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 HP.
Tasas de retorno
HP Inc., tasas mensuales de retorno
| HP Inc. (HPQ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHPQ,t1 | DividendoHPQ,t1 | RHPQ,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 nov 2012 | $12.99 | 1,416.18 | ||||
| 1. | 31 dic 2012 | $14.25 | $0.132 | 10.72% | 1,426.19 | 0.71% |
| 2. | 31 ene 2013 | $16.51 | 15.86% | 1,498.11 | 5.04% | |
| 3. | 28 feb 2013 | $20.14 | 21.99% | 1,514.68 | 1.11% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 sept 2018 | $25.77 | $0.139 | 5.11% | 2,913.98 | 0.43% |
| 71. | 31 oct 2018 | $24.14 | -6.33% | 2,711.74 | -6.94% | |
| Promedio (R): | 1.77% | 0.96% | ||||
| Desviación estándar: | 10.53% | 2.87% | ||||
| HP Inc. (HPQ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioHPQ,t1 | DividendoHPQ,t1 | RHPQ,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 nov 2012 | $12.99 | 1,416.18 | ||||
| 1. | 31 dic 2012 | $14.25 | $0.132 | 10.72% | 1,426.19 | 0.71% |
| 2. | 31 ene 2013 | $16.51 | 15.86% | 1,498.11 | 5.04% | |
| 3. | 28 feb 2013 | $20.14 | 21.99% | 1,514.68 | 1.11% | |
| 4. | 31 mar 2013 | $23.84 | $0.132 | 19.03% | 1,569.19 | 3.60% |
| 5. | 30 abr 2013 | $20.60 | -13.59% | 1,597.57 | 1.81% | |
| 6. | 31 may 2013 | $24.42 | 18.54% | 1,630.74 | 2.08% | |
| 7. | 30 jun 2013 | $24.80 | $0.1452 | 2.15% | 1,606.28 | -1.50% |
| 8. | 31 jul 2013 | $25.68 | 3.55% | 1,685.73 | 4.95% | |
| 9. | 31 ago 2013 | $22.34 | -13.01% | 1,632.97 | -3.13% | |
| 10. | 30 sept 2013 | $20.99 | $0.1452 | -5.39% | 1,681.55 | 2.97% |
| 11. | 31 oct 2013 | $24.37 | 16.10% | 1,756.54 | 4.46% | |
| 12. | 30 nov 2013 | $27.35 | 12.23% | 1,805.81 | 2.80% | |
| 13. | 31 dic 2013 | $27.98 | $0.1452 | 2.83% | 1,848.36 | 2.36% |
| 14. | 31 ene 2014 | $29.00 | 3.65% | 1,782.59 | -3.56% | |
| 15. | 28 feb 2014 | $29.88 | 3.03% | 1,859.45 | 4.31% | |
| 16. | 31 mar 2014 | $32.36 | $0.1452 | 8.79% | 1,872.34 | 0.69% |
| 17. | 30 abr 2014 | $33.06 | 2.16% | 1,883.95 | 0.62% | |
| 18. | 31 may 2014 | $33.50 | 1.33% | 1,923.57 | 2.10% | |
| 19. | 30 jun 2014 | $33.68 | $0.16 | 1.01% | 1,960.23 | 1.91% |
| 20. | 31 jul 2014 | $35.61 | 5.73% | 1,930.67 | -1.51% | |
| 21. | 31 ago 2014 | $38.00 | 6.71% | 2,003.37 | 3.77% | |
| 22. | 30 sept 2014 | $35.47 | $0.16 | -6.24% | 1,972.29 | -1.55% |
| 23. | 31 oct 2014 | $35.88 | 1.16% | 2,018.05 | 2.32% | |
