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 NXP.
Tasas de retorno
NXP Semiconductors N.V., tasas mensuales de retorno
| NXP Semiconductors N.V. (NXPI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioNXPI,t1 | DividendoNXPI,t1 | RNXPI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $97.85 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $102.81 | 5.07% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $103.50 | 0.67% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $105.75 | 2.17% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $223.36 | 11.20% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $227.78 | $0.5625 | 2.23% | 4,766.18 | 4.36% |
| Promedio (R): | 1.93% | 1.36% | ||||
| Desviación estándar: | 9.12% | 4.48% | ||||
| NXP Semiconductors N.V. (NXPI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioNXPI,t1 | DividendoNXPI,t1 | RNXPI,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $97.85 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $102.81 | 5.07% | 2,363.64 | 3.72% | |
| 2. | 31 mar. 2017 | $103.50 | 0.67% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $105.75 | 2.17% | 2,384.20 | 0.91% | |
| 4. | 31 may. 2017 | $109.90 | 3.92% | 2,411.80 | 1.16% | |
| 5. | 30 jun. 2017 | $109.45 | -0.41% | 2,423.41 | 0.48% | |
| 6. | 31 jul. 2017 | $110.33 | 0.80% | 2,470.30 | 1.93% | |
| 7. | 31 ago. 2017 | $112.96 | 2.38% | 2,471.65 | 0.05% | |
| 8. | 30 sept. 2017 | $113.09 | 0.12% | 2,519.36 | 1.93% | |
| 9. | 31 oct. 2017 | $117.05 | 3.50% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $113.39 | -3.13% | 2,647.58 | 2.81% | |
| 11. | 31 dic. 2017 | $117.09 | 3.26% | 2,673.61 | 0.98% | |
| 12. | 31 ene. 2018 | $120.32 | 2.76% | 2,823.81 | 5.62% | |
| 13. | 28 feb. 2018 | $124.66 | 3.61% | 2,713.83 | -3.89% | |
| 14. | 31 mar. 2018 | $117.00 | -6.14% | 2,640.87 | -2.69% | |
| 15. | 30 abr. 2018 | $104.90 | -10.34% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $114.00 | 8.67% | 2,705.27 | 2.16% | |
| 17. | 30 jun. 2018 | $109.27 | -4.15% | 2,718.37 | 0.48% | |
| 18. | 31 jul. 2018 | $95.34 | -12.75% | 2,816.29 | 3.60% | |
| 19. | 31 ago. 2018 | $93.14 | -2.31% | 2,901.52 | 3.03% | |
| 20. | 30 sept. 2018 | $85.50 | $0.25 | -7.93% | 2,913.98 | 0.43% |
| 21. | 31 oct. 2018 | $74.99 | -12.29% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $83.37 | 11.17% | 2,760.17 | 1.79% | |
| 23. | 31 dic. 2018 | $73.28 | $0.25 | -11.80% | 2,506.85 | -9.18% |
| 24. | 31 ene. 2019 | $87.03 | 18.76% | 2,704.10 | 7.87% | |
| 25. | 28 feb. 2019 | $91.32 | 4.93% | 2,784.49 | 2.97% | |
| 26. | 31 mar. 2019 | $88.39 | $0.25 | -2.93% | 2,834.40 | 1.79% |
