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 UAL.
Taux de rendement
United Airlines Holdings Inc., taux de rendement mensuels
| United Airlines Holdings Inc. (UAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixUAL,t1 | DividendeUAL,t1 | RUAL,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2021 | $39.99 | 3,714.24 | ||||
| 1. | 28 févr. 2021 | $52.68 | 31.73% | 3,811.15 | 2.61% | |
| 2. | 31 mars 2021 | $57.54 | 9.23% | 3,972.89 | 4.24% | |
| 3. | 30 avr. 2021 | $54.40 | -5.46% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2025 | $101.96 | 8.42% | 6,849.09 | 0.13% | |
| 59. | 31 déc. 2025 | $111.82 | 9.67% | 6,845.50 | -0.05% | |
| Moyenne (R): | 2.61% | 1.14% | ||||
| Écart type: | 13.44% | 4.37% | ||||
| United Airlines Holdings Inc. (UAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PrixUAL,t1 | DividendeUAL,t1 | RUAL,t2 | PrixS&P 500,t | RS&P 500,t3 |
| 31 janv. 2021 | $39.99 | 3,714.24 | ||||
| 1. | 28 févr. 2021 | $52.68 | 31.73% | 3,811.15 | 2.61% | |
| 2. | 31 mars 2021 | $57.54 | 9.23% | 3,972.89 | 4.24% | |
| 3. | 30 avr. 2021 | $54.40 | -5.46% | 4,181.17 | 5.24% | |
| 4. | 31 mai 2021 | $58.35 | 7.26% | 4,204.11 | 0.55% | |
| 5. | 30 juin 2021 | $52.29 | -10.39% | 4,297.50 | 2.22% | |
| 6. | 31 juil. 2021 | $46.72 | -10.65% | 4,395.26 | 2.27% | |
| 7. | 31 août 2021 | $46.51 | -0.45% | 4,522.68 | 2.90% | |
| 8. | 30 sept. 2021 | $47.57 | 2.28% | 4,307.54 | -4.76% | |
| 9. | 31 oct. 2021 | $46.14 | -3.01% | 4,605.38 | 6.91% | |
| 10. | 30 nov. 2021 | $42.26 | -8.41% | 4,567.00 | -0.83% | |
| 11. | 31 déc. 2021 | $43.78 | 3.60% | 4,766.18 | 4.36% | |
| 12. | 31 janv. 2022 | $42.88 | -2.06% | 4,515.55 | -5.26% | |
| 13. | 28 févr. 2022 | $44.40 | 3.54% | 4,373.94 | -3.14% | |
| 14. | 31 mars 2022 | $46.36 | 4.41% | 4,530.41 | 3.58% | |
| 15. | 30 avr. 2022 | $50.50 | 8.93% | 4,131.93 | -8.80% | |
| 16. | 31 mai 2022 | $47.63 | -5.68% | 4,132.15 | 0.01% | |
| 17. | 30 juin 2022 | $35.42 | -25.64% | 3,785.38 | -8.39% | |
| 18. | 31 juil. 2022 | $36.75 | 3.75% | 4,130.29 | 9.11% | |
| 19. | 31 août 2022 | $35.01 | -4.73% | 3,955.00 | -4.24% | |
| 20. | 30 sept. 2022 | $32.53 | -7.08% | 3,585.62 | -9.34% | |
| 21. | 31 oct. 2022 | $43.08 | 32.43% | 3,871.98 | 7.99% | |
| 22. | 30 nov. 2022 | $44.17 | 2.53% | 4,080.11 | 5.38% | |
| 23. | 31 déc. 2022 | $37.70 | -14.65% | 3,839.50 | -5.90% | |
| 24. | 31 janv. 2023 | $48.96 | 29.87% | 4,076.60 | 6.18% | |
| 25. | 28 févr. 2023 | $51.96 | 6.13% | 3,970.15 | -2.61% | |
| 26. | 31 mars 2023 | $44.25 | -14.84% | 4,109.31 | 3.51% | |
| 27. | 30 avr. 2023 | $43.80 | -1.02% | 4,169.48 | 1.46% | |
