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 Marathon Oil.
Tasas de retorno
Marathon Oil Corp., tasas mensuales de retorno
| Marathon Oil Corp. (MRO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMRO,t1 | DividendoMRO,t1 | RMRO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $16.75 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $16.00 | $0.05 | -4.18% | 2,363.64 | 3.72% |
| 2. | 31 mar. 2017 | $15.80 | -1.25% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $14.87 | -5.89% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $15.49 | $0.06 | -4.72% | 4,567.00 | -0.83% |
| 59. | 31 dic. 2021 | $16.42 | 6.00% | 4,766.18 | 4.36% | |
| Promedio (R): | 2.04% | 1.36% | ||||
| Desviación estándar: | 20.26% | 4.48% | ||||
| Marathon Oil Corp. (MRO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMRO,t1 | DividendoMRO,t1 | RMRO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $16.75 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $16.00 | $0.05 | -4.18% | 2,363.64 | 3.72% |
| 2. | 31 mar. 2017 | $15.80 | -1.25% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $14.87 | -5.89% | 2,384.20 | 0.91% | |
| 4. | 31 may. 2017 | $13.02 | $0.05 | -12.10% | 2,411.80 | 1.16% |
| 5. | 30 jun. 2017 | $11.85 | -8.99% | 2,423.41 | 0.48% | |
| 6. | 31 jul. 2017 | $12.23 | 3.21% | 2,470.30 | 1.93% | |
| 7. | 31 ago. 2017 | $11.12 | $0.05 | -8.67% | 2,471.65 | 0.05% |
| 8. | 30 sept. 2017 | $13.56 | 21.94% | 2,519.36 | 1.93% | |
| 9. | 31 oct. 2017 | $14.22 | 4.87% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $14.84 | $0.05 | 4.71% | 2,647.58 | 2.81% |
| 11. | 31 dic. 2017 | $16.93 | 14.08% | 2,673.61 | 0.98% | |
| 12. | 31 ene. 2018 | $18.19 | 7.44% | 2,823.81 | 5.62% | |
| 13. | 28 feb. 2018 | $14.52 | $0.05 | -19.90% | 2,713.83 | -3.89% |
| 14. | 31 mar. 2018 | $16.13 | 11.09% | 2,640.87 | -2.69% | |
| 15. | 30 abr. 2018 | $18.25 | 13.14% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $21.43 | $0.05 | 17.70% | 2,705.27 | 2.16% |
| 17. | 30 jun. 2018 | $20.86 | -2.66% | 2,718.37 | 0.48% | |
| 18. | 31 jul. 2018 | $21.12 | 1.25% | 2,816.29 | 3.60% | |
| 19. | 31 ago. 2018 | $21.51 | $0.05 | 2.08% | 2,901.52 | 3.03% |
| 20. | 30 sept. 2018 | $23.28 | 8.23% | 2,913.98 | 0.43% | |
| 21. | 31 oct. 2018 | $18.99 | -18.43% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $16.69 | $0.05 | -11.85% | 2,760.17 | 1.79% |
| 23. | 31 dic. 2018 | $14.34 | -14.08% | 2,506.85 | -9.18% | |
| 24. | 31 ene. 2019 | $15.79 | 10.11% | 2,704.10 | 7.87% | |
| 25. | 28 feb. 2019 | $16.60 | $0.05 | 5.45% | 2,784.49 | 2.97% |
| 26. | 31 mar. 2019 | $16.71 | 0.66% | 2,834.40 | 1.79% | |
