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 Boeing.
Tasas de retorno
Boeing Co., tasas mensuales de retorno
| Boeing Co. (BA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioBA,t1 | DividendoBA,t1 | RBA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $163.42 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $180.23 | $1.42 | 11.16% | 2,363.64 | 3.72% |
| 2. | 31 mar. 2017 | $176.86 | -1.87% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $184.83 | 4.51% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $197.85 | -4.43% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $201.32 | 1.75% | 4,766.18 | 4.36% | |
| Promedio (R): | 1.28% | 1.36% | ||||
| Desviación estándar: | 12.54% | 4.48% | ||||
| Boeing Co. (BA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioBA,t1 | DividendoBA,t1 | RBA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $163.42 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $180.23 | $1.42 | 11.16% | 2,363.64 | 3.72% |
| 2. | 31 mar. 2017 | $176.86 | -1.87% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $184.83 | 4.51% | 2,384.20 | 0.91% | |
| 4. | 31 may. 2017 | $187.63 | $1.42 | 2.28% | 2,411.80 | 1.16% |
| 5. | 30 jun. 2017 | $197.75 | 5.39% | 2,423.41 | 0.48% | |
| 6. | 31 jul. 2017 | $242.46 | 22.61% | 2,470.30 | 1.93% | |
| 7. | 31 ago. 2017 | $239.66 | $1.42 | -0.57% | 2,471.65 | 0.05% |
| 8. | 30 sept. 2017 | $254.21 | 6.07% | 2,519.36 | 1.93% | |
| 9. | 31 oct. 2017 | $257.98 | 1.48% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $276.80 | $1.42 | 7.85% | 2,647.58 | 2.81% |
| 11. | 31 dic. 2017 | $294.91 | 6.54% | 2,673.61 | 0.98% | |
| 12. | 31 ene. 2018 | $354.37 | 20.16% | 2,823.81 | 5.62% | |
| 13. | 28 feb. 2018 | $362.21 | $1.71 | 2.69% | 2,713.83 | -3.89% |
| 14. | 31 mar. 2018 | $327.88 | -9.48% | 2,640.87 | -2.69% | |
| 15. | 30 abr. 2018 | $333.56 | 1.73% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $352.16 | $1.71 | 6.09% | 2,705.27 | 2.16% |
| 17. | 30 jun. 2018 | $335.51 | -4.73% | 2,718.37 | 0.48% | |
| 18. | 31 jul. 2018 | $356.30 | 6.20% | 2,816.29 | 3.60% | |
| 19. | 31 ago. 2018 | $342.79 | $1.71 | -3.31% | 2,901.52 | 3.03% |
| 20. | 30 sept. 2018 | $371.90 | 8.49% | 2,913.98 | 0.43% | |
| 21. | 31 oct. 2018 | $354.86 | -4.58% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $346.76 | $1.71 | -1.80% | 2,760.17 | 1.79% |
| 23. | 31 dic. 2018 | $322.50 | -7.00% | 2,506.85 | -9.18% | |
| 24. | 31 ene. 2019 | $385.62 | 19.57% | 2,704.10 | 7.87% | |
| 25. | 28 feb. 2019 | $439.96 | $2.055 | 14.62% | 2,784.49 | 2.97% |
| 26. | 31 mar. 2019 | $381.42 | -13.31% | 2,834.40 | 1.79% | |
