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 Synopsys.
Tasas de retorno
Synopsys Inc., tasas mensuales de retorno
| Synopsys Inc. (SNPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioSNPS,t1 | DividendoSNPS,t1 | RSNPS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 nov. 2017 | $90.38 | 2,647.58 | ||||
| 1. | 31 dic. 2017 | $85.24 | -5.69% | 2,673.61 | 0.98% | |
| 2. | 31 ene. 2018 | $92.61 | 8.65% | 2,823.81 | 5.62% | |
| 3. | 28 feb. 2018 | $84.67 | -8.57% | 2,713.83 | -3.89% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 sept. 2023 | $458.97 | 0.02% | 4,288.05 | -4.87% | |
| 71. | 31 oct. 2023 | $469.44 | 2.28% | 4,193.80 | -2.20% | |
| Promedio (R): | 2.68% | 0.78% | ||||
| Desviación estándar: | 8.38% | 5.13% | ||||
| Synopsys Inc. (SNPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioSNPS,t1 | DividendoSNPS,t1 | RSNPS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 nov. 2017 | $90.38 | 2,647.58 | ||||
| 1. | 31 dic. 2017 | $85.24 | -5.69% | 2,673.61 | 0.98% | |
| 2. | 31 ene. 2018 | $92.61 | 8.65% | 2,823.81 | 5.62% | |
| 3. | 28 feb. 2018 | $84.67 | -8.57% | 2,713.83 | -3.89% | |
| 4. | 31 mar. 2018 | $83.24 | -1.69% | 2,640.87 | -2.69% | |
| 5. | 30 abr. 2018 | $85.51 | 2.73% | 2,648.05 | 0.27% | |
| 6. | 31 may. 2018 | $88.07 | 2.99% | 2,705.27 | 2.16% | |
| 7. | 30 jun. 2018 | $85.57 | -2.84% | 2,718.37 | 0.48% | |
| 8. | 31 jul. 2018 | $89.43 | 4.51% | 2,816.29 | 3.60% | |
| 9. | 31 ago. 2018 | $102.14 | 14.21% | 2,901.52 | 3.03% | |
| 10. | 30 sept. 2018 | $98.61 | -3.46% | 2,913.98 | 0.43% | |
| 11. | 31 oct. 2018 | $89.53 | -9.21% | 2,711.74 | -6.94% | |
| 12. | 30 nov. 2018 | $91.94 | 2.69% | 2,760.17 | 1.79% | |
| 13. | 31 dic. 2018 | $84.24 | -8.38% | 2,506.85 | -9.18% | |
| 14. | 31 ene. 2019 | $93.35 | 10.81% | 2,704.10 | 7.87% | |
| 15. | 28 feb. 2019 | $101.68 | 8.92% | 2,784.49 | 2.97% | |
| 16. | 31 mar. 2019 | $115.15 | 13.25% | 2,834.40 | 1.79% | |
| 17. | 30 abr. 2019 | $121.08 | 5.15% | 2,945.83 | 3.93% | |
| 18. | 31 may. 2019 | $116.44 | -3.83% | 2,752.06 | -6.58% | |
| 19. | 30 jun. 2019 | $128.69 | 10.52% | 2,941.76 | 6.89% | |
| 20. | 31 jul. 2019 | $132.76 | 3.16% | 2,980.38 | 1.31% | |
| 21. | 31 ago. 2019 | $141.81 | 6.82% | 2,926.46 | -1.81% | |
| 22. | 30 sept. 2019 | $137.25 | -3.22% | 2,976.74 | 1.72% | |
| 23. | 31 oct. 2019 | $135.75 | -1.09% | 3,037.56 | 2.04% | |
| 24. | 30 nov. 2019 | $141.04 | 3.90% | 3,140.98 | 3.40% | |
| 25. | 31 dic. 2019 | $139.20 | -1.30% | 3,230.78 | 2.86% | |
| 26. | 31 ene. 2020 | $147.51 | 5.97% | 3,225.52 | -0.16% | |
| 27. | 29 feb. 2020 | $137.93 | -6.49% | 2,954.22 | -8.41% | |
| 28. | 31 mar. 2020 | $128.79 | -6.63% | 2,584.59 | -12.51% | |
| 29. | 30 abr. 2020 | $157.12 | 22.00% | 2,912.43 | 12.68% | |
| 30. | 31 may. 2020 | $180.91 | 15.14% | 3,044.31 | 4.53% | |
| 31. | 30 jun. 2020 | $195.00 | 7.79% | 3,100.29 | 1.84% | |
