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 sobre activos de riesgo como las acciones ordinarias de EQT.
Tasas de retorno
EQT Corp., tasas mensuales de retorno
| EQT Corp. (EQT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEQT,t1 | DividendoEQT,t1 | REQT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $60.63 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $59.89 | $0.03 | -1.17% | 2,363.64 | 3.72% |
| 2. | 31 mar. 2017 | $61.10 | 2.02% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $58.14 | -4.84% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | $19.43 | -2.41% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $21.81 | 12.25% | 4,766.18 | 4.36% | |
| Promedio (R): | 0.82% | 1.36% | ||||
| Desviación estándar: | 18.95% | 4.48% | ||||
| EQT Corp. (EQT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEQT,t1 | DividendoEQT,t1 | REQT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2017 | $60.63 | 2,278.87 | ||||
| 1. | 28 feb. 2017 | $59.89 | $0.03 | -1.17% | 2,363.64 | 3.72% |
| 2. | 31 mar. 2017 | $61.10 | 2.02% | 2,362.72 | -0.04% | |
| 3. | 30 abr. 2017 | $58.14 | -4.84% | 2,384.20 | 0.91% | |
| 4. | 31 may. 2017 | $55.27 | $0.03 | -4.88% | 2,411.80 | 1.16% |
| 5. | 30 jun. 2017 | $58.59 | 6.01% | 2,423.41 | 0.48% | |
| 6. | 31 jul. 2017 | $63.70 | 8.72% | 2,470.30 | 1.93% | |
| 7. | 31 ago. 2017 | $62.34 | $0.03 | -2.09% | 2,471.65 | 0.05% |
| 8. | 30 sept. 2017 | $65.24 | 4.65% | 2,519.36 | 1.93% | |
| 9. | 31 oct. 2017 | $62.54 | -4.14% | 2,575.26 | 2.22% | |
| 10. | 30 nov. 2017 | $59.60 | $0.03 | -4.65% | 2,647.58 | 2.81% |
| 11. | 31 dic. 2017 | $56.92 | -4.50% | 2,673.61 | 0.98% | |
| 12. | 31 ene. 2018 | $54.29 | -4.62% | 2,823.81 | 5.62% | |
| 13. | 28 feb. 2018 | $50.31 | $0.03 | -7.28% | 2,713.83 | -3.89% |
| 14. | 31 mar. 2018 | $47.51 | -5.57% | 2,640.87 | -2.69% | |
| 15. | 30 abr. 2018 | $50.19 | 5.64% | 2,648.05 | 0.27% | |
| 16. | 31 may. 2018 | $51.54 | $0.03 | 2.75% | 2,705.27 | 2.16% |
| 17. | 30 jun. 2018 | $55.18 | 7.06% | 2,718.37 | 0.48% | |
| 18. | 31 jul. 2018 | $49.68 | -9.97% | 2,816.29 | 3.60% | |
| 19. | 31 ago. 2018 | $51.02 | $0.03 | 2.76% | 2,901.52 | 3.03% |
| 20. | 30 sept. 2018 | $44.23 | -13.31% | 2,913.98 | 0.43% | |
| 21. | 31 oct. 2018 | $33.97 | -23.20% | 2,711.74 | -6.94% | |
| 22. | 30 nov. 2018 | $18.71 | $15.91 | 1.91% | 2,760.17 | 1.79% |
| 23. | 31 dic. 2018 | $18.89 | 0.96% | 2,506.85 | -9.18% | |
| 24. | 31 ene. 2019 | $19.47 | 3.07% | 2,704.10 | 7.87% | |
| 25. | 28 feb. 2019 | $18.12 | $0.03 | -6.78% | 2,784.49 | 2.97% |
| 26. | 31 mar. 2019 | $20.74 | 14.46% | 2,834.40 | 1.79% | |
