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 McKesson.
Tasas de retorno
McKesson Corp., tasas mensuales de retorno
| McKesson Corp. (MCK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMCK,t1 | DividendoMCK,t1 | RMCK,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 abr. 2010 | $64.81 | 1,186.69 | ||||
| 1. | 31 may. 2010 | $70.00 | 8.01% | 1,089.41 | -8.20% | |
| 2. | 30 jun. 2010 | $67.16 | $0.18 | -3.80% | 1,030.71 | -5.39% |
| 3. | 31 jul. 2010 | $62.82 | -6.46% | 1,101.60 | 6.88% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 29 feb. 2016 | $155.62 | $0.28 | -3.16% | 1,932.23 | -0.41% |
| 71. | 31 mar. 2016 | $157.25 | 1.05% | 2,059.74 | 6.60% | |
| Promedio (R): | 1.50% | 0.85% | ||||
| Desviación estándar: | 6.06% | 3.85% | ||||
| McKesson Corp. (MCK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMCK,t1 | DividendoMCK,t1 | RMCK,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 abr. 2010 | $64.81 | 1,186.69 | ||||
| 1. | 31 may. 2010 | $70.00 | 8.01% | 1,089.41 | -8.20% | |
| 2. | 30 jun. 2010 | $67.16 | $0.18 | -3.80% | 1,030.71 | -5.39% |
| 3. | 31 jul. 2010 | $62.82 | -6.46% | 1,101.60 | 6.88% | |
| 4. | 31 ago. 2010 | $58.05 | $0.18 | -7.31% | 1,049.33 | -4.74% |
| 5. | 30 sept. 2010 | $61.78 | 6.43% | 1,141.20 | 8.76% | |
| 6. | 31 oct. 2010 | $65.98 | 6.80% | 1,183.26 | 3.69% | |
| 7. | 30 nov. 2010 | $63.90 | $0.18 | -2.88% | 1,180.55 | -0.23% |
| 8. | 31 dic. 2010 | $70.38 | 10.14% | 1,257.64 | 6.53% | |
| 9. | 31 ene. 2011 | $75.17 | 6.81% | 1,286.12 | 2.26% | |
| 10. | 28 feb. 2011 | $79.28 | $0.18 | 5.71% | 1,327.22 | 3.20% |
| 11. | 31 mar. 2011 | $79.05 | -0.29% | 1,325.83 | -0.10% | |
| 12. | 30 abr. 2011 | $83.01 | 5.01% | 1,363.61 | 2.85% | |
| 13. | 31 may. 2011 | $85.61 | 3.13% | 1,345.20 | -1.35% | |
| 14. | 30 jun. 2011 | $83.65 | $0.20 | -2.06% | 1,320.64 | -1.83% |
| 15. | 31 jul. 2011 | $81.12 | -3.02% | 1,292.28 | -2.15% | |
| 16. | 31 ago. 2011 | $79.93 | $0.20 | -1.22% | 1,218.89 | -5.68% |
| 17. | 30 sept. 2011 | $72.70 | -9.05% | 1,131.42 | -7.18% | |
| 18. | 31 oct. 2011 | $81.55 | 12.17% | 1,253.30 | 10.77% | |
| 19. | 30 nov. 2011 | $81.31 | $0.20 | -0.05% | 1,246.96 | -0.51% |
| 20. | 31 dic. 2011 | $77.91 | -4.18% | 1,257.60 | 0.85% | |
| 21. | 31 ene. 2012 | $81.72 | 4.89% | 1,312.41 | 4.36% | |
| 22. | 29 feb. 2012 | $83.51 | $0.20 | 2.44% | 1,365.68 | 4.06% |
| 23. | 31 mar. 2012 | $87.77 | 5.10% | 1,408.47 | 3.13% | |
