Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida sobre activos de riesgo como las acciones ordinarias de AAG.
Tasas de retorno
American Airlines Group Inc., tasas mensuales de retorno
| American Airlines Group Inc. (AAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAAL,t1 | DividendoAAL,t1 | RAAL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $35.77 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $35.63 | $0.10 | -0.11% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $31.76 | -10.86% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $34.18 | 7.62% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $12.43 | 11.48% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $13.74 | 10.54% | 4,769.83 | 4.42% | |
| Promedio (R): | -0.64% | 1.11% | ||||
| Desviación estándar: | 13.55% | 5.31% | ||||
| American Airlines Group Inc. (AAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAAL,t1 | DividendoAAL,t1 | RAAL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $35.77 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $35.63 | $0.10 | -0.11% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $31.76 | -10.86% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $34.18 | 7.62% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $27.23 | $0.10 | -20.04% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $32.61 | 19.76% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $30.51 | -6.44% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $26.31 | $0.10 | -13.44% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $26.97 | 2.51% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $30.06 | 11.46% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $28.74 | $0.10 | -4.06% | 3,140.98 | 3.40% |
| 11. | 31 dic. 2019 | $28.68 | -0.21% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $26.84 | -6.42% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $19.05 | $0.10 | -28.65% | 2,954.22 | -8.41% |
| 14. | 31 mar. 2020 | $12.19 | -36.01% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $12.01 | -1.48% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $10.50 | -12.57% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $13.07 | 24.48% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $11.12 | -14.92% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $13.05 | 17.36% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $12.29 | -5.82% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $11.28 | -8.22% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $14.13 | 25.27% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $15.77 | 11.61% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $17.17 | 8.88% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $20.94 | 21.96% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $23.90 | 14.14% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $21.72 | -9.12% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $24.24 | 11.60% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $21.21 | -12.50% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $20.38 | -3.91% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $19.94 | -2.16% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $20.52 | 2.91% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $19.20 | -6.43% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $17.69 | -7.86% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $17.96 | 1.53% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $16.47 | -8.30% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $17.25 | 4.74% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $18.25 | 5.80% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $18.77 | 2.85% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $17.87 | -4.79% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $12.68 | -29.04% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $13.71 | 8.12% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $12.99 | -5.25% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $12.04 | -7.31% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $14.18 | 17.77% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $14.43 | 1.76% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $12.72 | -11.85% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $16.14 | 26.89% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $15.98 | -0.99% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $14.75 | -7.70% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $13.64 | -7.53% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $14.78 | 8.36% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $17.94 | 21.38% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $16.75 | -6.63% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $14.73 | -12.06% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $12.81 | -13.03% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $11.15 | -12.96% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $12.43 | 11.48% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $13.74 | 10.54% | 4,769.83 | 4.42% | |
| Promedio (R): | -0.64% | 1.11% | ||||
| Desviación estándar: | 13.55% | 5.31% | ||||
Mostrar todo
1 Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de AAL durante el período t.
