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 DuPont.
Tasas de retorno
DuPont de Nemours Inc., tasas mensuales de retorno
| DuPont de Nemours Inc. (DD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioDD,t1 | DividendoDD,t1 | RDD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2015 | $45.16 | 1,994.99 | ||||
| 1. | 28 feb. 2015 | $49.24 | 9.03% | 2,104.50 | 5.49% | |
| 2. | 31 mar. 2015 | $47.98 | $0.42 | -1.71% | 2,067.89 | -1.74% |
| 3. | 30 abr. 2015 | $51.00 | 6.29% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | $64.81 | $0.30 | -1.21% | 3,140.98 | 3.40% |
| 59. | 31 dic. 2019 | $64.20 | -0.94% | 3,230.78 | 2.86% | |
| Promedio (R): | 2.10% | 0.88% | ||||
| Desviación estándar: | 20.60% | 3.45% | ||||
| DuPont de Nemours Inc. (DD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioDD,t1 | DividendoDD,t1 | RDD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2015 | $45.16 | 1,994.99 | ||||
| 1. | 28 feb. 2015 | $49.24 | 9.03% | 2,104.50 | 5.49% | |
| 2. | 31 mar. 2015 | $47.98 | $0.42 | -1.71% | 2,067.89 | -1.74% |
| 3. | 30 abr. 2015 | $51.00 | 6.29% | 2,085.51 | 0.85% | |
| 4. | 31 may. 2015 | $52.07 | 2.10% | 2,107.39 | 1.05% | |
| 5. | 30 jun. 2015 | $51.17 | $0.42 | -0.92% | 2,063.11 | -2.10% |
| 6. | 31 jul. 2015 | $47.06 | -8.03% | 2,103.84 | 1.97% | |
| 7. | 31 ago. 2015 | $43.76 | -7.01% | 1,972.18 | -6.26% | |
| 8. | 30 sept. 2015 | $42.40 | $0.42 | -2.15% | 1,920.03 | -2.64% |
| 9. | 31 oct. 2015 | $51.67 | 21.86% | 2,079.36 | 8.30% | |
| 10. | 30 nov. 2015 | $52.13 | 0.89% | 2,080.41 | 0.05% | |
| 11. | 31 dic. 2015 | $51.48 | $0.46 | -0.36% | 2,043.94 | -1.75% |
| 12. | 31 ene. 2016 | $42.00 | -18.41% | 1,940.24 | -5.07% | |
| 13. | 29 feb. 2016 | $48.61 | 15.74% | 1,932.23 | -0.41% | |
| 14. | 31 mar. 2016 | $50.86 | $0.46 | 5.57% | 2,059.74 | 6.60% |
| 15. | 30 abr. 2016 | $52.61 | 3.44% | 2,065.30 | 0.27% | |
| 16. | 31 may. 2016 | $51.36 | -2.38% | 2,096.95 | 1.53% | |
| 17. | 30 jun. 2016 | $49.71 | $0.46 | -2.32% | 2,098.86 | 0.09% |
| 18. | 31 jul. 2016 | $53.67 | 7.97% | 2,173.60 | 3.56% | |
| 19. | 31 ago. 2016 | $53.64 | -0.06% | 2,170.95 | -0.12% | |
| 20. | 30 sept. 2016 | $51.83 | $0.46 | -2.52% | 2,168.27 | -0.12% |
| 21. | 31 oct. 2016 | $53.81 | 3.82% | 2,126.15 | -1.94% | |
| 22. | 30 nov. 2016 | $55.72 | 3.55% | 2,198.81 | 3.42% | |
| 23. | 31 dic. 2016 | $57.22 | $0.46 | 3.52% | 2,238.83 | 1.82% |
| 24. | 31 ene. 2017 | $59.63 | 4.21% | 2,278.87 | 1.79% | |
| 25. | 28 feb. 2017 | $62.26 | 4.41% | 2,363.64 | 3.72% | |
| 26. | 31 mar. 2017 | $63.54 | $0.46 | 2.79% | 2,362.72 | -0.04% |
