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 Lam Research.
Tasas de retorno
Lam Research Corp., tasas mensuales de retorno
| Lam Research Corp. (LRCX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioLRCX,t1 | DividendoLRCX,t1 | RLRCX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 jul. 2018 | $19.06 | 2,816.29 | ||||
| 1. | 31 ago. 2018 | $17.31 | -9.18% | 2,901.52 | 3.03% | |
| 2. | 30 sept. 2018 | $15.17 | $0.11 | -11.73% | 2,913.98 | 0.43% |
| 3. | 31 oct. 2018 | $14.17 | -6.59% | 2,711.74 | -6.94% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 may. 2024 | $93.24 | 4.25% | 5,277.51 | 4.80% | |
| 71. | 30 jun. 2024 | $106.49 | $0.20 | 14.43% | 5,460.48 | 3.47% |
| Promedio (R): | 3.21% | 1.07% | ||||
| Desviación estándar: | 11.42% | 5.24% | ||||
| Lam Research Corp. (LRCX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioLRCX,t1 | DividendoLRCX,t1 | RLRCX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 jul. 2018 | $19.06 | 2,816.29 | ||||
| 1. | 31 ago. 2018 | $17.31 | -9.18% | 2,901.52 | 3.03% | |
| 2. | 30 sept. 2018 | $15.17 | $0.11 | -11.73% | 2,913.98 | 0.43% |
| 3. | 31 oct. 2018 | $14.17 | -6.59% | 2,711.74 | -6.94% | |
| 4. | 30 nov. 2018 | $15.70 | 10.80% | 2,760.17 | 1.79% | |
| 5. | 31 dic. 2018 | $13.62 | $0.11 | -12.55% | 2,506.85 | -9.18% |
| 6. | 31 ene. 2019 | $16.96 | 24.52% | 2,704.10 | 7.87% | |
| 7. | 28 feb. 2019 | $17.61 | 3.83% | 2,784.49 | 2.97% | |
| 8. | 31 mar. 2019 | $17.90 | $0.11 | 2.27% | 2,834.40 | 1.79% |
| 9. | 30 abr. 2019 | $20.74 | 15.87% | 2,945.83 | 3.93% | |
| 10. | 31 may. 2019 | $17.46 | -15.81% | 2,752.06 | -6.58% | |
| 11. | 30 jun. 2019 | $18.78 | $0.11 | 8.19% | 2,941.76 | 6.89% |
| 12. | 31 jul. 2019 | $20.86 | 11.08% | 2,980.38 | 1.31% | |
| 13. | 31 ago. 2019 | $21.05 | 0.91% | 2,926.46 | -1.81% | |
| 14. | 30 sept. 2019 | $23.11 | $0.115 | 10.33% | 2,976.74 | 1.72% |
| 15. | 31 oct. 2019 | $27.10 | 17.27% | 3,037.56 | 2.04% | |
| 16. | 30 nov. 2019 | $26.68 | -1.55% | 3,140.98 | 3.40% | |
| 17. | 31 dic. 2019 | $29.24 | $0.115 | 10.03% | 3,230.78 | 2.86% |
| 18. | 31 ene. 2020 | $29.82 | 1.98% | 3,225.52 | -0.16% | |
| 19. | 29 feb. 2020 | $29.34 | -1.61% | 2,954.22 | -8.41% | |
| 20. | 31 mar. 2020 | $24.00 | $0.115 | -17.81% | 2,584.59 | -12.51% |
| 21. | 30 abr. 2020 | $25.53 | 6.38% | 2,912.43 | 12.68% | |
| 22. | 31 may. 2020 | $27.37 | 7.21% | 3,044.31 | 4.53% | |
| 23. | 30 jun. 2020 | $32.35 | $0.115 | 18.62% | 3,100.29 | 1.84% |
