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 Illumina.
Tasas de retorno
Illumina Inc., tasas mensuales de retorno
| Illumina Inc. (ILMN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioILMN,t1 | DividendoILMN,t1 | RILMN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene 2016 | $157.95 | 1,940.24 | ||||
| 1. | 29 feb 2016 | $150.24 | -4.88% | 1,932.23 | -0.41% | |
| 2. | 31 mar 2016 | $162.11 | 7.90% | 2,059.74 | 6.60% | |
| 3. | 30 abr 2016 | $134.99 | -16.73% | 2,065.30 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov 2020 | $322.09 | 10.04% | 3,621.63 | 10.75% | |
| 59. | 31 dic 2020 | $370.00 | 14.87% | 3,756.07 | 3.71% | |
| Promedio (R): | 1.96% | 1.22% | ||||
| Desviación estándar: | 10.13% | 4.36% | ||||
| Illumina Inc. (ILMN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioILMN,t1 | DividendoILMN,t1 | RILMN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene 2016 | $157.95 | 1,940.24 | ||||
| 1. | 29 feb 2016 | $150.24 | -4.88% | 1,932.23 | -0.41% | |
| 2. | 31 mar 2016 | $162.11 | 7.90% | 2,059.74 | 6.60% | |
| 3. | 30 abr 2016 | $134.99 | -16.73% | 2,065.30 | 0.27% | |
| 4. | 31 may 2016 | $144.83 | 7.29% | 2,096.95 | 1.53% | |
| 5. | 30 jun 2016 | $140.38 | -3.07% | 2,098.86 | 0.09% | |
| 6. | 31 jul 2016 | $166.35 | 18.50% | 2,173.60 | 3.56% | |
| 7. | 31 ago 2016 | $168.34 | 1.20% | 2,170.95 | -0.12% | |
| 8. | 30 sept 2016 | $181.66 | 7.91% | 2,168.27 | -0.12% | |
| 9. | 31 oct 2016 | $136.14 | -25.06% | 2,126.15 | -1.94% | |
| 10. | 30 nov 2016 | $133.14 | -2.20% | 2,198.81 | 3.42% | |
| 11. | 31 dic 2016 | $128.04 | -3.83% | 2,238.83 | 1.82% | |
| 12. | 31 ene 2017 | $160.10 | 25.04% | 2,278.87 | 1.79% | |
| 13. | 28 feb 2017 | $167.40 | 4.56% | 2,363.64 | 3.72% | |
| 14. | 31 mar 2017 | $170.64 | 1.94% | 2,362.72 | -0.04% | |
| 15. | 30 abr 2017 | $184.86 | 8.33% | 2,384.20 | 0.91% | |
| 16. | 31 may 2017 | $177.36 | -4.06% | 2,411.80 | 1.16% | |
| 17. | 30 jun 2017 | $173.52 | -2.17% | 2,423.41 | 0.48% | |
| 18. | 31 jul 2017 | $173.85 | 0.19% | 2,470.30 | 1.93% | |
| 19. | 31 ago 2017 | $204.46 | 17.61% | 2,471.65 | 0.05% | |
| 20. | 30 sept 2017 | $199.20 | -2.57% | 2,519.36 | 1.93% | |
| 21. | 31 oct 2017 | $205.19 | 3.01% | 2,575.26 | 2.22% | |
| 22. | 30 nov 2017 | $230.03 | 12.11% | 2,647.58 | 2.81% | |
| 23. | 31 dic 2017 | $218.49 | -5.02% | 2,673.61 | 0.98% | |
| 24. | 31 ene 2018 | $232.64 | 6.48% | 2,823.81 | 5.62% | |
| 25. | 28 feb 2018 | $228.02 | -1.99% | 2,713.83 | -3.89% | |
| 26. | 31 mar 2018 | $236.42 | 3.68% | 2,640.87 | -2.69% | |
| 27. | 30 abr 2018 | $240.93 | 1.91% | 2,648.05 | 0.27% | |