| 27. | 30 abr. 2019 | $105.62 | 19.49% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $88.16 | -16.53% | 2,752.06 | -6.58% | |
| 29. | 30 jun. 2019 | $97.61 | $0.25 | 11.00% | 2,941.76 | 6.89% |
| 30. | 31 jul. 2019 | $103.39 | 5.92% | 2,980.38 | 1.31% | |
| 31. | 31 ago. 2019 | $102.14 | -1.21% | 2,926.46 | -1.81% | |
| 32. | 30 sept. 2019 | $109.12 | $0.375 | 7.20% | 2,976.74 | 1.72% |
| 33. | 31 oct. 2019 | $113.68 | 4.18% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $115.58 | 1.67% | 3,140.98 | 3.40% | |
| 35. | 31 dic. 2019 | $127.26 | $0.375 | 10.43% | 3,230.78 | 2.86% |
| 36. | 31 ene. 2020 | $126.86 | -0.31% | 3,225.52 | -0.16% | |
| 37. | 29 feb. 2020 | $113.69 | -10.38% | 2,954.22 | -8.41% | |
| 38. | 31 mar. 2020 | $82.93 | $0.375 | -26.73% | 2,584.59 | -12.51% |
| 39. | 30 abr. 2020 | $99.57 | 20.07% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $96.10 | -3.48% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $114.04 | $0.375 | 19.06% | 3,100.29 | 1.84% |
| 42. | 31 jul. 2020 | $117.53 | 3.06% | 3,271.12 | 5.51% | |
| 43. | 31 ago. 2020 | $125.76 | 7.00% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $124.81 | $0.375 | -0.46% | 3,363.00 | -3.92% |
| 45. | 31 oct. 2020 | $135.12 | 8.26% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $158.42 | 17.24% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $159.01 | $0.375 | 0.61% | 3,756.07 | 3.71% |
| 48. | 31 ene. 2021 | $160.47 | 0.92% | 3,714.24 | -1.11% | |
| 49. | 28 feb. 2021 | $182.55 | 13.76% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $201.34 | $0.5625 | 10.60% | 3,972.89 | 4.24% |
| 51. | 30 abr. 2021 | $192.51 | -4.39% | 4,181.17 | 5.24% | |
| 52. | 31 may. 2021 | $211.42 | 9.82% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $205.72 | $0.5625 | -2.43% | 4,297.50 | 2.22% |
| 54. | 31 jul. 2021 | $206.39 | 0.33% | 4,395.26 | 2.27% | |
| 55. | 31 ago. 2021 | $215.13 | 4.23% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $195.87 | $0.5625 | -8.69% | 4,307.54 | -4.76% |
| 57. | 31 oct. 2021 | $200.86 | 2.55% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $223.36 | 11.20% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $227.78 | $0.5625 | 2.23% | 4,766.18 | 4.36% |
| Promedio (R): | 1.93% | 1.36% | ||||
| Desviación estándar: | 9.12% | 4.48% | ||||
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 NXPI 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
NXP Semiconductors N.V., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RNXPI,t | RS&P 500,t | (RNXPI,t–RNXPI)2 | (RS&P 500,t–RS&P 500)2 | (RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 5.07% | 3.72% | 9.86 | 5.58 | 7.41 |
| 2. | 31 mar. 2017 | 0.67% | -0.04% | 1.58 | 1.95 | 1.76 |
