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 de activos de riesgo como las acciones ordinarias de Humana.
Tasas de retorno
Humana Inc., tasas mensuales de retorno
| Humana Inc. (HUM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHUM,t1 | DividendoHUM,t1 | RHUM,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $198.50 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $211.25 | 6.42% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $206.14 | $0.40 | -2.23% | 2,362.72 | -0.04% |
| 3. | 30 abr. 2017 | $221.98 | 7.68% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $419.71 | -9.38% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $463.86 | $0.70 | 10.69% | 4,766.18 | 4.36% |
| Promedio (R): | 1.78% | 1.36% | ||||
| Desviación estándar: | 7.57% | 4.48% | ||||
| Humana Inc. (HUM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHUM,t1 | DividendoHUM,t1 | RHUM,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $198.50 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $211.25 | 6.42% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $206.14 | $0.40 | -2.23% | 2,362.72 | -0.04% |
| 3. | 30 abr. 2017 | $221.98 | 7.68% | 2,384.20 | 0.91% | |
| 4. | 31 may. 2017 | $232.26 | 4.63% | 2,411.80 | 1.16% | |
| 5. | 30 jun. 2017 | $240.62 | $0.40 | 3.77% | 2,423.41 | 0.48% |
| 6. | 31 jul. 2017 | $231.20 | -3.91% | 2,470.30 | 1.93% | |
| 7. | 31 ago. 2017 | $257.62 | 11.43% | 2,471.65 | 0.05% | |
| 8. | 30 sept. 2017 | $243.63 | $0.40 | -5.28% | 2,519.36 | 1.93% |
| 9. | 31 oct. 2017 | $255.35 | 4.81% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $260.86 | 2.16% | 2,647.58 | 2.81% | |
| 11. | 31 dic. 2017 | $248.07 | $0.40 | -4.75% | 2,673.61 | 0.98% |
| 12. | 31 ene. 2018 | $281.83 | 13.61% | 2,823.81 | 5.62% | |
| 13. | 28 feb. 2018 | $271.82 | -3.55% | 2,713.83 | -3.89% | |
| 14. | 31 mar. 2018 | $268.83 | $0.50 | -0.92% | 2,640.87 | -2.69% |
| 15. | 30 abr. 2018 | $294.18 | 9.43% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $290.98 | -1.09% | 2,705.27 | 2.16% | |
| 17. | 30 jun. 2018 | $297.63 | $0.50 | 2.46% | 2,718.37 | 0.48% |
| 18. | 31 jul. 2018 | $314.18 | 5.56% | 2,816.29 | 3.60% | |
| 19. | 31 ago. 2018 | $333.26 | 6.07% | 2,901.52 | 3.03% | |
| 20. | 30 sept. 2018 | $338.52 | $0.50 | 1.73% | 2,913.98 | 0.43% |
| 21. | 31 oct. 2018 | $320.41 | -5.35% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $329.47 | 2.83% | 2,760.17 | 1.79% | |
| 23. | 31 dic. 2018 | $286.48 | $0.50 | -12.90% | 2,506.85 | -9.18% |
| 24. | 31 ene. 2019 | $308.99 | 7.86% | 2,704.10 | 7.87% | |
| 25. | 28 feb. 2019 | $285.04 | -7.75% | 2,784.49 | 2.97% | |
| 26. | 31 mar. 2019 | $266.00 | $0.55 | -6.49% | 2,834.40 | 1.79% |