| 24. | 30 nov 2014 | $39.06 | 8.86% | 2,067.56 | 2.45% | |
| 25. | 31 dic 2014 | $40.13 | $0.16 | 3.15% | 2,058.90 | -0.42% |
| 26. | 31 ene 2015 | $36.13 | -9.97% | 1,994.99 | -3.10% | |
| 27. | 28 feb 2015 | $34.84 | -3.57% | 2,104.50 | 5.49% | |
| 28. | 31 mar 2015 | $31.16 | $0.16 | -10.10% | 2,067.89 | -1.74% |
| 29. | 30 abr 2015 | $32.97 | 5.81% | 2,085.51 | 0.85% | |
| 30. | 31 may 2015 | $33.40 | 1.30% | 2,107.39 | 1.05% | |
| 31. | 30 jun 2015 | $30.01 | $0.176 | -9.62% | 2,063.11 | -2.10% |
| 32. | 31 jul 2015 | $30.52 | 1.70% | 2,103.84 | 1.97% | |
| 33. | 31 ago 2015 | $28.06 | -8.06% | 1,972.18 | -6.26% | |
| 34. | 30 sept 2015 | $25.61 | $0.176 | -8.10% | 1,920.03 | -2.64% |
| 35. | 31 oct 2015 | $26.96 | 5.27% | 2,079.36 | 8.30% | |
| 36. | 30 nov 2015 | $12.54 | -53.49% | 2,080.41 | 0.05% | |
| 37. | 31 dic 2015 | $11.84 | $0.124 | -4.59% | 2,043.94 | -1.75% |
| 38. | 31 ene 2016 | $9.71 | -17.99% | 1,940.24 | -5.07% | |
| 39. | 29 feb 2016 | $10.69 | 10.09% | 1,932.23 | -0.41% | |
| 40. | 31 mar 2016 | $12.32 | $0.124 | 16.41% | 2,059.74 | 6.60% |
| 41. | 30 abr 2016 | $12.27 | -0.41% | 2,065.30 | 0.27% | |
| 42. | 31 may 2016 | $13.38 | 9.05% | 2,096.95 | 1.53% | |
| 43. | 30 jun 2016 | $12.55 | $0.124 | -5.28% | 2,098.86 | 0.09% |
| 44. | 31 jul 2016 | $14.01 | 11.63% | 2,173.60 | 3.56% | |
| 45. | 31 ago 2016 | $14.37 | 2.57% | 2,170.95 | -0.12% | |
| 46. | 30 sept 2016 | $15.53 | $0.124 | 8.94% | 2,168.27 | -0.12% |
| 47. | 31 oct 2016 | $14.49 | -6.70% | 2,126.15 | -1.94% | |
| 48. | 30 nov 2016 | $15.40 | 6.28% | 2,198.81 | 3.42% | |
| 49. | 31 dic 2016 | $14.84 | $0.133 | -2.77% | 2,238.83 | 1.82% |
| 50. | 31 ene 2017 | $15.05 | 1.42% | 2,278.87 | 1.79% | |
| 51. | 28 feb 2017 | $17.37 | 15.42% | 2,363.64 | 3.72% | |
| 52. | 31 mar 2017 | $17.88 | $0.133 | 3.70% | 2,362.72 | -0.04% |
| 53. | 30 abr 2017 | $18.82 | 5.26% | 2,384.20 | 0.91% | |
| 54. | 31 may 2017 | $18.76 | -0.32% | 2,411.80 | 1.16% | |
| 55. | 30 jun 2017 | $17.48 | $0.133 | -6.11% | 2,423.41 | 0.48% |
| 56. | 31 jul 2017 | $19.10 | 9.27% | 2,470.30 | 1.93% | |
| 57. | 31 ago 2017 | $19.08 | -0.10% | 2,471.65 | 0.05% | |
| 58. | 30 sept 2017 | $19.96 | $0.133 | 5.31% | 2,519.36 | 1.93% |
| 59. | 31 oct 2017 | $21.55 | 7.97% | 2,575.26 | 2.22% | |
| 60. | 30 nov 2017 | $21.45 | -0.46% | 2,647.58 | 2.81% | |
| 61. | 31 dic 2017 | $21.01 | $0.139 | -1.40% | 2,673.61 | 0.98% |