| 3. | 30 abr. 2017 | 2.17% | 0.91% | 0.06 | 0.20 | -0.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | 11.20% | -0.83% | 85.97 | 4.80 | -20.32 |
| 59. | 31 dic. 2021 | 2.23% | 4.36% | 0.09 | 9.02 | 0.90 |
| Total (Σ): | 4,825.79 | 1,164.17 | 1,605.82 | |||
| t | Fecha | RNXPI,t | RS&P 500,t | (RNXPI,t–RNXPI)2 | (RS&P 500,t–RS&P 500)2 | (RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | 5.07% | 3.72% | 9.86 | 5.58 | 7.41 |
| 2. | 31 mar. 2017 | 0.67% | -0.04% | 1.58 | 1.95 | 1.76 |
| 3. | 30 abr. 2017 | 2.17% | 0.91% | 0.06 | 0.20 | -0.11 |
| 4. | 31 may. 2017 | 3.92% | 1.16% | 3.98 | 0.04 | -0.40 |
| 5. | 30 jun. 2017 | -0.41% | 0.48% | 5.47 | 0.77 | 2.05 |
| 6. | 31 jul. 2017 | 0.80% | 1.93% | 1.27 | 0.33 | -0.65 |
| 7. | 31 ago. 2017 | 2.38% | 0.05% | 0.21 | 1.70 | -0.59 |
| 8. | 30 sept. 2017 | 0.12% | 1.93% | 3.29 | 0.33 | -1.04 |
| 9. | 31 oct. 2017 | 3.50% | 2.22% | 2.47 | 0.74 | 1.35 |
| 10. | 30 nov. 2017 | -3.13% | 2.81% | 25.57 | 2.10 | -7.33 |
| 11. | 31 dic. 2017 | 3.26% | 0.98% | 1.78 | 0.14 | -0.50 |
| 12. | 31 ene. 2018 | 2.76% | 5.62% | 0.69 | 18.15 | 3.53 |
| 13. | 28 feb. 2018 | 3.61% | -3.89% | 2.81 | 27.59 | -8.81 |
| 14. | 31 mar. 2018 | -6.14% | -2.69% | 65.20 | 16.37 | 32.67 |
| 15. | 30 abr. 2018 | -10.34% | 0.27% | 150.59 | 1.18 | 13.33 |
| 16. | 31 may. 2018 | 8.67% | 2.16% | 45.50 | 0.64 | 5.42 |
| 17. | 30 jun. 2018 | -4.15% | 0.48% | 36.95 | 0.76 | 5.31 |
| 18. | 31 jul. 2018 | -12.75% | 3.60% | 215.44 | 5.04 | -32.94 |
| 19. | 31 ago. 2018 | -2.31% | 3.03% | 17.95 | 2.78 | -7.07 |
| 20. | 30 sept. 2018 | -7.93% | 0.43% | 97.30 | 0.86 | 9.16 |
| 21. | 31 oct. 2018 | -12.29% | -6.94% | 202.27 | 68.86 | 118.02 |
| 22. | 30 nov. 2018 | 11.17% | 1.79% | 85.47 | 0.18 | 3.96 |
| 23. | 31 dic. 2018 | -11.80% | -9.18% | 188.58 | 111.00 | 144.68 |
| 24. | 31 ene. 2019 | 18.76% | 7.87% | 283.38 | 42.39 | 109.60 |
| 25. | 28 feb. 2019 | 4.93% | 2.97% | 9.00 | 2.61 | 4.84 |
| 26. | 31 mar. 2019 | -2.93% | 1.79% | 23.66 | 0.19 | -2.11 |
| 27. | 30 abr. 2019 | 19.49% | 3.93% | 308.48 | 6.62 | 45.20 |
| 28. | 31 may. 2019 | -16.53% | -6.58% | 340.80 | 62.97 | 146.50 |
| 29. | 30 jun. 2019 | 11.00% | 6.89% | 82.32 | 30.64 | 50.22 |
| 30. | 31 jul. 2019 | 5.92% | 1.31% | 15.93 | 0.00 | -0.18 |
| 31. | 31 ago. 2019 | -1.21% | -1.81% | 9.85 | 10.03 | 9.94 |
| 32. | 30 sept. 2019 | 7.20% | 1.72% | 27.79 | 0.13 | 1.90 |
| 33. | 31 oct. 2019 | 4.18% | 2.04% | 5.06 | 0.47 | 1.54 |
| 34. | 30 nov. 2019 | 1.67% | 3.40% | 0.07 | 4.19 | -0.53 |
| 35. | 31 dic. 2019 | 10.43% | 2.86% | 72.26 | 2.25 | 12.76 |
| 36. | 31 ene. 2020 | -0.31% | -0.16% | 5.04 | 2.31 | 3.41 |
