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 Altria.
Tasas de retorno
Altria Group Inc., tasas mensuales de retorno
| Altria Group Inc. (MO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMO,t1 | DividendoMO,t1 | RMO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $71.18 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $74.92 | 5.25% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $71.42 | $0.61 | -3.86% | 2,362.72 | -0.04% |
| 3. | 30 abr. 2017 | $71.78 | 0.50% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $42.64 | -3.33% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $47.39 | $0.90 | 13.25% | 4,766.18 | 4.36% |
| Promedio (R): | 0.09% | 1.36% | ||||
| Desviación estándar: | 7.02% | 4.48% | ||||
| Altria Group Inc. (MO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioMO,t1 | DividendoMO,t1 | RMO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $71.18 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $74.92 | 5.25% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $71.42 | $0.61 | -3.86% | 2,362.72 | -0.04% |
| 3. | 30 abr. 2017 | $71.78 | 0.50% | 2,384.20 | 0.91% | |
| 4. | 31 may. 2017 | $75.44 | 5.10% | 2,411.80 | 1.16% | |
| 5. | 30 jun. 2017 | $74.47 | $0.61 | -0.48% | 2,423.41 | 0.48% |
| 6. | 31 jul. 2017 | $64.97 | -12.76% | 2,470.30 | 1.93% | |
| 7. | 31 ago. 2017 | $63.40 | -2.42% | 2,471.65 | 0.05% | |
| 8. | 30 sept. 2017 | $63.42 | $0.66 | 1.07% | 2,519.36 | 1.93% |
| 9. | 31 oct. 2017 | $64.22 | 1.26% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $67.83 | 5.62% | 2,647.58 | 2.81% | |
| 11. | 31 dic. 2017 | $71.41 | $0.66 | 6.25% | 2,673.61 | 0.98% |
| 12. | 31 ene. 2018 | $70.34 | -1.50% | 2,823.81 | 5.62% | |
| 13. | 28 feb. 2018 | $62.95 | -10.51% | 2,713.83 | -3.89% | |
| 14. | 31 mar. 2018 | $62.32 | $0.70 | 0.11% | 2,640.87 | -2.69% |
| 15. | 30 abr. 2018 | $56.11 | -9.96% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $55.74 | -0.66% | 2,705.27 | 2.16% | |
| 17. | 30 jun. 2018 | $56.79 | $0.70 | 3.14% | 2,718.37 | 0.48% |
| 18. | 31 jul. 2018 | $58.68 | 3.33% | 2,816.29 | 3.60% | |
| 19. | 31 ago. 2018 | $58.52 | -0.27% | 2,901.52 | 3.03% | |
| 20. | 30 sept. 2018 | $60.31 | $0.80 | 4.43% | 2,913.98 | 0.43% |
| 21. | 31 oct. 2018 | $65.04 | 7.84% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $54.83 | -15.70% | 2,760.17 | 1.79% | |
| 23. | 31 dic. 2018 | $49.39 | $0.80 | -8.46% | 2,506.85 | -9.18% |
| 24. | 31 ene. 2019 | $49.35 | -0.08% | 2,704.10 | 7.87% | |
| 25. | 28 feb. 2019 | $52.41 | 6.20% | 2,784.49 | 2.97% | |
| 26. | 31 mar. 2019 | $57.43 | $0.80 | 11.10% | 2,834.40 | 1.79% |
