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 LyondellBasell.
Taux de rendement
LyondellBasell Industries N.V., taux de rendement mensuels
| LyondellBasell Industries N.V. (LYB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixLYB,t1 | DividendeLYB,t1 | RLYB,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2014 | $78.76 | 1,782.59 | ||||
| 1. | 28 févr. 2014 | $88.08 | $0.60 | 12.60% | 1,859.45 | 4.31% |
| 2. | 31 mars 2014 | $88.94 | 0.98% | 1,872.34 | 0.69% | |
| 3. | 30 avr. 2014 | $92.50 | $0.70 | 4.79% | 1,883.95 | 0.62% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2018 | $93.31 | 4.53% | 2,760.17 | 1.79% | |
| 59. | 31 déc. 2018 | $83.16 | $1.00 | -9.81% | 2,506.85 | -9.18% |
| Moyenne (R): | 0.66% | 0.63% | ||||
| Écart type: | 7.34% | 3.13% | ||||
| LyondellBasell Industries N.V. (LYB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixLYB,t1 | DividendeLYB,t1 | RLYB,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2014 | $78.76 | 1,782.59 | ||||
| 1. | 28 févr. 2014 | $88.08 | $0.60 | 12.60% | 1,859.45 | 4.31% |
| 2. | 31 mars 2014 | $88.94 | 0.98% | 1,872.34 | 0.69% | |
| 3. | 30 avr. 2014 | $92.50 | $0.70 | 4.79% | 1,883.95 | 0.62% |
| 4. | 31 mai 2014 | $99.57 | 7.64% | 1,923.57 | 2.10% | |
| 5. | 30 juin 2014 | $97.65 | -1.93% | 1,960.23 | 1.91% | |
| 6. | 31 juil. 2014 | $106.25 | 8.81% | 1,930.67 | -1.51% | |
| 7. | 31 août 2014 | $114.35 | $0.70 | 8.28% | 2,003.37 | 3.77% |
| 8. | 30 sept. 2014 | $108.66 | -4.98% | 1,972.29 | -1.55% | |
| 9. | 31 oct. 2014 | $91.63 | -15.67% | 2,018.05 | 2.32% | |
| 10. | 30 nov. 2014 | $78.86 | $0.70 | -13.17% | 2,067.56 | 2.45% |
| 11. | 31 déc. 2014 | $79.39 | 0.67% | 2,058.90 | -0.42% | |
| 12. | 31 janv. 2015 | $79.09 | -0.38% | 1,994.99 | -3.10% | |
| 13. | 28 févr. 2015 | $85.91 | $0.70 | 9.51% | 2,104.50 | 5.49% |
| 14. | 31 mars 2015 | $87.80 | 2.20% | 2,067.89 | -1.74% | |
| 15. | 30 avr. 2015 | $103.52 | 17.90% | 2,085.51 | 0.85% | |
| 16. | 31 mai 2015 | $101.10 | $0.78 | -1.58% | 2,107.39 | 1.05% |
| 17. | 30 juin 2015 | $103.52 | 2.39% | 2,063.11 | -2.10% | |
| 18. | 31 juil. 2015 | $93.83 | -9.36% | 2,103.84 | 1.97% | |
| 19. | 31 août 2015 | $85.38 | $0.78 | -8.17% | 1,972.18 | -6.26% |
| 20. | 30 sept. 2015 | $83.36 | -2.37% | 1,920.03 | -2.64% | |
| 21. | 31 oct. 2015 | $92.91 | 11.46% | 2,079.36 | 8.30% | |
| 22. | 30 nov. 2015 | $95.82 | $0.78 | 3.97% | 2,080.41 | 0.05% |
| 23. | 31 déc. 2015 | $86.90 | -9.31% | 2,043.94 | -1.75% | |
| 24. | 31 janv. 2016 | $77.97 | -10.28% | 1,940.24 | -5.07% | |
| 25. | 29 févr. 2016 | $80.21 | $0.78 | 3.87% | 1,932.23 | -0.41% |
| 26. | 31 mars 2016 | $85.58 | 6.69% | 2,059.74 | 6.60% | |
