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 Applied.
Tasas de retorno
Applied Materials Inc., tasas mensuales de retorno
| Applied Materials Inc. (AMAT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAMAT,t1 | DividendoAMAT,t1 | RAMAT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 nov. 2017 | $52.77 | 2,647.58 | ||||
| 1. | 31 dic. 2017 | $51.12 | -3.13% | 2,673.61 | 0.98% | |
| 2. | 31 ene. 2018 | $53.63 | 4.91% | 2,823.81 | 5.62% | |
| 3. | 28 feb. 2018 | $57.59 | $0.10 | 7.57% | 2,713.83 | -3.89% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 sept. 2023 | $138.45 | -9.37% | 4,288.05 | -4.87% | |
| 71. | 31 oct. 2023 | $132.35 | -4.41% | 4,193.80 | -2.20% | |
| Promedio (R): | 2.00% | 0.78% | ||||
| Desviación estándar: | 11.13% | 5.13% | ||||
| Applied Materials Inc. (AMAT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioAMAT,t1 | DividendoAMAT,t1 | RAMAT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 nov. 2017 | $52.77 | 2,647.58 | ||||
| 1. | 31 dic. 2017 | $51.12 | -3.13% | 2,673.61 | 0.98% | |
| 2. | 31 ene. 2018 | $53.63 | 4.91% | 2,823.81 | 5.62% | |
| 3. | 28 feb. 2018 | $57.59 | $0.10 | 7.57% | 2,713.83 | -3.89% |
| 4. | 31 mar. 2018 | $55.61 | -3.44% | 2,640.87 | -2.69% | |
| 5. | 30 abr. 2018 | $49.67 | -10.68% | 2,648.05 | 0.27% | |
| 6. | 31 may. 2018 | $50.78 | $0.20 | 2.64% | 2,705.27 | 2.16% |
| 7. | 30 jun. 2018 | $46.19 | -9.04% | 2,718.37 | 0.48% | |
| 8. | 31 jul. 2018 | $48.63 | 5.28% | 2,816.29 | 3.60% | |
| 9. | 31 ago. 2018 | $43.02 | $0.20 | -11.12% | 2,901.52 | 3.03% |
| 10. | 30 sept. 2018 | $38.65 | -10.16% | 2,913.98 | 0.43% | |
| 11. | 31 oct. 2018 | $32.88 | -14.93% | 2,711.74 | -6.94% | |
| 12. | 30 nov. 2018 | $37.28 | $0.20 | 13.99% | 2,760.17 | 1.79% |
| 13. | 31 dic. 2018 | $32.74 | -12.18% | 2,506.85 | -9.18% | |
| 14. | 31 ene. 2019 | $39.08 | 19.36% | 2,704.10 | 7.87% | |
| 15. | 28 feb. 2019 | $38.34 | $0.20 | -1.38% | 2,784.49 | 2.97% |
| 16. | 31 mar. 2019 | $39.66 | 3.44% | 2,834.40 | 1.79% | |
| 17. | 30 abr. 2019 | $44.07 | 11.12% | 2,945.83 | 3.93% | |
| 18. | 31 may. 2019 | $38.69 | $0.21 | -11.73% | 2,752.06 | -6.58% |
| 19. | 30 jun. 2019 | $44.91 | 16.08% | 2,941.76 | 6.89% | |
| 20. | 31 jul. 2019 | $49.37 | 9.93% | 2,980.38 | 1.31% | |
| 21. | 31 ago. 2019 | $48.02 | $0.21 | -2.31% | 2,926.46 | -1.81% |
| 22. | 30 sept. 2019 | $49.90 | 3.92% | 2,976.74 | 1.72% | |
| 23. | 31 oct. 2019 | $54.26 | 8.74% | 3,037.56 | 2.04% | |
