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 Eaton.
Tasas de retorno
Eaton Corp. plc, tasas mensuales de retorno
| Eaton Corp. plc (ETN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioETN,t1 | DividendoETN,t1 | RETN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $76.25 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $79.77 | 4.62% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $80.56 | $0.71 | 1.88% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $82.82 | 2.81% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $227.69 | $0.86 | 9.93% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $240.82 | 5.77% | 4,769.83 | 4.42% | |
| Promedio (R): | 2.42% | 1.11% | ||||
| Desviación estándar: | 6.94% | 5.31% | ||||
| Eaton Corp. plc (ETN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioETN,t1 | DividendoETN,t1 | RETN,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $76.25 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $79.77 | 4.62% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $80.56 | $0.71 | 1.88% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $82.82 | 2.81% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $74.49 | $0.71 | -9.20% | 2,752.06 | -6.58% |
| 5. | 30 jun. 2019 | $83.28 | 11.80% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $82.19 | -1.31% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $80.72 | $0.71 | -0.92% | 2,926.46 | -1.81% |
| 8. | 30 sept. 2019 | $83.15 | 3.01% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $87.11 | $0.71 | 5.62% | 3,037.56 | 2.04% |
| 10. | 30 nov. 2019 | $92.50 | 6.19% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $94.72 | 2.40% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $94.47 | -0.26% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $90.72 | -3.97% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $77.69 | $0.73 | -13.56% | 2,584.59 | -12.51% |
| 15. | 30 abr. 2020 | $83.50 | 7.48% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $84.90 | $0.73 | 2.55% | 3,044.31 | 4.53% |
| 17. | 30 jun. 2020 | $87.48 | 3.04% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $93.13 | 6.46% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $102.10 | $0.73 | 10.42% | 3,500.31 | 7.01% |
| 20. | 30 sept. 2020 | $102.03 | -0.07% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $103.79 | 1.72% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $121.11 | $0.73 | 17.39% | 3,621.63 | 10.75% |
| 23. | 31 dic. 2020 | $120.14 | -0.80% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $117.70 | -2.03% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $130.19 | 10.61% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $138.28 | $0.76 | 6.80% | 3,972.89 | 4.24% |
| 27. | 30 abr. 2021 | $142.93 | 3.36% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $145.25 | $0.76 | 2.15% | 4,204.11 | 0.55% |
| 29. | 30 jun. 2021 | $148.18 | 2.02% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $158.05 | 6.66% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $168.36 | $0.76 | 7.00% | 4,522.68 | 2.90% |
| 32. | 30 sept. 2021 | $149.31 | -11.32% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $164.76 | 10.35% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $162.06 | $0.76 | -1.18% | 4,567.00 | -0.83% |
| 35. | 31 dic. 2021 | $172.82 | 6.64% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $158.43 | -8.33% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $154.29 | -2.61% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $151.76 | $0.81 | -1.11% | 4,530.41 | 3.58% |
