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 Twenty-First Century Fox.
Tasas de retorno
Twenty-First Century Fox Inc., tasas mensuales de retorno
| Twenty-First Century Fox Inc. (FOX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioFOX,t1 | DividendoFOX,t1 | RFOX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 jul. 2012 | $23.02 | 1,379.32 | ||||
| 1. | 31 ago. 2012 | $23.39 | 1.61% | 1,406.58 | 1.98% | |
| 2. | 30 sept. 2012 | $24.51 | $0.085 | 5.15% | 1,440.67 | 2.42% |
| 3. | 31 oct. 2012 | $23.93 | -2.37% | 1,412.16 | -1.98% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 may. 2018 | $38.55 | 5.44% | 2,705.27 | 2.16% | |
| 71. | 30 jun. 2018 | $49.69 | 28.90% | 2,718.37 | 0.48% | |
| Promedio (R): | 1.45% | 1.00% | ||||
| Desviación estándar: | 7.59% | 2.71% | ||||
| Twenty-First Century Fox Inc. (FOX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioFOX,t1 | DividendoFOX,t1 | RFOX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 jul. 2012 | $23.02 | 1,379.32 | ||||
| 1. | 31 ago. 2012 | $23.39 | 1.61% | 1,406.58 | 1.98% | |
| 2. | 30 sept. 2012 | $24.51 | $0.085 | 5.15% | 1,440.67 | 2.42% |
| 3. | 31 oct. 2012 | $23.93 | -2.37% | 1,412.16 | -1.98% | |
| 4. | 30 nov. 2012 | $24.64 | 2.97% | 1,416.18 | 0.28% | |
| 5. | 31 dic. 2012 | $25.51 | 3.53% | 1,426.19 | 0.71% | |
| 6. | 31 ene. 2013 | $27.74 | 8.74% | 1,498.11 | 5.04% | |
| 7. | 28 feb. 2013 | $28.81 | 3.86% | 1,514.68 | 1.11% | |
| 8. | 31 mar. 2013 | $30.51 | $0.085 | 6.20% | 1,569.19 | 3.60% |
| 9. | 30 abr. 2013 | $30.97 | 1.51% | 1,597.57 | 1.81% | |
| 10. | 31 may. 2013 | $32.11 | 3.68% | 1,630.74 | 2.08% | |
| 11. | 30 jun. 2013 | $32.58 | 1.46% | 1,606.28 | -1.50% | |
| 12. | 31 jul. 2013 | $29.88 | -8.29% | 1,685.73 | 4.95% | |
| 13. | 31 ago. 2013 | $31.33 | 4.85% | 1,632.97 | -3.13% | |
| 14. | 30 sept. 2013 | $33.51 | $0.125 | 7.36% | 1,681.55 | 2.97% |
| 15. | 31 oct. 2013 | $34.08 | 1.70% | 1,756.54 | 4.46% | |
| 16. | 30 nov. 2013 | $33.49 | -1.73% | 1,805.81 | 2.80% | |
| 17. | 31 dic. 2013 | $35.17 | 5.02% | 1,848.36 | 2.36% | |
| 18. | 31 ene. 2014 | $31.82 | -9.53% | 1,782.59 | -3.56% | |
| 19. | 28 feb. 2014 | $33.54 | 5.41% | 1,859.45 | 4.31% | |
| 20. | 31 mar. 2014 | $31.97 | $0.125 | -4.31% | 1,872.34 | 0.69% |
| 21. | 30 abr. 2014 | $32.02 | 0.16% | 1,883.95 | 0.62% | |
| 22. | 31 may. 2014 | $35.41 | 10.59% | 1,923.57 | 2.10% | |
| 23. | 30 jun. 2014 | $35.15 | -0.73% | 1,960.23 | 1.91% | |
