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 Emerson.
Tasas de retorno
Emerson Electric Co., tasas mensuales de retorno
| Emerson Electric Co. (EMR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEMR,t1 | DividendoEMR,t1 | REMR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 oct. 2013 | $66.97 | 1,756.54 | ||||
| 1. | 30 nov. 2013 | $66.99 | $0.43 | 0.67% | 1,805.81 | 2.80% |
| 2. | 31 dic. 2013 | $70.18 | 4.76% | 1,848.36 | 2.36% | |
| 3. | 31 ene. 2014 | $65.94 | -6.04% | 1,782.59 | -3.56% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 ago. 2019 | $59.59 | $0.49 | -7.40% | 2,926.46 | -1.81% |
| 71. | 30 sept. 2019 | $66.86 | 12.20% | 2,976.74 | 1.72% | |
| Promedio (R): | 0.42% | 0.80% | ||||
| Desviación estándar: | 5.69% | 3.29% | ||||
| Emerson Electric Co. (EMR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEMR,t1 | DividendoEMR,t1 | REMR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 oct. 2013 | $66.97 | 1,756.54 | ||||
| 1. | 30 nov. 2013 | $66.99 | $0.43 | 0.67% | 1,805.81 | 2.80% |
| 2. | 31 dic. 2013 | $70.18 | 4.76% | 1,848.36 | 2.36% | |
| 3. | 31 ene. 2014 | $65.94 | -6.04% | 1,782.59 | -3.56% | |
| 4. | 28 feb. 2014 | $65.26 | $0.43 | -0.38% | 1,859.45 | 4.31% |
| 5. | 31 mar. 2014 | $66.80 | 2.36% | 1,872.34 | 0.69% | |
| 6. | 30 abr. 2014 | $68.18 | 2.07% | 1,883.95 | 0.62% | |
| 7. | 31 may. 2014 | $66.73 | $0.43 | -1.50% | 1,923.57 | 2.10% |
| 8. | 30 jun. 2014 | $66.36 | -0.55% | 1,960.23 | 1.91% | |
| 9. | 31 jul. 2014 | $63.65 | -4.08% | 1,930.67 | -1.51% | |
| 10. | 31 ago. 2014 | $64.02 | $0.43 | 1.26% | 2,003.37 | 3.77% |
| 11. | 30 sept. 2014 | $62.58 | -2.25% | 1,972.29 | -1.55% | |
| 12. | 31 oct. 2014 | $64.06 | 2.36% | 2,018.05 | 2.32% | |
| 13. | 30 nov. 2014 | $63.75 | $0.47 | 0.25% | 2,067.56 | 2.45% |
| 14. | 31 dic. 2014 | $61.73 | -3.17% | 2,058.90 | -0.42% | |
| 15. | 31 ene. 2015 | $56.94 | -7.76% | 1,994.99 | -3.10% | |
| 16. | 28 feb. 2015 | $57.92 | $0.47 | 2.55% | 2,104.50 | 5.49% |
| 17. | 31 mar. 2015 | $56.62 | -2.24% | 2,067.89 | -1.74% | |
| 18. | 30 abr. 2015 | $58.83 | 3.90% | 2,085.51 | 0.85% | |
| 19. | 31 may. 2015 | $60.31 | $0.47 | 3.31% | 2,107.39 | 1.05% |
| 20. | 30 jun. 2015 | $55.43 | -8.09% | 2,063.11 | -2.10% | |
| 21. | 31 jul. 2015 | $51.75 | -6.64% | 2,103.84 | 1.97% | |
| 22. | 31 ago. 2015 | $47.72 | $0.47 | -6.88% | 1,972.18 | -6.26% |
