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 Estée Lauder.
Tasas de retorno
Estée Lauder Cos. Inc., tasas mensuales de retorno
| Estée Lauder Cos. Inc. (EL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEL,t1 | DividendoEL,t1 | REL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 jul. 2017 | $98.99 | 2,470.30 | ||||
| 1. | 31 ago. 2017 | $106.99 | $0.34 | 8.43% | 2,471.65 | 0.05% |
| 2. | 30 sept. 2017 | $107.84 | 0.79% | 2,519.36 | 1.93% | |
| 3. | 31 oct. 2017 | $111.81 | 3.68% | 2,575.26 | 2.22% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 may. 2023 | $184.03 | $0.66 | -25.14% | 4,179.83 | 0.25% |
| 71. | 30 jun. 2023 | $196.38 | 6.71% | 4,376.86 | 4.71% | |
| Promedio (R): | 1.41% | 0.94% | ||||
| Desviación estándar: | 8.51% | 5.05% | ||||
| Estée Lauder Cos. Inc. (EL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioEL,t1 | DividendoEL,t1 | REL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 jul. 2017 | $98.99 | 2,470.30 | ||||
| 1. | 31 ago. 2017 | $106.99 | $0.34 | 8.43% | 2,471.65 | 0.05% |
| 2. | 30 sept. 2017 | $107.84 | 0.79% | 2,519.36 | 1.93% | |
| 3. | 31 oct. 2017 | $111.81 | 3.68% | 2,575.26 | 2.22% | |
| 4. | 30 nov. 2017 | $124.83 | $0.38 | 11.98% | 2,647.58 | 2.81% |
| 5. | 31 dic. 2017 | $127.24 | 1.93% | 2,673.61 | 0.98% | |
| 6. | 31 ene. 2018 | $134.96 | 6.07% | 2,823.81 | 5.62% | |
| 7. | 28 feb. 2018 | $138.44 | $0.38 | 2.86% | 2,713.83 | -3.89% |
| 8. | 31 mar. 2018 | $149.72 | 8.15% | 2,640.87 | -2.69% | |
| 9. | 30 abr. 2018 | $148.09 | -1.09% | 2,648.05 | 0.27% | |
| 10. | 31 may. 2018 | $149.44 | $0.38 | 1.17% | 2,705.27 | 2.16% |
| 11. | 30 jun. 2018 | $142.69 | -4.52% | 2,718.37 | 0.48% | |
| 12. | 31 jul. 2018 | $134.94 | -5.43% | 2,816.29 | 3.60% | |
| 13. | 31 ago. 2018 | $140.12 | $0.38 | 4.12% | 2,901.52 | 3.03% |
| 14. | 30 sept. 2018 | $145.32 | 3.71% | 2,913.98 | 0.43% | |
| 15. | 31 oct. 2018 | $137.44 | -5.42% | 2,711.74 | -6.94% | |
| 16. | 30 nov. 2018 | $142.66 | $0.43 | 4.11% | 2,760.17 | 1.79% |
| 17. | 31 dic. 2018 | $130.10 | -8.80% | 2,506.85 | -9.18% | |
| 18. | 31 ene. 2019 | $136.42 | 4.86% | 2,704.10 | 7.87% | |
| 19. | 28 feb. 2019 | $156.94 | $0.43 | 15.36% | 2,784.49 | 2.97% |
| 20. | 31 mar. 2019 | $165.55 | 5.49% | 2,834.40 | 1.79% | |
| 21. | 30 abr. 2019 | $171.81 | 3.78% | 2,945.83 | 3.93% | |
| 22. | 31 may. 2019 | $161.03 | $0.43 | -6.02% | 2,752.06 | -6.58% |
| 23. | 30 jun. 2019 | $183.11 | 13.71% | 2,941.76 | 6.89% | |