| 27. | 30 avr. 2016 | $82.67 | -3.40% | 2,065.30 | 0.27% | |
| 28. | 31 mai 2016 | $81.36 | $0.85 | -0.56% | 2,096.95 | 1.53% |
| 29. | 30 juin 2016 | $74.42 | -8.53% | 2,098.86 | 0.09% | |
| 30. | 31 juil. 2016 | $75.26 | 1.13% | 2,173.60 | 3.56% | |
| 31. | 31 août 2016 | $78.89 | $0.85 | 5.95% | 2,170.95 | -0.12% |
| 32. | 30 sept. 2016 | $80.66 | 2.24% | 2,168.27 | -0.12% | |
| 33. | 31 oct. 2016 | $79.55 | -1.38% | 2,126.15 | -1.94% | |
| 34. | 30 nov. 2016 | $90.32 | $0.85 | 14.61% | 2,198.81 | 3.42% |
| 35. | 31 déc. 2016 | $85.78 | -5.03% | 2,238.83 | 1.82% | |
| 36. | 31 janv. 2017 | $93.27 | 8.73% | 2,278.87 | 1.79% | |
| 37. | 28 févr. 2017 | $91.24 | -2.18% | 2,363.64 | 3.72% | |
| 38. | 31 mars 2017 | $91.19 | $0.85 | 0.88% | 2,362.72 | -0.04% |
| 39. | 30 avr. 2017 | $84.76 | -7.05% | 2,384.20 | 0.91% | |
| 40. | 31 mai 2017 | $80.52 | -5.00% | 2,411.80 | 1.16% | |
| 41. | 30 juin 2017 | $84.39 | $0.90 | 5.92% | 2,423.41 | 0.48% |
| 42. | 31 juil. 2017 | $90.09 | 6.75% | 2,470.30 | 1.93% | |
| 43. | 31 août 2017 | $90.59 | 0.56% | 2,471.65 | 0.05% | |
| 44. | 30 sept. 2017 | $99.05 | $0.90 | 10.33% | 2,519.36 | 1.93% |
| 45. | 31 oct. 2017 | $103.53 | 4.52% | 2,575.26 | 2.22% | |
| 46. | 30 nov. 2017 | $104.70 | 1.13% | 2,647.58 | 2.81% | |
| 47. | 31 déc. 2017 | $110.32 | $0.90 | 6.23% | 2,673.61 | 0.98% |
| 48. | 31 janv. 2018 | $119.84 | 8.63% | 2,823.81 | 5.62% | |
| 49. | 28 févr. 2018 | $108.22 | -9.70% | 2,713.83 | -3.89% | |
| 50. | 31 mars 2018 | $105.68 | $1.00 | -1.42% | 2,640.87 | -2.69% |
| 51. | 30 avr. 2018 | $105.73 | 0.05% | 2,648.05 | 0.27% | |
| 52. | 31 mai 2018 | $112.12 | 6.04% | 2,705.27 | 2.16% | |
| 53. | 30 juin 2018 | $109.85 | $1.00 | -1.13% | 2,718.37 | 0.48% |
| 54. | 31 juil. 2018 | $110.79 | 0.86% | 2,816.29 | 3.60% | |
| 55. | 31 août 2018 | $112.78 | 1.80% | 2,901.52 | 3.03% | |
| 56. | 30 sept. 2018 | $102.51 | $1.00 | -8.22% | 2,913.98 | 0.43% |
| 57. | 31 oct. 2018 | $89.27 | -12.92% | 2,711.74 | -6.94% | |
| 58. | 30 nov. 2018 | $93.31 | 4.53% | 2,760.17 | 1.79% | |
| 59. | 31 déc. 2018 | $83.16 | $1.00 | -9.81% | 2,506.85 | -9.18% |
| Moyenne (R): | 0.66% | 0.63% | ||||
| Écart type: | 7.34% | 3.13% | ||||
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 LYB 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
LyondellBasell Industries N.V., calcul de la variance et de la covariance des rendements
| t | Date | RLYB,t | RS&P 500,t | (RLYB,t–RLYB)2 | (RS&P 500,t–RS&P 500)2 | (RLYB,t–RLYB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2014 | 12.60% | 4.31% | 142.37 | 13.57 | 43.95 |