| 24. | 30 nov. 2019 | $57.90 | $0.21 | 7.10% | 3,140.98 | 3.40% |
| 25. | 31 dic. 2019 | $61.04 | 5.42% | 3,230.78 | 2.86% | |
| 26. | 31 ene. 2020 | $57.99 | -5.00% | 3,225.52 | -0.16% | |
| 27. | 29 feb. 2020 | $58.12 | $0.21 | 0.59% | 2,954.22 | -8.41% |
| 28. | 31 mar. 2020 | $45.82 | -21.16% | 2,584.59 | -12.51% | |
| 29. | 30 abr. 2020 | $49.68 | 8.42% | 2,912.43 | 12.68% | |
| 30. | 31 may. 2020 | $56.18 | $0.22 | 13.53% | 3,044.31 | 4.53% |
| 31. | 30 jun. 2020 | $60.45 | 7.60% | 3,100.29 | 1.84% | |
| 32. | 31 jul. 2020 | $64.33 | 6.42% | 3,271.12 | 5.51% | |
| 33. | 31 ago. 2020 | $61.60 | $0.22 | -3.90% | 3,500.31 | 7.01% |
| 34. | 30 sept. 2020 | $59.45 | -3.49% | 3,363.00 | -3.92% | |
| 35. | 31 oct. 2020 | $59.23 | -0.37% | 3,269.96 | -2.77% | |
| 36. | 30 nov. 2020 | $82.48 | $0.22 | 39.63% | 3,621.63 | 10.75% |
| 37. | 31 dic. 2020 | $86.30 | 4.63% | 3,756.07 | 3.71% | |
| 38. | 31 ene. 2021 | $96.68 | 12.03% | 3,714.24 | -1.11% | |
| 39. | 28 feb. 2021 | $118.19 | $0.22 | 22.48% | 3,811.15 | 2.61% |
| 40. | 31 mar. 2021 | $133.60 | 13.04% | 3,972.89 | 4.24% | |
| 41. | 30 abr. 2021 | $132.71 | -0.67% | 4,181.17 | 5.24% | |
| 42. | 31 may. 2021 | $138.13 | $0.24 | 4.26% | 4,204.11 | 0.55% |
| 43. | 30 jun. 2021 | $142.40 | 3.09% | 4,297.50 | 2.22% | |
| 44. | 31 jul. 2021 | $139.93 | -1.73% | 4,395.26 | 2.27% | |
| 45. | 31 ago. 2021 | $135.13 | $0.24 | -3.26% | 4,522.68 | 2.90% |
| 46. | 30 sept. 2021 | $128.73 | -4.74% | 4,307.54 | -4.76% | |
| 47. | 31 oct. 2021 | $136.65 | 6.15% | 4,605.38 | 6.91% | |
| 48. | 30 nov. 2021 | $147.19 | $0.24 | 7.89% | 4,567.00 | -0.83% |
| 49. | 31 dic. 2021 | $157.36 | 6.91% | 4,766.18 | 4.36% | |
| 50. | 31 ene. 2022 | $138.18 | -12.19% | 4,515.55 | -5.26% | |
| 51. | 28 feb. 2022 | $134.20 | $0.24 | -2.71% | 4,373.94 | -3.14% |
| 52. | 31 mar. 2022 | $131.80 | -1.79% | 4,530.41 | 3.58% | |
| 53. | 30 abr. 2022 | $110.35 | -16.27% | 4,131.93 | -8.80% | |
| 54. | 31 may. 2022 | $117.29 | $0.26 | 6.52% | 4,132.15 | 0.01% |
| 55. | 30 jun. 2022 | $90.98 | -22.43% | 3,785.38 | -8.39% | |
| 56. | 31 jul. 2022 | $105.98 | 16.49% | 4,130.29 | 9.11% | |
| 57. | 31 ago. 2022 | $94.07 | $0.26 | -10.99% | 3,955.00 | -4.24% |
| 58. | 30 sept. 2022 | $81.93 | -12.91% | 3,585.62 | -9.34% | |
| 59. | 31 oct. 2022 | $88.29 | 7.76% | 3,871.98 | 7.99% | |
| 60. | 30 nov. 2022 | $109.60 | $0.26 | 24.43% | 4,080.11 | 5.38% |
| 61. | 31 dic. 2022 | $97.38 | -11.15% | 3,839.50 | -5.90% | |
