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 Royal Caribbean.
Tasas de retorno
Royal Caribbean Cruises Ltd., tasas mensuales de retorno
| Royal Caribbean Cruises Ltd. (RCL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioRCL,t1 | DividendoRCL,t1 | RRCL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $93.63 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $96.10 | 2.64% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $98.11 | $0.48 | 2.59% | 2,362.72 | -0.04% |
| 3. | 30 abr. 2017 | $106.60 | 8.65% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $69.82 | -17.30% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $76.90 | 10.14% | 4,766.18 | 4.36% | |
| Promedio (R): | 1.25% | 1.36% | ||||
| Desviación estándar: | 16.31% | 4.48% | ||||
| Royal Caribbean Cruises Ltd. (RCL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioRCL,t1 | DividendoRCL,t1 | RRCL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $93.63 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $96.10 | 2.64% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $98.11 | $0.48 | 2.59% | 2,362.72 | -0.04% |
| 3. | 30 abr. 2017 | $106.60 | 8.65% | 2,384.20 | 0.91% | |
| 4. | 31 may. 2017 | $110.18 | $0.48 | 3.81% | 2,411.80 | 1.16% |
| 5. | 30 jun. 2017 | $109.23 | -0.86% | 2,423.41 | 0.48% | |
| 6. | 31 jul. 2017 | $113.07 | 3.52% | 2,470.30 | 1.93% | |
| 7. | 31 ago. 2017 | $124.46 | 10.07% | 2,471.65 | 0.05% | |
| 8. | 30 sept. 2017 | $118.54 | $0.60 | -4.27% | 2,519.36 | 1.93% |
| 9. | 31 oct. 2017 | $123.77 | 4.41% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $123.88 | 0.09% | 2,647.58 | 2.81% | |
| 11. | 31 dic. 2017 | $119.28 | $0.60 | -3.23% | 2,673.61 | 0.98% |
| 12. | 31 ene. 2018 | $133.55 | 11.96% | 2,823.81 | 5.62% | |
| 13. | 28 feb. 2018 | $126.60 | -5.20% | 2,713.83 | -3.89% | |
| 14. | 31 mar. 2018 | $117.74 | $0.60 | -6.52% | 2,640.87 | -2.69% |
| 15. | 30 abr. 2018 | $108.19 | -8.11% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $104.98 | -2.97% | 2,705.27 | 2.16% | |
| 17. | 30 jun. 2018 | $103.60 | $0.60 | -0.74% | 2,718.37 | 0.48% |
| 18. | 31 jul. 2018 | $112.76 | 8.84% | 2,816.29 | 3.60% | |
| 19. | 31 ago. 2018 | $122.58 | 8.71% | 2,901.52 | 3.03% | |
| 20. | 30 sept. 2018 | $129.94 | $0.70 | 6.58% | 2,913.98 | 0.43% |
| 21. | 31 oct. 2018 | $104.73 | -19.40% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $113.07 | 7.96% | 2,760.17 | 1.79% | |
| 23. | 31 dic. 2018 | $97.79 | $0.70 | -12.89% | 2,506.85 | -9.18% |
| 24. | 31 ene. 2019 | $120.05 | 22.76% | 2,704.10 | 7.87% | |
| 25. | 28 feb. 2019 | $118.48 | -1.31% | 2,784.49 | 2.97% | |
| 26. | 31 mar. 2019 | $114.62 | $0.70 | -2.67% | 2,834.40 | 1.79% |