| 24. | 31 jul. 2020 | $37.72 | 16.60% | 3,271.12 | 5.51% | |
| 25. | 31 ago. 2020 | $33.63 | -10.84% | 3,500.31 | 7.01% | |
| 26. | 30 sept. 2020 | $33.18 | $0.13 | -0.95% | 3,363.00 | -3.92% |
| 27. | 31 oct. 2020 | $34.21 | 3.10% | 3,269.96 | -2.77% | |
| 28. | 30 nov. 2020 | $45.27 | 32.33% | 3,621.63 | 10.75% | |
| 29. | 31 dic. 2020 | $47.23 | $0.13 | 4.62% | 3,756.07 | 3.71% |
| 30. | 31 ene. 2021 | $48.40 | 2.48% | 3,714.24 | -1.11% | |
| 31. | 28 feb. 2021 | $56.72 | 17.19% | 3,811.15 | 2.61% | |
| 32. | 31 mar. 2021 | $59.52 | $0.13 | 5.17% | 3,972.89 | 4.24% |
| 33. | 30 abr. 2021 | $62.05 | 4.25% | 4,181.17 | 5.24% | |
| 34. | 31 may. 2021 | $64.99 | 4.74% | 4,204.11 | 0.55% | |
| 35. | 30 jun. 2021 | $65.07 | $0.13 | 0.32% | 4,297.50 | 2.22% |
| 36. | 31 jul. 2021 | $63.74 | -2.04% | 4,395.26 | 2.27% | |
| 37. | 31 ago. 2021 | $60.48 | -5.11% | 4,522.68 | 2.90% | |
| 38. | 30 sept. 2021 | $56.92 | $0.15 | -5.64% | 4,307.54 | -4.76% |
| 39. | 31 oct. 2021 | $56.36 | -0.98% | 4,605.38 | 6.91% | |
| 40. | 30 nov. 2021 | $67.99 | 20.64% | 4,567.00 | -0.83% | |
| 41. | 31 dic. 2021 | $71.92 | $0.15 | 6.00% | 4,766.18 | 4.36% |
| 42. | 31 ene. 2022 | $58.99 | -17.98% | 4,515.55 | -5.26% | |
| 43. | 28 feb. 2022 | $56.14 | -4.83% | 4,373.94 | -3.14% | |
| 44. | 31 mar. 2022 | $53.76 | $0.15 | -3.97% | 4,530.41 | 3.58% |
| 45. | 30 abr. 2022 | $46.58 | -13.36% | 4,131.93 | -8.80% | |
| 46. | 31 may. 2022 | $52.00 | 11.64% | 4,132.15 | 0.01% | |
| 47. | 30 jun. 2022 | $42.62 | $0.15 | -17.75% | 3,785.38 | -8.39% |
| 48. | 31 jul. 2022 | $50.05 | 17.43% | 4,130.29 | 9.11% | |
| 49. | 31 ago. 2022 | $43.79 | -12.51% | 3,955.00 | -4.24% | |
| 50. | 30 sept. 2022 | $36.60 | $0.1725 | -16.03% | 3,585.62 | -9.34% |
| 51. | 31 oct. 2022 | $40.48 | 10.60% | 3,871.98 | 7.99% | |
| 52. | 30 nov. 2022 | $47.24 | 16.70% | 4,080.11 | 5.38% | |
| 53. | 31 dic. 2022 | $42.03 | $0.1725 | -10.66% | 3,839.50 | -5.90% |
| 54. | 31 ene. 2023 | $50.01 | 18.99% | 4,076.60 | 6.18% | |
| 55. | 28 feb. 2023 | $48.60 | -2.82% | 3,970.15 | -2.61% | |
| 56. | 31 mar. 2023 | $53.01 | $0.1725 | 9.43% | 4,109.31 | 3.51% |
| 57. | 30 abr. 2023 | $52.41 | -1.13% | 4,169.48 | 1.46% | |
| 58. | 31 may. 2023 | $61.67 | 17.67% | 4,179.83 | 0.25% | |
| 59. | 30 jun. 2023 | $64.29 | $0.1725 | 4.53% | 4,376.86 | 4.71% |
| 60. | 31 jul. 2023 | $71.85 | 11.76% | 4,588.96 | 4.85% | |
| 61. | 31 ago. 2023 | $70.24 | -2.24% | 4,507.66 | -1.77% | |