| 24. | 31 jul. 2019 | $184.19 | 0.59% | 2,980.38 | 1.31% | |
| 25. | 31 ago. 2019 | $197.99 | $0.43 | 7.73% | 2,926.46 | -1.81% |
| 26. | 30 sept. 2019 | $198.95 | 0.48% | 2,976.74 | 1.72% | |
| 27. | 31 oct. 2019 | $186.27 | -6.37% | 3,037.56 | 2.04% | |
| 28. | 30 nov. 2019 | $195.47 | $0.48 | 5.20% | 3,140.98 | 3.40% |
| 29. | 31 dic. 2019 | $206.54 | 5.66% | 3,230.78 | 2.86% | |
| 30. | 31 ene. 2020 | $195.16 | -5.51% | 3,225.52 | -0.16% | |
| 31. | 29 feb. 2020 | $183.60 | $0.48 | -5.68% | 2,954.22 | -8.41% |
| 32. | 31 mar. 2020 | $159.34 | -13.21% | 2,584.59 | -12.51% | |
| 33. | 30 abr. 2020 | $176.40 | 10.71% | 2,912.43 | 12.68% | |
| 34. | 31 may. 2020 | $197.47 | 11.94% | 3,044.31 | 4.53% | |
| 35. | 30 jun. 2020 | $188.68 | -4.45% | 3,100.29 | 1.84% | |
| 36. | 31 jul. 2020 | $197.54 | 4.70% | 3,271.12 | 5.51% | |
| 37. | 31 ago. 2020 | $221.72 | $0.48 | 12.48% | 3,500.31 | 7.01% |
| 38. | 30 sept. 2020 | $218.25 | -1.57% | 3,363.00 | -3.92% | |
| 39. | 31 oct. 2020 | $219.66 | 0.65% | 3,269.96 | -2.77% | |
| 40. | 30 nov. 2020 | $245.32 | $0.53 | 11.92% | 3,621.63 | 10.75% |
| 41. | 31 dic. 2020 | $266.19 | 8.51% | 3,756.07 | 3.71% | |
| 42. | 31 ene. 2021 | $236.65 | -11.10% | 3,714.24 | -1.11% | |
| 43. | 28 feb. 2021 | $285.86 | $0.53 | 21.02% | 3,811.15 | 2.61% |
| 44. | 31 mar. 2021 | $290.85 | 1.75% | 3,972.89 | 4.24% | |
| 45. | 30 abr. 2021 | $313.80 | 7.89% | 4,181.17 | 5.24% | |
| 46. | 31 may. 2021 | $306.52 | $0.53 | -2.15% | 4,204.11 | 0.55% |
| 47. | 30 jun. 2021 | $318.08 | 3.77% | 4,297.50 | 2.22% | |
| 48. | 31 jul. 2021 | $333.83 | 4.95% | 4,395.26 | 2.27% | |
| 49. | 31 ago. 2021 | $340.49 | $0.53 | 2.15% | 4,522.68 | 2.90% |
| 50. | 30 sept. 2021 | $299.93 | -11.91% | 4,307.54 | -4.76% | |
| 51. | 31 oct. 2021 | $324.33 | 8.14% | 4,605.38 | 6.91% | |
| 52. | 30 nov. 2021 | $332.07 | $0.60 | 2.57% | 4,567.00 | -0.83% |
| 53. | 31 dic. 2021 | $370.20 | 11.48% | 4,766.18 | 4.36% | |
| 54. | 31 ene. 2022 | $311.79 | -15.78% | 4,515.55 | -5.26% | |
| 55. | 28 feb. 2022 | $296.33 | $0.60 | -4.77% | 4,373.94 | -3.14% |
| 56. | 31 mar. 2022 | $272.32 | -8.10% | 4,530.41 | 3.58% | |
| 57. | 30 abr. 2022 | $264.06 | -3.03% | 4,131.93 | -8.80% | |
| 58. | 31 may. 2022 | $254.65 | $0.60 | -3.34% | 4,132.15 | 0.01% |
| 59. | 30 jun. 2022 | $254.67 | 0.01% | 3,785.38 | -8.39% | |
| 60. | 31 jul. 2022 | $273.10 | 7.24% | 4,130.29 | 9.11% | |
