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 General Dynamics.
Tasas de retorno
General Dynamics Corp., tasas mensuales de retorno
| General Dynamics Corp. (GD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGD,t1 | DividendoGD,t1 | RGD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2015 | $133.21 | 1,994.99 | ||||
| 1. | 28 feb. 2015 | $138.78 | 4.18% | 2,104.50 | 5.49% | |
| 2. | 31 mar. 2015 | $135.73 | -2.20% | 2,067.89 | -1.74% | |
| 3. | 30 abr. 2015 | $137.32 | $0.69 | 1.68% | 2,085.51 | 0.85% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | $181.74 | 2.79% | 3,140.98 | 3.40% | |
| 59. | 31 dic. 2019 | $176.35 | -2.97% | 3,230.78 | 2.86% | |
| Promedio (R): | 0.80% | 0.88% | ||||
| Desviación estándar: | 5.84% | 3.45% | ||||
| General Dynamics Corp. (GD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGD,t1 | DividendoGD,t1 | RGD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2015 | $133.21 | 1,994.99 | ||||
| 1. | 28 feb. 2015 | $138.78 | 4.18% | 2,104.50 | 5.49% | |
| 2. | 31 mar. 2015 | $135.73 | -2.20% | 2,067.89 | -1.74% | |
| 3. | 30 abr. 2015 | $137.32 | $0.69 | 1.68% | 2,085.51 | 0.85% |
| 4. | 31 may. 2015 | $140.16 | 2.07% | 2,107.39 | 1.05% | |
| 5. | 30 jun. 2015 | $141.69 | $0.69 | 1.58% | 2,063.11 | -2.10% |
| 6. | 31 jul. 2015 | $149.11 | 5.24% | 2,103.84 | 1.97% | |
| 7. | 31 ago. 2015 | $142.03 | -4.75% | 1,972.18 | -6.26% | |
| 8. | 30 sept. 2015 | $137.95 | -2.87% | 1,920.03 | -2.64% | |
| 9. | 31 oct. 2015 | $148.58 | $0.69 | 8.21% | 2,079.36 | 8.30% |
| 10. | 30 nov. 2015 | $146.46 | -1.43% | 2,080.41 | 0.05% | |
| 11. | 31 dic. 2015 | $137.36 | -6.21% | 2,043.94 | -1.75% | |
| 12. | 31 ene. 2016 | $133.77 | $0.69 | -2.11% | 1,940.24 | -5.07% |
| 13. | 29 feb. 2016 | $136.27 | 1.87% | 1,932.23 | -0.41% | |
| 14. | 31 mar. 2016 | $131.37 | -3.60% | 2,059.74 | 6.60% | |
| 15. | 30 abr. 2016 | $140.52 | $0.76 | 7.54% | 2,065.30 | 0.27% |
| 16. | 31 may. 2016 | $141.87 | 0.96% | 2,096.95 | 1.53% | |
| 17. | 30 jun. 2016 | $139.24 | $0.76 | -1.32% | 2,098.86 | 0.09% |
| 18. | 31 jul. 2016 | $146.89 | 5.49% | 2,173.60 | 3.56% | |
| 19. | 31 ago. 2016 | $152.22 | 3.63% | 2,170.95 | -0.12% | |
| 20. | 30 sept. 2016 | $155.16 | 1.93% | 2,168.27 | -0.12% | |
| 21. | 31 oct. 2016 | $150.74 | $0.76 | -2.36% | 2,126.15 | -1.94% |
| 22. | 30 nov. 2016 | $175.35 | 16.33% | 2,198.81 | 3.42% | |
| 23. | 31 dic. 2016 | $172.66 | -1.53% | 2,238.83 | 1.82% | |
| 24. | 31 ene. 2017 | $181.08 | $0.76 | 5.32% | 2,278.87 | 1.79% |
| 25. | 28 feb. 2017 | $189.81 | 4.82% | 2,363.64 | 3.72% | |
| 26. | 31 mar. 2017 | $187.20 | -1.38% | 2,362.72 | -0.04% | |