| 62. | 31 ene. 2023 | $111.49 | 14.49% | 4,076.60 | 6.18% | |
| 63. | 28 feb. 2023 | $116.15 | $0.26 | 4.41% | 3,970.15 | -2.61% |
| 64. | 31 mar. 2023 | $122.83 | 5.75% | 4,109.31 | 3.51% | |
| 65. | 30 abr. 2023 | $113.03 | -7.98% | 4,169.48 | 1.46% | |
| 66. | 31 may. 2023 | $133.30 | $0.32 | 18.22% | 4,179.83 | 0.25% |
| 67. | 30 jun. 2023 | $144.54 | 8.43% | 4,376.86 | 4.71% | |
| 68. | 31 jul. 2023 | $151.59 | 4.88% | 4,588.96 | 4.85% | |
| 69. | 31 ago. 2023 | $152.76 | $0.32 | 0.98% | 4,507.66 | -1.77% |
| 70. | 30 sept. 2023 | $138.45 | -9.37% | 4,288.05 | -4.87% | |
| 71. | 31 oct. 2023 | $132.35 | -4.41% | 4,193.80 | -2.20% | |
| Promedio (R): | 2.00% | 0.78% | ||||
| Desviación estándar: | 11.13% | 5.13% | ||||
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 AMAT 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
Applied Materials Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RAMAT,t | RS&P 500,t | (RAMAT,t–RAMAT)2 | (RS&P 500,t–RS&P 500)2 | (RAMAT,t–RAMAT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 dic. 2017 | -3.13% | 0.98% | 26.27 | 0.04 | -1.04 |
| 2. | 31 ene. 2018 | 4.91% | 5.62% | 8.47 | 23.40 | 14.08 |
| 3. | 28 feb. 2018 | 7.57% | -3.89% | 31.04 | 21.86 | -26.05 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 sept. 2023 | -9.37% | -4.87% | 129.20 | 31.95 | 64.25 |
| 71. | 31 oct. 2023 | -4.41% | -2.20% | 41.02 | 8.87 | 19.08 |
| Total (Σ): | 8,676.22 | 1,843.80 | 2,853.21 | |||
| t | Fecha | RAMAT,t | RS&P 500,t | (RAMAT,t–RAMAT)2 | (RS&P 500,t–RS&P 500)2 | (RAMAT,t–RAMAT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 dic. 2017 | -3.13% | 0.98% | 26.27 | 0.04 | -1.04 |
| 2. | 31 ene. 2018 | 4.91% | 5.62% | 8.47 | 23.40 | 14.08 |
| 3. | 28 feb. 2018 | 7.57% | -3.89% | 31.04 | 21.86 | -26.05 |
| 4. | 31 mar. 2018 | -3.44% | -2.69% | 29.56 | 12.04 | 18.86 |
| 5. | 30 abr. 2018 | -10.68% | 0.27% | 160.79 | 0.26 | 6.45 |
| 6. | 31 may. 2018 | 2.64% | 2.16% | 0.41 | 1.90 | 0.88 |
| 7. | 30 jun. 2018 | -9.04% | 0.48% | 121.84 | 0.09 | 3.27 |
| 8. | 31 jul. 2018 | 5.28% | 3.60% | 10.78 | 7.96 | 9.26 |
| 9. | 31 ago. 2018 | -11.12% | 3.03% | 172.23 | 5.04 | -29.47 |
| 10. | 30 sept. 2018 | -10.16% | 0.43% | 147.79 | 0.12 | 4.27 |
| 11. | 31 oct. 2018 | -14.93% | -6.94% | 286.55 | 59.62 | 130.70 |
| 12. | 30 nov. 2018 | 13.99% | 1.79% | 143.79 | 1.01 | 12.05 |
| 13. | 31 dic. 2018 | -12.18% | -9.18% | 200.99 | 99.17 | 141.18 |