| 62. | 31 ene 2018 | $23.32 | 10.99% | 2,823.81 | 5.62% | |
| 63. | 28 feb 2018 | $23.39 | 0.30% | 2,713.83 | -3.89% | |
| 64. | 31 mar 2018 | $21.92 | $0.139 | -5.69% | 2,640.87 | -2.69% |
| 65. | 30 abr 2018 | $21.49 | -1.96% | 2,648.05 | 0.27% | |
| 66. | 31 may 2018 | $22.03 | 2.51% | 2,705.27 | 2.16% | |
| 67. | 30 jun 2018 | $22.69 | $0.139 | 3.63% | 2,718.37 | 0.48% |
| 68. | 31 jul 2018 | $23.08 | 1.72% | 2,816.29 | 3.60% | |
| 69. | 31 ago 2018 | $24.65 | 6.80% | 2,901.52 | 3.03% | |
| 70. | 30 sept 2018 | $25.77 | $0.139 | 5.11% | 2,913.98 | 0.43% |
| 71. | 31 oct 2018 | $24.14 | -6.33% | 2,711.74 | -6.94% | |
| Promedio (R): | 1.77% | 0.96% | ||||
| Desviación estándar: | 10.53% | 2.87% | ||||
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 HPQ 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
HP Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RHPQ,t | RS&P 500,t | (RHPQ,t–RHPQ)2 | (RS&P 500,t–RS&P 500)2 | (RHPQ,t–RHPQ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 dic 2012 | 10.72% | 0.71% | 80.01 | 0.06 | -2.26 |
| 2. | 31 ene 2013 | 15.86% | 5.04% | 198.48 | 16.67 | 57.52 |
| 3. | 28 feb 2013 | 21.99% | 1.11% | 408.66 | 0.02 | 2.96 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 sept 2018 | 5.11% | 0.43% | 11.13 | 0.28 | -1.77 |
| 71. | 31 oct 2018 | -6.33% | -6.94% | 65.55 | 62.41 | 63.96 |
| Total (Σ): | 7,757.62 | 576.08 | 1,004.69 | |||
| t | Fecha | RHPQ,t | RS&P 500,t | (RHPQ,t–RHPQ)2 | (RS&P 500,t–RS&P 500)2 | (RHPQ,t–RHPQ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 dic 2012 | 10.72% | 0.71% | 80.01 | 0.06 | -2.26 |
| 2. | 31 ene 2013 | 15.86% | 5.04% | 198.48 | 16.67 | 57.52 |
| 3. | 28 feb 2013 | 21.99% | 1.11% | 408.66 | 0.02 | 2.96 |
| 4. | 31 mar 2013 | 19.03% | 3.60% | 297.75 | 6.97 | 45.54 |
| 5. | 30 abr 2013 | -13.59% | 1.81% | 235.99 | 0.72 | -13.04 |
| 6. | 31 may 2013 | 18.54% | 2.08% | 281.31 | 1.25 | 18.73 |
| 7. | 30 jun 2013 | 2.15% | -1.50% | 0.14 | 6.05 | -0.93 |
| 8. | 31 jul 2013 | 3.55% | 4.95% | 3.16 | 15.89 | 7.08 |
| 9. | 31 ago 2013 | -13.01% | -3.13% | 218.38 | 16.72 | 60.43 |
| 10. | 30 sept 2013 | -5.39% | 2.97% | 51.33 | 4.06 | -14.44 |
| 11. | 31 oct 2013 | 16.10% | 4.46% | 205.39 | 12.25 | 50.16 |
| 12. | 30 nov 2013 | 12.23% | 2.80% | 109.34 | 3.41 | 19.30 |
| 13. | 31 dic 2013 | 2.83% | 2.36% | 1.13 | 1.95 | 1.48 |
| 14. | 31 ene 2014 | 3.65% | -3.56% | 3.51 | 20.41 | -8.47 |