| 27. | 30 abr. 2017 | $62.80 | -1.16% | 2,384.20 | 0.91% | |
| 28. | 31 may. 2017 | $61.96 | -1.34% | 2,411.80 | 1.16% | |
| 29. | 30 jun. 2017 | $63.07 | $0.46 | 2.53% | 2,423.41 | 0.48% |
| 30. | 31 jul. 2017 | $64.24 | $0.46 | 2.58% | 2,470.30 | 1.93% |
| 31. | 31 ago. 2017 | $66.65 | 3.75% | 2,471.65 | 0.05% | |
| 32. | 30 sept. 2017 | $69.23 | 3.87% | 2,519.36 | 1.93% | |
| 33. | 31 oct. 2017 | $72.31 | 4.45% | 2,575.26 | 2.22% | |
| 34. | 30 nov. 2017 | $71.96 | $0.38 | 0.04% | 2,647.58 | 2.81% |
| 35. | 31 dic. 2017 | $71.22 | -1.03% | 2,673.61 | 0.98% | |
| 36. | 31 ene. 2018 | $75.58 | 6.12% | 2,823.81 | 5.62% | |
| 37. | 28 feb. 2018 | $70.30 | $0.38 | -6.48% | 2,713.83 | -3.89% |
| 38. | 31 mar. 2018 | $63.71 | -9.37% | 2,640.87 | -2.69% | |
| 39. | 30 abr. 2018 | $63.24 | -0.74% | 2,648.05 | 0.27% | |
| 40. | 31 may. 2018 | $64.11 | $0.38 | 1.98% | 2,705.27 | 2.16% |
| 41. | 30 jun. 2018 | $65.92 | 2.82% | 2,718.37 | 0.48% | |
| 42. | 31 jul. 2018 | $68.77 | 4.32% | 2,816.29 | 3.60% | |
| 43. | 31 ago. 2018 | $70.13 | $0.38 | 2.53% | 2,901.52 | 3.03% |
| 44. | 30 sept. 2018 | $64.31 | -8.30% | 2,913.98 | 0.43% | |
| 45. | 31 oct. 2018 | $53.92 | -16.16% | 2,711.74 | -6.94% | |
| 46. | 30 nov. 2018 | $57.85 | $0.38 | 7.99% | 2,760.17 | 1.79% |
| 47. | 31 dic. 2018 | $53.48 | -7.55% | 2,506.85 | -9.18% | |
| 48. | 31 ene. 2019 | $53.81 | 0.62% | 2,704.10 | 7.87% | |
| 49. | 28 feb. 2019 | $53.23 | $0.38 | -0.37% | 2,784.49 | 2.97% |
| 50. | 31 mar. 2019 | $53.31 | 0.15% | 2,834.40 | 1.79% | |
| 51. | 30 abr. 2019 | $38.45 | -27.87% | 2,945.83 | 3.93% | |
| 52. | 31 may. 2019 | $30.52 | -20.62% | 2,752.06 | -6.58% | |
| 53. | 30 jun. 2019 | $75.07 | 145.97% | 2,941.76 | 6.89% | |
| 54. | 31 jul. 2019 | $72.16 | $0.30 | -3.48% | 2,980.38 | 1.31% |
| 55. | 31 ago. 2019 | $67.93 | -5.86% | 2,926.46 | -1.81% | |
| 56. | 30 sept. 2019 | $71.31 | 4.98% | 2,976.74 | 1.72% | |
| 57. | 31 oct. 2019 | $65.91 | -7.57% | 3,037.56 | 2.04% | |
| 58. | 30 nov. 2019 | $64.81 | $0.30 | -1.21% | 3,140.98 | 3.40% |
| 59. | 31 dic. 2019 | $64.20 | -0.94% | 3,230.78 | 2.86% | |
| Promedio (R): | 2.10% | 0.88% | ||||
| Desviación estándar: | 20.60% | 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 DD 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
DuPont de Nemours Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RDD,t | RS&P 500,t | (RDD,t–RDD)2 | (RS&P 500,t–RS&P 500)2 | (RDD,t–RDD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2015 | 9.03% | 5.49% | 48.07 | 21.25 | 31.96 |
| 2. | 31 mar. 2015 | -1.71% | -1.74% | 14.50 | 6.86 | 9.97 |