| 27. | 30 abr. 2019 | $377.69 | -0.98% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $341.61 | $2.055 | -9.01% | 2,752.06 | -6.58% |
| 29. | 30 jun. 2019 | $364.01 | 6.56% | 2,941.76 | 6.89% | |
| 30. | 31 jul. 2019 | $341.18 | -6.27% | 2,980.38 | 1.31% | |
| 31. | 31 ago. 2019 | $364.09 | $2.055 | 7.32% | 2,926.46 | -1.81% |
| 32. | 30 sept. 2019 | $380.47 | 4.50% | 2,976.74 | 1.72% | |
| 33. | 31 oct. 2019 | $339.91 | -10.66% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $366.18 | $2.055 | 8.33% | 3,140.98 | 3.40% |
| 35. | 31 dic. 2019 | $325.76 | -11.04% | 3,230.78 | 2.86% | |
| 36. | 31 ene. 2020 | $318.27 | -2.30% | 3,225.52 | -0.16% | |
| 37. | 29 feb. 2020 | $275.11 | $2.055 | -12.92% | 2,954.22 | -8.41% |
| 38. | 31 mar. 2020 | $149.14 | -45.79% | 2,584.59 | -12.51% | |
| 39. | 30 abr. 2020 | $141.02 | -5.44% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $145.85 | 3.43% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $183.30 | 25.68% | 3,100.29 | 1.84% | |
| 42. | 31 jul. 2020 | $158.00 | -13.80% | 3,271.12 | 5.51% | |
| 43. | 31 ago. 2020 | $171.82 | 8.75% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $165.26 | -3.82% | 3,363.00 | -3.92% | |
| 45. | 31 oct. 2020 | $144.39 | -12.63% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $210.71 | 45.93% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $214.06 | 1.59% | 3,756.07 | 3.71% | |
| 48. | 31 ene. 2021 | $194.19 | -9.28% | 3,714.24 | -1.11% | |
| 49. | 28 feb. 2021 | $212.01 | 9.18% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $254.72 | 20.15% | 3,972.89 | 4.24% | |
| 51. | 30 abr. 2021 | $234.31 | -8.01% | 4,181.17 | 5.24% | |
| 52. | 31 may. 2021 | $247.02 | 5.42% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $239.56 | -3.02% | 4,297.50 | 2.22% | |
| 54. | 31 jul. 2021 | $226.48 | -5.46% | 4,395.26 | 2.27% | |
| 55. | 31 ago. 2021 | $219.50 | -3.08% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $219.94 | 0.20% | 4,307.54 | -4.76% | |
| 57. | 31 oct. 2021 | $207.03 | -5.87% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $197.85 | -4.43% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $201.32 | 1.75% | 4,766.18 | 4.36% | |
| Promedio (R): | 1.28% | 1.36% | ||||
| Desviación estándar: | 12.54% | 4.48% | ||||
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de BA 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
Boeing Co., cálculo de varianza y covarianza de rendimientos
| t | Fecha | RBA,t | RS&P 500,t | (RBA,t–RBA)2 | (RS&P 500,t–RS&P 500)2 | (RBA,t–RBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 11.16% | 3.72% | 97.44 | 5.58 | 23.31 |
| 2. | 31 mar. 2017 | -1.87% | -0.04% | 9.95 | 1.95 | 4.41 |
