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 Marriott.
Taux de rendement
Marriott International Inc., taux de rendement mensuels
| Marriott International Inc. (MAR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMAR,t1 | DividendeMAR,t1 | RMAR,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2015 | $74.50 | 1,994.99 | ||||
| 1. | 28 févr. 2015 | $83.10 | $0.20 | 11.81% | 2,104.50 | 5.49% |
| 2. | 31 mars 2015 | $80.32 | -3.35% | 2,067.89 | -1.74% | |
| 3. | 30 avr. 2015 | $80.05 | -0.34% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | $140.36 | $0.48 | 11.29% | 3,140.98 | 3.40% |
| 59. | 31 déc. 2019 | $151.43 | 7.89% | 3,230.78 | 2.86% | |
| Moyenne (R): | 1.53% | 0.88% | ||||
| Écart type: | 6.56% | 3.45% | ||||
| Marriott International Inc. (MAR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixMAR,t1 | DividendeMAR,t1 | RMAR,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2015 | $74.50 | 1,994.99 | ||||
| 1. | 28 févr. 2015 | $83.10 | $0.20 | 11.81% | 2,104.50 | 5.49% |
| 2. | 31 mars 2015 | $80.32 | -3.35% | 2,067.89 | -1.74% | |
| 3. | 30 avr. 2015 | $80.05 | -0.34% | 2,085.51 | 0.85% | |
| 4. | 31 mai 2015 | $77.99 | $0.25 | -2.26% | 2,107.39 | 1.05% |
| 5. | 30 juin 2015 | $74.39 | -4.62% | 2,063.11 | -2.10% | |
| 6. | 31 juil. 2015 | $72.61 | -2.39% | 2,103.84 | 1.97% | |
| 7. | 31 août 2015 | $70.66 | $0.25 | -2.34% | 1,972.18 | -6.26% |
| 8. | 30 sept. 2015 | $68.20 | -3.48% | 1,920.03 | -2.64% | |
| 9. | 31 oct. 2015 | $76.78 | 12.58% | 2,079.36 | 8.30% | |
| 10. | 30 nov. 2015 | $70.91 | $0.25 | -7.32% | 2,080.41 | 0.05% |
| 11. | 31 déc. 2015 | $67.04 | -5.46% | 2,043.94 | -1.75% | |
| 12. | 31 janv. 2016 | $61.28 | -8.59% | 1,940.24 | -5.07% | |
| 13. | 29 févr. 2016 | $68.15 | $0.25 | 11.62% | 1,932.23 | -0.41% |
| 14. | 31 mars 2016 | $71.18 | 4.45% | 2,059.74 | 6.60% | |
| 15. | 30 avr. 2016 | $70.09 | -1.53% | 2,065.30 | 0.27% | |
| 16. | 31 mai 2016 | $66.04 | $0.30 | -5.35% | 2,096.95 | 1.53% |
| 17. | 30 juin 2016 | $66.46 | 0.64% | 2,098.86 | 0.09% | |
| 18. | 31 juil. 2016 | $71.70 | 7.88% | 2,173.60 | 3.56% | |
| 19. | 31 août 2016 | $71.33 | -0.52% | 2,170.95 | -0.12% | |
| 20. | 30 sept. 2016 | $67.33 | $0.30 | -5.19% | 2,168.27 | -0.12% |
| 21. | 31 oct. 2016 | $68.70 | 2.03% | 2,126.15 | -1.94% | |
| 22. | 30 nov. 2016 | $78.78 | $0.30 | 15.11% | 2,198.81 | 3.42% |
| 23. | 31 déc. 2016 | $82.68 | 4.95% | 2,238.83 | 1.82% | |
| 24. | 31 janv. 2017 | $84.60 | 2.32% | 2,278.87 | 1.79% | |
| 25. | 28 févr. 2017 | $86.99 | $0.30 | 3.18% | 2,363.64 | 3.72% |
| 26. | 31 mars 2017 | $94.18 | 8.27% | 2,362.72 | -0.04% | |
