Modelo de valoración 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 activos de riesgo como las acciones ordinarias de Cigna.
Tasas de retorno
Cigna Corp., tasas mensuales de retorno
| Cigna Corp. (CI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCI,t1 | DividendoCI,t1 | RCI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $208.35 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $195.89 | -5.98% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $167.74 | $0.04 | -14.35% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $171.82 | 2.43% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $328.89 | 1.80% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $331.34 | $1.12 | 1.09% | 3,839.50 | -5.90% |
| Promedio (R): | 1.17% | 0.67% | ||||
| Desviación estándar: | 8.19% | 5.40% | ||||
| Cigna Corp. (CI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCI,t1 | DividendoCI,t1 | RCI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $208.35 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $195.89 | -5.98% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $167.74 | $0.04 | -14.35% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $171.82 | 2.43% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $169.37 | -1.43% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $169.95 | 0.34% | 2,718.37 | 0.48% | |
| 6. | 31 jul. 2018 | $179.42 | 5.57% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $188.34 | 4.97% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $208.25 | 10.57% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $213.81 | 2.67% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $223.38 | 4.48% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $189.92 | -14.98% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $199.81 | 5.21% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $174.44 | -12.70% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $160.82 | $0.04 | -7.78% | 2,834.40 | 1.79% |
| 15. | 30 abr. 2019 | $158.84 | -1.23% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $148.02 | -6.81% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $157.55 | 6.44% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $169.92 | 7.85% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $153.97 | -9.39% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $151.79 | -1.42% | 2,976.74 | 1.72% | |
| 21. | 31 oct. 2019 | $178.46 | 17.57% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $199.92 | 12.03% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $204.49 | 2.29% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $192.38 | -5.92% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $182.94 | -4.91% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $177.18 | $0.04 | -3.13% | 2,584.59 | -12.51% |
| 27. | 30 abr. 2020 | $195.78 | 10.50% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $197.32 | 0.79% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $187.65 | -4.90% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $172.69 | -7.97% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $177.37 | 2.71% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $169.41 | -4.49% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $166.97 | -1.44% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $209.14 | 25.26% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $208.18 | -0.46% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $217.05 | 4.26% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $209.90 | -3.29% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $241.74 | $1.00 | 15.65% | 3,972.89 | 4.24% |