| 27. | 30 abr. 2019 | $255.41 | -3.98% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $244.86 | -4.13% | 2,752.06 | -6.58% | |
| 29. | 30 jun. 2019 | $265.30 | $0.55 | 8.57% | 2,941.76 | 6.89% |
| 30. | 31 jul. 2019 | $296.75 | 11.85% | 2,980.38 | 1.31% | |
| 31. | 31 ago. 2019 | $283.21 | -4.56% | 2,926.46 | -1.81% | |
| 32. | 30 sept. 2019 | $255.67 | $0.55 | -9.53% | 2,976.74 | 1.72% |
| 33. | 31 oct. 2019 | $294.20 | 15.07% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $341.23 | 15.99% | 3,140.98 | 3.40% | |
| 35. | 31 dic. 2019 | $366.52 | $0.55 | 7.57% | 3,230.78 | 2.86% |
| 36. | 31 ene. 2020 | $336.24 | -8.26% | 3,225.52 | -0.16% | |
| 37. | 29 feb. 2020 | $319.68 | -4.93% | 2,954.22 | -8.41% | |
| 38. | 31 mar. 2020 | $314.02 | $0.625 | -1.58% | 2,584.59 | -12.51% |
| 39. | 30 abr. 2020 | $381.82 | 21.59% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $410.65 | 7.55% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $387.75 | $0.625 | -5.42% | 3,100.29 | 1.84% |
| 42. | 31 jul. 2020 | $392.45 | 1.21% | 3,271.12 | 5.51% | |
| 43. | 31 ago. 2020 | $415.17 | 5.79% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $413.89 | $0.625 | -0.16% | 3,363.00 | -3.92% |
| 45. | 31 oct. 2020 | $399.28 | -3.53% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $400.52 | 0.31% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $410.27 | $0.625 | 2.59% | 3,756.07 | 3.71% |
| 48. | 31 ene. 2021 | $383.11 | -6.62% | 3,714.24 | -1.11% | |
| 49. | 28 feb. 2021 | $379.65 | -0.90% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $419.25 | $0.70 | 10.62% | 3,972.89 | 4.24% |
| 51. | 30 abr. 2021 | $445.24 | 6.20% | 4,181.17 | 5.24% | |
| 52. | 31 may. 2021 | $437.70 | -1.69% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $442.72 | $0.70 | 1.31% | 4,297.50 | 2.22% |
| 54. | 31 jul. 2021 | $425.86 | -3.81% | 4,395.26 | 2.27% | |
| 55. | 31 ago. 2021 | $405.42 | -4.80% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $389.15 | $0.70 | -3.84% | 4,307.54 | -4.76% |
| 57. | 31 oct. 2021 | $463.16 | 19.02% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $419.71 | -9.38% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $463.86 | $0.70 | 10.69% | 4,766.18 | 4.36% |
| Promedio (R): | 1.78% | 1.36% | ||||
| Desviación estándar: | 7.57% | 4.48% | ||||
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de HUM 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
Humana Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RHUM,t | RS&P 500,t | (RHUM,t–RHUM)2 | (RS&P 500,t–RS&P 500)2 | (RHUM,t–RHUM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 6.42% | 3.72% | 21.56 | 5.58 | 10.97 |
| 2. | 31 mar. 2017 | -2.23% | -0.04% | 16.08 | 1.95 | 5.60 |