| 28. | 31 may 2018 | $272.44 | 13.08% | 2,705.27 | 2.16% | |
| 29. | 30 jun 2018 | $279.29 | 2.51% | 2,718.37 | 0.48% | |
| 30. | 31 jul 2018 | $324.36 | 16.14% | 2,816.29 | 3.60% | |
| 31. | 31 ago 2018 | $354.83 | 9.39% | 2,901.52 | 3.03% | |
| 32. | 30 sept 2018 | $367.06 | 3.45% | 2,913.98 | 0.43% | |
| 33. | 31 oct 2018 | $311.15 | -15.23% | 2,711.74 | -6.94% | |
| 34. | 30 nov 2018 | $337.50 | 8.47% | 2,760.17 | 1.79% | |
| 35. | 31 dic 2018 | $299.93 | -11.13% | 2,506.85 | -9.18% | |
| 36. | 31 ene 2019 | $279.79 | -6.71% | 2,704.10 | 7.87% | |
| 37. | 28 feb 2019 | $312.77 | 11.79% | 2,784.49 | 2.97% | |
| 38. | 31 mar 2019 | $310.69 | -0.67% | 2,834.40 | 1.79% | |
| 39. | 30 abr 2019 | $312.00 | 0.42% | 2,945.83 | 3.93% | |
| 40. | 31 may 2019 | $306.91 | -1.63% | 2,752.06 | -6.58% | |
| 41. | 30 jun 2019 | $368.15 | 19.95% | 2,941.76 | 6.89% | |
| 42. | 31 jul 2019 | $299.38 | -18.68% | 2,980.38 | 1.31% | |
| 43. | 31 ago 2019 | $281.34 | -6.03% | 2,926.46 | -1.81% | |
| 44. | 30 sept 2019 | $304.22 | 8.13% | 2,976.74 | 1.72% | |
| 45. | 31 oct 2019 | $295.52 | -2.86% | 3,037.56 | 2.04% | |
| 46. | 30 nov 2019 | $320.76 | 8.54% | 3,140.98 | 3.40% | |
| 47. | 31 dic 2019 | $331.74 | 3.42% | 3,230.78 | 2.86% | |
| 48. | 31 ene 2020 | $290.07 | -12.56% | 3,225.52 | -0.16% | |
| 49. | 29 feb 2020 | $265.67 | -8.41% | 2,954.22 | -8.41% | |
| 50. | 31 mar 2020 | $273.12 | 2.80% | 2,584.59 | -12.51% | |
| 51. | 30 abr 2020 | $319.03 | 16.81% | 2,912.43 | 12.68% | |
| 52. | 31 may 2020 | $363.05 | 13.80% | 3,044.31 | 4.53% | |
| 53. | 30 jun 2020 | $370.35 | 2.01% | 3,100.29 | 1.84% | |
| 54. | 31 jul 2020 | $382.16 | 3.19% | 3,271.12 | 5.51% | |
| 55. | 31 ago 2020 | $357.22 | -6.53% | 3,500.31 | 7.01% | |
| 56. | 30 sept 2020 | $309.08 | -13.48% | 3,363.00 | -3.92% | |
| 57. | 31 oct 2020 | $292.70 | -5.30% | 3,269.96 | -2.77% | |
| 58. | 30 nov 2020 | $322.09 | 10.04% | 3,621.63 | 10.75% | |
| 59. | 31 dic 2020 | $370.00 | 14.87% | 3,756.07 | 3.71% | |
| Promedio (R): | 1.96% | 1.22% | ||||
| Desviación estándar: | 10.13% | 4.36% | ||||
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 ILMN 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
Illumina Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RILMN,t | RS&P 500,t | (RILMN,t–RILMN)2 | (RS&P 500,t–RS&P 500)2 | (RILMN,t–RILMN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 feb 2016 | -4.88% | -0.41% | 46.81 | 2.67 | 11.17 |
| 2. | 31 mar 2016 | 7.90% | 6.60% | 35.28 | 28.93 | 31.95 |
| 3. | 30 abr 2016 | -16.73% | 0.27% | 349.32 | 0.90 | 17.76 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov 2020 | 10.04% | 10.75% | 65.29 | 90.91 | 77.04 |