| 39. | 30 abr. 2021 | $249.01 | 3.01% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $258.85 | 3.95% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $237.07 | $1.00 | -8.03% | 4,297.50 | 2.22% |
| 42. | 31 jul. 2021 | $229.49 | -3.20% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $211.65 | -7.77% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $200.16 | $1.00 | -4.96% | 4,307.54 | -4.76% |
| 45. | 31 oct. 2021 | $213.61 | 6.72% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $191.90 | -10.16% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $229.63 | $1.00 | 20.18% | 4,766.18 | 4.36% |
| 48. | 31 ene. 2022 | $230.46 | 0.36% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $237.78 | 3.18% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $239.61 | $1.12 | 1.24% | 4,530.41 | 3.58% |
| 51. | 30 abr. 2022 | $246.78 | 2.99% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $268.29 | 8.72% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $263.52 | $1.12 | -1.36% | 3,785.38 | -8.39% |
| 54. | 31 jul. 2022 | $275.36 | 4.49% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $283.45 | 2.94% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $277.47 | $1.12 | -1.71% | 3,585.62 | -9.34% |
| 57. | 31 oct. 2022 | $323.06 | 16.43% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $328.89 | 1.80% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $331.34 | $1.12 | 1.09% | 3,839.50 | -5.90% |
| Promedio (R): | 1.17% | 0.67% | ||||
| Desviación estándar: | 8.19% | 5.40% | ||||
Mostrar todo
1 Datos en US$ por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de IC 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
Cigna Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RCI,t | RS&P 500,t | (RCI,t–RCI)2 | (RS&P 500,t–RS&P 500)2 | (RCI,t–RCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -5.98% | -3.89% | 51.10 | 20.81 | 32.61 |
| 2. | 31 mar. 2018 | -14.35% | -2.69% | 240.80 | 11.26 | 52.06 |
| 3. | 30 abr. 2018 | 2.43% | 0.27% | 1.60 | 0.16 | -0.50 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | 1.80% | 5.38% | 0.41 | 22.17 | 3.00 |
| 59. | 31 dic. 2022 | 1.09% | -5.90% | 0.01 | 43.08 | 0.54 |
| Total (Σ): | 3,890.49 | 1,691.48 | 1,184.36 | |||
| t | Fecha | RCI,t | RS&P 500,t | (RCI,t–RCI)2 | (RS&P 500,t–RS&P 500)2 | (RCI,t–RCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -5.98% | -3.89% | 51.10 | 20.81 | 32.61 |
| 2. | 31 mar. 2018 | -14.35% | -2.69% | 240.80 | 11.26 | 52.06 |
| 3. | 30 abr. 2018 | 2.43% | 0.27% | 1.60 | 0.16 | -0.50 |
| 4. | 31 may. 2018 | -1.43% | 2.16% | 6.73 | 2.23 | -3.88 |
| 5. | 30 jun. 2018 | 0.34% | 0.48% | 0.68 | 0.03 | 0.15 |
| 6. | 31 jul. 2018 | 5.57% | 3.60% | 19.40 | 8.62 | 12.93 |
| 7. | 31 ago. 2018 | 4.97% | 3.03% | 14.47 | 5.57 | 8.98 |
| 8. | 30 sept. 2018 | 10.57% | 0.43% | 88.42 | 0.06 | -2.23 |
| 9. | 31 oct. 2018 | 2.67% | -6.94% | 2.26 | 57.87 | -11.43 |
| 10. | 30 nov. 2018 | 4.48% | 1.79% | 10.94 | 1.25 | 3.70 |
| 11. | 31 dic. 2018 | -14.98% | -9.18% | 260.72 | 96.91 | 158.95 |
| 12. | 31 ene. 2019 | 5.21% | 7.87% | 16.32 | 51.87 | 29.09 |
| 13. | 28 feb. 2019 | -12.70% | 2.97% | 192.24 | 5.32 | -31.98 |
| 14. | 31 mar. 2019 | -7.78% | 1.79% | 80.15 | 1.27 | -10.08 |
| 15. | 30 abr. 2019 | -1.23% | 3.93% | 5.76 | 10.66 | -7.83 |
| 16. | 31 may. 2019 | -6.81% | -6.58% | 63.68 | 52.48 | 57.81 |
| 17. | 30 jun. 2019 | 6.44% | 6.89% | 27.78 | 38.77 | 32.82 |
| 18. | 31 jul. 2019 | 7.85% | 1.31% | 44.67 | 0.42 | 4.32 |
| 19. | 31 ago. 2019 | -9.39% | -1.81% | 111.40 | 6.13 | 26.13 |
| 20. | 30 sept. 2019 | -1.42% | 1.72% | 6.68 | 1.11 | -2.72 |
| 21. | 31 oct. 2019 | 17.57% | 2.04% | 269.04 | 1.89 | 22.58 |
| 22. | 30 nov. 2019 | 12.03% | 3.40% | 117.88 | 7.50 | 29.73 |
