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 Kimberly-Clark.
Tasas de retorno
Kimberly-Clark Corp., tasas mensuales de retorno
| Kimberly-Clark Corp. (KMB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioKMB,t1 | DividendoKMB,t1 | RKMB,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2016 | $128.42 | 1,940.24 | ||||
| 1. | 29 feb. 2016 | $130.30 | 1.46% | 1,932.23 | -0.41% | |
| 2. | 31 mar. 2016 | $134.51 | $0.92 | 3.94% | 2,059.74 | 6.60% |
| 3. | 30 abr. 2016 | $125.19 | -6.93% | 2,065.30 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2020 | $139.31 | 5.07% | 3,621.63 | 10.75% | |
| 59. | 31 dic. 2020 | $134.83 | $1.07 | -2.45% | 3,756.07 | 3.71% |
| Promedio (R): | 0.47% | 1.22% | ||||
| Desviación estándar: | 4.97% | 4.36% | ||||
| Kimberly-Clark Corp. (KMB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioKMB,t1 | DividendoKMB,t1 | RKMB,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2016 | $128.42 | 1,940.24 | ||||
| 1. | 29 feb. 2016 | $130.30 | 1.46% | 1,932.23 | -0.41% | |
| 2. | 31 mar. 2016 | $134.51 | $0.92 | 3.94% | 2,059.74 | 6.60% |
| 3. | 30 abr. 2016 | $125.19 | -6.93% | 2,065.30 | 0.27% | |
| 4. | 31 may. 2016 | $127.04 | 1.48% | 2,096.95 | 1.53% | |
| 5. | 30 jun. 2016 | $137.48 | $0.92 | 8.94% | 2,098.86 | 0.09% |
| 6. | 31 jul. 2016 | $129.55 | -5.77% | 2,173.60 | 3.56% | |
| 7. | 31 ago. 2016 | $128.06 | -1.15% | 2,170.95 | -0.12% | |
| 8. | 30 sept. 2016 | $126.14 | $0.92 | -0.78% | 2,168.27 | -0.12% |
| 9. | 31 oct. 2016 | $114.41 | -9.30% | 2,126.15 | -1.94% | |
| 10. | 30 nov. 2016 | $115.61 | 1.05% | 2,198.81 | 3.42% | |
| 11. | 31 dic. 2016 | $114.12 | $0.92 | -0.49% | 2,238.83 | 1.82% |
| 12. | 31 ene. 2017 | $121.13 | 6.14% | 2,278.87 | 1.79% | |
| 13. | 28 feb. 2017 | $132.55 | 9.43% | 2,363.64 | 3.72% | |
| 14. | 31 mar. 2017 | $131.63 | $0.97 | 0.04% | 2,362.72 | -0.04% |
| 15. | 30 abr. 2017 | $129.75 | -1.43% | 2,384.20 | 0.91% | |
| 16. | 31 may. 2017 | $129.73 | -0.02% | 2,411.80 | 1.16% | |
| 17. | 30 jun. 2017 | $129.11 | $0.97 | 0.27% | 2,423.41 | 0.48% |
| 18. | 31 jul. 2017 | $123.16 | -4.61% | 2,470.30 | 1.93% | |
| 19. | 31 ago. 2017 | $123.29 | 0.11% | 2,471.65 | 0.05% | |
| 20. | 30 sept. 2017 | $117.68 | $0.97 | -3.76% | 2,519.36 | 1.93% |
| 21. | 31 oct. 2017 | $112.51 | -4.39% | 2,575.26 | 2.22% | |
| 22. | 30 nov. 2017 | $119.76 | 6.44% | 2,647.58 | 2.81% | |
| 23. | 31 dic. 2017 | $120.66 | $0.97 | 1.56% | 2,673.61 | 0.98% |
| 24. | 31 ene. 2018 | $117.00 | -3.03% | 2,823.81 | 5.62% | |
| 25. | 28 feb. 2018 | $110.92 | -5.20% | 2,713.83 | -3.89% | |
| 26. | 31 mar. 2018 | $110.13 | $1.00 | 0.19% | 2,640.87 | -2.69% |
