Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida de los activos de riesgo, como las acciones ordinarias de AbbVie.
Tasas de retorno
AbbVie Inc., tasas de rendimiento mensuales
| AbbVie Inc. (ABBV) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioABBV,t1 | DividendoABBV,t1 | RABBV,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $61.11 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $61.84 | 1.19% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $65.16 | 5.37% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $65.94 | $0.64 | 2.18% | 2,384.20 | 0.91% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $115.28 | 0.53% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $135.40 | 17.45% | 4,766.18 | 4.36% | |
| Promedio (R): | 2.08% | 1.36% | ||||
| Desviación estándar: | 8.34% | 4.48% | ||||
| AbbVie Inc. (ABBV) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioABBV,t1 | DividendoABBV,t1 | RABBV,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $61.11 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $61.84 | 1.19% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $65.16 | 5.37% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $65.94 | $0.64 | 2.18% | 2,384.20 | 0.91% |
| 4. | 31 may. 2017 | $66.02 | 0.12% | 2,411.80 | 1.16% | |
| 5. | 30 jun. 2017 | $72.51 | 9.83% | 2,423.41 | 0.48% | |
| 6. | 31 jul. 2017 | $69.91 | $0.64 | -2.70% | 2,470.30 | 1.93% |
| 7. | 31 ago. 2017 | $75.30 | 7.71% | 2,471.65 | 0.05% | |
| 8. | 30 sept. 2017 | $88.86 | 18.01% | 2,519.36 | 1.93% | |
| 9. | 31 oct. 2017 | $90.25 | $0.64 | 2.28% | 2,575.26 | 2.22% |
| 10. | 30 nov. 2017 | $96.92 | 7.39% | 2,647.58 | 2.81% | |
| 11. | 31 dic. 2017 | $96.71 | -0.22% | 2,673.61 | 0.98% | |
| 12. | 31 ene. 2018 | $112.22 | $0.71 | 16.77% | 2,823.81 | 5.62% |
| 13. | 28 feb. 2018 | $115.83 | 3.22% | 2,713.83 | -3.89% | |
| 14. | 31 mar. 2018 | $94.65 | -18.29% | 2,640.87 | -2.69% | |
| 15. | 30 abr. 2018 | $96.55 | $0.96 | 3.02% | 2,648.05 | 0.27% |
| 16. | 31 may. 2018 | $98.94 | 2.48% | 2,705.27 | 2.16% | |
| 17. | 30 jun. 2018 | $92.65 | -6.36% | 2,718.37 | 0.48% | |
| 18. | 31 jul. 2018 | $92.23 | $0.96 | 0.58% | 2,816.29 | 3.60% |
| 19. | 31 ago. 2018 | $95.98 | 4.07% | 2,901.52 | 3.03% | |
| 20. | 30 sept. 2018 | $94.58 | -1.46% | 2,913.98 | 0.43% | |
| 21. | 31 oct. 2018 | $77.85 | $0.96 | -16.67% | 2,711.74 | -6.94% |
| 22. | 30 nov. 2018 | $94.27 | 21.09% | 2,760.17 | 1.79% | |
| 23. | 31 dic. 2018 | $92.19 | -2.21% | 2,506.85 | -9.18% | |
| 24. | 31 ene. 2019 | $80.29 | $1.07 | -11.75% | 2,704.10 | 7.87% |
| 25. | 28 feb. 2019 | $79.24 | -1.31% | 2,784.49 | 2.97% | |
| 26. | 31 mar. 2019 | $80.59 | 1.70% | 2,834.40 | 1.79% | |
