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 Activision Blizzard.
Tasas de retorno
Activision Blizzard Inc., tasas mensuales de retorno
| Activision Blizzard Inc. (ATVI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioATVI,t1 | DividendoATVI,t1 | RATVI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $74.13 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $73.13 | -1.35% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $67.46 | $0.34 | -7.29% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $66.35 | -1.65% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $73.95 | 1.58% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $76.55 | 3.52% | 3,839.50 | -5.90% | |
| Promedio (R): | 0.49% | 0.67% | ||||
| Desviación estándar: | 8.64% | 5.40% | ||||
| Activision Blizzard Inc. (ATVI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioATVI,t1 | DividendoATVI,t1 | RATVI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $74.13 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $73.13 | -1.35% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $67.46 | $0.34 | -7.29% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $66.35 | -1.65% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $70.91 | 6.87% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $76.32 | 7.63% | 2,718.37 | 0.48% | |
| 6. | 31 jul. 2018 | $73.42 | -3.80% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $72.10 | -1.80% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $83.19 | 15.38% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $69.05 | -17.00% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $49.88 | -27.76% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $46.57 | -6.64% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $47.24 | 1.44% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $42.14 | -10.80% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $45.53 | $0.37 | 8.92% | 2,834.40 | 1.79% |
| 15. | 30 abr. 2019 | $48.21 | 5.89% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $43.37 | -10.04% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $47.20 | 8.83% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $48.74 | 3.26% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $50.60 | 3.82% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $52.92 | 4.58% | 2,976.74 | 1.72% | |
| 21. | 31 oct. 2019 | $56.03 | 5.88% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $54.83 | -2.14% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $59.42 | 8.37% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $58.48 | -1.58% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $58.13 | -0.60% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $59.48 | 2.32% | 2,584.59 | -12.51% | |
| 27. | 30 abr. 2020 | $63.73 | $0.41 | 7.83% | 2,912.43 | 12.68% |
| 28. | 31 may. 2020 | $71.98 | 12.95% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $75.90 | 5.45% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $82.63 | 8.87% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $83.52 | 1.08% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $80.95 | -3.08% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $75.73 | -6.45% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $79.48 | 4.95% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $92.85 | 16.82% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $91.00 | -1.99% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $95.61 | 5.07% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $93.00 | -2.73% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $91.19 | $0.47 | -1.44% | 4,181.17 | 5.24% |
