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 Disney.
Tasas de retorno
Walt Disney Co., tasas mensuales de retorno
| Walt Disney Co. (DIS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioDIS,t1 | DividendoDIS,t1 | RDIS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 oct. 2017 | $97.81 | 2,575.26 | ||||
| 1. | 30 nov. 2017 | $104.82 | 7.17% | 2,647.58 | 2.81% | |
| 2. | 31 dic. 2017 | $107.51 | $0.84 | 3.37% | 2,673.61 | 0.98% |
| 3. | 31 ene. 2018 | $108.67 | 1.08% | 2,823.81 | 5.62% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 ago. 2023 | $83.68 | -5.86% | 4,507.66 | -1.77% | |
| 71. | 30 sept. 2023 | $81.05 | -3.14% | 4,288.05 | -4.87% | |
| Promedio (R): | 0.21% | 0.85% | ||||
| Desviación estándar: | 9.39% | 5.13% | ||||
| Walt Disney Co. (DIS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioDIS,t1 | DividendoDIS,t1 | RDIS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 oct. 2017 | $97.81 | 2,575.26 | ||||
| 1. | 30 nov. 2017 | $104.82 | 7.17% | 2,647.58 | 2.81% | |
| 2. | 31 dic. 2017 | $107.51 | $0.84 | 3.37% | 2,673.61 | 0.98% |
| 3. | 31 ene. 2018 | $108.67 | 1.08% | 2,823.81 | 5.62% | |
| 4. | 28 feb. 2018 | $103.16 | -5.07% | 2,713.83 | -3.89% | |
| 5. | 31 mar. 2018 | $100.44 | -2.64% | 2,640.87 | -2.69% | |
| 6. | 30 abr. 2018 | $100.33 | -0.11% | 2,648.05 | 0.27% | |
| 7. | 31 may. 2018 | $99.47 | -0.86% | 2,705.27 | 2.16% | |
| 8. | 30 jun. 2018 | $104.81 | 5.37% | 2,718.37 | 0.48% | |
| 9. | 31 jul. 2018 | $113.56 | $0.84 | 9.15% | 2,816.29 | 3.60% |
| 10. | 31 ago. 2018 | $112.02 | -1.36% | 2,901.52 | 3.03% | |
| 11. | 30 sept. 2018 | $116.94 | 4.39% | 2,913.98 | 0.43% | |
| 12. | 31 oct. 2018 | $114.83 | -1.80% | 2,711.74 | -6.94% | |
| 13. | 30 nov. 2018 | $115.49 | 0.57% | 2,760.17 | 1.79% | |
| 14. | 31 dic. 2018 | $109.65 | $0.88 | -4.29% | 2,506.85 | -9.18% |
| 15. | 31 ene. 2019 | $111.52 | 1.71% | 2,704.10 | 7.87% | |
| 16. | 28 feb. 2019 | $112.84 | 1.18% | 2,784.49 | 2.97% | |
| 17. | 31 mar. 2019 | $111.03 | -1.60% | 2,834.40 | 1.79% | |
| 18. | 30 abr. 2019 | $136.97 | 23.36% | 2,945.83 | 3.93% | |
| 19. | 31 may. 2019 | $132.04 | -3.60% | 2,752.06 | -6.58% | |
| 20. | 30 jun. 2019 | $139.64 | 5.76% | 2,941.76 | 6.89% | |
| 21. | 31 jul. 2019 | $143.01 | $0.88 | 3.04% | 2,980.38 | 1.31% |
| 22. | 31 ago. 2019 | $137.26 | -4.02% | 2,926.46 | -1.81% | |
| 23. | 30 sept. 2019 | $130.32 | -5.06% | 2,976.74 | 1.72% | |