| 24. | 30 abr. 2012 | $91.41 | 4.15% | 1,397.91 | -0.75% | |
| 25. | 31 may. 2012 | $87.28 | -4.52% | 1,310.33 | -6.27% | |
| 26. | 30 jun. 2012 | $93.75 | $0.20 | 7.64% | 1,362.16 | 3.96% |
| 27. | 31 jul. 2012 | $90.73 | -3.22% | 1,379.32 | 1.26% | |
| 28. | 31 ago. 2012 | $87.11 | $0.20 | -3.77% | 1,406.58 | 1.98% |
| 29. | 30 sept. 2012 | $86.03 | -1.24% | 1,440.67 | 2.42% | |
| 30. | 31 oct. 2012 | $93.31 | 8.46% | 1,412.16 | -1.98% | |
| 31. | 30 nov. 2012 | $94.47 | $0.20 | 1.46% | 1,416.18 | 0.28% |
| 32. | 31 dic. 2012 | $96.96 | 2.64% | 1,426.19 | 0.71% | |
| 33. | 31 ene. 2013 | $105.23 | 8.53% | 1,498.11 | 5.04% | |
| 34. | 28 feb. 2013 | $106.13 | $0.20 | 1.05% | 1,514.68 | 1.11% |
| 35. | 31 mar. 2013 | $107.96 | 1.72% | 1,569.19 | 3.60% | |
| 36. | 30 abr. 2013 | $105.82 | -1.98% | 1,597.57 | 1.81% | |
| 37. | 31 may. 2013 | $113.86 | 7.60% | 1,630.74 | 2.08% | |
| 38. | 30 jun. 2013 | $114.50 | $0.20 | 0.74% | 1,606.28 | -1.50% |
| 39. | 31 jul. 2013 | $122.66 | 7.13% | 1,685.73 | 4.95% | |
| 40. | 31 ago. 2013 | $121.41 | $0.24 | -0.82% | 1,632.97 | -3.13% |
| 41. | 30 sept. 2013 | $128.30 | 5.67% | 1,681.55 | 2.97% | |
| 42. | 31 oct. 2013 | $156.34 | 21.86% | 1,756.54 | 4.46% | |
| 43. | 30 nov. 2013 | $165.89 | $0.24 | 6.26% | 1,805.81 | 2.80% |
| 44. | 31 dic. 2013 | $161.40 | -2.71% | 1,848.36 | 2.36% | |
| 45. | 31 ene. 2014 | $174.41 | 8.06% | 1,782.59 | -3.56% | |
| 46. | 28 feb. 2014 | $177.05 | $0.24 | 1.65% | 1,859.45 | 4.31% |
| 47. | 31 mar. 2014 | $176.57 | -0.27% | 1,872.34 | 0.69% | |
| 48. | 30 abr. 2014 | $169.19 | -4.18% | 1,883.95 | 0.62% | |
| 49. | 31 may. 2014 | $189.64 | 12.09% | 1,923.57 | 2.10% | |
| 50. | 30 jun. 2014 | $186.21 | $0.24 | -1.68% | 1,960.23 | 1.91% |
| 51. | 31 jul. 2014 | $191.86 | 3.03% | 1,930.67 | -1.51% | |
| 52. | 31 ago. 2014 | $195.03 | $0.24 | 1.78% | 2,003.37 | 3.77% |
| 53. | 30 sept. 2014 | $194.67 | -0.18% | 1,972.29 | -1.55% | |
| 54. | 31 oct. 2014 | $203.41 | 4.49% | 2,018.05 | 2.32% | |
| 55. | 30 nov. 2014 | $210.76 | $0.24 | 3.73% | 2,067.56 | 2.45% |
| 56. | 31 dic. 2014 | $207.58 | -1.51% | 2,058.90 | -0.42% | |
| 57. | 31 ene. 2015 | $212.65 | 2.44% | 1,994.99 | -3.10% | |
| 58. | 28 feb. 2015 | $228.70 | $0.24 | 7.66% | 2,104.50 | 5.49% |
| 59. | 31 mar. 2015 | $226.20 | -1.09% | 2,067.89 | -1.74% | |
| 60. | 30 abr. 2015 | $223.40 | -1.24% | 2,085.51 | 0.85% | |