| 27. | 30 abr. 2019 | $17.04 | 1.97% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $13.15 | $0.05 | -22.54% | 2,752.06 | -6.58% |
| 29. | 30 jun. 2019 | $14.21 | 8.06% | 2,941.76 | 6.89% | |
| 30. | 31 jul. 2019 | $14.07 | -0.99% | 2,980.38 | 1.31% | |
| 31. | 31 ago. 2019 | $11.84 | $0.05 | -15.49% | 2,926.46 | -1.81% |
| 32. | 30 sept. 2019 | $12.27 | 3.63% | 2,976.74 | 1.72% | |
| 33. | 31 oct. 2019 | $11.53 | -6.03% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $11.65 | $0.05 | 1.47% | 3,140.98 | 3.40% |
| 35. | 31 dic. 2019 | $13.58 | 16.57% | 3,230.78 | 2.86% | |
| 36. | 31 ene. 2020 | $11.37 | -16.27% | 3,225.52 | -0.16% | |
| 37. | 29 feb. 2020 | $8.28 | $0.05 | -26.74% | 2,954.22 | -8.41% |
| 38. | 31 mar. 2020 | $3.29 | -60.27% | 2,584.59 | -12.51% | |
| 39. | 30 abr. 2020 | $6.12 | 86.02% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $5.34 | -12.75% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $6.12 | 14.61% | 3,100.29 | 1.84% | |
| 42. | 31 jul. 2020 | $5.49 | -10.29% | 3,271.12 | 5.51% | |
| 43. | 31 ago. 2020 | $5.28 | -3.83% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $4.09 | -22.54% | 3,363.00 | -3.92% | |
| 45. | 31 oct. 2020 | $3.96 | -3.18% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $5.92 | $0.03 | 50.25% | 3,621.63 | 10.75% |
| 47. | 31 dic. 2020 | $6.67 | 12.67% | 3,756.07 | 3.71% | |
| 48. | 31 ene. 2021 | $7.24 | 8.55% | 3,714.24 | -1.11% | |
| 49. | 28 feb. 2021 | $11.10 | $0.03 | 53.73% | 3,811.15 | 2.61% |
| 50. | 31 mar. 2021 | $10.68 | -3.78% | 3,972.89 | 4.24% | |
| 51. | 30 abr. 2021 | $11.26 | 5.43% | 4,181.17 | 5.24% | |
| 52. | 31 may. 2021 | $12.11 | $0.04 | 7.90% | 4,204.11 | 0.55% |
| 53. | 30 jun. 2021 | $13.62 | 12.47% | 4,297.50 | 2.22% | |
| 54. | 31 jul. 2021 | $11.59 | -14.90% | 4,395.26 | 2.27% | |
| 55. | 31 ago. 2021 | $11.75 | $0.05 | 1.81% | 4,522.68 | 2.90% |
| 56. | 30 sept. 2021 | $13.67 | 16.34% | 4,307.54 | -4.76% | |
| 57. | 31 oct. 2021 | $16.32 | 19.39% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $15.49 | $0.06 | -4.72% | 4,567.00 | -0.83% |
| 59. | 31 dic. 2021 | $16.42 | 6.00% | 4,766.18 | 4.36% | |
| Promedio (R): | 2.04% | 1.36% | ||||
| Desviación estándar: | 20.26% | 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 MRO 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
Marathon Oil Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RMRO,t | RS&P 500,t | (RMRO,t–RMRO)2 | (RS&P 500,t–RS&P 500)2 | (RMRO,t–RMRO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | -4.18% | 3.72% | 38.71 | 5.58 | -14.70 |
| 2. | 31 mar. 2017 | -1.25% | -0.04% | 10.84 | 1.95 | 4.60 |