| 23. | 30 sept. 2015 | $44.17 | -7.44% | 1,920.03 | -2.64% | |
| 24. | 31 oct. 2015 | $47.23 | 6.93% | 2,079.36 | 8.30% | |
| 25. | 30 nov. 2015 | $50.00 | $0.475 | 6.87% | 2,080.41 | 0.05% |
| 26. | 31 dic. 2015 | $47.83 | -4.34% | 2,043.94 | -1.75% | |
| 27. | 31 ene. 2016 | $45.98 | -3.87% | 1,940.24 | -5.07% | |
| 28. | 29 feb. 2016 | $48.83 | $0.475 | 7.23% | 1,932.23 | -0.41% |
| 29. | 31 mar. 2016 | $54.38 | 11.37% | 2,059.74 | 6.60% | |
| 30. | 30 abr. 2016 | $54.63 | 0.46% | 2,065.30 | 0.27% | |
| 31. | 31 may. 2016 | $52.02 | $0.475 | -3.91% | 2,096.95 | 1.53% |
| 32. | 30 jun. 2016 | $52.16 | 0.27% | 2,098.86 | 0.09% | |
| 33. | 31 jul. 2016 | $55.90 | 7.17% | 2,173.60 | 3.56% | |
| 34. | 31 ago. 2016 | $52.68 | $0.475 | -4.91% | 2,170.95 | -0.12% |
| 35. | 30 sept. 2016 | $54.51 | 3.47% | 2,168.27 | -0.12% | |
| 36. | 31 oct. 2016 | $50.68 | -7.03% | 2,126.15 | -1.94% | |
| 37. | 30 nov. 2016 | $56.44 | $0.48 | 12.31% | 2,198.81 | 3.42% |
| 38. | 31 dic. 2016 | $55.75 | -1.22% | 2,238.83 | 1.82% | |
| 39. | 31 ene. 2017 | $58.66 | 5.22% | 2,278.87 | 1.79% | |
| 40. | 28 feb. 2017 | $60.10 | $0.48 | 3.27% | 2,363.64 | 3.72% |
| 41. | 31 mar. 2017 | $59.86 | -0.40% | 2,362.72 | -0.04% | |
| 42. | 30 abr. 2017 | $60.28 | 0.70% | 2,384.20 | 0.91% | |
| 43. | 31 may. 2017 | $59.12 | $0.48 | -1.13% | 2,411.80 | 1.16% |
| 44. | 30 jun. 2017 | $59.62 | 0.85% | 2,423.41 | 0.48% | |
| 45. | 31 jul. 2017 | $59.61 | -0.02% | 2,470.30 | 1.93% | |
| 46. | 31 ago. 2017 | $59.04 | $0.48 | -0.15% | 2,471.65 | 0.05% |
| 47. | 30 sept. 2017 | $62.84 | 6.44% | 2,519.36 | 1.93% | |
| 48. | 31 oct. 2017 | $64.46 | 2.58% | 2,575.26 | 2.22% | |
| 49. | 30 nov. 2017 | $64.82 | $0.485 | 1.31% | 2,647.58 | 2.81% |
| 50. | 31 dic. 2017 | $69.69 | 7.51% | 2,673.61 | 0.98% | |
| 51. | 31 ene. 2018 | $72.23 | 3.64% | 2,823.81 | 5.62% | |
| 52. | 28 feb. 2018 | $71.06 | $0.485 | -0.95% | 2,713.83 | -3.89% |
| 53. | 31 mar. 2018 | $68.30 | -3.88% | 2,640.87 | -2.69% | |
| 54. | 30 abr. 2018 | $66.41 | -2.77% | 2,648.05 | 0.27% | |
| 55. | 31 may. 2018 | $70.84 | $0.485 | 7.40% | 2,705.27 | 2.16% |
| 56. | 30 jun. 2018 | $69.14 | -2.40% | 2,718.37 | 0.48% | |
| 57. | 31 jul. 2018 | $72.28 | 4.54% | 2,816.29 | 3.60% | |
| 58. | 31 ago. 2018 | $76.73 | $0.485 | 6.83% | 2,901.52 | 3.03% |
| 59. | 30 sept. 2018 | $76.58 | -0.20% | 2,913.98 | 0.43% | |
| 60. | 31 oct. 2018 | $67.88 | -11.36% | 2,711.74 | -6.94% | |