| 61. | 31 may. 2015 | $237.23 | 6.19% | 2,107.39 | 1.05% | |
| 62. | 30 jun. 2015 | $224.81 | $0.24 | -5.13% | 2,063.11 | -2.10% |
| 63. | 31 jul. 2015 | $220.57 | -1.89% | 2,103.84 | 1.97% | |
| 64. | 31 ago. 2015 | $197.58 | $0.28 | -10.30% | 1,972.18 | -6.26% |
| 65. | 30 sept. 2015 | $185.03 | -6.35% | 1,920.03 | -2.64% | |
| 66. | 31 oct. 2015 | $178.80 | -3.37% | 2,079.36 | 8.30% | |
| 67. | 30 nov. 2015 | $189.35 | $0.28 | 6.06% | 2,080.41 | 0.05% |
| 68. | 31 dic. 2015 | $197.23 | 4.16% | 2,043.94 | -1.75% | |
| 69. | 31 ene. 2016 | $160.98 | -18.38% | 1,940.24 | -5.07% | |
| 70. | 29 feb. 2016 | $155.62 | $0.28 | -3.16% | 1,932.23 | -0.41% |
| 71. | 31 mar. 2016 | $157.25 | 1.05% | 2,059.74 | 6.60% | |
| Promedio (R): | 1.50% | 0.85% | ||||
| Desviación estándar: | 6.06% | 3.85% | ||||
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 MCK 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
McKesson Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RMCK,t | RS&P 500,t | (RMCK,t–RMCK)2 | (RS&P 500,t–RS&P 500)2 | (RMCK,t–RMCK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 may. 2010 | 8.01% | -8.20% | 42.33 | 81.90 | -58.88 |
| 2. | 30 jun. 2010 | -3.80% | -5.39% | 28.11 | 38.94 | 33.08 |
| 3. | 31 jul. 2010 | -6.46% | 6.88% | 63.42 | 36.31 | -47.99 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 29 feb. 2016 | -3.16% | -0.41% | 21.69 | 1.60 | 5.89 |
| 71. | 31 mar. 2016 | 1.05% | 6.60% | 0.21 | 33.03 | -2.61 |
| Total (Σ): | 2,573.16 | 1,034.99 | 771.36 | |||
| t | Fecha | RMCK,t | RS&P 500,t | (RMCK,t–RMCK)2 | (RS&P 500,t–RS&P 500)2 | (RMCK,t–RMCK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 may. 2010 | 8.01% | -8.20% | 42.33 | 81.90 | -58.88 |
| 2. | 30 jun. 2010 | -3.80% | -5.39% | 28.11 | 38.94 | 33.08 |
| 3. | 31 jul. 2010 | -6.46% | 6.88% | 63.42 | 36.31 | -47.99 |
| 4. | 31 ago. 2010 | -7.31% | -4.74% | 77.58 | 31.33 | 49.30 |
| 5. | 30 sept. 2010 | 6.43% | 8.76% | 24.24 | 62.46 | 38.91 |
| 6. | 31 oct. 2010 | 6.80% | 3.69% | 28.06 | 8.03 | 15.01 |
| 7. | 30 nov. 2010 | -2.88% | -0.23% | 19.20 | 1.17 | 4.74 |
| 8. | 31 dic. 2010 | 10.14% | 6.53% | 74.64 | 32.24 | 49.05 |
| 9. | 31 ene. 2011 | 6.81% | 2.26% | 28.14 | 1.99 | 7.49 |
| 10. | 28 feb. 2011 | 5.71% | 3.20% | 17.69 | 5.49 | 9.86 |
| 11. | 31 mar. 2011 | -0.29% | -0.10% | 3.21 | 0.92 | 1.71 |
| 12. | 30 abr. 2011 | 5.01% | 2.85% | 12.31 | 3.99 | 7.01 |
| 13. | 31 may. 2011 | 3.13% | -1.35% | 2.66 | 4.85 | -3.59 |
