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 Gilead.
Tasas de retorno
Gilead Sciences Inc., tasas mensuales de retorno
| Gilead Sciences Inc. (GILD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGILD,t1 | DividendoGILD,t1 | RGILD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $70.01 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $65.02 | -7.13% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $65.01 | $0.63 | 0.95% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $65.04 | 0.05% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $76.60 | -2.47% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $81.01 | $0.75 | 6.74% | 4,769.83 | 4.42% |
| Promedio (R): | 0.80% | 1.11% | ||||
| Desviación estándar: | 6.72% | 5.31% | ||||
| Gilead Sciences Inc. (GILD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGILD,t1 | DividendoGILD,t1 | RGILD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $70.01 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $65.02 | -7.13% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $65.01 | $0.63 | 0.95% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $65.04 | 0.05% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $62.25 | -4.29% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $67.56 | $0.63 | 9.54% | 2,941.76 | 6.89% |
| 6. | 31 jul. 2019 | $65.52 | -3.02% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $63.54 | -3.02% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $63.38 | $0.63 | 0.74% | 2,976.74 | 1.72% |
| 9. | 31 oct. 2019 | $63.71 | 0.52% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $67.24 | 5.54% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $64.98 | $0.63 | -2.42% | 3,230.78 | 2.86% |
| 12. | 31 ene. 2020 | $63.20 | -2.74% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $69.36 | 9.75% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $74.76 | $0.68 | 8.77% | 2,584.59 | -12.51% |
| 15. | 30 abr. 2020 | $84.00 | 12.36% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $77.83 | -7.35% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $76.94 | $0.68 | -0.27% | 3,100.29 | 1.84% |
| 18. | 31 jul. 2020 | $69.53 | -9.63% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $66.75 | -4.00% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $63.19 | $0.68 | -4.31% | 3,363.00 | -3.92% |
| 21. | 31 oct. 2020 | $58.15 | -7.98% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $60.67 | 4.33% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $58.26 | $0.68 | -2.85% | 3,756.07 | 3.71% |
| 24. | 31 ene. 2021 | $65.60 | 12.60% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $61.40 | -6.40% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $64.63 | $0.71 | 6.42% | 3,972.89 | 4.24% |
| 27. | 30 abr. 2021 | $63.47 | -1.79% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $66.11 | 4.16% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $68.86 | $0.71 | 5.23% | 4,297.50 | 2.22% |
| 30. | 31 jul. 2021 | $68.29 | -0.83% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $72.78 | 6.57% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $69.85 | $0.71 | -3.05% | 4,307.54 | -4.76% |
| 33. | 31 oct. 2021 | $64.88 | -7.12% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $68.93 | 6.24% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $72.61 | $0.71 | 6.37% | 4,766.18 | 4.36% |
| 36. | 31 ene. 2022 | $68.68 | -5.41% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $60.40 | -12.06% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $59.45 | $0.73 | -0.36% | 4,530.41 | 3.58% |