| 24. | 31 jul. 2014 | $31.67 | -9.90% | 1,930.67 | -1.51% | |
| 25. | 31 ago. 2014 | $35.42 | 11.84% | 2,003.37 | 3.77% | |
| 26. | 30 sept. 2014 | $34.29 | $0.125 | -2.84% | 1,972.29 | -1.55% |
| 27. | 31 oct. 2014 | $34.48 | 0.55% | 2,018.05 | 2.32% | |
| 28. | 30 nov. 2014 | $36.80 | 6.73% | 2,067.56 | 2.45% | |
| 29. | 31 dic. 2014 | $38.41 | 4.38% | 2,058.90 | -0.42% | |
| 30. | 31 ene. 2015 | $33.16 | -13.67% | 1,994.99 | -3.10% | |
| 31. | 28 feb. 2015 | $35.00 | 5.55% | 2,104.50 | 5.49% | |
| 32. | 31 mar. 2015 | $33.84 | $0.15 | -2.89% | 2,067.89 | -1.74% |
| 33. | 30 abr. 2015 | $34.08 | 0.71% | 2,085.51 | 0.85% | |
| 34. | 31 may. 2015 | $33.60 | -1.41% | 2,107.39 | 1.05% | |
| 35. | 30 jun. 2015 | $32.55 | -3.13% | 2,063.11 | -2.10% | |
| 36. | 31 jul. 2015 | $34.49 | 5.96% | 2,103.84 | 1.97% | |
| 37. | 31 ago. 2015 | $27.39 | -20.59% | 1,972.18 | -6.26% | |
| 38. | 30 sept. 2015 | $26.98 | $0.15 | -0.95% | 1,920.03 | -2.64% |
| 39. | 31 oct. 2015 | $30.69 | 13.75% | 2,079.36 | 8.30% | |
| 40. | 30 nov. 2015 | $29.51 | -3.84% | 2,080.41 | 0.05% | |
| 41. | 31 dic. 2015 | $27.16 | -7.96% | 2,043.94 | -1.75% | |
| 42. | 31 ene. 2016 | $26.97 | -0.70% | 1,940.24 | -5.07% | |
| 43. | 29 feb. 2016 | $27.02 | 0.19% | 1,932.23 | -0.41% | |
| 44. | 31 mar. 2016 | $27.88 | $0.15 | 3.74% | 2,059.74 | 6.60% |
| 45. | 30 abr. 2016 | $30.26 | 8.54% | 2,065.30 | 0.27% | |
| 46. | 31 may. 2016 | $28.88 | -4.56% | 2,096.95 | 1.53% | |
| 47. | 30 jun. 2016 | $27.05 | -6.34% | 2,098.86 | 0.09% | |
| 48. | 31 jul. 2016 | $26.64 | -1.52% | 2,173.60 | 3.56% | |
| 49. | 31 ago. 2016 | $24.54 | -7.88% | 2,170.95 | -0.12% | |
| 50. | 30 sept. 2016 | $24.22 | $0.18 | -0.57% | 2,168.27 | -0.12% |
| 51. | 31 oct. 2016 | $26.27 | 8.46% | 2,126.15 | -1.94% | |
| 52. | 30 nov. 2016 | $28.11 | 7.00% | 2,198.81 | 3.42% | |
| 53. | 31 dic. 2016 | $28.04 | -0.25% | 2,238.83 | 1.82% | |
| 54. | 31 ene. 2017 | $31.38 | 11.91% | 2,278.87 | 1.79% | |
| 55. | 28 feb. 2017 | $29.92 | -4.65% | 2,363.64 | 3.72% | |
| 56. | 31 mar. 2017 | $32.39 | $0.18 | 8.86% | 2,362.72 | -0.04% |
| 57. | 30 abr. 2017 | $30.54 | -5.71% | 2,384.20 | 0.91% | |
| 58. | 31 may. 2017 | $27.12 | -11.20% | 2,411.80 | 1.16% | |
| 59. | 30 jun. 2017 | $28.34 | 4.50% | 2,423.41 | 0.48% | |
| 60. | 31 jul. 2017 | $29.10 | 2.68% | 2,470.30 | 1.93% | |
| 61. | 31 ago. 2017 | $27.59 | -5.19% | 2,471.65 | 0.05% | |
