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 sobre activos de riesgo como las acciones ordinarias de Northrop Grumman.
Tasas de retorno
Northrop Grumman Corp., tasas mensuales de retorno
| Northrop Grumman Corp. (NOC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioNOC,t1 | DividendoNOC,t1 | RNOC,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $340.53 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $350.04 | 2.79% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $349.12 | $1.10 | 0.05% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $322.04 | -7.76% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $533.29 | $1.73 | -2.55% | 4,080.11 | 5.38% |
| 59. | 31 dic. 2022 | $545.61 | 2.31% | 3,839.50 | -5.90% | |
| Promedio (R): | 1.17% | 0.67% | ||||
| Desviación estándar: | 6.86% | 5.40% | ||||
| Northrop Grumman Corp. (NOC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioNOC,t1 | DividendoNOC,t1 | RNOC,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $340.53 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $350.04 | 2.79% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $349.12 | $1.10 | 0.05% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $322.04 | -7.76% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $327.25 | 1.62% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $307.70 | $1.20 | -5.61% | 2,718.37 | 0.48% |
| 6. | 31 jul. 2018 | $300.49 | -2.34% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $298.49 | $1.20 | -0.27% | 2,901.52 | 3.03% |
| 8. | 30 sept. 2018 | $317.37 | 6.33% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $261.95 | -17.46% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $259.88 | $1.20 | -0.33% | 2,760.17 | 1.79% |
| 11. | 31 dic. 2018 | $244.90 | -5.76% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $275.55 | 12.52% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $289.96 | $1.20 | 5.67% | 2,784.49 | 2.97% |
| 14. | 31 mar. 2019 | $269.60 | -7.02% | 2,834.40 | 1.79% | |
| 15. | 30 abr. 2019 | $289.91 | 7.53% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $303.25 | $1.32 | 5.06% | 2,752.06 | -6.58% |
| 17. | 30 jun. 2019 | $323.11 | 6.55% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $345.57 | 6.95% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $367.87 | 6.45% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $374.79 | $1.32 | 2.24% | 2,976.74 | 1.72% |
| 21. | 31 oct. 2019 | $352.48 | -5.95% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $351.77 | $1.32 | 0.17% | 3,140.98 | 3.40% |
| 23. | 31 dic. 2019 | $343.97 | -2.22% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $374.57 | 8.90% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $328.84 | $1.32 | -11.86% | 2,954.22 | -8.41% |
| 26. | 31 mar. 2020 | $302.55 | -7.99% | 2,584.59 | -12.51% | |
| 27. | 30 abr. 2020 | $330.67 | 9.29% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $335.20 | $1.45 | 1.81% | 3,044.31 | 4.53% |
| 29. | 30 jun. 2020 | $307.44 | -8.28% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $325.01 | 5.71% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $342.61 | $1.45 | 5.86% | 3,500.31 | 7.01% |
| 32. | 30 sept. 2020 | $315.49 | -7.92% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $289.82 | -8.14% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $302.26 | $1.45 | 4.79% | 3,621.63 | 10.75% |
| 35. | 31 dic. 2020 | $304.72 | 0.81% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $286.61 | -5.94% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $291.66 | $1.45 | 2.27% | 3,811.15 | 2.61% |
| 38. | 31 mar. 2021 | $323.64 | 10.96% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $354.44 | 9.52% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $365.87 | $1.57 | 3.67% | 4,204.11 | 0.55% |