3 Tasa de rendimiento del S&P 500 (el proxy de la cartera de mercado) durante el período t.
Varianza y covarianza
American Airlines Group Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RAAL,t | RS&P 500,t | (RAAL,t–RAAL)2 | (RS&P 500,t–RS&P 500)2 | (RAAL,t–RAAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -0.11% | 2.97% | 0.28 | 3.49 | 0.99 |
| 2. | 31 mar. 2019 | -10.86% | 1.79% | 104.42 | 0.47 | -7.02 |
| 3. | 30 abr. 2019 | 7.62% | 3.93% | 68.27 | 7.98 | 23.35 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 11.48% | 8.92% | 146.97 | 61.03 | 94.71 |
| 59. | 31 dic. 2023 | 10.54% | 4.42% | 125.04 | 11.00 | 37.09 |
| Total (Σ): | 10,647.91 | 1,634.30 | 2,506.67 | |||
| t | Fecha | RAAL,t | RS&P 500,t | (RAAL,t–RAAL)2 | (RS&P 500,t–RS&P 500)2 | (RAAL,t–RAAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -0.11% | 2.97% | 0.28 | 3.49 | 0.99 |
| 2. | 31 mar. 2019 | -10.86% | 1.79% | 104.42 | 0.47 | -7.02 |
| 3. | 30 abr. 2019 | 7.62% | 3.93% | 68.27 | 7.98 | 23.35 |
| 4. | 31 may. 2019 | -20.04% | -6.58% | 376.27 | 59.04 | 149.05 |
| 5. | 30 jun. 2019 | 19.76% | 6.89% | 416.19 | 33.49 | 118.06 |
| 6. | 31 jul. 2019 | -6.44% | 1.31% | 33.60 | 0.04 | -1.20 |
| 7. | 31 ago. 2019 | -13.44% | -1.81% | 163.71 | 8.50 | 37.30 |
| 8. | 30 sept. 2019 | 2.51% | 1.72% | 9.93 | 0.37 | 1.93 |
| 9. | 31 oct. 2019 | 11.46% | 2.04% | 146.42 | 0.88 | 11.34 |
| 10. | 30 nov. 2019 | -4.06% | 3.40% | 11.66 | 5.28 | -7.85 |
| 11. | 31 dic. 2019 | -0.21% | 2.86% | 0.19 | 3.07 | 0.76 |
| 12. | 31 ene. 2020 | -6.42% | -0.16% | 33.32 | 1.61 | 7.32 |
| 13. | 29 feb. 2020 | -28.65% | -8.41% | 784.45 | 90.57 | 266.55 |
| 14. | 31 mar. 2020 | -36.01% | -12.51% | 1,250.85 | 185.44 | 481.62 |
| 15. | 30 abr. 2020 | -1.48% | 12.68% | 0.69 | 134.06 | -9.65 |
| 16. | 31 may. 2020 | -12.57% | 4.53% | 142.32 | 11.71 | -40.83 |
| 17. | 30 jun. 2020 | 24.48% | 1.84% | 630.98 | 0.54 | 18.41 |
| 18. | 31 jul. 2020 | -14.92% | 5.51% | 203.82 | 19.40 | -62.88 |
| 19. | 31 ago. 2020 | 17.36% | 7.01% | 323.97 | 34.82 | 106.21 |
| 20. | 30 sept. 2020 | -5.82% | -3.92% | 26.84 | 25.29 | 26.05 |
| 21. | 31 oct. 2020 | -8.22% | -2.77% | 57.38 | 15.00 | 29.33 |
| 22. | 30 nov. 2020 | 25.27% | 10.75% | 671.28 | 93.10 | 249.99 |
| 23. | 31 dic. 2020 | 11.61% | 3.71% | 150.05 | 6.79 | 31.93 |
| 24. | 31 ene. 2021 | 8.88% | -1.11% | 90.65 | 4.93 | -21.13 |
| 25. | 28 feb. 2021 | 21.96% | 2.61% | 510.76 | 2.26 | 33.97 |
| 26. | 31 mar. 2021 | 14.14% | 4.24% | 218.41 | 9.85 | 46.38 |
| 27. | 30 abr. 2021 | -9.12% | 5.24% | 71.88 | 17.11 | -35.07 |
| 28. | 31 may. 2021 | 11.60% | 0.55% | 149.95 | 0.31 | -6.82 |
| 29. | 30 jun. 2021 | -12.50% | 2.22% | 140.58 | 1.24 | -13.23 |
| 30. | 31 jul. 2021 | -3.91% | 2.27% | 10.69 | 1.37 | -3.82 |
| 31. | 31 ago. 2021 | -2.16% | 2.90% | 2.30 | 3.22 | -2.72 |
| 32. | 30 sept. 2021 | 2.91% | -4.76% | 12.62 | 34.37 | -20.82 |
| 33. | 31 oct. 2021 | -6.43% | 6.91% | 33.52 | 33.74 | -33.63 |
| 34. | 30 nov. 2021 | -7.86% | -0.83% | 52.15 | 3.76 | 14.00 |