| 61. | 31 ago. 2022 | $254.38 | $0.60 | -6.63% | 3,955.00 | -4.24% |
| 62. | 30 sept. 2022 | $215.90 | -15.13% | 3,585.62 | -9.34% | |
| 63. | 31 oct. 2022 | $200.49 | -7.14% | 3,871.98 | 7.99% | |
| 64. | 30 nov. 2022 | $235.79 | $0.66 | 17.94% | 4,080.11 | 5.38% |
| 65. | 31 dic. 2022 | $248.11 | 5.22% | 3,839.50 | -5.90% | |
| 66. | 31 ene. 2023 | $277.08 | 11.68% | 4,076.60 | 6.18% | |
| 67. | 28 feb. 2023 | $243.05 | $0.66 | -12.04% | 3,970.15 | -2.61% |
| 68. | 31 mar. 2023 | $246.46 | 1.40% | 4,109.31 | 3.51% | |
| 69. | 30 abr. 2023 | $246.72 | 0.11% | 4,169.48 | 1.46% | |
| 70. | 31 may. 2023 | $184.03 | $0.66 | -25.14% | 4,179.83 | 0.25% |
| 71. | 30 jun. 2023 | $196.38 | 6.71% | 4,376.86 | 4.71% | |
| Promedio (R): | 1.41% | 0.94% | ||||
| Desviación estándar: | 8.51% | 5.05% | ||||
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 EL 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
Estée Lauder Cos. Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | REL,t | RS&P 500,t | (REL,t–REL)2 | (RS&P 500,t–RS&P 500)2 | (REL,t–REL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ago. 2017 | 8.43% | 0.05% | 49.15 | 0.78 | -6.18 |
| 2. | 30 sept. 2017 | 0.79% | 1.93% | 0.38 | 0.99 | -0.62 |
| 3. | 31 oct. 2017 | 3.68% | 2.22% | 5.14 | 1.65 | 2.91 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 may. 2023 | -25.14% | 0.25% | 705.25 | 0.47 | 18.26 |
| 71. | 30 jun. 2023 | 6.71% | 4.71% | 28.05 | 14.27 | 20.01 |
| Total (Σ): | 5,074.61 | 1,786.26 | 1,772.52 | |||
| t | Fecha | REL,t | RS&P 500,t | (REL,t–REL)2 | (RS&P 500,t–RS&P 500)2 | (REL,t–REL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ago. 2017 | 8.43% | 0.05% | 49.15 | 0.78 | -6.18 |
| 2. | 30 sept. 2017 | 0.79% | 1.93% | 0.38 | 0.99 | -0.62 |
| 3. | 31 oct. 2017 | 3.68% | 2.22% | 5.14 | 1.65 | 2.91 |
| 4. | 30 nov. 2017 | 11.98% | 2.81% | 111.72 | 3.51 | 19.79 |
| 5. | 31 dic. 2017 | 1.93% | 0.98% | 0.27 | 0.00 | 0.02 |
| 6. | 31 ene. 2018 | 6.07% | 5.62% | 21.65 | 21.92 | 21.78 |
| 7. | 28 feb. 2018 | 2.86% | -3.89% | 2.09 | 23.33 | -6.98 |
| 8. | 31 mar. 2018 | 8.15% | -2.69% | 45.34 | 13.14 | -24.40 |
| 9. | 30 abr. 2018 | -1.09% | 0.27% | 6.27 | 0.44 | 1.66 |
| 10. | 31 may. 2018 | 1.17% | 2.16% | 0.06 | 1.50 | -0.30 |
| 11. | 30 jun. 2018 | -4.52% | 0.48% | 35.18 | 0.20 | 2.68 |
| 12. | 31 jul. 2018 | -5.43% | 3.60% | 46.87 | 7.11 | -18.25 |
| 13. | 31 ago. 2018 | 4.12% | 3.03% | 7.32 | 4.37 | 5.66 |