| 15. | 28 feb 2014 | 3.03% | 4.31% | 1.60 | 11.24 | 4.23 |
| 16. | 31 mar 2014 | 8.79% | 0.69% | 49.20 | 0.07 | -1.87 |
| 17. | 30 abr 2014 | 2.16% | 0.62% | 0.15 | 0.12 | -0.13 |
| 18. | 31 may 2014 | 1.33% | 2.10% | 0.19 | 1.31 | -0.50 |
| 19. | 30 jun 2014 | 1.01% | 1.91% | 0.57 | 0.90 | -0.72 |
| 20. | 31 jul 2014 | 5.73% | -1.51% | 15.67 | 6.09 | -9.77 |
| 21. | 31 ago 2014 | 6.71% | 3.77% | 24.41 | 7.87 | 13.86 |
| 22. | 30 sept 2014 | -6.24% | -1.55% | 64.13 | 6.31 | 20.11 |
| 23. | 31 oct 2014 | 1.16% | 2.32% | 0.38 | 1.85 | -0.84 |
| 24. | 30 nov 2014 | 8.86% | 2.45% | 50.29 | 2.23 | 10.59 |
| 25. | 31 dic 2014 | 3.15% | -0.42% | 1.90 | 1.90 | -1.90 |
| 26. | 31 ene 2015 | -9.97% | -3.10% | 137.80 | 16.51 | 47.70 |
| 27. | 28 feb 2015 | -3.57% | 5.49% | 28.54 | 20.52 | -24.20 |
| 28. | 31 mar 2015 | -10.10% | -1.74% | 141.01 | 7.29 | 32.05 |
| 29. | 30 abr 2015 | 5.81% | 0.85% | 16.30 | 0.01 | -0.43 |
| 30. | 31 may 2015 | 1.30% | 1.05% | 0.22 | 0.01 | -0.04 |
| 31. | 30 jun 2015 | -9.62% | -2.10% | 129.83 | 9.37 | 34.88 |
| 32. | 31 jul 2015 | 1.70% | 1.97% | 0.01 | 1.03 | -0.07 |
| 33. | 31 ago 2015 | -8.06% | -6.26% | 96.66 | 52.10 | 70.96 |
| 34. | 30 sept 2015 | -8.10% | -2.64% | 97.52 | 12.99 | 35.59 |
| 35. | 31 oct 2015 | 5.27% | 8.30% | 12.25 | 53.86 | 25.69 |
| 36. | 30 nov 2015 | -53.49% | 0.05% | 3,053.45 | 0.83 | 50.24 |
| 37. | 31 dic 2015 | -4.59% | -1.75% | 40.51 | 7.36 | 17.27 |
| 38. | 31 ene 2016 | -17.99% | -5.07% | 390.51 | 36.40 | 119.22 |
| 39. | 29 feb 2016 | 10.09% | -0.41% | 69.24 | 1.88 | -11.42 |
| 40. | 31 mar 2016 | 16.41% | 6.60% | 214.23 | 31.80 | 82.54 |
| 41. | 30 abr 2016 | -0.41% | 0.27% | 4.74 | 0.48 | 1.50 |
| 42. | 31 may 2016 | 9.05% | 1.53% | 52.93 | 0.33 | 4.17 |
| 43. | 30 jun 2016 | -5.28% | 0.09% | 49.67 | 0.75 | 6.12 |
| 44. | 31 jul 2016 | 11.63% | 3.56% | 97.26 | 6.77 | 25.65 |
| 45. | 31 ago 2016 | 2.57% | -0.12% | 0.64 | 1.17 | -0.86 |
| 46. | 30 sept 2016 | 8.94% | -0.12% | 51.32 | 1.17 | -7.76 |
| 47. | 31 oct 2016 | -6.70% | -1.94% | 71.71 | 8.42 | 24.58 |
| 48. | 30 nov 2016 | 6.28% | 3.42% | 20.33 | 6.04 | 11.08 |
| 49. | 31 dic 2016 | -2.77% | 1.82% | 20.65 | 0.74 | -3.91 |
| 50. | 31 ene 2017 | 1.42% | 1.79% | 0.13 | 0.69 | -0.30 |
| 51. | 28 feb 2017 | 15.42% | 3.72% | 186.16 | 7.62 | 37.66 |
| 52. | 31 mar 2017 | 3.70% | -0.04% | 3.73 | 1.00 | -1.93 |