| 3. | 30 abr. 2015 | 6.29% | 0.85% | 17.58 | 0.00 | -0.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | -1.21% | 3.40% | 10.99 | 6.38 | -8.37 |
| 59. | 31 dic. 2019 | -0.94% | 2.86% | 9.26 | 3.92 | -6.02 |
| Total (Σ): | 24,624.11 | 688.77 | 1,707.82 | |||
| t | Fecha | RDD,t | RS&P 500,t | (RDD,t–RDD)2 | (RS&P 500,t–RS&P 500)2 | (RDD,t–RDD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2015 | 9.03% | 5.49% | 48.07 | 21.25 | 31.96 |
| 2. | 31 mar. 2015 | -1.71% | -1.74% | 14.50 | 6.86 | 9.97 |
| 3. | 30 abr. 2015 | 6.29% | 0.85% | 17.58 | 0.00 | -0.11 |
| 4. | 31 may. 2015 | 2.10% | 1.05% | 0.00 | 0.03 | 0.00 |
| 5. | 30 jun. 2015 | -0.92% | -2.10% | 9.14 | 8.88 | 9.01 |
| 6. | 31 jul. 2015 | -8.03% | 1.97% | 102.69 | 1.20 | -11.10 |
| 7. | 31 ago. 2015 | -7.01% | -6.26% | 83.06 | 50.94 | 65.05 |
| 8. | 30 sept. 2015 | -2.15% | -2.64% | 18.06 | 12.41 | 14.97 |
| 9. | 31 oct. 2015 | 21.86% | 8.30% | 390.53 | 55.04 | 146.62 |
| 10. | 30 nov. 2015 | 0.89% | 0.05% | 1.47 | 0.69 | 1.00 |
| 11. | 31 dic. 2015 | -0.36% | -1.75% | 6.08 | 6.93 | 6.49 |
| 12. | 31 ene. 2016 | -18.41% | -5.07% | 420.92 | 35.43 | 122.13 |
| 13. | 29 feb. 2016 | 15.74% | -0.41% | 185.96 | 1.67 | -17.62 |
| 14. | 31 mar. 2016 | 5.57% | 6.60% | 12.07 | 32.72 | 19.87 |
| 15. | 30 abr. 2016 | 3.44% | 0.27% | 1.79 | 0.37 | -0.82 |
| 16. | 31 may. 2016 | -2.38% | 1.53% | 20.05 | 0.43 | -2.93 |
| 17. | 30 jun. 2016 | -2.32% | 0.09% | 19.52 | 0.62 | 3.48 |
| 18. | 31 jul. 2016 | 7.97% | 3.56% | 34.40 | 7.19 | 15.73 |
| 19. | 31 ago. 2016 | -0.06% | -0.12% | 4.65 | 1.00 | 2.16 |
| 20. | 30 sept. 2016 | -2.52% | -0.12% | 21.33 | 1.01 | 4.63 |
| 21. | 31 oct. 2016 | 3.82% | -1.94% | 2.95 | 7.96 | -4.85 |
| 22. | 30 nov. 2016 | 3.55% | 3.42% | 2.10 | 6.44 | 3.68 |
| 23. | 31 dic. 2016 | 3.52% | 1.82% | 2.01 | 0.89 | 1.33 |
| 24. | 31 ene. 2017 | 4.21% | 1.79% | 4.45 | 0.83 | 1.92 |
| 25. | 28 feb. 2017 | 4.41% | 3.72% | 5.33 | 8.07 | 6.56 |
| 26. | 31 mar. 2017 | 2.79% | -0.04% | 0.48 | 0.84 | -0.64 |
| 27. | 30 abr. 2017 | -1.16% | 0.91% | 10.67 | 0.00 | -0.10 |
| 28. | 31 may. 2017 | -1.34% | 1.16% | 11.83 | 0.08 | -0.96 |
| 29. | 30 jun. 2017 | 2.53% | 0.48% | 0.19 | 0.16 | -0.17 |
| 30. | 31 jul. 2017 | 2.58% | 1.93% | 0.23 | 1.11 | 0.51 |
| 31. | 31 ago. 2017 | 3.75% | 0.05% | 2.72 | 0.68 | -1.36 |
| 32. | 30 sept. 2017 | 3.87% | 1.93% | 3.13 | 1.10 | 1.86 |
| 33. | 31 oct. 2017 | 4.45% | 2.22% | 5.51 | 1.79 | 3.15 |
| 34. | 30 nov. 2017 | 0.04% | 2.81% | 4.24 | 3.72 | -3.97 |
| 35. | 31 dic. 2017 | -1.03% | 0.98% | 9.80 | 0.01 | -0.33 |
| 36. | 31 ene. 2018 | 6.12% | 5.62% | 16.16 | 22.46 | 19.05 |
| 37. | 28 feb. 2018 | -6.48% | -3.89% | 73.69 | 22.79 | 40.98 |