| 62. | 30 sept. 2023 | $62.68 | $0.20 | -10.48% | 4,288.05 | -4.87% |
| 63. | 31 oct. 2023 | $58.82 | -6.16% | 4,193.80 | -2.20% | |
| 64. | 30 nov. 2023 | $71.59 | 21.71% | 4,567.80 | 8.92% | |
| 65. | 31 dic. 2023 | $78.33 | $0.20 | 9.69% | 4,769.83 | 4.42% |
| 66. | 31 ene. 2024 | $82.52 | 5.35% | 4,845.65 | 1.59% | |
| 67. | 29 feb. 2024 | $93.83 | 13.71% | 5,096.27 | 5.17% | |
| 68. | 31 mar. 2024 | $97.16 | $0.20 | 3.76% | 5,254.35 | 3.10% |
| 69. | 30 abr. 2024 | $89.44 | -7.95% | 5,035.69 | -4.16% | |
| 70. | 31 may. 2024 | $93.24 | 4.25% | 5,277.51 | 4.80% | |
| 71. | 30 jun. 2024 | $106.49 | $0.20 | 14.43% | 5,460.48 | 3.47% |
| Promedio (R): | 3.21% | 1.07% | ||||
| Desviación estándar: | 11.42% | 5.24% | ||||
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 LRCX 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
Lam Research Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RLRCX,t | RS&P 500,t | (RLRCX,t–RLRCX)2 | (RS&P 500,t–RS&P 500)2 | (RLRCX,t–RLRCX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ago. 2018 | -9.18% | 3.03% | 153.61 | 3.81 | -24.20 |
| 2. | 30 sept. 2018 | -11.73% | 0.43% | 223.19 | 0.41 | 9.62 |
| 3. | 31 oct. 2018 | -6.59% | -6.94% | 96.12 | 64.22 | 78.57 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 may. 2024 | 4.25% | 4.80% | 1.07 | 13.90 | 3.86 |
| 71. | 30 jun. 2024 | 14.43% | 3.47% | 125.73 | 5.73 | 26.84 |
| Total (Σ): | 9,135.72 | 1,922.79 | 2,980.70 | |||
| t | Fecha | RLRCX,t | RS&P 500,t | (RLRCX,t–RLRCX)2 | (RS&P 500,t–RS&P 500)2 | (RLRCX,t–RLRCX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ago. 2018 | -9.18% | 3.03% | 153.61 | 3.81 | -24.20 |
| 2. | 30 sept. 2018 | -11.73% | 0.43% | 223.19 | 0.41 | 9.62 |
| 3. | 31 oct. 2018 | -6.59% | -6.94% | 96.12 | 64.22 | 78.57 |
| 4. | 30 nov. 2018 | 10.80% | 1.79% | 57.53 | 0.51 | 5.41 |
| 5. | 31 dic. 2018 | -12.55% | -9.18% | 248.38 | 105.08 | 161.56 |
| 6. | 31 ene. 2019 | 24.52% | 7.87% | 454.13 | 46.17 | 144.81 |
| 7. | 28 feb. 2019 | 3.83% | 2.97% | 0.38 | 3.61 | 1.18 |
| 8. | 31 mar. 2019 | 2.27% | 1.79% | 0.89 | 0.52 | -0.68 |
| 9. | 30 abr. 2019 | 15.87% | 3.93% | 160.11 | 8.17 | 36.16 |
| 10. | 31 may. 2019 | -15.81% | -6.58% | 362.03 | 58.54 | 145.58 |
| 11. | 30 jun. 2019 | 8.19% | 6.89% | 24.78 | 33.87 | 28.97 |
| 12. | 31 jul. 2019 | 11.08% | 1.31% | 61.83 | 0.06 | 1.88 |
| 13. | 31 ago. 2019 | 0.91% | -1.81% | 5.30 | 8.31 | 6.63 |
| 14. | 30 sept. 2019 | 10.33% | 1.72% | 50.70 | 0.42 | 4.59 |