| 14. | 31 ene. 2019 | 19.36% | 7.87% | 301.57 | 50.24 | 123.08 |
| 15. | 28 feb. 2019 | -1.38% | 2.97% | 11.43 | 4.81 | -7.41 |
| 16. | 31 mar. 2019 | 3.44% | 1.79% | 2.09 | 1.02 | 1.46 |
| 17. | 30 abr. 2019 | 11.12% | 3.93% | 83.19 | 9.93 | 28.74 |
| 18. | 31 may. 2019 | -11.73% | -6.58% | 188.52 | 54.15 | 101.03 |
| 19. | 30 jun. 2019 | 16.08% | 6.89% | 198.18 | 37.36 | 86.05 |
| 20. | 31 jul. 2019 | 9.93% | 1.31% | 62.92 | 0.28 | 4.22 |
| 21. | 31 ago. 2019 | -2.31% | -1.81% | 18.56 | 6.71 | 11.16 |
| 22. | 30 sept. 2019 | 3.92% | 1.72% | 3.67 | 0.88 | 1.80 |
| 23. | 31 oct. 2019 | 8.74% | 2.04% | 45.41 | 1.59 | 8.51 |
| 24. | 30 nov. 2019 | 7.10% | 3.40% | 25.97 | 6.89 | 13.37 |
| 25. | 31 dic. 2019 | 5.42% | 2.86% | 11.73 | 4.32 | 7.12 |
| 26. | 31 ene. 2020 | -5.00% | -0.16% | 48.94 | 0.89 | 6.60 |
| 27. | 29 feb. 2020 | 0.59% | -8.41% | 2.00 | 84.49 | 12.98 |
| 28. | 31 mar. 2020 | -21.16% | -12.51% | 536.48 | 176.70 | 307.89 |
| 29. | 30 abr. 2020 | 8.42% | 12.68% | 41.29 | 141.70 | 76.49 |
| 30. | 31 may. 2020 | 13.53% | 4.53% | 132.89 | 14.04 | 43.20 |
| 31. | 30 jun. 2020 | 7.60% | 1.84% | 31.38 | 1.12 | 5.93 |
| 32. | 31 jul. 2020 | 6.42% | 5.51% | 19.53 | 22.37 | 20.90 |
| 33. | 31 ago. 2020 | -3.90% | 7.01% | 34.82 | 38.76 | -36.74 |
| 34. | 30 sept. 2020 | -3.49% | -3.92% | 30.13 | 22.12 | 25.82 |
| 35. | 31 oct. 2020 | -0.37% | -2.77% | 5.61 | 12.58 | 8.40 |
| 36. | 30 nov. 2020 | 39.63% | 10.75% | 1,415.74 | 99.48 | 375.28 |
| 37. | 31 dic. 2020 | 4.63% | 3.71% | 6.93 | 8.59 | 7.72 |
| 38. | 31 ene. 2021 | 12.03% | -1.11% | 100.58 | 3.59 | -19.00 |
| 39. | 28 feb. 2021 | 22.48% | 2.61% | 419.32 | 3.34 | 37.44 |
| 40. | 31 mar. 2021 | 13.04% | 4.24% | 121.87 | 11.99 | 38.23 |
| 41. | 30 abr. 2021 | -0.67% | 5.24% | 7.10 | 19.91 | -11.89 |
| 42. | 31 may. 2021 | 4.26% | 0.55% | 5.13 | 0.05 | -0.53 |
| 43. | 30 jun. 2021 | 3.09% | 2.22% | 1.19 | 2.08 | 1.57 |
| 44. | 31 jul. 2021 | -1.73% | 2.27% | 13.94 | 2.23 | -5.58 |
| 45. | 31 ago. 2021 | -3.26% | 2.90% | 27.64 | 4.49 | -11.14 |
| 46. | 30 sept. 2021 | -4.74% | -4.76% | 45.36 | 30.67 | 37.30 |
| 47. | 31 oct. 2021 | 6.15% | 6.91% | 17.25 | 37.62 | 25.48 |
| 48. | 30 nov. 2021 | 7.89% | -0.83% | 34.69 | 2.61 | -9.51 |
| 49. | 31 dic. 2021 | 6.91% | 4.36% | 24.11 | 12.82 | 17.58 |
| 50. | 31 ene. 2022 | -12.19% | -5.26% | 201.29 | 36.47 | 85.68 |
| 51. | 28 feb. 2022 | -2.71% | -3.14% | 22.14 | 15.34 | 18.43 |
| 52. | 31 mar. 2022 | -1.79% | 3.58% | 14.34 | 7.82 | -10.59 |