| 14. | 30 jun. 2011 | -2.06% | -1.83% | 12.66 | 7.17 | 9.53 |
| 15. | 31 jul. 2011 | -3.02% | -2.15% | 20.49 | 9.00 | 13.58 |
| 16. | 31 ago. 2011 | -1.22% | -5.68% | 7.41 | 42.66 | 17.78 |
| 17. | 30 sept. 2011 | -9.05% | -7.18% | 111.24 | 64.46 | 84.68 |
| 18. | 31 oct. 2011 | 12.17% | 10.77% | 113.89 | 98.41 | 105.86 |
| 19. | 30 nov. 2011 | -0.05% | -0.51% | 2.40 | 1.84 | 2.11 |
| 20. | 31 dic. 2011 | -4.18% | 0.85% | 32.30 | 0.00 | -0.01 |
| 21. | 31 ene. 2012 | 4.89% | 4.36% | 11.48 | 12.29 | 11.88 |
| 22. | 29 feb. 2012 | 2.44% | 4.06% | 0.87 | 10.28 | 2.99 |
| 23. | 31 mar. 2012 | 5.10% | 3.13% | 12.96 | 5.20 | 8.21 |
| 24. | 30 abr. 2012 | 4.15% | -0.75% | 7.00 | 2.57 | -4.24 |
| 25. | 31 may. 2012 | -4.52% | -6.27% | 36.24 | 50.66 | 42.84 |
| 26. | 30 jun. 2012 | 7.64% | 3.96% | 37.71 | 9.63 | 19.06 |
| 27. | 31 jul. 2012 | -3.22% | 1.26% | 22.31 | 0.17 | -1.92 |
| 28. | 31 ago. 2012 | -3.77% | 1.98% | 27.78 | 1.26 | -5.93 |
| 29. | 30 sept. 2012 | -1.24% | 2.42% | 7.52 | 2.47 | -4.31 |
| 30. | 31 oct. 2012 | 8.46% | -1.98% | 48.45 | 8.02 | -19.71 |
| 31. | 30 nov. 2012 | 1.46% | 0.28% | 0.00 | 0.32 | 0.03 |
| 32. | 31 dic. 2012 | 2.64% | 0.71% | 1.29 | 0.02 | -0.16 |
| 33. | 31 ene. 2013 | 8.53% | 5.04% | 49.39 | 17.56 | 29.45 |
| 34. | 28 feb. 2013 | 1.05% | 1.11% | 0.21 | 0.06 | -0.12 |
| 35. | 31 mar. 2013 | 1.72% | 3.60% | 0.05 | 7.54 | 0.61 |
| 36. | 30 abr. 2013 | -1.98% | 1.81% | 12.14 | 0.91 | -3.33 |
| 37. | 31 may. 2013 | 7.60% | 2.08% | 37.16 | 1.50 | 7.46 |
| 38. | 30 jun. 2013 | 0.74% | -1.50% | 0.58 | 5.53 | 1.80 |
| 39. | 31 jul. 2013 | 7.13% | 4.95% | 31.64 | 16.76 | 23.03 |
| 40. | 31 ago. 2013 | -0.82% | -3.13% | 5.41 | 15.86 | 9.26 |
| 41. | 30 sept. 2013 | 5.67% | 2.97% | 17.42 | 4.51 | 8.86 |
| 42. | 31 oct. 2013 | 21.86% | 4.46% | 414.26 | 13.01 | 73.42 |
| 43. | 30 nov. 2013 | 6.26% | 2.80% | 22.66 | 3.81 | 9.30 |
| 44. | 31 dic. 2013 | -2.71% | 2.36% | 17.71 | 2.26 | -6.33 |
| 45. | 31 ene. 2014 | 8.06% | -3.56% | 43.02 | 19.45 | -28.93 |
| 46. | 28 feb. 2014 | 1.65% | 4.31% | 0.02 | 11.97 | 0.52 |
| 47. | 31 mar. 2014 | -0.27% | 0.69% | 3.14 | 0.03 | 0.28 |
| 48. | 30 abr. 2014 | -4.18% | 0.62% | 32.28 | 0.05 | 1.32 |
| 49. | 31 may. 2014 | 12.09% | 2.10% | 112.05 | 1.56 | 13.24 |
| 50. | 30 jun. 2014 | -1.68% | 1.91% | 10.14 | 1.11 | -3.35 |
| 51. | 31 jul. 2014 | 3.03% | -1.51% | 2.35 | 5.57 | -3.62 |