| 27. | 30 abr. 2017 | $193.79 | $0.84 | 3.97% | 2,384.20 | 0.91% |
| 28. | 31 may. 2017 | $203.25 | 4.88% | 2,411.80 | 1.16% | |
| 29. | 30 jun. 2017 | $198.10 | -2.53% | 2,423.41 | 0.48% | |
| 30. | 31 jul. 2017 | $196.33 | $0.84 | -0.47% | 2,470.30 | 1.93% |
| 31. | 31 ago. 2017 | $201.35 | 2.56% | 2,471.65 | 0.05% | |
| 32. | 30 sept. 2017 | $205.58 | 2.10% | 2,519.36 | 1.93% | |
| 33. | 31 oct. 2017 | $202.98 | $0.84 | -0.86% | 2,575.26 | 2.22% |
| 34. | 30 nov. 2017 | $207.16 | 2.06% | 2,647.58 | 2.81% | |
| 35. | 31 dic. 2017 | $203.45 | -1.79% | 2,673.61 | 0.98% | |
| 36. | 31 ene. 2018 | $222.48 | $0.84 | 9.77% | 2,823.81 | 5.62% |
| 37. | 28 feb. 2018 | $222.45 | -0.01% | 2,713.83 | -3.89% | |
| 38. | 31 mar. 2018 | $220.90 | -0.70% | 2,640.87 | -2.69% | |
| 39. | 30 abr. 2018 | $201.31 | $0.93 | -8.45% | 2,648.05 | 0.27% |
| 40. | 31 may. 2018 | $201.71 | 0.20% | 2,705.27 | 2.16% | |
| 41. | 30 jun. 2018 | $186.41 | -7.59% | 2,718.37 | 0.48% | |
| 42. | 31 jul. 2018 | $199.76 | $0.93 | 7.66% | 2,816.29 | 3.60% |
| 43. | 31 ago. 2018 | $193.40 | -3.18% | 2,901.52 | 3.03% | |
| 44. | 30 sept. 2018 | $204.72 | 5.85% | 2,913.98 | 0.43% | |
| 45. | 31 oct. 2018 | $172.58 | $0.93 | -15.25% | 2,711.74 | -6.94% |
| 46. | 30 nov. 2018 | $184.89 | 7.13% | 2,760.17 | 1.79% | |
| 47. | 31 dic. 2018 | $157.21 | -14.97% | 2,506.85 | -9.18% | |
| 48. | 31 ene. 2019 | $171.17 | $0.93 | 9.47% | 2,704.10 | 7.87% |
| 49. | 28 feb. 2019 | $170.22 | -0.56% | 2,784.49 | 2.97% | |
| 50. | 31 mar. 2019 | $169.28 | -0.55% | 2,834.40 | 1.79% | |
| 51. | 30 abr. 2019 | $178.72 | $1.02 | 6.18% | 2,945.83 | 3.93% |
| 52. | 31 may. 2019 | $160.82 | -10.02% | 2,752.06 | -6.58% | |
| 53. | 30 jun. 2019 | $181.82 | 13.06% | 2,941.76 | 6.89% | |
| 54. | 31 jul. 2019 | $185.94 | $1.02 | 2.83% | 2,980.38 | 1.31% |
| 55. | 31 ago. 2019 | $191.27 | 2.87% | 2,926.46 | -1.81% | |
| 56. | 30 sept. 2019 | $182.73 | -4.46% | 2,976.74 | 1.72% | |
| 57. | 31 oct. 2019 | $176.80 | $1.02 | -2.69% | 3,037.56 | 2.04% |
| 58. | 30 nov. 2019 | $181.74 | 2.79% | 3,140.98 | 3.40% | |
| 59. | 31 dic. 2019 | $176.35 | -2.97% | 3,230.78 | 2.86% | |
| Promedio (R): | 0.80% | 0.88% | ||||
| Desviación estándar: | 5.84% | 3.45% | ||||
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 GD 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
General Dynamics Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RGD,t | RS&P 500,t | (RGD,t–RGD)2 | (RS&P 500,t–RS&P 500)2 | (RGD,t–RGD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2015 | 4.18% | 5.49% | 11.41 | 21.25 | 15.57 |
| 2. | 31 mar. 2015 | -2.20% | -1.74% | 9.01 | 6.86 | 7.86 |