| 61. | 30 nov. 2018 | $67.52 | $0.49 | 0.19% | 2,760.17 | 1.79% |
| 62. | 31 dic. 2018 | $59.75 | -11.51% | 2,506.85 | -9.18% | |
| 63. | 31 ene. 2019 | $65.47 | 9.57% | 2,704.10 | 7.87% | |
| 64. | 28 feb. 2019 | $68.15 | $0.49 | 4.84% | 2,784.49 | 2.97% |
| 65. | 31 mar. 2019 | $68.47 | 0.47% | 2,834.40 | 1.79% | |
| 66. | 30 abr. 2019 | $70.99 | 3.68% | 2,945.83 | 3.93% | |
| 67. | 31 may. 2019 | $60.24 | $0.49 | -14.45% | 2,752.06 | -6.58% |
| 68. | 30 jun. 2019 | $66.72 | 10.76% | 2,941.76 | 6.89% | |
| 69. | 31 jul. 2019 | $64.88 | -2.76% | 2,980.38 | 1.31% | |
| 70. | 31 ago. 2019 | $59.59 | $0.49 | -7.40% | 2,926.46 | -1.81% |
| 71. | 30 sept. 2019 | $66.86 | 12.20% | 2,976.74 | 1.72% | |
| Promedio (R): | 0.42% | 0.80% | ||||
| Desviación estándar: | 5.69% | 3.29% | ||||
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 EMR 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
Emerson Electric Co., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | REMR,t | RS&P 500,t | (REMR,t–REMR)2 | (RS&P 500,t–RS&P 500)2 | (REMR,t–REMR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 nov. 2013 | 0.67% | 2.80% | 0.06 | 4.02 | 0.50 |
| 2. | 31 dic. 2013 | 4.76% | 2.36% | 18.84 | 2.42 | 6.76 |
| 3. | 31 ene. 2014 | -6.04% | -3.56% | 41.77 | 18.99 | 28.16 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 ago. 2019 | -7.40% | -1.81% | 61.15 | 6.80 | 20.40 |
| 71. | 30 sept. 2019 | 12.20% | 1.72% | 138.74 | 0.84 | 10.82 |
| Total (Σ): | 2,262.58 | 758.73 | 1,001.26 | |||
| t | Fecha | REMR,t | RS&P 500,t | (REMR,t–REMR)2 | (RS&P 500,t–RS&P 500)2 | (REMR,t–REMR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 nov. 2013 | 0.67% | 2.80% | 0.06 | 4.02 | 0.50 |
| 2. | 31 dic. 2013 | 4.76% | 2.36% | 18.84 | 2.42 | 6.76 |
| 3. | 31 ene. 2014 | -6.04% | -3.56% | 41.77 | 18.99 | 28.16 |
| 4. | 28 feb. 2014 | -0.38% | 4.31% | 0.64 | 12.34 | -2.81 |
| 5. | 31 mar. 2014 | 2.36% | 0.69% | 3.76 | 0.01 | -0.21 |
| 6. | 30 abr. 2014 | 2.07% | 0.62% | 2.70 | 0.03 | -0.29 |
| 7. | 31 may. 2014 | -1.50% | 2.10% | 3.68 | 1.70 | -2.50 |
| 8. | 30 jun. 2014 | -0.55% | 1.91% | 0.95 | 1.22 | -1.08 |
| 9. | 31 jul. 2014 | -4.08% | -1.51% | 20.30 | 5.32 | 10.39 |
| 10. | 31 ago. 2014 | 1.26% | 3.77% | 0.70 | 8.80 | 2.48 |
| 11. | 30 sept. 2014 | -2.25% | -1.55% | 7.13 | 5.53 | 6.28 |
| 12. | 31 oct. 2014 | 2.36% | 2.32% | 3.78 | 2.31 | 2.96 |
| 13. | 30 nov. 2014 | 0.25% | 2.45% | 0.03 | 2.74 | -0.28 |