| 53. | 30 abr 2017 | 5.26% | 0.91% | 12.15 | 0.00 | -0.18 |
| 54. | 31 may 2017 | -0.32% | 1.16% | 4.37 | 0.04 | -0.41 |
| 55. | 30 jun 2017 | -6.11% | 0.48% | 62.18 | 0.23 | 3.77 |
| 56. | 31 jul 2017 | 9.27% | 1.93% | 56.20 | 0.95 | 7.31 |
| 57. | 31 ago 2017 | -0.10% | 0.05% | 3.52 | 0.82 | 1.70 |
| 58. | 30 sept 2017 | 5.31% | 1.93% | 12.52 | 0.94 | 3.43 |
| 59. | 31 oct 2017 | 7.97% | 2.22% | 38.37 | 1.59 | 7.80 |
| 60. | 30 nov 2017 | -0.46% | 2.81% | 5.00 | 3.42 | -4.13 |
| 61. | 31 dic 2017 | -1.40% | 0.98% | 10.08 | 0.00 | -0.07 |
| 62. | 31 ene 2018 | 10.99% | 5.62% | 85.07 | 21.70 | 42.96 |
| 63. | 28 feb 2018 | 0.30% | -3.89% | 2.16 | 23.57 | 7.14 |
| 64. | 31 mar 2018 | -5.69% | -2.69% | 55.68 | 13.31 | 27.22 |
| 65. | 30 abr 2018 | -1.96% | 0.27% | 13.94 | 0.47 | 2.57 |
| 66. | 31 may 2018 | 2.51% | 2.16% | 0.55 | 1.44 | 0.89 |
| 67. | 30 jun 2018 | 3.63% | 0.48% | 3.44 | 0.23 | -0.88 |
| 68. | 31 jul 2018 | 1.72% | 3.60% | 0.00 | 6.98 | -0.14 |
| 69. | 31 ago 2018 | 6.80% | 3.03% | 25.31 | 4.27 | 10.40 |
| 70. | 30 sept 2018 | 5.11% | 0.43% | 11.13 | 0.28 | -1.77 |
| 71. | 31 oct 2018 | -6.33% | -6.94% | 65.55 | 62.41 | 63.96 |
| Total (Σ): | 7,757.62 | 576.08 | 1,004.69 | |||
Mostrar todo
VarianzaHPQ = Σ(RHPQ,t–RHPQ)2 ÷ (71 – 1)
= 7,757.62 ÷ (71 – 1)
= 110.82
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 576.08 ÷ (71 – 1)
= 8.23
CovarianzaHPQ, S&P 500 = Σ(RHPQ,t–RHPQ)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,004.69 ÷ (71 – 1)
= 14.35
Estimación sistemática del riesgo (β)
| VarianzaHPQ | 110.82 |
| VarianzaS&P 500 | 8.23 |
| CovarianzaHPQ, S&P 500 | 14.35 |
| Coeficiente de correlaciónHPQ, S&P 5001 | 0.48 |
| βHPQ2 | 1.74 |
| αHPQ3 | 0.10% |
Cálculos
1 Coeficiente de correlaciónHPQ, S&P 500
= CovarianzaHPQ, S&P 500 ÷ (Desviación estándarHPQ × Desviación estándarS&P 500)
= 14.35 ÷ (10.53% × 2.87%)
= 0.48
2 βHPQ
= CovarianzaHPQ, S&P 500 ÷ VarianzaS&P 500
= 14.35 ÷ 8.23
= 1.74
3 αHPQ
= PromedioHPQ – βHPQ × PromedioS&P 500
= 1.77% – 1.74 × 0.96%
= 0.10%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.81% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 14.72% |
| Riesgo sistemático de HP acciones ordinarias | βHPQ | 1.74 |
| Tasa de rendimiento esperada de las acciones ordinarias de HP3 | E(RHPQ) | 22.09% |
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(RHPQ) = RF + βHPQ [E(RM) – RF]
= 4.81% + 1.74 [14.72% – 4.81%]
= 22.09%