| 27. | 30 avr. 2017 | $94.42 | 0.25% | 2,384.20 | 0.91% | |
| 28. | 31 mai 2017 | $107.65 | $0.33 | 14.36% | 2,411.80 | 1.16% |
| 29. | 30 juin 2017 | $100.31 | -6.82% | 2,423.41 | 0.48% | |
| 30. | 31 juil. 2017 | $104.19 | 3.87% | 2,470.30 | 1.93% | |
| 31. | 31 août 2017 | $103.58 | $0.33 | -0.27% | 2,471.65 | 0.05% |
| 32. | 30 sept. 2017 | $110.26 | 6.45% | 2,519.36 | 1.93% | |
| 33. | 31 oct. 2017 | $119.48 | 8.36% | 2,575.26 | 2.22% | |
| 34. | 30 nov. 2017 | $127.00 | $0.33 | 6.57% | 2,647.58 | 2.81% |
| 35. | 31 déc. 2017 | $135.73 | 6.87% | 2,673.61 | 0.98% | |
| 36. | 31 janv. 2018 | $147.34 | 8.55% | 2,823.81 | 5.62% | |
| 37. | 28 févr. 2018 | $141.21 | $0.33 | -3.94% | 2,713.83 | -3.89% |
| 38. | 31 mars 2018 | $135.98 | -3.70% | 2,640.87 | -2.69% | |
| 39. | 30 avr. 2018 | $136.68 | 0.51% | 2,648.05 | 0.27% | |
| 40. | 31 mai 2018 | $135.36 | $0.41 | -0.67% | 2,705.27 | 2.16% |
| 41. | 30 juin 2018 | $126.60 | -6.47% | 2,718.37 | 0.48% | |
| 42. | 31 juil. 2018 | $127.84 | 0.98% | 2,816.29 | 3.60% | |
| 43. | 31 août 2018 | $126.47 | $0.41 | -0.75% | 2,901.52 | 3.03% |
| 44. | 30 sept. 2018 | $132.03 | 4.40% | 2,913.98 | 0.43% | |
| 45. | 31 oct. 2018 | $116.89 | -11.47% | 2,711.74 | -6.94% | |
| 46. | 30 nov. 2018 | $115.03 | $0.41 | -1.24% | 2,760.17 | 1.79% |
| 47. | 31 déc. 2018 | $108.56 | -5.62% | 2,506.85 | -9.18% | |
| 48. | 31 janv. 2019 | $114.53 | 5.50% | 2,704.10 | 7.87% | |
| 49. | 28 févr. 2019 | $125.27 | $0.41 | 9.74% | 2,784.49 | 2.97% |
| 50. | 31 mars 2019 | $125.09 | -0.14% | 2,834.40 | 1.79% | |
| 51. | 30 avr. 2019 | $136.42 | 9.06% | 2,945.83 | 3.93% | |
| 52. | 31 mai 2019 | $124.84 | $0.48 | -8.14% | 2,752.06 | -6.58% |
| 53. | 30 juin 2019 | $140.29 | 12.38% | 2,941.76 | 6.89% | |
| 54. | 31 juil. 2019 | $139.06 | -0.88% | 2,980.38 | 1.31% | |
| 55. | 31 août 2019 | $126.06 | $0.48 | -9.00% | 2,926.46 | -1.81% |
| 56. | 30 sept. 2019 | $124.37 | -1.34% | 2,976.74 | 1.72% | |
| 57. | 31 oct. 2019 | $126.55 | 1.75% | 3,037.56 | 2.04% | |
| 58. | 30 nov. 2019 | $140.36 | $0.48 | 11.29% | 3,140.98 | 3.40% |
| 59. | 31 déc. 2019 | $151.43 | 7.89% | 3,230.78 | 2.86% | |
| Moyenne (R): | 1.53% | 0.88% | ||||
| Écart type: | 6.56% | 3.45% | ||||
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 MAR 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
Marriott International Inc., calcul de la variance et de la covariance des rendements
| t | Date | RMAR,t | RS&P 500,t | (RMAR,t–RMAR)2 | (RS&P 500,t–RS&P 500)2 | (RMAR,t–RMAR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2015 | 11.81% | 5.49% | 105.66 | 21.25 | 47.39 |
| 2. | 31 mars 2015 | -3.35% | -1.74% | 23.80 | 6.86 | 12.78 |