| 28. | 31 mai 2023 | $47.47 | 8.38% | 4,179.83 | 0.25% | |
| 29. | 30 juin 2023 | $54.87 | 15.59% | 4,376.86 | 4.71% | |
| 30. | 31 juil. 2023 | $54.31 | -1.02% | 4,588.96 | 4.85% | |
| 31. | 31 août 2023 | $49.81 | -8.29% | 4,507.66 | -1.77% | |
| 32. | 30 sept. 2023 | $42.30 | -15.08% | 4,288.05 | -4.87% | |
| 33. | 31 oct. 2023 | $35.01 | -17.23% | 4,193.80 | -2.20% | |
| 34. | 30 nov. 2023 | $39.40 | 12.54% | 4,567.80 | 8.92% | |
| 35. | 31 déc. 2023 | $41.26 | 4.72% | 4,769.83 | 4.42% | |
| 36. | 31 janv. 2024 | $41.38 | 0.29% | 4,845.65 | 1.59% | |
| 37. | 29 févr. 2024 | $45.49 | 9.93% | 5,096.27 | 5.17% | |
| 38. | 31 mars 2024 | $47.88 | 5.25% | 5,254.35 | 3.10% | |
| 39. | 30 avr. 2024 | $51.46 | 7.48% | 5,035.69 | -4.16% | |
| 40. | 31 mai 2024 | $52.99 | 2.97% | 5,277.51 | 4.80% | |
| 41. | 30 juin 2024 | $48.66 | -8.17% | 5,460.48 | 3.47% | |
| 42. | 31 juil. 2024 | $45.42 | -6.66% | 5,522.30 | 1.13% | |
| 43. | 31 août 2024 | $44.04 | -3.04% | 5,648.40 | 2.28% | |
| 44. | 30 sept. 2024 | $57.06 | 29.56% | 5,762.48 | 2.02% | |
| 45. | 31 oct. 2024 | $78.26 | 37.15% | 5,705.45 | -0.99% | |
| 46. | 30 nov. 2024 | $96.83 | 23.73% | 6,032.38 | 5.73% | |
| 47. | 31 déc. 2024 | $97.10 | 0.28% | 5,881.63 | -2.50% | |
| 48. | 31 janv. 2025 | $105.84 | 9.00% | 6,040.53 | 2.70% | |
| 49. | 28 févr. 2025 | $93.81 | -11.37% | 5,954.50 | -1.42% | |
| 50. | 31 mars 2025 | $69.05 | -26.39% | 5,611.85 | -5.75% | |
| 51. | 30 avr. 2025 | $68.82 | -0.33% | 5,569.06 | -0.76% | |
| 52. | 31 mai 2025 | $79.45 | 15.45% | 5,911.69 | 6.15% | |
| 53. | 30 juin 2025 | $79.63 | 0.23% | 6,204.95 | 4.96% | |
| 54. | 31 juil. 2025 | $88.31 | 10.90% | 6,339.39 | 2.17% | |
| 55. | 31 août 2025 | $105.00 | 18.90% | 6,460.26 | 1.91% | |
| 56. | 30 sept. 2025 | $96.50 | -8.10% | 6,688.46 | 3.53% | |
| 57. | 31 oct. 2025 | $94.04 | -2.55% | 6,840.20 | 2.27% | |
| 58. | 30 nov. 2025 | $101.96 | 8.42% | 6,849.09 | 0.13% | |
| 59. | 31 déc. 2025 | $111.82 | 9.67% | 6,845.50 | -0.05% | |
| Moyenne (R): | 2.61% | 1.14% | ||||
| Écart type: | 13.44% | 4.37% | ||||
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 d’UAL 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
United Airlines Holdings Inc., calcul de la variance et de la covariance des rendements
| t | Date | RUAL,t | RS&P 500,t | (RUAL,t–RUAL)2 | (RS&P 500,t–RS&P 500)2 | (RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2021 | 31.73% | 2.61% | 848.27 | 2.17 | 42.90 |
| 2. | 31 mars 2021 | 9.23% | 4.24% | 43.79 | 9.66 | 20.57 |
| 3. | 30 avr. 2021 | -5.46% | 5.24% | 65.04 | 16.86 | -33.12 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2025 | 8.42% | 0.13% | 33.80 | 1.01 | -5.85 |