| 39. | 30 abr. 2022 | $59.34 | -0.19% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $64.85 | 9.29% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $61.81 | $0.73 | -3.56% | 3,785.38 | -8.39% |
| 42. | 31 jul. 2022 | $59.75 | -3.33% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $63.47 | 6.23% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $61.69 | $0.73 | -1.65% | 3,585.62 | -9.34% |
| 45. | 31 oct. 2022 | $78.46 | 27.18% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $87.83 | 11.94% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $85.85 | $0.73 | -1.42% | 3,839.50 | -5.90% |
| 48. | 31 ene. 2023 | $83.94 | -2.22% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $80.53 | -4.06% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $82.97 | $0.75 | 3.96% | 4,109.31 | 3.51% |
| 51. | 30 abr. 2023 | $82.21 | -0.92% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $76.94 | -6.41% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $77.07 | $0.75 | 1.14% | 4,376.86 | 4.71% |
| 54. | 31 jul. 2023 | $76.14 | -1.21% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $76.48 | 0.45% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $74.94 | $0.75 | -1.03% | 4,288.05 | -4.87% |
| 57. | 31 oct. 2023 | $78.54 | 4.80% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $76.60 | -2.47% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $81.01 | $0.75 | 6.74% | 4,769.83 | 4.42% |
| Promedio (R): | 0.80% | 1.11% | ||||
| Desviación estándar: | 6.72% | 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 GILD 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
Gilead Sciences Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RGILD,t | RS&P 500,t | (RGILD,t–RGILD)2 | (RS&P 500,t–RS&P 500)2 | (RGILD,t–RGILD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -7.13% | 2.97% | 62.89 | 3.49 | -14.81 |
| 2. | 31 mar. 2019 | 0.95% | 1.79% | 0.02 | 0.47 | 0.10 |
| 3. | 30 abr. 2019 | 0.05% | 3.93% | 0.57 | 7.98 | -2.14 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | -2.47% | 8.92% | 10.71 | 61.03 | -25.57 |
| 59. | 31 dic. 2023 | 6.74% | 4.42% | 35.21 | 11.00 | 19.68 |
| Total (Σ): | 2,622.61 | 1,634.30 | 323.59 | |||
| t | Fecha | RGILD,t | RS&P 500,t | (RGILD,t–RGILD)2 | (RS&P 500,t–RS&P 500)2 | (RGILD,t–RGILD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -7.13% | 2.97% | 62.89 | 3.49 | -14.81 |
| 2. | 31 mar. 2019 | 0.95% | 1.79% | 0.02 | 0.47 | 0.10 |
| 3. | 30 abr. 2019 | 0.05% | 3.93% | 0.57 | 7.98 | -2.14 |
| 4. | 31 may. 2019 | -4.29% | -6.58% | 25.93 | 59.04 | 39.13 |
| 5. | 30 jun. 2019 | 9.54% | 6.89% | 76.38 | 33.49 | 50.58 |
| 6. | 31 jul. 2019 | -3.02% | 1.31% | 14.61 | 0.04 | -0.79 |
| 7. | 31 ago. 2019 | -3.02% | -1.81% | 14.63 | 8.50 | 11.15 |
| 8. | 30 sept. 2019 | 0.74% | 1.72% | 0.00 | 0.37 | -0.04 |
| 9. | 31 oct. 2019 | 0.52% | 2.04% | 0.08 | 0.88 | -0.26 |
| 10. | 30 nov. 2019 | 5.54% | 3.40% | 22.45 | 5.28 | 10.89 |
| 11. | 31 dic. 2019 | -2.42% | 2.86% | 10.41 | 3.07 | -5.66 |
| 12. | 31 ene. 2020 | -2.74% | -0.16% | 12.55 | 1.61 | 4.49 |
| 13. | 29 feb. 2020 | 9.75% | -8.41% | 80.00 | 90.57 | -85.12 |
| 14. | 31 mar. 2020 | 8.77% | -12.51% | 63.41 | 185.44 | -108.44 |
| 15. | 30 abr. 2020 | 12.36% | 12.68% | 133.56 | 134.06 | 133.81 |
| 16. | 31 may. 2020 | -7.35% | 4.53% | 66.39 | 11.71 | -27.89 |
| 17. | 30 jun. 2020 | -0.27% | 1.84% | 1.15 | 0.54 | -0.79 |
| 18. | 31 jul. 2020 | -9.63% | 5.51% | 108.86 | 19.40 | -45.95 |
| 19. | 31 ago. 2020 | -4.00% | 7.01% | 23.05 | 34.82 | -28.33 |
| 20. | 30 sept. 2020 | -4.31% | -3.92% | 26.19 | 25.29 | 25.73 |
| 21. | 31 oct. 2020 | -7.98% | -2.77% | 77.07 | 15.00 | 33.99 |
