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 Anadarko.
Tasas de retorno
Anadarko Petroleum Corp., tasas mensuales de retorno
| Anadarko Petroleum Corp. (APC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAPC,t1 | DividendoAPC,t1 | RAPC,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene 2012 | $80.72 | 1,312.41 | ||||
| 1. | 29 feb 2012 | $84.12 | 4.21% | 1,365.68 | 4.06% | |
| 2. | 31 mar 2012 | $78.34 | $0.09 | -6.76% | 1,408.47 | 3.13% |
| 3. | 30 abr 2012 | $73.21 | -6.55% | 1,397.91 | -0.75% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov 2016 | $69.15 | 16.34% | 2,198.81 | 3.42% | |
| 59. | 31 dic 2016 | $69.73 | $0.05 | 0.91% | 2,238.83 | 1.82% |
| Promedio (R): | 0.22% | 0.95% | ||||
| Desviación estándar: | 8.95% | 2.98% | ||||
| Anadarko Petroleum Corp. (APC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAPC,t1 | DividendoAPC,t1 | RAPC,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene 2012 | $80.72 | 1,312.41 | ||||
| 1. | 29 feb 2012 | $84.12 | 4.21% | 1,365.68 | 4.06% | |
| 2. | 31 mar 2012 | $78.34 | $0.09 | -6.76% | 1,408.47 | 3.13% |
| 3. | 30 abr 2012 | $73.21 | -6.55% | 1,397.91 | -0.75% | |
| 4. | 31 may 2012 | $61.00 | -16.68% | 1,310.33 | -6.27% | |
| 5. | 30 jun 2012 | $66.20 | $0.09 | 8.67% | 1,362.16 | 3.96% |
| 6. | 31 jul 2012 | $69.44 | 4.89% | 1,379.32 | 1.26% | |
| 7. | 31 ago 2012 | $69.27 | -0.24% | 1,406.58 | 1.98% | |
| 8. | 30 sept 2012 | $69.92 | $0.09 | 1.07% | 1,440.67 | 2.42% |
| 9. | 31 oct 2012 | $68.81 | -1.59% | 1,412.16 | -1.98% | |
| 10. | 30 nov 2012 | $73.19 | 6.37% | 1,416.18 | 0.28% | |
| 11. | 31 dic 2012 | $74.31 | $0.09 | 1.65% | 1,426.19 | 0.71% |
| 12. | 31 ene 2013 | $80.02 | 7.68% | 1,498.11 | 5.04% | |
| 13. | 28 feb 2013 | $79.58 | -0.55% | 1,514.68 | 1.11% | |
| 14. | 31 mar 2013 | $87.45 | $0.09 | 10.00% | 1,569.19 | 3.60% |
| 15. | 30 abr 2013 | $84.76 | -3.08% | 1,597.57 | 1.81% | |
| 16. | 31 may 2013 | $87.47 | 3.20% | 1,630.74 | 2.08% | |
| 17. | 30 jun 2013 | $85.93 | $0.09 | -1.66% | 1,606.28 | -1.50% |
| 18. | 31 jul 2013 | $88.52 | 3.01% | 1,685.73 | 4.95% | |
| 19. | 31 ago 2013 | $91.42 | 3.28% | 1,632.97 | -3.13% | |
| 20. | 30 sept 2013 | $92.99 | $0.18 | 1.91% | 1,681.55 | 2.97% |
| 21. | 31 oct 2013 | $95.29 | 2.47% | 1,756.54 | 4.46% | |
| 22. | 30 nov 2013 | $88.82 | -6.79% | 1,805.81 | 2.80% | |
| 23. | 31 dic 2013 | $79.32 | $0.18 | -10.49% | 1,848.36 | 2.36% |
| 24. | 31 ene 2014 | $80.69 | 1.73% | 1,782.59 | -3.56% | |
| 25. | 28 feb 2014 | $84.16 | 4.30% | 1,859.45 | 4.31% | |
| 26. | 31 mar 2014 | $84.76 | $0.18 | 0.93% | 1,872.34 | 0.69% |