| 27. | 30 abr. 2019 | $54.33 | -5.40% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $49.06 | -9.70% | 2,752.06 | -6.58% | |
| 29. | 30 jun. 2019 | $47.35 | $0.80 | -1.85% | 2,941.76 | 6.89% |
| 30. | 31 jul. 2019 | $47.07 | -0.59% | 2,980.38 | 1.31% | |
| 31. | 31 ago. 2019 | $43.74 | -7.07% | 2,926.46 | -1.81% | |
| 32. | 30 sept. 2019 | $40.90 | $0.84 | -4.57% | 2,976.74 | 1.72% |
| 33. | 31 oct. 2019 | $44.79 | 9.51% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $49.70 | 10.96% | 3,140.98 | 3.40% | |
| 35. | 31 dic. 2019 | $49.91 | $0.84 | 2.11% | 3,230.78 | 2.86% |
| 36. | 31 ene. 2020 | $47.53 | -4.77% | 3,225.52 | -0.16% | |
| 37. | 29 feb. 2020 | $40.37 | -15.06% | 2,954.22 | -8.41% | |
| 38. | 31 mar. 2020 | $38.67 | $0.84 | -2.13% | 2,584.59 | -12.51% |
| 39. | 30 abr. 2020 | $39.25 | 1.50% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $39.05 | -0.51% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $39.25 | $0.84 | 2.66% | 3,100.29 | 1.84% |
| 42. | 31 jul. 2020 | $41.15 | 4.84% | 3,271.12 | 5.51% | |
| 43. | 31 ago. 2020 | $43.74 | 6.29% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $38.64 | $0.86 | -9.69% | 3,363.00 | -3.92% |
| 45. | 31 oct. 2020 | $36.08 | -6.63% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $39.83 | 10.39% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $41.00 | $0.86 | 5.10% | 3,756.07 | 3.71% |
| 48. | 31 ene. 2021 | $41.08 | 0.20% | 3,714.24 | -1.11% | |
| 49. | 28 feb. 2021 | $43.60 | 6.13% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $51.16 | $0.86 | 19.31% | 3,972.89 | 4.24% |
| 51. | 30 abr. 2021 | $47.75 | -6.67% | 4,181.17 | 5.24% | |
| 52. | 31 may. 2021 | $49.22 | 3.08% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $47.68 | $0.86 | -1.38% | 4,297.50 | 2.22% |
| 54. | 31 jul. 2021 | $48.04 | 0.76% | 4,395.26 | 2.27% | |
| 55. | 31 ago. 2021 | $50.23 | 4.56% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $45.52 | $0.90 | -7.59% | 4,307.54 | -4.76% |
| 57. | 31 oct. 2021 | $44.11 | -3.10% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $42.64 | -3.33% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $47.39 | $0.90 | 13.25% | 4,766.18 | 4.36% |
| Promedio (R): | 0.09% | 1.36% | ||||
| Desviación estándar: | 7.02% | 4.48% | ||||
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de MO 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
Altria Group Inc., cálculo de varianza y covarianza de rendimientos
| t | Fecha | RMO,t | RS&P 500,t | (RMO,t–RMO)2 | (RS&P 500,t–RS&P 500)2 | (RMO,t–RMO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 5.25% | 3.72% | 26.69 | 5.58 | 12.20 |
| 2. | 31 mar. 2017 | -3.86% | -0.04% | 15.56 | 1.95 | 5.51 |
