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 Celgene.
Tasas de retorno
Celgene Corp., tasas mensuales de retorno
| Celgene Corp. (CELG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCELG,t1 | DividendoCELG,t1 | RCELG,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2014 | $75.97 | 1,782.59 | ||||
| 1. | 28 feb. 2014 | $80.38 | 5.80% | 1,859.45 | 4.31% | |
| 2. | 31 mar. 2014 | $69.80 | -13.16% | 1,872.34 | 0.69% | |
| 3. | 30 abr. 2014 | $73.51 | 5.32% | 1,883.95 | 0.62% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2018 | $72.22 | 0.87% | 2,760.17 | 1.79% | |
| 59. | 31 dic. 2018 | $64.09 | -11.26% | 2,506.85 | -9.18% | |
| Promedio (R): | 0.14% | 0.63% | ||||
| Desviación estándar: | 9.04% | 3.13% | ||||
| Celgene Corp. (CELG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCELG,t1 | DividendoCELG,t1 | RCELG,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2014 | $75.97 | 1,782.59 | ||||
| 1. | 28 feb. 2014 | $80.38 | 5.80% | 1,859.45 | 4.31% | |
| 2. | 31 mar. 2014 | $69.80 | -13.16% | 1,872.34 | 0.69% | |
| 3. | 30 abr. 2014 | $73.51 | 5.32% | 1,883.95 | 0.62% | |
| 4. | 31 may. 2014 | $76.52 | 4.09% | 1,923.57 | 2.10% | |
| 5. | 30 jun. 2014 | $85.88 | 12.23% | 1,960.23 | 1.91% | |
| 6. | 31 jul. 2014 | $87.15 | 1.48% | 1,930.67 | -1.51% | |
| 7. | 31 ago. 2014 | $95.02 | 9.03% | 2,003.37 | 3.77% | |
| 8. | 30 sept. 2014 | $94.78 | -0.25% | 1,972.29 | -1.55% | |
| 9. | 31 oct. 2014 | $107.09 | 12.99% | 2,018.05 | 2.32% | |
| 10. | 30 nov. 2014 | $113.69 | 6.16% | 2,067.56 | 2.45% | |
| 11. | 31 dic. 2014 | $111.86 | -1.61% | 2,058.90 | -0.42% | |
| 12. | 31 ene. 2015 | $119.16 | 6.53% | 1,994.99 | -3.10% | |
| 13. | 28 feb. 2015 | $121.53 | 1.99% | 2,104.50 | 5.49% | |
| 14. | 31 mar. 2015 | $115.28 | -5.14% | 2,067.89 | -1.74% | |
| 15. | 30 abr. 2015 | $108.06 | -6.26% | 2,085.51 | 0.85% | |
| 16. | 31 may. 2015 | $114.44 | 5.90% | 2,107.39 | 1.05% | |
| 17. | 30 jun. 2015 | $115.74 | 1.14% | 2,063.11 | -2.10% | |
| 18. | 31 jul. 2015 | $131.25 | 13.40% | 2,103.84 | 1.97% | |
| 19. | 31 ago. 2015 | $118.08 | -10.03% | 1,972.18 | -6.26% | |
| 20. | 30 sept. 2015 | $108.17 | -8.39% | 1,920.03 | -2.64% | |
| 21. | 31 oct. 2015 | $122.71 | 13.44% | 2,079.36 | 8.30% | |
| 22. | 30 nov. 2015 | $109.45 | -10.81% | 2,080.41 | 0.05% | |
| 23. | 31 dic. 2015 | $119.76 | 9.42% | 2,043.94 | -1.75% | |
| 24. | 31 ene. 2016 | $100.32 | -16.23% | 1,940.24 | -5.07% | |
| 25. | 29 feb. 2016 | $100.83 | 0.51% | 1,932.23 | -0.41% | |
| 26. | 31 mar. 2016 | $100.09 | -0.73% | 2,059.74 | 6.60% | |
| 27. | 30 abr. 2016 | $103.41 | 3.32% | 2,065.30 | 0.27% | |