| 35. | 31 dic. 2021 | 1.53% | 4.36% | 4.71 | 10.60 | 7.06 |
| 36. | 31 ene. 2022 | -8.30% | -5.26% | 58.57 | 40.51 | 48.71 |
| 37. | 28 feb. 2022 | 4.74% | -3.14% | 28.93 | 17.99 | -22.82 |
| 38. | 31 mar. 2022 | 5.80% | 3.58% | 41.48 | 6.11 | 15.92 |
| 39. | 30 abr. 2022 | 2.85% | -8.80% | 12.20 | 98.04 | -34.58 |
| 40. | 31 may. 2022 | -4.79% | 0.01% | 17.24 | 1.21 | 4.57 |
| 41. | 30 jun. 2022 | -29.04% | -8.39% | 806.56 | 90.21 | 269.74 |
| 42. | 31 jul. 2022 | 8.12% | 9.11% | 76.85 | 64.09 | 70.18 |
| 43. | 31 ago. 2022 | -5.25% | -4.24% | 21.24 | 28.62 | 24.65 |
| 44. | 30 sept. 2022 | -7.31% | -9.34% | 44.49 | 109.11 | 69.67 |
| 45. | 31 oct. 2022 | 17.77% | 7.99% | 339.20 | 47.34 | 126.72 |
| 46. | 30 nov. 2022 | 1.76% | 5.38% | 5.79 | 18.23 | 10.27 |
| 47. | 31 dic. 2022 | -11.85% | -5.90% | 125.60 | 49.04 | 78.48 |
| 48. | 31 ene. 2023 | 26.89% | 6.18% | 757.90 | 25.70 | 139.56 |
| 49. | 28 feb. 2023 | -0.99% | -2.61% | 0.12 | 13.82 | 1.29 |
| 50. | 31 mar. 2023 | -7.70% | 3.51% | 49.76 | 5.76 | -16.92 |
| 51. | 30 abr. 2023 | -7.53% | 1.46% | 47.37 | 0.13 | -2.47 |
| 52. | 31 may. 2023 | 8.36% | 0.25% | 81.02 | 0.74 | -7.72 |
| 53. | 30 jun. 2023 | 21.38% | 4.71% | 485.03 | 13.02 | 79.46 |
| 54. | 31 jul. 2023 | -6.63% | 4.85% | 35.88 | 13.99 | -22.40 |
| 55. | 31 ago. 2023 | -12.06% | -1.77% | 130.34 | 8.28 | 32.85 |
| 56. | 30 sept. 2023 | -13.03% | -4.87% | 153.55 | 35.73 | 74.07 |
| 57. | 31 oct. 2023 | -12.96% | -2.20% | 151.67 | 10.92 | 40.69 |
| 58. | 30 nov. 2023 | 11.48% | 8.92% | 146.97 | 61.03 | 94.71 |
| 59. | 31 dic. 2023 | 10.54% | 4.42% | 125.04 | 11.00 | 37.09 |
| Total (Σ): | 10,647.91 | 1,634.30 | 2,506.67 | |||
Mostrar todo
VarianzaAAL = Σ(RAAL,t–RAAL)2 ÷ (59 – 1)
= 10,647.91 ÷ (59 – 1)
= 183.58
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaAAL, S&P 500 = Σ(RAAL,t–RAAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,506.67 ÷ (59 – 1)
= 43.22
Estimación sistemática del riesgo (β)
| VarianzaAAL | 183.58 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaAAL, S&P 500 | 43.22 |
| Coeficiente de correlaciónAAL, S&P 5001 | 0.60 |
| βAAL2 | 1.53 |
| αAAL3 | -2.34% |
Cálculos
1 Coeficiente de correlaciónAAL, S&P 500
= CovarianzaAAL, S&P 500 ÷ (Desviación estándarAAL × Desviación estándarS&P 500)
= 43.22 ÷ (13.55% × 5.31%)
= 0.60
2 βAAL
= CovarianzaAAL, S&P 500 ÷ VarianzaS&P 500
= 43.22 ÷ 28.18
= 1.53
3 αAAL
= PromedioAAL – βAAL × PromedioS&P 500
= -0.64% – 1.53 × 1.11%
= -2.34%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.67% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.42% |
| Riesgo sistemático de AAG acciones ordinarias | βAAL | 1.53 |
| Tasa de rendimiento esperada de las acciones ordinarias de AAG3 | E(RAAL) | 18.09% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. con cupón fijo en circulación que no vencen ni son rescatables en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RAAL) = RF + βAAL [E(RM) – RF]
= 4.67% + 1.53 [13.42% – 4.67%]
= 18.09%