| 3. | 30 avr. 2015 | -0.34% | 0.85% | 3.49 | 0.00 | 0.05 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | 11.29% | 3.40% | 95.24 | 6.38 | 24.65 |
| 59. | 31 déc. 2019 | 7.89% | 2.86% | 40.37 | 3.92 | 12.58 |
| Total (Σ): | 2,496.73 | 688.77 | 893.73 | |||
| t | Date | RMAR,t | RS&P 500,t | (RMAR,t–RMAR)2 | (RS&P 500,t–RS&P 500)2 | (RMAR,t–RMAR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2015 | 11.81% | 5.49% | 105.66 | 21.25 | 47.39 |
| 2. | 31 mars 2015 | -3.35% | -1.74% | 23.80 | 6.86 | 12.78 |
| 3. | 30 avr. 2015 | -0.34% | 0.85% | 3.49 | 0.00 | 0.05 |
| 4. | 31 mai 2015 | -2.26% | 1.05% | 14.39 | 0.03 | -0.65 |
| 5. | 30 juin 2015 | -4.62% | -2.10% | 37.81 | 8.88 | 18.33 |
| 6. | 31 juil. 2015 | -2.39% | 1.97% | 15.41 | 1.20 | -4.30 |
| 7. | 31 août 2015 | -2.34% | -6.26% | 15.01 | 50.94 | 27.65 |
| 8. | 30 sept. 2015 | -3.48% | -2.64% | 25.14 | 12.41 | 17.67 |
| 9. | 31 oct. 2015 | 12.58% | 8.30% | 122.05 | 55.04 | 81.96 |
| 10. | 30 nov. 2015 | -7.32% | 0.05% | 78.37 | 0.69 | 7.34 |
| 11. | 31 déc. 2015 | -5.46% | -1.75% | 48.87 | 6.93 | 18.40 |
| 12. | 31 janv. 2016 | -8.59% | -5.07% | 102.51 | 35.43 | 60.27 |
| 13. | 29 févr. 2016 | 11.62% | -0.41% | 101.72 | 1.67 | -13.03 |
| 14. | 31 mars 2016 | 4.45% | 6.60% | 8.49 | 32.72 | 16.66 |
| 15. | 30 avr. 2016 | -1.53% | 0.27% | 9.39 | 0.37 | 1.87 |
| 16. | 31 mai 2016 | -5.35% | 1.53% | 47.38 | 0.43 | -4.50 |
| 17. | 30 juin 2016 | 0.64% | 0.09% | 0.80 | 0.62 | 0.71 |
| 18. | 31 juil. 2016 | 7.88% | 3.56% | 40.34 | 7.19 | 17.03 |
| 19. | 31 août 2016 | -0.52% | -0.12% | 4.20 | 1.00 | 2.05 |
| 20. | 30 sept. 2016 | -5.19% | -0.12% | 45.16 | 1.01 | 6.74 |
| 21. | 31 oct. 2016 | 2.03% | -1.94% | 0.25 | 7.96 | -1.42 |
| 22. | 30 nov. 2016 | 15.11% | 3.42% | 184.31 | 6.44 | 34.46 |
| 23. | 31 déc. 2016 | 4.95% | 1.82% | 11.68 | 0.89 | 3.22 |
| 24. | 31 janv. 2017 | 2.32% | 1.79% | 0.62 | 0.83 | 0.72 |
| 25. | 28 févr. 2017 | 3.18% | 3.72% | 2.71 | 8.07 | 4.68 |
| 26. | 31 mars 2017 | 8.27% | -0.04% | 45.32 | 0.84 | -6.18 |
| 27. | 30 avr. 2017 | 0.25% | 0.91% | 1.63 | 0.00 | -0.04 |
| 28. | 31 mai 2017 | 14.36% | 1.16% | 164.57 | 0.08 | 3.57 |
| 29. | 30 juin 2017 | -6.82% | 0.48% | 69.75 | 0.16 | 3.32 |
| 30. | 31 juil. 2017 | 3.87% | 1.93% | 5.45 | 1.11 | 2.47 |
| 31. | 31 août 2017 | -0.27% | 0.05% | 3.25 | 0.68 | 1.49 |
| 32. | 30 sept. 2017 | 6.45% | 1.93% | 24.17 | 1.10 | 5.17 |
| 33. | 31 oct. 2017 | 8.36% | 2.22% | 46.64 | 1.79 | 9.15 |
| 34. | 30 nov. 2017 | 6.57% | 2.81% | 25.37 | 3.72 | 9.72 |
| 35. | 31 déc. 2017 | 6.87% | 0.98% | 28.53 | 0.01 | 0.56 |
| 36. | 31 janv. 2018 | 8.55% | 5.62% | 49.29 | 22.46 | 33.27 |
