% | 1.31% | 0.11 | 0.00 | -0.02 |
| 31. | 31 août 2019 | -6.62% | -1.81% | 50.12 | 10.03 | 22.42 |
| 32. | 30 sept. 2019 | 1.66% | 1.72% | 1.43 | 0.13 | 0.43 |
| 33. | 31 oct. 2019 | 0.36% | 2.04% | 0.01 | 0.47 | -0.07 |
| 34. | 30 nov. 2019 | 3.77% | 3.40% | 10.94 | 4.19 | 6.77 |
| 35. | 31 déc. 2019 | 3.92% | 2.86% | 11.93 | 2.25 | 5.18 |
| 36. | 31 janv. 2020 | -10.07% | -0.16% | 110.88 | 2.31 | 16.01 |
| 37. | 29 févr. 2020 | -5.01% | -8.41% | 29.96 | 95.43 | 53.47 |
| 38. | 31 mars 2020 | -8.53% | -12.51% | 80.87 | 192.37 | 124.73 |
| 39. | 30 avr. 2020 | 11.29% | 12.68% | 117.19 | 128.29 | 122.62 |
| 40. | 31 mai 2020 | 3.94% | 4.53% | 12.11 | 10.05 | 11.03 |
| 41. | 30 juin 2020 | -0.29% | 1.84% | 0.56 | 0.23 | -0.36 |
| 42. | 31 juil. 2020 | -3.54% | 5.51% | 16.01 | 17.24 | -16.62 |
| 43. | 31 août 2020 | 9.32% | 7.01% | 78.40 | 31.91 | 50.02 |
| 44. | 30 sept. 2020 | -1.74% | -3.92% | 4.86 | 27.89 | 11.64 |
| 45. | 31 oct. 2020 | -0.14% | -2.77% | 0.36 | 17.01 | 2.48 |
| 46. | 30 nov. 2020 | 8.90% | 10.75% | 71.22 | 88.30 | 79.30 |
| 47. | 31 déc. 2020 | 1.19% | 3.71% | 0.53 | 5.54 | 1.72 |
| 48. | 31 janv. 2021 | 0.50% | -1.11% | 0.00 | 6.11 | -0.09 |
| 49. | 28 févr. 2021 | 0.50% | 2.61% | 0.00 | 1.57 | 0.05 |
| 50. | 31 mars 2021 | 10.07% | 4.24% | 92.20 | 8.33 | 27.71 |
| 51. | 30 avr. 2021 | 2.31% | 5.24% | 3.43 | 15.09 | 7.19 |
| 52. | 31 mai 2021 | 3.74% | 0.55% | 10.76 | 0.65 | -2.65 |
| 53. | 30 juin 2021 | -2.17% | 2.22% | 6.94 | 0.75 | -2.28 |
| 54. | 31 juil. 2021 | -0.35% | 2.27% | 0.66 | 0.84 | -0.74 |
| 55. | 31 août 2021 | -0.87% | 2.90% | 1.77 | 2.38 | -2.05 |
| 56. | 30 sept. 2021 | -9.92% | -4.76% | 107.83 | 37.39 | 63.50 |
| 57. | 31 oct. 2021 | 1.86% | 6.91% | 1.95 | 30.87 | 7.75 |
| 58. | 30 nov. 2021 | -4.01% | -0.83% | 19.98 | 4.80 | 9.80 |
| 59. | 31 déc. 2021 | 4.46% | 4.36% | 16.01 | 9.02 | 12.02 |
| Total (Σ): | 2,109.95 | 1,164.17 | 1,113.30 | |||
Tout afficher
VarianceMMM = Σ(RMMM,t–RMMM)2 ÷ (59 – 1)
= 2,109.95 ÷ (59 – 1)
= 36.38
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianceMMM, S&P 500 = Σ(RMMM,t–RMMM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,113.30 ÷ (59 – 1)
= 19.19
Estimation systématique des risques (β)
| VarianceMMM | 36.38 |
| VarianceS&P 500 | 20.07 |
| CovarianceMMM, S&P 500 | 19.19 |
| Coefficient de corrélationMMM, S&P 5001 | 0.71 |
| βMMM2 | 0.96 |
| αMMM3 | -0.84% |
Calculs
1 Coefficient de corrélationMMM, S&P 500
= CovarianceMMM, S&P 500 ÷ (Écart typeMMM × Écart typeS&P 500)
= 19.19 ÷ (6.03% × 4.48%)
= 0.71
2 βMMM
= CovarianceMMM, S&P 500 ÷ VarianceS&P 500
= 19.19 ÷ 20.07
= 0.96
3 αMMM
= MoyenneMMM – βMMM × MoyenneS&P 500
= 0.46% – 0.96 × 1.36%
= -0.84%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.67% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 13.79% |
| Risque systématique lié à 3M actions ordinaires | βMMM | 0.96 |
| Taux de rendement prévu des actions ordinaires de 3M3 | E(RMMM) | 13.39% |
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(RMMM) = RF + βMMM [E(RM) – RF]
= 4.67% + 0.96 [13.79% – 4.67%]
= 13.39%