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 RAI.
Taux de rendement
Reynolds American Inc., taux de rendement mensuels
| Reynolds American Inc. (RAI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixRAI,t1 | DividendeRAI,t1 | RRAI,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2012 | $19.62 | 1,312.41 | ||||
| 1. | 29 févr. 2012 | $20.97 | 6.88% | 1,365.68 | 4.06% | |
| 2. | 31 mars 2012 | $20.72 | $0.28 | 0.14% | 1,408.47 | 3.13% |
| 3. | 30 avr. 2012 | $20.42 | -1.45% | 1,397.91 | -0.75% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2016 | $54.10 | -1.78% | 2,198.81 | 3.42% | |
| 59. | 31 déc. 2016 | $56.04 | $0.46 | 4.44% | 2,238.83 | 1.82% |
| Moyenne (R): | 2.30% | 0.95% | ||||
| Écart type: | 5.18% | 2.98% | ||||
| Reynolds American Inc. (RAI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixRAI,t1 | DividendeRAI,t1 | RRAI,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2012 | $19.62 | 1,312.41 | ||||
| 1. | 29 févr. 2012 | $20.97 | 6.88% | 1,365.68 | 4.06% | |
| 2. | 31 mars 2012 | $20.72 | $0.28 | 0.14% | 1,408.47 | 3.13% |
| 3. | 30 avr. 2012 | $20.42 | -1.45% | 1,397.91 | -0.75% | |
| 4. | 31 mai 2012 | $20.92 | 2.45% | 1,310.33 | -6.27% | |
| 5. | 30 juin 2012 | $22.44 | $0.295 | 8.68% | 1,362.16 | 3.96% |
| 6. | 31 juil. 2012 | $23.14 | 3.12% | 1,379.32 | 1.26% | |
| 7. | 31 août 2012 | $23.05 | -0.39% | 1,406.58 | 1.98% | |
| 8. | 30 sept. 2012 | $21.67 | $0.295 | -4.71% | 1,440.67 | 2.42% |
| 9. | 31 oct. 2012 | $20.82 | -3.92% | 1,412.16 | -1.98% | |
| 10. | 30 nov. 2012 | $21.86 | 5.00% | 1,416.18 | 0.28% | |
| 11. | 31 déc. 2012 | $20.72 | $0.295 | -3.87% | 1,426.19 | 0.71% |
| 12. | 31 janv. 2013 | $21.99 | 6.13% | 1,498.11 | 5.04% | |
| 13. | 28 févr. 2013 | $21.84 | -0.68% | 1,514.68 | 1.11% | |
| 14. | 31 mars 2013 | $22.25 | $0.295 | 3.23% | 1,569.19 | 3.60% |
| 15. | 30 avr. 2013 | $23.71 | 6.56% | 1,597.57 | 1.81% | |
| 16. | 31 mai 2013 | $24.06 | 1.48% | 1,630.74 | 2.08% | |
| 17. | 30 juin 2013 | $24.19 | $0.315 | 1.85% | 1,606.28 | -1.50% |
| 18. | 31 juil. 2013 | $24.72 | 2.19% | 1,685.73 | 4.95% | |
| 19. | 31 août 2013 | $23.82 | -3.64% | 1,632.97 | -3.13% | |
| 20. | 30 sept. 2013 | $24.39 | $0.315 | 3.72% | 1,681.55 | 2.97% |
| 21. | 31 oct. 2013 | $25.69 | 5.33% | 1,756.54 | 4.46% | |
| 22. | 30 nov. 2013 | $25.23 | -1.79% | 1,805.81 | 2.80% | |
| 23. | 31 déc. 2013 | $25.00 | $0.315 | 0.34% | 1,848.36 | 2.36% |
| 24. | 31 janv. 2014 | $24.25 | -3.00% | 1,782.59 | -3.56% | |
| 25. | 28 févr. 2014 | $25.42 | 4.82% | 1,859.45 | 4.31% | |
| 26. | 31 mars 2014 | $26.71 | $0.335 | 6.39% | 1,872.34 | 0.69% |