| 27. | 30 abr. 2018 | $103.54 | -5.98% | 2,648.05 | 0.27% | |
| 28. | 31 may. 2018 | $100.85 | -2.60% | 2,705.27 | 2.16% | |
| 29. | 30 jun. 2018 | $105.34 | $1.00 | 5.44% | 2,718.37 | 0.48% |
| 30. | 31 jul. 2018 | $113.86 | 8.09% | 2,816.29 | 3.60% | |
| 31. | 31 ago. 2018 | $115.54 | 1.48% | 2,901.52 | 3.03% | |
| 32. | 30 sept. 2018 | $113.64 | $1.00 | -0.78% | 2,913.98 | 0.43% |
| 33. | 31 oct. 2018 | $104.30 | -8.22% | 2,711.74 | -6.94% | |
| 34. | 30 nov. 2018 | $115.37 | 10.61% | 2,760.17 | 1.79% | |
| 35. | 31 dic. 2018 | $113.94 | $1.00 | -0.37% | 2,506.85 | -9.18% |
| 36. | 31 ene. 2019 | $111.38 | -2.25% | 2,704.10 | 7.87% | |
| 37. | 28 feb. 2019 | $116.83 | 4.89% | 2,784.49 | 2.97% | |
| 38. | 31 mar. 2019 | $123.90 | $1.03 | 6.93% | 2,834.40 | 1.79% |
| 39. | 30 abr. 2019 | $128.38 | 3.62% | 2,945.83 | 3.93% | |
| 40. | 31 may. 2019 | $127.89 | -0.38% | 2,752.06 | -6.58% | |
| 41. | 30 jun. 2019 | $133.28 | $1.03 | 5.02% | 2,941.76 | 6.89% |
| 42. | 31 jul. 2019 | $135.65 | 1.78% | 2,980.38 | 1.31% | |
| 43. | 31 ago. 2019 | $141.11 | 4.03% | 2,926.46 | -1.81% | |
| 44. | 30 sept. 2019 | $142.05 | $1.03 | 1.40% | 2,976.74 | 1.72% |
| 45. | 31 oct. 2019 | $132.88 | -6.46% | 3,037.56 | 2.04% | |
| 46. | 30 nov. 2019 | $136.34 | 2.60% | 3,140.98 | 3.40% | |
| 47. | 31 dic. 2019 | $137.55 | $1.03 | 1.64% | 3,230.78 | 2.86% |
| 48. | 31 ene. 2020 | $143.24 | 4.14% | 3,225.52 | -0.16% | |
| 49. | 29 feb. 2020 | $131.19 | -8.41% | 2,954.22 | -8.41% | |
| 50. | 31 mar. 2020 | $127.87 | $1.07 | -1.72% | 2,584.59 | -12.51% |
| 51. | 30 abr. 2020 | $138.48 | 8.30% | 2,912.43 | 12.68% | |
| 52. | 31 may. 2020 | $141.44 | 2.14% | 3,044.31 | 4.53% | |
| 53. | 30 jun. 2020 | $141.35 | $1.07 | 0.69% | 3,100.29 | 1.84% |
| 54. | 31 jul. 2020 | $152.04 | 7.56% | 3,271.12 | 5.51% | |
| 55. | 31 ago. 2020 | $157.76 | 3.76% | 3,500.31 | 7.01% | |
| 56. | 30 sept. 2020 | $147.66 | $1.07 | -5.72% | 3,363.00 | -3.92% |
| 57. | 31 oct. 2020 | $132.59 | -10.21% | 3,269.96 | -2.77% | |
| 58. | 30 nov. 2020 | $139.31 | 5.07% | 3,621.63 | 10.75% | |
| 59. | 31 dic. 2020 | $134.83 | $1.07 | -2.45% | 3,756.07 | 3.71% |
| Promedio (R): | 0.47% | 1.22% | ||||
| Desviación estándar: | 4.97% | 4.36% | ||||
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 KMB 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
Kimberly-Clark Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RKMB,t | RS&P 500,t | (RKMB,t–RKMB)2 | (RS&P 500,t–RS&P 500)2 | (RKMB,t–RKMB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 feb. 2016 | 1.46% | -0.41% | 0.98 | 2.67 | -1.62 |
| 2. | 31 mar. 2016 | 3.94% | 6.60% | 12.01 | 28.93 | 18.64 |
