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 EOG.
Tasas de retorno
EOG Resources Inc., tasas mensuales de retorno
| EOG Resources Inc. (EOG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEOG,t1 | DividendoEOG,t1 | REOG,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2015 | $89.03 | 1,994.99 | ||||
| 1. | 28 feb. 2015 | $89.72 | 0.78% | 2,104.50 | 5.49% | |
| 2. | 31 mar. 2015 | $91.69 | 2.20% | 2,067.89 | -1.74% | |
| 3. | 30 abr. 2015 | $98.95 | $0.1675 | 8.10% | 2,085.51 | 0.85% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | $70.90 | 2.29% | 3,140.98 | 3.40% | |
| 59. | 31 dic. 2019 | $83.76 | 18.14% | 3,230.78 | 2.86% | |
| Promedio (R): | 0.35% | 0.88% | ||||
| Desviación estándar: | 8.80% | 3.45% | ||||
| EOG Resources Inc. (EOG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEOG,t1 | DividendoEOG,t1 | REOG,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2015 | $89.03 | 1,994.99 | ||||
| 1. | 28 feb. 2015 | $89.72 | 0.78% | 2,104.50 | 5.49% | |
| 2. | 31 mar. 2015 | $91.69 | 2.20% | 2,067.89 | -1.74% | |
| 3. | 30 abr. 2015 | $98.95 | $0.1675 | 8.10% | 2,085.51 | 0.85% |
| 4. | 31 may. 2015 | $88.69 | -10.37% | 2,107.39 | 1.05% | |
| 5. | 30 jun. 2015 | $87.55 | -1.29% | 2,063.11 | -2.10% | |
| 6. | 31 jul. 2015 | $77.19 | $0.1675 | -11.64% | 2,103.84 | 1.97% |
| 7. | 31 ago. 2015 | $78.31 | 1.45% | 1,972.18 | -6.26% | |
| 8. | 30 sept. 2015 | $72.80 | -7.04% | 1,920.03 | -2.64% | |
| 9. | 31 oct. 2015 | $85.85 | $0.1675 | 18.16% | 2,079.36 | 8.30% |
| 10. | 30 nov. 2015 | $83.43 | -2.82% | 2,080.41 | 0.05% | |
| 11. | 31 dic. 2015 | $70.79 | -15.15% | 2,043.94 | -1.75% | |
| 12. | 31 ene. 2016 | $71.02 | $0.1675 | 0.56% | 1,940.24 | -5.07% |
| 13. | 29 feb. 2016 | $64.74 | -8.84% | 1,932.23 | -0.41% | |
| 14. | 31 mar. 2016 | $72.58 | 12.11% | 2,059.74 | 6.60% | |
| 15. | 30 abr. 2016 | $82.62 | $0.1675 | 14.06% | 2,065.30 | 0.27% |
| 16. | 31 may. 2016 | $81.36 | -1.53% | 2,096.95 | 1.53% | |
| 17. | 30 jun. 2016 | $83.42 | 2.53% | 2,098.86 | 0.09% | |
| 18. | 31 jul. 2016 | $81.70 | $0.1675 | -1.86% | 2,173.60 | 3.56% |
| 19. | 31 ago. 2016 | $88.49 | 8.31% | 2,170.95 | -0.12% | |
| 20. | 30 sept. 2016 | $96.71 | 9.29% | 2,168.27 | -0.12% | |
| 21. | 31 oct. 2016 | $90.42 | $0.1675 | -6.33% | 2,126.15 | -1.94% |
| 22. | 30 nov. 2016 | $102.52 | 13.38% | 2,198.81 | 3.42% | |
| 23. | 31 dic. 2016 | $101.10 | -1.39% | 2,238.83 | 1.82% | |
| 24. | 31 ene. 2017 | $101.58 | $0.1675 | 0.64% | 2,278.87 | 1.79% |
| 25. | 28 feb. 2017 | $96.99 | -4.52% | 2,363.64 | 3.72% | |
| 26. | 31 mar. 2017 | $97.55 | 0.58% | 2,362.72 | -0.04% | |
