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 sobre activos de riesgo como las acciones ordinarias de Paramount.
Tasas de retorno
Paramount Global, tasas mensuales de retorno
| Paramount Global (PARA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPARA,t1 | DividendoPARA,t1 | RPARA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $57.61 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $52.97 | -8.05% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $51.39 | $0.18 | -2.64% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $49.20 | -4.26% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $20.08 | 9.61% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $16.88 | $0.24 | -14.74% | 3,839.50 | -5.90% |
| Promedio (R): | -0.66% | 0.67% | ||||
| Desviación estándar: | 14.93% | 5.40% | ||||
| Paramount Global (PARA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPARA,t1 | DividendoPARA,t1 | RPARA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $57.61 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $52.97 | -8.05% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $51.39 | $0.18 | -2.64% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $49.20 | -4.26% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $50.37 | 2.38% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $56.22 | $0.18 | 11.97% | 2,718.37 | 0.48% |
| 6. | 31 jul. 2018 | $52.67 | -6.31% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $53.02 | 0.66% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $57.45 | $0.18 | 8.69% | 2,913.98 | 0.43% |
| 9. | 31 oct. 2018 | $57.35 | -0.17% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $54.18 | -5.53% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $43.72 | $0.18 | -18.97% | 2,506.85 | -9.18% |
| 12. | 31 ene. 2019 | $49.46 | 13.13% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $50.21 | 1.52% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $47.53 | $0.18 | -4.98% | 2,834.40 | 1.79% |
| 15. | 30 abr. 2019 | $51.27 | 7.87% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $48.28 | -5.83% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $49.90 | $0.18 | 3.73% | 2,941.76 | 6.89% |
| 18. | 31 jul. 2019 | $51.51 | 3.23% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $42.06 | -18.35% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $40.37 | $0.18 | -3.59% | 2,976.74 | 1.72% |
| 21. | 31 oct. 2019 | $36.04 | -10.73% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $40.38 | 12.04% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $41.97 | $0.24 | 4.53% | 3,230.78 | 2.86% |
| 24. | 31 ene. 2020 | $34.13 | -18.68% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $24.61 | -27.89% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $14.01 | $0.24 | -42.10% | 2,584.59 | -12.51% |
| 27. | 30 abr. 2020 | $17.26 | 23.20% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $20.74 | 20.16% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $23.32 | $0.24 | 13.60% | 3,100.29 | 1.84% |
| 30. | 31 jul. 2020 | $26.07 | 11.79% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $27.85 | 6.83% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $28.01 | $0.24 | 1.44% | 3,363.00 | -3.92% |
| 33. | 31 oct. 2020 | $28.57 | 2.00% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $35.28 | 23.49% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $37.26 | $0.24 | 6.29% | 3,756.07 | 3.71% |
| 36. | 31 ene. 2021 | $48.50 | 30.17% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $64.49 | 32.97% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $45.10 | $0.24 | -29.69% | 3,972.89 | 4.24% |