| 27. | 30 avr. 2014 | $28.22 | 5.65% | 1,883.95 | 0.62% | |
| 28. | 31 mai 2014 | $29.82 | 5.67% | 1,923.57 | 2.10% | |
| 29. | 30 juin 2014 | $30.18 | $0.335 | 2.33% | 1,960.23 | 1.91% |
| 30. | 31 juil. 2014 | $27.93 | -7.46% | 1,930.67 | -1.51% | |
| 31. | 31 août 2014 | $29.24 | 4.69% | 2,003.37 | 3.77% | |
| 32. | 30 sept. 2014 | $29.50 | $0.335 | 2.03% | 1,972.29 | -1.55% |
| 33. | 31 oct. 2014 | $31.46 | 6.64% | 2,018.05 | 2.32% | |
| 34. | 30 nov. 2014 | $32.96 | 4.77% | 2,067.56 | 2.45% | |
| 35. | 31 déc. 2014 | $32.14 | $0.335 | -1.47% | 2,058.90 | -0.42% |
| 36. | 31 janv. 2015 | $33.98 | 5.72% | 1,994.99 | -3.10% | |
| 37. | 28 févr. 2015 | $37.81 | 11.27% | 2,104.50 | 5.49% | |
| 38. | 31 mars 2015 | $34.46 | $0.335 | -7.97% | 2,067.89 | -1.74% |
| 39. | 30 avr. 2015 | $36.65 | 6.36% | 2,085.51 | 0.85% | |
| 40. | 31 mai 2015 | $38.38 | 4.72% | 2,107.39 | 1.05% | |
| 41. | 30 juin 2015 | $37.33 | $0.335 | -1.86% | 2,063.11 | -2.10% |
| 42. | 31 juil. 2015 | $42.90 | 14.92% | 2,103.84 | 1.97% | |
| 43. | 31 août 2015 | $41.88 | -2.38% | 1,972.18 | -6.26% | |
| 44. | 30 sept. 2015 | $44.27 | $0.36 | 6.57% | 1,920.03 | -2.64% |
| 45. | 31 oct. 2015 | $48.32 | 9.15% | 2,079.36 | 8.30% | |
| 46. | 30 nov. 2015 | $46.25 | -4.28% | 2,080.41 | 0.05% | |
| 47. | 31 déc. 2015 | $46.15 | $0.36 | 0.56% | 2,043.94 | -1.75% |
| 48. | 31 janv. 2016 | $49.95 | 8.23% | 1,940.24 | -5.07% | |
| 49. | 29 févr. 2016 | $50.43 | 0.96% | 1,932.23 | -0.41% | |
| 50. | 31 mars 2016 | $50.31 | $0.42 | 0.59% | 2,059.74 | 6.60% |
| 51. | 30 avr. 2016 | $49.60 | -1.41% | 2,065.30 | 0.27% | |
| 52. | 31 mai 2016 | $49.70 | 0.20% | 2,096.95 | 1.53% | |
| 53. | 30 juin 2016 | $53.93 | $0.42 | 9.36% | 2,098.86 | 0.09% |
| 54. | 31 juil. 2016 | $50.06 | -7.18% | 2,173.60 | 3.56% | |
| 55. | 31 août 2016 | $49.57 | -0.98% | 2,170.95 | -0.12% | |
| 56. | 30 sept. 2016 | $47.15 | $0.46 | -3.95% | 2,168.27 | -0.12% |
| 57. | 31 oct. 2016 | $55.08 | 16.82% | 2,126.15 | -1.94% | |
| 58. | 30 nov. 2016 | $54.10 | -1.78% | 2,198.81 | 3.42% | |
| 59. | 31 déc. 2016 | $56.04 | $0.46 | 4.44% | 2,238.83 | 1.82% |
| Moyenne (R): | 2.30% | 0.95% | ||||
| Écart type: | 5.18% | 2.98% | ||||
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 RAI 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
Reynolds American Inc., calcul de la variance et de la covariance des rendements
| t | Date | RRAI,t | RS&P 500,t | (RRAI,t–RRAI)2 | (RS&P 500,t–RS&P 500)2 | (RRAI,t–RRAI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 févr. 2012 | 6.88% | 4.06% | 20.97 | 9.65 | 14.22 |
| 2. | 31 mars 2012 | 0.14% | 3.13% | 4.66 | 4.75 | -4.71 |