| 27. | 30 abr. 2019 | $20.45 | -1.40% | 2,945.83 | 3.93% | |
| 28. | 31 may. 2019 | $18.30 | $0.03 | -10.37% | 2,752.06 | -6.58% |
| 29. | 30 jun. 2019 | $15.81 | -13.61% | 2,941.76 | 6.89% | |
| 30. | 31 jul. 2019 | $15.11 | -4.43% | 2,980.38 | 1.31% | |
| 31. | 31 ago. 2019 | $10.17 | $0.03 | -32.50% | 2,926.46 | -1.81% |
| 32. | 30 sept. 2019 | $10.64 | 4.62% | 2,976.74 | 1.72% | |
| 33. | 31 oct. 2019 | $10.74 | 0.94% | 3,037.56 | 2.04% | |
| 34. | 30 nov. 2019 | $8.73 | $0.03 | -18.44% | 3,140.98 | 3.40% |
| 35. | 31 dic. 2019 | $10.90 | 24.86% | 3,230.78 | 2.86% | |
| 36. | 31 ene. 2020 | $6.05 | -44.50% | 3,225.52 | -0.16% | |
| 37. | 29 feb. 2020 | $5.87 | $0.03 | -2.48% | 2,954.22 | -8.41% |
| 38. | 31 mar. 2020 | $7.07 | 20.44% | 2,584.59 | -12.51% | |
| 39. | 30 abr. 2020 | $14.59 | 106.36% | 2,912.43 | 12.68% | |
| 40. | 31 may. 2020 | $13.34 | -8.57% | 3,044.31 | 4.53% | |
| 41. | 30 jun. 2020 | $11.90 | -10.79% | 3,100.29 | 1.84% | |
| 42. | 31 jul. 2020 | $14.52 | 22.02% | 3,271.12 | 5.51% | |
| 43. | 31 ago. 2020 | $15.87 | 9.30% | 3,500.31 | 7.01% | |
| 44. | 30 sept. 2020 | $12.93 | -18.53% | 3,363.00 | -3.92% | |
| 45. | 31 oct. 2020 | $15.14 | 17.09% | 3,269.96 | -2.77% | |
| 46. | 30 nov. 2020 | $14.88 | -1.72% | 3,621.63 | 10.75% | |
| 47. | 31 dic. 2020 | $12.71 | -14.58% | 3,756.07 | 3.71% | |
| 48. | 31 ene. 2021 | $16.31 | 28.32% | 3,714.24 | -1.11% | |
| 49. | 28 feb. 2021 | $17.79 | 9.07% | 3,811.15 | 2.61% | |
| 50. | 31 mar. 2021 | $18.58 | 4.44% | 3,972.89 | 4.24% | |
| 51. | 30 abr. 2021 | $19.10 | 2.80% | 4,181.17 | 5.24% | |
| 52. | 31 may. 2021 | $20.88 | 9.32% | 4,204.11 | 0.55% | |
| 53. | 30 jun. 2021 | $22.26 | 6.61% | 4,297.50 | 2.22% | |
| 54. | 31 jul. 2021 | $18.39 | -17.39% | 4,395.26 | 2.27% | |
| 55. | 31 ago. 2021 | $18.33 | -0.33% | 4,522.68 | 2.90% | |
| 56. | 30 sept. 2021 | $20.46 | 11.62% | 4,307.54 | -4.76% | |
| 57. | 31 oct. 2021 | $19.91 | -2.69% | 4,605.38 | 6.91% | |
| 58. | 30 nov. 2021 | $19.43 | -2.41% | 4,567.00 | -0.83% | |
| 59. | 31 dic. 2021 | $21.81 | 12.25% | 4,766.18 | 4.36% | |
| Promedio (R): | 0.82% | 1.36% | ||||
| Desviación estándar: | 18.95% | 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 EQT 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
EQT Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | REQT,t | RS&P 500,t | (REQT,t–REQT)2 | (RS&P 500,t–RS&P 500)2 | (REQT,t–REQT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | -1.17% | 3.72% | 3.96 | 5.58 | -4.70 |
| 2. | 31 mar. 2017 | 2.02% | -0.04% | 1.44 | 1.95 | -1.68 |