| 39. | 30 abr. 2022 | $145.02 | -4.44% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $138.60 | $0.81 | -3.87% | 4,132.15 | 0.01% |
| 41. | 30 jun. 2022 | $125.99 | -9.10% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $148.39 | 17.78% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $136.64 | $0.81 | -7.37% | 3,955.00 | -4.24% |
| 44. | 30 sept. 2022 | $133.36 | -2.40% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $150.07 | 12.53% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $163.45 | $0.81 | 9.46% | 4,080.11 | 5.38% |
| 47. | 31 dic. 2022 | $156.95 | -3.98% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $162.21 | 3.35% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $174.93 | 7.84% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $171.34 | $0.86 | -1.56% | 4,109.31 | 3.51% |
| 51. | 30 abr. 2023 | $167.12 | -2.46% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $175.90 | $0.86 | 5.77% | 4,179.83 | 0.25% |
| 53. | 30 jun. 2023 | $201.10 | 14.33% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $205.32 | 2.10% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $230.37 | $0.86 | 12.62% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $213.28 | -7.42% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $207.91 | -2.52% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $227.69 | $0.86 | 9.93% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $240.82 | 5.77% | 4,769.83 | 4.42% | |
| Promedio (R): | 2.42% | 1.11% | ||||
| Desviación estándar: | 6.94% | 5.31% | ||||
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 ETN 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
Eaton Corp. plc, cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RETN,t | RS&P 500,t | (RETN,t–RETN)2 | (RS&P 500,t–RS&P 500)2 | (RETN,t–RETN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 4.62% | 2.97% | 4.83 | 3.49 | 4.11 |
| 2. | 31 mar. 2019 | 1.88% | 1.79% | 0.29 | 0.47 | -0.37 |
| 3. | 30 abr. 2019 | 2.81% | 3.93% | 0.15 | 7.98 | 1.10 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 9.93% | 8.92% | 56.40 | 61.03 | 58.67 |
| 59. | 31 dic. 2023 | 5.77% | 4.42% | 11.22 | 11.00 | 11.11 |
| Total (Σ): | 2,793.38 | 1,634.30 | 1,689.89 | |||
| t | Fecha | RETN,t | RS&P 500,t | (RETN,t–RETN)2 | (RS&P 500,t–RS&P 500)2 | (RETN,t–RETN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 4.62% | 2.97% | 4.83 | 3.49 | 4.11 |
| 2. | 31 mar. 2019 | 1.88% | 1.79% | 0.29 | 0.47 | -0.37 |
| 3. | 30 abr. 2019 | 2.81% | 3.93% | 0.15 | 7.98 | 1.10 |
| 4. | 31 may. 2019 | -9.20% | -6.58% | 134.99 | 59.04 | 89.27 |
| 5. | 30 jun. 2019 | 11.80% | 6.89% | 88.03 | 33.49 | 54.30 |
| 6. | 31 jul. 2019 | -1.31% | 1.31% | 13.89 | 0.04 | -0.77 |
| 7. | 31 ago. 2019 | -0.92% | -1.81% | 11.17 | 8.50 | 9.74 |
| 8. | 30 sept. 2019 | 3.01% | 1.72% | 0.35 | 0.37 | 0.36 |
| 9. | 31 oct. 2019 | 5.62% | 2.04% | 10.23 | 0.88 | 3.00 |
| 10. | 30 nov. 2019 | 6.19% | 3.40% | 14.21 | 5.28 | 8.67 |
| 11. | 31 dic. 2019 | 2.40% | 2.86% | 0.00 | 3.07 | -0.03 |
| 12. | 31 ene. 2020 | -0.26% | -0.16% | 7.19 | 1.61 | 3.40 |
| 13. | 29 feb. 2020 | -3.97% | -8.41% | 40.80 | 90.57 | 60.79 |
| 14. | 31 mar. 2020 | -13.56% | -12.51% | 255.23 | 185.44 | 217.56 |
| 15. | 30 abr. 2020 | 7.48% | 12.68% | 25.61 | 134.06 | 58.60 |
| 16. | 31 may. 2020 | 2.55% | 4.53% | 0.02 | 11.71 | 0.46 |
| 17. | 30 jun. 2020 | 3.04% | 1.84% | 0.39 | 0.54 | 0.46 |
| 18. | 31 jul. 2020 | 6.46% | 5.51% | 16.33 | 19.40 | 17.80 |
| 19. | 31 ago. 2020 | 10.42% | 7.01% | 63.97 | 34.82 | 47.19 |
| 20. | 30 sept. 2020 | -0.07% | -3.92% | 6.18 | 25.29 | 12.50 |
| 21. | 31 oct. 2020 | 1.72% | -2.77% | 0.48 | 15.00 | 2.68 |
