Modelo de fijación de precios de activos de capital (CAPM)
El modelo de valoración de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de Abiomed.
Tasas de retorno
Abiomed Inc., tasas mensuales de retorno
| Abiomed Inc. (ABMD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioABMD,t1 | DividendoABMD,t1 | RABMD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 abr. 2016 | $97.14 | 2,065.30 | ||||
| 1. | 31 may. 2016 | $99.31 | 2.23% | 2,096.95 | 1.53% | |
| 2. | 30 jun. 2016 | $109.29 | 10.05% | 2,098.86 | 0.09% | |
| 3. | 31 jul. 2016 | $117.97 | 7.94% | 2,173.60 | 3.56% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 28 feb. 2022 | $310.74 | 5.03% | 4,373.94 | -3.14% | |
| 71. | 31 mar. 2022 | $331.24 | 6.60% | 4,530.41 | 3.58% | |
| Promedio (R): | 2.44% | 1.20% | ||||
| Desviación estándar: | 11.78% | 4.24% | ||||
| Abiomed Inc. (ABMD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioABMD,t1 | DividendoABMD,t1 | RABMD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 abr. 2016 | $97.14 | 2,065.30 | ||||
| 1. | 31 may. 2016 | $99.31 | 2.23% | 2,096.95 | 1.53% | |
| 2. | 30 jun. 2016 | $109.29 | 10.05% | 2,098.86 | 0.09% | |
| 3. | 31 jul. 2016 | $117.97 | 7.94% | 2,173.60 | 3.56% | |
| 4. | 31 ago. 2016 | $117.94 | -0.03% | 2,170.95 | -0.12% | |
| 5. | 30 sept. 2016 | $128.58 | 9.02% | 2,168.27 | -0.12% | |
| 6. | 31 oct. 2016 | $104.99 | -18.35% | 2,126.15 | -1.94% | |
| 7. | 30 nov. 2016 | $112.24 | 6.91% | 2,198.81 | 3.42% | |
| 8. | 31 dic. 2016 | $112.68 | 0.39% | 2,238.83 | 1.82% | |
| 9. | 31 ene. 2017 | $106.37 | -5.60% | 2,278.87 | 1.79% | |
| 10. | 28 feb. 2017 | $117.97 | 10.91% | 2,363.64 | 3.72% | |
| 11. | 31 mar. 2017 | $125.20 | 6.13% | 2,362.72 | -0.04% | |
| 12. | 30 abr. 2017 | $130.32 | 4.09% | 2,384.20 | 0.91% | |
| 13. | 31 may. 2017 | $137.43 | 5.46% | 2,411.80 | 1.16% | |
| 14. | 30 jun. 2017 | $143.30 | 4.27% | 2,423.41 | 0.48% | |
| 15. | 31 jul. 2017 | $148.09 | 3.34% | 2,470.30 | 1.93% | |
| 16. | 31 ago. 2017 | $150.80 | 1.83% | 2,471.65 | 0.05% | |
| 17. | 30 sept. 2017 | $168.60 | 11.80% | 2,519.36 | 1.93% | |
| 18. | 31 oct. 2017 | $192.92 | 14.42% | 2,575.26 | 2.22% | |
| 19. | 30 nov. 2017 | $194.84 | 1.00% | 2,647.58 | 2.81% | |
| 20. | 31 dic. 2017 | $187.41 | -3.81% | 2,673.61 | 0.98% | |
| 21. | 31 ene. 2018 | $235.00 | 25.39% | 2,823.81 | 5.62% | |
| 22. | 28 feb. 2018 | $268.18 | 14.12% | 2,713.83 | -3.89% | |