| 39. | 30 abr. 2021 | $41.02 | -9.05% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $42.42 | 3.41% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $45.20 | $0.24 | 7.12% | 4,297.50 | 2.22% |
| 42. | 31 jul. 2021 | $40.93 | -9.45% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $41.45 | 1.27% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $39.51 | $0.24 | -4.10% | 4,307.54 | -4.76% |
| 45. | 31 oct. 2021 | $36.22 | -8.33% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $30.95 | -14.55% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $30.18 | $0.24 | -1.71% | 4,766.18 | 4.36% |
| 48. | 31 ene. 2022 | $33.45 | 10.83% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $30.61 | -8.49% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $37.81 | $0.24 | 24.31% | 4,530.41 | 3.58% |
| 51. | 30 abr. 2022 | $29.12 | -22.98% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $34.33 | 17.89% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $24.68 | $0.24 | -27.41% | 3,785.38 | -8.39% |
| 54. | 31 jul. 2022 | $23.65 | -4.17% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $23.39 | -1.10% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $19.04 | $0.24 | -17.57% | 3,585.62 | -9.34% |
| 57. | 31 oct. 2022 | $18.32 | -3.78% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $20.08 | 9.61% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $16.88 | $0.24 | -14.74% | 3,839.50 | -5.90% |
| Promedio (R): | -0.66% | 0.67% | ||||
| Desviación estándar: | 14.93% | 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 PARA 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
Paramount Global, cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RPARA,t | RS&P 500,t | (RPARA,t–RPARA)2 | (RS&P 500,t–RS&P 500)2 | (RPARA,t–RPARA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -8.05% | -3.89% | 54.63 | 20.81 | 33.72 |
| 2. | 31 mar. 2018 | -2.64% | -2.69% | 3.92 | 11.26 | 6.64 |
| 3. | 30 abr. 2018 | -4.26% | 0.27% | 12.95 | 0.16 | 1.42 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | 9.61% | 5.38% | 105.47 | 22.17 | 48.36 |
| 59. | 31 dic. 2022 | -14.74% | -5.90% | 198.20 | 43.08 | 92.41 |
| Total (Σ): | 12,926.67 | 1,691.48 | 2,605.93 | |||
| t | Fecha | RPARA,t | RS&P 500,t | (RPARA,t–RPARA)2 | (RS&P 500,t–RS&P 500)2 | (RPARA,t–RPARA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -8.05% | -3.89% | 54.63 | 20.81 | 33.72 |
| 2. | 31 mar. 2018 | -2.64% | -2.69% | 3.92 | 11.26 | 6.64 |
| 3. | 30 abr. 2018 | -4.26% | 0.27% | 12.95 | 0.16 | 1.42 |
| 4. | 31 may. 2018 | 2.38% | 2.16% | 9.25 | 2.23 | 4.54 |
| 5. | 30 jun. 2018 | 11.97% | 0.48% | 159.62 | 0.03 | -2.30 |
| 6. | 31 jul. 2018 | -6.31% | 3.60% | 31.94 | 8.62 | -16.59 |
| 7. | 31 ago. 2018 | 0.66% | 3.03% | 1.76 | 5.57 | 3.13 |
| 8. | 30 sept. 2018 | 8.69% | 0.43% | 87.56 | 0.06 | -2.22 |
| 9. | 31 oct. 2018 | -0.17% | -6.94% | 0.24 | 57.87 | -3.72 |
| 10. | 30 nov. 2018 | -5.53% | 1.79% | 23.67 | 1.25 | -5.45 |
| 11. | 31 dic. 2018 | -18.97% | -9.18% | 335.30 | 96.91 | 180.26 |
| 12. | 31 ene. 2019 | 13.13% | 7.87% | 190.21 | 51.87 | 99.33 |
| 13. | 28 feb. 2019 | 1.52% | 2.97% | 4.75 | 5.32 | 5.03 |
| 14. | 31 mar. 2019 | -4.98% | 1.79% | 18.63 | 1.27 | -4.86 |
| 15. | 30 abr. 2019 | 7.87% | 3.93% | 72.79 | 10.66 | 27.85 |
| 16. | 31 may. 2019 | -5.83% | -6.58% | 26.72 | 52.48 | 37.45 |
| 17. | 30 jun. 2019 | 3.73% | 6.89% | 19.28 | 38.77 | 27.34 |
| 18. | 31 jul. 2019 | 3.23% | 1.31% | 15.13 | 0.42 | 2.51 |
| 19. | 31 ago. 2019 | -18.35% | -1.81% | 312.70 | 6.13 | 43.78 |
| 20. | 30 sept. 2019 | -3.59% | 1.72% | 8.57 | 1.11 | -3.08 |
| 21. | 31 oct. 2019 | -10.73% | 2.04% | 101.27 | 1.89 | -13.85 |
| 22. | 30 nov. 2019 | 12.04% | 3.40% | 161.41 | 7.50 | 34.79 |
