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 Oracle.
Tasas de retorno
Oracle Corp., tasas mensuales de retorno
| Oracle Corp. (ORCL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioORCL,t1 | DividendoORCL,t1 | RORCL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 jun. 2018 | $44.06 | 2,718.37 | ||||
| 1. | 31 jul. 2018 | $47.68 | $0.19 | 8.65% | 2,816.29 | 3.60% |
| 2. | 31 ago. 2018 | $48.58 | 1.89% | 2,901.52 | 3.03% | |
| 3. | 30 sept. 2018 | $51.56 | 6.13% | 2,913.98 | 0.43% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 abr. 2024 | $113.75 | $0.40 | -9.12% | 5,035.69 | -4.16% |
| 71. | 31 may. 2024 | $117.19 | 3.02% | 5,277.51 | 4.80% | |
| Promedio (R): | 1.81% | 1.08% | ||||
| Desviación estándar: | 7.69% | 5.24% | ||||
| Oracle Corp. (ORCL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioORCL,t1 | DividendoORCL,t1 | RORCL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 jun. 2018 | $44.06 | 2,718.37 | ||||
| 1. | 31 jul. 2018 | $47.68 | $0.19 | 8.65% | 2,816.29 | 3.60% |
| 2. | 31 ago. 2018 | $48.58 | 1.89% | 2,901.52 | 3.03% | |
| 3. | 30 sept. 2018 | $51.56 | 6.13% | 2,913.98 | 0.43% | |
| 4. | 31 oct. 2018 | $48.84 | $0.19 | -4.91% | 2,711.74 | -6.94% |
| 5. | 30 nov. 2018 | $48.76 | -0.16% | 2,760.17 | 1.79% | |
| 6. | 31 dic. 2018 | $45.15 | -7.40% | 2,506.85 | -9.18% | |
| 7. | 31 ene. 2019 | $50.23 | $0.19 | 11.67% | 2,704.10 | 7.87% |
| 8. | 28 feb. 2019 | $52.13 | 3.78% | 2,784.49 | 2.97% | |
| 9. | 31 mar. 2019 | $53.71 | 3.03% | 2,834.40 | 1.79% | |
| 10. | 30 abr. 2019 | $55.33 | $0.24 | 3.46% | 2,945.83 | 3.93% |
| 11. | 31 may. 2019 | $50.60 | -8.55% | 2,752.06 | -6.58% | |
| 12. | 30 jun. 2019 | $56.97 | 12.59% | 2,941.76 | 6.89% | |
| 13. | 31 jul. 2019 | $56.30 | $0.24 | -0.75% | 2,980.38 | 1.31% |
| 14. | 31 ago. 2019 | $52.06 | -7.53% | 2,926.46 | -1.81% | |
| 15. | 30 sept. 2019 | $55.03 | 5.70% | 2,976.74 | 1.72% | |
| 16. | 31 oct. 2019 | $54.49 | $0.24 | -0.55% | 3,037.56 | 2.04% |
| 17. | 30 nov. 2019 | $56.14 | 3.03% | 3,140.98 | 3.40% | |
| 18. | 31 dic. 2019 | $52.98 | -5.63% | 3,230.78 | 2.86% | |
| 19. | 31 ene. 2020 | $52.45 | $0.24 | -0.55% | 3,225.52 | -0.16% |
| 20. | 29 feb. 2020 | $49.46 | -5.70% | 2,954.22 | -8.41% | |
| 21. | 31 mar. 2020 | $48.33 | -2.28% | 2,584.59 | -12.51% | |
| 22. | 30 abr. 2020 | $52.97 | $0.24 | 10.10% | 2,912.43 | 12.68% |
| 23. | 31 may. 2020 | $53.77 | 1.51% | 3,044.31 | 4.53% | |
