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 BMS.
Tasas de retorno
Bristol-Myers Squibb Co., tasas mensuales de retorno
| Bristol-Myers Squibb Co. (BMY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioBMY,t1 | DividendoBMY,t1 | RBMY,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $49.37 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $51.66 | 4.64% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $47.71 | -7.65% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $46.43 | $0.41 | -1.82% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $49.38 | -4.17% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $51.31 | 3.91% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.49% | 1.11% | ||||
| Desviación estándar: | 5.87% | 5.31% | ||||
| Bristol-Myers Squibb Co. (BMY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioBMY,t1 | DividendoBMY,t1 | RBMY,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $49.37 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $51.66 | 4.64% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $47.71 | -7.65% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $46.43 | $0.41 | -1.82% | 2,945.83 | 3.93% |
| 4. | 31 may. 2019 | $45.37 | -2.28% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $45.35 | -0.04% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $44.41 | $0.41 | -1.17% | 2,980.38 | 1.31% |
| 7. | 31 ago. 2019 | $48.07 | 8.24% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $50.71 | 5.49% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $57.37 | $0.41 | 13.94% | 3,037.56 | 2.04% |
| 10. | 30 nov. 2019 | $56.94 | -0.75% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $64.19 | 12.73% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $62.95 | $0.45 | -1.23% | 3,225.52 | -0.16% |
| 13. | 29 feb. 2020 | $59.06 | -6.18% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $55.74 | -5.62% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $60.81 | $0.45 | 9.90% | 2,912.43 | 12.68% |
| 16. | 31 may. 2020 | $59.72 | -1.79% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $58.80 | -1.54% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $58.66 | $0.45 | 0.53% | 3,271.12 | 5.51% |
| 19. | 31 ago. 2020 | $62.20 | 6.03% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $60.29 | -3.07% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $58.45 | $0.45 | -2.31% | 3,269.96 | -2.77% |
| 22. | 30 nov. 2020 | $62.40 | 6.76% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $62.03 | $0.49 | 0.19% | 3,756.07 | 3.71% |
| 24. | 31 ene. 2021 | $61.43 | -0.97% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $61.33 | -0.16% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $63.13 | $0.49 | 3.73% | 3,972.89 | 4.24% |
| 27. | 30 abr. 2021 | $62.42 | -1.12% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $65.72 | 5.29% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $66.82 | 1.67% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $67.87 | $0.49 | 2.30% | 4,395.26 | 2.27% |
| 31. | 31 ago. 2021 | $66.86 | -1.49% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $59.17 | $0.49 | -10.77% | 4,307.54 | -4.76% |
| 33. | 31 oct. 2021 | $58.40 | -1.30% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $53.63 | -8.17% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $62.35 | 16.26% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $64.89 | $0.54 | 4.94% | 4,515.55 | -5.26% |
| 37. | 28 feb. 2022 | $68.67 | 5.83% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $73.03 | $0.54 | 7.14% | 4,530.41 | 3.58% |