| 23. | 31 mar. 2018 | $290.99 | 8.51% | 2,640.87 | -2.69% | |
| 24. | 30 abr. 2018 | $300.95 | 3.42% | 2,648.05 | 0.27% | |
| 25. | 31 may. 2018 | $381.14 | 26.65% | 2,705.27 | 2.16% | |
| 26. | 30 jun. 2018 | $409.05 | 7.32% | 2,718.37 | 0.48% | |
| 27. | 31 jul. 2018 | $354.53 | -13.33% | 2,816.29 | 3.60% | |
| 28. | 31 ago. 2018 | $406.58 | 14.68% | 2,901.52 | 3.03% | |
| 29. | 30 sept. 2018 | $449.75 | 10.62% | 2,913.98 | 0.43% | |
| 30. | 31 oct. 2018 | $341.20 | -24.14% | 2,711.74 | -6.94% | |
| 31. | 30 nov. 2018 | $332.68 | -2.50% | 2,760.17 | 1.79% | |
| 32. | 31 dic. 2018 | $325.04 | -2.30% | 2,506.85 | -9.18% | |
| 33. | 31 ene. 2019 | $351.07 | 8.01% | 2,704.10 | 7.87% | |
| 34. | 28 feb. 2019 | $334.50 | -4.72% | 2,784.49 | 2.97% | |
| 35. | 31 mar. 2019 | $285.59 | -14.62% | 2,834.40 | 1.79% | |
| 36. | 30 abr. 2019 | $277.41 | -2.86% | 2,945.83 | 3.93% | |
| 37. | 31 may. 2019 | $261.92 | -5.58% | 2,752.06 | -6.58% | |
| 38. | 30 jun. 2019 | $260.49 | -0.55% | 2,941.76 | 6.89% | |
| 39. | 31 jul. 2019 | $278.56 | 6.94% | 2,980.38 | 1.31% | |
| 40. | 31 ago. 2019 | $193.07 | -30.69% | 2,926.46 | -1.81% | |
| 41. | 30 sept. 2019 | $177.89 | -7.86% | 2,976.74 | 1.72% | |
| 42. | 31 oct. 2019 | $207.58 | 16.69% | 3,037.56 | 2.04% | |
| 43. | 30 nov. 2019 | $196.18 | -5.49% | 3,140.98 | 3.40% | |
| 44. | 31 dic. 2019 | $170.59 | -13.04% | 3,230.78 | 2.86% | |
| 45. | 31 ene. 2020 | $186.29 | 9.20% | 3,225.52 | -0.16% | |
| 46. | 29 feb. 2020 | $150.26 | -19.34% | 2,954.22 | -8.41% | |
| 47. | 31 mar. 2020 | $145.16 | -3.39% | 2,584.59 | -12.51% | |
| 48. | 30 abr. 2020 | $191.25 | 31.75% | 2,912.43 | 12.68% | |
| 49. | 31 may. 2020 | $223.90 | 17.07% | 3,044.31 | 4.53% | |
| 50. | 30 jun. 2020 | $241.56 | 7.89% | 3,100.29 | 1.84% | |
| 51. | 31 jul. 2020 | $299.94 | 24.17% | 3,271.12 | 5.51% | |
| 52. | 31 ago. 2020 | $307.62 | 2.56% | 3,500.31 | 7.01% | |
| 53. | 30 sept. 2020 | $277.06 | -9.93% | 3,363.00 | -3.92% | |
| 54. | 31 oct. 2020 | $251.88 | -9.09% | 3,269.96 | -2.77% | |
| 55. | 30 nov. 2020 | $274.10 | 8.82% | 3,621.63 | 10.75% | |
| 56. | 31 dic. 2020 | $324.20 | 18.28% | 3,756.07 | 3.71% | |
| 57. | 31 ene. 2021 | $348.25 | 7.42% | 3,714.24 | -1.11% | |
| 58. | 28 feb. 2021 | $324.55 | -6.81% | 3,811.15 | 2.61% | |
| 59. | 31 mar. 2021 | $318.73 | -1.79% | 3,972.89 | 4.24% | |
| 60. | 30 abr. 2021 | $320.73 | 0.63% | 4,181.17 | 5.24% | |
| 61. | 31 may. 2021 | $284.58 | -11.27% | 4,204.11 | 0.55% | |