| 27. | 30 abr 2014 | $99.02 | 16.82% | 1,883.95 | 0.62% | |
| 28. | 31 may 2014 | $102.86 | 3.88% | 1,923.57 | 2.10% | |
| 29. | 30 jun 2014 | $109.47 | $0.27 | 6.69% | 1,960.23 | 1.91% |
| 30. | 31 jul 2014 | $106.85 | -2.39% | 1,930.67 | -1.51% | |
| 31. | 31 ago 2014 | $112.69 | 5.47% | 2,003.37 | 3.77% | |
| 32. | 30 sept 2014 | $101.44 | $0.27 | -9.74% | 1,972.29 | -1.55% |
| 33. | 31 oct 2014 | $91.78 | -9.52% | 2,018.05 | 2.32% | |
| 34. | 30 nov 2014 | $79.15 | -13.76% | 2,067.56 | 2.45% | |
| 35. | 31 dic 2014 | $82.50 | $0.27 | 4.57% | 2,058.90 | -0.42% |
| 36. | 31 ene 2015 | $81.75 | -0.91% | 1,994.99 | -3.10% | |
| 37. | 28 feb 2015 | $84.23 | 3.03% | 2,104.50 | 5.49% | |
| 38. | 31 mar 2015 | $82.81 | $0.27 | -1.37% | 2,067.89 | -1.74% |
| 39. | 30 abr 2015 | $94.10 | 13.63% | 2,085.51 | 0.85% | |
| 40. | 31 may 2015 | $83.61 | -11.15% | 2,107.39 | 1.05% | |
| 41. | 30 jun 2015 | $78.06 | $0.27 | -6.32% | 2,063.11 | -2.10% |
| 42. | 31 jul 2015 | $74.35 | -4.75% | 2,103.84 | 1.97% | |
| 43. | 31 ago 2015 | $71.58 | -3.73% | 1,972.18 | -6.26% | |
| 44. | 30 sept 2015 | $60.39 | $0.27 | -15.26% | 1,920.03 | -2.64% |
| 45. | 31 oct 2015 | $66.88 | 10.75% | 2,079.36 | 8.30% | |
| 46. | 30 nov 2015 | $59.90 | -10.44% | 2,080.41 | 0.05% | |
| 47. | 31 dic 2015 | $48.58 | $0.27 | -18.45% | 2,043.94 | -1.75% |
| 48. | 31 ene 2016 | $39.09 | -19.53% | 1,940.24 | -5.07% | |
| 49. | 29 feb 2016 | $37.95 | -2.92% | 1,932.23 | -0.41% | |
| 50. | 31 mar 2016 | $46.57 | $0.05 | 22.85% | 2,059.74 | 6.60% |
| 51. | 30 abr 2016 | $52.76 | 13.29% | 2,065.30 | 0.27% | |
| 52. | 31 may 2016 | $51.86 | -1.71% | 2,096.95 | 1.53% | |
| 53. | 30 jun 2016 | $53.25 | $0.05 | 2.78% | 2,098.86 | 0.09% |
| 54. | 31 jul 2016 | $54.53 | 2.40% | 2,173.60 | 3.56% | |
| 55. | 31 ago 2016 | $53.47 | -1.94% | 2,170.95 | -0.12% | |
| 56. | 30 sept 2016 | $63.36 | $0.05 | 18.59% | 2,168.27 | -0.12% |
| 57. | 31 oct 2016 | $59.44 | -6.19% | 2,126.15 | -1.94% | |
| 58. | 30 nov 2016 | $69.15 | 16.34% | 2,198.81 | 3.42% | |
| 59. | 31 dic 2016 | $69.73 | $0.05 | 0.91% | 2,238.83 | 1.82% |
| Promedio (R): | 0.22% | 0.95% | ||||
| Desviación estándar: | 8.95% | 2.98% | ||||
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 APC 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
Anadarko Petroleum Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RAPC,t | RS&P 500,t | (RAPC,t–RAPC)2 | (RS&P 500,t–RS&P 500)2 | (RAPC,t–RAPC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 feb 2012 | 4.21% | 4.06% | 15.94 | 9.65 | 12.40 |
| 2. | 31 mar 2012 | -6.76% | 3.13% | 48.77 | 4.75 | -15.23 |