| 28. | 31 may. 2016 | $105.52 | 2.04% | 2,096.95 | 1.53% | |
| 29. | 30 jun. 2016 | $98.63 | -6.53% | 2,098.86 | 0.09% | |
| 30. | 31 jul. 2016 | $112.19 | 13.75% | 2,173.60 | 3.56% | |
| 31. | 31 ago. 2016 | $106.74 | -4.86% | 2,170.95 | -0.12% | |
| 32. | 30 sept. 2016 | $104.53 | -2.07% | 2,168.27 | -0.12% | |
| 33. | 31 oct. 2016 | $102.18 | -2.25% | 2,126.15 | -1.94% | |
| 34. | 30 nov. 2016 | $118.51 | 15.98% | 2,198.81 | 3.42% | |
| 35. | 31 dic. 2016 | $115.75 | -2.33% | 2,238.83 | 1.82% | |
| 36. | 31 ene. 2017 | $116.15 | 0.35% | 2,278.87 | 1.79% | |
| 37. | 28 feb. 2017 | $123.51 | 6.34% | 2,363.64 | 3.72% | |
| 38. | 31 mar. 2017 | $124.43 | 0.74% | 2,362.72 | -0.04% | |
| 39. | 30 abr. 2017 | $124.05 | -0.31% | 2,384.20 | 0.91% | |
| 40. | 31 may. 2017 | $114.41 | -7.77% | 2,411.80 | 1.16% | |
| 41. | 30 jun. 2017 | $129.87 | 13.51% | 2,423.41 | 0.48% | |
| 42. | 31 jul. 2017 | $135.41 | 4.27% | 2,470.30 | 1.93% | |
| 43. | 31 ago. 2017 | $138.93 | 2.60% | 2,471.65 | 0.05% | |
| 44. | 30 sept. 2017 | $145.82 | 4.96% | 2,519.36 | 1.93% | |
| 45. | 31 oct. 2017 | $100.97 | -30.76% | 2,575.26 | 2.22% | |
| 46. | 30 nov. 2017 | $100.83 | -0.14% | 2,647.58 | 2.81% | |
| 47. | 31 dic. 2017 | $104.36 | 3.50% | 2,673.61 | 0.98% | |
| 48. | 31 ene. 2018 | $101.16 | -3.07% | 2,823.81 | 5.62% | |
| 49. | 28 feb. 2018 | $87.12 | -13.88% | 2,713.83 | -3.89% | |
| 50. | 31 mar. 2018 | $89.21 | 2.40% | 2,640.87 | -2.69% | |
| 51. | 30 abr. 2018 | $87.10 | -2.37% | 2,648.05 | 0.27% | |
| 52. | 31 may. 2018 | $78.68 | -9.67% | 2,705.27 | 2.16% | |
| 53. | 30 jun. 2018 | $79.42 | 0.94% | 2,718.37 | 0.48% | |
| 54. | 31 jul. 2018 | $90.09 | 13.43% | 2,816.29 | 3.60% | |
| 55. | 31 ago. 2018 | $94.45 | 4.84% | 2,901.52 | 3.03% | |
| 56. | 30 sept. 2018 | $89.49 | -5.25% | 2,913.98 | 0.43% | |
| 57. | 31 oct. 2018 | $71.60 | -19.99% | 2,711.74 | -6.94% | |
| 58. | 30 nov. 2018 | $72.22 | 0.87% | 2,760.17 | 1.79% | |
| 59. | 31 dic. 2018 | $64.09 | -11.26% | 2,506.85 | -9.18% | |
| Promedio (R): | 0.14% | 0.63% | ||||
| Desviación estándar: | 9.04% | 3.13% | ||||
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 CELG 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
Celgene Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RCELG,t | RS&P 500,t | (RCELG,t–RCELG)2 | (RS&P 500,t–RS&P 500)2 | (RCELG,t–RCELG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2014 | 5.80% | 4.31% | 32.11 | 13.57 | 20.87 |
| 2. | 31 mar. 2014 | -13.16% | 0.69% | 176.91 | 0.00 | -0.87 |
| 3. | 30 abr. 2014 | 5.32% | 0.62% | 26.80 | 0.00 | -0.04 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2018 | 0.87% | 1.79% | 0.53 | 1.34 | 0.84 |