| 38. | 31 mar. 2018 | -9.37% | -2.69% | 131.69 | 12.73 | 40.94 |
| 39. | 30 abr. 2018 | -0.74% | 0.27% | 8.06 | 0.37 | 1.72 |
| 40. | 31 may. 2018 | 1.98% | 2.16% | 0.02 | 1.64 | -0.16 |
| 41. | 30 jun. 2018 | 2.82% | 0.48% | 0.52 | 0.16 | -0.29 |
| 42. | 31 jul. 2018 | 4.32% | 3.60% | 4.94 | 7.41 | 6.05 |
| 43. | 31 ago. 2018 | 2.53% | 3.03% | 0.18 | 4.61 | 0.92 |
| 44. | 30 sept. 2018 | -8.30% | 0.43% | 108.17 | 0.20 | 4.68 |
| 45. | 31 oct. 2018 | -16.16% | -6.94% | 333.34 | 61.14 | 142.76 |
| 46. | 30 nov. 2018 | 7.99% | 1.79% | 34.72 | 0.82 | 5.34 |
| 47. | 31 dic. 2018 | -7.55% | -9.18% | 93.23 | 101.14 | 97.10 |
| 48. | 31 ene. 2019 | 0.62% | 7.87% | 2.20 | 48.85 | -10.37 |
| 49. | 28 feb. 2019 | -0.37% | 2.97% | 6.12 | 4.38 | -5.18 |
| 50. | 31 mar. 2019 | 0.15% | 1.79% | 3.81 | 0.83 | -1.78 |
| 51. | 30 abr. 2019 | -27.87% | 3.93% | 898.56 | 9.32 | -91.49 |
| 52. | 31 may. 2019 | -20.62% | -6.58% | 516.45 | 55.61 | 169.46 |
| 53. | 30 jun. 2019 | 145.97% | 6.89% | 20,698.14 | 36.17 | 865.21 |
| 54. | 31 jul. 2019 | -3.48% | 1.31% | 31.12 | 0.19 | -2.42 |
| 55. | 31 ago. 2019 | -5.86% | -1.81% | 63.41 | 7.23 | 21.41 |
| 56. | 30 sept. 2019 | 4.98% | 1.72% | 8.26 | 0.70 | 2.41 |
| 57. | 31 oct. 2019 | -7.57% | 2.04% | 93.59 | 1.36 | -11.26 |
| 58. | 30 nov. 2019 | -1.21% | 3.40% | 10.99 | 6.38 | -8.37 |
| 59. | 31 dic. 2019 | -0.94% | 2.86% | 9.26 | 3.92 | -6.02 |
| Total (Σ): | 24,624.11 | 688.77 | 1,707.82 | |||
Mostrar todo
VarianzaDD = Σ(RDD,t–RDD)2 ÷ (59 – 1)
= 24,624.11 ÷ (59 – 1)
= 424.55
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
CovarianzaDD, S&P 500 = Σ(RDD,t–RDD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,707.82 ÷ (59 – 1)
= 29.45
Estimación sistemática del riesgo (β)
| VarianzaDD | 424.55 |
| VarianzaS&P 500 | 11.88 |
| CovarianzaDD, S&P 500 | 29.45 |
| Coeficiente de correlaciónDD, S&P 5001 | 0.41 |
| βDD2 | 2.48 |
| αDD3 | -0.08% |
Cálculos
1 Coeficiente de correlaciónDD, S&P 500
= CovarianzaDD, S&P 500 ÷ (Desviación estándarDD × Desviación estándarS&P 500)
= 29.45 ÷ (20.60% × 3.45%)
= 0.41
2 βDD
= CovarianzaDD, S&P 500 ÷ VarianzaS&P 500
= 29.45 ÷ 11.88
= 2.48
3 αDD
= PromedioDD – βDD × PromedioS&P 500
= 2.10% – 2.48 × 0.88%
= -0.08%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.72% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.51% |
| Riesgo sistemático de DuPont acciones ordinarias | βDD | 2.48 |
| Tasa de rendimiento esperada de las acciones ordinarias de DuPont3 | E(RDD) | 26.52% |
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(RDD) = RF + βDD [E(RM) – RF]
= 4.72% + 2.48 [13.51% – 4.72%]
= 26.52%