| 62. | 30 jun. 2021 | $312.11 | 9.67% | 4,297.50 | 2.22% | |
| 63. | 31 jul. 2021 | $327.14 | 4.82% | 4,395.26 | 2.27% | |
| 64. | 31 ago. 2021 | $363.96 | 11.26% | 4,522.68 | 2.90% | |
| 65. | 30 sept. 2021 | $325.52 | -10.56% | 4,307.54 | -4.76% | |
| 66. | 31 oct. 2021 | $332.04 | 2.00% | 4,605.38 | 6.91% | |
| 67. | 30 nov. 2021 | $314.78 | -5.20% | 4,567.00 | -0.83% | |
| 68. | 31 dic. 2021 | $359.17 | 14.10% | 4,766.18 | 4.36% | |
| 69. | 31 ene. 2022 | $295.87 | -17.62% | 4,515.55 | -5.26% | |
| 70. | 28 feb. 2022 | $310.74 | 5.03% | 4,373.94 | -3.14% | |
| 71. | 31 mar. 2022 | $331.24 | 6.60% | 4,530.41 | 3.58% | |
| Promedio (R): | 2.44% | 1.20% | ||||
| Desviación estándar: | 11.78% | 4.24% | ||||
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 ABMD 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
Abiomed Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RABMD,t | RS&P 500,t | (RABMD,t–RABMD)2 | (RS&P 500,t–RS&P 500)2 | (RABMD,t–RABMD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 may. 2016 | 2.23% | 1.53% | 0.04 | 0.11 | -0.07 |
| 2. | 30 jun. 2016 | 10.05% | 0.09% | 57.97 | 1.23 | -8.46 |
| 3. | 31 jul. 2016 | 7.94% | 3.56% | 30.32 | 5.57 | 12.99 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 28 feb. 2022 | 5.03% | -3.14% | 6.71 | 18.82 | -11.24 |
| 71. | 31 mar. 2022 | 6.60% | 3.58% | 17.32 | 5.64 | 9.89 |
| Total (Σ): | 9,718.37 | 1,257.74 | 1,707.27 | |||
| t | Fecha | RABMD,t | RS&P 500,t | (RABMD,t–RABMD)2 | (RS&P 500,t–RS&P 500)2 | (RABMD,t–RABMD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 may. 2016 | 2.23% | 1.53% | 0.04 | 0.11 | -0.07 |
| 2. | 30 jun. 2016 | 10.05% | 0.09% | 57.97 | 1.23 | -8.46 |
| 3. | 31 jul. 2016 | 7.94% | 3.56% | 30.32 | 5.57 | 12.99 |
| 4. | 31 ago. 2016 | -0.03% | -0.12% | 6.06 | 1.75 | 3.26 |
| 5. | 30 sept. 2016 | 9.02% | -0.12% | 43.38 | 1.76 | -8.73 |
| 6. | 31 oct. 2016 | -18.35% | -1.94% | 431.89 | 9.89 | 65.34 |
| 7. | 30 nov. 2016 | 6.91% | 3.42% | 19.98 | 4.91 | 9.90 |
| 8. | 31 dic. 2016 | 0.39% | 1.82% | 4.18 | 0.38 | -1.26 |
| 9. | 31 ene. 2017 | -5.60% | 1.79% | 64.57 | 0.34 | -4.71 |
| 10. | 28 feb. 2017 | 10.91% | 3.72% | 71.74 | 6.34 | 21.33 |
| 11. | 31 mar. 2017 | 6.13% | -0.04% | 13.64 | 1.54 | -4.58 |
| 12. | 30 abr. 2017 | 4.09% | 0.91% | 2.74 | 0.09 | -0.48 |
| 13. | 31 may. 2017 | 5.46% | 1.16% | 9.12 | 0.00 | -0.13 |
| 14. | 30 jun. 2017 | 4.27% | 0.48% | 3.37 | 0.52 | -1.32 |