| 24. | 30 jun. 2020 | $55.27 | 2.79% | 3,100.29 | 1.84% | |
| 25. | 31 jul. 2020 | $55.45 | $0.24 | 0.76% | 3,271.12 | 5.51% |
| 26. | 31 ago. 2020 | $57.22 | 3.19% | 3,500.31 | 7.01% | |
| 27. | 30 sept. 2020 | $59.70 | 4.33% | 3,363.00 | -3.92% | |
| 28. | 31 oct. 2020 | $56.11 | $0.24 | -5.61% | 3,269.96 | -2.77% |
| 29. | 30 nov. 2020 | $57.72 | 2.87% | 3,621.63 | 10.75% | |
| 30. | 31 dic. 2020 | $64.69 | 12.08% | 3,756.07 | 3.71% | |
| 31. | 31 ene. 2021 | $60.43 | $0.24 | -6.21% | 3,714.24 | -1.11% |
| 32. | 28 feb. 2021 | $64.51 | 6.75% | 3,811.15 | 2.61% | |
| 33. | 31 mar. 2021 | $70.17 | 8.77% | 3,972.89 | 4.24% | |
| 34. | 30 abr. 2021 | $75.79 | $0.32 | 8.47% | 4,181.17 | 5.24% |
| 35. | 31 may. 2021 | $78.74 | 3.89% | 4,204.11 | 0.55% | |
| 36. | 30 jun. 2021 | $77.84 | -1.14% | 4,297.50 | 2.22% | |
| 37. | 31 jul. 2021 | $87.14 | $0.32 | 12.36% | 4,395.26 | 2.27% |
| 38. | 31 ago. 2021 | $89.13 | 2.28% | 4,522.68 | 2.90% | |
| 39. | 30 sept. 2021 | $87.13 | -2.24% | 4,307.54 | -4.76% | |
| 40. | 31 oct. 2021 | $95.94 | $0.32 | 10.48% | 4,605.38 | 6.91% |
| 41. | 30 nov. 2021 | $90.74 | -5.42% | 4,567.00 | -0.83% | |
| 42. | 31 dic. 2021 | $87.21 | -3.89% | 4,766.18 | 4.36% | |
| 43. | 31 ene. 2022 | $81.16 | $0.32 | -6.57% | 4,515.55 | -5.26% |
| 44. | 28 feb. 2022 | $75.97 | -6.39% | 4,373.94 | -3.14% | |
| 45. | 31 mar. 2022 | $82.73 | 8.90% | 4,530.41 | 3.58% | |
| 46. | 30 abr. 2022 | $73.40 | $0.32 | -10.89% | 4,131.93 | -8.80% |
| 47. | 31 may. 2022 | $71.92 | -2.02% | 4,132.15 | 0.01% | |
| 48. | 30 jun. 2022 | $69.87 | -2.85% | 3,785.38 | -8.39% | |
| 49. | 31 jul. 2022 | $77.84 | $0.32 | 11.86% | 4,130.29 | 9.11% |
| 50. | 31 ago. 2022 | $74.15 | -4.74% | 3,955.00 | -4.24% | |
| 51. | 30 sept. 2022 | $61.07 | -17.64% | 3,585.62 | -9.34% | |
| 52. | 31 oct. 2022 | $78.07 | $0.32 | 28.36% | 3,871.98 | 7.99% |
| 53. | 30 nov. 2022 | $83.03 | 6.35% | 4,080.11 | 5.38% | |
| 54. | 31 dic. 2022 | $81.74 | -1.55% | 3,839.50 | -5.90% | |
| 55. | 31 ene. 2023 | $88.46 | $0.32 | 8.61% | 4,076.60 | 6.18% |
| 56. | 28 feb. 2023 | $87.40 | -1.20% | 3,970.15 | -2.61% | |
| 57. | 31 mar. 2023 | $92.92 | 6.32% | 4,109.31 | 3.51% | |
| 58. | 30 abr. 2023 | $94.72 | $0.40 | 2.37% | 4,169.48 | 1.46% |
| 59. | 31 may. 2023 | $105.94 | 11.85% | 4,179.83 | 0.25% | |
| 60. | 30 jun. 2023 | $119.09 | 12.41% | 4,376.86 | 4.71% | |
| 61. | 31 jul. 2023 | $117.23 | $0.40 | -1.23% | 4,588.96 | 4.85% |
