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 en activos de riesgo como las acciones ordinarias de Hilton.
Tasas de retorno
Hilton Worldwide Holdings Inc., tasas mensuales de retorno
| Hilton Worldwide Holdings Inc. (HLT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHLT,t1 | DividendoHLT,t1 | RHLT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $74.48 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $83.10 | $0.15 | 11.77% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $83.11 | 0.01% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $86.99 | 4.67% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $167.52 | $0.15 | 10.65% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $182.09 | 8.70% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.99% | 1.11% | ||||
| Desviación estándar: | 9.31% | 5.31% | ||||
| Hilton Worldwide Holdings Inc. (HLT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHLT,t1 | DividendoHLT,t1 | RHLT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $74.48 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $83.10 | $0.15 | 11.77% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $83.11 | 0.01% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $86.99 | 4.67% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $89.44 | $0.15 | 2.99% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $97.74 | 9.28% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $96.55 | -1.22% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $92.37 | $0.15 | -4.17% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $93.11 | 0.80% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $96.96 | 4.13% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $105.00 | $0.15 | 8.45% | 3,140.98 | 3.40% |
| 11. | 31 dic. 2019 | $110.91 | 5.63% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $107.80 | -2.80% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $97.20 | $0.15 | -9.69% | 2,954.22 | -8.41% |
| 14. | 31 mar. 2020 | $68.24 | -29.79% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $75.71 | 10.95% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $79.31 | 4.75% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $73.45 | -7.39% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $75.05 | 2.18% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $90.36 | 20.40% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $85.32 | -5.58% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $87.81 | 2.92% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $103.63 | 18.02% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $111.26 | 7.36% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $101.39 | -8.87% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $123.68 | 21.98% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $120.92 | -2.23% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $128.70 | 6.43% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $125.27 | -2.67% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $120.62 | -3.71% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $131.45 | 8.98% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $124.86 | -5.01% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $132.11 | 5.81% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $143.95 | 8.96% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $135.07 | -6.17% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $155.99 | 15.49% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $145.11 | -6.97% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $148.86 | 2.58% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $151.74 | 1.93% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $155.29 | 2.34% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $140.86 | $0.15 | -9.20% | 4,132.15 | 0.01% |