| 37. | 28 févr. 2018 | -3.94% | -3.89% | 29.91 | 22.79 | 26.11 |
| 38. | 31 mars 2018 | -3.70% | -2.69% | 27.42 | 12.73 | 18.68 |
| 39. | 30 avr. 2018 | 0.51% | 0.27% | 1.04 | 0.37 | 0.62 |
| 40. | 31 mai 2018 | -0.67% | 2.16% | 4.83 | 1.64 | -2.82 |
| 41. | 30 juin 2018 | -6.47% | 0.48% | 64.07 | 0.16 | 3.16 |
| 42. | 31 juil. 2018 | 0.98% | 3.60% | 0.31 | 7.41 | -1.51 |
| 43. | 31 août 2018 | -0.75% | 3.03% | 5.22 | 4.61 | -4.90 |
| 44. | 30 sept. 2018 | 4.40% | 0.43% | 8.20 | 0.20 | -1.29 |
| 45. | 31 oct. 2018 | -11.47% | -6.94% | 169.00 | 61.14 | 101.65 |
| 46. | 30 nov. 2018 | -1.24% | 1.79% | 7.69 | 0.82 | -2.52 |
| 47. | 31 déc. 2018 | -5.62% | -9.18% | 51.23 | 101.14 | 71.98 |
| 48. | 31 janv. 2019 | 5.50% | 7.87% | 15.73 | 48.85 | 27.72 |
| 49. | 28 févr. 2019 | 9.74% | 2.97% | 67.28 | 4.38 | 17.17 |
| 50. | 31 mars 2019 | -0.14% | 1.79% | 2.81 | 0.83 | -1.53 |
| 51. | 30 avr. 2019 | 9.06% | 3.93% | 56.62 | 9.32 | 22.97 |
| 52. | 31 mai 2019 | -8.14% | -6.58% | 93.50 | 55.61 | 72.11 |
| 53. | 30 juin 2019 | 12.38% | 6.89% | 117.57 | 36.17 | 65.21 |
| 54. | 31 juil. 2019 | -0.88% | 1.31% | 5.81 | 0.19 | -1.05 |
| 55. | 31 août 2019 | -9.00% | -1.81% | 111.01 | 7.23 | 28.32 |
| 56. | 30 sept. 2019 | -1.34% | 1.72% | 8.26 | 0.70 | -2.41 |
| 57. | 31 oct. 2019 | 1.75% | 2.04% | 0.05 | 1.36 | 0.26 |
| 58. | 30 nov. 2019 | 11.29% | 3.40% | 95.24 | 6.38 | 24.65 |
| 59. | 31 déc. 2019 | 7.89% | 2.86% | 40.37 | 3.92 | 12.58 |
| Total (Σ): | 2,496.73 | 688.77 | 893.73 | |||
Tout afficher
VarianceMAR = Σ(RMAR,t–RMAR)2 ÷ (59 – 1)
= 2,496.73 ÷ (59 – 1)
= 43.05
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
CovarianceMAR, S&P 500 = Σ(RMAR,t–RMAR)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 893.73 ÷ (59 – 1)
= 15.41
Estimation systématique des risques (β)
| VarianceMAR | 43.05 |
| VarianceS&P 500 | 11.88 |
| CovarianceMAR, S&P 500 | 15.41 |
| Coefficient de corrélationMAR, S&P 5001 | 0.68 |
| βMAR2 | 1.30 |
| αMAR3 | 0.39% |
Calculs
1 Coefficient de corrélationMAR, S&P 500
= CovarianceMAR, S&P 500 ÷ (Écart typeMAR × Écart typeS&P 500)
= 15.41 ÷ (6.56% × 3.45%)
= 0.68
2 βMAR
= CovarianceMAR, S&P 500 ÷ VarianceS&P 500
= 15.41 ÷ 11.88
= 1.30
3 αMAR
= MoyenneMAR – βMAR × MoyenneS&P 500
= 1.53% – 1.30 × 0.88%
= 0.39%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.76% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 15.13% |
| Risque systématique lié à Marriott actions ordinaires | βMAR | 1.30 |
| Taux de rendement attendu des actions ordinaires de Marriott3 | E(RMAR) | 18.22% |
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(RMAR) = RF + βMAR [E(RM) – RF]
= 4.76% + 1.30 [15.13% – 4.76%]
= 18.22%