| 62. | 31 ago. 2023 | $120.39 | 2.70% | 4,507.66 | -1.77% | |
| 63. | 30 sept. 2023 | $105.92 | -12.02% | 4,288.05 | -4.87% | |
| 64. | 31 oct. 2023 | $103.40 | $0.40 | -2.00% | 4,193.80 | -2.20% |
| 65. | 30 nov. 2023 | $116.21 | 12.39% | 4,567.80 | 8.92% | |
| 66. | 31 dic. 2023 | $105.43 | -9.28% | 4,769.83 | 4.42% | |
| 67. | 31 ene. 2024 | $111.70 | $0.40 | 6.33% | 4,845.65 | 1.59% |
| 68. | 29 feb. 2024 | $111.68 | -0.02% | 5,096.27 | 5.17% | |
| 69. | 31 mar. 2024 | $125.61 | 12.47% | 5,254.35 | 3.10% | |
| 70. | 30 abr. 2024 | $113.75 | $0.40 | -9.12% | 5,035.69 | -4.16% |
| 71. | 31 may. 2024 | $117.19 | 3.02% | 5,277.51 | 4.80% | |
| Promedio (R): | 1.81% | 1.08% | ||||
| Desviación estándar: | 7.69% | 5.24% | ||||
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 ORCL 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
Oracle Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RORCL,t | RS&P 500,t | (RORCL,t–RORCL)2 | (RS&P 500,t–RS&P 500)2 | (RORCL,t–RORCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 jul. 2018 | 8.65% | 3.60% | 46.76 | 6.39 | 17.28 |
| 2. | 31 ago. 2018 | 1.89% | 3.03% | 0.01 | 3.81 | 0.15 |
| 3. | 30 sept. 2018 | 6.13% | 0.43% | 18.71 | 0.42 | -2.79 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 abr. 2024 | -9.12% | -4.16% | 119.52 | 27.42 | 57.25 |
| 71. | 31 may. 2024 | 3.02% | 4.80% | 1.48 | 13.89 | 4.53 |
| Total (Σ): | 4,144.31 | 1,923.46 | 1,947.49 | |||
| t | Fecha | RORCL,t | RS&P 500,t | (RORCL,t–RORCL)2 | (RS&P 500,t–RS&P 500)2 | (RORCL,t–RORCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 jul. 2018 | 8.65% | 3.60% | 46.76 | 6.39 | 17.28 |
| 2. | 31 ago. 2018 | 1.89% | 3.03% | 0.01 | 3.81 | 0.15 |
| 3. | 30 sept. 2018 | 6.13% | 0.43% | 18.71 | 0.42 | -2.79 |
| 4. | 31 oct. 2018 | -4.91% | -6.94% | 45.11 | 64.25 | 53.83 |
| 5. | 30 nov. 2018 | -0.16% | 1.79% | 3.89 | 0.51 | -1.40 |
| 6. | 31 dic. 2018 | -7.40% | -9.18% | 84.88 | 105.12 | 94.46 |
| 7. | 31 ene. 2019 | 11.67% | 7.87% | 97.28 | 46.15 | 67.00 |
| 8. | 28 feb. 2019 | 3.78% | 2.97% | 3.89 | 3.60 | 3.74 |
| 9. | 31 mar. 2019 | 3.03% | 1.79% | 1.49 | 0.51 | 0.88 |
| 10. | 30 abr. 2019 | 3.46% | 3.93% | 2.74 | 8.16 | 4.72 |
| 11. | 31 may. 2019 | -8.55% | -6.58% | 107.29 | 58.57 | 79.27 |
| 12. | 30 jun. 2019 | 12.59% | 6.89% | 116.20 | 33.85 | 62.71 |
| 13. | 31 jul. 2019 | -0.75% | 1.31% | 6.57 | 0.06 | -0.61 |
| 14. | 31 ago. 2019 | -7.53% | -1.81% | 87.24 | 8.32 | 26.94 |