| 3. | 30 abr. 2017 | -4.84% | 0.91% | 32.09 | 0.20 | 2.54 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2021 | -2.41% | -0.83% | 10.44 | 4.80 | 7.08 |
| 59. | 31 dic. 2021 | 12.25% | 4.36% | 130.62 | 9.02 | 34.33 |
| Total (Σ): | 20,818.66 | 1,164.17 | 1,330.87 | |||
| t | Fecha | REQT,t | RS&P 500,t | (REQT,t–REQT)2 | (RS&P 500,t–RS&P 500)2 | (REQT,t–REQT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2017 | -1.17% | 3.72% | 3.96 | 5.58 | -4.70 |
| 2. | 31 mar. 2017 | 2.02% | -0.04% | 1.44 | 1.95 | -1.68 |
| 3. | 30 abr. 2017 | -4.84% | 0.91% | 32.09 | 0.20 | 2.54 |
| 4. | 31 may. 2017 | -4.88% | 1.16% | 32.55 | 0.04 | 1.14 |
| 5. | 30 jun. 2017 | 6.01% | 0.48% | 26.90 | 0.77 | -4.55 |
| 6. | 31 jul. 2017 | 8.72% | 1.93% | 62.43 | 0.33 | 4.56 |
| 7. | 31 ago. 2017 | -2.09% | 0.05% | 8.46 | 1.70 | 3.79 |
| 8. | 30 sept. 2017 | 4.65% | 1.93% | 14.68 | 0.33 | 2.19 |
| 9. | 31 oct. 2017 | -4.14% | 2.22% | 24.59 | 0.74 | -4.27 |
| 10. | 30 nov. 2017 | -4.65% | 2.81% | 29.96 | 2.10 | -7.94 |
| 11. | 31 dic. 2017 | -4.50% | 0.98% | 28.27 | 0.14 | 1.99 |
| 12. | 31 ene. 2018 | -4.62% | 5.62% | 29.60 | 18.15 | -23.18 |
| 13. | 28 feb. 2018 | -7.28% | -3.89% | 65.54 | 27.59 | 42.52 |
| 14. | 31 mar. 2018 | -5.57% | -2.69% | 40.78 | 16.37 | 25.84 |
| 15. | 30 abr. 2018 | 5.64% | 0.27% | 23.24 | 1.18 | -5.24 |
| 16. | 31 may. 2018 | 2.75% | 2.16% | 3.72 | 0.64 | 1.55 |
| 17. | 30 jun. 2018 | 7.06% | 0.48% | 38.97 | 0.76 | -5.45 |
| 18. | 31 jul. 2018 | -9.97% | 3.60% | 116.37 | 5.04 | -24.21 |
| 19. | 31 ago. 2018 | 2.76% | 3.03% | 3.75 | 2.78 | 3.23 |
| 20. | 30 sept. 2018 | -13.31% | 0.43% | 199.62 | 0.86 | 13.12 |
| 21. | 31 oct. 2018 | -23.20% | -6.94% | 576.82 | 68.86 | 199.30 |
| 22. | 30 nov. 2018 | 1.91% | 1.79% | 1.20 | 0.18 | 0.47 |
| 23. | 31 dic. 2018 | 0.96% | -9.18% | 0.02 | 111.00 | -1.49 |
| 24. | 31 ene. 2019 | 3.07% | 7.87% | 5.06 | 42.39 | 14.65 |
| 25. | 28 feb. 2019 | -6.78% | 2.97% | 57.76 | 2.61 | -12.27 |
| 26. | 31 mar. 2019 | 14.46% | 1.79% | 186.02 | 0.19 | 5.93 |
| 27. | 30 abr. 2019 | -1.40% | 3.93% | 4.92 | 6.62 | -5.71 |
| 28. | 31 may. 2019 | -10.37% | -6.58% | 125.15 | 62.97 | 88.78 |
| 29. | 30 jun. 2019 | -13.61% | 6.89% | 208.13 | 30.64 | -79.85 |
| 30. | 31 jul. 2019 | -4.43% | 1.31% | 27.54 | 0.00 | 0.24 |
| 31. | 31 ago. 2019 | -32.50% | -1.81% | 1,109.90 | 10.03 | 105.51 |
| 32. | 30 sept. 2019 | 4.62% | 1.72% | 14.45 | 0.13 | 1.37 |
| 33. | 31 oct. 2019 | 0.94% | 2.04% | 0.01 | 0.47 | 0.08 |
| 34. | 30 nov. 2019 | -18.44% | 3.40% | 370.79 | 4.19 | -39.41 |
| 35. | 31 dic. 2019 | 24.86% | 2.86% | 577.76 | 2.25 | 36.08 |
| 36. | 31 ene. 2020 | -44.50% | -0.16% | 2,053.50 | 2.31 | 68.91 |
