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 Time Warner.
Taux de rendement
Time Warner Inc., taux de rendement mensuels
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixTWX,t1 | DividendeTWX,t1 | RTWX,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2013 | $50.52 | 1,498.11 | ||||
| 1. | 28 févr. 2013 | $53.17 | $0.2875 | 5.81% | 1,514.68 | 1.11% |
| 2. | 31 mars 2013 | $57.62 | 8.37% | 1,569.19 | 3.60% | |
| 3. | 30 avr. 2013 | $59.78 | 3.75% | 1,597.57 | 1.81% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2017 | $91.51 | -6.90% | 2,647.58 | 2.81% | |
| 59. | 31 déc. 2017 | $91.47 | -0.04% | 2,673.61 | 0.98% | |
| Moyenne (R): | 1.35% | 1.02% | ||||
| Écart type: | 6.00% | 2.71% | ||||
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixTWX,t1 | DividendeTWX,t1 | RTWX,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2013 | $50.52 | 1,498.11 | ||||
| 1. | 28 févr. 2013 | $53.17 | $0.2875 | 5.81% | 1,514.68 | 1.11% |
| 2. | 31 mars 2013 | $57.62 | 8.37% | 1,569.19 | 3.60% | |
| 3. | 30 avr. 2013 | $59.78 | 3.75% | 1,597.57 | 1.81% | |
| 4. | 31 mai 2013 | $58.37 | $0.2875 | -1.88% | 1,630.74 | 2.08% |
| 5. | 30 juin 2013 | $57.82 | -0.94% | 1,606.28 | -1.50% | |
| 6. | 31 juil. 2013 | $62.26 | 7.68% | 1,685.73 | 4.95% | |
| 7. | 31 août 2013 | $60.53 | $0.2875 | -2.32% | 1,632.97 | -3.13% |
| 8. | 30 sept. 2013 | $65.81 | 8.72% | 1,681.55 | 2.97% | |
| 9. | 31 oct. 2013 | $68.74 | 4.45% | 1,756.54 | 4.46% | |
| 10. | 30 nov. 2013 | $65.71 | $0.2875 | -3.99% | 1,805.81 | 2.80% |
| 11. | 31 déc. 2013 | $69.72 | 6.10% | 1,848.36 | 2.36% | |
| 12. | 31 janv. 2014 | $62.83 | -9.88% | 1,782.59 | -3.56% | |
| 13. | 28 févr. 2014 | $67.13 | $0.3175 | 7.35% | 1,859.45 | 4.31% |
| 14. | 31 mars 2014 | $65.33 | -2.68% | 1,872.34 | 0.69% | |
| 15. | 30 avr. 2014 | $66.46 | 1.73% | 1,883.95 | 0.62% | |
| 16. | 31 mai 2014 | $69.83 | $0.3175 | 5.55% | 1,923.57 | 2.10% |
| 17. | 30 juin 2014 | $70.25 | 0.60% | 1,960.23 | 1.91% | |
| 18. | 31 juil. 2014 | $83.02 | 18.18% | 1,930.67 | -1.51% | |
| 19. | 31 août 2014 | $77.03 | $0.3175 | -6.83% | 2,003.37 | 3.77% |
| 20. | 30 sept. 2014 | $75.21 | -2.36% | 1,972.29 | -1.55% | |
| 21. | 31 oct. 2014 | $79.47 | 5.66% | 2,018.05 | 2.32% | |
| 22. | 30 nov. 2014 | $85.12 | $0.3175 | 7.51% | 2,067.56 | 2.45% |
| 23. | 31 déc. 2014 | $85.42 | 0.35% | 2,058.90 | -0.42% | |
| 24. | 31 janv. 2015 | $77.93 | -8.77% | 1,994.99 | -3.10% | |
| 25. | 28 févr. 2015 | $81.86 | $0.35 | 5.49% | 2,104.50 | 5.49% |
| 26. | 31 mars 2015 | $84.44 | 3.15% | 2,067.89 | -1.74% | |