| 14. | 31 dic. 2014 | -3.17% | -0.42% | 12.89 | 1.48 | 4.37 |
| 15. | 31 ene. 2015 | -7.76% | -3.10% | 66.93 | 15.24 | 31.93 |
| 16. | 28 feb. 2015 | 2.55% | 5.49% | 4.52 | 22.00 | 9.97 |
| 17. | 31 mar. 2015 | -2.24% | -1.74% | 7.11 | 6.45 | 6.77 |
| 18. | 30 abr. 2015 | 3.90% | 0.85% | 12.12 | 0.00 | 0.18 |
| 19. | 31 may. 2015 | 3.31% | 1.05% | 8.37 | 0.06 | 0.72 |
| 20. | 30 jun. 2015 | -8.09% | -2.10% | 72.47 | 8.41 | 24.69 |
| 21. | 31 jul. 2015 | -6.64% | 1.97% | 49.85 | 1.38 | -8.29 |
| 22. | 31 ago. 2015 | -6.88% | -6.26% | 53.30 | 49.81 | 51.52 |
| 23. | 30 sept. 2015 | -7.44% | -2.64% | 61.79 | 11.86 | 27.07 |
| 24. | 31 oct. 2015 | 6.93% | 8.30% | 42.33 | 56.23 | 48.79 |
| 25. | 30 nov. 2015 | 6.87% | 0.05% | 41.59 | 0.56 | -4.83 |
| 26. | 31 dic. 2015 | -4.34% | -1.75% | 22.67 | 6.51 | 12.15 |
| 27. | 31 ene. 2016 | -3.87% | -5.07% | 18.40 | 34.49 | 25.19 |
| 28. | 29 feb. 2016 | 7.23% | -0.41% | 46.38 | 1.47 | -8.26 |
| 29. | 31 mar. 2016 | 11.37% | 6.60% | 119.78 | 33.64 | 63.48 |
| 30. | 30 abr. 2016 | 0.46% | 0.27% | 0.00 | 0.28 | -0.02 |
| 31. | 31 may. 2016 | -3.91% | 1.53% | 18.74 | 0.54 | -3.17 |
| 32. | 30 jun. 2016 | 0.27% | 0.09% | 0.02 | 0.50 | 0.11 |
| 33. | 31 jul. 2016 | 7.17% | 3.56% | 45.55 | 7.63 | 18.64 |
| 34. | 31 ago. 2016 | -4.91% | -0.12% | 28.43 | 0.85 | 4.91 |
| 35. | 30 sept. 2016 | 3.47% | -0.12% | 9.32 | 0.85 | -2.82 |
| 36. | 31 oct. 2016 | -7.03% | -1.94% | 55.47 | 7.52 | 20.42 |
| 37. | 30 nov. 2016 | 12.31% | 3.42% | 141.40 | 6.85 | 31.13 |
| 38. | 31 dic. 2016 | -1.22% | 1.82% | 2.70 | 1.04 | -1.68 |
| 39. | 31 ene. 2017 | 5.22% | 1.79% | 23.02 | 0.98 | 4.75 |
| 40. | 28 feb. 2017 | 3.27% | 3.72% | 8.13 | 8.53 | 8.33 |
| 41. | 31 mar. 2017 | -0.40% | -0.04% | 0.67 | 0.70 | 0.69 |
| 42. | 30 abr. 2017 | 0.70% | 0.91% | 0.08 | 0.01 | 0.03 |
| 43. | 31 may. 2017 | -1.13% | 1.16% | 2.40 | 0.13 | -0.56 |
| 44. | 30 jun. 2017 | 0.85% | 0.48% | 0.18 | 0.10 | -0.13 |
| 45. | 31 jul. 2017 | -0.02% | 1.93% | 0.19 | 1.29 | -0.50 |
| 46. | 31 ago. 2017 | -0.15% | 0.05% | 0.33 | 0.55 | 0.43 |
| 47. | 30 sept. 2017 | 6.44% | 1.93% | 36.18 | 1.28 | 6.80 |
| 48. | 31 oct. 2017 | 2.58% | 2.22% | 4.65 | 2.01 | 3.06 |
| 49. | 30 nov. 2017 | 1.31% | 2.81% | 0.79 | 4.04 | 1.79 |
| 50. | 31 dic. 2017 | 7.51% | 0.98% | 50.29 | 0.03 | 1.30 |
| 51. | 31 ene. 2018 | 3.64% | 5.62% | 10.39 | 23.22 | 15.53 |