| 3. | 30 abr. 2017 | 0.50% | 0.91% | 0.17 | 0.20 | -0.19 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -3.33% | -0.83% | 11.70 | 4.80 | 7.49 |
| 59. | 31 dic. 2021 | 13.25% | 4.36% | 173.26 | 9.02 | 39.53 |
| Total (Σ): | 2,858.17 | 1,164.17 | 778.25 | |||
| t | Fecha | RMO,t | RS&P 500,t | (RMO,t–RMO)2 | (RS&P 500,t–RS&P 500)2 | (RMO,t–RMO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 5.25% | 3.72% | 26.69 | 5.58 | 12.20 |
| 2. | 31 mar. 2017 | -3.86% | -0.04% | 15.56 | 1.95 | 5.51 |
| 3. | 30 abr. 2017 | 0.50% | 0.91% | 0.17 | 0.20 | -0.19 |
| 4. | 31 may. 2017 | 5.10% | 1.16% | 25.11 | 0.04 | -1.00 |
| 5. | 30 jun. 2017 | -0.48% | 0.48% | 0.32 | 0.77 | 0.50 |
| 6. | 31 jul. 2017 | -12.76% | 1.93% | 164.98 | 0.33 | -7.41 |
| 7. | 31 ago. 2017 | -2.42% | 0.05% | 6.27 | 1.70 | 3.26 |
| 8. | 30 sept. 2017 | 1.07% | 1.93% | 0.97 | 0.33 | 0.56 |
| 9. | 31 oct. 2017 | 1.26% | 2.22% | 1.38 | 0.74 | 1.01 |
| 10. | 30 nov. 2017 | 5.62% | 2.81% | 30.62 | 2.10 | 8.03 |
| 11. | 31 dic. 2017 | 6.25% | 0.98% | 37.98 | 0.14 | -2.31 |
| 12. | 31 ene. 2018 | -1.50% | 5.62% | 2.52 | 18.15 | -6.76 |
| 13. | 28 feb. 2018 | -10.51% | -3.89% | 112.23 | 27.59 | 55.65 |
| 14. | 31 mar. 2018 | 0.11% | -2.69% | 0.00 | 16.37 | -0.09 |
| 15. | 30 abr. 2018 | -9.96% | 0.27% | 101.05 | 1.18 | 10.92 |
| 16. | 31 may. 2018 | -0.66% | 2.16% | 0.56 | 0.64 | -0.60 |
| 17. | 30 jun. 2018 | 3.14% | 0.48% | 9.31 | 0.76 | -2.67 |
| 18. | 31 jul. 2018 | 3.33% | 3.60% | 10.50 | 5.04 | 7.27 |
| 19. | 31 ago. 2018 | -0.27% | 3.03% | 0.13 | 2.78 | -0.60 |
| 20. | 30 sept. 2018 | 4.43% | 0.43% | 18.82 | 0.86 | -4.03 |
| 21. | 31 oct. 2018 | 7.84% | -6.94% | 60.14 | 68.86 | -64.35 |
| 22. | 30 nov. 2018 | -15.70% | 1.79% | 249.19 | 0.18 | -6.76 |
| 23. | 31 dic. 2018 | -8.46% | -9.18% | 73.11 | 111.00 | 90.08 |
| 24. | 31 ene. 2019 | -0.08% | 7.87% | 0.03 | 42.39 | -1.10 |
| 25. | 28 feb. 2019 | 6.20% | 2.97% | 37.37 | 2.61 | 9.87 |
| 26. | 31 mar. 2019 | 11.10% | 1.79% | 121.37 | 0.19 | 4.79 |
| 27. | 30 abr. 2019 | -5.40% | 3.93% | 30.09 | 6.62 | -14.12 |
| 28. | 31 may. 2019 | -9.70% | -6.58% | 95.80 | 62.97 | 77.67 |
| 29. | 30 jun. 2019 | -1.85% | 6.89% | 3.77 | 30.64 | -10.75 |
| 30. | 31 jul. 2019 | -0.59% | 1.31% | 0.46 | 0.00 | 0.03 |
| 31. | 31 ago. 2019 | -7.07% | -1.81% | 51.30 | 10.03 | 22.68 |
| 32. | 30 sept. 2019 | -4.57% | 1.72% | 21.72 | 0.13 | -1.68 |
| 33. | 31 oct. 2019 | 9.51% | 2.04% | 88.80 | 0.47 | 6.46 |
| 34. | 30 nov. 2019 | 10.96% | 3.40% | 118.25 | 4.19 | 22.26 |
| 35. | 31 dic. 2019 | 2.11% | 2.86% | 4.10 | 2.25 | 3.04 |
| 36. | 31 ene. 2020 | -4.77% | -0.16% | 23.58 | 2.31 | 7.39 |