| 59. | 31 dic. 2018 | -11.26% | -9.18% | 129.86 | 96.15 | 111.74 |
| Total (Σ): | 4,741.72 | 566.60 | 801.25 | |||
| t | Fecha | RCELG,t | RS&P 500,t | (RCELG,t–RCELG)2 | (RS&P 500,t–RS&P 500)2 | (RCELG,t–RCELG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2014 | 5.80% | 4.31% | 32.11 | 13.57 | 20.87 |
| 2. | 31 mar. 2014 | -13.16% | 0.69% | 176.91 | 0.00 | -0.87 |
| 3. | 30 abr. 2014 | 5.32% | 0.62% | 26.80 | 0.00 | -0.04 |
| 4. | 31 may. 2014 | 4.09% | 2.10% | 15.65 | 2.18 | 5.84 |
| 5. | 30 jun. 2014 | 12.23% | 1.91% | 146.26 | 1.63 | 15.45 |
| 6. | 31 jul. 2014 | 1.48% | -1.51% | 1.80 | 4.56 | -2.86 |
| 7. | 31 ago. 2014 | 9.03% | 3.77% | 79.07 | 9.84 | 27.90 |
| 8. | 30 sept. 2014 | -0.25% | -1.55% | 0.15 | 4.75 | 0.85 |
| 9. | 31 oct. 2014 | 12.99% | 2.32% | 165.12 | 2.86 | 21.74 |
| 10. | 30 nov. 2014 | 6.16% | 2.45% | 36.30 | 3.33 | 11.00 |
| 11. | 31 dic. 2014 | -1.61% | -0.42% | 3.05 | 1.10 | 1.83 |
| 12. | 31 ene. 2015 | 6.53% | -3.10% | 40.80 | 13.93 | -23.84 |
| 13. | 28 feb. 2015 | 1.99% | 5.49% | 3.43 | 23.63 | 9.00 |
| 14. | 31 mar. 2015 | -5.14% | -1.74% | 27.89 | 5.61 | 12.50 |
| 15. | 30 abr. 2015 | -6.26% | 0.85% | 40.98 | 0.05 | -1.43 |
| 16. | 31 may. 2015 | 5.90% | 1.05% | 33.25 | 0.18 | 2.43 |
| 17. | 30 jun. 2015 | 1.14% | -2.10% | 1.00 | 7.45 | -2.72 |
| 18. | 31 jul. 2015 | 13.40% | 1.97% | 175.90 | 1.81 | 17.85 |
| 19. | 31 ago. 2015 | -10.03% | -6.26% | 103.48 | 47.42 | 70.05 |
| 20. | 30 sept. 2015 | -8.39% | -2.64% | 72.77 | 10.71 | 27.91 |
| 21. | 31 oct. 2015 | 13.44% | 8.30% | 176.99 | 58.83 | 102.04 |
| 22. | 30 nov. 2015 | -10.81% | 0.05% | 119.77 | 0.33 | 6.32 |
| 23. | 31 dic. 2015 | 9.42% | -1.75% | 86.15 | 5.67 | -22.10 |
| 24. | 31 ene. 2016 | -16.23% | -5.07% | 268.00 | 32.51 | 93.34 |
| 25. | 29 feb. 2016 | 0.51% | -0.41% | 0.14 | 1.08 | -0.39 |
| 26. | 31 mar. 2016 | -0.73% | 6.60% | 0.76 | 35.65 | -5.21 |
| 27. | 30 abr. 2016 | 3.32% | 0.27% | 10.11 | 0.13 | -1.14 |
| 28. | 31 may. 2016 | 2.04% | 1.53% | 3.62 | 0.82 | 1.72 |
| 29. | 30 jun. 2016 | -6.53% | 0.09% | 44.46 | 0.29 | 3.58 |
| 30. | 31 jul. 2016 | 13.75% | 3.56% | 185.24 | 8.60 | 39.92 |
| 31. | 31 ago. 2016 | -4.86% | -0.12% | 24.96 | 0.56 | 3.75 |
| 32. | 30 sept. 2016 | -2.07% | -0.12% | 4.88 | 0.56 | 1.66 |
| 33. | 31 oct. 2016 | -2.25% | -1.94% | 5.69 | 6.61 | 6.13 |
| 34. | 30 nov. 2016 | 15.98% | 3.42% | 251.01 | 7.78 | 44.20 |
| 35. | 31 dic. 2016 | -2.33% | 1.82% | 6.09 | 1.42 | -2.94 |
| 36. | 31 ene. 2017 | 0.35% | 1.79% | 0.04 | 1.35 | 0.24 |
| 37. | 28 feb. 2017 | 6.34% | 3.72% | 38.42 | 9.56 | 19.16 |