| 41. | 30 jun. 2022 | $111.44 | -20.89% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $128.07 | 14.92% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $127.36 | $0.15 | -0.44% | 3,955.00 | -4.24% |
| 44. | 30 sept. 2022 | $120.62 | -5.29% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $135.26 | 12.14% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $142.62 | $0.15 | 5.55% | 4,080.11 | 5.38% |
| 47. | 31 dic. 2022 | $126.36 | -11.40% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $145.09 | 14.82% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $144.51 | $0.15 | -0.30% | 3,970.15 | -2.61% |
| 50. | 31 mar. 2023 | $140.87 | -2.52% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $144.02 | 2.24% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $136.12 | $0.15 | -5.38% | 4,179.83 | 0.25% |
| 53. | 30 jun. 2023 | $145.55 | 6.93% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $155.49 | 6.83% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $148.65 | $0.15 | -4.30% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $150.18 | 1.03% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $151.53 | 0.90% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $167.52 | $0.15 | 10.65% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $182.09 | 8.70% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.99% | 1.11% | ||||
| Desviación estándar: | 9.31% | 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 HLT 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
Hilton Worldwide Holdings Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RHLT,t | RS&P 500,t | (RHLT,t–RHLT)2 | (RS&P 500,t–RS&P 500)2 | (RHLT,t–RHLT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 11.77% | 2.97% | 95.70 | 3.49 | 18.27 |
| 2. | 31 mar. 2019 | 0.01% | 1.79% | 3.92 | 0.47 | -1.36 |
| 3. | 30 abr. 2019 | 4.67% | 3.93% | 7.16 | 7.98 | 7.56 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 10.65% | 8.92% | 74.98 | 61.03 | 67.65 |
| 59. | 31 dic. 2023 | 8.70% | 4.42% | 44.96 | 11.00 | 22.24 |
| Total (Σ): | 5,022.46 | 1,634.30 | 2,071.12 | |||
| t | Fecha | RHLT,t | RS&P 500,t | (RHLT,t–RHLT)2 | (RS&P 500,t–RS&P 500)2 | (RHLT,t–RHLT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 11.77% | 2.97% | 95.70 | 3.49 | 18.27 |
| 2. | 31 mar. 2019 | 0.01% | 1.79% | 3.92 | 0.47 | -1.36 |
| 3. | 30 abr. 2019 | 4.67% | 3.93% | 7.16 | 7.98 | 7.56 |
| 4. | 31 may. 2019 | 2.99% | -6.58% | 0.99 | 59.04 | -7.66 |
| 5. | 30 jun. 2019 | 9.28% | 6.89% | 53.11 | 33.49 | 42.18 |
| 6. | 31 jul. 2019 | -1.22% | 1.31% | 10.30 | 0.04 | -0.66 |
| 7. | 31 ago. 2019 | -4.17% | -1.81% | 38.02 | 8.50 | 17.97 |
| 8. | 30 sept. 2019 | 0.80% | 1.72% | 1.42 | 0.37 | -0.73 |
| 9. | 31 oct. 2019 | 4.13% | 2.04% | 4.59 | 0.88 | 2.01 |
| 10. | 30 nov. 2019 | 8.45% | 3.40% | 41.66 | 5.28 | 14.84 |
| 11. | 31 dic. 2019 | 5.63% | 2.86% | 13.22 | 3.07 | 6.38 |
| 12. | 31 ene. 2020 | -2.80% | -0.16% | 23.00 | 1.61 | 6.08 |
| 13. | 29 feb. 2020 | -9.69% | -8.41% | 136.56 | 90.57 | 111.21 |
| 14. | 31 mar. 2020 | -29.79% | -12.51% | 1,010.37 | 185.44 | 432.86 |
| 15. | 30 abr. 2020 | 10.95% | 12.68% | 80.18 | 134.06 | 103.68 |
| 16. | 31 may. 2020 | 4.75% | 4.53% | 7.63 | 11.71 | 9.46 |
| 17. | 30 jun. 2020 | -7.39% | 1.84% | 88.00 | 0.54 | -6.88 |
| 18. | 31 jul. 2020 | 2.18% | 5.51% | 0.03 | 19.40 | 0.82 |
| 19. | 31 ago. 2020 | 20.40% | 7.01% | 338.84 | 34.82 | 108.62 |
| 20. | 30 sept. 2020 | -5.58% | -3.92% | 57.30 | 25.29 | 38.07 |