| 27. | 30 abr. 2017 | $92.50 | $0.1675 | -5.01% | 2,384.20 | 0.91% |
| 28. | 31 may. 2017 | $90.31 | -2.37% | 2,411.80 | 1.16% | |
| 29. | 30 jun. 2017 | $90.52 | 0.23% | 2,423.41 | 0.48% | |
| 30. | 31 jul. 2017 | $95.14 | $0.1675 | 5.29% | 2,470.30 | 1.93% |
| 31. | 31 ago. 2017 | $84.99 | -10.67% | 2,471.65 | 0.05% | |
| 32. | 30 sept. 2017 | $96.74 | 13.83% | 2,519.36 | 1.93% | |
| 33. | 31 oct. 2017 | $99.87 | $0.1675 | 3.41% | 2,575.26 | 2.22% |
| 34. | 30 nov. 2017 | $102.32 | 2.45% | 2,647.58 | 2.81% | |
| 35. | 31 dic. 2017 | $107.91 | 5.46% | 2,673.61 | 0.98% | |
| 36. | 31 ene. 2018 | $115.00 | $0.1675 | 6.73% | 2,823.81 | 5.62% |
| 37. | 28 feb. 2018 | $101.42 | -11.81% | 2,713.83 | -3.89% | |
| 38. | 31 mar. 2018 | $105.27 | 3.80% | 2,640.87 | -2.69% | |
| 39. | 30 abr. 2018 | $118.17 | $0.185 | 12.43% | 2,648.05 | 0.27% |
| 40. | 31 may. 2018 | $117.81 | -0.30% | 2,705.27 | 2.16% | |
| 41. | 30 jun. 2018 | $124.43 | 5.62% | 2,718.37 | 0.48% | |
| 42. | 31 jul. 2018 | $128.94 | $0.185 | 3.77% | 2,816.29 | 3.60% |
| 43. | 31 ago. 2018 | $118.23 | -8.31% | 2,901.52 | 3.03% | |
| 44. | 30 sept. 2018 | $127.57 | 7.90% | 2,913.98 | 0.43% | |
| 45. | 31 oct. 2018 | $105.34 | $0.22 | -17.25% | 2,711.74 | -6.94% |
| 46. | 30 nov. 2018 | $103.31 | -1.93% | 2,760.17 | 1.79% | |
| 47. | 31 dic. 2018 | $87.21 | -15.58% | 2,506.85 | -9.18% | |
| 48. | 31 ene. 2019 | $99.20 | $0.22 | 14.00% | 2,704.10 | 7.87% |
| 49. | 28 feb. 2019 | $94.00 | -5.24% | 2,784.49 | 2.97% | |
| 50. | 31 mar. 2019 | $95.18 | 1.26% | 2,834.40 | 1.79% | |
| 51. | 30 abr. 2019 | $96.05 | $0.22 | 1.15% | 2,945.83 | 3.93% |
| 52. | 31 may. 2019 | $81.88 | -14.75% | 2,752.06 | -6.58% | |
| 53. | 30 jun. 2019 | $93.16 | 13.78% | 2,941.76 | 6.89% | |
| 54. | 31 jul. 2019 | $85.85 | $0.2875 | -7.54% | 2,980.38 | 1.31% |
| 55. | 31 ago. 2019 | $74.19 | -13.58% | 2,926.46 | -1.81% | |
| 56. | 30 sept. 2019 | $74.22 | 0.04% | 2,976.74 | 1.72% | |
| 57. | 31 oct. 2019 | $69.31 | $0.2875 | -6.23% | 3,037.56 | 2.04% |
| 58. | 30 nov. 2019 | $70.90 | 2.29% | 3,140.98 | 3.40% | |
| 59. | 31 dic. 2019 | $83.76 | 18.14% | 3,230.78 | 2.86% | |
| Promedio (R): | 0.35% | 0.88% | ||||
| Desviación estándar: | 8.80% | 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 EOG 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
EOG Resources Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | REOG,t | RS&P 500,t | (REOG,t–REOG)2 | (RS&P 500,t–RS&P 500)2 | (REOG,t–REOG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2015 | 0.78% | 5.49% | 0.18 | 21.25 | 1.98 |
| 2. | 31 mar. 2015 | 2.20% | -1.74% | 3.42 | 6.86 | -4.85 |