| 3. | 30 abr. 2017 | 7.68% | 0.91% | 34.85 | 0.20 | -2.65 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -9.38% | -0.83% | 124.58 | 4.80 | 24.46 |
| 59. | 31 dic. 2021 | 10.69% | 4.36% | 79.31 | 9.02 | 26.75 |
| Total (Σ): | 3,327.40 | 1,164.17 | 1,093.65 | |||
| t | Fecha | RHUM,t | RS&P 500,t | (RHUM,t–RHUM)2 | (RS&P 500,t–RS&P 500)2 | (RHUM,t–RHUM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 6.42% | 3.72% | 21.56 | 5.58 | 10.97 |
| 2. | 31 mar. 2017 | -2.23% | -0.04% | 16.08 | 1.95 | 5.60 |
| 3. | 30 abr. 2017 | 7.68% | 0.91% | 34.85 | 0.20 | -2.65 |
| 4. | 31 may. 2017 | 4.63% | 1.16% | 8.13 | 0.04 | -0.57 |
| 5. | 30 jun. 2017 | 3.77% | 0.48% | 3.97 | 0.77 | -1.75 |
| 6. | 31 jul. 2017 | -3.91% | 1.93% | 32.44 | 0.33 | -3.29 |
| 7. | 31 ago. 2017 | 11.43% | 0.05% | 93.06 | 1.70 | -12.57 |
| 8. | 30 sept. 2017 | -5.28% | 1.93% | 49.78 | 0.33 | -4.04 |
| 9. | 31 oct. 2017 | 4.81% | 2.22% | 9.18 | 0.74 | 2.61 |
| 10. | 30 nov. 2017 | 2.16% | 2.81% | 0.14 | 2.10 | 0.55 |
| 11. | 31 dic. 2017 | -4.75% | 0.98% | 42.64 | 0.14 | 2.45 |
| 12. | 31 ene. 2018 | 13.61% | 5.62% | 139.92 | 18.15 | 50.39 |
| 13. | 28 feb. 2018 | -3.55% | -3.89% | 28.43 | 27.59 | 28.01 |
| 14. | 31 mar. 2018 | -0.92% | -2.69% | 7.27 | 16.37 | 10.91 |
| 15. | 30 abr. 2018 | 9.43% | 0.27% | 58.51 | 1.18 | -8.31 |
| 16. | 31 may. 2018 | -1.09% | 2.16% | 8.23 | 0.64 | -2.30 |
| 17. | 30 jun. 2018 | 2.46% | 0.48% | 0.46 | 0.76 | -0.59 |
| 18. | 31 jul. 2018 | 5.56% | 3.60% | 14.29 | 5.04 | 8.48 |
| 19. | 31 ago. 2018 | 6.07% | 3.03% | 18.43 | 2.78 | 7.16 |
| 20. | 30 sept. 2018 | 1.73% | 0.43% | 0.00 | 0.86 | 0.05 |
| 21. | 31 oct. 2018 | -5.35% | -6.94% | 50.84 | 68.86 | 59.17 |
| 22. | 30 nov. 2018 | 2.83% | 1.79% | 1.10 | 0.18 | 0.45 |
| 23. | 31 dic. 2018 | -12.90% | -9.18% | 215.41 | 111.00 | 154.63 |
| 24. | 31 ene. 2019 | 7.86% | 7.87% | 36.93 | 42.39 | 39.57 |
| 25. | 28 feb. 2019 | -7.75% | 2.97% | 90.85 | 2.61 | -15.39 |
| 26. | 31 mar. 2019 | -6.49% | 1.79% | 68.35 | 0.19 | -3.59 |
| 27. | 30 abr. 2019 | -3.98% | 3.93% | 33.20 | 6.62 | -14.83 |
| 28. | 31 may. 2019 | -4.13% | -6.58% | 34.94 | 62.97 | 46.91 |
| 29. | 30 jun. 2019 | 8.57% | 6.89% | 46.13 | 30.64 | 37.59 |
| 30. | 31 jul. 2019 | 11.85% | 1.31% | 101.49 | 0.00 | -0.45 |
| 31. | 31 ago. 2019 | -4.56% | -1.81% | 40.23 | 10.03 | 20.09 |
| 32. | 30 sept. 2019 | -9.53% | 1.72% | 127.92 | 0.13 | -4.07 |
| 33. | 31 oct. 2019 | 15.07% | 2.04% | 176.62 | 0.47 | 9.11 |
| 34. | 30 nov. 2019 | 15.99% | 3.40% | 201.79 | 4.19 | 29.08 |
| 35. | 31 dic. 2019 | 7.57% | 2.86% | 33.55 | 2.25 | 8.69 |
| 36. | 31 ene. 2020 | -8.26% | -0.16% | 100.84 | 2.31 | 15.27 |
| 37. | 29 feb. 2020 | -4.93% | -8.41% | 44.96 | 95.43 | 65.50 |
| 38. | 31 mar. 2020 | -1.58% | -12.51% | 11.26 | 192.37 | 46.54 |