| 27. | 30 abr. 2019 | $120.94 | 5.51% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $121.76 | 0.68% | 2,752.06 | -6.58% | |
| 29. | 30 jun. 2019 | $121.21 | $0.70 | 0.12% | 2,941.76 | 6.89% |
| 30. | 31 jul. 2019 | $116.34 | -4.02% | 2,980.38 | 1.31% | |
| 31. | 31 ago. 2019 | $104.28 | -10.37% | 2,926.46 | -1.81% | |
| 32. | 30 sept. 2019 | $108.33 | $0.78 | 4.63% | 2,976.74 | 1.72% |
| 33. | 31 oct. 2019 | $108.83 | 0.46% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $120.02 | 10.28% | 3,140.98 | 3.40% | |
| 35. | 31 dic. 2019 | $133.51 | $0.78 | 11.89% | 3,230.78 | 2.86% |
| 36. | 31 ene. 2020 | $117.08 | -12.31% | 3,225.52 | -0.16% | |
| 37. | 29 feb. 2020 | $80.41 | -31.32% | 2,954.22 | -8.41% | |
| 38. | 31 mar. 2020 | $32.17 | $0.78 | -59.02% | 2,584.59 | -12.51% |
| 39. | 30 abr. 2020 | $46.77 | 45.38% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $51.87 | 10.90% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $50.30 | -3.03% | 3,100.29 | 1.84% | |
| 42. | 31 jul. 2020 | $48.71 | -3.16% | 3,271.12 | 5.51% | |
| 43. | 31 ago. 2020 | $68.84 | 41.33% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $64.73 | -5.97% | 3,363.00 | -3.92% | |
| 45. | 31 oct. 2020 | $56.42 | -12.84% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $78.81 | 39.68% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $74.69 | -5.23% | 3,756.07 | 3.71% | |
| 48. | 31 ene. 2021 | $65.00 | -12.97% | 3,714.24 | -1.11% | |
| 49. | 28 feb. 2021 | $93.27 | 43.49% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $85.61 | -8.21% | 3,972.89 | 4.24% | |
| 51. | 30 abr. 2021 | $86.95 | 1.57% | 4,181.17 | 5.24% | |
| 52. | 31 may. 2021 | $93.27 | 7.27% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $85.28 | -8.57% | 4,297.50 | 2.22% | |
| 54. | 31 jul. 2021 | $76.87 | -9.86% | 4,395.26 | 2.27% | |
| 55. | 31 ago. 2021 | $82.73 | 7.62% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $88.95 | 7.52% | 4,307.54 | -4.76% | |
| 57. | 31 oct. 2021 | $84.43 | -5.08% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $69.82 | -17.30% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $76.90 | 10.14% | 4,766.18 | 4.36% | |
| Promedio (R): | 1.25% | 1.36% | ||||
| Desviación estándar: | 16.31% | 4.48% | ||||
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 RCL 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
Royal Caribbean Cruises Ltd., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RRCL,t | RS&P 500,t | (RRCL,t–RRCL)2 | (RS&P 500,t–RS&P 500)2 | (RRCL,t–RRCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 2.64% | 3.72% | 1.93 | 5.58 | 3.28 |
| 2. | 31 mar. 2017 | 2.59% | -0.04% | 1.80 | 1.95 | -1.88 |
