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 Walgreens Boots Alliance.
Tasas de retorno
Walgreens Boots Alliance Inc., tasas mensuales de retorno
| Walgreens Boots Alliance Inc. (WBA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioWBA,t1 | DividendoWBA,t1 | RWBA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 sept. 2013 | $53.80 | 1,681.55 | ||||
| 1. | 31 oct. 2013 | $59.24 | 10.11% | 1,756.54 | 4.46% | |
| 2. | 30 nov. 2013 | $59.20 | $0.315 | 0.46% | 1,805.81 | 2.80% |
| 3. | 31 dic. 2013 | $57.44 | -2.97% | 1,848.36 | 2.36% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 jul. 2019 | $54.49 | -0.33% | 2,980.38 | 1.31% | |
| 71. | 31 ago. 2019 | $51.19 | $0.458 | -5.22% | 2,926.46 | -1.81% |
| Promedio (R): | 0.37% | 0.84% | ||||
| Desviación estándar: | 7.21% | 3.32% | ||||
| Walgreens Boots Alliance Inc. (WBA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioWBA,t1 | DividendoWBA,t1 | RWBA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 sept. 2013 | $53.80 | 1,681.55 | ||||
| 1. | 31 oct. 2013 | $59.24 | 10.11% | 1,756.54 | 4.46% | |
| 2. | 30 nov. 2013 | $59.20 | $0.315 | 0.46% | 1,805.81 | 2.80% |
| 3. | 31 dic. 2013 | $57.44 | -2.97% | 1,848.36 | 2.36% | |
| 4. | 31 ene. 2014 | $57.35 | -0.16% | 1,782.59 | -3.56% | |
| 5. | 28 feb. 2014 | $67.95 | $0.315 | 19.03% | 1,859.45 | 4.31% |
| 6. | 31 mar. 2014 | $66.03 | -2.83% | 1,872.34 | 0.69% | |
| 7. | 30 abr. 2014 | $67.90 | 2.83% | 1,883.95 | 0.62% | |
| 8. | 31 may. 2014 | $71.91 | $0.315 | 6.37% | 1,923.57 | 2.10% |
| 9. | 30 jun. 2014 | $74.13 | 3.09% | 1,960.23 | 1.91% | |
| 10. | 31 jul. 2014 | $68.77 | -7.23% | 1,930.67 | -1.51% | |
| 11. | 31 ago. 2014 | $60.52 | $0.3375 | -11.51% | 2,003.37 | 3.77% |
| 12. | 30 sept. 2014 | $59.27 | -2.07% | 1,972.29 | -1.55% | |
| 13. | 31 oct. 2014 | $64.22 | 8.35% | 2,018.05 | 2.32% | |
| 14. | 30 nov. 2014 | $68.61 | $0.3375 | 7.36% | 2,067.56 | 2.45% |
| 15. | 31 dic. 2014 | $76.20 | 11.06% | 2,058.90 | -0.42% | |
| 16. | 31 ene. 2015 | $73.75 | -3.22% | 1,994.99 | -3.10% | |
| 17. | 28 feb. 2015 | $83.08 | $0.3375 | 13.11% | 2,104.50 | 5.49% |
| 18. | 31 mar. 2015 | $84.68 | 1.93% | 2,067.89 | -1.74% | |
| 19. | 30 abr. 2015 | $82.93 | -2.07% | 2,085.51 | 0.85% | |
| 20. | 31 may. 2015 | $85.84 | $0.3375 | 3.92% | 2,107.39 | 1.05% |
| 21. | 30 jun. 2015 | $84.44 | -1.63% | 2,063.11 | -2.10% | |
| 22. | 31 jul. 2015 | $96.63 | 14.44% | 2,103.84 | 1.97% | |