| 3. | 30 abr. 2016 | -6.93% | 0.27% | 54.77 | 0.90 | 7.03 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2020 | 5.07% | 10.75% | 21.13 | 90.91 | 43.83 |
| 59. | 31 dic. 2020 | -2.45% | 3.71% | 8.52 | 6.21 | -7.28 |
| Total (Σ): | 1,434.68 | 1,103.45 | 572.75 | |||
| t | Fecha | RKMB,t | RS&P 500,t | (RKMB,t–RKMB)2 | (RS&P 500,t–RS&P 500)2 | (RKMB,t–RKMB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 29 feb. 2016 | 1.46% | -0.41% | 0.98 | 2.67 | -1.62 |
| 2. | 31 mar. 2016 | 3.94% | 6.60% | 12.01 | 28.93 | 18.64 |
| 3. | 30 abr. 2016 | -6.93% | 0.27% | 54.77 | 0.90 | 7.03 |
| 4. | 31 may. 2016 | 1.48% | 1.53% | 1.01 | 0.10 | 0.31 |
| 5. | 30 jun. 2016 | 8.94% | 0.09% | 71.75 | 1.27 | -9.56 |
| 6. | 31 jul. 2016 | -5.77% | 3.56% | 38.94 | 5.48 | -14.61 |
| 7. | 31 ago. 2016 | -1.15% | -0.12% | 2.63 | 1.80 | 2.18 |
| 8. | 30 sept. 2016 | -0.78% | -0.12% | 1.57 | 1.81 | 1.68 |
| 9. | 31 oct. 2016 | -9.30% | -1.94% | 95.47 | 10.00 | 30.90 |
| 10. | 30 nov. 2016 | 1.05% | 3.42% | 0.33 | 4.83 | 1.27 |
| 11. | 31 dic. 2016 | -0.49% | 1.82% | 0.93 | 0.36 | -0.58 |
| 12. | 31 ene. 2017 | 6.14% | 1.79% | 32.16 | 0.32 | 3.22 |
| 13. | 28 feb. 2017 | 9.43% | 3.72% | 80.21 | 6.25 | 22.39 |
| 14. | 31 mar. 2017 | 0.04% | -0.04% | 0.19 | 1.59 | 0.55 |
| 15. | 30 abr. 2017 | -1.43% | 0.91% | 3.61 | 0.10 | 0.59 |
| 16. | 31 may. 2017 | -0.02% | 1.16% | 0.24 | 0.00 | 0.03 |
| 17. | 30 jun. 2017 | 0.27% | 0.48% | 0.04 | 0.55 | 0.15 |
| 18. | 31 jul. 2017 | -4.61% | 1.93% | 25.81 | 0.51 | -3.63 |
| 19. | 31 ago. 2017 | 0.11% | 0.05% | 0.13 | 1.36 | 0.43 |
| 20. | 30 sept. 2017 | -3.76% | 1.93% | 17.94 | 0.50 | -3.01 |
| 21. | 31 oct. 2017 | -4.39% | 2.22% | 23.67 | 1.00 | -4.86 |
| 22. | 30 nov. 2017 | 6.44% | 2.81% | 35.67 | 2.52 | 9.48 |
| 23. | 31 dic. 2017 | 1.56% | 0.98% | 1.19 | 0.06 | -0.26 |
| 24. | 31 ene. 2018 | -3.03% | 5.62% | 12.29 | 19.34 | -15.41 |
| 25. | 28 feb. 2018 | -5.20% | -3.89% | 32.13 | 26.16 | 28.99 |
| 26. | 31 mar. 2018 | 0.19% | -2.69% | 0.08 | 15.28 | 1.10 |
| 27. | 30 abr. 2018 | -5.98% | 0.27% | 41.67 | 0.90 | 6.12 |
| 28. | 31 may. 2018 | -2.60% | 2.16% | 9.42 | 0.89 | -2.89 |
| 29. | 30 jun. 2018 | 5.44% | 0.48% | 24.72 | 0.54 | -3.66 |
| 30. | 31 jul. 2018 | 8.09% | 3.60% | 58.01 | 5.67 | 18.14 |
| 31. | 31 ago. 2018 | 1.48% | 3.03% | 1.01 | 3.26 | 1.81 |
| 32. | 30 sept. 2018 | -0.78% | 0.43% | 1.56 | 0.63 | 0.99 |
| 33. | 31 oct. 2018 | -8.22% | -6.94% | 75.53 | 66.59 | 70.92 |
| 34. | 30 nov. 2018 | 10.61% | 1.79% | 102.86 | 0.32 | 5.74 |
| 35. | 31 dic. 2018 | -0.37% | -9.18% | 0.71 | 108.11 | 8.78 |
| 36. | 31 ene. 2019 | -2.25% | 7.87% | 7.39 | 44.20 | -18.07 |
| 37. | 28 feb. 2019 | 4.89% | 2.97% | 19.55 | 3.07 | 7.75 |