| 62. | 30 sept. 2017 | $26.38 | $0.18 | -3.73% | 2,519.36 | 1.93% |
| 63. | 31 oct. 2017 | $26.15 | -0.87% | 2,575.26 | 2.22% | |
| 64. | 30 nov. 2017 | $31.94 | 22.14% | 2,647.58 | 2.81% | |
| 65. | 31 dic. 2017 | $34.53 | 8.11% | 2,673.61 | 0.98% | |
| 66. | 31 ene. 2018 | $36.90 | 6.86% | 2,823.81 | 5.62% | |
| 67. | 28 feb. 2018 | $36.82 | -0.22% | 2,713.83 | -3.89% | |
| 68. | 31 mar. 2018 | $36.69 | $0.18 | 0.14% | 2,640.87 | -2.69% |
| 69. | 30 abr. 2018 | $36.56 | -0.35% | 2,648.05 | 0.27% | |
| 70. | 31 may. 2018 | $38.55 | 5.44% | 2,705.27 | 2.16% | |
| 71. | 30 jun. 2018 | $49.69 | 28.90% | 2,718.37 | 0.48% | |
| Promedio (R): | 1.45% | 1.00% | ||||
| Desviación estándar: | 7.59% | 2.71% | ||||
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 FOX 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
Twenty-First Century Fox Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RFOX,t | RS&P 500,t | (RFOX,t–RFOX)2 | (RS&P 500,t–RS&P 500)2 | (RFOX,t–RFOX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ago. 2012 | 1.61% | 1.98% | 0.03 | 0.96 | 0.16 |
| 2. | 30 sept. 2012 | 5.15% | 2.42% | 13.71 | 2.04 | 5.29 |
| 3. | 31 oct. 2012 | -2.37% | -1.98% | 14.55 | 8.85 | 11.35 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 may. 2018 | 5.44% | 2.16% | 15.96 | 1.36 | 4.65 |
| 71. | 30 jun. 2018 | 28.90% | 0.48% | 753.44 | 0.26 | -14.05 |
| Total (Σ): | 4,030.79 | 514.30 | 633.77 | |||
| t | Fecha | RFOX,t | RS&P 500,t | (RFOX,t–RFOX)2 | (RS&P 500,t–RS&P 500)2 | (RFOX,t–RFOX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ago. 2012 | 1.61% | 1.98% | 0.03 | 0.96 | 0.16 |
| 2. | 30 sept. 2012 | 5.15% | 2.42% | 13.71 | 2.04 | 5.29 |
| 3. | 31 oct. 2012 | -2.37% | -1.98% | 14.55 | 8.85 | 11.35 |
| 4. | 30 nov. 2012 | 2.97% | 0.28% | 2.31 | 0.51 | -1.08 |
| 5. | 31 dic. 2012 | 3.53% | 0.71% | 4.34 | 0.08 | -0.60 |
| 6. | 31 ene. 2013 | 8.74% | 5.04% | 53.19 | 16.38 | 29.51 |
| 7. | 28 feb. 2013 | 3.86% | 1.11% | 5.80 | 0.01 | 0.26 |
| 8. | 31 mar. 2013 | 6.20% | 3.60% | 22.54 | 6.77 | 12.36 |
| 9. | 30 abr. 2013 | 1.51% | 1.81% | 0.00 | 0.66 | 0.05 |
| 10. | 31 may. 2013 | 3.68% | 2.08% | 4.98 | 1.17 | 2.41 |
| 11. | 30 jun. 2013 | 1.46% | -1.50% | 0.00 | 6.23 | -0.04 |
| 12. | 31 jul. 2013 | -8.29% | 4.95% | 94.79 | 15.60 | -38.46 |
| 13. | 31 ago. 2013 | 4.85% | -3.13% | 11.59 | 17.02 | -14.05 |
| 14. | 30 sept. 2013 | 7.36% | 2.97% | 34.91 | 3.92 | 11.69 |
