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 Mosaic.
Taux de rendement
Mosaic Co., taux de rendement mensuels
| Mosaic Co. (MOS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMOS,t1 | DividendeMOS,t1 | RMOS,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2017 | $31.37 | 2,278.87 | ||||
| 1. | 28 févr. 2017 | $31.19 | $0.275 | 0.30% | 2,363.64 | 3.72% |
| 2. | 31 mars 2017 | $29.18 | -6.44% | 2,362.72 | -0.04% | |
| 3. | 30 avr. 2017 | $26.93 | -7.71% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $34.22 | -17.68% | 4,567.00 | -0.83% | |
| 59. | 31 déc. 2021 | $39.29 | $0.075 | 15.04% | 4,766.18 | 4.36% |
| Moyenne (R): | 1.25% | 1.36% | ||||
| Écart type: | 12.24% | 4.48% | ||||
| Mosaic Co. (MOS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMOS,t1 | DividendeMOS,t1 | RMOS,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2017 | $31.37 | 2,278.87 | ||||
| 1. | 28 févr. 2017 | $31.19 | $0.275 | 0.30% | 2,363.64 | 3.72% |
| 2. | 31 mars 2017 | $29.18 | -6.44% | 2,362.72 | -0.04% | |
| 3. | 30 avr. 2017 | $26.93 | -7.71% | 2,384.20 | 0.91% | |
| 4. | 31 mai 2017 | $22.63 | $0.15 | -15.41% | 2,411.80 | 1.16% |
| 5. | 30 juin 2017 | $22.83 | 0.88% | 2,423.41 | 0.48% | |
| 6. | 31 juil. 2017 | $24.14 | 5.74% | 2,470.30 | 1.93% | |
| 7. | 31 août 2017 | $19.98 | -17.23% | 2,471.65 | 0.05% | |
| 8. | 30 sept. 2017 | $21.59 | $0.15 | 8.81% | 2,519.36 | 1.93% |
| 9. | 31 oct. 2017 | $22.34 | 3.47% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $24.29 | 8.73% | 2,647.58 | 2.81% | |
| 11. | 31 déc. 2017 | $25.66 | $0.025 | 5.74% | 2,673.61 | 0.98% |
| 12. | 31 janv. 2018 | $27.30 | 6.39% | 2,823.81 | 5.62% | |
| 13. | 28 févr. 2018 | $26.32 | $0.025 | -3.50% | 2,713.83 | -3.89% |
| 14. | 31 mars 2018 | $24.28 | -7.75% | 2,640.87 | -2.69% | |
| 15. | 30 avr. 2018 | $26.95 | 11.00% | 2,648.05 | 0.27% | |
| 16. | 31 mai 2018 | $27.49 | 2.00% | 2,705.27 | 2.16% | |
| 17. | 30 juin 2018 | $28.05 | $0.025 | 2.13% | 2,718.37 | 0.48% |
| 18. | 31 juil. 2018 | $30.11 | 7.34% | 2,816.29 | 3.60% | |
| 19. | 31 août 2018 | $31.27 | 3.85% | 2,901.52 | 3.03% | |
| 20. | 30 sept. 2018 | $32.48 | $0.025 | 3.95% | 2,913.98 | 0.43% |
| 21. | 31 oct. 2018 | $30.94 | -4.74% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $36.00 | 16.35% | 2,760.17 | 1.79% | |
| 23. | 31 déc. 2018 | $29.21 | $0.025 | -18.79% | 2,506.85 | -9.18% |
| 24. | 31 janv. 2019 | $32.28 | 10.51% | 2,704.10 | 7.87% | |
| 25. | 28 févr. 2019 | $31.27 | -3.13% | 2,784.49 | 2.97% | |
| 26. | 31 mars 2019 | $27.31 | $0.025 | -12.58% | 2,834.40 | 1.79% |
| 27. | 30 avr. 2019 | $26.11 | -4.39% | 2,945.83 | 3.93% | |