| 41. | 30 jun. 2021 | $363.43 | -0.67% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $363.02 | -0.11% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $367.70 | $1.57 | 1.72% | 4,522.68 | 2.90% |
| 44. | 30 sept. 2021 | $360.15 | -2.05% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $357.22 | -0.81% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $348.80 | $1.57 | -1.92% | 4,567.00 | -0.83% |
| 47. | 31 dic. 2021 | $387.07 | 10.97% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $369.90 | -4.44% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $442.14 | $1.57 | 19.95% | 4,373.94 | -3.14% |
| 50. | 31 mar. 2022 | $447.22 | 1.15% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $439.40 | -1.75% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $467.97 | $1.73 | 6.90% | 4,132.15 | 0.01% |
| 53. | 30 jun. 2022 | $478.57 | 2.27% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $478.90 | 0.07% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $477.99 | $1.73 | 0.17% | 3,955.00 | -4.24% |
| 56. | 30 sept. 2022 | $470.32 | -1.60% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $549.01 | 16.73% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $533.29 | $1.73 | -2.55% | 4,080.11 | 5.38% |
| 59. | 31 dic. 2022 | $545.61 | 2.31% | 3,839.50 | -5.90% | |
| Promedio (R): | 1.17% | 0.67% | ||||
| Desviación estándar: | 6.86% | 5.40% | ||||
Mostrar todo
1 Datos en US$ por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de NOC 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
Northrop Grumman Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RNOC,t | RS&P 500,t | (RNOC,t–RNOC)2 | (RS&P 500,t–RS&P 500)2 | (RNOC,t–RNOC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | 2.79% | -3.89% | 2.63 | 20.81 | -7.40 |
| 2. | 31 mar. 2018 | 0.05% | -2.69% | 1.25 | 11.26 | 3.75 |
| 3. | 30 abr. 2018 | -7.76% | 0.27% | 79.68 | 0.16 | 3.52 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | -2.55% | 5.38% | 13.82 | 22.17 | -17.51 |
| 59. | 31 dic. 2022 | 2.31% | -5.90% | 1.30 | 43.08 | -7.49 |
| Total (Σ): | 2,731.47 | 1,691.48 | 976.36 | |||
| t | Fecha | RNOC,t | RS&P 500,t | (RNOC,t–RNOC)2 | (RS&P 500,t–RS&P 500)2 | (RNOC,t–RNOC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | 2.79% | -3.89% | 2.63 | 20.81 | -7.40 |
| 2. | 31 mar. 2018 | 0.05% | -2.69% | 1.25 | 11.26 | 3.75 |
| 3. | 30 abr. 2018 | -7.76% | 0.27% | 79.68 | 0.16 | 3.52 |
| 4. | 31 may. 2018 | 1.62% | 2.16% | 0.20 | 2.23 | 0.67 |
| 5. | 30 jun. 2018 | -5.61% | 0.48% | 45.93 | 0.03 | 1.24 |
| 6. | 31 jul. 2018 | -2.34% | 3.60% | 12.34 | 8.62 | -10.31 |
| 7. | 31 ago. 2018 | -0.27% | 3.03% | 2.06 | 5.57 | -3.39 |
| 8. | 30 sept. 2018 | 6.33% | 0.43% | 26.58 | 0.06 | -1.22 |
| 9. | 31 oct. 2018 | -17.46% | -6.94% | 347.15 | 57.87 | 141.73 |
| 10. | 30 nov. 2018 | -0.33% | 1.79% | 2.26 | 1.25 | -1.68 |
| 11. | 31 dic. 2018 | -5.76% | -9.18% | 48.08 | 96.91 | 68.26 |
| 12. | 31 ene. 2019 | 12.52% | 7.87% | 128.72 | 51.87 | 81.71 |
| 13. | 28 feb. 2019 | 5.67% | 2.97% | 20.21 | 5.32 | 10.37 |
| 14. | 31 mar. 2019 | -7.02% | 1.79% | 67.10 | 1.27 | -9.22 |
| 15. | 30 abr. 2019 | 7.53% | 3.93% | 40.50 | 10.66 | 20.78 |
| 16. | 31 may. 2019 | 5.06% | -6.58% | 15.11 | 52.48 | -28.16 |
| 17. | 30 jun. 2019 | 6.55% | 6.89% | 28.94 | 38.77 | 33.49 |
| 18. | 31 jul. 2019 | 6.95% | 1.31% | 33.43 | 0.42 | 3.74 |
| 19. | 31 ago. 2019 | 6.45% | -1.81% | 27.92 | 6.13 | -13.08 |
| 20. | 30 sept. 2019 | 2.24% | 1.72% | 1.15 | 1.11 | 1.13 |
| 21. | 31 oct. 2019 | -5.95% | 2.04% | 50.73 | 1.89 | -9.80 |
| 22. | 30 nov. 2019 | 0.17% | 3.40% | 0.99 | 7.50 | -2.73 |
