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 GlaxoSmithKline.
Tasas de retorno
GlaxoSmithKline PLC, tasas mensuales de retorno
| GlaxoSmithKline PLC (GSK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGSK,t1 | DividendoGSK,t1 | RGSK,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2010 | $39.01 | 1,073.87 | ||||
| 1. | 28 feb. 2010 | $37.14 | $0.5737 | -3.32% | 1,104.49 | 2.85% |
| 2. | 31 mar. 2010 | $38.52 | 3.72% | 1,169.43 | 5.88% | |
| 3. | 30 abr. 2010 | $37.29 | -3.19% | 1,186.69 | 1.48% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2014 | $46.45 | $0.613 | 3.46% | 2,067.56 | 2.45% |
| 59. | 31 dic. 2014 | $42.74 | -7.99% | 2,058.90 | -0.42% | |
| Promedio (R): | 0.71% | 1.18% | ||||
| Desviación estándar: | 4.66% | 3.73% | ||||
| GlaxoSmithKline PLC (GSK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGSK,t1 | DividendoGSK,t1 | RGSK,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2010 | $39.01 | 1,073.87 | ||||
| 1. | 28 feb. 2010 | $37.14 | $0.5737 | -3.32% | 1,104.49 | 2.85% |
| 2. | 31 mar. 2010 | $38.52 | 3.72% | 1,169.43 | 5.88% | |
| 3. | 30 abr. 2010 | $37.29 | -3.19% | 1,186.69 | 1.48% | |
| 4. | 31 may. 2010 | $33.46 | $0.4603 | -9.04% | 1,089.41 | -8.20% |
| 5. | 30 jun. 2010 | $34.01 | 1.64% | 1,030.71 | -5.39% | |
| 6. | 31 jul. 2010 | $35.17 | $0.4573 | 4.76% | 1,101.60 | 6.88% |
| 7. | 31 ago. 2010 | $37.40 | 6.34% | 1,049.33 | -4.74% | |
| 8. | 30 sept. 2010 | $39.52 | 5.67% | 1,141.20 | 8.76% | |
| 9. | 31 oct. 2010 | $39.04 | $0.5074 | 0.07% | 1,183.26 | 3.69% |
| 10. | 30 nov. 2010 | $38.28 | -1.95% | 1,180.55 | -0.23% | |
| 11. | 31 dic. 2010 | $39.22 | 2.46% | 1,257.64 | 6.53% | |
| 12. | 31 ene. 2011 | $36.33 | -7.37% | 1,286.12 | 2.26% | |
| 13. | 28 feb. 2011 | $38.61 | $0.6153 | 7.97% | 1,327.22 | 3.20% |
| 14. | 31 mar. 2011 | $38.41 | -0.52% | 1,325.83 | -0.10% | |
| 15. | 30 abr. 2011 | $43.66 | 13.67% | 1,363.61 | 2.85% | |
| 16. | 31 may. 2011 | $43.46 | $0.5263 | 0.75% | 1,345.20 | -1.35% |
| 17. | 30 jun. 2011 | $42.90 | -1.29% | 1,320.64 | -1.83% | |
| 18. | 31 jul. 2011 | $44.42 | 3.54% | 1,292.28 | -2.15% | |
| 19. | 31 ago. 2011 | $42.83 | $0.5211 | -2.41% | 1,218.89 | -5.68% |
| 20. | 30 sept. 2011 | $41.29 | -3.60% | 1,131.42 | -7.18% | |
| 21. | 31 oct. 2011 | $44.79 | 8.48% | 1,253.30 | 10.77% | |
| 22. | 30 nov. 2011 | $44.48 | $0.543 | 0.52% | 1,246.96 | -0.51% |
| 23. | 31 dic. 2011 | $45.63 | 2.59% | 1,257.60 | 0.85% | |
| 24. | 31 ene. 2012 | $44.54 | -2.39% | 1,312.41 | 4.36% | |
| 25. | 29 feb. 2012 | $44.31 | $0.8213 | 1.33% | 1,365.68 | 4.06% |
| 26. | 31 mar. 2012 | $44.91 | 1.35% | 1,408.47 | 3.13% | |