| 15. | 31 jul. 2017 | 3.34% | 1.93% | 0.82 | 0.54 | 0.67 |
| 16. | 31 ago. 2017 | 1.83% | 0.05% | 0.37 | 1.32 | 0.69 |
| 17. | 30 sept. 2017 | 11.80% | 1.93% | 87.76 | 0.53 | 6.83 |
| 18. | 31 oct. 2017 | 14.42% | 2.22% | 143.74 | 1.03 | 12.19 |
| 19. | 30 nov. 2017 | 1.00% | 2.81% | 2.07 | 2.58 | -2.31 |
| 20. | 31 dic. 2017 | -3.81% | 0.98% | 39.05 | 0.05 | 1.37 |
| 21. | 31 ene. 2018 | 25.39% | 5.62% | 527.07 | 19.50 | 101.39 |
| 22. | 28 feb. 2018 | 14.12% | -3.89% | 136.51 | 25.97 | -59.55 |
| 23. | 31 mar. 2018 | 8.51% | -2.69% | 36.85 | 15.13 | -23.61 |
| 24. | 30 abr. 2018 | 3.42% | 0.27% | 0.97 | 0.86 | -0.92 |
| 25. | 31 may. 2018 | 26.65% | 2.16% | 586.13 | 0.92 | 23.22 |
| 26. | 30 jun. 2018 | 7.32% | 0.48% | 23.89 | 0.51 | -3.51 |
| 27. | 31 jul. 2018 | -13.33% | 3.60% | 248.50 | 5.76 | -37.84 |
| 28. | 31 ago. 2018 | 14.68% | 3.03% | 149.96 | 3.33 | 22.34 |
| 29. | 30 sept. 2018 | 10.62% | 0.43% | 66.95 | 0.60 | -6.32 |
| 30. | 31 oct. 2018 | -24.14% | -6.94% | 706.02 | 66.29 | 216.34 |
| 31. | 30 nov. 2018 | -2.50% | 1.79% | 24.33 | 0.34 | -2.88 |
| 32. | 31 dic. 2018 | -2.30% | -9.18% | 22.39 | 107.73 | 49.11 |
| 33. | 31 ene. 2019 | 8.01% | 7.87% | 31.06 | 44.45 | 37.15 |
| 34. | 28 feb. 2019 | -4.72% | 2.97% | 51.20 | 3.14 | -12.67 |
| 35. | 31 mar. 2019 | -14.62% | 1.79% | 290.95 | 0.35 | -10.08 |
| 36. | 30 abr. 2019 | -2.86% | 3.93% | 28.09 | 7.45 | -14.47 |
| 37. | 31 may. 2019 | -5.58% | -6.58% | 64.31 | 60.52 | 62.39 |
| 38. | 30 jun. 2019 | -0.55% | 6.89% | 8.89 | 32.39 | -16.97 |
| 39. | 31 jul. 2019 | 6.94% | 1.31% | 20.26 | 0.01 | 0.50 |
| 40. | 31 ago. 2019 | -30.69% | -1.81% | 1,097.29 | 9.07 | 99.74 |
| 41. | 30 sept. 2019 | -7.86% | 1.72% | 106.05 | 0.27 | -5.32 |
| 42. | 31 oct. 2019 | 16.69% | 2.04% | 203.19 | 0.71 | 11.99 |
| 43. | 30 nov. 2019 | -5.49% | 3.40% | 62.84 | 4.85 | -17.46 |
| 44. | 31 dic. 2019 | -13.04% | 2.86% | 239.62 | 2.75 | -25.65 |
| 45. | 31 ene. 2020 | 9.20% | -0.16% | 45.80 | 1.86 | -9.23 |
| 46. | 29 feb. 2020 | -19.34% | -8.41% | 474.21 | 92.41 | 209.33 |
| 47. | 31 mar. 2020 | -3.39% | -12.51% | 33.98 | 188.06 | 79.94 |
| 48. | 30 abr. 2020 | 31.75% | 12.68% | 859.41 | 131.85 | 336.62 |
| 49. | 31 may. 2020 | 17.07% | 4.53% | 214.23 | 11.07 | 48.69 |
| 50. | 30 jun. 2020 | 7.89% | 1.84% | 29.72 | 0.41 | 3.47 |
| 51. | 31 jul. 2020 | 24.17% | 5.51% | 472.30 | 18.56 | 93.63 |
| 52. | 31 ago. 2020 | 2.56% | 7.01% | 0.02 | 33.70 | 0.73 |