| 28. | 31 mai 2019 | $21.47 | -17.77% | 2,752.06 | -6.58% | |
| 29. | 30 juin 2019 | $25.03 | $0.05 | 16.81% | 2,941.76 | 6.89% |
| 30. | 31 juil. 2019 | $25.19 | 0.64% | 2,980.38 | 1.31% | |
| 31. | 31 août 2019 | $18.39 | -26.99% | 2,926.46 | -1.81% | |
| 32. | 30 sept. 2019 | $20.50 | $0.05 | 11.75% | 2,976.74 | 1.72% |
| 33. | 31 oct. 2019 | $19.88 | -3.02% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $19.05 | -4.18% | 3,140.98 | 3.40% | |
| 35. | 31 déc. 2019 | $21.64 | $0.05 | 13.86% | 3,230.78 | 2.86% |
| 36. | 31 janv. 2020 | $19.84 | -8.32% | 3,225.52 | -0.16% | |
| 37. | 29 févr. 2020 | $17.03 | -14.16% | 2,954.22 | -8.41% | |
| 38. | 31 mars 2020 | $10.82 | $0.05 | -36.17% | 2,584.59 | -12.51% |
| 39. | 30 avr. 2020 | $11.51 | 6.38% | 2,912.43 | 12.68% | |
| 40. | 31 mai 2020 | $12.09 | 5.04% | 3,044.31 | 4.53% | |
| 41. | 30 juin 2020 | $12.51 | $0.05 | 3.89% | 3,100.29 | 1.84% |
| 42. | 31 juil. 2020 | $13.47 | 7.67% | 3,271.12 | 5.51% | |
| 43. | 31 août 2020 | $18.23 | 35.34% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $18.27 | $0.05 | 0.49% | 3,363.00 | -3.92% |
| 45. | 31 oct. 2020 | $18.50 | 1.26% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $21.96 | 18.70% | 3,621.63 | 10.75% | |
| 47. | 31 déc. 2020 | $23.01 | $0.05 | 5.01% | 3,756.07 | 3.71% |
| 48. | 31 janv. 2021 | $25.96 | 12.82% | 3,714.24 | -1.11% | |
| 49. | 28 févr. 2021 | $29.40 | 13.25% | 3,811.15 | 2.61% | |
| 50. | 31 mars 2021 | $31.61 | $0.05 | 7.69% | 3,972.89 | 4.24% |
| 51. | 30 avr. 2021 | $35.18 | 11.29% | 4,181.17 | 5.24% | |
| 52. | 31 mai 2021 | $36.14 | 2.73% | 4,204.11 | 0.55% | |
| 53. | 30 juin 2021 | $31.91 | $0.075 | -11.50% | 4,297.50 | 2.22% |
| 54. | 31 juil. 2021 | $31.23 | -2.13% | 4,395.26 | 2.27% | |
| 55. | 31 août 2021 | $32.18 | 3.04% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $35.72 | $0.075 | 11.23% | 4,307.54 | -4.76% |
| 57. | 31 oct. 2021 | $41.57 | 16.38% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $34.22 | -17.68% | 4,567.00 | -0.83% | |
| 59. | 31 déc. 2021 | $39.29 | $0.075 | 15.04% | 4,766.18 | 4.36% |
| Moyenne (R): | 1.25% | 1.36% | ||||
| Écart type: | 12.24% | 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 MOS 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
Mosaic Co., calcul de la variance et de la covariance des rendements
| t | Date | RMOS,t | RS&P 500,t | (RMOS,t–RMOS)2 | (RS&P 500,t–RS&P 500)2 | (RMOS,t–RMOS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2017 | 0.30% | 3.72% | 0.90 | 5.58 | -2.24 |
| 2. | 31 mars 2017 | -6.44% | -0.04% | 59.24 | 1.95 | 10.75 |
