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 Amgen.
Tasas de retorno
Amgen Inc., tasas mensuales de retorno
| Amgen Inc. (AMGN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAMGN,t1 | DividendoAMGN,t1 | RAMGN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $187.11 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $190.08 | $1.45 | 2.36% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $189.98 | -0.05% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $179.32 | -5.61% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $269.64 | $2.13 | 6.28% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $288.02 | 6.82% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.24% | 1.11% | ||||
| Desviación estándar: | 7.10% | 5.31% | ||||
| Amgen Inc. (AMGN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAMGN,t1 | DividendoAMGN,t1 | RAMGN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $187.11 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $190.08 | $1.45 | 2.36% | 2,784.49 | 2.97% |
| 2. | 31 mar. 2019 | $189.98 | -0.05% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $179.32 | -5.61% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $166.70 | $1.45 | -6.23% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $184.28 | 10.55% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $186.58 | 1.25% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $208.62 | $1.45 | 12.59% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $193.51 | -7.24% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $213.25 | 10.20% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $234.72 | $1.45 | 10.75% | 3,140.98 | 3.40% |
| 11. | 31 dic. 2019 | $241.07 | 2.71% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $216.05 | -10.38% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $199.73 | $1.60 | -6.81% | 2,954.22 | -8.41% |
| 14. | 31 mar. 2020 | $202.73 | 1.50% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $239.22 | 18.00% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $229.70 | $1.60 | -3.31% | 3,044.31 | 4.53% |
| 17. | 30 jun. 2020 | $235.86 | 2.68% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $244.67 | 3.74% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $253.32 | $1.60 | 4.19% | 3,500.31 | 7.01% |
| 20. | 30 sept. 2020 | $254.16 | 0.33% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $216.94 | -14.64% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $222.04 | $1.60 | 3.09% | 3,621.63 | 10.75% |
| 23. | 31 dic. 2020 | $229.92 | 3.55% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $241.43 | 5.01% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $224.92 | $1.76 | -6.11% | 3,811.15 | 2.61% |
| 26. | 31 mar. 2021 | $248.81 | 10.62% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $239.64 | -3.69% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $237.94 | $1.76 | 0.03% | 4,204.11 | 0.55% |
| 29. | 30 jun. 2021 | $243.75 | 2.44% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $241.54 | -0.91% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $225.53 | $1.76 | -5.90% | 4,522.68 | 2.90% |
| 32. | 30 sept. 2021 | $212.65 | -5.71% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $206.97 | -2.67% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $198.88 | $1.76 | -3.06% | 4,567.00 | -0.83% |
| 35. | 31 dic. 2021 | $224.97 | 13.12% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $227.14 | 0.96% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $226.48 | $1.94 | 0.56% | 4,373.94 | -3.14% |
| 38. | 31 mar. 2022 | $241.82 | 6.77% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $233.19 | -3.57% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $256.74 | $1.94 | 10.93% | 4,132.15 | 0.01% |