| 52. | 28 feb. 2018 | -0.95% | -3.89% | 1.88 | 22.03 | 6.43 |
| 53. | 31 mar. 2018 | -3.88% | -2.69% | 18.54 | 12.16 | 15.02 |
| 54. | 30 abr. 2018 | -2.77% | 0.27% | 10.17 | 0.28 | 1.68 |
| 55. | 31 may. 2018 | 7.40% | 2.16% | 48.72 | 1.85 | 9.50 |
| 56. | 30 jun. 2018 | -2.40% | 0.48% | 7.96 | 0.10 | 0.89 |
| 57. | 31 jul. 2018 | 4.54% | 3.60% | 16.98 | 7.86 | 11.55 |
| 58. | 31 ago. 2018 | 6.83% | 3.03% | 41.04 | 4.96 | 14.27 |
| 59. | 30 sept. 2018 | -0.20% | 0.43% | 0.38 | 0.14 | 0.23 |
| 60. | 31 oct. 2018 | -11.36% | -6.94% | 138.82 | 59.90 | 91.19 |
| 61. | 30 nov. 2018 | 0.19% | 1.79% | 0.05 | 0.97 | -0.23 |
| 62. | 31 dic. 2018 | -11.51% | -9.18% | 142.30 | 99.54 | 119.02 |
| 63. | 31 ene. 2019 | 9.57% | 7.87% | 83.76 | 49.97 | 64.70 |
| 64. | 28 feb. 2019 | 4.84% | 2.97% | 19.54 | 4.72 | 9.61 |
| 65. | 31 mar. 2019 | 0.47% | 1.79% | 0.00 | 0.99 | 0.05 |
| 66. | 30 abr. 2019 | 3.68% | 3.93% | 10.62 | 9.81 | 10.21 |
| 67. | 31 may. 2019 | -14.45% | -6.58% | 221.24 | 54.42 | 109.73 |
| 68. | 30 jun. 2019 | 10.76% | 6.89% | 106.83 | 37.13 | 62.98 |
| 69. | 31 jul. 2019 | -2.76% | 1.31% | 10.11 | 0.26 | -1.63 |
| 70. | 31 ago. 2019 | -7.40% | -1.81% | 61.15 | 6.80 | 20.40 |
| 71. | 30 sept. 2019 | 12.20% | 1.72% | 138.74 | 0.84 | 10.82 |
| Total (Σ): | 2,262.58 | 758.73 | 1,001.26 | |||
Mostrar todo
VarianzaEMR = Σ(REMR,t–REMR)2 ÷ (71 – 1)
= 2,262.58 ÷ (71 – 1)
= 32.32
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 758.73 ÷ (71 – 1)
= 10.84
CovarianzaEMR, S&P 500 = Σ(REMR,t–REMR)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,001.26 ÷ (71 – 1)
= 14.30
Estimación sistemática del riesgo (β)
| VarianzaEMR | 32.32 |
| VarianzaS&P 500 | 10.84 |
| CovarianzaEMR, S&P 500 | 14.30 |
| Coeficiente de correlaciónEMR, S&P 5001 | 0.76 |
| βEMR2 | 1.32 |
| αEMR3 | -0.63% |
Cálculos
1 Coeficiente de correlaciónEMR, S&P 500
= CovarianzaEMR, S&P 500 ÷ (Desviación estándarEMR × Desviación estándarS&P 500)
= 14.30 ÷ (5.69% × 3.29%)
= 0.76
2 βEMR
= CovarianzaEMR, S&P 500 ÷ VarianzaS&P 500
= 14.30 ÷ 10.84
= 1.32
3 αEMR
= PromedioEMR – βEMR × PromedioS&P 500
= 0.42% – 1.32 × 0.80%
= -0.63%
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 Emerson acciones ordinarias | βEMR | 1.32 |
| Tasa de rendimiento esperada de las acciones ordinarias de Emerson3 | E(REMR) | 16.70% |
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(REMR) = RF + βEMR [E(RM) – RF]
= 4.67% + 1.32 [13.79% – 4.67%]
= 16.70%