Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM, por sus siglas en inglés) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de Booking Holdings.
Tasas de retorno
Booking Holdings Inc., tasas mensuales de retorno
| Booking Holdings Inc. (BKNG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioBKNG,t1 | DividendoBKNG,t1 | RBKNG,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $1,832.81 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $1,697.04 | -7.41% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $1,744.91 | 2.82% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $1,854.99 | 6.31% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $3,125.70 | 12.05% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $3,547.22 | 13.49% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.62% | 1.11% | ||||
| Desviación estándar: | 10.03% | 5.31% | ||||
| Booking Holdings Inc. (BKNG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioBKNG,t1 | DividendoBKNG,t1 | RBKNG,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $1,832.81 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $1,697.04 | -7.41% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $1,744.91 | 2.82% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $1,854.99 | 6.31% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $1,656.22 | -10.72% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $1,874.71 | 13.19% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $1,886.61 | 0.63% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $1,966.41 | 4.23% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $1,962.61 | -0.19% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $2,048.77 | 4.39% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $1,904.03 | -7.06% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $2,053.73 | 7.86% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $1,830.55 | -10.87% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $1,695.66 | -7.37% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $1,345.32 | -20.66% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $1,480.57 | 10.05% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $1,639.42 | 10.73% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $1,592.34 | -2.87% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $1,662.13 | 4.38% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $1,910.45 | 14.94% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $1,710.68 | -10.46% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $1,622.50 | -5.15% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $2,028.45 | 25.02% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $2,227.27 | 9.80% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $1,944.33 | -12.70% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $2,328.51 | 19.76% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $2,329.84 | 0.06% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $2,466.08 | 5.85% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $2,361.55 | -4.24% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $2,188.09 | -7.35% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $2,178.26 | -0.45% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $2,299.67 | 5.57% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $2,373.87 | 3.23% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $2,420.78 | 1.98% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $2,101.85 | -13.17% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $2,399.23 | 14.15% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $2,456.13 | 2.37% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $2,172.25 | -11.56% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $2,348.45 | 8.11% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $2,210.31 | -5.88% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $2,243.56 | 1.50% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $1,748.99 | -22.04% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $1,935.69 | 10.67% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $1,875.81 | -3.09% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $1,643.21 | -12.40% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $1,869.48 | 13.77% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $2,079.45 | 11.23% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $2,015.28 | -3.09% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $2,434.10 | 20.78% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $2,524.00 | 3.69% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $2,652.41 | 5.09% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $2,686.31 | 1.28% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $2,508.77 | -6.61% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $2,700.33 | 7.64% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $2,970.80 | 10.02% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $3,105.03 | 4.52% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $3,083.95 | -0.68% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $2,789.56 | -9.55% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $3,125.70 | 12.05% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $3,547.22 | 13.49% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.62% | 1.11% | ||||
| Desviación estándar: | 10.03% | 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 BKNG 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
Booking Holdings Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RBKNG,t | RS&P 500,t | (RBKNG,t–RBKNG)2 | (RS&P 500,t–RS&P 500)2 | (RBKNG,t–RBKNG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -7.41% | 2.97% | 81.50 | 3.49 | -16.86 |
| 2. | 31 mar. 2019 | 2.82% | 1.79% | 1.44 | 0.47 | 0.82 |
| 3. | 30 abr. 2019 | 6.31% | 3.93% | 21.98 | 7.98 | 13.25 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 12.05% | 8.92% | 108.78 | 61.03 | 81.48 |
| 59. | 31 dic. 2023 | 13.49% | 4.42% | 140.79 | 11.00 | 39.36 |
| Total (Σ): | 5,832.06 | 1,634.30 | 2,319.48 | |||
| t | Fecha | RBKNG,t | RS&P 500,t | (RBKNG,t–RBKNG)2 | (RS&P 500,t–RS&P 500)2 | (RBKNG,t–RBKNG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -7.41% | 2.97% | 81.50 | 3.49 | -16.86 |
| 2. | 31 mar. 2019 | 2.82% | 1.79% | 1.44 | 0.47 | 0.82 |
| 3. | 30 abr. 2019 | 6.31% | 3.93% | 21.98 | 7.98 | 13.25 |
| 4. | 31 may. 2019 | -10.72% | -6.58% | 152.17 | 59.04 | 94.78 |
| 5. | 30 jun. 2019 | 13.19% | 6.89% | 133.91 | 33.49 | 66.97 |
| 6. | 31 jul. 2019 | 0.63% | 1.31% | 0.97 | 0.04 | -0.20 |
| 7. | 31 ago. 2019 | 4.23% | -1.81% | 6.81 | 8.50 | -7.61 |
| 8. | 30 sept. 2019 | -0.19% | 1.72% | 3.29 | 0.37 | -1.11 |
| 9. | 31 oct. 2019 | 4.39% | 2.04% | 7.67 | 0.88 | 2.60 |
| 10. | 30 nov. 2019 | -7.06% | 3.40% | 75.43 | 5.28 | -19.97 |
| 11. | 31 dic. 2019 | 7.86% | 2.86% | 38.96 | 3.07 | 10.94 |
| 12. | 31 ene. 2020 | -10.87% | -0.16% | 155.93 | 1.61 | 15.84 |
| 13. | 29 feb. 2020 | -7.37% | -8.41% | 80.80 | 90.57 | 85.55 |
| 14. | 31 mar. 2020 | -20.66% | -12.51% | 496.45 | 185.44 | 303.42 |
| 15. | 30 abr. 2020 | 10.05% | 12.68% | 71.12 | 134.06 | 97.64 |
| 16. | 31 may. 2020 | 10.73% | 4.53% | 82.97 | 11.71 | 31.17 |
| 17. | 30 jun. 2020 | -2.87% | 1.84% | 20.18 | 0.54 | -3.29 |
| 18. | 31 jul. 2020 | 4.38% | 5.51% | 7.63 | 19.40 | 12.17 |
| 19. | 31 ago. 2020 | 14.94% | 7.01% | 177.41 | 34.82 | 78.59 |
| 20. | 30 sept. 2020 | -10.46% | -3.92% | 145.85 | 25.29 | 60.73 |