| 41. | 30 jun. 2022 | $243.30 | -5.23% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $247.47 | 1.71% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $240.30 | $1.94 | -2.11% | 3,955.00 | -4.24% |
| 44. | 30 sept. 2022 | $225.40 | -6.20% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $270.35 | 19.94% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $286.40 | $1.94 | 6.65% | 4,080.11 | 5.38% |
| 47. | 31 dic. 2022 | $262.64 | -8.30% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $252.40 | -3.90% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $231.66 | $2.13 | -7.37% | 3,970.15 | -2.61% |
| 50. | 31 mar. 2023 | $241.75 | 4.36% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $239.74 | -0.83% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $220.65 | $2.13 | -7.07% | 4,179.83 | 0.25% |
| 53. | 30 jun. 2023 | $222.02 | 0.62% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $234.15 | 5.46% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $256.34 | $2.13 | 10.39% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $268.76 | 4.85% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $255.70 | -4.86% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $269.64 | $2.13 | 6.28% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $288.02 | 6.82% | 4,769.83 | 4.42% | |
| Promedio (R): | 1.24% | 1.11% | ||||
| Desviación estándar: | 7.10% | 5.31% | ||||
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 AMGN 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
Amgen Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RAMGN,t | RS&P 500,t | (RAMGN,t–RAMGN)2 | (RS&P 500,t–RS&P 500)2 | (RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 2.36% | 2.97% | 1.26 | 3.49 | 2.09 |
| 2. | 31 mar. 2019 | -0.05% | 1.79% | 1.67 | 0.47 | -0.89 |
| 3. | 30 abr. 2019 | -5.61% | 3.93% | 46.95 | 7.98 | -19.36 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 6.28% | 8.92% | 25.44 | 61.03 | 39.40 |
| 59. | 31 dic. 2023 | 6.82% | 4.42% | 31.08 | 11.00 | 18.49 |
| Total (Σ): | 2,927.75 | 1,634.30 | 1,013.07 | |||
| t | Fecha | RAMGN,t | RS&P 500,t | (RAMGN,t–RAMGN)2 | (RS&P 500,t–RS&P 500)2 | (RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 2.36% | 2.97% | 1.26 | 3.49 | 2.09 |
| 2. | 31 mar. 2019 | -0.05% | 1.79% | 1.67 | 0.47 | -0.89 |
| 3. | 30 abr. 2019 | -5.61% | 3.93% | 46.95 | 7.98 | -19.36 |
| 4. | 31 may. 2019 | -6.23% | -6.58% | 55.81 | 59.04 | 57.40 |
| 5. | 30 jun. 2019 | 10.55% | 6.89% | 86.58 | 33.49 | 53.85 |
| 6. | 31 jul. 2019 | 1.25% | 1.31% | 0.00 | 0.04 | 0.00 |
| 7. | 31 ago. 2019 | 12.59% | -1.81% | 128.79 | 8.50 | -33.08 |
| 8. | 30 sept. 2019 | -7.24% | 1.72% | 71.98 | 0.37 | -5.19 |
| 9. | 31 oct. 2019 | 10.20% | 2.04% | 80.28 | 0.88 | 8.40 |
| 10. | 30 nov. 2019 | 10.75% | 3.40% | 90.38 | 5.28 | 21.85 |
| 11. | 31 dic. 2019 | 2.71% | 2.86% | 2.14 | 3.07 | 2.57 |
| 12. | 31 ene. 2020 | -10.38% | -0.16% | 135.02 | 1.61 | 14.74 |
| 13. | 29 feb. 2020 | -6.81% | -8.41% | 64.87 | 90.57 | 76.65 |
| 14. | 31 mar. 2020 | 1.50% | -12.51% | 0.07 | 185.44 | -3.55 |
| 15. | 30 abr. 2020 | 18.00% | 12.68% | 280.83 | 134.06 | 194.03 |
| 16. | 31 may. 2020 | -3.31% | 4.53% | 20.72 | 11.71 | -15.58 |
| 17. | 30 jun. 2020 | 2.68% | 1.84% | 2.08 | 0.54 | 1.06 |
| 18. | 31 jul. 2020 | 3.74% | 5.51% | 6.22 | 19.40 | 10.98 |
| 19. | 31 ago. 2020 | 4.19% | 7.01% | 8.69 | 34.82 | 17.40 |
| 20. | 30 sept. 2020 | 0.33% | -3.92% | 0.83 | 25.29 | 4.57 |
| 21. | 31 oct. 2020 | -14.64% | -2.77% | 252.35 | 15.00 | 61.52 |