| 2. | 31 mars 2014 | 0.98% | 0.69% | 0.10 | 0.00 | 0.02 |
| 3. | 30 avr. 2014 | 4.79% | 0.62% | 17.03 | 0.00 | -0.03 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2018 | 4.53% | 1.79% | 14.92 | 1.34 | 4.47 |
| 59. | 31 déc. 2018 | -9.81% | -9.18% | 109.61 | 96.15 | 102.66 |
| Total (Σ): | 3,127.55 | 566.60 | 695.50 | |||
| t | Date | RLYB,t | RS&P 500,t | (RLYB,t–RLYB)2 | (RS&P 500,t–RS&P 500)2 | (RLYB,t–RLYB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2014 | 12.60% | 4.31% | 142.37 | 13.57 | 43.95 |
| 2. | 31 mars 2014 | 0.98% | 0.69% | 0.10 | 0.00 | 0.02 |
| 3. | 30 avr. 2014 | 4.79% | 0.62% | 17.03 | 0.00 | -0.03 |
| 4. | 31 mai 2014 | 7.64% | 2.10% | 48.72 | 2.18 | 10.30 |
| 5. | 30 juin 2014 | -1.93% | 1.91% | 6.72 | 1.63 | -3.31 |
| 6. | 31 juil. 2014 | 8.81% | -1.51% | 66.32 | 4.56 | -17.39 |
| 7. | 31 août 2014 | 8.28% | 3.77% | 58.05 | 9.84 | 23.90 |
| 8. | 30 sept. 2014 | -4.98% | -1.55% | 31.80 | 4.75 | 12.29 |
| 9. | 31 oct. 2014 | -15.67% | 2.32% | 266.87 | 2.86 | -27.64 |
| 10. | 30 nov. 2014 | -13.17% | 2.45% | 191.43 | 3.33 | -25.26 |
| 11. | 31 déc. 2014 | 0.67% | -0.42% | 0.00 | 1.10 | -0.01 |
| 12. | 31 janv. 2015 | -0.38% | -3.10% | 1.08 | 13.93 | 3.89 |
| 13. | 28 févr. 2015 | 9.51% | 5.49% | 78.23 | 23.63 | 43.00 |
| 14. | 31 mars 2015 | 2.20% | -1.74% | 2.36 | 5.61 | -3.64 |
| 15. | 30 avr. 2015 | 17.90% | 0.85% | 297.25 | 0.05 | 3.86 |
| 16. | 31 mai 2015 | -1.58% | 1.05% | 5.05 | 0.18 | -0.95 |
| 17. | 30 juin 2015 | 2.39% | -2.10% | 2.99 | 7.45 | -4.72 |
| 18. | 31 juil. 2015 | -9.36% | 1.97% | 100.48 | 1.81 | -13.49 |
| 19. | 31 août 2015 | -8.17% | -6.26% | 78.11 | 47.42 | 60.86 |
| 20. | 30 sept. 2015 | -2.37% | -2.64% | 9.18 | 10.71 | 9.91 |
| 21. | 31 oct. 2015 | 11.46% | 8.30% | 116.49 | 58.83 | 82.79 |
| 22. | 30 nov. 2015 | 3.97% | 0.05% | 10.94 | 0.33 | -1.91 |
| 23. | 31 déc. 2015 | -9.31% | -1.75% | 99.45 | 5.67 | 23.74 |
| 24. | 31 janv. 2016 | -10.28% | -5.07% | 119.68 | 32.51 | 62.37 |
| 25. | 29 févr. 2016 | 3.87% | -0.41% | 10.30 | 1.08 | -3.34 |
| 26. | 31 mars 2016 | 6.69% | 6.60% | 36.38 | 35.65 | 36.01 |
| 27. | 30 avr. 2016 | -3.40% | 0.27% | 16.51 | 0.13 | 1.45 |
| 28. | 31 mai 2016 | -0.56% | 1.53% | 1.49 | 0.82 | -1.10 |
| 29. | 30 juin 2016 | -8.53% | 0.09% | 84.52 | 0.29 | 4.94 |
| 30. | 31 juil. 2016 | 1.13% | 3.56% | 0.22 | 8.60 | 1.36 |
| 31. | 31 août 2016 | 5.95% | -0.12% | 27.98 | 0.56 | -3.97 |
| 32. | 30 sept. 2016 | 2.24% | -0.12% | 2.50 | 0.56 | -1.19 |
| 33. | 31 oct. 2016 | -1.38% | -1.94% | 4.16 | 6.61 | 5.24 |
| 34. | 30 nov. 2016 | 14.61% | 3.42% | 194.43 | 7.78 | 38.90 |
| 35. | 31 déc. 2016 | -5.03% | 1.82% | 32.38 | 1.42 | -6.78 |