| 21. | 31 oct. 2020 | -5.15% | -2.77% | 45.90 | 15.00 | 26.24 |
| 22. | 30 nov. 2020 | 25.02% | 10.75% | 547.55 | 93.10 | 225.78 |
| 23. | 31 dic. 2020 | 9.80% | 3.71% | 66.93 | 6.79 | 21.32 |
| 24. | 31 ene. 2021 | -12.70% | -1.11% | 205.17 | 4.93 | 31.79 |
| 25. | 28 feb. 2021 | 19.76% | 2.61% | 329.01 | 2.26 | 27.27 |
| 26. | 31 mar. 2021 | 0.06% | 4.24% | 2.44 | 9.85 | -4.91 |
| 27. | 30 abr. 2021 | 5.85% | 5.24% | 17.87 | 17.11 | 17.49 |
| 28. | 31 may. 2021 | -4.24% | 0.55% | 34.33 | 0.31 | 3.26 |
| 29. | 30 jun. 2021 | -7.35% | 2.22% | 80.38 | 1.24 | -10.00 |
| 30. | 31 jul. 2021 | -0.45% | 2.27% | 4.28 | 1.37 | -2.42 |
| 31. | 31 ago. 2021 | 5.57% | 2.90% | 15.63 | 3.22 | 7.09 |
| 32. | 30 sept. 2021 | 3.23% | -4.76% | 2.58 | 34.37 | -9.42 |
| 33. | 31 oct. 2021 | 1.98% | 6.91% | 0.13 | 33.74 | 2.07 |
| 34. | 30 nov. 2021 | -13.17% | -0.83% | 218.89 | 3.76 | 28.69 |
| 35. | 31 dic. 2021 | 14.15% | 4.36% | 156.96 | 10.60 | 40.78 |
| 36. | 31 ene. 2022 | 2.37% | -5.26% | 0.56 | 40.51 | -4.78 |
| 37. | 28 feb. 2022 | -11.56% | -3.14% | 173.67 | 17.99 | 55.90 |
| 38. | 31 mar. 2022 | 8.11% | 3.58% | 42.14 | 6.11 | 16.04 |
| 39. | 30 abr. 2022 | -5.88% | -8.80% | 56.29 | 98.04 | 74.29 |
| 40. | 31 may. 2022 | 1.50% | 0.01% | 0.01 | 1.21 | 0.13 |
| 41. | 30 jun. 2022 | -22.04% | -8.39% | 560.00 | 90.21 | 224.76 |
| 42. | 31 jul. 2022 | 10.67% | 9.11% | 81.98 | 64.09 | 72.49 |
| 43. | 31 ago. 2022 | -3.09% | -4.24% | 22.22 | 28.62 | 25.22 |
| 44. | 30 sept. 2022 | -12.40% | -9.34% | 196.57 | 109.11 | 146.45 |
| 45. | 31 oct. 2022 | 13.77% | 7.99% | 147.62 | 47.34 | 83.60 |
| 46. | 30 nov. 2022 | 11.23% | 5.38% | 92.38 | 18.23 | 41.03 |
| 47. | 31 dic. 2022 | -3.09% | -5.90% | 22.15 | 49.04 | 32.96 |
| 48. | 31 ene. 2023 | 20.78% | 6.18% | 367.18 | 25.70 | 97.14 |
| 49. | 28 feb. 2023 | 3.69% | -2.61% | 4.30 | 13.82 | -7.71 |
| 50. | 31 mar. 2023 | 5.09% | 3.51% | 12.02 | 5.76 | 8.32 |
| 51. | 30 abr. 2023 | 1.28% | 1.46% | 0.12 | 0.13 | -0.12 |
| 52. | 31 may. 2023 | -6.61% | 0.25% | 67.72 | 0.74 | 7.06 |
| 53. | 30 jun. 2023 | 7.64% | 4.71% | 36.18 | 13.02 | 21.70 |
| 54. | 31 jul. 2023 | 10.02% | 4.85% | 70.49 | 13.99 | 31.40 |
| 55. | 31 ago. 2023 | 4.52% | -1.77% | 8.40 | 8.28 | -8.34 |
| 56. | 30 sept. 2023 | -0.68% | -4.87% | 5.29 | 35.73 | 13.74 |
| 57. | 31 oct. 2023 | -9.55% | -2.20% | 124.68 | 10.92 | 36.89 |
| 58. | 30 nov. 2023 | 12.05% | 8.92% | 108.78 | 61.03 | 81.48 |
| 59. | 31 dic. 2023 | 13.49% | 4.42% | 140.79 | 11.00 | 39.36 |
| Total (Σ): | 5,832.06 | 1,634.30 | 2,319.48 | |||
Mostrar todo
VarianzaBKNG = Σ(RBKNG,t–RBKNG)2 ÷ (59 – 1)
= 5,832.06 ÷ (59 – 1)
= 100.55
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaBKNG, S&P 500 = Σ(RBKNG,t–RBKNG)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,319.48 ÷ (59 – 1)
= 39.99
Estimación sistemática del riesgo (β)
| VarianzaBKNG | 100.55 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaBKNG, S&P 500 | 39.99 |
| Coeficiente de correlaciónBKNG, S&P 5001 | 0.75 |
| βBKNG2 | 1.42 |
| αBKNG3 | 0.05% |
Cálculos
1 Coeficiente de correlaciónBKNG, S&P 500
= CovarianzaBKNG, S&P 500 ÷ (Desviación estándarBKNG × Desviación estándarS&P 500)
= 39.99 ÷ (10.03% × 5.31%)
= 0.75
2 βBKNG
= CovarianzaBKNG, S&P 500 ÷ VarianzaS&P 500
= 39.99 ÷ 28.18
= 1.42
3 αBKNG
= PromedioBKNG – βBKNG × PromedioS&P 500
= 1.62% – 1.42 × 1.11%
= 0.05%
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) | 13.79% |
| Riesgo sistemático de Booking Holdings acciones ordinarias | βBKNG | 1.42 |
| Tasa de rendimiento esperada de las acciones ordinarias de Booking Holdings3 | E(RBKNG) | 17.61% |
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(RBKNG) = RF + βBKNG [E(RM) – RF]
= 4.67% + 1.42 [13.79% – 4.67%]
= 17.61%