| 52. | 31 ago. 2014 | 1.78% | 3.77% | 0.08 | 8.49 | 0.80 |
| 53. | 30 sept. 2014 | -0.18% | -1.55% | 2.84 | 5.78 | 4.05 |
| 54. | 31 oct. 2014 | 4.49% | 2.32% | 8.93 | 2.15 | 4.39 |
| 55. | 30 nov. 2014 | 3.73% | 2.45% | 4.97 | 2.56 | 3.57 |
| 56. | 31 dic. 2014 | -1.51% | -0.42% | 9.06 | 1.62 | 3.83 |
| 57. | 31 ene. 2015 | 2.44% | -3.10% | 0.89 | 15.65 | -3.72 |
| 58. | 28 feb. 2015 | 7.66% | 5.49% | 37.93 | 21.50 | 28.56 |
| 59. | 31 mar. 2015 | -1.09% | -1.74% | 6.73 | 6.72 | 6.72 |
| 60. | 30 abr. 2015 | -1.24% | 0.85% | 7.50 | 0.00 | 0.00 |
| 61. | 31 may. 2015 | 6.19% | 1.05% | 21.99 | 0.04 | 0.92 |
| 62. | 30 jun. 2015 | -5.13% | -2.10% | 44.03 | 8.72 | 19.60 |
| 63. | 31 jul. 2015 | -1.89% | 1.97% | 11.48 | 1.26 | -3.80 |
| 64. | 31 ago. 2015 | -10.30% | -6.26% | 139.18 | 50.56 | 83.88 |
| 65. | 30 sept. 2015 | -6.35% | -2.64% | 61.68 | 12.23 | 27.46 |
| 66. | 31 oct. 2015 | -3.37% | 8.30% | 23.70 | 55.44 | -36.25 |
| 67. | 30 nov. 2015 | 6.06% | 0.05% | 20.75 | 0.64 | -3.65 |
| 68. | 31 dic. 2015 | 4.16% | -1.75% | 7.08 | 6.79 | -6.93 |
| 69. | 31 ene. 2016 | -18.38% | -5.07% | 395.26 | 35.11 | 117.81 |
| 70. | 29 feb. 2016 | -3.16% | -0.41% | 21.69 | 1.60 | 5.89 |
| 71. | 31 mar. 2016 | 1.05% | 6.60% | 0.21 | 33.03 | -2.61 |
| Total (Σ): | 2,573.16 | 1,034.99 | 771.36 | |||
Mostrar todo
VarianzaMCK = Σ(RMCK,t–RMCK)2 ÷ (71 – 1)
= 2,573.16 ÷ (71 – 1)
= 36.76
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,034.99 ÷ (71 – 1)
= 14.79
CovarianzaMCK, S&P 500 = Σ(RMCK,t–RMCK)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 771.36 ÷ (71 – 1)
= 11.02
Estimación sistemática del riesgo (β)
| VarianzaMCK | 36.76 |
| VarianzaS&P 500 | 14.79 |
| CovarianzaMCK, S&P 500 | 11.02 |
| Coeficiente de correlaciónMCK, S&P 5001 | 0.47 |
| βMCK2 | 0.75 |
| αMCK3 | 0.87% |
Cálculos
1 Coeficiente de correlaciónMCK, S&P 500
= CovarianzaMCK, S&P 500 ÷ (Desviación estándarMCK × Desviación estándarS&P 500)
= 11.02 ÷ (6.06% × 3.85%)
= 0.47
2 βMCK
= CovarianzaMCK, S&P 500 ÷ VarianzaS&P 500
= 11.02 ÷ 14.79
= 0.75
3 αMCK
= PromedioMCK – βMCK × PromedioS&P 500
= 1.50% – 0.75 × 0.85%
= 0.87%
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 McKesson acciones ordinarias | βMCK | 0.75 |
| Tasa de rendimiento esperada de las acciones ordinarias de McKesson3 | E(RMCK) | 11.32% |
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(RMCK) = RF + βMCK [E(RM) – RF]
= 4.86% + 0.75 [13.52% – 4.86%]
= 11.32%