| 24. | 31 oct. 2019 | $129.92 | -0.31% | 3,037.56 | 2.04% | |
| 25. | 30 nov. 2019 | $151.58 | 16.67% | 3,140.98 | 3.40% | |
| 26. | 31 dic. 2019 | $144.63 | $0.88 | -4.00% | 3,230.78 | 2.86% |
| 27. | 31 ene. 2020 | $138.31 | -4.37% | 3,225.52 | -0.16% | |
| 28. | 29 feb. 2020 | $117.65 | -14.94% | 2,954.22 | -8.41% | |
| 29. | 31 mar. 2020 | $96.60 | -17.89% | 2,584.59 | -12.51% | |
| 30. | 30 abr. 2020 | $108.15 | 11.96% | 2,912.43 | 12.68% | |
| 31. | 31 may. 2020 | $117.30 | 8.46% | 3,044.31 | 4.53% | |
| 32. | 30 jun. 2020 | $111.51 | -4.94% | 3,100.29 | 1.84% | |
| 33. | 31 jul. 2020 | $116.94 | 4.87% | 3,271.12 | 5.51% | |
| 34. | 31 ago. 2020 | $131.87 | 12.77% | 3,500.31 | 7.01% | |
| 35. | 30 sept. 2020 | $124.08 | -5.91% | 3,363.00 | -3.92% | |
| 36. | 31 oct. 2020 | $121.25 | -2.28% | 3,269.96 | -2.77% | |
| 37. | 30 nov. 2020 | $148.01 | 22.07% | 3,621.63 | 10.75% | |
| 38. | 31 dic. 2020 | $181.18 | 22.41% | 3,756.07 | 3.71% | |
| 39. | 31 ene. 2021 | $168.17 | -7.18% | 3,714.24 | -1.11% | |
| 40. | 28 feb. 2021 | $189.04 | 12.41% | 3,811.15 | 2.61% | |
| 41. | 31 mar. 2021 | $184.52 | -2.39% | 3,972.89 | 4.24% | |
| 42. | 30 abr. 2021 | $186.02 | 0.81% | 4,181.17 | 5.24% | |
| 43. | 31 may. 2021 | $178.65 | -3.96% | 4,204.11 | 0.55% | |
| 44. | 30 jun. 2021 | $175.77 | -1.61% | 4,297.50 | 2.22% | |
| 45. | 31 jul. 2021 | $176.02 | 0.14% | 4,395.26 | 2.27% | |
| 46. | 31 ago. 2021 | $181.30 | 3.00% | 4,522.68 | 2.90% | |
| 47. | 30 sept. 2021 | $169.17 | -6.69% | 4,307.54 | -4.76% | |
| 48. | 31 oct. 2021 | $169.07 | -0.06% | 4,605.38 | 6.91% | |
| 49. | 30 nov. 2021 | $144.90 | -14.30% | 4,567.00 | -0.83% | |
| 50. | 31 dic. 2021 | $154.89 | 6.89% | 4,766.18 | 4.36% | |
| 51. | 31 ene. 2022 | $142.97 | -7.70% | 4,515.55 | -5.26% | |
| 52. | 28 feb. 2022 | $148.46 | 3.84% | 4,373.94 | -3.14% | |
| 53. | 31 mar. 2022 | $137.16 | -7.61% | 4,530.41 | 3.58% | |
| 54. | 30 abr. 2022 | $111.63 | -18.61% | 4,131.93 | -8.80% | |
| 55. | 31 may. 2022 | $110.44 | -1.07% | 4,132.15 | 0.01% | |
| 56. | 30 jun. 2022 | $94.40 | -14.52% | 3,785.38 | -8.39% | |
| 57. | 31 jul. 2022 | $106.10 | 12.39% | 4,130.29 | 9.11% | |
| 58. | 31 ago. 2022 | $112.08 | 5.64% | 3,955.00 | -4.24% | |
| 59. | 30 sept. 2022 | $94.33 | -15.84% | 3,585.62 | -9.34% | |
| 60. | 31 oct. 2022 | $106.54 | 12.94% | 3,871.98 | 7.99% | |
| 61. | 30 nov. 2022 | $97.87 | -8.14% | 4,080.11 | 5.38% | |