| 38. | 31 mar. 2019 | 6.93% | 1.79% | 41.75 | 0.33 | 3.70 |
| 39. | 30 abr. 2019 | 3.62% | 3.93% | 9.89 | 7.35 | 8.52 |
| 40. | 31 may. 2019 | -0.38% | -6.58% | 0.73 | 60.81 | 6.66 |
| 41. | 30 jun. 2019 | 5.02% | 6.89% | 20.69 | 32.18 | 25.80 |
| 42. | 31 jul. 2019 | 1.78% | 1.31% | 1.71 | 0.01 | 0.12 |
| 43. | 31 ago. 2019 | 4.03% | -1.81% | 12.63 | 9.18 | -10.76 |
| 44. | 30 sept. 2019 | 1.40% | 1.72% | 0.85 | 0.25 | 0.46 |
| 45. | 31 oct. 2019 | -6.46% | 2.04% | 47.99 | 0.68 | -5.70 |
| 46. | 30 nov. 2019 | 2.60% | 3.40% | 4.55 | 4.77 | 4.66 |
| 47. | 31 dic. 2019 | 1.64% | 2.86% | 1.37 | 2.69 | 1.92 |
| 48. | 31 ene. 2020 | 4.14% | -0.16% | 13.43 | 1.91 | -5.07 |
| 49. | 29 feb. 2020 | -8.41% | -8.41% | 78.93 | 92.76 | 85.56 |
| 50. | 31 mar. 2020 | -1.72% | -12.51% | 4.78 | 188.57 | 30.03 |
| 51. | 30 abr. 2020 | 8.30% | 12.68% | 61.24 | 131.43 | 89.72 |
| 52. | 31 may. 2020 | 2.14% | 4.53% | 2.77 | 10.94 | 5.51 |
| 53. | 30 jun. 2020 | 0.69% | 1.84% | 0.05 | 0.38 | 0.14 |
| 54. | 31 jul. 2020 | 7.56% | 5.51% | 50.28 | 18.40 | 30.42 |
| 55. | 31 ago. 2020 | 3.76% | 7.01% | 10.83 | 33.48 | 19.04 |
| 56. | 30 sept. 2020 | -5.72% | -3.92% | 38.39 | 26.45 | 31.86 |
| 57. | 31 oct. 2020 | -10.21% | -2.77% | 114.01 | 15.89 | 42.57 |
| 58. | 30 nov. 2020 | 5.07% | 10.75% | 21.13 | 90.91 | 43.83 |
| 59. | 31 dic. 2020 | -2.45% | 3.71% | 8.52 | 6.21 | -7.28 |
| Total (Σ): | 1,434.68 | 1,103.45 | 572.75 | |||
Mostrar todo
VarianzaKMB = Σ(RKMB,t–RKMB)2 ÷ (59 – 1)
= 1,434.68 ÷ (59 – 1)
= 24.74
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,103.45 ÷ (59 – 1)
= 19.02
CovarianzaKMB, S&P 500 = Σ(RKMB,t–RKMB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 572.75 ÷ (59 – 1)
= 9.88
Estimación sistemática del riesgo (β)
| VarianzaKMB | 24.74 |
| VarianzaS&P 500 | 19.02 |
| CovarianzaKMB, S&P 500 | 9.88 |
| Coeficiente de correlaciónKMB, S&P 5001 | 0.46 |
| βKMB2 | 0.52 |
| αKMB3 | -0.16% |
Cálculos
1 Coeficiente de correlaciónKMB, S&P 500
= CovarianzaKMB, S&P 500 ÷ (Desviación estándarKMB × Desviación estándarS&P 500)
= 9.88 ÷ (4.97% × 4.36%)
= 0.46
2 βKMB
= CovarianzaKMB, S&P 500 ÷ VarianzaS&P 500
= 9.88 ÷ 19.02
= 0.52
3 αKMB
= PromedioKMB – βKMB × PromedioS&P 500
= 0.47% – 0.52 × 1.22%
= -0.16%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.90% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.55% |
| Riesgo sistemático de Kimberly-Clark acciones ordinarias | βKMB | 0.52 |
| Tasa de rendimiento esperada de las acciones ordinarias de Kimberly-Clark3 | E(RKMB) | 9.39% |
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(RKMB) = RF + βKMB [E(RM) – RF]
= 4.90% + 0.52 [13.55% – 4.90%]
= 9.39%