| 37. | 29 feb. 2020 | -2.48% | -8.41% | 10.89 | 95.43 | 32.23 |
| 38. | 31 mar. 2020 | 20.44% | -12.51% | 385.05 | 192.37 | -272.16 |
| 39. | 30 abr. 2020 | 106.36% | 12.68% | 11,139.69 | 128.29 | 1,195.45 |
| 40. | 31 may. 2020 | -8.57% | 4.53% | 88.13 | 10.05 | -29.76 |
| 41. | 30 jun. 2020 | -10.79% | 1.84% | 134.90 | 0.23 | -5.59 |
| 42. | 31 jul. 2020 | 22.02% | 5.51% | 449.30 | 17.24 | 88.01 |
| 43. | 31 ago. 2020 | 9.30% | 7.01% | 71.87 | 31.91 | 47.88 |
| 44. | 30 sept. 2020 | -18.53% | -3.92% | 374.26 | 27.89 | 102.16 |
| 45. | 31 oct. 2020 | 17.09% | -2.77% | 264.77 | 17.01 | -67.11 |
| 46. | 30 nov. 2020 | -1.72% | 10.75% | 6.44 | 88.30 | -23.84 |
| 47. | 31 dic. 2020 | -14.58% | 3.71% | 237.27 | 5.54 | -36.26 |
| 48. | 31 ene. 2021 | 28.32% | -1.11% | 756.47 | 6.11 | -67.98 |
| 49. | 28 feb. 2021 | 9.07% | 2.61% | 68.13 | 1.57 | 10.33 |
| 50. | 31 mar. 2021 | 4.44% | 4.24% | 13.11 | 8.33 | 10.45 |
| 51. | 30 abr. 2021 | 2.80% | 5.24% | 3.91 | 15.09 | 7.69 |
| 52. | 31 may. 2021 | 9.32% | 0.55% | 72.24 | 0.65 | -6.88 |
| 53. | 30 jun. 2021 | 6.61% | 2.22% | 33.51 | 0.75 | 5.00 |
| 54. | 31 jul. 2021 | -17.39% | 2.27% | 331.44 | 0.84 | -16.69 |
| 55. | 31 ago. 2021 | -0.33% | 2.90% | 1.31 | 2.38 | -1.77 |
| 56. | 30 sept. 2021 | 11.62% | -4.76% | 116.64 | 37.39 | -66.04 |
| 57. | 31 oct. 2021 | -2.69% | 6.91% | 12.31 | 30.87 | -19.49 |
| 58. | 30 nov. 2021 | -2.41% | -0.83% | 10.44 | 4.80 | 7.08 |
| 59. | 31 dic. 2021 | 12.25% | 4.36% | 130.62 | 9.02 | 34.33 |
| Total (Σ): | 20,818.66 | 1,164.17 | 1,330.87 | |||
Mostrar todo
VarianzaEQT = Σ(REQT,t–REQT)2 ÷ (59 – 1)
= 20,818.66 ÷ (59 – 1)
= 358.94
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianzaEQT, S&P 500 = Σ(REQT,t–REQT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,330.87 ÷ (59 – 1)
= 22.95
Estimación sistemática del riesgo (β)
| VarianzaEQT | 358.94 |
| VarianzaS&P 500 | 20.07 |
| CovarianzaEQT, S&P 500 | 22.95 |
| Coeficiente de correlaciónEQT, S&P 5001 | 0.27 |
| βEQT2 | 1.14 |
| αEQT3 | -0.73% |
Cálculos
1 Coeficiente de correlaciónEQT, S&P 500
= CovarianzaEQT, S&P 500 ÷ (Desviación estándarEQT × Desviación estándarS&P 500)
= 22.95 ÷ (18.95% × 4.48%)
= 0.27
2 βEQT
= CovarianzaEQT, S&P 500 ÷ VarianzaS&P 500
= 22.95 ÷ 20.07
= 1.14
3 αEQT
= PromedioEQT – βEQT × PromedioS&P 500
= 0.82% – 1.14 × 1.36%
= -0.73%
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 EQT acciones ordinarias | βEQT | 1.14 |
| Tasa de rendimiento esperada de las acciones ordinarias de EQT3 | E(REQT) | 15.09% |
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(REQT) = RF + βEQT [E(RM) – RF]
= 4.67% + 1.14 [13.79% – 4.67%]
= 15.09%