| 62. | 31 dic. 2022 | $86.88 | -11.23% | 3,839.50 | -5.90% | |
| 63. | 31 ene. 2023 | $108.49 | 24.87% | 4,076.60 | 6.18% | |
| 64. | 28 feb. 2023 | $99.61 | -8.19% | 3,970.15 | -2.61% | |
| 65. | 31 mar. 2023 | $100.13 | 0.52% | 4,109.31 | 3.51% | |
| 66. | 30 abr. 2023 | $102.50 | 2.37% | 4,169.48 | 1.46% | |
| 67. | 31 may. 2023 | $87.96 | -14.19% | 4,179.83 | 0.25% | |
| 68. | 30 jun. 2023 | $89.28 | 1.50% | 4,376.86 | 4.71% | |
| 69. | 31 jul. 2023 | $88.89 | -0.44% | 4,588.96 | 4.85% | |
| 70. | 31 ago. 2023 | $83.68 | -5.86% | 4,507.66 | -1.77% | |
| 71. | 30 sept. 2023 | $81.05 | -3.14% | 4,288.05 | -4.87% | |
| Promedio (R): | 0.21% | 0.85% | ||||
| Desviación estándar: | 9.39% | 5.13% | ||||
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 DIS 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
Walt Disney Co., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RDIS,t | RS&P 500,t | (RDIS,t–RDIS)2 | (RS&P 500,t–RS&P 500)2 | (RDIS,t–RDIS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 nov. 2017 | 7.17% | 2.81% | 48.39 | 3.83 | 13.61 |
| 2. | 31 dic. 2017 | 3.37% | 0.98% | 9.97 | 0.02 | 0.42 |
| 3. | 31 ene. 2018 | 1.08% | 5.62% | 0.75 | 22.72 | 4.14 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 ago. 2023 | -5.86% | -1.77% | 36.86 | 6.88 | 15.92 |
| 71. | 30 sept. 2023 | -3.14% | -4.87% | 11.24 | 32.75 | 19.19 |
| Total (Σ): | 6,172.98 | 1,838.69 | 2,310.12 | |||
| t | Fecha | RDIS,t | RS&P 500,t | (RDIS,t–RDIS)2 | (RS&P 500,t–RS&P 500)2 | (RDIS,t–RDIS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 nov. 2017 | 7.17% | 2.81% | 48.39 | 3.83 | 13.61 |
| 2. | 31 dic. 2017 | 3.37% | 0.98% | 9.97 | 0.02 | 0.42 |
| 3. | 31 ene. 2018 | 1.08% | 5.62% | 0.75 | 22.72 | 4.14 |
| 4. | 28 feb. 2018 | -5.07% | -3.89% | 27.89 | 22.52 | 25.06 |
| 5. | 31 mar. 2018 | -2.64% | -2.69% | 8.11 | 12.53 | 10.08 |
| 6. | 30 abr. 2018 | -0.11% | 0.27% | 0.10 | 0.34 | 0.19 |
| 7. | 31 may. 2018 | -0.86% | 2.16% | 1.14 | 1.71 | -1.40 |
| 8. | 30 jun. 2018 | 5.37% | 0.48% | 26.61 | 0.13 | -1.89 |
| 9. | 31 jul. 2018 | 9.15% | 3.60% | 79.92 | 7.57 | 24.59 |
| 10. | 31 ago. 2018 | -1.36% | 3.03% | 2.45 | 4.73 | -3.41 |
| 11. | 30 sept. 2018 | 4.39% | 0.43% | 17.49 | 0.18 | -1.76 |
| 12. | 31 oct. 2018 | -1.80% | -6.94% | 4.06 | 60.71 | 15.70 |
| 13. | 30 nov. 2018 | 0.57% | 1.79% | 0.13 | 0.87 | 0.34 |
| 14. | 31 dic. 2018 | -4.29% | -9.18% | 20.30 | 100.58 | 45.18 |
| 15. | 31 ene. 2019 | 1.71% | 7.87% | 2.24 | 49.24 | 10.49 |