| 53. | 30 abr. 2022 | -16.27% | -8.80% | 333.92 | 91.71 | 175.00 |
| 54. | 31 may. 2022 | 6.52% | 0.01% | 20.48 | 0.60 | -3.51 |
| 55. | 30 jun. 2022 | -22.43% | -8.39% | 596.85 | 84.14 | 224.09 |
| 56. | 31 jul. 2022 | 16.49% | 9.11% | 209.91 | 69.40 | 120.70 |
| 57. | 31 ago. 2022 | -10.99% | -4.24% | 168.78 | 25.25 | 65.28 |
| 58. | 30 sept. 2022 | -12.91% | -9.34% | 222.13 | 102.42 | 150.84 |
| 59. | 31 oct. 2022 | 7.76% | 7.99% | 33.22 | 51.92 | 41.53 |
| 60. | 30 nov. 2022 | 24.43% | 5.38% | 503.19 | 21.11 | 103.06 |
| 61. | 31 dic. 2022 | -11.15% | -5.90% | 172.88 | 44.59 | 87.80 |
| 62. | 31 ene. 2023 | 14.49% | 6.18% | 156.02 | 29.10 | 67.38 |
| 63. | 28 feb. 2023 | 4.41% | -2.61% | 5.83 | 11.51 | -8.19 |
| 64. | 31 mar. 2023 | 5.75% | 3.51% | 14.08 | 7.42 | 10.22 |
| 65. | 30 abr. 2023 | -7.98% | 1.46% | 99.55 | 0.47 | -6.82 |
| 66. | 31 may. 2023 | 18.22% | 0.25% | 263.01 | 0.28 | -8.64 |
| 67. | 30 jun. 2023 | 8.43% | 4.71% | 41.39 | 15.47 | 25.30 |
| 68. | 31 jul. 2023 | 4.88% | 4.85% | 8.29 | 16.53 | 11.70 |
| 69. | 31 ago. 2023 | 0.98% | -1.77% | 1.03 | 6.51 | 2.59 |
| 70. | 30 sept. 2023 | -9.37% | -4.87% | 129.20 | 31.95 | 64.25 |
| 71. | 31 oct. 2023 | -4.41% | -2.20% | 41.02 | 8.87 | 19.08 |
| Total (Σ): | 8,676.22 | 1,843.80 | 2,853.21 | |||
Mostrar todo
VarianzaAMAT = Σ(RAMAT,t–RAMAT)2 ÷ (71 – 1)
= 8,676.22 ÷ (71 – 1)
= 123.95
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,843.80 ÷ (71 – 1)
= 26.34
CovarianzaAMAT, S&P 500 = Σ(RAMAT,t–RAMAT)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,853.21 ÷ (71 – 1)
= 40.76
Estimación sistemática del riesgo (β)
| VarianzaAMAT | 123.95 |
| VarianzaS&P 500 | 26.34 |
| CovarianzaAMAT, S&P 500 | 40.76 |
| Coeficiente de correlaciónAMAT, S&P 5001 | 0.71 |
| βAMAT2 | 1.55 |
| αAMAT3 | 0.79% |
Cálculos
1 Coeficiente de correlaciónAMAT, S&P 500
= CovarianzaAMAT, S&P 500 ÷ (Desviación estándarAMAT × Desviación estándarS&P 500)
= 40.76 ÷ (11.13% × 5.13%)
= 0.71
2 βAMAT
= CovarianzaAMAT, S&P 500 ÷ VarianzaS&P 500
= 40.76 ÷ 26.34
= 1.55
3 αAMAT
= PromedioAMAT – βAMAT × PromedioS&P 500
= 2.00% – 1.55 × 0.78%
= 0.79%
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 Applied acciones ordinarias | βAMAT | 1.55 |
| Tasa de rendimiento esperada de las acciones ordinarias aplicadas3 | E(RAMAT) | 18.78% |
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(RAMAT) = RF + βAMAT [E(RM) – RF]
= 4.67% + 1.55 [13.79% – 4.67%]
= 18.78%