| 39. | 30 abr. 2022 | $75.27 | 3.07% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $75.45 | 0.24% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $77.00 | $0.54 | 2.77% | 3,785.38 | -8.39% |
| 42. | 31 jul. 2022 | $73.78 | -4.18% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $67.41 | -8.63% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $71.09 | 5.46% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $77.47 | $0.54 | 9.73% | 3,871.98 | 7.99% |
| 46. | 30 nov. 2022 | $80.28 | 3.63% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $71.95 | -10.38% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $72.65 | $0.57 | 1.77% | 4,076.60 | 6.18% |
| 49. | 28 feb. 2023 | $68.96 | -5.08% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $69.31 | 0.51% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $66.77 | $0.57 | -2.84% | 4,169.48 | 1.46% |
| 52. | 31 may. 2023 | $64.44 | -3.49% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $63.95 | -0.76% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $62.19 | $0.57 | -1.86% | 4,588.96 | 4.85% |
| 55. | 31 ago. 2023 | $61.65 | -0.87% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $58.04 | -5.86% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $51.53 | $0.57 | -10.23% | 4,193.80 | -2.20% |
| 58. | 30 nov. 2023 | $49.38 | -4.17% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $51.31 | 3.91% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.49% | 1.11% | ||||
| Desviación estándar: | 5.87% | 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 BMY 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
Bristol-Myers Squibb Co., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RBMY,t | RS&P 500,t | (RBMY,t–RBMY)2 | (RS&P 500,t–RS&P 500)2 | (RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 4.64% | 2.97% | 17.21 | 3.49 | 7.75 |
| 2. | 31 mar. 2019 | -7.65% | 1.79% | 66.20 | 0.47 | -5.59 |
| 3. | 30 abr. 2019 | -1.82% | 3.93% | 5.35 | 7.98 | -6.54 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | -4.17% | 8.92% | 21.74 | 61.03 | -36.42 |
| 59. | 31 dic. 2023 | 3.91% | 4.42% | 11.69 | 11.00 | 11.34 |
| Total (Σ): | 1,995.90 | 1,634.30 | 621.26 | |||
| t | Fecha | RBMY,t | RS&P 500,t | (RBMY,t–RBMY)2 | (RS&P 500,t–RS&P 500)2 | (RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 4.64% | 2.97% | 17.21 | 3.49 | 7.75 |
| 2. | 31 mar. 2019 | -7.65% | 1.79% | 66.20 | 0.47 | -5.59 |
| 3. | 30 abr. 2019 | -1.82% | 3.93% | 5.35 | 7.98 | -6.54 |
| 4. | 31 may. 2019 | -2.28% | -6.58% | 7.69 | 59.04 | 21.31 |
| 5. | 30 jun. 2019 | -0.04% | 6.89% | 0.29 | 33.49 | -3.09 |
| 6. | 31 jul. 2019 | -1.17% | 1.31% | 2.75 | 0.04 | -0.34 |
| 7. | 31 ago. 2019 | 8.24% | -1.81% | 60.08 | 8.50 | -22.60 |
| 8. | 30 sept. 2019 | 5.49% | 1.72% | 25.02 | 0.37 | 3.06 |
| 9. | 31 oct. 2019 | 13.94% | 2.04% | 180.96 | 0.88 | 12.61 |
| 10. | 30 nov. 2019 | -0.75% | 3.40% | 1.54 | 5.28 | -2.85 |
| 11. | 31 dic. 2019 | 12.73% | 2.86% | 149.88 | 3.07 | 21.46 |
| 12. | 31 ene. 2020 | -1.23% | -0.16% | 2.96 | 1.61 | 2.18 |
| 13. | 29 feb. 2020 | -6.18% | -8.41% | 44.48 | 90.57 | 63.47 |
| 14. | 31 mar. 2020 | -5.62% | -12.51% | 37.35 | 185.44 | 83.22 |
| 15. | 30 abr. 2020 | 9.90% | 12.68% | 88.61 | 134.06 | 108.99 |
| 16. | 31 may. 2020 | -1.79% | 4.53% | 5.21 | 11.71 | -7.81 |
| 17. | 30 jun. 2020 | -1.54% | 1.84% | 4.12 | 0.54 | -1.49 |
| 18. | 31 jul. 2020 | 0.53% | 5.51% | 0.00 | 19.40 | 0.16 |
| 19. | 31 ago. 2020 | 6.03% | 7.01% | 30.74 | 34.82 | 32.72 |
| 20. | 30 sept. 2020 | -3.07% | -3.92% | 12.68 | 25.29 | 17.91 |
| 21. | 31 oct. 2020 | -2.31% | -2.77% | 7.81 | 15.00 | 10.83 |