| 3. | 30 abr 2012 | -6.55% | -0.75% | 45.80 | 2.90 | 11.52 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov 2016 | 16.34% | 3.42% | 259.75 | 6.07 | 39.72 |
| 59. | 31 dic 2016 | 0.91% | 1.82% | 0.48 | 0.75 | 0.60 |
| Total (Σ): | 4,648.43 | 514.91 | 761.51 | |||
| t | Fecha | RAPC,t | RS&P 500,t | (RAPC,t–RAPC)2 | (RS&P 500,t–RS&P 500)2 | (RAPC,t–RAPC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 feb 2012 | 4.21% | 4.06% | 15.94 | 9.65 | 12.40 |
| 2. | 31 mar 2012 | -6.76% | 3.13% | 48.77 | 4.75 | -15.23 |
| 3. | 30 abr 2012 | -6.55% | -0.75% | 45.80 | 2.90 | 11.52 |
| 4. | 31 may 2012 | -16.68% | -6.27% | 285.51 | 52.10 | 121.96 |
| 5. | 30 jun 2012 | 8.67% | 3.96% | 71.45 | 9.02 | 25.38 |
| 6. | 31 jul 2012 | 4.89% | 1.26% | 21.86 | 0.09 | 1.44 |
| 7. | 31 ago 2012 | -0.24% | 1.98% | 0.22 | 1.05 | -0.47 |
| 8. | 30 sept 2012 | 1.07% | 2.42% | 0.72 | 2.16 | 1.25 |
| 9. | 31 oct 2012 | -1.59% | -1.98% | 3.26 | 8.60 | 5.30 |
| 10. | 30 nov 2012 | 6.37% | 0.28% | 37.78 | 0.45 | -4.11 |
| 11. | 31 dic 2012 | 1.65% | 0.71% | 2.06 | 0.06 | -0.35 |
| 12. | 31 ene 2013 | 7.68% | 5.04% | 55.73 | 16.73 | 30.53 |
| 13. | 28 feb 2013 | -0.55% | 1.11% | 0.59 | 0.02 | -0.12 |
| 14. | 31 mar 2013 | 10.00% | 3.60% | 95.72 | 7.00 | 25.89 |
| 15. | 30 abr 2013 | -3.08% | 1.81% | 10.86 | 0.73 | -2.82 |
| 16. | 31 may 2013 | 3.20% | 2.08% | 8.87 | 1.26 | 3.35 |
| 17. | 30 jun 2013 | -1.66% | -1.50% | 3.52 | 6.02 | 4.60 |
| 18. | 31 jul 2013 | 3.01% | 4.95% | 7.81 | 15.95 | 11.16 |
| 19. | 31 ago 2013 | 3.28% | -3.13% | 9.35 | 16.67 | -12.48 |
| 20. | 30 sept 2013 | 1.91% | 2.97% | 2.87 | 4.09 | 3.43 |
| 21. | 31 oct 2013 | 2.47% | 4.46% | 5.08 | 12.30 | 7.91 |
| 22. | 30 nov 2013 | -6.79% | 2.80% | 49.12 | 3.43 | -12.98 |
| 23. | 31 dic 2013 | -10.49% | 2.36% | 114.75 | 1.97 | -15.03 |
| 24. | 31 ene 2014 | 1.73% | -3.56% | 2.27 | 20.35 | -6.80 |
| 25. | 28 feb 2014 | 4.30% | 4.31% | 16.66 | 11.28 | 13.71 |
| 26. | 31 mar 2014 | 0.93% | 0.69% | 0.50 | 0.07 | -0.18 |
| 27. | 30 abr 2014 | 16.82% | 0.62% | 275.72 | 0.11 | -5.53 |
| 28. | 31 may 2014 | 3.88% | 2.10% | 13.39 | 1.32 | 4.21 |
| 29. | 30 jun 2014 | 6.69% | 1.91% | 41.86 | 0.91 | 6.17 |
| 30. | 31 jul 2014 | -2.39% | -1.51% | 6.82 | 6.06 | 6.43 |
| 31. | 31 ago 2014 | 5.47% | 3.77% | 27.53 | 7.91 | 14.76 |
| 32. | 30 sept 2014 | -9.74% | -1.55% | 99.25 | 6.27 | 24.95 |
| 33. | 31 oct 2014 | -9.52% | 2.32% | 94.91 | 1.87 | -13.32 |
| 34. | 30 nov 2014 | -13.76% | 2.45% | 195.45 | 2.25 | -20.98 |
| 35. | 31 dic 2014 | 4.57% | -0.42% | 18.96 | 1.88 | -5.97 |
| 36. | 31 ene 2015 | -0.91% | -3.10% | 1.27 | 16.46 | 4.58 |
| 37. | 28 feb 2015 | 3.03% | 5.49% | 7.92 | 20.58 | 12.77 |