| 15. | 31 oct. 2013 | 1.70% | 4.46% | 0.06 | 12.00 | 0.87 |
| 16. | 30 nov. 2013 | -1.73% | 2.80% | 10.11 | 3.27 | -5.75 |
| 17. | 31 dic. 2013 | 5.02% | 2.36% | 12.73 | 1.85 | 4.85 |
| 18. | 31 ene. 2014 | -9.53% | -3.56% | 120.42 | 20.74 | 49.98 |
| 19. | 28 feb. 2014 | 5.41% | 4.31% | 15.66 | 10.99 | 13.12 |
| 20. | 31 mar. 2014 | -4.31% | 0.69% | 33.14 | 0.09 | 1.74 |
| 21. | 30 abr. 2014 | 0.16% | 0.62% | 1.67 | 0.14 | 0.49 |
| 22. | 31 may. 2014 | 10.59% | 2.10% | 83.51 | 1.23 | 10.12 |
| 23. | 30 jun. 2014 | -0.73% | 1.91% | 4.76 | 0.83 | -1.99 |
| 24. | 31 jul. 2014 | -9.90% | -1.51% | 128.80 | 6.27 | 28.42 |
| 25. | 31 ago. 2014 | 11.84% | 3.77% | 108.00 | 7.67 | 28.78 |
| 26. | 30 sept. 2014 | -2.84% | -1.55% | 18.37 | 6.49 | 10.92 |
| 27. | 31 oct. 2014 | 0.55% | 2.32% | 0.80 | 1.75 | -1.18 |
| 28. | 30 nov. 2014 | 6.73% | 2.45% | 27.88 | 2.12 | 7.69 |
| 29. | 31 dic. 2014 | 4.38% | -0.42% | 8.56 | 2.00 | -4.14 |
| 30. | 31 ene. 2015 | -13.67% | -3.10% | 228.52 | 16.81 | 61.98 |
| 31. | 28 feb. 2015 | 5.55% | 5.49% | 16.81 | 20.19 | 18.42 |
| 32. | 31 mar. 2015 | -2.89% | -1.74% | 18.79 | 7.48 | 11.86 |
| 33. | 30 abr. 2015 | 0.71% | 0.85% | 0.55 | 0.02 | 0.11 |
| 34. | 31 may. 2015 | -1.41% | 1.05% | 8.16 | 0.00 | -0.15 |
| 35. | 30 jun. 2015 | -3.13% | -2.10% | 20.92 | 9.59 | 14.17 |
| 36. | 31 jul. 2015 | 5.96% | 1.97% | 20.35 | 0.96 | 4.41 |
| 37. | 31 ago. 2015 | -20.59% | -6.26% | 485.51 | 52.62 | 159.84 |
| 38. | 30 sept. 2015 | -0.95% | -2.64% | 5.75 | 13.25 | 8.73 |
| 39. | 31 oct. 2015 | 13.75% | 8.30% | 151.35 | 53.32 | 89.83 |
| 40. | 30 nov. 2015 | -3.84% | 0.05% | 28.02 | 0.89 | 5.01 |
| 41. | 31 dic. 2015 | -7.96% | -1.75% | 88.59 | 7.56 | 25.87 |
| 42. | 31 ene. 2016 | -0.70% | -5.07% | 4.61 | 36.84 | 13.04 |
| 43. | 29 feb. 2016 | 0.19% | -0.41% | 1.60 | 1.99 | 1.78 |
| 44. | 31 mar. 2016 | 3.74% | 6.60% | 5.24 | 31.39 | 12.83 |
| 45. | 30 abr. 2016 | 8.54% | 0.27% | 50.24 | 0.53 | -5.15 |
| 46. | 31 may. 2016 | -4.56% | 1.53% | 36.11 | 0.29 | -3.22 |
| 47. | 30 jun. 2016 | -6.34% | 0.09% | 60.61 | 0.82 | 7.05 |
| 48. | 31 jul. 2016 | -1.52% | 3.56% | 8.79 | 6.58 | -7.60 |
| 49. | 31 ago. 2016 | -7.88% | -0.12% | 87.08 | 1.25 | 10.43 |
| 50. | 30 sept. 2016 | -0.57% | -0.12% | 4.08 | 1.25 | 2.26 |
| 51. | 31 oct. 2016 | 8.46% | -1.94% | 49.22 | 8.64 | -20.62 |
| 52. | 30 nov. 2016 | 7.00% | 3.42% | 30.86 | 5.86 | 13.45 |
| 53. | 31 dic. 2016 | -0.25% | 1.82% | 2.88 | 0.68 | -1.40 |