| 27. | 30 abr. 2012 | $46.23 | 2.94% | 1,397.91 | -0.75% | |
| 28. | 31 may. 2012 | $44.11 | $0.5491 | -3.40% | 1,310.33 | -6.27% |
| 29. | 30 jun. 2012 | $45.57 | 3.31% | 1,362.16 | 3.96% | |
| 30. | 31 jul. 2012 | $46.00 | 0.94% | 1,379.32 | 1.26% | |
| 31. | 31 ago. 2012 | $45.49 | $0.5279 | 0.04% | 1,406.58 | 1.98% |
| 32. | 30 sept. 2012 | $46.24 | 1.65% | 1,440.67 | 2.42% | |
| 33. | 31 oct. 2012 | $44.90 | -2.90% | 1,412.16 | -1.98% | |
| 34. | 30 nov. 2012 | $43.01 | $0.579 | -2.92% | 1,416.18 | 0.28% |
| 35. | 31 dic. 2012 | $43.47 | 1.07% | 1,426.19 | 0.71% | |
| 36. | 31 ene. 2013 | $45.61 | 4.92% | 1,498.11 | 5.04% | |
| 37. | 28 feb. 2013 | $44.03 | $0.6895 | -1.95% | 1,514.68 | 1.11% |
| 38. | 31 mar. 2013 | $46.91 | 6.54% | 1,569.19 | 3.60% | |
| 39. | 30 abr. 2013 | $51.64 | 10.08% | 1,597.57 | 1.81% | |
| 40. | 31 may. 2013 | $51.77 | $0.5502 | 1.32% | 1,630.74 | 2.08% |
| 41. | 30 jun. 2013 | $49.97 | -3.48% | 1,606.28 | -1.50% | |
| 42. | 31 jul. 2013 | $50.96 | 1.98% | 1,685.73 | 4.95% | |
| 43. | 31 ago. 2013 | $50.89 | $0.5532 | 0.95% | 1,632.97 | -3.13% |
| 44. | 30 sept. 2013 | $50.17 | -1.41% | 1,681.55 | 2.97% | |
| 45. | 31 oct. 2013 | $52.63 | 4.90% | 1,756.54 | 4.46% | |
| 46. | 30 nov. 2013 | $52.92 | $0.6161 | 1.72% | 1,805.81 | 2.80% |
| 47. | 31 dic. 2013 | $53.39 | 0.89% | 1,848.36 | 2.36% | |
| 48. | 31 ene. 2014 | $51.54 | -3.47% | 1,782.59 | -3.56% | |
| 49. | 28 feb. 2014 | $55.94 | $0.7496 | 9.99% | 1,859.45 | 4.31% |
| 50. | 31 mar. 2014 | $53.43 | -4.49% | 1,872.34 | 0.69% | |
| 51. | 30 abr. 2014 | $55.37 | 3.63% | 1,883.95 | 0.62% | |
| 52. | 31 may. 2014 | $53.94 | $0.64 | -1.43% | 1,923.57 | 2.10% |
| 53. | 30 jun. 2014 | $53.48 | -0.85% | 1,960.23 | 1.91% | |
| 54. | 31 jul. 2014 | $48.37 | -9.55% | 1,930.67 | -1.51% | |
| 55. | 31 ago. 2014 | $49.10 | $0.6482 | 2.85% | 2,003.37 | 3.77% |
| 56. | 30 sept. 2014 | $45.97 | -6.37% | 1,972.29 | -1.55% | |
| 57. | 31 oct. 2014 | $45.49 | -1.04% | 2,018.05 | 2.32% | |
| 58. | 30 nov. 2014 | $46.45 | $0.613 | 3.46% | 2,067.56 | 2.45% |
| 59. | 31 dic. 2014 | $42.74 | -7.99% | 2,058.90 | -0.42% | |
| Promedio (R): | 0.71% | 1.18% | ||||
| Desviación estándar: | 4.66% | 3.73% | ||||
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 GSK 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
GlaxoSmithKline PLC, cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RGSK,t | RS&P 500,t | (RGSK,t–RGSK)2 | (RS&P 500,t–RS&P 500)2 | (RGSK,t–RGSK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2010 | -3.32% | 2.85% | 16.24 | 2.80 | -6.74 |
| 2. | 31 mar. 2010 | 3.72% | 5.88% | 9.05 | 22.11 | 14.15 |