| 16. | 28 feb. 2019 | 1.18% | 2.97% | 0.95 | 4.50 | 2.07 |
| 17. | 31 mar. 2019 | -1.60% | 1.79% | 3.29 | 0.89 | -1.71 |
| 18. | 30 abr. 2019 | 23.36% | 3.93% | 536.05 | 9.49 | 71.31 |
| 19. | 31 may. 2019 | -3.60% | -6.58% | 14.51 | 55.19 | 28.30 |
| 20. | 30 jun. 2019 | 5.76% | 6.89% | 30.75 | 36.50 | 33.50 |
| 21. | 31 jul. 2019 | 3.04% | 1.31% | 8.03 | 0.21 | 1.31 |
| 22. | 31 ago. 2019 | -4.02% | -1.81% | 17.90 | 7.08 | 11.26 |
| 23. | 30 sept. 2019 | -5.06% | 1.72% | 27.74 | 0.75 | -4.57 |
| 24. | 31 oct. 2019 | -0.31% | 2.04% | 0.27 | 1.42 | -0.62 |
| 25. | 30 nov. 2019 | 16.67% | 3.40% | 270.98 | 6.52 | 42.03 |
| 26. | 31 dic. 2019 | -4.00% | 2.86% | 17.76 | 4.03 | -8.46 |
| 27. | 31 ene. 2020 | -4.37% | -0.16% | 20.98 | 1.03 | 4.64 |
| 28. | 29 feb. 2020 | -14.94% | -8.41% | 229.45 | 85.79 | 140.30 |
| 29. | 31 mar. 2020 | -17.89% | -12.51% | 327.70 | 178.57 | 241.91 |
| 30. | 30 abr. 2020 | 11.96% | 12.68% | 137.97 | 140.02 | 138.99 |
| 31. | 31 may. 2020 | 8.46% | 4.53% | 68.07 | 13.52 | 30.34 |
| 32. | 30 jun. 2020 | -4.94% | 1.84% | 26.49 | 0.98 | -5.08 |
| 33. | 31 jul. 2020 | 4.87% | 5.51% | 21.71 | 21.71 | 21.71 |
| 34. | 31 ago. 2020 | 12.77% | 7.01% | 157.68 | 37.89 | 77.29 |
| 35. | 30 sept. 2020 | -5.91% | -3.92% | 37.43 | 22.79 | 29.21 |
| 36. | 31 oct. 2020 | -2.28% | -2.77% | 6.21 | 13.09 | 9.01 |
| 37. | 30 nov. 2020 | 22.07% | 10.75% | 477.85 | 98.08 | 216.48 |
| 38. | 31 dic. 2020 | 22.41% | 3.71% | 492.85 | 8.18 | 63.51 |
| 39. | 31 ene. 2021 | -7.18% | -1.11% | 54.63 | 3.86 | 14.52 |
| 40. | 28 feb. 2021 | 12.41% | 2.61% | 148.83 | 3.09 | 21.45 |
| 41. | 31 mar. 2021 | -2.39% | 4.24% | 6.77 | 11.51 | -8.83 |
| 42. | 30 abr. 2021 | 0.81% | 5.24% | 0.36 | 19.28 | 2.65 |
| 43. | 31 may. 2021 | -3.96% | 0.55% | 17.41 | 0.09 | 1.26 |
| 44. | 30 jun. 2021 | -1.61% | 2.22% | 3.32 | 1.88 | -2.50 |
| 45. | 31 jul. 2021 | 0.14% | 2.27% | 0.00 | 2.03 | -0.10 |
| 46. | 31 ago. 2021 | 3.00% | 2.90% | 7.78 | 4.19 | 5.71 |
| 47. | 30 sept. 2021 | -6.69% | -4.76% | 47.62 | 31.45 | 38.70 |
| 48. | 31 oct. 2021 | -0.06% | 6.91% | 0.07 | 36.76 | -1.63 |
| 49. | 30 nov. 2021 | -14.30% | -0.83% | 210.43 | 2.84 | 24.44 |
| 50. | 31 dic. 2021 | 6.89% | 4.36% | 44.68 | 12.32 | 23.46 |
| 51. | 31 ene. 2022 | -7.70% | -5.26% | 62.51 | 37.33 | 48.30 |
| 52. | 28 feb. 2022 | 3.84% | -3.14% | 13.17 | 15.90 | -14.47 |
| 53. | 31 mar. 2022 | -7.61% | 3.58% | 61.18 | 7.43 | -21.32 |