| 27. | 30 abr. 2019 | $79.39 | $1.07 | -0.16% | 2,945.83 | 3.93% |
| 28. | 31 may. 2019 | $76.71 | -3.38% | 2,752.06 | -6.58% | |
| 29. | 30 jun. 2019 | $72.72 | -5.20% | 2,941.76 | 6.89% | |
| 30. | 31 jul. 2019 | $66.62 | $1.07 | -6.92% | 2,980.38 | 1.31% |
| 31. | 31 ago. 2019 | $65.74 | -1.32% | 2,926.46 | -1.81% | |
| 32. | 30 sept. 2019 | $75.72 | 15.18% | 2,976.74 | 1.72% | |
| 33. | 31 oct. 2019 | $79.55 | $1.07 | 6.47% | 3,037.56 | 2.04% |
| 34. | 30 nov. 2019 | $87.73 | 10.28% | 3,140.98 | 3.40% | |
| 35. | 31 dic. 2019 | $88.54 | 0.92% | 3,230.78 | 2.86% | |
| 36. | 31 ene. 2020 | $81.02 | $1.18 | -7.16% | 3,225.52 | -0.16% |
| 37. | 29 feb. 2020 | $85.71 | 5.79% | 2,954.22 | -8.41% | |
| 38. | 31 mar. 2020 | $76.19 | -11.11% | 2,584.59 | -12.51% | |
| 39. | 30 abr. 2020 | $82.20 | $1.18 | 9.44% | 2,912.43 | 12.68% |
| 40. | 31 may. 2020 | $92.67 | 12.74% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $98.18 | 5.95% | 3,100.29 | 1.84% | |
| 42. | 31 jul. 2020 | $94.91 | $1.18 | -2.13% | 3,271.12 | 5.51% |
| 43. | 31 ago. 2020 | $95.77 | 0.91% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $87.59 | -8.54% | 3,363.00 | -3.92% | |
| 45. | 31 oct. 2020 | $85.10 | $1.18 | -1.50% | 3,269.96 | -2.77% |
| 46. | 30 nov. 2020 | $104.58 | 22.89% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $107.15 | 2.46% | 3,756.07 | 3.71% | |
| 48. | 31 ene. 2021 | $102.48 | $1.30 | -3.15% | 3,714.24 | -1.11% |
| 49. | 28 feb. 2021 | $107.74 | 5.13% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $108.22 | 0.45% | 3,972.89 | 4.24% | |
| 51. | 30 abr. 2021 | $111.50 | $1.30 | 4.23% | 4,181.17 | 5.24% |
| 52. | 31 may. 2021 | $113.20 | 1.52% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $112.64 | -0.49% | 4,297.50 | 2.22% | |
| 54. | 31 jul. 2021 | $116.30 | $1.30 | 4.40% | 4,395.26 | 2.27% |
| 55. | 31 ago. 2021 | $120.78 | 3.85% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $107.87 | -10.69% | 4,307.54 | -4.76% | |
| 57. | 31 oct. 2021 | $114.67 | $1.30 | 7.51% | 4,605.38 | 6.91% |
| 58. | 30 nov. 2021 | $115.28 | 0.53% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $135.40 | 17.45% | 4,766.18 | 4.36% | |
| Promedio (R): | 2.08% | 1.36% | ||||
| Desviación estándar: | 8.34% | 4.48% | ||||
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de ABBV 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
AbbVie Inc., cálculo de varianza y covarianza de rendimientos
| t | Fecha | RABBV,t | RS&P 500,t | (RABBV,t–RABBV)2 | (RS&P 500,t–RS&P 500)2 | (RABBV,t–RABBV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 1.19% | 3.72% | 0.78 | 5.58 | -2.08 |
| 2. | 31 mar. 2017 | 5.37% | -0.04% | 10.85 | 1.95 | -4.60 |