| 3. | 30 abr. 2015 | 8.10% | 0.85% | 60.14 | 0.00 | -0.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2019 | 2.29% | 3.40% | 3.80 | 6.38 | 4.92 |
| 59. | 31 dic. 2019 | 18.14% | 2.86% | 316.58 | 3.92 | 35.23 |
| Total (Σ): | 4,494.60 | 688.77 | 992.50 | |||
| t | Fecha | REOG,t | RS&P 500,t | (REOG,t–REOG)2 | (RS&P 500,t–RS&P 500)2 | (REOG,t–REOG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2015 | 0.78% | 5.49% | 0.18 | 21.25 | 1.98 |
| 2. | 31 mar. 2015 | 2.20% | -1.74% | 3.42 | 6.86 | -4.85 |
| 3. | 30 abr. 2015 | 8.10% | 0.85% | 60.14 | 0.00 | -0.21 |
| 4. | 31 may. 2015 | -10.37% | 1.05% | 114.80 | 0.03 | -1.82 |
| 5. | 30 jun. 2015 | -1.29% | -2.10% | 2.66 | 8.88 | 4.86 |
| 6. | 31 jul. 2015 | -11.64% | 1.97% | 143.70 | 1.20 | -13.13 |
| 7. | 31 ago. 2015 | 1.45% | -6.26% | 1.22 | 50.94 | -7.89 |
| 8. | 30 sept. 2015 | -7.04% | -2.64% | 54.49 | 12.41 | 26.01 |
| 9. | 31 oct. 2015 | 18.16% | 8.30% | 317.21 | 55.04 | 132.14 |
| 10. | 30 nov. 2015 | -2.82% | 0.05% | 10.01 | 0.69 | 2.62 |
| 11. | 31 dic. 2015 | -15.15% | -1.75% | 240.12 | 6.93 | 40.79 |
| 12. | 31 ene. 2016 | 0.56% | -5.07% | 0.05 | 35.43 | -1.29 |
| 13. | 29 feb. 2016 | -8.84% | -0.41% | 84.42 | 1.67 | 11.87 |
| 14. | 31 mar. 2016 | 12.11% | 6.60% | 138.41 | 32.72 | 67.29 |
| 15. | 30 abr. 2016 | 14.06% | 0.27% | 188.19 | 0.37 | -8.36 |
| 16. | 31 may. 2016 | -1.53% | 1.53% | 3.50 | 0.43 | -1.22 |
| 17. | 30 jun. 2016 | 2.53% | 0.09% | 4.78 | 0.62 | -1.72 |
| 18. | 31 jul. 2016 | -1.86% | 3.56% | 4.87 | 7.19 | -5.92 |
| 19. | 31 ago. 2016 | 8.31% | -0.12% | 63.45 | 1.00 | -7.97 |
| 20. | 30 sept. 2016 | 9.29% | -0.12% | 79.99 | 1.01 | -8.97 |
| 21. | 31 oct. 2016 | -6.33% | -1.94% | 44.57 | 7.96 | 18.84 |
| 22. | 30 nov. 2016 | 13.38% | 3.42% | 169.95 | 6.44 | 33.09 |
| 23. | 31 dic. 2016 | -1.39% | 1.82% | 2.99 | 0.89 | -1.63 |
| 24. | 31 ene. 2017 | 0.64% | 1.79% | 0.09 | 0.83 | 0.27 |
| 25. | 28 feb. 2017 | -4.52% | 3.72% | 23.66 | 8.07 | -13.82 |
| 26. | 31 mar. 2017 | 0.58% | -0.04% | 0.05 | 0.84 | -0.21 |
| 27. | 30 abr. 2017 | -5.01% | 0.91% | 28.63 | 0.00 | -0.16 |
| 28. | 31 may. 2017 | -2.37% | 1.16% | 7.36 | 0.08 | -0.76 |
| 29. | 30 jun. 2017 | 0.23% | 0.48% | 0.01 | 0.16 | 0.04 |
| 30. | 31 jul. 2017 | 5.29% | 1.93% | 24.44 | 1.11 | 5.22 |
| 31. | 31 ago. 2017 | -10.67% | 0.05% | 121.31 | 0.68 | 9.08 |
| 32. | 30 sept. 2017 | 13.83% | 1.93% | 181.70 | 1.10 | 14.17 |
| 33. | 31 oct. 2017 | 3.41% | 2.22% | 9.38 | 1.79 | 4.10 |
| 34. | 30 nov. 2017 | 2.45% | 2.81% | 4.44 | 3.72 | 4.07 |
| 35. | 31 dic. 2017 | 5.46% | 0.98% | 26.19 | 0.01 | 0.53 |
| 36. | 31 ene. 2018 | 6.73% | 5.62% | 40.71 | 22.46 | 30.23 |