| 3. | 30 abr. 2017 | 4.51% | 0.91% | 10.38 | 0.20 | -1.45 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -4.43% | -0.83% | 32.70 | 4.80 | 12.53 |
| 59. | 31 dic. 2021 | 1.75% | 4.36% | 0.22 | 9.02 | 1.41 |
| Total (Σ): | 9,116.17 | 1,164.17 | 1,752.14 | |||
| t | Fecha | RBA,t | RS&P 500,t | (RBA,t–RBA)2 | (RS&P 500,t–RS&P 500)2 | (RBA,t–RBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 11.16% | 3.72% | 97.44 | 5.58 | 23.31 |
| 2. | 31 mar. 2017 | -1.87% | -0.04% | 9.95 | 1.95 | 4.41 |
| 3. | 30 abr. 2017 | 4.51% | 0.91% | 10.38 | 0.20 | -1.45 |
| 4. | 31 may. 2017 | 2.28% | 1.16% | 1.00 | 0.04 | -0.20 |
| 5. | 30 jun. 2017 | 5.39% | 0.48% | 16.89 | 0.77 | -3.60 |
| 6. | 31 jul. 2017 | 22.61% | 1.93% | 454.76 | 0.33 | 12.30 |
| 7. | 31 ago. 2017 | -0.57% | 0.05% | 3.44 | 1.70 | 2.42 |
| 8. | 30 sept. 2017 | 6.07% | 1.93% | 22.91 | 0.33 | 2.74 |
| 9. | 31 oct. 2017 | 1.48% | 2.22% | 0.04 | 0.74 | 0.17 |
| 10. | 30 nov. 2017 | 7.85% | 2.81% | 43.05 | 2.10 | 9.52 |
| 11. | 31 dic. 2017 | 6.54% | 0.98% | 27.65 | 0.14 | -1.97 |
| 12. | 31 ene. 2018 | 20.16% | 5.62% | 356.37 | 18.15 | 80.42 |
| 13. | 28 feb. 2018 | 2.69% | -3.89% | 1.99 | 27.59 | -7.41 |
| 14. | 31 mar. 2018 | -9.48% | -2.69% | 115.83 | 16.37 | 43.55 |
| 15. | 30 abr. 2018 | 1.73% | 0.27% | 0.20 | 1.18 | -0.49 |
| 16. | 31 may. 2018 | 6.09% | 2.16% | 23.08 | 0.64 | 3.86 |
| 17. | 30 jun. 2018 | -4.73% | 0.48% | 36.15 | 0.76 | 5.25 |
| 18. | 31 jul. 2018 | 6.20% | 3.60% | 24.13 | 5.04 | 11.02 |
| 19. | 31 ago. 2018 | -3.31% | 3.03% | 21.12 | 2.78 | -7.67 |
| 20. | 30 sept. 2018 | 8.49% | 0.43% | 51.95 | 0.86 | -6.69 |
| 21. | 31 oct. 2018 | -4.58% | -6.94% | 34.41 | 68.86 | 48.68 |
| 22. | 30 nov. 2018 | -1.80% | 1.79% | 9.52 | 0.18 | -1.32 |
| 23. | 31 dic. 2018 | -7.00% | -9.18% | 68.57 | 111.00 | 87.24 |
| 24. | 31 ene. 2019 | 19.57% | 7.87% | 334.44 | 42.39 | 119.06 |
| 25. | 28 feb. 2019 | 14.62% | 2.97% | 177.96 | 2.61 | 21.54 |
| 26. | 31 mar. 2019 | -13.31% | 1.79% | 212.87 | 0.19 | -6.34 |
| 27. | 30 abr. 2019 | -0.98% | 3.93% | 5.12 | 6.62 | -5.82 |
| 28. | 31 may. 2019 | -9.01% | -6.58% | 105.95 | 62.97 | 81.68 |
| 29. | 30 jun. 2019 | 6.56% | 6.89% | 27.80 | 30.64 | 29.19 |
| 30. | 31 jul. 2019 | -6.27% | 1.31% | 57.09 | 0.00 | 0.34 |
| 31. | 31 ago. 2019 | 7.32% | -1.81% | 36.40 | 10.03 | -19.11 |
| 32. | 30 sept. 2019 | 4.50% | 1.72% | 10.33 | 0.13 | 1.16 |
| 33. | 31 oct. 2019 | -10.66% | 2.04% | 142.68 | 0.47 | -8.19 |
| 34. | 30 nov. 2019 | 8.33% | 3.40% | 49.69 | 4.19 | 14.43 |
| 35. | 31 dic. 2019 | -11.04% | 2.86% | 151.85 | 2.25 | -18.50 |
| 36. | 31 ene. 2020 | -2.30% | -0.16% | 12.84 | 2.31 | 5.45 |
| 37. | 29 feb. 2020 | -12.92% | -8.41% | 201.62 | 95.43 | 138.71 |