| 23. | 31 ago. 2015 | $86.55 | $0.36 | -10.06% | 1,972.18 | -6.26% |
| 24. | 30 sept. 2015 | $83.10 | -3.99% | 1,920.03 | -2.64% | |
| 25. | 31 oct. 2015 | $84.68 | 1.90% | 2,079.36 | 8.30% | |
| 26. | 30 nov. 2015 | $84.03 | $0.36 | -0.34% | 2,080.41 | 0.05% |
| 27. | 31 dic. 2015 | $85.16 | 1.34% | 2,043.94 | -1.75% | |
| 28. | 31 ene. 2016 | $79.72 | -6.39% | 1,940.24 | -5.07% | |
| 29. | 29 feb. 2016 | $78.94 | $0.36 | -0.53% | 1,932.23 | -0.41% |
| 30. | 31 mar. 2016 | $84.24 | 6.71% | 2,059.74 | 6.60% | |
| 31. | 30 abr. 2016 | $79.28 | -5.89% | 2,065.30 | 0.27% | |
| 32. | 31 may. 2016 | $77.40 | $0.36 | -1.92% | 2,096.95 | 1.53% |
| 33. | 30 jun. 2016 | $83.27 | 7.58% | 2,098.86 | 0.09% | |
| 34. | 31 jul. 2016 | $79.25 | -4.83% | 2,173.60 | 3.56% | |
| 35. | 31 ago. 2016 | $80.71 | $0.375 | 2.32% | 2,170.95 | -0.12% |
| 36. | 30 sept. 2016 | $80.62 | -0.11% | 2,168.27 | -0.12% | |
| 37. | 31 oct. 2016 | $82.73 | 2.62% | 2,126.15 | -1.94% | |
| 38. | 30 nov. 2016 | $84.73 | $0.375 | 2.87% | 2,198.81 | 3.42% |
| 39. | 31 dic. 2016 | $82.76 | -2.33% | 2,238.83 | 1.82% | |
| 40. | 31 ene. 2017 | $81.94 | -0.99% | 2,278.87 | 1.79% | |
| 41. | 28 feb. 2017 | $86.38 | $0.375 | 5.88% | 2,363.64 | 3.72% |
| 42. | 31 mar. 2017 | $83.05 | -3.86% | 2,362.72 | -0.04% | |
| 43. | 30 abr. 2017 | $86.54 | 4.20% | 2,384.20 | 0.91% | |
| 44. | 31 may. 2017 | $81.02 | $0.375 | -5.95% | 2,411.80 | 1.16% |
| 45. | 30 jun. 2017 | $78.31 | -3.34% | 2,423.41 | 0.48% | |
| 46. | 31 jul. 2017 | $80.67 | 3.01% | 2,470.30 | 1.93% | |
| 47. | 31 ago. 2017 | $81.50 | $0.40 | 1.52% | 2,471.65 | 0.05% |
| 48. | 30 sept. 2017 | $77.22 | -5.25% | 2,519.36 | 1.93% | |
| 49. | 31 oct. 2017 | $66.27 | -14.18% | 2,575.26 | 2.22% | |
| 50. | 30 nov. 2017 | $72.76 | $0.40 | 10.40% | 2,647.58 | 2.81% |
| 51. | 31 dic. 2017 | $72.62 | -0.19% | 2,673.61 | 0.98% | |
| 52. | 31 ene. 2018 | $75.26 | 3.64% | 2,823.81 | 5.62% | |
| 53. | 28 feb. 2018 | $68.89 | $0.40 | -7.93% | 2,713.83 | -3.89% |
| 54. | 31 mar. 2018 | $65.47 | -4.96% | 2,640.87 | -2.69% | |
| 55. | 30 abr. 2018 | $66.45 | 1.50% | 2,648.05 | 0.27% | |
| 56. | 31 may. 2018 | $62.39 | $0.40 | -5.51% | 2,705.27 | 2.16% |
| 57. | 30 jun. 2018 | $60.02 | -3.80% | 2,718.37 | 0.48% | |
| 58. | 31 jul. 2018 | $67.62 | 12.66% | 2,816.29 | 3.60% | |
| 59. | 31 ago. 2018 | $68.56 | $0.44 | 2.04% | 2,901.52 | 3.03% |
| 60. | 30 sept. 2018 | $72.90 | 6.33% | 2,913.98 | 0.43% | |