| 3. | 30 abr. 2015 | 1.68% | 0.85% | 0.77 | 0.00 | -0.02 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | 2.79% | 3.40% | 3.96 | 6.38 | 5.03 |
| 59. | 31 dic. 2019 | -2.97% | 2.86% | 14.21 | 3.92 | -7.46 |
| Total (Σ): | 1,975.33 | 688.77 | 785.06 | |||
| t | Fecha | RGD,t | RS&P 500,t | (RGD,t–RGD)2 | (RS&P 500,t–RS&P 500)2 | (RGD,t–RGD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2015 | 4.18% | 5.49% | 11.41 | 21.25 | 15.57 |
| 2. | 31 mar. 2015 | -2.20% | -1.74% | 9.01 | 6.86 | 7.86 |
| 3. | 30 abr. 2015 | 1.68% | 0.85% | 0.77 | 0.00 | -0.02 |
| 4. | 31 may. 2015 | 2.07% | 1.05% | 1.60 | 0.03 | 0.21 |
| 5. | 30 jun. 2015 | 1.58% | -2.10% | 0.61 | 8.88 | -2.32 |
| 6. | 31 jul. 2015 | 5.24% | 1.97% | 19.65 | 1.20 | 4.85 |
| 7. | 31 ago. 2015 | -4.75% | -6.26% | 30.83 | 50.94 | 39.63 |
| 8. | 30 sept. 2015 | -2.87% | -2.64% | 13.52 | 12.41 | 12.95 |
| 9. | 31 oct. 2015 | 8.21% | 8.30% | 54.79 | 55.04 | 54.92 |
| 10. | 30 nov. 2015 | -1.43% | 0.05% | 4.98 | 0.69 | 1.85 |
| 11. | 31 dic. 2015 | -6.21% | -1.75% | 49.24 | 6.93 | 18.47 |
| 12. | 31 ene. 2016 | -2.11% | -5.07% | 8.50 | 35.43 | 17.35 |
| 13. | 29 feb. 2016 | 1.87% | -0.41% | 1.13 | 1.67 | -1.38 |
| 14. | 31 mar. 2016 | -3.60% | 6.60% | 19.36 | 32.72 | -25.17 |
| 15. | 30 abr. 2016 | 7.54% | 0.27% | 45.42 | 0.37 | -4.11 |
| 16. | 31 may. 2016 | 0.96% | 1.53% | 0.02 | 0.43 | 0.10 |
| 17. | 30 jun. 2016 | -1.32% | 0.09% | 4.50 | 0.62 | 1.67 |
| 18. | 31 jul. 2016 | 5.49% | 3.56% | 22.00 | 7.19 | 12.58 |
| 19. | 31 ago. 2016 | 3.63% | -0.12% | 7.98 | 1.00 | -2.83 |
| 20. | 30 sept. 2016 | 1.93% | -0.12% | 1.27 | 1.01 | -1.13 |
| 21. | 31 oct. 2016 | -2.36% | -1.94% | 10.00 | 7.96 | 8.92 |
| 22. | 30 nov. 2016 | 16.33% | 3.42% | 240.94 | 6.44 | 39.40 |
| 23. | 31 dic. 2016 | -1.53% | 1.82% | 5.47 | 0.89 | -2.20 |
| 24. | 31 ene. 2017 | 5.32% | 1.79% | 20.37 | 0.83 | 4.10 |
| 25. | 28 feb. 2017 | 4.82% | 3.72% | 16.14 | 8.07 | 11.41 |
| 26. | 31 mar. 2017 | -1.38% | -0.04% | 4.75 | 0.84 | 2.00 |
| 27. | 30 abr. 2017 | 3.97% | 0.91% | 10.02 | 0.00 | 0.09 |
| 28. | 31 may. 2017 | 4.88% | 1.16% | 16.63 | 0.08 | 1.14 |
| 29. | 30 jun. 2017 | -2.53% | 0.48% | 11.14 | 0.16 | 1.33 |
| 30. | 31 jul. 2017 | -0.47% | 1.93% | 1.62 | 1.11 | -1.34 |
| 31. | 31 ago. 2017 | 2.56% | 0.05% | 3.07 | 0.68 | -1.45 |
| 32. | 30 sept. 2017 | 2.10% | 1.93% | 1.68 | 1.10 | 1.36 |
| 33. | 31 oct. 2017 | -0.86% | 2.22% | 2.76 | 1.79 | -2.22 |
| 34. | 30 nov. 2017 | 2.06% | 2.81% | 1.58 | 3.72 | 2.42 |
| 35. | 31 dic. 2017 | -1.79% | 0.98% | 6.73 | 0.01 | -0.27 |
| 36. | 31 ene. 2018 | 9.77% | 5.62% | 80.33 | 22.46 | 42.47 |