| 59. | 31 déc. 2025 | 9.67% | -0.05% | 49.88 | 1.41 | -8.39 |
| Total (Σ): | 10,482.34 | 1,108.23 | 1,422.10 | |||
| t | Date | RUAL,t | RS&P 500,t | (RUAL,t–RUAL)2 | (RS&P 500,t–RS&P 500)2 | (RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 févr. 2021 | 31.73% | 2.61% | 848.27 | 2.17 | 42.90 |
| 2. | 31 mars 2021 | 9.23% | 4.24% | 43.79 | 9.66 | 20.57 |
| 3. | 30 avr. 2021 | -5.46% | 5.24% | 65.04 | 16.86 | -33.12 |
| 4. | 31 mai 2021 | 7.26% | 0.55% | 21.65 | 0.35 | -2.73 |
| 5. | 30 juin 2021 | -10.39% | 2.22% | 168.83 | 1.18 | -14.10 |
| 6. | 31 juil. 2021 | -10.65% | 2.27% | 175.83 | 1.30 | -15.10 |
| 7. | 31 août 2021 | -0.45% | 2.90% | 9.35 | 3.11 | -5.39 |
| 8. | 30 sept. 2021 | 2.28% | -4.76% | 0.11 | 34.73 | 1.94 |
| 9. | 31 oct. 2021 | -3.01% | 6.91% | 31.52 | 33.39 | -32.44 |
| 10. | 30 nov. 2021 | -8.41% | -0.83% | 121.38 | 3.88 | 21.70 |
| 11. | 31 déc. 2021 | 3.60% | 4.36% | 0.98 | 10.40 | 3.19 |
| 12. | 31 janv. 2022 | -2.06% | -5.26% | 21.75 | 40.89 | 29.82 |
| 13. | 28 févr. 2022 | 3.54% | -3.14% | 0.88 | 18.25 | -4.00 |
| 14. | 31 mars 2022 | 4.41% | 3.58% | 3.26 | 5.96 | 4.41 |
| 15. | 30 avr. 2022 | 8.93% | -8.80% | 39.97 | 98.64 | -62.79 |
| 16. | 31 mai 2022 | -5.68% | 0.01% | 68.74 | 1.28 | 9.38 |
| 17. | 30 juin 2022 | -25.64% | -8.39% | 797.67 | 90.79 | 269.10 |
| 18. | 31 juil. 2022 | 3.75% | 9.11% | 1.32 | 63.61 | 9.15 |
| 19. | 31 août 2022 | -4.73% | -4.24% | 53.91 | 28.95 | 39.50 |
| 20. | 30 sept. 2022 | -7.08% | -9.34% | 93.93 | 109.74 | 101.53 |
| 21. | 31 oct. 2022 | 32.43% | 7.99% | 889.46 | 46.93 | 204.30 |
| 22. | 30 nov. 2022 | 2.53% | 5.38% | 0.01 | 17.97 | -0.33 |
| 23. | 31 déc. 2022 | -14.65% | -5.90% | 297.76 | 49.47 | 121.36 |
| 24. | 31 janv. 2023 | 29.87% | 6.18% | 743.08 | 25.39 | 137.36 |
| 25. | 28 févr. 2023 | 6.13% | -2.61% | 12.39 | 14.04 | -13.19 |
| 26. | 31 mars 2023 | -14.84% | 3.51% | 304.37 | 5.61 | -41.33 |
| 27. | 30 avr. 2023 | -1.02% | 1.46% | 13.14 | 0.11 | -1.19 |
| 28. | 31 mai 2023 | 8.38% | 0.25% | 33.31 | 0.79 | -5.12 |
| 29. | 30 juin 2023 | 15.59% | 4.71% | 168.50 | 12.80 | 46.44 |
| 30. | 31 juil. 2023 | -1.02% | 4.85% | 13.17 | 13.76 | -13.46 |
| 31. | 31 août 2023 | -8.29% | -1.77% | 118.67 | 8.46 | 31.68 |
| 32. | 30 sept. 2023 | -15.08% | -4.87% | 312.76 | 36.10 | 106.25 |
| 33. | 31 oct. 2023 | -17.23% | -2.20% | 393.70 | 11.12 | 66.15 |
| 34. | 30 nov. 2023 | 12.54% | 8.92% | 98.63 | 60.56 | 77.28 |
| 35. | 31 déc. 2023 | 4.72% | 4.42% | 4.46 | 10.80 | 6.94 |
| 36. | 31 janv. 2024 | 0.29% | 1.59% | 5.37 | 0.21 | -1.05 |
| 37. | 29 févr. 2024 | 9.93% | 5.17% | 53.65 | 16.29 | 29.56 |