| 15. | 31 oct. 2019 | 17.27% | 2.04% | 197.48 | 0.94 | 13.63 |
| 16. | 30 nov. 2019 | -1.55% | 3.40% | 22.68 | 5.44 | -11.10 |
| 17. | 31 dic. 2019 | 10.03% | 2.86% | 46.43 | 3.19 | 12.17 |
| 18. | 31 ene. 2020 | 1.98% | -0.16% | 1.51 | 1.53 | 1.52 |
| 19. | 29 feb. 2020 | -1.61% | -8.41% | 23.25 | 89.95 | 45.73 |
| 20. | 31 mar. 2020 | -17.81% | -12.51% | 441.87 | 184.56 | 285.57 |
| 21. | 30 abr. 2020 | 6.38% | 12.68% | 10.00 | 134.82 | 36.72 |
| 22. | 31 may. 2020 | 7.21% | 4.53% | 15.96 | 11.94 | 13.80 |
| 23. | 30 jun. 2020 | 18.62% | 1.84% | 237.25 | 0.59 | 11.79 |
| 24. | 31 jul. 2020 | 16.60% | 5.51% | 179.22 | 19.68 | 59.40 |
| 25. | 31 ago. 2020 | -10.84% | 7.01% | 197.55 | 35.20 | -83.39 |
| 26. | 30 sept. 2020 | -0.95% | -3.92% | 17.34 | 24.96 | 20.80 |
| 27. | 31 oct. 2020 | 3.10% | -2.77% | 0.01 | 14.75 | 0.41 |
| 28. | 30 nov. 2020 | 32.33% | 10.75% | 847.82 | 93.73 | 281.89 |
| 29. | 31 dic. 2020 | 4.62% | 3.71% | 1.97 | 6.96 | 3.71 |
| 30. | 31 ene. 2021 | 2.48% | -1.11% | 0.54 | 4.78 | 1.61 |
| 31. | 28 feb. 2021 | 17.19% | 2.61% | 195.38 | 2.36 | 21.47 |
| 32. | 31 mar. 2021 | 5.17% | 4.24% | 3.82 | 10.05 | 6.19 |
| 33. | 30 abr. 2021 | 4.25% | 5.24% | 1.08 | 17.38 | 4.33 |
| 34. | 31 may. 2021 | 4.74% | 0.55% | 2.33 | 0.28 | -0.80 |
| 35. | 30 jun. 2021 | 0.32% | 2.22% | 8.35 | 1.32 | -3.32 |
| 36. | 31 jul. 2021 | -2.04% | 2.27% | 27.63 | 1.44 | -6.32 |
| 37. | 31 ago. 2021 | -5.11% | 2.90% | 69.34 | 3.33 | -15.20 |
| 38. | 30 sept. 2021 | -5.64% | -4.76% | 78.33 | 33.99 | 51.60 |
| 39. | 31 oct. 2021 | -0.98% | 6.91% | 17.61 | 34.12 | -24.51 |
| 40. | 30 nov. 2021 | 20.64% | -0.83% | 303.56 | 3.64 | -33.22 |
| 41. | 31 dic. 2021 | 6.00% | 4.36% | 7.78 | 10.81 | 9.17 |
| 42. | 31 ene. 2022 | -17.98% | -5.26% | 449.04 | 40.09 | 134.18 |
| 43. | 28 feb. 2022 | -4.83% | -3.14% | 64.70 | 17.72 | 33.86 |
| 44. | 31 mar. 2022 | -3.97% | 3.58% | 51.62 | 6.27 | -17.99 |
| 45. | 30 abr. 2022 | -13.36% | -8.80% | 274.50 | 97.40 | 163.51 |
| 46. | 31 may. 2022 | 11.64% | 0.01% | 70.96 | 1.14 | -9.00 |
| 47. | 30 jun. 2022 | -17.75% | -8.39% | 439.42 | 89.59 | 198.42 |
| 48. | 31 jul. 2022 | 17.43% | 9.11% | 202.23 | 64.61 | 114.31 |
| 49. | 31 ago. 2022 | -12.51% | -4.24% | 247.11 | 28.27 | 83.59 |
| 50. | 30 sept. 2022 | -16.03% | -9.34% | 370.09 | 108.43 | 200.32 |
| 51. | 31 oct. 2022 | 10.60% | 7.99% | 54.59 | 47.79 | 51.08 |
| 52. | 30 nov. 2022 | 16.70% | 5.38% | 181.91 | 18.51 | 58.02 |