| 59. | 31 dic 2020 | 14.87% | 3.71% | 166.77 | 6.21 | 32.18 |
| Total (Σ): | 5,951.36 | 1,103.45 | 1,173.17 | |||
| t | Fecha | RILMN,t | RS&P 500,t | (RILMN,t–RILMN)2 | (RS&P 500,t–RS&P 500)2 | (RILMN,t–RILMN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 feb 2016 | -4.88% | -0.41% | 46.81 | 2.67 | 11.17 |
| 2. | 31 mar 2016 | 7.90% | 6.60% | 35.28 | 28.93 | 31.95 |
| 3. | 30 abr 2016 | -16.73% | 0.27% | 349.32 | 0.90 | 17.76 |
| 4. | 31 may 2016 | 7.29% | 1.53% | 28.40 | 0.10 | 1.66 |
| 5. | 30 jun 2016 | -3.07% | 0.09% | 25.33 | 1.27 | 5.68 |
| 6. | 31 jul 2016 | 18.50% | 3.56% | 273.54 | 5.48 | 38.72 |
| 7. | 31 ago 2016 | 1.20% | -0.12% | 0.58 | 1.80 | 1.03 |
| 8. | 30 sept 2016 | 7.91% | -0.12% | 35.42 | 1.81 | -8.00 |
| 9. | 31 oct 2016 | -25.06% | -1.94% | 730.00 | 10.00 | 85.45 |
| 10. | 30 nov 2016 | -2.20% | 3.42% | 17.34 | 4.83 | -9.15 |
| 11. | 31 dic 2016 | -3.83% | 1.82% | 33.54 | 0.36 | -3.47 |
| 12. | 31 ene 2017 | 25.04% | 1.79% | 532.61 | 0.32 | 13.12 |
| 13. | 28 feb 2017 | 4.56% | 3.72% | 6.75 | 6.25 | 6.50 |
| 14. | 31 mar 2017 | 1.94% | -0.04% | 0.00 | 1.59 | 0.03 |
| 15. | 30 abr 2017 | 8.33% | 0.91% | 40.61 | 0.10 | -1.98 |
| 16. | 31 may 2017 | -4.06% | 1.16% | 36.21 | 0.00 | 0.38 |
| 17. | 30 jun 2017 | -2.17% | 0.48% | 17.02 | 0.55 | 3.05 |
| 18. | 31 jul 2017 | 0.19% | 1.93% | 3.13 | 0.51 | -1.27 |
| 19. | 31 ago 2017 | 17.61% | 0.05% | 244.81 | 1.36 | -18.23 |
| 20. | 30 sept 2017 | -2.57% | 1.93% | 20.55 | 0.50 | -3.22 |
| 21. | 31 oct 2017 | 3.01% | 2.22% | 1.09 | 1.00 | 1.05 |
| 22. | 30 nov 2017 | 12.11% | 2.81% | 102.92 | 2.52 | 16.11 |
| 23. | 31 dic 2017 | -5.02% | 0.98% | 48.68 | 0.06 | 1.65 |
| 24. | 31 ene 2018 | 6.48% | 5.62% | 20.39 | 19.34 | 19.86 |
| 25. | 28 feb 2018 | -1.99% | -3.89% | 15.58 | 26.16 | 20.19 |
| 26. | 31 mar 2018 | 3.68% | -2.69% | 2.97 | 15.28 | -6.74 |
| 27. | 30 abr 2018 | 1.91% | 0.27% | 0.00 | 0.90 | 0.05 |
| 28. | 31 may 2018 | 13.08% | 2.16% | 123.60 | 0.89 | 10.46 |
| 29. | 30 jun 2018 | 2.51% | 0.48% | 0.31 | 0.54 | -0.41 |
| 30. | 31 jul 2018 | 16.14% | 3.60% | 200.98 | 5.67 | 33.77 |
| 31. | 31 ago 2018 | 9.39% | 3.03% | 55.25 | 3.26 | 13.43 |
| 32. | 30 sept 2018 | 3.45% | 0.43% | 2.21 | 0.63 | -1.17 |
| 33. | 31 oct 2018 | -15.23% | -6.94% | 295.58 | 66.59 | 140.30 |
| 34. | 30 nov 2018 | 8.47% | 1.79% | 42.35 | 0.32 | 3.68 |
| 35. | 31 dic 2018 | -11.13% | -9.18% | 171.42 | 108.11 | 136.13 |
| 36. | 31 ene 2019 | -6.71% | 7.87% | 75.27 | 44.20 | -57.68 |
| 37. | 28 feb 2019 | 11.79% | 2.97% | 96.56 | 3.07 | 17.22 |
| 38. | 31 mar 2019 | -0.67% | 1.79% | 6.89 | 0.33 | -1.50 |