| 61. | 31 oct. 2018 | $79.77 | 9.42% | 2,711.74 | -6.94% | |
| 62. | 30 nov. 2018 | $84.67 | $0.44 | 6.69% | 2,760.17 | 1.79% |
| 63. | 31 dic. 2018 | $68.33 | -19.30% | 2,506.85 | -9.18% | |
| 64. | 31 ene. 2019 | $72.26 | 5.75% | 2,704.10 | 7.87% | |
| 65. | 28 feb. 2019 | $71.19 | $0.44 | -0.87% | 2,784.49 | 2.97% |
| 66. | 31 mar. 2019 | $63.27 | -11.13% | 2,834.40 | 1.79% | |
| 67. | 30 abr. 2019 | $53.57 | -15.33% | 2,945.83 | 3.93% | |
| 68. | 31 may. 2019 | $49.34 | $0.44 | -7.07% | 2,752.06 | -6.58% |
| 69. | 30 jun. 2019 | $54.67 | 10.80% | 2,941.76 | 6.89% | |
| 70. | 31 jul. 2019 | $54.49 | -0.33% | 2,980.38 | 1.31% | |
| 71. | 31 ago. 2019 | $51.19 | $0.458 | -5.22% | 2,926.46 | -1.81% |
| Promedio (R): | 0.37% | 0.84% | ||||
| Desviación estándar: | 7.21% | 3.32% | ||||
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 WBA 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
Walgreens Boots Alliance Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RWBA,t | RS&P 500,t | (RWBA,t–RWBA)2 | (RS&P 500,t–RS&P 500)2 | (RWBA,t–RWBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 oct. 2013 | 10.11% | 4.46% | 94.97 | 13.12 | 35.29 |
| 2. | 30 nov. 2013 | 0.46% | 2.80% | 0.01 | 3.87 | 0.19 |
| 3. | 31 dic. 2013 | -2.97% | 2.36% | 11.15 | 2.31 | -5.07 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 jul. 2019 | -0.33% | 1.31% | 0.48 | 0.23 | -0.33 |
| 71. | 31 ago. 2019 | -5.22% | -1.81% | 31.16 | 7.01 | 14.78 |
| Total (Σ): | 3,643.64 | 771.17 | 709.61 | |||
| t | Fecha | RWBA,t | RS&P 500,t | (RWBA,t–RWBA)2 | (RS&P 500,t–RS&P 500)2 | (RWBA,t–RWBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 oct. 2013 | 10.11% | 4.46% | 94.97 | 13.12 | 35.29 |
| 2. | 30 nov. 2013 | 0.46% | 2.80% | 0.01 | 3.87 | 0.19 |
| 3. | 31 dic. 2013 | -2.97% | 2.36% | 11.15 | 2.31 | -5.07 |
| 4. | 31 ene. 2014 | -0.16% | -3.56% | 0.27 | 19.33 | 2.30 |
| 5. | 28 feb. 2014 | 19.03% | 4.31% | 348.42 | 12.07 | 64.84 |
| 6. | 31 mar. 2014 | -2.83% | 0.69% | 10.19 | 0.02 | 0.46 |
| 7. | 30 abr. 2014 | 2.83% | 0.62% | 6.08 | 0.05 | -0.54 |
| 8. | 31 may. 2014 | 6.37% | 2.10% | 36.04 | 1.60 | 7.59 |
| 9. | 30 jun. 2014 | 3.09% | 1.91% | 7.40 | 1.14 | 2.91 |
| 10. | 31 jul. 2014 | -7.23% | -1.51% | 57.71 | 5.50 | 17.82 |
| 11. | 31 ago. 2014 | -11.51% | 3.77% | 140.95 | 8.57 | -34.76 |
| 12. | 30 sept. 2014 | -2.07% | -1.55% | 5.91 | 5.71 | 5.81 |
| 13. | 31 oct. 2014 | 8.35% | 2.32% | 63.77 | 2.20 | 11.84 |
