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 | 4.67% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Anadarko acciones ordinarias | βAPC | 1.48 |
| Tasa de rendimiento esperada de las acciones ordinarias de Anadarko3 | E(RAPC) | 18.15% |
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]
= 4.67% + 1.48 [13.79% – 4.67%]
= 18.15%