| 53. | 31 dic. 2022 | -10.66% | -5.90% | 192.54 | 48.59 | 96.72 |
| 54. | 31 ene. 2023 | 18.99% | 6.18% | 248.82 | 26.03 | 80.48 |
| 55. | 28 feb. 2023 | -2.82% | -2.61% | 36.38 | 13.58 | 22.22 |
| 56. | 31 mar. 2023 | 9.43% | 3.51% | 38.65 | 5.91 | 15.12 |
| 57. | 30 abr. 2023 | -1.13% | 1.46% | 18.87 | 0.15 | -1.70 |
| 58. | 31 may. 2023 | 17.67% | 0.25% | 208.98 | 0.68 | -11.93 |
| 59. | 30 jun. 2023 | 4.53% | 4.71% | 1.73 | 13.25 | 4.79 |
| 60. | 31 jul. 2023 | 11.76% | 4.85% | 73.05 | 14.23 | 32.24 |
| 61. | 31 ago. 2023 | -2.24% | -1.77% | 29.74 | 8.09 | 15.51 |
| 62. | 30 sept. 2023 | -10.48% | -4.87% | 187.43 | 35.35 | 81.39 |
| 63. | 31 oct. 2023 | -6.16% | -2.20% | 87.81 | 10.70 | 30.65 |
| 64. | 30 nov. 2023 | 21.71% | 8.92% | 342.18 | 61.54 | 145.11 |
| 65. | 31 dic. 2023 | 9.69% | 4.42% | 42.01 | 11.22 | 21.71 |
| 66. | 31 ene. 2024 | 5.35% | 1.59% | 4.57 | 0.27 | 1.10 |
| 67. | 29 feb. 2024 | 13.71% | 5.17% | 110.11 | 16.80 | 43.01 |
| 68. | 31 mar. 2024 | 3.76% | 3.10% | 0.30 | 4.11 | 1.12 |
| 69. | 30 abr. 2024 | -7.95% | -4.16% | 124.50 | 27.40 | 58.41 |
| 70. | 31 may. 2024 | 4.25% | 4.80% | 1.07 | 13.90 | 3.86 |
| 71. | 30 jun. 2024 | 14.43% | 3.47% | 125.73 | 5.73 | 26.84 |
| Total (Σ): | 9,135.72 | 1,922.79 | 2,980.70 | |||
Mostrar todo
VarianzaLRCX = Σ(RLRCX,t–RLRCX)2 ÷ (71 – 1)
= 9,135.72 ÷ (71 – 1)
= 130.51
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,922.79 ÷ (71 – 1)
= 27.47
CovarianzaLRCX, S&P 500 = Σ(RLRCX,t–RLRCX)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,980.70 ÷ (71 – 1)
= 42.58
Estimación sistemática del riesgo (β)
| VarianzaLRCX | 130.51 |
| VarianzaS&P 500 | 27.47 |
| CovarianzaLRCX, S&P 500 | 42.58 |
| Coeficiente de correlaciónLRCX, S&P 5001 | 0.71 |
| βLRCX2 | 1.55 |
| αLRCX3 | 1.55% |
Cálculos
1 Coeficiente de correlaciónLRCX, S&P 500
= CovarianzaLRCX, S&P 500 ÷ (Desviación estándarLRCX × Desviación estándarS&P 500)
= 42.58 ÷ (11.42% × 5.24%)
= 0.71
2 βLRCX
= CovarianzaLRCX, S&P 500 ÷ VarianzaS&P 500
= 42.58 ÷ 27.47
= 1.55
3 αLRCX
= PromedioLRCX – βLRCX × PromedioS&P 500
= 3.21% – 1.55 × 1.07%
= 1.55%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.65% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Lam Research acciones ordinarias | βLRCX | 1.55 |
| Tasa de rendimiento esperada de las acciones ordinarias de Lam Research3 | E(RLRCX) | 18.81% |
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(RLRCX) = RF + βLRCX [E(RM) – RF]
= 4.65% + 1.55 [13.79% – 4.65%]
= 18.81%