| 3. | 30 abr. 2017 | 2.18% | 0.91% | 0.01 | 0.20 | -0.05 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | 0.53% | -0.83% | 2.38 | 4.80 | 3.38 |
| 59. | 31 dic. 2021 | 17.45% | 4.36% | 236.49 | 9.02 | 46.19 |
| Total (Σ): | 4,038.60 | 1,164.17 | 992.14 | |||
| t | Fecha | RABBV,t | RS&P 500,t | (RABBV,t–RABBV)2 | (RS&P 500,t–RS&P 500)2 | (RABBV,t–RABBV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 1.19% | 3.72% | 0.78 | 5.58 | -2.08 |
| 2. | 31 mar. 2017 | 5.37% | -0.04% | 10.85 | 1.95 | -4.60 |
| 3. | 30 abr. 2017 | 2.18% | 0.91% | 0.01 | 0.20 | -0.05 |
| 4. | 31 may. 2017 | 0.12% | 1.16% | 3.82 | 0.04 | 0.39 |
| 5. | 30 jun. 2017 | 9.83% | 0.48% | 60.14 | 0.77 | -6.80 |
| 6. | 31 jul. 2017 | -2.70% | 1.93% | 22.83 | 0.33 | -2.76 |
| 7. | 31 ago. 2017 | 7.71% | 0.05% | 31.75 | 1.70 | -7.34 |
| 8. | 30 sept. 2017 | 18.01% | 1.93% | 253.86 | 0.33 | 9.12 |
| 9. | 31 oct. 2017 | 2.28% | 2.22% | 0.04 | 0.74 | 0.18 |
| 10. | 30 nov. 2017 | 7.39% | 2.81% | 28.25 | 2.10 | 7.71 |
| 11. | 31 dic. 2017 | -0.22% | 0.98% | 5.25 | 0.14 | 0.86 |
| 12. | 31 ene. 2018 | 16.77% | 5.62% | 215.99 | 18.15 | 62.61 |
| 13. | 28 feb. 2018 | 3.22% | -3.89% | 1.30 | 27.59 | -6.00 |
| 14. | 31 mar. 2018 | -18.29% | -2.69% | 414.55 | 16.37 | 82.39 |
| 15. | 30 abr. 2018 | 3.02% | 0.27% | 0.90 | 1.18 | -1.03 |
| 16. | 31 may. 2018 | 2.48% | 2.16% | 0.16 | 0.64 | 0.32 |
| 17. | 30 jun. 2018 | -6.36% | 0.48% | 71.11 | 0.76 | 7.37 |
| 18. | 31 jul. 2018 | 0.58% | 3.60% | 2.23 | 5.04 | -3.35 |
| 19. | 31 ago. 2018 | 4.07% | 3.03% | 3.96 | 2.78 | 3.32 |
| 20. | 30 sept. 2018 | -1.46% | 0.43% | 12.49 | 0.86 | 3.28 |
| 21. | 31 oct. 2018 | -16.67% | -6.94% | 351.52 | 68.86 | 155.58 |
| 22. | 30 nov. 2018 | 21.09% | 1.79% | 361.64 | 0.18 | 8.14 |
| 23. | 31 dic. 2018 | -2.21% | -9.18% | 18.33 | 111.00 | 45.11 |
| 24. | 31 ene. 2019 | -11.75% | 7.87% | 191.06 | 42.39 | -89.99 |
| 25. | 28 feb. 2019 | -1.31% | 2.97% | 11.44 | 2.61 | -5.46 |
| 26. | 31 mar. 2019 | 1.70% | 1.79% | 0.14 | 0.19 | -0.16 |
| 27. | 30 abr. 2019 | -0.16% | 3.93% | 5.00 | 6.62 | -5.76 |
| 28. | 31 may. 2019 | -3.38% | -6.58% | 29.71 | 62.97 | 43.26 |
| 29. | 30 jun. 2019 | -5.20% | 6.89% | 52.95 | 30.64 | -40.28 |
| 30. | 31 jul. 2019 | -6.92% | 1.31% | 80.86 | 0.00 | 0.41 |
| 31. | 31 ago. 2019 | -1.32% | -1.81% | 11.53 | 10.03 | 10.76 |
| 32. | 30 sept. 2019 | 15.18% | 1.72% | 171.77 | 0.13 | 4.72 |
| 33. | 31 oct. 2019 | 6.47% | 2.04% | 19.33 | 0.47 | 3.01 |
| 34. | 30 nov. 2019 | 10.28% | 3.40% | 67.37 | 4.19 | 16.80 |
| 35. | 31 dic. 2019 | 0.92% | 2.86% | 1.33 | 2.25 | -1.73 |
| 36. | 31 ene. 2020 | -7.16% | -0.16% | 85.30 | 2.31 | 14.04 |
| 37. | 29 feb. 2020 | 5.79% | -8.41% | 13.79 | 95.43 | -36.28 |
| 38. | 31 mar. 2020 | -11.11% | -12.51% | 173.77 | 192.37 | 182.84 |