| 54. | 31 ene. 2017 | 11.91% | 1.79% | 109.47 | 0.63 | 8.29 |
| 55. | 28 feb. 2017 | -4.65% | 3.72% | 37.23 | 7.42 | -16.62 |
| 56. | 31 mar. 2017 | 8.86% | -0.04% | 54.88 | 1.07 | -7.67 |
| 57. | 30 abr. 2017 | -5.71% | 0.91% | 51.27 | 0.01 | 0.62 |
| 58. | 31 may. 2017 | -11.20% | 1.16% | 159.95 | 0.03 | -2.04 |
| 59. | 30 jun. 2017 | 4.50% | 0.48% | 9.30 | 0.26 | -1.57 |
| 60. | 31 jul. 2017 | 2.68% | 1.93% | 1.52 | 0.88 | 1.16 |
| 61. | 31 ago. 2017 | -5.19% | 0.05% | 44.06 | 0.89 | 6.25 |
| 62. | 30 sept. 2017 | -3.73% | 1.93% | 26.85 | 0.87 | -4.84 |
| 63. | 31 oct. 2017 | -0.87% | 2.22% | 5.38 | 1.50 | -2.84 |
| 64. | 30 nov. 2017 | 22.14% | 2.81% | 428.20 | 3.28 | 37.50 |
| 65. | 31 dic. 2017 | 8.11% | 0.98% | 44.36 | 0.00 | -0.09 |
| 66. | 31 ene. 2018 | 6.86% | 5.62% | 29.32 | 21.36 | 25.03 |
| 67. | 28 feb. 2018 | -0.22% | -3.89% | 2.77 | 23.92 | 8.15 |
| 68. | 31 mar. 2018 | 0.14% | -2.69% | 1.72 | 13.58 | 4.84 |
| 69. | 30 abr. 2018 | -0.35% | 0.27% | 3.25 | 0.52 | 1.31 |
| 70. | 31 may. 2018 | 5.44% | 2.16% | 15.96 | 1.36 | 4.65 |
| 71. | 30 jun. 2018 | 28.90% | 0.48% | 753.44 | 0.26 | -14.05 |
| Total (Σ): | 4,030.79 | 514.30 | 633.77 | |||
Mostrar todo
VarianzaFOX = Σ(RFOX,t–RFOX)2 ÷ (71 – 1)
= 4,030.79 ÷ (71 – 1)
= 57.58
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 514.30 ÷ (71 – 1)
= 7.35
CovarianzaFOX, S&P 500 = Σ(RFOX,t–RFOX)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 633.77 ÷ (71 – 1)
= 9.05
Estimación sistemática del riesgo (β)
| VarianzaFOX | 57.58 |
| VarianzaS&P 500 | 7.35 |
| CovarianzaFOX, S&P 500 | 9.05 |
| Coeficiente de correlaciónFOX, S&P 5001 | 0.44 |
| βFOX2 | 1.23 |
| αFOX3 | 0.22% |
Cálculos
1 Coeficiente de correlaciónFOX, S&P 500
= CovarianzaFOX, S&P 500 ÷ (Desviación estándarFOX × Desviación estándarS&P 500)
= 9.05 ÷ (7.59% × 2.71%)
= 0.44
2 βFOX
= CovarianzaFOX, S&P 500 ÷ VarianzaS&P 500
= 9.05 ÷ 7.35
= 1.23
3 αFOX
= PromedioFOX – βFOX × PromedioS&P 500
= 1.45% – 1.23 × 1.00%
= 0.22%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.79% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.53% |
| Riesgo sistemático de Twenty-First Century Fox acciones ordinarias | βFOX | 1.23 |
| Tasa de rendimiento esperada de las acciones ordinarias de Twenty-First Century Fox3 | E(RFOX) | 15.56% |
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(RFOX) = RF + βFOX [E(RM) – RF]
= 4.79% + 1.23 [13.53% – 4.79%]
= 15.56%