| 39. | 30 abr 2019 | 0.42% | 3.93% | 2.37 | 7.35 | -4.17 |
| 40. | 31 may 2019 | -1.63% | -6.58% | 12.90 | 60.81 | 28.01 |
| 41. | 30 jun 2019 | 19.95% | 6.89% | 323.75 | 32.18 | 102.07 |
| 42. | 31 jul 2019 | -18.68% | 1.31% | 426.03 | 0.01 | -1.91 |
| 43. | 31 ago 2019 | -6.03% | -1.81% | 63.78 | 9.18 | 24.19 |
| 44. | 30 sept 2019 | 8.13% | 1.72% | 38.09 | 0.25 | 3.07 |
| 45. | 31 oct 2019 | -2.86% | 2.04% | 23.24 | 0.68 | -3.97 |
| 46. | 30 nov 2019 | 8.54% | 3.40% | 43.30 | 4.77 | 14.38 |
| 47. | 31 dic 2019 | 3.42% | 2.86% | 2.14 | 2.69 | 2.40 |
| 48. | 31 ene 2020 | -12.56% | -0.16% | 210.88 | 1.91 | 20.08 |
| 49. | 29 feb 2020 | -8.41% | -8.41% | 107.59 | 92.76 | 99.90 |
| 50. | 31 mar 2020 | 2.80% | -12.51% | 0.71 | 188.57 | -11.58 |
| 51. | 30 abr 2020 | 16.81% | 12.68% | 220.49 | 131.43 | 170.23 |
| 52. | 31 may 2020 | 13.80% | 4.53% | 140.12 | 10.94 | 39.16 |
| 53. | 30 jun 2020 | 2.01% | 1.84% | 0.00 | 0.38 | 0.03 |
| 54. | 31 jul 2020 | 3.19% | 5.51% | 1.51 | 18.40 | 5.27 |
| 55. | 31 ago 2020 | -6.53% | 7.01% | 72.03 | 33.48 | -49.11 |
| 56. | 30 sept 2020 | -13.48% | -3.92% | 238.30 | 26.45 | 79.39 |
| 57. | 31 oct 2020 | -5.30% | -2.77% | 52.71 | 15.89 | 28.94 |
| 58. | 30 nov 2020 | 10.04% | 10.75% | 65.29 | 90.91 | 77.04 |
| 59. | 31 dic 2020 | 14.87% | 3.71% | 166.77 | 6.21 | 32.18 |
| Total (Σ): | 5,951.36 | 1,103.45 | 1,173.17 | |||
Mostrar todo
VarianzaILMN = Σ(RILMN,t–RILMN)2 ÷ (59 – 1)
= 5,951.36 ÷ (59 – 1)
= 102.61
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,103.45 ÷ (59 – 1)
= 19.02
CovarianzaILMN, S&P 500 = Σ(RILMN,t–RILMN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,173.17 ÷ (59 – 1)
= 20.23
Estimación sistemática del riesgo (β)
| VarianzaILMN | 102.61 |
| VarianzaS&P 500 | 19.02 |
| CovarianzaILMN, S&P 500 | 20.23 |
| Coeficiente de correlaciónILMN, S&P 5001 | 0.46 |
| βILMN2 | 1.06 |
| αILMN3 | 0.66% |
Cálculos
1 Coeficiente de correlaciónILMN, S&P 500
= CovarianzaILMN, S&P 500 ÷ (Desviación estándarILMN × Desviación estándarS&P 500)
= 20.23 ÷ (10.13% × 4.36%)
= 0.46
2 βILMN
= CovarianzaILMN, S&P 500 ÷ VarianzaS&P 500
= 20.23 ÷ 19.02
= 1.06
3 αILMN
= PromedioILMN – βILMN × PromedioS&P 500
= 1.96% – 1.06 × 1.22%
= 0.66%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.94% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 14.84% |
| Riesgo sistemático de Illumina acciones ordinarias | βILMN | 1.06 |
| Tasa de rendimiento esperada de las acciones ordinarias de Illumina3 | E(RILMN) | 15.46% |
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(RILMN) = RF + βILMN [E(RM) – RF]
= 4.94% + 1.06 [14.84% – 4.94%]
= 15.46%