| 23. | 31 dic. 2019 | -2.22% | 2.86% | 11.47 | 4.81 | -7.43 |
| 24. | 31 ene. 2020 | 8.90% | -0.16% | 59.70 | 0.69 | -6.41 |
| 25. | 29 feb. 2020 | -11.86% | -8.41% | 169.67 | 82.40 | 118.25 |
| 26. | 31 mar. 2020 | -7.99% | -12.51% | 83.99 | 173.67 | 120.77 |
| 27. | 30 abr. 2020 | 9.29% | 12.68% | 66.01 | 144.43 | 97.64 |
| 28. | 31 may. 2020 | 1.81% | 4.53% | 0.41 | 14.91 | 2.47 |
| 29. | 30 jun. 2020 | -8.28% | 1.84% | 89.33 | 1.37 | -11.08 |
| 30. | 31 jul. 2020 | 5.71% | 5.51% | 20.66 | 23.46 | 22.02 |
| 31. | 31 ago. 2020 | 5.86% | 7.01% | 22.01 | 40.19 | 29.74 |
| 32. | 30 sept. 2020 | -7.92% | -3.92% | 82.54 | 21.06 | 41.70 |
| 33. | 31 oct. 2020 | -8.14% | -2.77% | 86.61 | 11.79 | 31.95 |
| 34. | 30 nov. 2020 | 4.79% | 10.75% | 13.13 | 101.77 | 36.55 |
| 35. | 31 dic. 2020 | 0.81% | 3.71% | 0.13 | 9.28 | -1.08 |
| 36. | 31 ene. 2021 | -5.94% | -1.11% | 50.59 | 3.17 | 12.66 |
| 37. | 28 feb. 2021 | 2.27% | 2.61% | 1.21 | 3.77 | 2.13 |
| 38. | 31 mar. 2021 | 10.96% | 4.24% | 95.95 | 12.80 | 35.04 |
| 39. | 30 abr. 2021 | 9.52% | 5.24% | 69.67 | 20.94 | 38.20 |
| 40. | 31 may. 2021 | 3.67% | 0.55% | 6.24 | 0.01 | -0.29 |
| 41. | 30 jun. 2021 | -0.67% | 2.22% | 3.37 | 2.42 | -2.86 |
| 42. | 31 jul. 2021 | -0.11% | 2.27% | 1.64 | 2.59 | -2.06 |
| 43. | 31 ago. 2021 | 1.72% | 2.90% | 0.30 | 4.98 | 1.23 |
| 44. | 30 sept. 2021 | -2.05% | -4.76% | 10.39 | 29.42 | 17.48 |
| 45. | 31 oct. 2021 | -0.81% | 6.91% | 3.93 | 39.03 | -12.39 |
| 46. | 30 nov. 2021 | -1.92% | -0.83% | 9.53 | 2.25 | 4.63 |
| 47. | 31 dic. 2021 | 10.97% | 4.36% | 96.08 | 13.65 | 36.22 |
| 48. | 31 ene. 2022 | -4.44% | -5.26% | 31.42 | 35.11 | 33.21 |
| 49. | 28 feb. 2022 | 19.95% | -3.14% | 352.85 | 14.46 | -71.43 |
| 50. | 31 mar. 2022 | 1.15% | 3.58% | 0.00 | 8.47 | -0.06 |
| 51. | 30 abr. 2022 | -1.75% | -8.80% | 8.52 | 89.54 | 27.61 |
| 52. | 31 may. 2022 | 6.90% | 0.01% | 32.79 | 0.44 | -3.79 |
| 53. | 30 jun. 2022 | 2.27% | -8.39% | 1.20 | 82.06 | -9.92 |
| 54. | 31 jul. 2022 | 0.07% | 9.11% | 1.21 | 71.32 | -9.30 |
| 55. | 31 ago. 2022 | 0.17% | -4.24% | 1.00 | 24.11 | 4.90 |
| 56. | 30 sept. 2022 | -1.60% | -9.34% | 7.70 | 100.12 | 27.76 |
| 57. | 31 oct. 2022 | 16.73% | 7.99% | 242.16 | 53.58 | 113.91 |
| 58. | 30 nov. 2022 | -2.55% | 5.38% | 13.82 | 22.17 | -17.51 |
| 59. | 31 dic. 2022 | 2.31% | -5.90% | 1.30 | 43.08 | -7.49 |
| Total (Σ): | 2,731.47 | 1,691.48 | 976.36 | |||
Mostrar todo
VarianzaNOC = Σ(RNOC,t–RNOC)2 ÷ (59 – 1)
= 2,731.47 ÷ (59 – 1)
= 47.09
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaNOC, S&P 500 = Σ(RNOC,t–RNOC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 976.36 ÷ (59 – 1)
= 16.83
Estimación sistemática del riesgo (β)
| VarianzaNOC | 47.09 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaNOC, S&P 500 | 16.83 |
| Coeficiente de correlaciónNOC, S&P 5001 | 0.45 |
| βNOC2 | 0.58 |
| αNOC3 | 0.78% |
Cálculos
1 Coeficiente de correlaciónNOC, S&P 500
= CovarianzaNOC, S&P 500 ÷ (Desviación estándarNOC × Desviación estándarS&P 500)
= 16.83 ÷ (6.86% × 5.40%)
= 0.45
2 βNOC
= CovarianzaNOC, S&P 500 ÷ VarianzaS&P 500
= 16.83 ÷ 29.16
= 0.58
3 αNOC
= PromedioNOC – βNOC × PromedioS&P 500
= 1.17% – 0.58 × 0.67%
= 0.78%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento de LT Treasury Composite1 | RF | 3.84% |
| Tasa de rendimiento esperada en la cartera de mercado2 | E(RM) | 13.71% |
| Riesgo sistemático de Northrop Grumman acciones ordinarias | βNOC | 0.58 |
| Tasa de rendimiento esperada de las acciones ordinarias de Northrop Grumman3 | E(RNOC) | 9.53% |
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(RNOC) = RF + βNOC [E(RM) – RF]
= 3.84% + 0.58 [13.71% – 3.84%]
= 9.53%