| 3. | 30 avr. 2012 | -1.45% | -0.75% | 14.06 | 2.90 | 6.38 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2016 | -1.78% | 3.42% | 16.65 | 6.07 | -10.06 |
| 59. | 31 déc. 2016 | 4.44% | 1.82% | 4.56 | 0.75 | 1.85 |
| Total (Σ): | 1,555.42 | 514.91 | 214.12 | |||
| t | Date | RRAI,t | RS&P 500,t | (RRAI,t–RRAI)2 | (RS&P 500,t–RS&P 500)2 | (RRAI,t–RRAI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 févr. 2012 | 6.88% | 4.06% | 20.97 | 9.65 | 14.22 |
| 2. | 31 mars 2012 | 0.14% | 3.13% | 4.66 | 4.75 | -4.71 |
| 3. | 30 avr. 2012 | -1.45% | -0.75% | 14.06 | 2.90 | 6.38 |
| 4. | 31 mai 2012 | 2.45% | -6.27% | 0.02 | 52.10 | -1.06 |
| 5. | 30 juin 2012 | 8.68% | 3.96% | 40.63 | 9.02 | 19.14 |
| 6. | 31 juil. 2012 | 3.12% | 1.26% | 0.67 | 0.09 | 0.25 |
| 7. | 31 août 2012 | -0.39% | 1.98% | 7.24 | 1.05 | -2.75 |
| 8. | 30 sept. 2012 | -4.71% | 2.42% | 49.12 | 2.16 | -10.31 |
| 9. | 31 oct. 2012 | -3.92% | -1.98% | 38.74 | 8.60 | 18.25 |
| 10. | 30 nov. 2012 | 5.00% | 0.28% | 7.26 | 0.45 | -1.80 |
| 11. | 31 déc. 2012 | -3.87% | 0.71% | 38.03 | 0.06 | 1.52 |
| 12. | 31 janv. 2013 | 6.13% | 5.04% | 14.65 | 16.73 | 15.66 |
| 13. | 28 févr. 2013 | -0.68% | 1.11% | 8.90 | 0.02 | -0.46 |
| 14. | 31 mars 2013 | 3.23% | 3.60% | 0.86 | 7.00 | 2.45 |
| 15. | 30 avr. 2013 | 6.56% | 1.81% | 18.15 | 0.73 | 3.65 |
| 16. | 31 mai 2013 | 1.48% | 2.08% | 0.68 | 1.26 | -0.93 |
| 17. | 30 juin 2013 | 1.85% | -1.50% | 0.20 | 6.02 | 1.11 |
| 18. | 31 juil. 2013 | 2.19% | 4.95% | 0.01 | 15.95 | -0.44 |
| 19. | 31 août 2013 | -3.64% | -3.13% | 35.31 | 16.67 | 24.26 |
| 20. | 30 sept. 2013 | 3.72% | 2.97% | 2.00 | 4.09 | 2.86 |
| 21. | 31 oct. 2013 | 5.33% | 4.46% | 9.17 | 12.30 | 10.62 |
| 22. | 30 nov. 2013 | -1.79% | 2.80% | 16.75 | 3.43 | -7.58 |
| 23. | 31 déc. 2013 | 0.34% | 2.36% | 3.86 | 1.97 | -2.76 |
| 24. | 31 janv. 2014 | -3.00% | -3.56% | 28.11 | 20.35 | 23.92 |
| 25. | 28 févr. 2014 | 4.82% | 4.31% | 6.37 | 11.28 | 8.48 |
| 26. | 31 mars 2014 | 6.39% | 0.69% | 16.74 | 0.07 | -1.06 |
| 27. | 30 avr. 2014 | 5.65% | 0.62% | 11.23 | 0.11 | -1.12 |
| 28. | 31 mai 2014 | 5.67% | 2.10% | 11.34 | 1.32 | 3.87 |
| 29. | 30 juin 2014 | 2.33% | 1.91% | 0.00 | 0.91 | 0.03 |
| 30. | 31 juil. 2014 | -7.46% | -1.51% | 95.20 | 6.06 | 24.01 |
| 31. | 31 août 2014 | 4.69% | 3.77% | 5.71 | 7.91 | 6.72 |
| 32. | 30 sept. 2014 | 2.03% | -1.55% | 0.07 | 6.27 | 0.67 |
| 33. | 31 oct. 2014 | 6.64% | 2.32% | 18.86 | 1.87 | 5.94 |
| 34. | 30 nov. 2014 | 4.77% | 2.45% | 6.08 | 2.25 | 3.70 |
| 35. | 31 déc. 2014 | -1.47% | -0.42% | 14.24 | 1.88 | 5.18 |
| 36. | 31 janv. 2015 | 5.72% | -3.10% | 11.72 | 16.46 | -13.89 |