| 37. | 29 feb. 2020 | -10.38% | -8.41% | 151.57 | 95.43 | 120.27 |
| 38. | 31 mar. 2020 | -26.73% | -12.51% | 821.16 | 192.37 | 397.45 |
| 39. | 30 abr. 2020 | 20.07% | 12.68% | 328.89 | 128.29 | 205.41 |
| 40. | 31 may. 2020 | -3.48% | 4.53% | 29.32 | 10.05 | -17.17 |
| 41. | 30 jun. 2020 | 19.06% | 1.84% | 293.39 | 0.23 | 8.24 |
| 42. | 31 jul. 2020 | 3.06% | 5.51% | 1.28 | 17.24 | 4.69 |
| 43. | 31 ago. 2020 | 7.00% | 7.01% | 25.73 | 31.91 | 28.65 |
| 44. | 30 sept. 2020 | -0.46% | -3.92% | 5.70 | 27.89 | 12.60 |
| 45. | 31 oct. 2020 | 8.26% | -2.77% | 40.08 | 17.01 | -26.11 |
| 46. | 30 nov. 2020 | 17.24% | 10.75% | 234.53 | 88.30 | 143.90 |
| 47. | 31 dic. 2020 | 0.61% | 3.71% | 1.74 | 5.54 | -3.11 |
| 48. | 31 ene. 2021 | 0.92% | -1.11% | 1.02 | 6.11 | 2.50 |
| 49. | 28 feb. 2021 | 13.76% | 2.61% | 139.95 | 1.57 | 14.80 |
| 50. | 31 mar. 2021 | 10.60% | 4.24% | 75.20 | 8.33 | 25.03 |
| 51. | 30 abr. 2021 | -4.39% | 5.24% | 39.88 | 15.09 | -24.53 |
| 52. | 31 may. 2021 | 9.82% | 0.55% | 62.30 | 0.65 | -6.39 |
| 53. | 30 jun. 2021 | -2.43% | 2.22% | 19.01 | 0.75 | -3.76 |
| 54. | 31 jul. 2021 | 0.33% | 2.27% | 2.57 | 0.84 | -1.47 |
| 55. | 31 ago. 2021 | 4.23% | 2.90% | 5.31 | 2.38 | 3.55 |
| 56. | 30 sept. 2021 | -8.69% | -4.76% | 112.80 | 37.39 | 64.95 |
| 57. | 31 oct. 2021 | 2.55% | 6.91% | 0.38 | 30.87 | 3.43 |
| 58. | 30 nov. 2021 | 11.20% | -0.83% | 85.97 | 4.80 | -20.32 |
| 59. | 31 dic. 2021 | 2.23% | 4.36% | 0.09 | 9.02 | 0.90 |
| Total (Σ): | 4,825.79 | 1,164.17 | 1,605.82 | |||
Mostrar todo
VarianzaNXPI = Σ(RNXPI,t–RNXPI)2 ÷ (59 – 1)
= 4,825.79 ÷ (59 – 1)
= 83.20
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaNXPI, S&P 500 = Σ(RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,605.82 ÷ (59 – 1)
= 27.69
Estimación sistemática del riesgo (β)
| VarianzaNXPI | 83.20 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaNXPI, S&P 500 | 27.69 |
| Coeficiente de correlaciónNXPI, S&P 5001 | 0.68 |
| βNXPI2 | 1.38 |
| αNXPI3 | 0.06% |
Cálculos
1 Coeficiente de correlaciónNXPI, S&P 500
= CovarianzaNXPI, S&P 500 ÷ (Desviación estándarNXPI × Desviación estándarS&P 500)
= 27.69 ÷ (9.12% × 4.48%)
= 0.68
2 βNXPI
= CovarianzaNXPI, S&P 500 ÷ VarianzaS&P 500
= 27.69 ÷ 20.07
= 1.38
3 αNXPI
= PromedioNXPI – βNXPI × PromedioS&P 500
= 1.93% – 1.38 × 1.36%
= 0.06%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.81% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.54% |
| Riesgo sistemático de NXP acciones ordinarias | βNXPI | 1.38 |
| Tasa de rendimiento esperada de las acciones ordinarias de NXP3 | E(RNXPI) | 16.85% |
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(RNXPI) = RF + βNXPI [E(RM) – RF]
= 4.81% + 1.38 [13.54% – 4.81%]
= 16.85%