| 15. | 30 sept. 2019 | 5.70% | 1.72% | 15.18 | 0.41 | 2.50 |
| 16. | 31 oct. 2019 | -0.55% | 2.04% | 5.54 | 0.94 | -2.28 |
| 17. | 30 nov. 2019 | 3.03% | 3.40% | 1.49 | 5.43 | 2.84 |
| 18. | 31 dic. 2019 | -5.63% | 2.86% | 55.32 | 3.18 | -13.27 |
| 19. | 31 ene. 2020 | -0.55% | -0.16% | 5.55 | 1.53 | 2.92 |
| 20. | 29 feb. 2020 | -5.70% | -8.41% | 56.40 | 89.99 | 71.24 |
| 21. | 31 mar. 2020 | -2.28% | -12.51% | 16.76 | 184.61 | 55.62 |
| 22. | 30 abr. 2020 | 10.10% | 12.68% | 68.69 | 134.77 | 96.22 |
| 23. | 31 may. 2020 | 1.51% | 4.53% | 0.09 | 11.92 | -1.03 |
| 24. | 30 jun. 2020 | 2.79% | 1.84% | 0.96 | 0.58 | 0.75 |
| 25. | 31 jul. 2020 | 0.76% | 5.51% | 1.10 | 19.67 | -4.65 |
| 26. | 31 ago. 2020 | 3.19% | 7.01% | 1.91 | 35.18 | 8.20 |
| 27. | 30 sept. 2020 | 4.33% | -3.92% | 6.38 | 24.98 | -12.62 |
| 28. | 31 oct. 2020 | -5.61% | -2.77% | 55.07 | 14.76 | 28.51 |
| 29. | 30 nov. 2020 | 2.87% | 10.75% | 1.12 | 93.69 | 10.26 |
| 30. | 31 dic. 2020 | 12.08% | 3.71% | 105.40 | 6.95 | 27.07 |
| 31. | 31 ene. 2021 | -6.21% | -1.11% | 64.38 | 4.79 | 17.56 |
| 32. | 28 feb. 2021 | 6.75% | 2.61% | 24.43 | 2.35 | 7.58 |
| 33. | 31 mar. 2021 | 8.77% | 4.24% | 48.51 | 10.04 | 22.07 |
| 34. | 30 abr. 2021 | 8.47% | 5.24% | 44.30 | 17.37 | 27.74 |
| 35. | 31 may. 2021 | 3.89% | 0.55% | 4.34 | 0.28 | -1.10 |
| 36. | 30 jun. 2021 | -1.14% | 2.22% | 8.72 | 1.31 | -3.38 |
| 37. | 31 jul. 2021 | 12.36% | 2.27% | 111.29 | 1.44 | 12.65 |
| 38. | 31 ago. 2021 | 2.28% | 2.90% | 0.23 | 3.33 | 0.87 |
| 39. | 30 sept. 2021 | -2.24% | -4.76% | 16.43 | 34.01 | 23.64 |
| 40. | 31 oct. 2021 | 10.48% | 6.91% | 75.16 | 34.10 | 50.62 |
| 41. | 30 nov. 2021 | -5.42% | -0.83% | 52.26 | 3.64 | 13.80 |
| 42. | 31 dic. 2021 | -3.89% | 4.36% | 32.48 | 10.80 | -18.73 |
| 43. | 31 ene. 2022 | -6.57% | -5.26% | 70.22 | 40.12 | 53.07 |
| 44. | 28 feb. 2022 | -6.39% | -3.14% | 67.31 | 17.74 | 34.55 |
| 45. | 31 mar. 2022 | 8.90% | 3.58% | 50.25 | 6.26 | 17.74 |
| 46. | 30 abr. 2022 | -10.89% | -8.80% | 161.29 | 97.44 | 125.36 |
| 47. | 31 may. 2022 | -2.02% | 0.01% | 14.63 | 1.14 | 4.09 |
| 48. | 30 jun. 2022 | -2.85% | -8.39% | 21.71 | 89.63 | 44.11 |
| 49. | 31 jul. 2022 | 11.86% | 9.11% | 101.12 | 64.58 | 80.81 |
| 50. | 31 ago. 2022 | -4.74% | -4.24% | 42.90 | 28.29 | 34.84 |
| 51. | 30 sept. 2022 | -17.64% | -9.34% | 378.27 | 108.47 | 202.56 |
| 52. | 31 oct. 2022 | 28.36% | 7.99% | 704.99 | 47.76 | 183.50 |