| 38. | 31 mars 2024 | 5.25% | 3.10% | 7.00 | 3.86 | 5.20 |
| 39. | 30 avr. 2024 | 7.48% | -4.16% | 23.71 | 28.06 | -25.80 |
| 40. | 31 mai 2024 | 2.97% | 4.80% | 0.13 | 13.44 | 1.34 |
| 41. | 30 juin 2024 | -8.17% | 3.47% | 116.19 | 5.43 | -25.12 |
| 42. | 31 juil. 2024 | -6.66% | 1.13% | 85.86 | 0.00 | 0.04 |
| 43. | 31 août 2024 | -3.04% | 2.28% | 31.88 | 1.32 | -6.48 |
| 44. | 30 sept. 2024 | 29.56% | 2.02% | 726.64 | 0.78 | 23.82 |
| 45. | 31 oct. 2024 | 37.15% | -0.99% | 1,193.43 | 4.52 | -73.44 |
| 46. | 30 nov. 2024 | 23.73% | 5.73% | 446.09 | 21.10 | 97.03 |
| 47. | 31 déc. 2024 | 0.28% | -2.50% | 5.42 | 13.21 | 8.47 |
| 48. | 31 janv. 2025 | 9.00% | 2.70% | 40.87 | 2.45 | 10.01 |
| 49. | 28 févr. 2025 | -11.37% | -1.42% | 195.27 | 6.56 | 35.78 |
| 50. | 31 mars 2025 | -26.39% | -5.75% | 841.10 | 47.48 | 199.84 |
| 51. | 30 avr. 2025 | -0.33% | -0.76% | 8.65 | 3.60 | 5.58 |
| 52. | 31 mai 2025 | 15.45% | 6.15% | 164.82 | 25.16 | 64.40 |
| 53. | 30 juin 2025 | 0.23% | 4.96% | 5.67 | 14.63 | -9.11 |
| 54. | 31 juil. 2025 | 10.90% | 2.17% | 68.77 | 1.06 | 8.55 |
| 55. | 31 août 2025 | 18.90% | 1.91% | 265.41 | 0.59 | 12.55 |
| 56. | 30 sept. 2025 | -8.10% | 3.53% | 114.56 | 5.74 | -25.65 |
| 57. | 31 oct. 2025 | -2.55% | 2.27% | 26.60 | 1.28 | -5.84 |
| 58. | 30 nov. 2025 | 8.42% | 0.13% | 33.80 | 1.01 | -5.85 |
| 59. | 31 déc. 2025 | 9.67% | -0.05% | 49.88 | 1.41 | -8.39 |
| Total (Σ): | 10,482.34 | 1,108.23 | 1,422.10 | |||
Tout afficher
VarianceUAL = Σ(RUAL,t–RUAL)2 ÷ (59 – 1)
= 10,482.34 ÷ (59 – 1)
= 180.73
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
CovarianceUAL, S&P 500 = Σ(RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,422.10 ÷ (59 – 1)
= 24.52
Estimation systématique des risques (β)
| VarianceUAL | 180.73 |
| VarianceS&P 500 | 19.11 |
| CovarianceUAL, S&P 500 | 24.52 |
| Coefficient de corrélationUAL, S&P 5001 | 0.42 |
| βUAL2 | 1.28 |
| αUAL3 | 1.15% |
Calculs
1 Coefficient de corrélationUAL, S&P 500
= CovarianceUAL, S&P 500 ÷ (Écart typeUAL × Écart typeS&P 500)
= 24.52 ÷ (13.44% × 4.37%)
= 0.42
2 βUAL
= CovarianceUAL, S&P 500 ÷ VarianceS&P 500
= 24.52 ÷ 19.11
= 1.28
3 αUAL
= MoyenneUAL – βUAL × MoyenneS&P 500
= 2.61% – 1.28 × 1.14%
= 1.15%
Taux de rendement attendu
| Hypothèses | ||
| Taux de rendement de LT Treasury Composite1 | RF | 4.54% |
| Taux de rendement attendu du portefeuille de marché2 | E(RM) | 17.37% |
| Risque systématique de UAL actions ordinaires | βUAL | 1.28 |
| Taux de rendement attendu sur les actions ordinaires d’UAL3 | E(RUAL) | 21.00% |
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(RUAL) = RF + βUAL [E(RM) – RF]
= 4.54% + 1.28 [17.37% – 4.54%]
= 21.00%