| 14. | 30 sept. 2018 | 3.71% | 0.43% | 5.27 | 0.26 | -1.16 |
| 15. | 31 oct. 2018 | -5.42% | -6.94% | 46.75 | 62.03 | 53.85 |
| 16. | 30 nov. 2018 | 4.11% | 1.79% | 7.27 | 0.72 | 2.29 |
| 17. | 31 dic. 2018 | -8.80% | -9.18% | 104.43 | 102.28 | 103.35 |
| 18. | 31 ene. 2019 | 4.86% | 7.87% | 11.85 | 48.06 | 23.87 |
| 19. | 28 feb. 2019 | 15.36% | 2.97% | 194.39 | 4.15 | 28.40 |
| 20. | 31 mar. 2019 | 5.49% | 1.79% | 16.58 | 0.73 | 3.49 |
| 21. | 30 abr. 2019 | 3.78% | 3.93% | 5.60 | 8.97 | 7.09 |
| 22. | 31 may. 2019 | -6.02% | -6.58% | 55.34 | 56.45 | 55.89 |
| 23. | 30 jun. 2019 | 13.71% | 6.89% | 151.22 | 35.49 | 73.26 |
| 24. | 31 jul. 2019 | 0.59% | 1.31% | 0.68 | 0.14 | -0.31 |
| 25. | 31 ago. 2019 | 7.73% | -1.81% | 39.83 | 7.53 | -17.32 |
| 26. | 30 sept. 2019 | 0.48% | 1.72% | 0.86 | 0.61 | -0.73 |
| 27. | 31 oct. 2019 | -6.37% | 2.04% | 60.66 | 1.23 | -8.62 |
| 28. | 30 nov. 2019 | 5.20% | 3.40% | 14.30 | 6.10 | 9.34 |
| 29. | 31 dic. 2019 | 5.66% | 2.86% | 18.05 | 3.70 | 8.17 |
| 30. | 31 ene. 2020 | -5.51% | -0.16% | 47.95 | 1.21 | 7.61 |
| 31. | 29 feb. 2020 | -5.68% | -8.41% | 50.30 | 87.36 | 66.29 |
| 32. | 31 mar. 2020 | -13.21% | -12.51% | 213.99 | 180.84 | 196.72 |
| 33. | 30 abr. 2020 | 10.71% | 12.68% | 86.34 | 138.03 | 109.17 |
| 34. | 31 may. 2020 | 11.94% | 4.53% | 110.87 | 12.91 | 37.83 |
| 35. | 30 jun. 2020 | -4.45% | 1.84% | 34.41 | 0.82 | -5.30 |
| 36. | 31 jul. 2020 | 4.70% | 5.51% | 10.77 | 20.92 | 15.01 |
| 37. | 31 ago. 2020 | 12.48% | 7.01% | 122.52 | 36.85 | 67.20 |
| 38. | 30 sept. 2020 | -1.57% | -3.92% | 8.88 | 23.61 | 14.48 |
| 39. | 31 oct. 2020 | 0.65% | -2.77% | 0.59 | 13.71 | 2.85 |
| 40. | 30 nov. 2020 | 11.92% | 10.75% | 110.42 | 96.41 | 103.18 |
| 41. | 31 dic. 2020 | 8.51% | 3.71% | 50.30 | 7.71 | 19.69 |
| 42. | 31 ene. 2021 | -11.10% | -1.11% | 156.55 | 4.20 | 25.64 |
| 43. | 28 feb. 2021 | 21.02% | 2.61% | 384.30 | 2.80 | 32.80 |
| 44. | 31 mar. 2021 | 1.75% | 4.24% | 0.11 | 10.94 | 1.09 |
| 45. | 30 abr. 2021 | 7.89% | 5.24% | 41.94 | 18.55 | 27.89 |
| 46. | 31 may. 2021 | -2.15% | 0.55% | 12.71 | 0.15 | 1.38 |
| 47. | 30 jun. 2021 | 3.77% | 2.22% | 5.55 | 1.65 | 3.03 |
| 48. | 31 jul. 2021 | 4.95% | 2.27% | 12.51 | 1.79 | 4.74 |
| 49. | 31 ago. 2021 | 2.15% | 2.90% | 0.55 | 3.85 | 1.45 |
| 50. | 30 sept. 2021 | -11.91% | -4.76% | 177.61 | 32.41 | 75.87 |
| 51. | 31 oct. 2021 | 8.14% | 6.91% | 45.17 | 35.74 | 40.18 |
| 52. | 30 nov. 2021 | 2.57% | -0.83% | 1.34 | 3.13 | -2.05 |