| 27. | 30 avr. 2015 | $84.41 | -0.04% | 2,085.51 | 0.85% | |
| 28. | 31 mai 2015 | $84.48 | $0.35 | 0.50% | 2,107.39 | 1.05% |
| 29. | 30 juin 2015 | $87.41 | 3.47% | 2,063.11 | -2.10% | |
| 30. | 31 juil. 2015 | $88.04 | 0.72% | 2,103.84 | 1.97% | |
| 31. | 31 août 2015 | $71.10 | $0.35 | -18.84% | 1,972.18 | -6.26% |
| 32. | 30 sept. 2015 | $68.75 | -3.31% | 1,920.03 | -2.64% | |
| 33. | 31 oct. 2015 | $75.34 | 9.59% | 2,079.36 | 8.30% | |
| 34. | 30 nov. 2015 | $69.98 | $0.35 | -6.65% | 2,080.41 | 0.05% |
| 35. | 31 déc. 2015 | $64.67 | -7.59% | 2,043.94 | -1.75% | |
| 36. | 31 janv. 2016 | $70.44 | 8.92% | 1,940.24 | -5.07% | |
| 37. | 29 févr. 2016 | $66.20 | $0.4025 | -5.45% | 1,932.23 | -0.41% |
| 38. | 31 mars 2016 | $72.55 | 9.59% | 2,059.74 | 6.60% | |
| 39. | 30 avr. 2016 | $75.14 | 3.57% | 2,065.30 | 0.27% | |
| 40. | 31 mai 2016 | $75.66 | $0.4025 | 1.23% | 2,096.95 | 1.53% |
| 41. | 30 juin 2016 | $73.54 | -2.80% | 2,098.86 | 0.09% | |
| 42. | 31 juil. 2016 | $76.65 | 4.23% | 2,173.60 | 3.56% | |
| 43. | 31 août 2016 | $78.41 | $0.4025 | 2.82% | 2,170.95 | -0.12% |
| 44. | 30 sept. 2016 | $79.61 | 1.53% | 2,168.27 | -0.12% | |
| 45. | 31 oct. 2016 | $88.99 | 11.78% | 2,126.15 | -1.94% | |
| 46. | 30 nov. 2016 | $91.82 | $0.4025 | 3.63% | 2,198.81 | 3.42% |
| 47. | 31 déc. 2016 | $96.53 | 5.13% | 2,238.83 | 1.82% | |
| 48. | 31 janv. 2017 | $96.85 | 0.33% | 2,278.87 | 1.79% | |
| 49. | 28 févr. 2017 | $98.21 | $0.4025 | 1.82% | 2,363.64 | 3.72% |
| 50. | 31 mars 2017 | $97.71 | -0.51% | 2,362.72 | -0.04% | |
| 51. | 30 avr. 2017 | $99.27 | 1.60% | 2,384.20 | 0.91% | |
| 52. | 31 mai 2017 | $99.49 | $0.4025 | 0.63% | 2,411.80 | 1.16% |
| 53. | 30 juin 2017 | $100.41 | 0.92% | 2,423.41 | 0.48% | |
| 54. | 31 juil. 2017 | $102.42 | $0.4025 | 2.40% | 2,470.30 | 1.93% |
| 55. | 31 août 2017 | $101.10 | -1.29% | 2,471.65 | 0.05% | |
| 56. | 30 sept. 2017 | $102.45 | 1.34% | 2,519.36 | 1.93% | |
| 57. | 31 oct. 2017 | $98.29 | $0.4025 | -3.67% | 2,575.26 | 2.22% |
| 58. | 30 nov. 2017 | $91.51 | -6.90% | 2,647.58 | 2.81% | |
| 59. | 31 déc. 2017 | $91.47 | -0.04% | 2,673.61 | 0.98% | |
| Moyenne (R): | 1.35% | 1.02% | ||||
| Écart type: | 6.00% | 2.71% | ||||
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 TWX 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
Time Warner Inc., calcul de la variance et de la covariance des rendements
| t | Date | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2013 | 5.81% | 1.11% | 19.96 | 0.01 | 0.37 |
| 2. | 31 mars 2013 | 8.37% | 3.60% | 49.31 | 6.64 | 18.09 |