| 22. | 30 nov. 2020 | 4.33% | 10.75% | 12.47 | 93.10 | 34.07 |
| 23. | 31 dic. 2020 | -2.85% | 3.71% | 13.35 | 6.79 | -9.52 |
| 24. | 31 ene. 2021 | 12.60% | -1.11% | 139.14 | 4.93 | -26.18 |
| 25. | 28 feb. 2021 | -6.40% | 2.61% | 51.91 | 2.26 | -10.83 |
| 26. | 31 mar. 2021 | 6.42% | 4.24% | 31.52 | 9.85 | 17.62 |
| 27. | 30 abr. 2021 | -1.79% | 5.24% | 6.75 | 17.11 | -10.75 |
| 28. | 31 may. 2021 | 4.16% | 0.55% | 11.27 | 0.31 | -1.87 |
| 29. | 30 jun. 2021 | 5.23% | 2.22% | 19.63 | 1.24 | 4.94 |
| 30. | 31 jul. 2021 | -0.83% | 2.27% | 2.66 | 1.37 | -1.91 |
| 31. | 31 ago. 2021 | 6.57% | 2.90% | 33.32 | 3.22 | 10.35 |
| 32. | 30 sept. 2021 | -3.05% | -4.76% | 14.85 | 34.37 | 22.59 |
| 33. | 31 oct. 2021 | -7.12% | 6.91% | 62.69 | 33.74 | -45.99 |
| 34. | 30 nov. 2021 | 6.24% | -0.83% | 29.59 | 3.76 | -10.55 |
| 35. | 31 dic. 2021 | 6.37% | 4.36% | 30.98 | 10.60 | 18.12 |
| 36. | 31 ene. 2022 | -5.41% | -5.26% | 38.63 | 40.51 | 39.56 |
| 37. | 28 feb. 2022 | -12.06% | -3.14% | 165.34 | 17.99 | 54.55 |
| 38. | 31 mar. 2022 | -0.36% | 3.58% | 1.36 | 6.11 | -2.88 |
| 39. | 30 abr. 2022 | -0.19% | -8.80% | 0.98 | 98.04 | 9.78 |
| 40. | 31 may. 2022 | 9.29% | 0.01% | 71.96 | 1.21 | -9.34 |
| 41. | 30 jun. 2022 | -3.56% | -8.39% | 19.05 | 90.21 | 41.46 |
| 42. | 31 jul. 2022 | -3.33% | 9.11% | 17.10 | 64.09 | -33.11 |
| 43. | 31 ago. 2022 | 6.23% | -4.24% | 29.41 | 28.62 | -29.01 |
| 44. | 30 sept. 2022 | -1.65% | -9.34% | 6.04 | 109.11 | 25.66 |
| 45. | 31 oct. 2022 | 27.18% | 7.99% | 695.99 | 47.34 | 181.52 |
| 46. | 30 nov. 2022 | 11.94% | 5.38% | 124.09 | 18.23 | 47.56 |
| 47. | 31 dic. 2022 | -1.42% | -5.90% | 4.95 | 49.04 | 15.59 |
| 48. | 31 ene. 2023 | -2.22% | 6.18% | 9.17 | 25.70 | -15.35 |
| 49. | 28 feb. 2023 | -4.06% | -2.61% | 23.67 | 13.82 | 18.08 |
| 50. | 31 mar. 2023 | 3.96% | 3.51% | 9.98 | 5.76 | 7.58 |
| 51. | 30 abr. 2023 | -0.92% | 1.46% | 2.95 | 0.13 | -0.62 |
| 52. | 31 may. 2023 | -6.41% | 0.25% | 52.03 | 0.74 | 6.19 |
| 53. | 30 jun. 2023 | 1.14% | 4.71% | 0.12 | 13.02 | 1.23 |
| 54. | 31 jul. 2023 | -1.21% | 4.85% | 4.04 | 13.99 | -7.52 |
| 55. | 31 ago. 2023 | 0.45% | -1.77% | 0.13 | 8.28 | 1.02 |
| 56. | 30 sept. 2023 | -1.03% | -4.87% | 3.37 | 35.73 | 10.97 |
| 57. | 31 oct. 2023 | 4.80% | -2.20% | 16.01 | 10.92 | -13.22 |
| 58. | 30 nov. 2023 | -2.47% | 8.92% | 10.71 | 61.03 | -25.57 |
| 59. | 31 dic. 2023 | 6.74% | 4.42% | 35.21 | 11.00 | 19.68 |
| Total (Σ): | 2,622.61 | 1,634.30 | 323.59 | |||
Mostrar todo
VarianzaGILD = Σ(RGILD,t–RGILD)2 ÷ (59 – 1)
= 2,622.61 ÷ (59 – 1)
= 45.22
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaGILD, S&P 500 = Σ(RGILD,t–RGILD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 323.59 ÷ (59 – 1)
= 5.58
Estimación sistemática del riesgo (β)
| VarianzaGILD | 45.22 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaGILD, S&P 500 | 5.58 |
| Coeficiente de correlaciónGILD, S&P 5001 | 0.16 |
| βGILD2 | 0.20 |
| αGILD3 | 0.58% |
Cálculos
1 Coeficiente de correlaciónGILD, S&P 500
= CovarianzaGILD, S&P 500 ÷ (Desviación estándarGILD × Desviación estándarS&P 500)
= 5.58 ÷ (6.72% × 5.31%)
= 0.16
2 βGILD
= CovarianzaGILD, S&P 500 ÷ VarianzaS&P 500
= 5.58 ÷ 28.18
= 0.20
3 αGILD
= PromedioGILD – βGILD × PromedioS&P 500
= 0.80% – 0.20 × 1.11%
= 0.58%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.67% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Gilead acciones ordinarias | βGILD | 0.20 |
| Tasa de rendimiento esperada de las acciones ordinarias de Gilead3 | E(RGILD) | 6.48% |
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(RGILD) = RF + βGILD [E(RM) – RF]
= 4.67% + 0.20 [13.79% – 4.67%]
= 6.48%