| 40. | 31 may. 2021 | $97.25 | 6.65% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $95.44 | -1.86% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $83.62 | -12.38% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $82.37 | -1.49% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $77.39 | -6.05% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $78.19 | 1.03% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $58.60 | -25.05% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $66.53 | 13.53% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $79.01 | 18.76% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $81.50 | 3.15% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $80.11 | -1.71% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $75.60 | $0.47 | -5.04% | 4,131.93 | -8.80% |
| 52. | 31 may. 2022 | $77.88 | 3.02% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $77.86 | -0.03% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $79.95 | 2.68% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $78.49 | -1.83% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $74.34 | -5.29% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $72.80 | -2.07% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $73.95 | 1.58% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $76.55 | 3.52% | 3,839.50 | -5.90% | |
| Promedio (R): | 0.49% | 0.67% | ||||
| Desviación estándar: | 8.64% | 5.40% | ||||
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 ATVI 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
Activision Blizzard Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RATVI,t | RS&P 500,t | (RATVI,t–RATVI)2 | (RS&P 500,t–RS&P 500)2 | (RATVI,t–RATVI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -1.35% | -3.89% | 3.40 | 20.81 | 8.41 |
| 2. | 31 mar. 2018 | -7.29% | -2.69% | 60.58 | 11.26 | 26.11 |
| 3. | 30 abr. 2018 | -1.65% | 0.27% | 4.58 | 0.16 | 0.84 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | 1.58% | 5.38% | 1.18 | 22.17 | 5.11 |
| 59. | 31 dic. 2022 | 3.52% | -5.90% | 9.13 | 43.08 | -19.83 |
| Total (Σ): | 4,326.65 | 1,691.48 | 727.55 | |||
| t | Fecha | RATVI,t | RS&P 500,t | (RATVI,t–RATVI)2 | (RS&P 500,t–RS&P 500)2 | (RATVI,t–RATVI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -1.35% | -3.89% | 3.40 | 20.81 | 8.41 |
| 2. | 31 mar. 2018 | -7.29% | -2.69% | 60.58 | 11.26 | 26.11 |
| 3. | 30 abr. 2018 | -1.65% | 0.27% | 4.58 | 0.16 | 0.84 |
| 4. | 31 may. 2018 | 6.87% | 2.16% | 40.68 | 2.23 | 9.53 |
| 5. | 30 jun. 2018 | 7.63% | 0.48% | 50.90 | 0.03 | -1.30 |
| 6. | 31 jul. 2018 | -3.80% | 3.60% | 18.44 | 8.62 | -12.61 |
| 7. | 31 ago. 2018 | -1.80% | 3.03% | 5.26 | 5.57 | -5.41 |
| 8. | 30 sept. 2018 | 15.38% | 0.43% | 221.61 | 0.06 | -3.53 |
| 9. | 31 oct. 2018 | -17.00% | -6.94% | 305.98 | 57.87 | 133.06 |
| 10. | 30 nov. 2018 | -27.76% | 1.79% | 798.48 | 1.25 | -31.63 |
| 11. | 31 dic. 2018 | -6.64% | -9.18% | 50.85 | 96.91 | 70.20 |
| 12. | 31 ene. 2019 | 1.44% | 7.87% | 0.89 | 51.87 | 6.80 |
| 13. | 28 feb. 2019 | -10.80% | 2.97% | 127.48 | 5.32 | -26.04 |
| 14. | 31 mar. 2019 | 8.92% | 1.79% | 71.03 | 1.27 | 9.49 |
| 15. | 30 abr. 2019 | 5.89% | 3.93% | 29.07 | 10.66 | 17.60 |
| 16. | 31 may. 2019 | -10.04% | -6.58% | 110.97 | 52.48 | 76.32 |
| 17. | 30 jun. 2019 | 8.83% | 6.89% | 69.49 | 38.77 | 51.90 |
| 18. | 31 jul. 2019 | 3.26% | 1.31% | 7.66 | 0.42 | 1.79 |
| 19. | 31 ago. 2019 | 3.82% | -1.81% | 11.03 | 6.13 | -8.22 |
| 20. | 30 sept. 2019 | 4.58% | 1.72% | 16.73 | 1.11 | 4.30 |
| 21. | 31 oct. 2019 | 5.88% | 2.04% | 28.96 | 1.89 | 7.41 |
| 22. | 30 nov. 2019 | -2.14% | 3.40% | 6.95 | 7.50 | -7.22 |