| 3. | 30 avr. 2013 | 3.75% | 1.81% | 5.77 | 0.62 | 1.89 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2017 | -6.90% | 2.81% | 67.98 | 3.19 | -14.73 |
| 59. | 31 déc. 2017 | -0.04% | 0.98% | 1.93 | 0.00 | 0.05 |
| Total (Σ): | 2,090.08 | 424.45 | 406.20 | |||
| t | Date | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2013 | 5.81% | 1.11% | 19.96 | 0.01 | 0.37 |
| 2. | 31 mars 2013 | 8.37% | 3.60% | 49.31 | 6.64 | 18.09 |
| 3. | 30 avr. 2013 | 3.75% | 1.81% | 5.77 | 0.62 | 1.89 |
| 4. | 31 mai 2013 | -1.88% | 2.08% | 10.40 | 1.11 | -3.40 |
| 5. | 30 juin 2013 | -0.94% | -1.50% | 5.24 | 6.36 | 5.77 |
| 6. | 31 juil. 2013 | 7.68% | 4.95% | 40.09 | 15.40 | 24.85 |
| 7. | 31 août 2013 | -2.32% | -3.13% | 13.42 | 17.24 | 15.21 |
| 8. | 30 sept. 2013 | 8.72% | 2.97% | 54.40 | 3.81 | 14.40 |
| 9. | 31 oct. 2013 | 4.45% | 4.46% | 9.64 | 11.81 | 10.67 |
| 10. | 30 nov. 2013 | -3.99% | 2.80% | 28.48 | 3.18 | -9.51 |
| 11. | 31 déc. 2013 | 6.10% | 2.36% | 22.61 | 1.78 | 6.34 |
| 12. | 31 janv. 2014 | -9.88% | -3.56% | 126.10 | 20.98 | 51.44 |
| 13. | 28 févr. 2014 | 7.35% | 4.31% | 36.03 | 10.82 | 19.74 |
| 14. | 31 mars 2014 | -2.68% | 0.69% | 16.23 | 0.11 | 1.33 |
| 15. | 30 avr. 2014 | 1.73% | 0.62% | 0.15 | 0.16 | -0.15 |
| 16. | 31 mai 2014 | 5.55% | 2.10% | 17.65 | 1.17 | 4.54 |
| 17. | 30 juin 2014 | 0.60% | 1.91% | 0.56 | 0.78 | -0.66 |
| 18. | 31 juil. 2014 | 18.18% | -1.51% | 283.28 | 6.40 | -42.59 |
| 19. | 31 août 2014 | -6.83% | 3.77% | 66.91 | 7.53 | -22.44 |
| 20. | 30 sept. 2014 | -2.36% | -1.55% | 13.76 | 6.62 | 9.55 |
| 21. | 31 oct. 2014 | 5.66% | 2.32% | 18.64 | 1.68 | 5.60 |
| 22. | 30 nov. 2014 | 7.51% | 2.45% | 37.97 | 2.05 | 8.82 |
| 23. | 31 déc. 2014 | 0.35% | -0.42% | 0.99 | 2.08 | 1.43 |
| 24. | 31 janv. 2015 | -8.77% | -3.10% | 102.32 | 17.03 | 41.74 |
| 25. | 28 févr. 2015 | 5.49% | 5.49% | 17.18 | 19.95 | 18.52 |
| 26. | 31 mars 2015 | 3.15% | -1.74% | 3.26 | 7.63 | -4.98 |
| 27. | 30 avr. 2015 | -0.04% | 0.85% | 1.91 | 0.03 | 0.24 |
| 28. | 31 mai 2015 | 0.50% | 1.05% | 0.72 | 0.00 | -0.02 |
| 29. | 30 juin 2015 | 3.47% | -2.10% | 4.50 | 9.76 | -6.63 |
| 30. | 31 juil. 2015 | 0.72% | 1.97% | 0.39 | 0.91 | -0.60 |
| 31. | 31 août 2015 | -18.84% | -6.26% | 407.67 | 53.00 | 147.00 |
| 32. | 30 sept. 2015 | -3.31% | -2.64% | 21.64 | 13.44 | 17.06 |
| 33. | 31 oct. 2015 | 9.59% | 8.30% | 67.87 | 52.94 | 59.94 |
| 34. | 30 nov. 2015 | -6.65% | 0.05% | 63.95 | 0.94 | 7.77 |
| 35. | 31 déc. 2015 | -7.59% | -1.75% | 79.83 | 7.70 | 24.80 |
| 36. | 31 janv. 2016 | 8.92% | -5.07% | 57.38 | 37.16 | -46.18 |
| 37. | 29 févr. 2016 | -5.45% | -0.41% | 46.17 | 2.06 | 9.75 |