| 38. | 31 mar. 2020 | -45.79% | -12.51% | 2,215.89 | 192.37 | 652.90 |
| 39. | 30 abr. 2020 | -5.44% | 12.68% | 45.28 | 128.29 | -76.21 |
| 40. | 31 may. 2020 | 3.43% | 4.53% | 4.58 | 10.05 | 6.79 |
| 41. | 30 jun. 2020 | 25.68% | 1.84% | 595.01 | 0.23 | 11.73 |
| 42. | 31 jul. 2020 | -13.80% | 5.51% | 227.61 | 17.24 | -62.64 |
| 43. | 31 ago. 2020 | 8.75% | 7.01% | 55.69 | 31.91 | 42.15 |
| 44. | 30 sept. 2020 | -3.82% | -3.92% | 26.03 | 27.89 | 26.94 |
| 45. | 31 oct. 2020 | -12.63% | -2.77% | 193.57 | 17.01 | 57.38 |
| 46. | 30 nov. 2020 | 45.93% | 10.75% | 1,993.34 | 88.30 | 419.53 |
| 47. | 31 dic. 2020 | 1.59% | 3.71% | 0.09 | 5.54 | 0.72 |
| 48. | 31 ene. 2021 | -9.28% | -1.11% | 111.66 | 6.11 | 26.12 |
| 49. | 28 feb. 2021 | 9.18% | 2.61% | 62.29 | 1.57 | 9.88 |
| 50. | 31 mar. 2021 | 20.15% | 4.24% | 355.74 | 8.33 | 54.43 |
| 51. | 30 abr. 2021 | -8.01% | 5.24% | 86.43 | 15.09 | -36.12 |
| 52. | 31 may. 2021 | 5.42% | 0.55% | 17.14 | 0.65 | -3.35 |
| 53. | 30 jun. 2021 | -3.02% | 2.22% | 18.53 | 0.75 | -3.72 |
| 54. | 31 jul. 2021 | -5.46% | 2.27% | 45.49 | 0.84 | -6.18 |
| 55. | 31 ago. 2021 | -3.08% | 2.90% | 19.06 | 2.38 | -6.73 |
| 56. | 30 sept. 2021 | 0.20% | -4.76% | 1.17 | 37.39 | 6.63 |
| 57. | 31 oct. 2021 | -5.87% | 6.91% | 51.18 | 30.87 | -39.75 |
| 58. | 30 nov. 2021 | -4.43% | -0.83% | 32.70 | 4.80 | 12.53 |
| 59. | 31 dic. 2021 | 1.75% | 4.36% | 0.22 | 9.02 | 1.41 |
| Total (Σ): | 9,116.17 | 1,164.17 | 1,752.14 | |||
Mostrar todo
VarianzaBA = Σ(RBA,t–RBA)2 ÷ (59 – 1)
= 9,116.17 ÷ (59 – 1)
= 157.18
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaBA, S&P 500 = Σ(RBA,t–RBA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,752.14 ÷ (59 – 1)
= 30.21
Estimación sistemática del riesgo (β)
| VarianzaBA | 157.18 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaBA, S&P 500 | 30.21 |
| Coeficiente de correlaciónBA, S&P 5001 | 0.54 |
| βBA2 | 1.51 |
| αBA3 | -0.76% |
Cálculos
1 Coeficiente de correlaciónBA, S&P 500
= CovarianzaBA, S&P 500 ÷ (Desviación estándarBA × Desviación estándarS&P 500)
= 30.21 ÷ (12.54% × 4.48%)
= 0.54
2 βBA
= CovarianzaBA, S&P 500 ÷ VarianzaS&P 500
= 30.21 ÷ 20.07
= 1.51
3 αBA
= PromedioBA – βBA × PromedioS&P 500
= 1.28% – 1.51 × 1.36%
= -0.76%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.24% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.24% |
| Riesgo sistemático de acciones ordinarias Boeing | βBA | 1.51 |
| Tasa de rendimiento esperada de las acciones ordinarias de Boeing3 | E(RBA) | 16.79% |
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(RBA) = RF + βBA [E(RM) – RF]
= 3.24% + 1.51 [12.24% – 3.24%]
= 16.79%