| 54. | 30 abr. 2022 | -18.61% | -8.80% | 354.33 | 93.06 | 181.59 |
| 55. | 31 may. 2022 | -1.07% | 0.01% | 1.63 | 0.72 | 1.08 |
| 56. | 30 jun. 2022 | -14.52% | -8.39% | 217.09 | 85.44 | 136.19 |
| 57. | 31 jul. 2022 | 12.39% | 9.11% | 148.44 | 68.23 | 100.64 |
| 58. | 31 ago. 2022 | 5.64% | -4.24% | 29.44 | 25.96 | -27.65 |
| 59. | 30 sept. 2022 | -15.84% | -9.34% | 257.51 | 103.85 | 163.53 |
| 60. | 31 oct. 2022 | 12.94% | 7.99% | 162.14 | 50.91 | 90.86 |
| 61. | 30 nov. 2022 | -8.14% | 5.38% | 69.69 | 20.47 | -37.77 |
| 62. | 31 dic. 2022 | -11.23% | -5.90% | 130.86 | 45.54 | 77.20 |
| 63. | 31 ene. 2023 | 24.87% | 6.18% | 608.27 | 28.35 | 131.31 |
| 64. | 28 feb. 2023 | -8.19% | -2.61% | 70.48 | 11.99 | 29.07 |
| 65. | 31 mar. 2023 | 0.52% | 3.51% | 0.10 | 7.04 | 0.83 |
| 66. | 30 abr. 2023 | 2.37% | 1.46% | 4.65 | 0.38 | 1.32 |
| 67. | 31 may. 2023 | -14.19% | 0.25% | 207.24 | 0.36 | 8.68 |
| 68. | 30 jun. 2023 | 1.50% | 4.71% | 1.67 | 14.92 | 4.98 |
| 69. | 31 jul. 2023 | -0.44% | 4.85% | 0.42 | 15.96 | -2.59 |
| 70. | 31 ago. 2023 | -5.86% | -1.77% | 36.86 | 6.88 | 15.92 |
| 71. | 30 sept. 2023 | -3.14% | -4.87% | 11.24 | 32.75 | 19.19 |
| Total (Σ): | 6,172.98 | 1,838.69 | 2,310.12 | |||
Mostrar todo
VarianzaDIS = Σ(RDIS,t–RDIS)2 ÷ (71 – 1)
= 6,172.98 ÷ (71 – 1)
= 88.19
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,838.69 ÷ (71 – 1)
= 26.27
CovarianzaDIS, S&P 500 = Σ(RDIS,t–RDIS)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,310.12 ÷ (71 – 1)
= 33.00
Estimación sistemática del riesgo (β)
| VarianzaDIS | 88.19 |
| VarianzaS&P 500 | 26.27 |
| CovarianzaDIS, S&P 500 | 33.00 |
| Coeficiente de correlaciónDIS, S&P 5001 | 0.69 |
| βDIS2 | 1.26 |
| αDIS3 | -0.86% |
Cálculos
1 Coeficiente de correlaciónDIS, S&P 500
= CovarianzaDIS, S&P 500 ÷ (Desviación estándarDIS × Desviación estándarS&P 500)
= 33.00 ÷ (9.39% × 5.13%)
= 0.69
2 βDIS
= CovarianzaDIS, S&P 500 ÷ VarianzaS&P 500
= 33.00 ÷ 26.27
= 1.26
3 αDIS
= PromedioDIS – βDIS × PromedioS&P 500
= 0.21% – 1.26 × 0.85%
= -0.86%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.86% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.52% |
| Riesgo sistemático de Disney acciones ordinarias | βDIS | 1.26 |
| Tasa de rendimiento esperada de las acciones ordinarias de Disney3 | E(RDIS) | 15.74% |
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(RDIS) = RF + βDIS [E(RM) – RF]
= 4.86% + 1.26 [13.52% – 4.86%]
= 15.74%