| 3. | 30 abr. 2017 | 8.65% | 0.91% | 54.84 | 0.20 | -3.32 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -17.30% | -0.83% | 344.19 | 4.80 | 40.65 |
| 59. | 31 dic. 2021 | 10.14% | 4.36% | 79.07 | 9.02 | 26.71 |
| Total (Σ): | 15,435.70 | 1,164.17 | 3,067.23 | |||
| t | Fecha | RRCL,t | RS&P 500,t | (RRCL,t–RRCL)2 | (RS&P 500,t–RS&P 500)2 | (RRCL,t–RRCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 2.64% | 3.72% | 1.93 | 5.58 | 3.28 |
| 2. | 31 mar. 2017 | 2.59% | -0.04% | 1.80 | 1.95 | -1.88 |
| 3. | 30 abr. 2017 | 8.65% | 0.91% | 54.84 | 0.20 | -3.32 |
| 4. | 31 may. 2017 | 3.81% | 1.16% | 6.56 | 0.04 | -0.51 |
| 5. | 30 jun. 2017 | -0.86% | 0.48% | 4.45 | 0.77 | 1.85 |
| 6. | 31 jul. 2017 | 3.52% | 1.93% | 5.14 | 0.33 | 1.31 |
| 7. | 31 ago. 2017 | 10.07% | 0.05% | 77.89 | 1.70 | -11.50 |
| 8. | 30 sept. 2017 | -4.27% | 1.93% | 30.50 | 0.33 | -3.16 |
| 9. | 31 oct. 2017 | 4.41% | 2.22% | 10.01 | 0.74 | 2.72 |
| 10. | 30 nov. 2017 | 0.09% | 2.81% | 1.34 | 2.10 | -1.68 |
| 11. | 31 dic. 2017 | -3.23% | 0.98% | 20.04 | 0.14 | 1.68 |
| 12. | 31 ene. 2018 | 11.96% | 5.62% | 114.82 | 18.15 | 45.65 |
| 13. | 28 feb. 2018 | -5.20% | -3.89% | 41.63 | 27.59 | 33.89 |
| 14. | 31 mar. 2018 | -6.52% | -2.69% | 60.41 | 16.37 | 31.45 |
| 15. | 30 abr. 2018 | -8.11% | 0.27% | 87.60 | 1.18 | 10.16 |
| 16. | 31 may. 2018 | -2.97% | 2.16% | 17.77 | 0.64 | -3.38 |
| 17. | 30 jun. 2018 | -0.74% | 0.48% | 3.96 | 0.76 | 1.74 |
| 18. | 31 jul. 2018 | 8.84% | 3.60% | 57.66 | 5.04 | 17.04 |
| 19. | 31 ago. 2018 | 8.71% | 3.03% | 55.66 | 2.78 | 12.45 |
| 20. | 30 sept. 2018 | 6.58% | 0.43% | 28.38 | 0.86 | -4.95 |
| 21. | 31 oct. 2018 | -19.40% | -6.94% | 426.40 | 68.86 | 171.35 |
| 22. | 30 nov. 2018 | 7.96% | 1.79% | 45.09 | 0.18 | 2.87 |
| 23. | 31 dic. 2018 | -12.89% | -9.18% | 200.02 | 111.00 | 149.00 |
| 24. | 31 ene. 2019 | 22.76% | 7.87% | 462.89 | 42.39 | 140.07 |
| 25. | 28 feb. 2019 | -1.31% | 2.97% | 6.53 | 2.61 | -4.13 |
| 26. | 31 mar. 2019 | -2.67% | 1.79% | 15.33 | 0.19 | -1.70 |
| 27. | 30 abr. 2019 | 5.51% | 3.93% | 18.20 | 6.62 | 10.98 |
| 28. | 31 may. 2019 | 0.68% | -6.58% | 0.33 | 62.97 | 4.52 |
| 29. | 30 jun. 2019 | 0.12% | 6.89% | 1.27 | 30.64 | -6.23 |
| 30. | 31 jul. 2019 | -4.02% | 1.31% | 27.73 | 0.00 | 0.24 |
| 31. | 31 ago. 2019 | -10.37% | -1.81% | 134.89 | 10.03 | 36.78 |
| 32. | 30 sept. 2019 | 4.63% | 1.72% | 11.45 | 0.13 | 1.22 |
| 33. | 31 oct. 2019 | 0.46% | 2.04% | 0.62 | 0.47 | -0.54 |
| 34. | 30 nov. 2019 | 10.28% | 3.40% | 81.61 | 4.19 | 18.49 |
| 35. | 31 dic. 2019 | 11.89% | 2.86% | 113.24 | 2.25 | 15.97 |
| 36. | 31 ene. 2020 | -12.31% | -0.16% | 183.72 | 2.31 | 20.61 |
| 37. | 29 feb. 2020 | -31.32% | -8.41% | 1,060.71 | 95.43 | 318.16 |