| 38. | 31 mar. 2017 | 0.74% | -0.04% | 0.37 | 0.44 | -0.40 |
| 39. | 30 abr. 2017 | -0.31% | 0.91% | 0.20 | 0.08 | -0.12 |
| 40. | 31 may. 2017 | -7.77% | 1.16% | 62.56 | 0.28 | -4.19 |
| 41. | 30 jun. 2017 | 13.51% | 0.48% | 178.88 | 0.02 | -1.96 |
| 42. | 31 jul. 2017 | 4.27% | 1.93% | 17.04 | 1.71 | 5.39 |
| 43. | 31 ago. 2017 | 2.60% | 0.05% | 6.06 | 0.33 | -1.41 |
| 44. | 30 sept. 2017 | 4.96% | 1.93% | 23.24 | 1.70 | 6.28 |
| 45. | 31 oct. 2017 | -30.76% | 2.22% | 954.52 | 2.53 | -49.15 |
| 46. | 30 nov. 2017 | -0.14% | 2.81% | 0.08 | 4.75 | -0.60 |
| 47. | 31 dic. 2017 | 3.50% | 0.98% | 11.31 | 0.13 | 1.19 |
| 48. | 31 ene. 2018 | -3.07% | 5.62% | 10.27 | 24.90 | -15.99 |
| 49. | 28 feb. 2018 | -13.88% | -3.89% | 196.48 | 20.45 | 63.40 |
| 50. | 31 mar. 2018 | 2.40% | -2.69% | 5.11 | 11.00 | -7.50 |
| 51. | 30 abr. 2018 | -2.37% | 0.27% | 6.27 | 0.13 | 0.89 |
| 52. | 31 may. 2018 | -9.67% | 2.16% | 96.14 | 2.35 | -15.03 |
| 53. | 30 jun. 2018 | 0.94% | 0.48% | 0.64 | 0.02 | -0.12 |
| 54. | 31 jul. 2018 | 13.43% | 3.60% | 176.80 | 8.85 | 39.55 |
| 55. | 31 ago. 2018 | 4.84% | 3.03% | 22.10 | 5.75 | 11.28 |
| 56. | 30 sept. 2018 | -5.25% | 0.43% | 29.05 | 0.04 | 1.07 |
| 57. | 31 oct. 2018 | -19.99% | -6.94% | 405.19 | 57.28 | 152.34 |
| 58. | 30 nov. 2018 | 0.87% | 1.79% | 0.53 | 1.34 | 0.84 |
| 59. | 31 dic. 2018 | -11.26% | -9.18% | 129.86 | 96.15 | 111.74 |
| Total (Σ): | 4,741.72 | 566.60 | 801.25 | |||
Mostrar todo
VarianzaCELG = Σ(RCELG,t–RCELG)2 ÷ (59 – 1)
= 4,741.72 ÷ (59 – 1)
= 81.75
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 566.60 ÷ (59 – 1)
= 9.77
CovarianzaCELG, S&P 500 = Σ(RCELG,t–RCELG)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 801.25 ÷ (59 – 1)
= 13.81
Estimación sistemática del riesgo (β)
| VarianzaCELG | 81.75 |
| VarianzaS&P 500 | 9.77 |
| CovarianzaCELG, S&P 500 | 13.81 |
| Coeficiente de correlaciónCELG, S&P 5001 | 0.49 |
| βCELG2 | 1.41 |
| αCELG3 | -0.75% |
Cálculos
1 Coeficiente de correlaciónCELG, S&P 500
= CovarianzaCELG, S&P 500 ÷ (Desviación estándarCELG × Desviación estándarS&P 500)
= 13.81 ÷ (9.04% × 3.13%)
= 0.49
2 βCELG
= CovarianzaCELG, S&P 500 ÷ VarianzaS&P 500
= 13.81 ÷ 9.77
= 1.41
3 αCELG
= PromedioCELG – βCELG × PromedioS&P 500
= 0.14% – 1.41 × 0.63%
= -0.75%
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 Celgene acciones ordinarias | βCELG | 1.41 |
| Tasa de rendimiento esperada de las acciones ordinarias de Celgene3 | E(RCELG) | 17.56% |
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(RCELG) = RF + βCELG [E(RM) – RF]
= 4.67% + 1.41 [13.79% – 4.67%]
= 17.56%