| 14. | 30 nov. 2014 | 7.36% | 2.45% | 48.93 | 2.61 | 11.30 |
| 15. | 31 dic. 2014 | 11.06% | -0.42% | 114.41 | 1.58 | -13.44 |
| 16. | 31 ene. 2015 | -3.22% | -3.10% | 12.83 | 15.54 | 14.12 |
| 17. | 28 feb. 2015 | 13.11% | 5.49% | 162.36 | 21.63 | 59.27 |
| 18. | 31 mar. 2015 | 1.93% | -1.74% | 2.43 | 6.64 | -4.02 |
| 19. | 30 abr. 2015 | -2.07% | 0.85% | 5.92 | 0.00 | -0.03 |
| 20. | 31 may. 2015 | 3.92% | 1.05% | 12.60 | 0.04 | 0.75 |
| 21. | 30 jun. 2015 | -1.63% | -2.10% | 3.99 | 8.64 | 5.87 |
| 22. | 31 jul. 2015 | 14.44% | 1.97% | 197.96 | 1.29 | 15.99 |
| 23. | 31 ago. 2015 | -10.06% | -6.26% | 108.69 | 50.35 | 73.98 |
| 24. | 30 sept. 2015 | -3.99% | -2.64% | 18.94 | 12.13 | 15.16 |
| 25. | 31 oct. 2015 | 1.90% | 8.30% | 2.36 | 55.66 | 11.45 |
| 26. | 30 nov. 2015 | -0.34% | 0.05% | 0.50 | 0.62 | 0.56 |
| 27. | 31 dic. 2015 | 1.34% | -1.75% | 0.96 | 6.71 | -2.54 |
| 28. | 31 ene. 2016 | -6.39% | -5.07% | 45.62 | 34.95 | 39.93 |
| 29. | 29 feb. 2016 | -0.53% | -0.41% | 0.80 | 1.56 | 1.12 |
| 30. | 31 mar. 2016 | 6.71% | 6.60% | 40.29 | 33.19 | 36.57 |
| 31. | 30 abr. 2016 | -5.89% | 0.27% | 39.12 | 0.32 | 3.55 |
| 32. | 31 may. 2016 | -1.92% | 1.53% | 5.21 | 0.48 | -1.59 |
| 33. | 30 jun. 2016 | 7.58% | 0.09% | 52.10 | 0.56 | -5.39 |
| 34. | 31 jul. 2016 | -4.83% | 3.56% | 26.98 | 7.41 | -14.14 |
| 35. | 31 ago. 2016 | 2.32% | -0.12% | 3.80 | 0.92 | -1.87 |
| 36. | 30 sept. 2016 | -0.11% | -0.12% | 0.23 | 0.92 | 0.46 |
| 37. | 31 oct. 2016 | 2.62% | -1.94% | 5.07 | 7.73 | -6.26 |
| 38. | 30 nov. 2016 | 2.87% | 3.42% | 6.27 | 6.65 | 6.46 |
| 39. | 31 dic. 2016 | -2.33% | 1.82% | 7.24 | 0.96 | -2.64 |
| 40. | 31 ene. 2017 | -0.99% | 1.79% | 1.84 | 0.90 | -1.29 |
| 41. | 28 feb. 2017 | 5.88% | 3.72% | 30.36 | 8.31 | 15.88 |
| 42. | 31 mar. 2017 | -3.86% | -0.04% | 17.82 | 0.77 | 3.70 |
| 43. | 30 abr. 2017 | 4.20% | 0.91% | 14.71 | 0.01 | 0.27 |
| 44. | 31 may. 2017 | -5.95% | 1.16% | 39.84 | 0.10 | -2.02 |
| 45. | 30 jun. 2017 | -3.34% | 0.48% | 13.77 | 0.13 | 1.32 |
| 46. | 31 jul. 2017 | 3.01% | 1.93% | 7.01 | 1.20 | 2.90 |
| 47. | 31 ago. 2017 | 1.52% | 0.05% | 1.34 | 0.61 | -0.91 |
| 48. | 30 sept. 2017 | -5.25% | 1.93% | 31.56 | 1.19 | -6.14 |
| 49. | 31 oct. 2017 | -14.18% | 2.22% | 211.60 | 1.91 | -20.09 |
| 50. | 30 nov. 2017 | 10.40% | 2.81% | 100.61 | 3.88 | 19.76 |
| 51. | 31 dic. 2017 | -0.19% | 0.98% | 0.31 | 0.02 | -0.08 |
| 52. | 31 ene. 2018 | 3.64% | 5.62% | 10.69 | 22.85 | 15.63 |