| 39. | 30 abr. 2020 | 21.59% | 12.68% | 392.46 | 128.29 | 224.39 |
| 40. | 31 may. 2020 | 7.55% | 4.53% | 33.30 | 10.05 | 18.29 |
| 41. | 30 jun. 2020 | -5.42% | 1.84% | 51.91 | 0.23 | -3.46 |
| 42. | 31 jul. 2020 | 1.21% | 5.51% | 0.32 | 17.24 | -2.36 |
| 43. | 31 ago. 2020 | 5.79% | 7.01% | 16.07 | 31.91 | 22.64 |
| 44. | 30 sept. 2020 | -0.16% | -3.92% | 3.76 | 27.89 | 10.23 |
| 45. | 31 oct. 2020 | -3.53% | -2.77% | 28.20 | 17.01 | 21.90 |
| 46. | 30 nov. 2020 | 0.31% | 10.75% | 2.16 | 88.30 | -13.81 |
| 47. | 31 dic. 2020 | 2.59% | 3.71% | 0.66 | 5.54 | 1.91 |
| 48. | 31 ene. 2021 | -6.62% | -1.11% | 70.57 | 6.11 | 20.76 |
| 49. | 28 feb. 2021 | -0.90% | 2.61% | 7.20 | 1.57 | -3.36 |
| 50. | 31 mar. 2021 | 10.62% | 4.24% | 78.05 | 8.33 | 25.50 |
| 51. | 30 abr. 2021 | 6.20% | 5.24% | 19.53 | 15.09 | 17.17 |
| 52. | 31 may. 2021 | -1.69% | 0.55% | 12.07 | 0.65 | 2.81 |
| 53. | 30 jun. 2021 | 1.31% | 2.22% | 0.22 | 0.75 | -0.41 |
| 54. | 31 jul. 2021 | -3.81% | 2.27% | 31.23 | 0.84 | -5.12 |
| 55. | 31 ago. 2021 | -4.80% | 2.90% | 43.30 | 2.38 | -10.14 |
| 56. | 30 sept. 2021 | -3.84% | -4.76% | 31.59 | 37.39 | 34.37 |
| 57. | 31 oct. 2021 | 19.02% | 6.91% | 297.15 | 30.87 | 95.78 |
| 58. | 30 nov. 2021 | -9.38% | -0.83% | 124.58 | 4.80 | 24.46 |
| 59. | 31 dic. 2021 | 10.69% | 4.36% | 79.31 | 9.02 | 26.75 |
| Total (Σ): | 3,327.40 | 1,164.17 | 1,093.65 | |||
Mostrar todo
VarianzaHUM = Σ(RHUM,t–RHUM)2 ÷ (59 – 1)
= 3,327.40 ÷ (59 – 1)
= 57.37
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaHUM, S&P 500 = Σ(RHUM,t–RHUM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,093.65 ÷ (59 – 1)
= 18.86
Estimación sistemática del riesgo (β)
| VarianzaHUM | 57.37 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaHUM, S&P 500 | 18.86 |
| Coeficiente de correlaciónHUM, S&P 5001 | 0.56 |
| βHUM2 | 0.94 |
| αHUM3 | 0.50% |
Cálculos
1 Coeficiente de correlaciónHUM, S&P 500
= CovarianzaHUM, S&P 500 ÷ (Desviación estándarHUM × Desviación estándarS&P 500)
= 18.86 ÷ (7.57% × 4.48%)
= 0.56
2 βHUM
= CovarianzaHUM, S&P 500 ÷ VarianzaS&P 500
= 18.86 ÷ 20.07
= 0.94
3 αHUM
= PromedioHUM – βHUM × PromedioS&P 500
= 1.78% – 0.94 × 1.36%
= 0.50%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.72% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.54% |
| Riesgo sistemático de acciones ordinarias Humana | βHUM | 0.94 |
| Tasa de rendimiento esperada de las acciones ordinarias de Humana3 | E(RHUM) | 12.01% |
1 Promedio no ponderado de los rendimientos de las ofertas en todos los bonos del Tesoro de los Estados Unidos con cupón fijo pendientes, ni vencidos ni exigibles en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RHUM) = RF + βHUM [E(RM) – RF]
= 3.72% + 0.94 [12.54% – 3.72%]
= 12.01%