| 3. | 30 abr. 2017 | -5.89% | 0.91% | 62.87 | 0.20 | 3.56 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -4.72% | -0.83% | 45.71 | 4.80 | 14.82 |
| 59. | 31 dic. 2021 | 6.00% | 4.36% | 15.69 | 9.02 | 11.90 |
| Total (Σ): | 23,800.60 | 1,164.17 | 3,520.83 | |||
| t | Fecha | RMRO,t | RS&P 500,t | (RMRO,t–RMRO)2 | (RS&P 500,t–RS&P 500)2 | (RMRO,t–RMRO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | -4.18% | 3.72% | 38.71 | 5.58 | -14.70 |
| 2. | 31 mar. 2017 | -1.25% | -0.04% | 10.84 | 1.95 | 4.60 |
| 3. | 30 abr. 2017 | -5.89% | 0.91% | 62.87 | 0.20 | 3.56 |
| 4. | 31 may. 2017 | -12.10% | 1.16% | 200.16 | 0.04 | 2.83 |
| 5. | 30 jun. 2017 | -8.99% | 0.48% | 121.64 | 0.77 | 9.67 |
| 6. | 31 jul. 2017 | 3.21% | 1.93% | 1.35 | 0.33 | 0.67 |
| 7. | 31 ago. 2017 | -8.67% | 0.05% | 114.71 | 1.70 | 13.96 |
| 8. | 30 sept. 2017 | 21.94% | 1.93% | 395.99 | 0.33 | 11.39 |
| 9. | 31 oct. 2017 | 4.87% | 2.22% | 7.98 | 0.74 | 2.43 |
| 10. | 30 nov. 2017 | 4.71% | 2.81% | 7.12 | 2.10 | 3.87 |
| 11. | 31 dic. 2017 | 14.08% | 0.98% | 144.97 | 0.14 | -4.51 |
| 12. | 31 ene. 2018 | 7.44% | 5.62% | 29.15 | 18.15 | 23.00 |
| 13. | 28 feb. 2018 | -19.90% | -3.89% | 481.54 | 27.59 | 115.26 |
| 14. | 31 mar. 2018 | 11.09% | -2.69% | 81.81 | 16.37 | -36.60 |
| 15. | 30 abr. 2018 | 13.14% | 0.27% | 123.21 | 1.18 | -12.06 |
| 16. | 31 may. 2018 | 17.70% | 2.16% | 245.10 | 0.64 | 12.57 |
| 17. | 30 jun. 2018 | -2.66% | 0.48% | 22.12 | 0.76 | 4.11 |
| 18. | 31 jul. 2018 | 1.25% | 3.60% | 0.63 | 5.04 | -1.79 |
| 19. | 31 ago. 2018 | 2.08% | 3.03% | 0.00 | 2.78 | 0.07 |
| 20. | 30 sept. 2018 | 8.23% | 0.43% | 38.26 | 0.86 | -5.74 |
| 21. | 31 oct. 2018 | -18.43% | -6.94% | 419.06 | 68.86 | 169.87 |
| 22. | 30 nov. 2018 | -11.85% | 1.79% | 192.97 | 0.18 | -5.95 |
| 23. | 31 dic. 2018 | -14.08% | -9.18% | 259.96 | 111.00 | 169.87 |
| 24. | 31 ene. 2019 | 10.11% | 7.87% | 65.10 | 42.39 | 52.53 |
| 25. | 28 feb. 2019 | 5.45% | 2.97% | 11.58 | 2.61 | 5.50 |
| 26. | 31 mar. 2019 | 0.66% | 1.79% | 1.91 | 0.19 | -0.60 |
| 27. | 30 abr. 2019 | 1.97% | 3.93% | 0.00 | 6.62 | -0.18 |
| 28. | 31 may. 2019 | -22.54% | -6.58% | 604.09 | 62.97 | 195.04 |
| 29. | 30 jun. 2019 | 8.06% | 6.89% | 36.21 | 30.64 | 33.31 |
| 30. | 31 jul. 2019 | -0.99% | 1.31% | 9.17 | 0.00 | 0.14 |
| 31. | 31 ago. 2019 | -15.49% | -1.81% | 307.55 | 10.03 | 55.54 |
| 32. | 30 sept. 2019 | 3.63% | 1.72% | 2.52 | 0.13 | 0.57 |
| 33. | 31 oct. 2019 | -6.03% | 2.04% | 65.19 | 0.47 | -5.53 |
| 34. | 30 nov. 2019 | 1.47% | 3.40% | 0.32 | 4.19 | -1.16 |
| 35. | 31 dic. 2019 | 16.57% | 2.86% | 210.93 | 2.25 | 21.80 |
| 36. | 31 ene. 2020 | -16.27% | -0.16% | 335.51 | 2.31 | 27.85 |