| 53. | 31 dic. 2021 | 11.48% | 4.36% | 101.36 | 11.73 | 34.49 |
| 54. | 31 ene. 2022 | -15.78% | -5.26% | 295.59 | 38.37 | 106.50 |
| 55. | 28 feb. 2022 | -4.77% | -3.14% | 38.20 | 16.58 | 25.17 |
| 56. | 31 mar. 2022 | -8.10% | 3.58% | 90.58 | 6.98 | -25.14 |
| 57. | 30 abr. 2022 | -3.03% | -8.80% | 19.78 | 94.70 | 43.28 |
| 58. | 31 may. 2022 | -3.34% | 0.01% | 22.57 | 0.87 | 4.42 |
| 59. | 30 jun. 2022 | 0.01% | -8.39% | 1.98 | 87.01 | 13.12 |
| 60. | 31 jul. 2022 | 7.24% | 9.11% | 33.90 | 66.84 | 47.60 |
| 61. | 31 ago. 2022 | -6.63% | -4.24% | 64.80 | 26.83 | 41.70 |
| 62. | 30 sept. 2022 | -15.13% | -9.34% | 273.63 | 105.58 | 169.97 |
| 63. | 31 oct. 2022 | -7.14% | 7.99% | 73.14 | 49.71 | -60.30 |
| 64. | 30 nov. 2022 | 17.94% | 5.38% | 272.95 | 19.71 | 73.35 |
| 65. | 31 dic. 2022 | 5.22% | -5.90% | 14.52 | 46.69 | -26.04 |
| 66. | 31 ene. 2023 | 11.68% | 6.18% | 105.30 | 27.45 | 53.77 |
| 67. | 28 feb. 2023 | -12.04% | -2.61% | 181.12 | 12.58 | 47.74 |
| 68. | 31 mar. 2023 | 1.40% | 3.51% | 0.00 | 6.60 | -0.03 |
| 69. | 30 abr. 2023 | 0.11% | 1.46% | 1.71 | 0.28 | -0.69 |
| 70. | 31 may. 2023 | -25.14% | 0.25% | 705.25 | 0.47 | 18.26 |
| 71. | 30 jun. 2023 | 6.71% | 4.71% | 28.05 | 14.27 | 20.01 |
| Total (Σ): | 5,074.61 | 1,786.26 | 1,772.52 | |||
Mostrar todo
VarianzaEL = Σ(REL,t–REL)2 ÷ (71 – 1)
= 5,074.61 ÷ (71 – 1)
= 72.49
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,786.26 ÷ (71 – 1)
= 25.52
CovarianzaEL, S&P 500 = Σ(REL,t–REL)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,772.52 ÷ (71 – 1)
= 25.32
Estimación sistemática del riesgo (β)
| VarianzaEL | 72.49 |
| VarianzaS&P 500 | 25.52 |
| CovarianzaEL, S&P 500 | 25.32 |
| Coeficiente de correlaciónEL, S&P 5001 | 0.59 |
| βEL2 | 0.99 |
| αEL3 | 0.49% |
Cálculos
1 Coeficiente de correlaciónEL, S&P 500
= CovarianzaEL, S&P 500 ÷ (Desviación estándarEL × Desviación estándarS&P 500)
= 25.32 ÷ (8.51% × 5.05%)
= 0.59
2 βEL
= CovarianzaEL, S&P 500 ÷ VarianzaS&P 500
= 25.32 ÷ 25.52
= 0.99
3 αEL
= PromedioEL – βEL × PromedioS&P 500
= 1.41% – 0.99 × 0.94%
= 0.49%
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) | 13.54% |
| Riesgo sistemático de Estée Lauder acciones ordinarias | βEL | 0.99 |
| Tasa de rendimiento esperada de las acciones ordinarias de Estée Lauder3 | E(REL) | 13.47% |
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(REL) = RF + βEL [E(RM) – RF]
= 4.86% + 0.99 [13.54% – 4.86%]
= 13.47%