| 36. | 31 janv. 2017 | 8.73% | 1.79% | 65.10 | 1.35 | 9.36 |
| 37. | 28 févr. 2017 | -2.18% | 3.72% | 8.07 | 9.56 | -8.78 |
| 38. | 31 mars 2017 | 0.88% | -0.04% | 0.05 | 0.44 | -0.14 |
| 39. | 30 avr. 2017 | -7.05% | 0.91% | 59.52 | 0.08 | -2.17 |
| 40. | 31 mai 2017 | -5.00% | 1.16% | 32.10 | 0.28 | -3.00 |
| 41. | 30 juin 2017 | 5.92% | 0.48% | 27.67 | 0.02 | -0.77 |
| 42. | 31 juil. 2017 | 6.75% | 1.93% | 37.10 | 1.71 | 7.96 |
| 43. | 31 août 2017 | 0.56% | 0.05% | 0.01 | 0.33 | 0.06 |
| 44. | 30 sept. 2017 | 10.33% | 1.93% | 93.49 | 1.70 | 12.59 |
| 45. | 31 oct. 2017 | 4.52% | 2.22% | 14.90 | 2.53 | 6.14 |
| 46. | 30 nov. 2017 | 1.13% | 2.81% | 0.22 | 4.75 | 1.02 |
| 47. | 31 déc. 2017 | 6.23% | 0.98% | 30.96 | 0.13 | 1.98 |
| 48. | 31 janv. 2018 | 8.63% | 5.62% | 63.46 | 24.90 | 39.75 |
| 49. | 28 févr. 2018 | -9.70% | -3.89% | 107.32 | 20.45 | 46.85 |
| 50. | 31 mars 2018 | -1.42% | -2.69% | 4.35 | 11.00 | 6.92 |
| 51. | 30 avr. 2018 | 0.05% | 0.27% | 0.38 | 0.13 | 0.22 |
| 52. | 31 mai 2018 | 6.04% | 2.16% | 28.95 | 2.35 | 8.25 |
| 53. | 30 juin 2018 | -1.13% | 0.48% | 3.23 | 0.02 | 0.26 |
| 54. | 31 juil. 2018 | 0.86% | 3.60% | 0.04 | 8.85 | 0.57 |
| 55. | 31 août 2018 | 1.80% | 3.03% | 1.28 | 5.75 | 2.72 |
| 56. | 30 sept. 2018 | -8.22% | 0.43% | 78.91 | 0.04 | 1.76 |
| 57. | 31 oct. 2018 | -12.92% | -6.94% | 184.40 | 57.28 | 102.77 |
| 58. | 30 nov. 2018 | 4.53% | 1.79% | 14.92 | 1.34 | 4.47 |
| 59. | 31 déc. 2018 | -9.81% | -9.18% | 109.61 | 96.15 | 102.66 |
| Total (Σ): | 3,127.55 | 566.60 | 695.50 | |||
Tout afficher
VarianceLYB = Σ(RLYB,t–RLYB)2 ÷ (59 – 1)
= 3,127.55 ÷ (59 – 1)
= 53.92
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 566.60 ÷ (59 – 1)
= 9.77
CovarianceLYB, S&P 500 = Σ(RLYB,t–RLYB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 695.50 ÷ (59 – 1)
= 11.99
Estimation systématique des risques (β)
| VarianceLYB | 53.92 |
| VarianceS&P 500 | 9.77 |
| CovarianceLYB, S&P 500 | 11.99 |
| Coefficient de corrélationLYB, S&P 5001 | 0.52 |
| βLYB2 | 1.23 |
| αLYB3 | -0.11% |
Calculs
1 Coefficient de corrélationLYB, S&P 500
= CovarianceLYB, S&P 500 ÷ (Écart typeLYB × Écart typeS&P 500)
= 11.99 ÷ (7.34% × 3.13%)
= 0.52
2 βLYB
= CovarianceLYB, S&P 500 ÷ VarianceS&P 500
= 11.99 ÷ 9.77
= 1.23
3 αLYB
= MoyenneLYB – βLYB × MoyenneS&P 500
= 0.66% – 1.23 × 0.63%
= -0.11%
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 LyondellBasell actions ordinaires | βLYB | 1.23 |
| Taux de rendement attendu des actions ordinaires de LyondellBasell3 | E(RLYB) | 15.86% |
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(RLYB) = RF + βLYB [E(RM) – RF]
= 4.67% + 1.23 [13.79% – 4.67%]
= 15.86%