| 3. | 30 abr. 2010 | -3.19% | 1.48% | 15.21 | 0.09 | -1.16 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2014 | 3.46% | 2.45% | 7.57 | 1.63 | 3.51 |
| 59. | 31 dic. 2014 | -7.99% | -0.42% | 75.59 | 2.55 | 13.88 |
| Total (Σ): | 1,259.77 | 809.11 | 507.46 | |||
| t | Fecha | RGSK,t | RS&P 500,t | (RGSK,t–RGSK)2 | (RS&P 500,t–RS&P 500)2 | (RGSK,t–RGSK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2010 | -3.32% | 2.85% | 16.24 | 2.80 | -6.74 |
| 2. | 31 mar. 2010 | 3.72% | 5.88% | 9.05 | 22.11 | 14.15 |
| 3. | 30 abr. 2010 | -3.19% | 1.48% | 15.21 | 0.09 | -1.16 |
| 4. | 31 may. 2010 | -9.04% | -8.20% | 94.93 | 87.90 | 91.35 |
| 5. | 30 jun. 2010 | 1.64% | -5.39% | 0.88 | 43.11 | -6.15 |
| 6. | 31 jul. 2010 | 4.76% | 6.88% | 16.39 | 32.49 | 23.08 |
| 7. | 31 ago. 2010 | 6.34% | -4.74% | 31.74 | 35.08 | -33.37 |
| 8. | 30 sept. 2010 | 5.67% | 8.76% | 24.62 | 57.42 | 37.60 |
| 9. | 31 oct. 2010 | 0.07% | 3.69% | 0.41 | 6.29 | -1.60 |
| 10. | 30 nov. 2010 | -1.95% | -0.23% | 7.04 | 1.98 | 3.73 |
| 11. | 31 dic. 2010 | 2.46% | 6.53% | 3.06 | 28.65 | 9.36 |
| 12. | 31 ene. 2011 | -7.37% | 2.26% | 65.22 | 1.18 | -8.78 |
| 13. | 28 feb. 2011 | 7.97% | 3.20% | 52.74 | 4.07 | 14.66 |
| 14. | 31 mar. 2011 | -0.52% | -0.10% | 1.50 | 1.64 | 1.57 |
| 15. | 30 abr. 2011 | 13.67% | 2.85% | 168.00 | 2.79 | 21.67 |
| 16. | 31 may. 2011 | 0.75% | -1.35% | 0.00 | 6.39 | -0.10 |
| 17. | 30 jun. 2011 | -1.29% | -1.83% | 3.98 | 9.02 | 5.99 |
| 18. | 31 jul. 2011 | 3.54% | -2.15% | 8.04 | 11.06 | -9.43 |
| 19. | 31 ago. 2011 | -2.41% | -5.68% | 9.69 | 47.02 | 21.35 |
| 20. | 30 sept. 2011 | -3.60% | -7.18% | 18.51 | 69.79 | 35.94 |
| 21. | 31 oct. 2011 | 8.48% | 10.77% | 60.37 | 92.06 | 74.55 |
| 22. | 30 nov. 2011 | 0.52% | -0.51% | 0.03 | 2.83 | 0.31 |
| 23. | 31 dic. 2011 | 2.59% | 0.85% | 3.53 | 0.11 | -0.61 |
| 24. | 31 ene. 2012 | -2.39% | 4.36% | 9.58 | 10.12 | -9.85 |
| 25. | 29 feb. 2012 | 1.33% | 4.06% | 0.39 | 8.30 | 1.79 |
| 26. | 31 mar. 2012 | 1.35% | 3.13% | 0.42 | 3.82 | 1.27 |
| 27. | 30 abr. 2012 | 2.94% | -0.75% | 4.98 | 3.72 | -4.30 |
| 28. | 31 may. 2012 | -3.40% | -6.27% | 16.85 | 55.40 | 30.55 |
| 29. | 30 jun. 2012 | 3.31% | 3.96% | 6.78 | 7.72 | 7.23 |
| 30. | 31 jul. 2012 | 0.94% | 1.26% | 0.06 | 0.01 | 0.02 |
| 31. | 31 ago. 2012 | 0.04% | 1.98% | 0.45 | 0.64 | -0.53 |
| 32. | 30 sept. 2012 | 1.65% | 2.42% | 0.89 | 1.55 | 1.17 |
| 33. | 31 oct. 2012 | -2.90% | -1.98% | 13.00 | 9.96 | 11.38 |
| 34. | 30 nov. 2012 | -2.92% | 0.28% | 13.15 | 0.80 | 3.24 |
| 35. | 31 dic. 2012 | 1.07% | 0.71% | 0.13 | 0.22 | -0.17 |
| 36. | 31 ene. 2013 | 4.92% | 5.04% | 17.77 | 14.94 | 16.30 |
| 37. | 28 feb. 2013 | -1.95% | 1.11% | 7.07 | 0.01 | 0.19 |