| 53. | 30 nov. 2022 | 6.35% | 5.38% | 20.65 | 18.49 | 19.54 |
| 54. | 31 dic. 2022 | -1.55% | -5.90% | 11.31 | 48.61 | 23.45 |
| 55. | 31 ene. 2023 | 8.61% | 6.18% | 46.29 | 26.01 | 34.70 |
| 56. | 28 feb. 2023 | -1.20% | -2.61% | 9.04 | 13.59 | 11.09 |
| 57. | 31 mar. 2023 | 6.32% | 3.51% | 20.31 | 5.90 | 10.95 |
| 58. | 30 abr. 2023 | 2.37% | 1.46% | 0.31 | 0.15 | 0.22 |
| 59. | 31 may. 2023 | 11.85% | 0.25% | 100.73 | 0.68 | -8.30 |
| 60. | 30 jun. 2023 | 12.41% | 4.71% | 112.43 | 13.24 | 38.58 |
| 61. | 31 jul. 2023 | -1.23% | 4.85% | 9.21 | 14.22 | -11.44 |
| 62. | 31 ago. 2023 | 2.70% | -1.77% | 0.79 | 8.10 | -2.52 |
| 63. | 30 sept. 2023 | -12.02% | -4.87% | 191.23 | 35.37 | 82.24 |
| 64. | 31 oct. 2023 | -2.00% | -2.20% | 14.52 | 10.71 | 12.47 |
| 65. | 30 nov. 2023 | 12.39% | 8.92% | 111.93 | 61.51 | 82.97 |
| 66. | 31 dic. 2023 | -9.28% | 4.42% | 122.89 | 11.21 | -37.11 |
| 67. | 31 ene. 2024 | 6.33% | 1.59% | 20.41 | 0.26 | 2.32 |
| 68. | 29 feb. 2024 | -0.02% | 5.17% | 3.34 | 16.78 | -7.49 |
| 69. | 31 mar. 2024 | 12.47% | 3.10% | 113.72 | 4.11 | 21.61 |
| 70. | 30 abr. 2024 | -9.12% | -4.16% | 119.52 | 27.42 | 57.25 |
| 71. | 31 may. 2024 | 3.02% | 4.80% | 1.48 | 13.89 | 4.53 |
| Total (Σ): | 4,144.31 | 1,923.46 | 1,947.49 | |||
Mostrar todo
VarianzaORCL = Σ(RORCL,t–RORCL)2 ÷ (71 – 1)
= 4,144.31 ÷ (71 – 1)
= 59.20
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,923.46 ÷ (71 – 1)
= 27.48
CovarianzaORCL, S&P 500 = Σ(RORCL,t–RORCL)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,947.49 ÷ (71 – 1)
= 27.82
Estimación sistemática del riesgo (β)
| VarianzaORCL | 59.20 |
| VarianzaS&P 500 | 27.48 |
| CovarianzaORCL, S&P 500 | 27.82 |
| Coeficiente de correlaciónORCL, S&P 5001 | 0.69 |
| βORCL2 | 1.01 |
| αORCL3 | 0.72% |
Cálculos
1 Coeficiente de correlaciónORCL, S&P 500
= CovarianzaORCL, S&P 500 ÷ (Desviación estándarORCL × Desviación estándarS&P 500)
= 27.82 ÷ (7.69% × 5.24%)
= 0.69
2 βORCL
= CovarianzaORCL, S&P 500 ÷ VarianzaS&P 500
= 27.82 ÷ 27.48
= 1.01
3 αORCL
= PromedioORCL – βORCL × PromedioS&P 500
= 1.81% – 1.01 × 1.08%
= 0.72%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.65% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Oracle acciones ordinarias | βORCL | 1.01 |
| Tasa de rendimiento esperada de las acciones ordinarias de Oracle3 | E(RORCL) | 13.90% |
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(RORCL) = RF + βORCL [E(RM) – RF]
= 4.65% + 1.01 [13.79% – 4.65%]
= 13.90%