| 37. | 29 feb. 2020 | -15.06% | -8.41% | 229.58 | 95.43 | 148.02 |
| 38. | 31 mar. 2020 | -2.13% | -12.51% | 4.92 | 192.37 | 30.76 |
| 39. | 30 abr. 2020 | 1.50% | 12.68% | 1.99 | 128.29 | 15.99 |
| 40. | 31 may. 2020 | -0.51% | 4.53% | 0.36 | 10.05 | -1.89 |
| 41. | 30 jun. 2020 | 2.66% | 1.84% | 6.63 | 0.23 | 1.24 |
| 42. | 31 jul. 2020 | 4.84% | 5.51% | 22.59 | 17.24 | 19.74 |
| 43. | 31 ago. 2020 | 6.29% | 7.01% | 38.52 | 31.91 | 35.06 |
| 44. | 30 sept. 2020 | -9.69% | -3.92% | 95.68 | 27.89 | 51.65 |
| 45. | 31 oct. 2020 | -6.63% | -2.77% | 45.06 | 17.01 | 27.69 |
| 46. | 30 nov. 2020 | 10.39% | 10.75% | 106.21 | 88.30 | 96.84 |
| 47. | 31 dic. 2020 | 5.10% | 3.71% | 25.09 | 5.54 | 11.79 |
| 48. | 31 ene. 2021 | 0.20% | -1.11% | 0.01 | 6.11 | -0.27 |
| 49. | 28 feb. 2021 | 6.13% | 2.61% | 36.56 | 1.57 | 7.57 |
| 50. | 31 mar. 2021 | 19.31% | 4.24% | 369.57 | 8.33 | 55.48 |
| 51. | 30 abr. 2021 | -6.67% | 5.24% | 45.60 | 15.09 | -26.23 |
| 52. | 31 may. 2021 | 3.08% | 0.55% | 8.94 | 0.65 | -2.42 |
| 53. | 30 jun. 2021 | -1.38% | 2.22% | 2.16 | 0.75 | -1.27 |
| 54. | 31 jul. 2021 | 0.76% | 2.27% | 0.45 | 0.84 | 0.61 |
| 55. | 31 ago. 2021 | 4.56% | 2.90% | 19.99 | 2.38 | 6.89 |
| 56. | 30 sept. 2021 | -7.59% | -4.76% | 58.87 | 37.39 | 46.92 |
| 57. | 31 oct. 2021 | -3.10% | 6.91% | 10.15 | 30.87 | -17.70 |
| 58. | 30 nov. 2021 | -3.33% | -0.83% | 11.70 | 4.80 | 7.49 |
| 59. | 31 dic. 2021 | 13.25% | 4.36% | 173.26 | 9.02 | 39.53 |
| Total (Σ): | 2,858.17 | 1,164.17 | 778.25 | |||
Mostrar todo
VarianzaMO = Σ(RMO,t–RMO)2 ÷ (59 – 1)
= 2,858.17 ÷ (59 – 1)
= 49.28
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaMO, S&P 500 = Σ(RMO,t–RMO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 778.25 ÷ (59 – 1)
= 13.42
Estimación sistemática del riesgo (β)
| VarianzaMO | 49.28 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaMO, S&P 500 | 13.42 |
| Coeficiente de correlaciónMO, S&P 5001 | 0.43 |
| βMO2 | 0.67 |
| αMO3 | -0.82% |
Cálculos
1 Coeficiente de correlaciónMO, S&P 500
= CovarianzaMO, S&P 500 ÷ (Desviación estándarMO × Desviación estándarS&P 500)
= 13.42 ÷ (7.02% × 4.48%)
= 0.43
2 βMO
= CovarianzaMO, S&P 500 ÷ VarianzaS&P 500
= 13.42 ÷ 20.07
= 0.67
3 αMO
= PromedioMO – βMO × PromedioS&P 500
= 0.09% – 0.67 × 1.36%
= -0.82%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.99% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.76% |
| Riesgo sistemático de acciones ordinarias Altria | βMO | 0.67 |
| Tasa de rendimiento esperada de las acciones ordinarias de Altria3 | E(RMO) | 9.85% |
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(RMO) = RF + βMO [E(RM) – RF]
= 3.99% + 0.67 [12.76% – 3.99%]
= 9.85%