| 38. | 31 mar. 2013 | 6.54% | 3.60% | 34.04 | 5.86 | 14.12 |
| 39. | 30 abr. 2013 | 10.08% | 1.81% | 87.91 | 0.40 | 5.91 |
| 40. | 31 may. 2013 | 1.32% | 2.08% | 0.37 | 0.81 | 0.55 |
| 41. | 30 jun. 2013 | -3.48% | -1.50% | 17.50 | 7.17 | 11.20 |
| 42. | 31 jul. 2013 | 1.98% | 4.95% | 1.62 | 14.20 | 4.80 |
| 43. | 31 ago. 2013 | 0.95% | -3.13% | 0.06 | 18.55 | -1.04 |
| 44. | 30 sept. 2013 | -1.41% | 2.97% | 4.50 | 3.23 | -3.81 |
| 45. | 31 oct. 2013 | 4.90% | 4.46% | 17.61 | 10.77 | 13.77 |
| 46. | 30 nov. 2013 | 1.72% | 2.80% | 1.03 | 2.65 | 1.65 |
| 47. | 31 dic. 2013 | 0.89% | 2.36% | 0.03 | 1.39 | 0.21 |
| 48. | 31 ene. 2014 | -3.47% | -3.56% | 17.41 | 22.43 | 19.76 |
| 49. | 28 feb. 2014 | 9.99% | 4.31% | 86.20 | 9.82 | 29.10 |
| 50. | 31 mar. 2014 | -4.49% | 0.69% | 26.98 | 0.23 | 2.52 |
| 51. | 30 abr. 2014 | 3.63% | 0.62% | 8.55 | 0.31 | -1.63 |
| 52. | 31 may. 2014 | -1.43% | 2.10% | 4.55 | 0.86 | -1.97 |
| 53. | 30 jun. 2014 | -0.85% | 1.91% | 2.43 | 0.53 | -1.14 |
| 54. | 31 jul. 2014 | -9.55% | -1.51% | 105.31 | 7.21 | 27.56 |
| 55. | 31 ago. 2014 | 2.85% | 3.77% | 4.59 | 6.70 | 5.54 |
| 56. | 30 sept. 2014 | -6.37% | -1.55% | 50.15 | 7.45 | 19.33 |
| 57. | 31 oct. 2014 | -1.04% | 2.32% | 3.07 | 1.31 | -2.00 |
| 58. | 30 nov. 2014 | 3.46% | 2.45% | 7.57 | 1.63 | 3.51 |
| 59. | 31 dic. 2014 | -7.99% | -0.42% | 75.59 | 2.55 | 13.88 |
| Total (Σ): | 1,259.77 | 809.11 | 507.46 | |||
Mostrar todo
VarianzaGSK = Σ(RGSK,t–RGSK)2 ÷ (59 – 1)
= 1,259.77 ÷ (59 – 1)
= 21.72
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 809.11 ÷ (59 – 1)
= 13.95
CovarianzaGSK, S&P 500 = Σ(RGSK,t–RGSK)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 507.46 ÷ (59 – 1)
= 8.75
Estimación sistemática del riesgo (β)
| VarianzaGSK | 21.72 |
| VarianzaS&P 500 | 13.95 |
| CovarianzaGSK, S&P 500 | 8.75 |
| Coeficiente de correlaciónGSK, S&P 5001 | 0.50 |
| βGSK2 | 0.63 |
| αGSK3 | -0.03% |
Cálculos
1 Coeficiente de correlaciónGSK, S&P 500
= CovarianzaGSK, S&P 500 ÷ (Desviación estándarGSK × Desviación estándarS&P 500)
= 8.75 ÷ (4.66% × 3.73%)
= 0.50
2 βGSK
= CovarianzaGSK, S&P 500 ÷ VarianzaS&P 500
= 8.75 ÷ 13.95
= 0.63
3 αGSK
= PromedioGSK – βGSK × PromedioS&P 500
= 0.71% – 0.63 × 1.18%
= -0.03%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.86% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.52% |
| Riesgo sistemático de GlaxoSmithKline acciones ordinarias | βGSK | 0.63 |
| Tasa de rendimiento esperada de las acciones ordinarias de GlaxoSmithKline3 | E(RGSK) | 10.29% |
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(RGSK) = RF + βGSK [E(RM) – RF]
= 4.86% + 0.63 [13.52% – 4.86%]
= 10.29%