| 21. | 31 oct. 2020 | 2.92% | -2.77% | 0.86 | 15.00 | -3.59 |
| 22. | 30 nov. 2020 | 18.02% | 10.75% | 256.77 | 93.10 | 154.61 |
| 23. | 31 dic. 2020 | 7.36% | 3.71% | 28.84 | 6.79 | 14.00 |
| 24. | 31 ene. 2021 | -8.87% | -1.11% | 118.01 | 4.93 | 24.11 |
| 25. | 28 feb. 2021 | 21.98% | 2.61% | 399.69 | 2.26 | 30.05 |
| 26. | 31 mar. 2021 | -2.23% | 4.24% | 17.84 | 9.85 | -13.25 |
| 27. | 30 abr. 2021 | 6.43% | 5.24% | 19.73 | 17.11 | 18.37 |
| 28. | 31 may. 2021 | -2.67% | 0.55% | 21.69 | 0.31 | 2.59 |
| 29. | 30 jun. 2021 | -3.71% | 2.22% | 32.54 | 1.24 | -6.36 |
| 30. | 31 jul. 2021 | 8.98% | 2.27% | 48.81 | 1.37 | 8.17 |
| 31. | 31 ago. 2021 | -5.01% | 2.90% | 49.08 | 3.22 | -12.56 |
| 32. | 30 sept. 2021 | 5.81% | -4.76% | 14.55 | 34.37 | -22.36 |
| 33. | 31 oct. 2021 | 8.96% | 6.91% | 48.58 | 33.74 | 40.49 |
| 34. | 30 nov. 2021 | -6.17% | -0.83% | 66.60 | 3.76 | 15.83 |
| 35. | 31 dic. 2021 | 15.49% | 4.36% | 182.15 | 10.60 | 43.94 |
| 36. | 31 ene. 2022 | -6.97% | -5.26% | 80.41 | 40.51 | 57.07 |
| 37. | 28 feb. 2022 | 2.58% | -3.14% | 0.35 | 17.99 | -2.51 |
| 38. | 31 mar. 2022 | 1.93% | 3.58% | 0.00 | 6.11 | -0.14 |
| 39. | 30 abr. 2022 | 2.34% | -8.80% | 0.12 | 98.04 | -3.44 |
| 40. | 31 may. 2022 | -9.20% | 0.01% | 125.17 | 1.21 | 12.31 |
| 41. | 30 jun. 2022 | -20.89% | -8.39% | 523.41 | 90.21 | 217.29 |
| 42. | 31 jul. 2022 | 14.92% | 9.11% | 167.20 | 64.09 | 103.52 |
| 43. | 31 ago. 2022 | -0.44% | -4.24% | 5.90 | 28.62 | 13.00 |
| 44. | 30 sept. 2022 | -5.29% | -9.34% | 53.06 | 109.11 | 76.09 |
| 45. | 31 oct. 2022 | 12.14% | 7.99% | 102.93 | 47.34 | 69.80 |
| 46. | 30 nov. 2022 | 5.55% | 5.38% | 12.67 | 18.23 | 15.20 |
| 47. | 31 dic. 2022 | -11.40% | -5.90% | 179.37 | 49.04 | 93.79 |
| 48. | 31 ene. 2023 | 14.82% | 6.18% | 164.63 | 25.70 | 65.04 |
| 49. | 28 feb. 2023 | -0.30% | -2.61% | 5.24 | 13.82 | 8.51 |
| 50. | 31 mar. 2023 | -2.52% | 3.51% | 20.35 | 5.76 | -10.82 |
| 51. | 30 abr. 2023 | 2.24% | 1.46% | 0.06 | 0.13 | 0.09 |
| 52. | 31 may. 2023 | -5.38% | 0.25% | 54.37 | 0.74 | 6.32 |
| 53. | 30 jun. 2023 | 6.93% | 4.71% | 24.36 | 13.02 | 17.81 |
| 54. | 31 jul. 2023 | 6.83% | 4.85% | 23.40 | 13.99 | 18.09 |
| 55. | 31 ago. 2023 | -4.30% | -1.77% | 39.62 | 8.28 | 18.11 |
| 56. | 30 sept. 2023 | 1.03% | -4.87% | 0.93 | 35.73 | 5.76 |
| 57. | 31 oct. 2023 | 0.90% | -2.20% | 1.19 | 10.92 | 3.61 |
| 58. | 30 nov. 2023 | 10.65% | 8.92% | 74.98 | 61.03 | 67.65 |
| 59. | 31 dic. 2023 | 8.70% | 4.42% | 44.96 | 11.00 | 22.24 |
| Total (Σ): | 5,022.46 | 1,634.30 | 2,071.12 | |||
Mostrar todo
VarianzaHLT = Σ(RHLT,t–RHLT)2 ÷ (59 – 1)
= 5,022.46 ÷ (59 – 1)
= 86.59
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaHLT, S&P 500 = Σ(RHLT,t–RHLT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,071.12 ÷ (59 – 1)
= 35.71
Estimación sistemática del riesgo (β)
| VarianzaHLT | 86.59 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaHLT, S&P 500 | 35.71 |
| Coeficiente de correlaciónHLT, S&P 5001 | 0.72 |
| βHLT2 | 1.27 |
| αHLT3 | 0.59% |
Cálculos
1 Coeficiente de correlaciónHLT, S&P 500
= CovarianzaHLT, S&P 500 ÷ (Desviación estándarHLT × Desviación estándarS&P 500)
= 35.71 ÷ (9.31% × 5.31%)
= 0.72
2 βHLT
= CovarianzaHLT, S&P 500 ÷ VarianzaS&P 500
= 35.71 ÷ 28.18
= 1.27
3 αHLT
= PromedioHLT – βHLT × PromedioS&P 500
= 1.99% – 1.27 × 1.11%
= 0.59%
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 Hilton acciones ordinarias | βHLT | 1.27 |
| Tasa de rendimiento esperada de las acciones ordinarias de Hilton3 | E(RHLT) | 16.22% |
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(RHLT) = RF + βHLT [E(RM) – RF]
= 4.67% + 1.27 [13.79% – 4.67%]
= 16.22%