| 37. | 29 feb. 2020 | -26.74% | -8.41% | 828.29 | 95.43 | 281.15 |
| 38. | 31 mar. 2020 | -60.27% | -12.51% | 3,882.38 | 192.37 | 864.21 |
| 39. | 30 abr. 2020 | 86.02% | 12.68% | 7,051.84 | 128.29 | 951.15 |
| 40. | 31 may. 2020 | -12.75% | 4.53% | 218.69 | 10.05 | -46.88 |
| 41. | 30 jun. 2020 | 14.61% | 1.84% | 157.85 | 0.23 | 6.04 |
| 42. | 31 jul. 2020 | -10.29% | 5.51% | 152.21 | 17.24 | -51.23 |
| 43. | 31 ago. 2020 | -3.83% | 7.01% | 34.44 | 31.91 | -33.15 |
| 44. | 30 sept. 2020 | -22.54% | -3.92% | 604.22 | 27.89 | 129.80 |
| 45. | 31 oct. 2020 | -3.18% | -2.77% | 27.26 | 17.01 | 21.54 |
| 46. | 30 nov. 2020 | 50.25% | 10.75% | 2,324.16 | 88.30 | 453.01 |
| 47. | 31 dic. 2020 | 12.67% | 3.71% | 112.91 | 5.54 | 25.02 |
| 48. | 31 ene. 2021 | 8.55% | -1.11% | 42.29 | 6.11 | -16.07 |
| 49. | 28 feb. 2021 | 53.73% | 2.61% | 2,671.47 | 1.57 | 64.67 |
| 50. | 31 mar. 2021 | -3.78% | 4.24% | 33.95 | 8.33 | -16.82 |
| 51. | 30 abr. 2021 | 5.43% | 5.24% | 11.48 | 15.09 | 13.16 |
| 52. | 31 may. 2021 | 7.90% | 0.55% | 34.35 | 0.65 | -4.74 |
| 53. | 30 jun. 2021 | 12.47% | 2.22% | 108.70 | 0.75 | 9.00 |
| 54. | 31 jul. 2021 | -14.90% | 2.27% | 287.22 | 0.84 | -15.54 |
| 55. | 31 ago. 2021 | 1.81% | 2.90% | 0.05 | 2.38 | -0.36 |
| 56. | 30 sept. 2021 | 16.34% | -4.76% | 204.42 | 37.39 | -87.43 |
| 57. | 31 oct. 2021 | 19.39% | 6.91% | 300.76 | 30.87 | 96.36 |
| 58. | 30 nov. 2021 | -4.72% | -0.83% | 45.71 | 4.80 | 14.82 |
| 59. | 31 dic. 2021 | 6.00% | 4.36% | 15.69 | 9.02 | 11.90 |
| Total (Σ): | 23,800.60 | 1,164.17 | 3,520.83 | |||
Mostrar todo
VarianzaMRO = Σ(RMRO,t–RMRO)2 ÷ (59 – 1)
= 23,800.60 ÷ (59 – 1)
= 410.36
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaMRO, S&P 500 = Σ(RMRO,t–RMRO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,520.83 ÷ (59 – 1)
= 60.70
Estimación sistemática del riesgo (β)
| VarianzaMRO | 410.36 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaMRO, S&P 500 | 60.70 |
| Coeficiente de correlaciónMRO, S&P 5001 | 0.67 |
| βMRO2 | 3.02 |
| αMRO3 | -2.06% |
Cálculos
1 Coeficiente de correlaciónMRO, S&P 500
= CovarianzaMRO, S&P 500 ÷ (Desviación estándarMRO × Desviación estándarS&P 500)
= 60.70 ÷ (20.26% × 4.48%)
= 0.67
2 βMRO
= CovarianzaMRO, S&P 500 ÷ VarianzaS&P 500
= 60.70 ÷ 20.07
= 3.02
3 αMRO
= PromedioMRO – βMRO × PromedioS&P 500
= 2.04% – 3.02 × 1.36%
= -2.06%
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 Marathon Oil acciones ordinarias | βMRO | 3.02 |
| Tasa de rendimiento esperada de las acciones ordinarias de Marathon Oil3 | E(RMRO) | 32.24% |
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(RMRO) = RF + βMRO [E(RM) – RF]
= 4.67% + 3.02 [13.79% – 4.67%]
= 32.24%