| 3. | 30 avr. 2017 | -7.71% | 0.91% | 80.34 | 0.20 | 4.02 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -17.68% | -0.83% | 358.48 | 4.80 | 41.49 |
| 59. | 31 déc. 2021 | 15.04% | 4.36% | 189.96 | 9.02 | 41.39 |
| Total (Σ): | 8,684.53 | 1,164.17 | 2,070.45 | |||
| t | Date | RMOS,t | RS&P 500,t | (RMOS,t–RMOS)2 | (RS&P 500,t–RS&P 500)2 | (RMOS,t–RMOS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2017 | 0.30% | 3.72% | 0.90 | 5.58 | -2.24 |
| 2. | 31 mars 2017 | -6.44% | -0.04% | 59.24 | 1.95 | 10.75 |
| 3. | 30 avr. 2017 | -7.71% | 0.91% | 80.34 | 0.20 | 4.02 |
| 4. | 31 mai 2017 | -15.41% | 1.16% | 277.65 | 0.04 | 3.34 |
| 5. | 30 juin 2017 | 0.88% | 0.48% | 0.14 | 0.77 | 0.32 |
| 6. | 31 juil. 2017 | 5.74% | 1.93% | 20.12 | 0.33 | 2.59 |
| 7. | 31 août 2017 | -17.23% | 0.05% | 341.71 | 1.70 | 24.09 |
| 8. | 30 sept. 2017 | 8.81% | 1.93% | 57.10 | 0.33 | 4.33 |
| 9. | 31 oct. 2017 | 3.47% | 2.22% | 4.93 | 0.74 | 1.91 |
| 10. | 30 nov. 2017 | 8.73% | 2.81% | 55.89 | 2.10 | 10.84 |
| 11. | 31 déc. 2017 | 5.74% | 0.98% | 20.16 | 0.14 | -1.68 |
| 12. | 31 janv. 2018 | 6.39% | 5.62% | 26.41 | 18.15 | 21.89 |
| 13. | 28 févr. 2018 | -3.50% | -3.89% | 22.57 | 27.59 | 24.95 |
| 14. | 31 mars 2018 | -7.75% | -2.69% | 81.06 | 16.37 | 36.43 |
| 15. | 30 avr. 2018 | 11.00% | 0.27% | 94.95 | 1.18 | -10.58 |
| 16. | 31 mai 2018 | 2.00% | 2.16% | 0.56 | 0.64 | 0.60 |
| 17. | 30 juin 2018 | 2.13% | 0.48% | 0.77 | 0.76 | -0.76 |
| 18. | 31 juil. 2018 | 7.34% | 3.60% | 37.11 | 5.04 | 13.67 |
| 19. | 31 août 2018 | 3.85% | 3.03% | 6.76 | 2.78 | 4.34 |
| 20. | 30 sept. 2018 | 3.95% | 0.43% | 7.27 | 0.86 | -2.50 |
| 21. | 31 oct. 2018 | -4.74% | -6.94% | 35.93 | 68.86 | 49.74 |
| 22. | 30 nov. 2018 | 16.35% | 1.79% | 228.06 | 0.18 | 6.46 |
| 23. | 31 déc. 2018 | -18.79% | -9.18% | 401.77 | 111.00 | 211.18 |
| 24. | 31 janv. 2019 | 10.51% | 7.87% | 85.70 | 42.39 | 60.27 |
| 25. | 28 févr. 2019 | -3.13% | 2.97% | 19.20 | 2.61 | -7.08 |
| 26. | 31 mars 2019 | -12.58% | 1.79% | 191.45 | 0.19 | -6.01 |
| 27. | 30 avr. 2019 | -4.39% | 3.93% | 31.88 | 6.62 | -14.53 |
| 28. | 31 mai 2019 | -17.77% | -6.58% | 361.90 | 62.97 | 150.96 |
| 29. | 30 juin 2019 | 16.81% | 6.89% | 242.16 | 30.64 | 86.14 |
| 30. | 31 juil. 2019 | 0.64% | 1.31% | 0.38 | 0.00 | 0.03 |
| 31. | 31 août 2019 | -26.99% | -1.81% | 797.92 | 10.03 | 89.46 |
| 32. | 30 sept. 2019 | 11.75% | 1.72% | 110.10 | 0.13 | 3.78 |
| 33. | 31 oct. 2019 | -3.02% | 2.04% | 18.29 | 0.47 | -2.93 |
| 34. | 30 nov. 2019 | -4.18% | 3.40% | 29.46 | 4.19 | -11.11 |
| 35. | 31 déc. 2019 | 13.86% | 2.86% | 158.90 | 2.25 | 18.92 |
| 36. | 31 janv. 2020 | -8.32% | -0.16% | 91.59 | 2.31 | 14.55 |