| 38. | 31 mar. 2020 | -59.02% | -12.51% | 3,632.55 | 192.37 | 835.94 |
| 39. | 30 abr. 2020 | 45.38% | 12.68% | 1,947.96 | 128.29 | 499.90 |
| 40. | 31 may. 2020 | 10.90% | 4.53% | 93.24 | 10.05 | 30.61 |
| 41. | 30 jun. 2020 | -3.03% | 1.84% | 18.28 | 0.23 | -2.06 |
| 42. | 31 jul. 2020 | -3.16% | 5.51% | 19.44 | 17.24 | -18.31 |
| 43. | 31 ago. 2020 | 41.33% | 7.01% | 1,606.25 | 31.91 | 226.38 |
| 44. | 30 sept. 2020 | -5.97% | -3.92% | 52.11 | 27.89 | 38.12 |
| 45. | 31 oct. 2020 | -12.84% | -2.77% | 198.42 | 17.01 | 58.10 |
| 46. | 30 nov. 2020 | 39.68% | 10.75% | 1,477.35 | 88.30 | 361.17 |
| 47. | 31 dic. 2020 | -5.23% | 3.71% | 41.94 | 5.54 | -15.25 |
| 48. | 31 ene. 2021 | -12.97% | -1.11% | 202.26 | 6.11 | 35.15 |
| 49. | 28 feb. 2021 | 43.49% | 2.61% | 1,784.57 | 1.57 | 52.86 |
| 50. | 31 mar. 2021 | -8.21% | 4.24% | 89.51 | 8.33 | -27.30 |
| 51. | 30 abr. 2021 | 1.57% | 5.24% | 0.10 | 15.09 | 1.23 |
| 52. | 31 may. 2021 | 7.27% | 0.55% | 36.25 | 0.65 | -4.87 |
| 53. | 30 jun. 2021 | -8.57% | 2.22% | 96.33 | 0.75 | -8.47 |
| 54. | 31 jul. 2021 | -9.86% | 2.27% | 123.43 | 0.84 | -10.19 |
| 55. | 31 ago. 2021 | 7.62% | 2.90% | 40.64 | 2.38 | 9.82 |
| 56. | 30 sept. 2021 | 7.52% | -4.76% | 39.32 | 37.39 | -38.34 |
| 57. | 31 oct. 2021 | -5.08% | 6.91% | 40.06 | 30.87 | -35.17 |
| 58. | 30 nov. 2021 | -17.30% | -0.83% | 344.19 | 4.80 | 40.65 |
| 59. | 31 dic. 2021 | 10.14% | 4.36% | 79.07 | 9.02 | 26.71 |
| Total (Σ): | 15,435.70 | 1,164.17 | 3,067.23 | |||
Mostrar todo
VarianzaRCL = Σ(RRCL,t–RRCL)2 ÷ (59 – 1)
= 15,435.70 ÷ (59 – 1)
= 266.13
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaRCL, S&P 500 = Σ(RRCL,t–RRCL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,067.23 ÷ (59 – 1)
= 52.88
Estimación sistemática del riesgo (β)
| VarianzaRCL | 266.13 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaRCL, S&P 500 | 52.88 |
| Coeficiente de correlaciónRCL, S&P 5001 | 0.72 |
| βRCL2 | 2.63 |
| αRCL3 | -2.33% |
Cálculos
1 Coeficiente de correlaciónRCL, S&P 500
= CovarianzaRCL, S&P 500 ÷ (Desviación estándarRCL × Desviación estándarS&P 500)
= 52.88 ÷ (16.31% × 4.48%)
= 0.72
2 βRCL
= CovarianzaRCL, S&P 500 ÷ VarianzaS&P 500
= 52.88 ÷ 20.07
= 2.63
3 αRCL
= PromedioRCL – βRCL × PromedioS&P 500
= 1.25% – 2.63 × 1.36%
= -2.33%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.87% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.54% |
| Riesgo sistemático de Royal Caribbean acciones ordinarias | βRCL | 2.63 |
| Tasa de rendimiento esperada de las acciones ordinarias de Royal Caribbean3 | E(RRCL) | 27.72% |
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(RRCL) = RF + βRCL [E(RM) – RF]
= 4.87% + 2.63 [13.54% – 4.87%]
= 27.72%