| 22. | 30 nov. 2020 | 17.39% | 10.75% | 224.20 | 93.10 | 144.47 |
| 23. | 31 dic. 2020 | -0.80% | 3.71% | 10.36 | 6.79 | -8.39 |
| 24. | 31 ene. 2021 | -2.03% | -1.11% | 19.79 | 4.93 | 9.87 |
| 25. | 28 feb. 2021 | 10.61% | 2.61% | 67.14 | 2.26 | 12.32 |
| 26. | 31 mar. 2021 | 6.80% | 4.24% | 19.18 | 9.85 | 13.74 |
| 27. | 30 abr. 2021 | 3.36% | 5.24% | 0.89 | 17.11 | 3.91 |
| 28. | 31 may. 2021 | 2.15% | 0.55% | 0.07 | 0.31 | 0.15 |
| 29. | 30 jun. 2021 | 2.02% | 2.22% | 0.16 | 1.24 | -0.45 |
| 30. | 31 jul. 2021 | 6.66% | 2.27% | 18.00 | 1.37 | 4.96 |
| 31. | 31 ago. 2021 | 7.00% | 2.90% | 21.04 | 3.22 | 8.22 |
| 32. | 30 sept. 2021 | -11.32% | -4.76% | 188.59 | 34.37 | 80.51 |
| 33. | 31 oct. 2021 | 10.35% | 6.91% | 62.88 | 33.74 | 46.06 |
| 34. | 30 nov. 2021 | -1.18% | -0.83% | 12.93 | 3.76 | 6.97 |
| 35. | 31 dic. 2021 | 6.64% | 4.36% | 17.82 | 10.60 | 13.74 |
| 36. | 31 ene. 2022 | -8.33% | -5.26% | 115.44 | 40.51 | 68.38 |
| 37. | 28 feb. 2022 | -2.61% | -3.14% | 25.31 | 17.99 | 21.34 |
| 38. | 31 mar. 2022 | -1.11% | 3.58% | 12.48 | 6.11 | -8.73 |
| 39. | 30 abr. 2022 | -4.44% | -8.80% | 47.04 | 98.04 | 67.91 |
| 40. | 31 may. 2022 | -3.87% | 0.01% | 39.52 | 1.21 | 6.92 |
| 41. | 30 jun. 2022 | -9.10% | -8.39% | 132.61 | 90.21 | 109.38 |
| 42. | 31 jul. 2022 | 17.78% | 9.11% | 235.97 | 64.09 | 122.98 |
| 43. | 31 ago. 2022 | -7.37% | -4.24% | 95.85 | 28.62 | 52.38 |
| 44. | 30 sept. 2022 | -2.40% | -9.34% | 23.21 | 109.11 | 50.33 |
| 45. | 31 oct. 2022 | 12.53% | 7.99% | 102.26 | 47.34 | 69.58 |
| 46. | 30 nov. 2022 | 9.46% | 5.38% | 49.53 | 18.23 | 30.05 |
| 47. | 31 dic. 2022 | -3.98% | -5.90% | 40.89 | 49.04 | 44.78 |
| 48. | 31 ene. 2023 | 3.35% | 6.18% | 0.87 | 25.70 | 4.73 |
| 49. | 28 feb. 2023 | 7.84% | -2.61% | 29.42 | 13.82 | -20.16 |
| 50. | 31 mar. 2023 | -1.56% | 3.51% | 15.83 | 5.76 | -9.55 |
| 51. | 30 abr. 2023 | -2.46% | 1.46% | 23.82 | 0.13 | -1.75 |
| 52. | 31 may. 2023 | 5.77% | 0.25% | 11.23 | 0.74 | -2.87 |
| 53. | 30 jun. 2023 | 14.33% | 4.71% | 141.82 | 13.02 | 42.97 |
| 54. | 31 jul. 2023 | 2.10% | 4.85% | 0.10 | 13.99 | -1.19 |
| 55. | 31 ago. 2023 | 12.62% | -1.77% | 104.07 | 8.28 | -29.36 |
| 56. | 30 sept. 2023 | -7.42% | -4.87% | 96.75 | 35.73 | 58.80 |
| 57. | 31 oct. 2023 | -2.52% | -2.20% | 24.36 | 10.92 | 16.31 |
| 58. | 30 nov. 2023 | 9.93% | 8.92% | 56.40 | 61.03 | 58.67 |
| 59. | 31 dic. 2023 | 5.77% | 4.42% | 11.22 | 11.00 | 11.11 |
| Total (Σ): | 2,793.38 | 1,634.30 | 1,689.89 | |||
Mostrar todo
VarianzaETN = Σ(RETN,t–RETN)2 ÷ (59 – 1)
= 2,793.38 ÷ (59 – 1)
= 48.16
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaETN, S&P 500 = Σ(RETN,t–RETN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,689.89 ÷ (59 – 1)
= 29.14
Estimación sistemática del riesgo (β)
| VarianzaETN | 48.16 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaETN, S&P 500 | 29.14 |
| Coeficiente de correlaciónETN, S&P 5001 | 0.79 |
| βETN2 | 1.03 |
| αETN3 | 1.27% |
Cálculos
1 Coeficiente de correlaciónETN, S&P 500
= CovarianzaETN, S&P 500 ÷ (Desviación estándarETN × Desviación estándarS&P 500)
= 29.14 ÷ (6.94% × 5.31%)
= 0.79
2 βETN
= CovarianzaETN, S&P 500 ÷ VarianzaS&P 500
= 29.14 ÷ 28.18
= 1.03
3 αETN
= PromedioETN – βETN × PromedioS&P 500
= 2.42% – 1.03 × 1.11%
= 1.27%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.65% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Eaton acciones ordinarias | βETN | 1.03 |
| Tasa de rendimiento esperada de las acciones ordinarias de Eaton3 | E(RETN) | 14.10% |
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(RETN) = RF + βETN [E(RM) – RF]
= 4.65% + 1.03 [13.79% – 4.65%]
= 14.10%