| 22. | 30 nov. 2020 | 6.76% | 10.75% | 39.29 | 93.10 | 60.48 |
| 23. | 31 dic. 2020 | 0.19% | 3.71% | 0.09 | 6.79 | -0.78 |
| 24. | 31 ene. 2021 | -0.97% | -1.11% | 2.12 | 4.93 | 3.23 |
| 25. | 28 feb. 2021 | -0.16% | 2.61% | 0.43 | 2.26 | -0.98 |
| 26. | 31 mar. 2021 | 3.73% | 4.24% | 10.52 | 9.85 | 10.18 |
| 27. | 30 abr. 2021 | -1.12% | 5.24% | 2.61 | 17.11 | -6.68 |
| 28. | 31 may. 2021 | 5.29% | 0.55% | 23.01 | 0.31 | -2.67 |
| 29. | 30 jun. 2021 | 1.67% | 2.22% | 1.40 | 1.24 | 1.32 |
| 30. | 31 jul. 2021 | 2.30% | 2.27% | 3.29 | 1.37 | 2.12 |
| 31. | 31 ago. 2021 | -1.49% | 2.90% | 3.91 | 3.22 | -3.55 |
| 32. | 30 sept. 2021 | -10.77% | -4.76% | 126.76 | 34.37 | 66.01 |
| 33. | 31 oct. 2021 | -1.30% | 6.91% | 3.21 | 33.74 | -10.40 |
| 34. | 30 nov. 2021 | -8.17% | -0.83% | 74.96 | 3.76 | 16.79 |
| 35. | 31 dic. 2021 | 16.26% | 4.36% | 248.68 | 10.60 | 51.34 |
| 36. | 31 ene. 2022 | 4.94% | -5.26% | 19.80 | 40.51 | -28.32 |
| 37. | 28 feb. 2022 | 5.83% | -3.14% | 28.47 | 17.99 | -22.63 |
| 38. | 31 mar. 2022 | 7.14% | 3.58% | 44.16 | 6.11 | 16.42 |
| 39. | 30 abr. 2022 | 3.07% | -8.80% | 6.64 | 98.04 | -25.52 |
| 40. | 31 may. 2022 | 0.24% | 0.01% | 0.06 | 1.21 | 0.28 |
| 41. | 30 jun. 2022 | 2.77% | -8.39% | 5.20 | 90.21 | -21.66 |
| 42. | 31 jul. 2022 | -4.18% | 9.11% | 21.83 | 64.09 | -37.40 |
| 43. | 31 ago. 2022 | -8.63% | -4.24% | 83.24 | 28.62 | 48.81 |
| 44. | 30 sept. 2022 | 5.46% | -9.34% | 24.69 | 109.11 | -51.90 |
| 45. | 31 oct. 2022 | 9.73% | 7.99% | 85.45 | 47.34 | 63.60 |
| 46. | 30 nov. 2022 | 3.63% | 5.38% | 9.84 | 18.23 | 13.39 |
| 47. | 31 dic. 2022 | -10.38% | -5.90% | 118.07 | 49.04 | 76.10 |
| 48. | 31 ene. 2023 | 1.77% | 6.18% | 1.63 | 25.70 | 6.46 |
| 49. | 28 feb. 2023 | -5.08% | -2.61% | 31.02 | 13.82 | 20.70 |
| 50. | 31 mar. 2023 | 0.51% | 3.51% | 0.00 | 5.76 | 0.04 |
| 51. | 30 abr. 2023 | -2.84% | 1.46% | 11.10 | 0.13 | -1.19 |
| 52. | 31 may. 2023 | -3.49% | 0.25% | 15.84 | 0.74 | 3.41 |
| 53. | 30 jun. 2023 | -0.76% | 4.71% | 1.56 | 13.02 | -4.51 |
| 54. | 31 jul. 2023 | -1.86% | 4.85% | 5.53 | 13.99 | -8.79 |
| 55. | 31 ago. 2023 | -0.87% | -1.77% | 1.84 | 8.28 | 3.91 |
| 56. | 30 sept. 2023 | -5.86% | -4.87% | 40.27 | 35.73 | 37.93 |
| 57. | 31 oct. 2023 | -10.23% | -2.20% | 115.01 | 10.92 | 35.43 |
| 58. | 30 nov. 2023 | -4.17% | 8.92% | 21.74 | 61.03 | -36.42 |
| 59. | 31 dic. 2023 | 3.91% | 4.42% | 11.69 | 11.00 | 11.34 |
| Total (Σ): | 1,995.90 | 1,634.30 | 621.26 | |||
Mostrar todo
VarianzaBMY = Σ(RBMY,t–RBMY)2 ÷ (59 – 1)
= 1,995.90 ÷ (59 – 1)
= 34.41
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaBMY, S&P 500 = Σ(RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 621.26 ÷ (59 – 1)
= 10.71
Estimación sistemática del riesgo (β)
| VarianzaBMY | 34.41 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaBMY, S&P 500 | 10.71 |
| Coeficiente de correlaciónBMY, S&P 5001 | 0.34 |
| βBMY2 | 0.38 |
| αBMY3 | 0.07% |
Cálculos
1 Coeficiente de correlaciónBMY, S&P 500
= CovarianzaBMY, S&P 500 ÷ (Desviación estándarBMY × Desviación estándarS&P 500)
= 10.71 ÷ (5.87% × 5.31%)
= 0.34
2 βBMY
= CovarianzaBMY, S&P 500 ÷ VarianzaS&P 500
= 10.71 ÷ 28.18
= 0.38
3 αBMY
= PromedioBMY – βBMY × PromedioS&P 500
= 0.49% – 0.38 × 1.11%
= 0.07%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.65% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de BMS acciones ordinarias | βBMY | 0.38 |
| Tasa de rendimiento esperada de las acciones ordinarias de BMS3 | E(RBMY) | 8.12% |
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(RBMY) = RF + βBMY [E(RM) – RF]
= 4.65% + 0.38 [13.79% – 4.65%]
= 8.12%