| 23. | 31 dic. 2019 | 4.53% | 2.86% | 26.98 | 4.81 | 11.39 |
| 24. | 31 ene. 2020 | -18.68% | -0.16% | 324.62 | 0.69 | 14.94 |
| 25. | 29 feb. 2020 | -27.89% | -8.41% | 741.51 | 82.40 | 247.19 |
| 26. | 31 mar. 2020 | -42.10% | -12.51% | 1,716.78 | 173.67 | 546.04 |
| 27. | 30 abr. 2020 | 23.20% | 12.68% | 569.32 | 144.43 | 286.75 |
| 28. | 31 may. 2020 | 20.16% | 4.53% | 433.68 | 14.91 | 80.42 |
| 29. | 30 jun. 2020 | 13.60% | 1.84% | 203.34 | 1.37 | 16.72 |
| 30. | 31 jul. 2020 | 11.79% | 5.51% | 155.13 | 23.46 | 60.33 |
| 31. | 31 ago. 2020 | 6.83% | 7.01% | 56.11 | 40.19 | 47.49 |
| 32. | 30 sept. 2020 | 1.44% | -3.92% | 4.41 | 21.06 | -9.63 |
| 33. | 31 oct. 2020 | 2.00% | -2.77% | 7.09 | 11.79 | -9.14 |
| 34. | 30 nov. 2020 | 23.49% | 10.75% | 583.17 | 101.77 | 243.61 |
| 35. | 31 dic. 2020 | 6.29% | 3.71% | 48.38 | 9.28 | 21.18 |
| 36. | 31 ene. 2021 | 30.17% | -1.11% | 950.43 | 3.17 | -54.89 |
| 37. | 28 feb. 2021 | 32.97% | 2.61% | 1,131.10 | 3.77 | 65.33 |
| 38. | 31 mar. 2021 | -29.69% | 4.24% | 842.85 | 12.80 | -103.85 |
| 39. | 30 abr. 2021 | -9.05% | 5.24% | 70.29 | 20.94 | -38.36 |
| 40. | 31 may. 2021 | 3.41% | 0.55% | 16.61 | 0.01 | -0.48 |
| 41. | 30 jun. 2021 | 7.12% | 2.22% | 60.56 | 2.42 | 12.10 |
| 42. | 31 jul. 2021 | -9.45% | 2.27% | 77.16 | 2.59 | -14.13 |
| 43. | 31 ago. 2021 | 1.27% | 2.90% | 3.74 | 4.98 | 4.32 |
| 44. | 30 sept. 2021 | -4.10% | -4.76% | 11.82 | 29.42 | 18.65 |
| 45. | 31 oct. 2021 | -8.33% | 6.91% | 58.74 | 39.03 | -47.88 |
| 46. | 30 nov. 2021 | -14.55% | -0.83% | 192.86 | 2.25 | 20.83 |
| 47. | 31 dic. 2021 | -1.71% | 4.36% | 1.10 | 13.65 | -3.88 |
| 48. | 31 ene. 2022 | 10.83% | -5.26% | 132.20 | 35.11 | -68.13 |
| 49. | 28 feb. 2022 | -8.49% | -3.14% | 61.27 | 14.46 | 29.77 |
| 50. | 31 mar. 2022 | 24.31% | 3.58% | 623.43 | 8.47 | 72.68 |
| 51. | 30 abr. 2022 | -22.98% | -8.80% | 498.21 | 89.54 | 211.20 |
| 52. | 31 may. 2022 | 17.89% | 0.01% | 344.26 | 0.44 | -12.27 |
| 53. | 30 jun. 2022 | -27.41% | -8.39% | 715.44 | 82.06 | 242.30 |
| 54. | 31 jul. 2022 | -4.17% | 9.11% | 12.32 | 71.32 | -29.65 |
| 55. | 31 ago. 2022 | -1.10% | -4.24% | 0.19 | 24.11 | 2.14 |
| 56. | 30 sept. 2022 | -17.57% | -9.34% | 285.91 | 100.12 | 169.19 |
| 57. | 31 oct. 2022 | -3.78% | 7.99% | 9.73 | 53.58 | -22.83 |
| 58. | 30 nov. 2022 | 9.61% | 5.38% | 105.47 | 22.17 | 48.36 |
| 59. | 31 dic. 2022 | -14.74% | -5.90% | 198.20 | 43.08 | 92.41 |
| Total (Σ): | 12,926.67 | 1,691.48 | 2,605.93 | |||
Mostrar todo
VarianzaPARA = Σ(RPARA,t–RPARA)2 ÷ (59 – 1)
= 12,926.67 ÷ (59 – 1)
= 222.87
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaPARA, S&P 500 = Σ(RPARA,t–RPARA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,605.93 ÷ (59 – 1)
= 44.93
Estimación sistemática del riesgo (β)
| VarianzaPARA | 222.87 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaPARA, S&P 500 | 44.93 |
| Coeficiente de correlaciónPARA, S&P 5001 | 0.56 |
| βPARA2 | 1.54 |
| αPARA3 | -1.69% |
Cálculos
1 Coeficiente de correlaciónPARA, S&P 500
= CovarianzaPARA, S&P 500 ÷ (Desviación estándarPARA × Desviación estándarS&P 500)
= 44.93 ÷ (14.93% × 5.40%)
= 0.56
2 βPARA
= CovarianzaPARA, S&P 500 ÷ VarianzaS&P 500
= 44.93 ÷ 29.16
= 1.54
3 αPARA
= PromedioPARA – βPARA × PromedioS&P 500
= -0.66% – 1.54 × 0.67%
= -1.69%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.62% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.69% |
| Riesgo sistemático de Paramount acciones ordinarias | βPARA | 1.54 |
| Tasa de rendimiento esperada de las acciones ordinarias de Paramount3 | E(RPARA) | 18.59% |
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(RPARA) = RF + βPARA [E(RM) – RF]
= 4.62% + 1.54 [13.69% – 4.62%]
= 18.59%