| 53. | 28 feb. 2018 | -7.93% | -3.89% | 68.87 | 22.40 | 39.28 |
| 54. | 31 mar. 2018 | -4.96% | -2.69% | 28.42 | 12.44 | 18.80 |
| 55. | 30 abr. 2018 | 1.50% | 0.27% | 1.28 | 0.32 | -0.64 |
| 56. | 31 may. 2018 | -5.51% | 2.16% | 34.51 | 1.75 | -7.77 |
| 57. | 30 jun. 2018 | -3.80% | 0.48% | 17.35 | 0.13 | 1.47 |
| 58. | 31 jul. 2018 | 12.66% | 3.60% | 151.20 | 7.64 | 33.99 |
| 59. | 31 ago. 2018 | 2.04% | 3.03% | 2.80 | 4.79 | 3.66 |
| 60. | 30 sept. 2018 | 6.33% | 0.43% | 35.57 | 0.17 | -2.44 |
| 61. | 31 oct. 2018 | 9.42% | -6.94% | 82.04 | 60.50 | -70.45 |
| 62. | 30 nov. 2018 | 6.69% | 1.79% | 40.04 | 0.90 | 6.00 |
| 63. | 31 dic. 2018 | -19.30% | -9.18% | 386.70 | 100.31 | 196.96 |
| 64. | 31 ene. 2019 | 5.75% | 7.87% | 29.00 | 49.43 | 37.86 |
| 65. | 28 feb. 2019 | -0.87% | 2.97% | 1.53 | 4.56 | -2.64 |
| 66. | 31 mar. 2019 | -11.13% | 1.79% | 132.05 | 0.91 | -10.97 |
| 67. | 30 abr. 2019 | -15.33% | 3.93% | 246.41 | 9.57 | -48.56 |
| 68. | 31 may. 2019 | -7.07% | -6.58% | 55.37 | 54.99 | 55.18 |
| 69. | 30 jun. 2019 | 10.80% | 6.89% | 108.92 | 36.66 | 63.19 |
| 70. | 31 jul. 2019 | -0.33% | 1.31% | 0.48 | 0.23 | -0.33 |
| 71. | 31 ago. 2019 | -5.22% | -1.81% | 31.16 | 7.01 | 14.78 |
| Total (Σ): | 3,643.64 | 771.17 | 709.61 | |||
Mostrar todo
VarianzaWBA = Σ(RWBA,t–RWBA)2 ÷ (71 – 1)
= 3,643.64 ÷ (71 – 1)
= 52.05
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 771.17 ÷ (71 – 1)
= 11.02
CovarianzaWBA, S&P 500 = Σ(RWBA,t–RWBA)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 709.61 ÷ (71 – 1)
= 10.14
Estimación sistemática del riesgo (β)
| VarianzaWBA | 52.05 |
| VarianzaS&P 500 | 11.02 |
| CovarianzaWBA, S&P 500 | 10.14 |
| Coeficiente de correlaciónWBA, S&P 5001 | 0.42 |
| βWBA2 | 0.92 |
| αWBA3 | -0.40% |
Cálculos
1 Coeficiente de correlaciónWBA, S&P 500
= CovarianzaWBA, S&P 500 ÷ (Desviación estándarWBA × Desviación estándarS&P 500)
= 10.14 ÷ (7.21% × 3.32%)
= 0.42
2 βWBA
= CovarianzaWBA, S&P 500 ÷ VarianzaS&P 500
= 10.14 ÷ 11.02
= 0.92
3 αWBA
= PromedioWBA – βWBA × PromedioS&P 500
= 0.37% – 0.92 × 0.84%
= -0.40%
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 Walgreens Boots Alliance acciones ordinarias | βWBA | 0.92 |
| Tasa de rendimiento esperada de las acciones ordinarias de Walgreens Boots Alliance3 | E(RWBA) | 13.06% |
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(RWBA) = RF + βWBA [E(RM) – RF]
= 4.67% + 0.92 [13.79% – 4.67%]
= 13.06%