| 37. | 28 feb. 2018 | -11.81% | -3.89% | 147.72 | 22.79 | 58.02 |
| 38. | 31 mar. 2018 | 3.80% | -2.69% | 11.91 | 12.73 | -12.31 |
| 39. | 30 abr. 2018 | 12.43% | 0.27% | 146.04 | 0.37 | -7.34 |
| 40. | 31 may. 2018 | -0.30% | 2.16% | 0.42 | 1.64 | -0.83 |
| 41. | 30 jun. 2018 | 5.62% | 0.48% | 27.81 | 0.16 | -2.08 |
| 42. | 31 jul. 2018 | 3.77% | 3.60% | 11.75 | 7.41 | 9.33 |
| 43. | 31 ago. 2018 | -8.31% | 3.03% | 74.85 | 4.61 | -18.58 |
| 44. | 30 sept. 2018 | 7.90% | 0.43% | 57.07 | 0.20 | -3.40 |
| 45. | 31 oct. 2018 | -17.25% | -6.94% | 309.71 | 61.14 | 137.61 |
| 46. | 30 nov. 2018 | -1.93% | 1.79% | 5.16 | 0.82 | -2.06 |
| 47. | 31 dic. 2018 | -15.58% | -9.18% | 253.75 | 101.14 | 160.20 |
| 48. | 31 ene. 2019 | 14.00% | 7.87% | 186.47 | 48.85 | 95.44 |
| 49. | 28 feb. 2019 | -5.24% | 2.97% | 31.22 | 4.38 | -11.70 |
| 50. | 31 mar. 2019 | 1.26% | 1.79% | 0.83 | 0.83 | 0.83 |
| 51. | 30 abr. 2019 | 1.15% | 3.93% | 0.64 | 9.32 | 2.44 |
| 52. | 31 may. 2019 | -14.75% | -6.58% | 227.95 | 55.61 | 112.59 |
| 53. | 30 jun. 2019 | 13.78% | 6.89% | 180.39 | 36.17 | 80.77 |
| 54. | 31 jul. 2019 | -7.54% | 1.31% | 62.15 | 0.19 | -3.42 |
| 55. | 31 ago. 2019 | -13.58% | -1.81% | 193.97 | 7.23 | 37.44 |
| 56. | 30 sept. 2019 | 0.04% | 1.72% | 0.09 | 0.70 | -0.26 |
| 57. | 31 oct. 2019 | -6.23% | 2.04% | 43.21 | 1.36 | -7.65 |
| 58. | 30 nov. 2019 | 2.29% | 3.40% | 3.80 | 6.38 | 4.92 |
| 59. | 31 dic. 2019 | 18.14% | 2.86% | 316.58 | 3.92 | 35.23 |
| Total (Σ): | 4,494.60 | 688.77 | 992.50 | |||
Mostrar todo
VarianzaEOG = Σ(REOG,t–REOG)2 ÷ (59 – 1)
= 4,494.60 ÷ (59 – 1)
= 77.49
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
CovarianzaEOG, S&P 500 = Σ(REOG,t–REOG)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 992.50 ÷ (59 – 1)
= 17.11
Estimación sistemática del riesgo (β)
| VarianzaEOG | 77.49 |
| VarianzaS&P 500 | 11.88 |
| CovarianzaEOG, S&P 500 | 17.11 |
| Coeficiente de correlaciónEOG, S&P 5001 | 0.56 |
| βEOG2 | 1.44 |
| αEOG3 | -0.92% |
Cálculos
1 Coeficiente de correlaciónEOG, S&P 500
= CovarianzaEOG, S&P 500 ÷ (Desviación estándarEOG × Desviación estándarS&P 500)
= 17.11 ÷ (8.80% × 3.45%)
= 0.56
2 βEOG
= CovarianzaEOG, S&P 500 ÷ VarianzaS&P 500
= 17.11 ÷ 11.88
= 1.44
3 αEOG
= PromedioEOG – βEOG × PromedioS&P 500
= 0.35% – 1.44 × 0.88%
= -0.92%
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 EOG acciones ordinarias | βEOG | 1.44 |
| Tasa de rendimiento esperada de las acciones ordinarias de EOG3 | E(REOG) | 17.39% |
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(REOG) = RF + βEOG [E(RM) – RF]
= 4.72% + 1.44 [13.51% – 4.72%]
= 17.39%