| 53. | 30 sept. 2020 | -9.93% | -3.92% | 153.01 | 26.26 | 63.39 |
| 54. | 31 oct. 2020 | -9.09% | -2.77% | 132.80 | 15.75 | 45.73 |
| 55. | 30 nov. 2020 | 8.82% | 10.75% | 40.78 | 91.26 | 61.01 |
| 56. | 31 dic. 2020 | 18.28% | 3.71% | 250.99 | 6.30 | 39.77 |
| 57. | 31 ene. 2021 | 7.42% | -1.11% | 24.83 | 5.36 | -11.54 |
| 58. | 28 feb. 2021 | -6.81% | 2.61% | 85.39 | 1.98 | -13.01 |
| 59. | 31 mar. 2021 | -1.79% | 4.24% | 17.88 | 9.25 | -12.86 |
| 60. | 30 abr. 2021 | 0.63% | 5.24% | 3.27 | 16.33 | -7.31 |
| 61. | 31 may. 2021 | -11.27% | 0.55% | 187.87 | 0.43 | 8.95 |
| 62. | 30 jun. 2021 | 9.67% | 2.22% | 52.40 | 1.04 | 7.38 |
| 63. | 31 jul. 2021 | 4.82% | 2.27% | 5.67 | 1.15 | 2.55 |
| 64. | 31 ago. 2021 | 11.26% | 2.90% | 77.79 | 2.88 | 14.97 |
| 65. | 30 sept. 2021 | -10.56% | -4.76% | 168.92 | 35.51 | 77.44 |
| 66. | 31 oct. 2021 | 2.00% | 6.91% | 0.19 | 32.63 | -2.47 |
| 67. | 30 nov. 2021 | -5.20% | -0.83% | 58.27 | 4.14 | 15.54 |
| 68. | 31 dic. 2021 | 14.10% | 4.36% | 136.11 | 9.98 | 36.86 |
| 69. | 31 ene. 2022 | -17.62% | -5.26% | 402.38 | 41.73 | 129.59 |
| 70. | 28 feb. 2022 | 5.03% | -3.14% | 6.71 | 18.82 | -11.24 |
| 71. | 31 mar. 2022 | 6.60% | 3.58% | 17.32 | 5.64 | 9.89 |
| Total (Σ): | 9,718.37 | 1,257.74 | 1,707.27 | |||
Mostrar todo
VarianzaABMD = Σ(RABMD,t–RABMD)2 ÷ (71 – 1)
= 9,718.37 ÷ (71 – 1)
= 138.83
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,257.74 ÷ (71 – 1)
= 17.97
CovarianzaABMD, S&P 500 = Σ(RABMD,t–RABMD)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,707.27 ÷ (71 – 1)
= 24.39
Estimación sistemática del riesgo (β)
| VarianzaABMD | 138.83 |
| VarianzaS&P 500 | 17.97 |
| CovarianzaABMD, S&P 500 | 24.39 |
| Coeficiente de correlaciónABMD, S&P 5001 | 0.49 |
| βABMD2 | 1.36 |
| αABMD3 | 0.80% |
Cálculos
1 Coeficiente de correlaciónABMD, S&P 500
= CovarianzaABMD, S&P 500 ÷ (Desviación estándarABMD × Desviación estándarS&P 500)
= 24.39 ÷ (11.78% × 4.24%)
= 0.49
2 βABMD
= CovarianzaABMD, S&P 500 ÷ VarianzaS&P 500
= 24.39 ÷ 17.97
= 1.36
3 αABMD
= PromedioABMD – βABMD × PromedioS&P 500
= 2.44% – 1.36 × 1.20%
= 0.80%
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 Abiomed acciones ordinarias | βABMD | 1.36 |
| Tasa de rendimiento esperada de las acciones ordinarias de Abiomed3 | E(RABMD) | 17.04% |
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(RABMD) = RF + βABMD [E(RM) – RF]
= 4.67% + 1.36 [13.79% – 4.67%]
= 17.04%