| 38. | 31 mar 2015 | -1.37% | -1.74% | 2.51 | 7.25 | 4.27 |
| 39. | 30 abr 2015 | 13.63% | 0.85% | 179.95 | 0.01 | -1.35 |
| 40. | 31 may 2015 | -11.15% | 1.05% | 129.20 | 0.01 | -1.09 |
| 41. | 30 jun 2015 | -6.32% | -2.10% | 42.69 | 9.33 | 19.96 |
| 42. | 31 jul 2015 | -4.75% | 1.97% | 24.72 | 1.04 | -5.08 |
| 43. | 31 ago 2015 | -3.73% | -6.26% | 15.56 | 52.00 | 28.44 |
| 44. | 30 sept 2015 | -15.26% | -2.64% | 239.47 | 12.94 | 55.66 |
| 45. | 31 oct 2015 | 10.75% | 8.30% | 110.83 | 53.96 | 77.33 |
| 46. | 30 nov 2015 | -10.44% | 0.05% | 113.54 | 0.81 | 9.61 |
| 47. | 31 dic 2015 | -18.45% | -1.75% | 348.44 | 7.32 | 50.51 |
| 48. | 31 ene 2016 | -19.53% | -5.07% | 390.22 | 36.32 | 119.04 |
| 49. | 29 feb 2016 | -2.92% | -0.41% | 9.83 | 1.87 | 4.28 |
| 50. | 31 mar 2016 | 22.85% | 6.60% | 511.97 | 31.88 | 127.76 |
| 51. | 30 abr 2016 | 13.29% | 0.27% | 170.90 | 0.47 | -8.93 |
| 52. | 31 may 2016 | -1.71% | 1.53% | 3.71 | 0.34 | -1.12 |
| 53. | 30 jun 2016 | 2.78% | 0.09% | 6.54 | 0.74 | -2.20 |
| 54. | 31 jul 2016 | 2.40% | 3.56% | 4.77 | 6.80 | 5.70 |
| 55. | 31 ago 2016 | -1.94% | -0.12% | 4.68 | 1.16 | 2.32 |
| 56. | 30 sept 2016 | 18.59% | -0.12% | 337.48 | 1.16 | -19.77 |
| 57. | 31 oct 2016 | -6.19% | -1.94% | 41.04 | 8.38 | 18.55 |
| 58. | 30 nov 2016 | 16.34% | 3.42% | 259.75 | 6.07 | 39.72 |
| 59. | 31 dic 2016 | 0.91% | 1.82% | 0.48 | 0.75 | 0.60 |
| Total (Σ): | 4,648.43 | 514.91 | 761.51 | |||
Mostrar todo
VarianzaAPC = Σ(RAPC,t–RAPC)2 ÷ (59 – 1)
= 4,648.43 ÷ (59 – 1)
= 80.15
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 514.91 ÷ (59 – 1)
= 8.88
CovarianzaAPC, S&P 500 = Σ(RAPC,t–RAPC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 761.51 ÷ (59 – 1)
= 13.13
Estimación sistemática del riesgo (β)
| VarianzaAPC | 80.15 |
| VarianzaS&P 500 | 8.88 |
| CovarianzaAPC, S&P 500 | 13.13 |
| Coeficiente de correlaciónAPC, S&P 5001 | 0.49 |
| βAPC2 | 1.48 |
| αAPC3 | -1.19% |
Cálculos
1 Coeficiente de correlaciónAPC, S&P 500
= CovarianzaAPC, S&P 500 ÷ (Desviación estándarAPC × Desviación estándarS&P 500)
= 13.13 ÷ (8.95% × 2.98%)
= 0.49
2 βAPC
= CovarianzaAPC, S&P 500 ÷ VarianzaS&P 500
= 13.13 ÷ 8.88
= 1.48
3 αAPC
= PromedioAPC – βAPC × PromedioS&P 500
= 0.22% – 1.48 × 0.95%
= -1.19%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.60% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 14.89% |
| Riesgo sistemático de Anadarko acciones ordinarias | βAPC | 1.48 |
| Tasa de rendimiento esperada de las acciones ordinarias de Anadarko3 | E(RAPC) | 19.82% |
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(RAPC) = RF + βAPC [E(RM) – RF]
= 4.60% + 1.48 [14.89% – 4.60%]
= 19.82%