| 39. | 30 abr. 2020 | 9.44% | 12.68% | 54.20 | 128.29 | 83.38 |
| 40. | 31 may. 2020 | 12.74% | 4.53% | 113.68 | 10.05 | 33.80 |
| 41. | 30 jun. 2020 | 5.95% | 1.84% | 14.98 | 0.23 | 1.86 |
| 42. | 31 jul. 2020 | -2.13% | 5.51% | 17.67 | 17.24 | -17.46 |
| 43. | 31 ago. 2020 | 0.91% | 7.01% | 1.37 | 31.91 | -6.60 |
| 44. | 30 sept. 2020 | -8.54% | -3.92% | 112.71 | 27.89 | 56.06 |
| 45. | 31 oct. 2020 | -1.50% | -2.77% | 12.75 | 17.01 | 14.73 |
| 46. | 30 nov. 2020 | 22.89% | 10.75% | 433.29 | 88.30 | 195.60 |
| 47. | 31 dic. 2020 | 2.46% | 3.71% | 0.15 | 5.54 | 0.90 |
| 48. | 31 ene. 2021 | -3.15% | -1.11% | 27.25 | 6.11 | 12.90 |
| 49. | 28 feb. 2021 | 5.13% | 2.61% | 9.35 | 1.57 | 3.83 |
| 50. | 31 mar. 2021 | 0.45% | 4.24% | 2.66 | 8.33 | -4.70 |
| 51. | 30 abr. 2021 | 4.23% | 5.24% | 4.65 | 15.09 | 8.38 |
| 52. | 31 may. 2021 | 1.52% | 0.55% | 0.30 | 0.65 | 0.45 |
| 53. | 30 jun. 2021 | -0.49% | 2.22% | 6.60 | 0.75 | -2.22 |
| 54. | 31 jul. 2021 | 4.40% | 2.27% | 5.42 | 0.84 | 2.13 |
| 55. | 31 ago. 2021 | 3.85% | 2.90% | 3.16 | 2.38 | 2.74 |
| 56. | 30 sept. 2021 | -10.69% | -4.76% | 162.92 | 37.39 | 78.05 |
| 57. | 31 oct. 2021 | 7.51% | 6.91% | 29.53 | 30.87 | 30.19 |
| 58. | 30 nov. 2021 | 0.53% | -0.83% | 2.38 | 4.80 | 3.38 |
| 59. | 31 dic. 2021 | 17.45% | 4.36% | 236.49 | 9.02 | 46.19 |
| Total (Σ): | 4,038.60 | 1,164.17 | 992.14 | |||
Mostrar todo
VarianzaABBV = Σ(RABBV,t–RABBV)2 ÷ (59 – 1)
= 4,038.60 ÷ (59 – 1)
= 69.63
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaABBV, S&P 500 = Σ(RABBV,t–RABBV)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 992.14 ÷ (59 – 1)
= 17.11
Estimación sistemática del riesgo (β)
| VarianzaABBV | 69.63 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaABBV, S&P 500 | 17.11 |
| Coeficiente de correlaciónABBV, S&P 5001 | 0.46 |
| βABBV2 | 0.85 |
| αABBV3 | 0.92% |
Cálculos
1 Coeficiente de correlaciónABBV, S&P 500
= CovarianzaABBV, S&P 500 ÷ (Desviación estándarABBV × Desviación estándarS&P 500)
= 17.11 ÷ (8.34% × 4.48%)
= 0.46
2 βABBV
= CovarianzaABBV, S&P 500 ÷ VarianzaS&P 500
= 17.11 ÷ 20.07
= 0.85
3 αABBV
= PromedioABBV – βABBV × PromedioS&P 500
= 2.08% – 0.85 × 1.36%
= 0.92%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.18% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.11% |
| Riesgo sistemático de acciones ordinarias AbbVie | βABBV | 0.85 |
| Tasa de rendimiento esperada de las acciones ordinarias de AbbVie3 | E(RABBV) | 11.65% |
1 Promedio no ponderado de los rendimientos de las ofertas en todos los bonos del Tesoro de los Estados Unidos con cupón fijo pendientes, ni vencidos ni exigibles en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RABBV) = RF + βABBV [E(RM) – RF]
= 3.18% + 0.85 [13.11% – 3.18%]
= 11.65%