| 23. | 31 dic. 2019 | 8.37% | 2.86% | 62.04 | 4.81 | 17.27 |
| 24. | 31 ene. 2020 | -1.58% | -0.16% | 4.31 | 0.69 | 1.72 |
| 25. | 29 feb. 2020 | -0.60% | -8.41% | 1.20 | 82.40 | 9.93 |
| 26. | 31 mar. 2020 | 2.32% | -12.51% | 3.34 | 173.67 | -24.08 |
| 27. | 30 abr. 2020 | 7.83% | 12.68% | 53.87 | 144.43 | 88.21 |
| 28. | 31 may. 2020 | 12.95% | 4.53% | 155.01 | 14.91 | 48.08 |
| 29. | 30 jun. 2020 | 5.45% | 1.84% | 24.51 | 1.37 | 5.80 |
| 30. | 31 jul. 2020 | 8.87% | 5.51% | 70.09 | 23.46 | 40.55 |
| 31. | 31 ago. 2020 | 1.08% | 7.01% | 0.34 | 40.19 | 3.69 |
| 32. | 30 sept. 2020 | -3.08% | -3.92% | 12.76 | 21.06 | 16.39 |
| 33. | 31 oct. 2020 | -6.45% | -2.77% | 48.21 | 11.79 | 23.84 |
| 34. | 30 nov. 2020 | 4.95% | 10.75% | 19.86 | 101.77 | 44.96 |
| 35. | 31 dic. 2020 | 16.82% | 3.71% | 266.57 | 9.28 | 49.72 |
| 36. | 31 ene. 2021 | -1.99% | -1.11% | 6.19 | 3.17 | 4.43 |
| 37. | 28 feb. 2021 | 5.07% | 2.61% | 20.89 | 3.77 | 8.88 |
| 38. | 31 mar. 2021 | -2.73% | 4.24% | 10.40 | 12.80 | -11.54 |
| 39. | 30 abr. 2021 | -1.44% | 5.24% | 3.75 | 20.94 | -8.86 |
| 40. | 31 may. 2021 | 6.65% | 0.55% | 37.83 | 0.01 | -0.73 |
| 41. | 30 jun. 2021 | -1.86% | 2.22% | 5.55 | 2.42 | -3.66 |
| 42. | 31 jul. 2021 | -12.38% | 2.27% | 165.89 | 2.59 | -20.71 |
| 43. | 31 ago. 2021 | -1.49% | 2.90% | 3.96 | 4.98 | -4.44 |
| 44. | 30 sept. 2021 | -6.05% | -4.76% | 42.78 | 29.42 | 35.47 |
| 45. | 31 oct. 2021 | 1.03% | 6.91% | 0.29 | 39.03 | 3.37 |
| 46. | 30 nov. 2021 | -25.05% | -0.83% | 652.77 | 2.25 | 38.32 |
| 47. | 31 dic. 2021 | 13.53% | 4.36% | 169.98 | 13.65 | 48.17 |
| 48. | 31 ene. 2022 | 18.76% | -5.26% | 333.56 | 35.11 | -108.21 |
| 49. | 28 feb. 2022 | 3.15% | -3.14% | 7.06 | 14.46 | -10.10 |
| 50. | 31 mar. 2022 | -1.71% | 3.58% | 4.84 | 8.47 | -6.40 |
| 51. | 30 abr. 2022 | -5.04% | -8.80% | 30.67 | 89.54 | 52.40 |
| 52. | 31 may. 2022 | 3.02% | 0.01% | 6.36 | 0.44 | -1.67 |
| 53. | 30 jun. 2022 | -0.03% | -8.39% | 0.27 | 82.06 | 4.72 |
| 54. | 31 jul. 2022 | 2.68% | 9.11% | 4.79 | 71.32 | 18.49 |
| 55. | 31 ago. 2022 | -1.83% | -4.24% | 5.39 | 24.11 | 11.40 |
| 56. | 30 sept. 2022 | -5.29% | -9.34% | 33.43 | 100.12 | 57.86 |
| 57. | 31 oct. 2022 | -2.07% | 7.99% | 6.59 | 53.58 | -18.79 |
| 58. | 30 nov. 2022 | 1.58% | 5.38% | 1.18 | 22.17 | 5.11 |
| 59. | 31 dic. 2022 | 3.52% | -5.90% | 9.13 | 43.08 | -19.83 |
| Total (Σ): | 4,326.65 | 1,691.48 | 727.55 | |||
Mostrar todo
VarianzaATVI = Σ(RATVI,t–RATVI)2 ÷ (59 – 1)
= 4,326.65 ÷ (59 – 1)
= 74.60
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaATVI, S&P 500 = Σ(RATVI,t–RATVI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 727.55 ÷ (59 – 1)
= 12.54
Estimación sistemática del riesgo (β)
| VarianzaATVI | 74.60 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaATVI, S&P 500 | 12.54 |
| Coeficiente de correlaciónATVI, S&P 5001 | 0.27 |
| βATVI2 | 0.43 |
| αATVI3 | 0.21% |
Cálculos
1 Coeficiente de correlaciónATVI, S&P 500
= CovarianzaATVI, S&P 500 ÷ (Desviación estándarATVI × Desviación estándarS&P 500)
= 12.54 ÷ (8.64% × 5.40%)
= 0.27
2 βATVI
= CovarianzaATVI, S&P 500 ÷ VarianzaS&P 500
= 12.54 ÷ 29.16
= 0.43
3 αATVI
= PromedioATVI – βATVI × PromedioS&P 500
= 0.49% – 0.43 × 0.67%
= 0.21%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.80% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.50% |
| Riesgo sistemático de Activision Blizzard acciones ordinarias | βATVI | 0.43 |
| Tasa de rendimiento esperada de las acciones ordinarias de Activision Blizzard3 | E(RATVI) | 8.54% |
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(RATVI) = RF + βATVI [E(RM) – RF]
= 4.80% + 0.43 [13.50% – 4.80%]
= 8.54%