| 38. | 31 mars 2016 | 9.59% | 6.60% | 67.98 | 31.10 | 45.98 |
| 39. | 30 avr. 2016 | 3.57% | 0.27% | 4.94 | 0.57 | -1.67 |
| 40. | 31 mai 2016 | 1.23% | 1.53% | 0.01 | 0.26 | -0.06 |
| 41. | 30 juin 2016 | -2.80% | 0.09% | 17.22 | 0.87 | 3.86 |
| 42. | 31 juil. 2016 | 4.23% | 3.56% | 8.31 | 6.44 | 7.32 |
| 43. | 31 août 2016 | 2.82% | -0.12% | 2.17 | 1.31 | -1.69 |
| 44. | 30 sept. 2016 | 1.53% | -0.12% | 0.03 | 1.31 | -0.21 |
| 45. | 31 oct. 2016 | 11.78% | -1.94% | 108.90 | 8.79 | -30.94 |
| 46. | 30 nov. 2016 | 3.63% | 3.42% | 5.22 | 5.74 | 5.47 |
| 47. | 31 déc. 2016 | 5.13% | 1.82% | 14.31 | 0.64 | 3.02 |
| 48. | 31 janv. 2017 | 0.33% | 1.79% | 1.03 | 0.59 | -0.78 |
| 49. | 28 févr. 2017 | 1.82% | 3.72% | 0.22 | 7.28 | 1.28 |
| 50. | 31 mars 2017 | -0.51% | -0.04% | 3.45 | 1.13 | 1.97 |
| 51. | 30 avr. 2017 | 1.60% | 0.91% | 0.06 | 0.01 | -0.03 |
| 52. | 31 mai 2017 | 0.63% | 1.16% | 0.52 | 0.02 | -0.10 |
| 53. | 30 juin 2017 | 0.92% | 0.48% | 0.18 | 0.29 | 0.23 |
| 54. | 31 juil. 2017 | 2.40% | 1.93% | 1.11 | 0.83 | 0.96 |
| 55. | 31 août 2017 | -1.29% | 0.05% | 6.95 | 0.94 | 2.55 |
| 56. | 30 sept. 2017 | 1.34% | 1.93% | 0.00 | 0.82 | -0.01 |
| 57. | 31 oct. 2017 | -3.67% | 2.22% | 25.15 | 1.43 | -6.00 |
| 58. | 30 nov. 2017 | -6.90% | 2.81% | 67.98 | 3.19 | -14.73 |
| 59. | 31 déc. 2017 | -0.04% | 0.98% | 1.93 | 0.00 | 0.05 |
| Total (Σ): | 2,090.08 | 424.45 | 406.20 | |||
Tout afficher
VarianceTWX = Σ(RTWX,t–RTWX)2 ÷ (59 – 1)
= 2,090.08 ÷ (59 – 1)
= 36.04
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 424.45 ÷ (59 – 1)
= 7.32
CovarianceTWX, S&P 500 = Σ(RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 406.20 ÷ (59 – 1)
= 7.00
Estimation systématique des risques (β)
| VarianceTWX | 36.04 |
| VarianceS&P 500 | 7.32 |
| CovarianceTWX, S&P 500 | 7.00 |
| Coefficient de corrélationTWX, S&P 5001 | 0.43 |
| βTWX2 | 0.96 |
| αTWX3 | 0.37% |
Calculs
1 Coefficient de corrélationTWX, S&P 500
= CovarianceTWX, S&P 500 ÷ (Écart typeTWX × Écart typeS&P 500)
= 7.00 ÷ (6.00% × 2.71%)
= 0.43
2 βTWX
= CovarianceTWX, S&P 500 ÷ VarianceS&P 500
= 7.00 ÷ 7.32
= 0.96
3 αTWX
= MoyenneTWX – βTWX × MoyenneS&P 500
= 1.35% – 0.96 × 1.02%
= 0.37%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.86% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 13.52% |
| Risque systématique lié à Time Warner actions ordinaires | βTWX | 0.96 |
| Taux de rendement attendu des actions ordinaires de Time Warner3 | E(RTWX) | 13.15% |
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(RTWX) = RF + βTWX [E(RM) – RF]
= 4.86% + 0.96 [13.52% – 4.86%]
= 13.15%