| 37. | 29 févr. 2020 | -14.16% | -8.41% | 237.65 | 95.43 | 150.60 |
| 38. | 31 mars 2020 | -36.17% | -12.51% | 1,400.56 | 192.37 | 519.07 |
| 39. | 30 avr. 2020 | 6.38% | 12.68% | 26.26 | 128.29 | 58.04 |
| 40. | 31 mai 2020 | 5.04% | 4.53% | 14.34 | 10.05 | 12.00 |
| 41. | 30 juin 2020 | 3.89% | 1.84% | 6.94 | 0.23 | 1.27 |
| 42. | 31 juil. 2020 | 7.67% | 5.51% | 41.23 | 17.24 | 26.66 |
| 43. | 31 août 2020 | 35.34% | 7.01% | 1,161.80 | 31.91 | 192.53 |
| 44. | 30 sept. 2020 | 0.49% | -3.92% | 0.58 | 27.89 | 4.01 |
| 45. | 31 oct. 2020 | 1.26% | -2.77% | 0.00 | 17.01 | -0.03 |
| 46. | 30 nov. 2020 | 18.70% | 10.75% | 304.51 | 88.30 | 163.97 |
| 47. | 31 déc. 2020 | 5.01% | 3.71% | 14.11 | 5.54 | 8.84 |
| 48. | 31 janv. 2021 | 12.82% | -1.11% | 133.82 | 6.11 | -28.59 |
| 49. | 28 févr. 2021 | 13.25% | 2.61% | 143.97 | 1.57 | 15.01 |
| 50. | 31 mars 2021 | 7.69% | 4.24% | 41.40 | 8.33 | 18.57 |
| 51. | 30 avr. 2021 | 11.29% | 5.24% | 100.83 | 15.09 | 39.01 |
| 52. | 31 mai 2021 | 2.73% | 0.55% | 2.18 | 0.65 | -1.19 |
| 53. | 30 juin 2021 | -11.50% | 2.22% | 162.55 | 0.75 | -11.01 |
| 54. | 31 juil. 2021 | -2.13% | 2.27% | 11.45 | 0.84 | -3.10 |
| 55. | 31 août 2021 | 3.04% | 2.90% | 3.20 | 2.38 | 2.76 |
| 56. | 30 sept. 2021 | 11.23% | -4.76% | 99.62 | 37.39 | -61.03 |
| 57. | 31 oct. 2021 | 16.38% | 6.91% | 228.76 | 30.87 | 84.04 |
| 58. | 30 nov. 2021 | -17.68% | -0.83% | 358.48 | 4.80 | 41.49 |
| 59. | 31 déc. 2021 | 15.04% | 4.36% | 189.96 | 9.02 | 41.39 |
| Total (Σ): | 8,684.53 | 1,164.17 | 2,070.45 | |||
Tout afficher
VarianceMOS = Σ(RMOS,t–RMOS)2 ÷ (59 – 1)
= 8,684.53 ÷ (59 – 1)
= 149.73
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianceMOS, S&P 500 = Σ(RMOS,t–RMOS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,070.45 ÷ (59 – 1)
= 35.70
Estimation systématique des risques (β)
| VarianceMOS | 149.73 |
| VarianceS&P 500 | 20.07 |
| CovarianceMOS, S&P 500 | 35.70 |
| Coefficient de corrélationMOS, S&P 5001 | 0.65 |
| βMOS2 | 1.78 |
| αMOS3 | -1.16% |
Calculs
1 Coefficient de corrélationMOS, S&P 500
= CovarianceMOS, S&P 500 ÷ (Écart typeMOS × Écart typeS&P 500)
= 35.70 ÷ (12.24% × 4.48%)
= 0.65
2 βMOS
= CovarianceMOS, S&P 500 ÷ VarianceS&P 500
= 35.70 ÷ 20.07
= 1.78
3 αMOS
= MoyenneMOS – βMOS × MoyenneS&P 500
= 1.25% – 1.78 × 1.36%
= -1.16%
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) | 14.84% |
| Risque systématique de Mosaic actions ordinaires | βMOS | 1.78 |
| Taux de rendement prévu sur les actions ordinaires de Mosaic3 | E(RMOS) | 22.57% |
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(RMOS) = RF + βMOS [E(RM) – RF]
= 4.91% + 1.78 [14.84% – 4.91%]
= 22.57%