| 22. | 30 nov. 2020 | 3.09% | 10.75% | 3.41 | 93.10 | 17.82 |
| 23. | 31 dic. 2020 | 3.55% | 3.71% | 5.33 | 6.79 | 6.01 |
| 24. | 31 ene. 2021 | 5.01% | -1.11% | 14.17 | 4.93 | -8.36 |
| 25. | 28 feb. 2021 | -6.11% | 2.61% | 54.03 | 2.26 | -11.05 |
| 26. | 31 mar. 2021 | 10.62% | 4.24% | 87.99 | 9.85 | 29.44 |
| 27. | 30 abr. 2021 | -3.69% | 5.24% | 24.27 | 17.11 | -20.38 |
| 28. | 31 may. 2021 | 0.03% | 0.55% | 1.48 | 0.31 | 0.68 |
| 29. | 30 jun. 2021 | 2.44% | 2.22% | 1.44 | 1.24 | 1.34 |
| 30. | 31 jul. 2021 | -0.91% | 2.27% | 4.61 | 1.37 | -2.51 |
| 31. | 31 ago. 2021 | -5.90% | 2.90% | 50.99 | 3.22 | -12.80 |
| 32. | 30 sept. 2021 | -5.71% | -4.76% | 48.33 | 34.37 | 40.76 |
| 33. | 31 oct. 2021 | -2.67% | 6.91% | 15.31 | 33.74 | -22.72 |
| 34. | 30 nov. 2021 | -3.06% | -0.83% | 18.49 | 3.76 | 8.34 |
| 35. | 31 dic. 2021 | 13.12% | 4.36% | 141.07 | 10.60 | 38.67 |
| 36. | 31 ene. 2022 | 0.96% | -5.26% | 0.08 | 40.51 | 1.76 |
| 37. | 28 feb. 2022 | 0.56% | -3.14% | 0.46 | 17.99 | 2.87 |
| 38. | 31 mar. 2022 | 6.77% | 3.58% | 30.60 | 6.11 | 13.67 |
| 39. | 30 abr. 2022 | -3.57% | -8.80% | 23.14 | 98.04 | 47.63 |
| 40. | 31 may. 2022 | 10.93% | 0.01% | 93.89 | 1.21 | -10.66 |
| 41. | 30 jun. 2022 | -5.23% | -8.39% | 41.94 | 90.21 | 61.51 |
| 42. | 31 jul. 2022 | 1.71% | 9.11% | 0.22 | 64.09 | 3.78 |
| 43. | 31 ago. 2022 | -2.11% | -4.24% | 11.25 | 28.62 | 17.95 |
| 44. | 30 sept. 2022 | -6.20% | -9.34% | 55.38 | 109.11 | 77.73 |
| 45. | 31 oct. 2022 | 19.94% | 7.99% | 349.73 | 47.34 | 128.67 |
| 46. | 30 nov. 2022 | 6.65% | 5.38% | 29.30 | 18.23 | 23.11 |
| 47. | 31 dic. 2022 | -8.30% | -5.90% | 90.96 | 49.04 | 66.79 |
| 48. | 31 ene. 2023 | -3.90% | 6.18% | 26.42 | 25.70 | -26.06 |
| 49. | 28 feb. 2023 | -7.37% | -2.61% | 74.21 | 13.82 | 32.02 |
| 50. | 31 mar. 2023 | 4.36% | 3.51% | 9.70 | 5.76 | 7.47 |
| 51. | 30 abr. 2023 | -0.83% | 1.46% | 4.30 | 0.13 | -0.74 |
| 52. | 31 may. 2023 | -7.07% | 0.25% | 69.15 | 0.74 | 7.13 |
| 53. | 30 jun. 2023 | 0.62% | 4.71% | 0.38 | 13.02 | -2.24 |
| 54. | 31 jul. 2023 | 5.46% | 4.85% | 17.83 | 13.99 | 15.79 |
| 55. | 31 ago. 2023 | 10.39% | -1.77% | 83.64 | 8.28 | -26.32 |
| 56. | 30 sept. 2023 | 4.85% | -4.87% | 12.99 | 35.73 | -21.54 |
| 57. | 31 oct. 2023 | -4.86% | -2.20% | 37.22 | 10.92 | 20.16 |
| 58. | 30 nov. 2023 | 6.28% | 8.92% | 25.44 | 61.03 | 39.40 |
| 59. | 31 dic. 2023 | 6.82% | 4.42% | 31.08 | 11.00 | 18.49 |
| Total (Σ): | 2,927.75 | 1,634.30 | 1,013.07 | |||
Mostrar todo
VarianzaAMGN = Σ(RAMGN,t–RAMGN)2 ÷ (59 – 1)
= 2,927.75 ÷ (59 – 1)
= 50.48
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaAMGN, S&P 500 = Σ(RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,013.07 ÷ (59 – 1)
= 17.47
Estimación sistemática del riesgo (β)
| VarianzaAMGN | 50.48 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaAMGN, S&P 500 | 17.47 |
| Coeficiente de correlaciónAMGN, S&P 5001 | 0.46 |
| βAMGN2 | 0.62 |
| αAMGN3 | 0.56% |
Cálculos
1 Coeficiente de correlaciónAMGN, S&P 500
= CovarianzaAMGN, S&P 500 ÷ (Desviación estándarAMGN × Desviación estándarS&P 500)
= 17.47 ÷ (7.10% × 5.31%)
= 0.46
2 βAMGN
= CovarianzaAMGN, S&P 500 ÷ VarianzaS&P 500
= 17.47 ÷ 28.18
= 0.62
3 αAMGN
= PromedioAMGN – βAMGN × PromedioS&P 500
= 1.24% – 0.62 × 1.11%
= 0.56%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.56% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.77% |
| Riesgo sistemático de Amgen acciones ordinarias | βAMGN | 0.62 |
| Tasa de rendimiento esperada de las acciones ordinarias de Amgen3 | E(RAMGN) | 10.27% |
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(RAMGN) = RF + βAMGN [E(RM) – RF]
= 4.56% + 0.62 [13.77% – 4.56%]
= 10.27%