| 37. | 28 feb. 2018 | -0.01% | -3.89% | 0.67 | 22.79 | 3.90 |
| 38. | 31 mar. 2018 | -0.70% | -2.69% | 2.25 | 12.73 | 5.35 |
| 39. | 30 abr. 2018 | -8.45% | 0.27% | 85.59 | 0.37 | 5.62 |
| 40. | 31 may. 2018 | 0.20% | 2.16% | 0.37 | 1.64 | -0.78 |
| 41. | 30 jun. 2018 | -7.59% | 0.48% | 70.38 | 0.16 | 3.31 |
| 42. | 31 jul. 2018 | 7.66% | 3.60% | 47.01 | 7.41 | 18.67 |
| 43. | 31 ago. 2018 | -3.18% | 3.03% | 15.90 | 4.61 | -8.56 |
| 44. | 30 sept. 2018 | 5.85% | 0.43% | 25.49 | 0.20 | -2.27 |
| 45. | 31 oct. 2018 | -15.25% | -6.94% | 257.58 | 61.14 | 125.50 |
| 46. | 30 nov. 2018 | 7.13% | 1.79% | 40.05 | 0.82 | 5.74 |
| 47. | 31 dic. 2018 | -14.97% | -9.18% | 248.85 | 101.14 | 158.65 |
| 48. | 31 ene. 2019 | 9.47% | 7.87% | 75.12 | 48.85 | 60.58 |
| 49. | 28 feb. 2019 | -0.56% | 2.97% | 1.85 | 4.38 | -2.85 |
| 50. | 31 mar. 2019 | -0.55% | 1.79% | 1.84 | 0.83 | -1.24 |
| 51. | 30 abr. 2019 | 6.18% | 3.93% | 28.89 | 9.32 | 16.41 |
| 52. | 31 may. 2019 | -10.02% | -6.58% | 117.07 | 55.61 | 80.68 |
| 53. | 30 jun. 2019 | 13.06% | 6.89% | 150.16 | 36.17 | 73.69 |
| 54. | 31 jul. 2019 | 2.83% | 1.31% | 4.09 | 0.19 | 0.88 |
| 55. | 31 ago. 2019 | 2.87% | -1.81% | 4.25 | 7.23 | -5.54 |
| 56. | 30 sept. 2019 | -4.46% | 1.72% | 27.76 | 0.70 | -4.42 |
| 57. | 31 oct. 2019 | -2.69% | 2.04% | 12.19 | 1.36 | -4.06 |
| 58. | 30 nov. 2019 | 2.79% | 3.40% | 3.96 | 6.38 | 5.03 |
| 59. | 31 dic. 2019 | -2.97% | 2.86% | 14.21 | 3.92 | -7.46 |
| Total (Σ): | 1,975.33 | 688.77 | 785.06 | |||
Mostrar todo
VarianzaGD = Σ(RGD,t–RGD)2 ÷ (59 – 1)
= 1,975.33 ÷ (59 – 1)
= 34.06
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
CovarianzaGD, S&P 500 = Σ(RGD,t–RGD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 785.06 ÷ (59 – 1)
= 13.54
Estimación sistemática del riesgo (β)
| VarianzaGD | 34.06 |
| VarianzaS&P 500 | 11.88 |
| CovarianzaGD, S&P 500 | 13.54 |
| Coeficiente de correlaciónGD, S&P 5001 | 0.67 |
| βGD2 | 1.14 |
| αGD3 | -0.20% |
Cálculos
1 Coeficiente de correlaciónGD, S&P 500
= CovarianzaGD, S&P 500 ÷ (Desviación estándarGD × Desviación estándarS&P 500)
= 13.54 ÷ (5.84% × 3.45%)
= 0.67
2 βGD
= CovarianzaGD, S&P 500 ÷ VarianzaS&P 500
= 13.54 ÷ 11.88
= 1.14
3 αGD
= PromedioGD – βGD × PromedioS&P 500
= 0.80% – 1.14 × 0.88%
= -0.20%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.67% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de General Dynamics acciones ordinarias | βGD | 1.14 |
| Tasa de rendimiento esperada de las acciones ordinarias de General Dynamics3 | E(RGD) | 15.06% |
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(RGD) = RF + βGD [E(RM) – RF]
= 4.67% + 1.14 [13.79% – 4.67%]
= 15.06%