| 23. | 31 dic. 2019 | 2.29% | 2.86% | 1.25 | 4.81 | 2.45 |
| 24. | 31 ene. 2020 | -5.92% | -0.16% | 50.27 | 0.69 | 5.88 |
| 25. | 29 feb. 2020 | -4.91% | -8.41% | 36.90 | 82.40 | 55.15 |
| 26. | 31 mar. 2020 | -3.13% | -12.51% | 18.44 | 173.67 | 56.60 |
| 27. | 30 abr. 2020 | 10.50% | 12.68% | 87.05 | 144.43 | 112.12 |
| 28. | 31 may. 2020 | 0.79% | 4.53% | 0.15 | 14.91 | -1.47 |
| 29. | 30 jun. 2020 | -4.90% | 1.84% | 36.83 | 1.37 | -7.11 |
| 30. | 31 jul. 2020 | -7.97% | 5.51% | 83.54 | 23.46 | -44.27 |
| 31. | 31 ago. 2020 | 2.71% | 7.01% | 2.38 | 40.19 | 9.78 |
| 32. | 30 sept. 2020 | -4.49% | -3.92% | 31.99 | 21.06 | 25.96 |
| 33. | 31 oct. 2020 | -1.44% | -2.77% | 6.80 | 11.79 | 8.95 |
| 34. | 30 nov. 2020 | 25.26% | 10.75% | 580.24 | 101.77 | 243.00 |
| 35. | 31 dic. 2020 | -0.46% | 3.71% | 2.65 | 9.28 | -4.95 |
| 36. | 31 ene. 2021 | 4.26% | -1.11% | 9.57 | 3.17 | -5.51 |
| 37. | 28 feb. 2021 | -3.29% | 2.61% | 19.91 | 3.77 | -8.67 |
| 38. | 31 mar. 2021 | 15.65% | 4.24% | 209.60 | 12.80 | 51.79 |
| 39. | 30 abr. 2021 | 3.01% | 5.24% | 3.38 | 20.94 | 8.42 |
| 40. | 31 may. 2021 | 3.95% | 0.55% | 7.75 | 0.01 | -0.33 |
| 41. | 30 jun. 2021 | -8.03% | 2.22% | 84.56 | 2.42 | -14.30 |
| 42. | 31 jul. 2021 | -3.20% | 2.27% | 19.06 | 2.59 | -7.02 |
| 43. | 31 ago. 2021 | -7.77% | 2.90% | 79.95 | 4.98 | -19.96 |
| 44. | 30 sept. 2021 | -4.96% | -4.76% | 37.51 | 29.42 | 33.21 |
| 45. | 31 oct. 2021 | 6.72% | 6.91% | 30.82 | 39.03 | 34.69 |
| 46. | 30 nov. 2021 | -10.16% | -0.83% | 128.40 | 2.25 | 17.00 |
| 47. | 31 dic. 2021 | 20.18% | 4.36% | 361.55 | 13.65 | 70.25 |
| 48. | 31 ene. 2022 | 0.36% | -5.26% | 0.65 | 35.11 | 4.78 |
| 49. | 28 feb. 2022 | 3.18% | -3.14% | 4.03 | 14.46 | -7.64 |
| 50. | 31 mar. 2022 | 1.24% | 3.58% | 0.01 | 8.47 | 0.21 |
| 51. | 30 abr. 2022 | 2.99% | -8.80% | 3.33 | 89.54 | -17.26 |
| 52. | 31 may. 2022 | 8.72% | 0.01% | 56.98 | 0.44 | -4.99 |
| 53. | 30 jun. 2022 | -1.36% | -8.39% | 6.39 | 82.06 | 22.90 |
| 54. | 31 jul. 2022 | 4.49% | 9.11% | 11.06 | 71.32 | 28.08 |
| 55. | 31 ago. 2022 | 2.94% | -4.24% | 3.13 | 24.11 | -8.69 |
| 56. | 30 sept. 2022 | -1.71% | -9.34% | 8.31 | 100.12 | 28.84 |
| 57. | 31 oct. 2022 | 16.43% | 7.99% | 232.95 | 53.58 | 111.72 |
| 58. | 30 nov. 2022 | 1.80% | 5.38% | 0.41 | 22.17 | 3.00 |
| 59. | 31 dic. 2022 | 1.09% | -5.90% | 0.01 | 43.08 | 0.54 |
| Total (Σ): | 3,890.49 | 1,691.48 | 1,184.36 | |||
Mostrar todo
VarianzaCI = Σ(RCI,t–RCI)2 ÷ (59 – 1)
= 3,890.49 ÷ (59 – 1)
= 67.08
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaCI, S&P 500 = Σ(RCI,t–RCI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,184.36 ÷ (59 – 1)
= 20.42
Estimación sistemática del riesgo (β)
| VarianzaCI | 67.08 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaCI, S&P 500 | 20.42 |
| Coeficiente de correlaciónCI, S&P 5001 | 0.46 |
| βCI2 | 0.70 |
| αCI3 | 0.70% |
Cálculos
1 Coeficiente de correlaciónCI, S&P 500
= CovarianzaCI, S&P 500 ÷ (Desviación estándarCI × Desviación estándarS&P 500)
= 20.42 ÷ (8.19% × 5.40%)
= 0.46
2 βCI
= CovarianzaCI, S&P 500 ÷ VarianzaS&P 500
= 20.42 ÷ 29.16
= 0.70
3 αCI
= PromedioCI – βCI × PromedioS&P 500
= 1.17% – 0.70 × 0.67%
= 0.70%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.72% |
| Tasa de rendimiento esperada en la cartera de mercado2 | E(RM) | 13.71% |
| Riesgo sistemático de acciones ordinarias Cigna | βCI | 0.70 |
| Tasa de rendimiento esperada de las acciones ordinarias de Cigna3 | E(RCI) | 10.71% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de los Estados Unidos de cupón fijo en circulación que no vencen ni se pueden exigir en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RCI) = RF + βCI [E(RM) – RF]
= 3.72% + 0.70 [13.71% – 3.72%]
= 10.71%