| 37. | 28 févr. 2015 | 11.27% | 5.49% | 80.46 | 20.58 | 40.69 |
| 38. | 31 mars 2015 | -7.97% | -1.74% | 105.59 | 7.25 | 27.67 |
| 39. | 30 avr. 2015 | 6.36% | 0.85% | 16.43 | 0.01 | -0.41 |
| 40. | 31 mai 2015 | 4.72% | 1.05% | 5.85 | 0.01 | 0.23 |
| 41. | 30 juin 2015 | -1.86% | -2.10% | 17.34 | 9.33 | 12.72 |
| 42. | 31 juil. 2015 | 14.92% | 1.97% | 159.25 | 1.04 | 12.89 |
| 43. | 31 août 2015 | -2.38% | -6.26% | 21.89 | 52.00 | 33.74 |
| 44. | 30 sept. 2015 | 6.57% | -2.64% | 18.19 | 12.94 | -15.34 |
| 45. | 31 oct. 2015 | 9.15% | 8.30% | 46.88 | 53.96 | 50.29 |
| 46. | 30 nov. 2015 | -4.28% | 0.05% | 43.37 | 0.81 | 5.94 |
| 47. | 31 déc. 2015 | 0.56% | -1.75% | 3.03 | 7.32 | 4.71 |
| 48. | 31 janv. 2016 | 8.23% | -5.07% | 35.19 | 36.32 | -35.75 |
| 49. | 29 févr. 2016 | 0.96% | -0.41% | 1.80 | 1.87 | 1.83 |
| 50. | 31 mars 2016 | 0.59% | 6.60% | 2.91 | 31.88 | -9.64 |
| 51. | 30 avr. 2016 | -1.41% | 0.27% | 13.78 | 0.47 | 2.54 |
| 52. | 31 mai 2016 | 0.20% | 1.53% | 4.41 | 0.34 | -1.22 |
| 53. | 30 juin 2016 | 9.36% | 0.09% | 49.77 | 0.74 | -6.08 |
| 54. | 31 juil. 2016 | -7.18% | 3.56% | 89.82 | 6.80 | -24.72 |
| 55. | 31 août 2016 | -0.98% | -0.12% | 10.76 | 1.16 | 3.53 |
| 56. | 30 sept. 2016 | -3.95% | -0.12% | 39.13 | 1.16 | 6.73 |
| 57. | 31 oct. 2016 | 16.82% | -1.94% | 210.75 | 8.38 | -42.03 |
| 58. | 30 nov. 2016 | -1.78% | 3.42% | 16.65 | 6.07 | -10.06 |
| 59. | 31 déc. 2016 | 4.44% | 1.82% | 4.56 | 0.75 | 1.85 |
| Total (Σ): | 1,555.42 | 514.91 | 214.12 | |||
Tout afficher
VarianceRAI = Σ(RRAI,t–RRAI)2 ÷ (59 – 1)
= 1,555.42 ÷ (59 – 1)
= 26.82
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 514.91 ÷ (59 – 1)
= 8.88
CovarianceRAI, S&P 500 = Σ(RRAI,t–RRAI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 214.12 ÷ (59 – 1)
= 3.69
Estimation systématique des risques (β)
| VarianceRAI | 26.82 |
| VarianceS&P 500 | 8.88 |
| CovarianceRAI, S&P 500 | 3.69 |
| Coefficient de corrélationRAI, S&P 5001 | 0.24 |
| βRAI2 | 0.42 |
| αRAI3 | 1.91% |
Calculs
1 Coefficient de corrélationRAI, S&P 500
= CovarianceRAI, S&P 500 ÷ (Écart typeRAI × Écart typeS&P 500)
= 3.69 ÷ (5.18% × 2.98%)
= 0.24
2 βRAI
= CovarianceRAI, S&P 500 ÷ VarianceS&P 500
= 3.69 ÷ 8.88
= 0.42
3 αRAI
= MoyenneRAI – βRAI × MoyenneS&P 500
= 2.30% – 0.42 × 0.95%
= 1.91%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.64% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 14.93% |
| Risque systématique lié à RAI actions ordinaires | βRAI | 0.42 |
| Taux de rendement attendu des actions ordinaires de RAI3 | E(RRAI) | 8.92% |
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(RRAI) = RF + βRAI [E(RM) – RF]
= 4.64% + 0.42 [14.93% – 4.64%]
= 8.92%