| 32. | 31 jul. 2020 | $199.22 | 2.16% | 3,271.12 | 5.51% | |
| 33. | 31 ago. 2020 | $221.30 | 11.08% | 3,500.31 | 7.01% | |
| 34. | 30 sept. 2020 | $213.98 | -3.31% | 3,363.00 | -3.92% | |
| 35. | 31 oct. 2020 | $213.86 | -0.06% | 3,269.96 | -2.77% | |
| 36. | 30 nov. 2020 | $227.50 | 6.38% | 3,621.63 | 10.75% | |
| 37. | 31 dic. 2020 | $259.24 | 13.95% | 3,756.07 | 3.71% | |
| 38. | 31 ene. 2021 | $255.45 | -1.46% | 3,714.24 | -1.11% | |
| 39. | 28 feb. 2021 | $245.21 | -4.01% | 3,811.15 | 2.61% | |
| 40. | 31 mar. 2021 | $247.78 | 1.05% | 3,972.89 | 4.24% | |
| 41. | 30 abr. 2021 | $247.06 | -0.29% | 4,181.17 | 5.24% | |
| 42. | 31 may. 2021 | $254.34 | 2.95% | 4,204.11 | 0.55% | |
| 43. | 30 jun. 2021 | $275.79 | 8.43% | 4,297.50 | 2.22% | |
| 44. | 31 jul. 2021 | $287.99 | 4.42% | 4,395.26 | 2.27% | |
| 45. | 31 ago. 2021 | $332.24 | 15.37% | 4,522.68 | 2.90% | |
| 46. | 30 sept. 2021 | $299.41 | -9.88% | 4,307.54 | -4.76% | |
| 47. | 31 oct. 2021 | $333.18 | 11.28% | 4,605.38 | 6.91% | |
| 48. | 30 nov. 2021 | $341.00 | 2.35% | 4,567.00 | -0.83% | |
| 49. | 31 dic. 2021 | $368.50 | 8.06% | 4,766.18 | 4.36% | |
| 50. | 31 ene. 2022 | $310.50 | -15.74% | 4,515.55 | -5.26% | |
| 51. | 28 feb. 2022 | $312.39 | 0.61% | 4,373.94 | -3.14% | |
| 52. | 31 mar. 2022 | $333.27 | 6.68% | 4,530.41 | 3.58% | |
| 53. | 30 abr. 2022 | $286.79 | -13.95% | 4,131.93 | -8.80% | |
| 54. | 31 may. 2022 | $319.20 | 11.30% | 4,132.15 | 0.01% | |
| 55. | 30 jun. 2022 | $303.70 | -4.86% | 3,785.38 | -8.39% | |
| 56. | 31 jul. 2022 | $367.50 | 21.01% | 4,130.29 | 9.11% | |
| 57. | 31 ago. 2022 | $346.02 | -5.84% | 3,955.00 | -4.24% | |
| 58. | 30 sept. 2022 | $305.51 | -11.71% | 3,585.62 | -9.34% | |
| 59. | 31 oct. 2022 | $292.55 | -4.24% | 3,871.98 | 7.99% | |
| 60. | 30 nov. 2022 | $339.54 | 16.06% | 4,080.11 | 5.38% | |
| 61. | 31 dic. 2022 | $319.29 | -5.96% | 3,839.50 | -5.90% | |
| 62. | 31 ene. 2023 | $353.75 | 10.79% | 4,076.60 | 6.18% | |
| 63. | 28 feb. 2023 | $363.76 | 2.83% | 3,970.15 | -2.61% | |
| 64. | 31 mar. 2023 | $386.25 | 6.18% | 4,109.31 | 3.51% | |
| 65. | 30 abr. 2023 | $371.32 | -3.87% | 4,169.48 | 1.46% | |
| 66. | 31 may. 2023 | $454.96 | 22.53% | 4,179.83 | 0.25% | |
| 67. | 30 jun. 2023 | $435.41 | -4.30% | 4,376.86 | 4.71% | |
| 68. | 31 jul. 2023 | $451.80 | 3.76% | 4,588.96 | 4.85% | |
| 69. | 31 ago. 2023 | $458.89 | 1.57% | 4,507.66 | -1.77% | |
| 70. | 30 sept. 2023 | $458.97 | 0.02% | 4,288.05 | -4.87% | |
| 71. | 31 oct. 2023 | $469.44 | 2.28% | 4,193.80 | -2.20% | |
| Promedio (R): | 2.68% | 0.78% | ||||
| Desviación estándar: | 8.38% | 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 SNPS 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
Synopsys Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RSNPS,t | RS&P 500,t | (RSNPS,t–RSNPS)2 | (RS&P 500,t–RS&P 500)2 | (RSNPS,t–RSNPS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 dic. 2017 | -5.69% | 0.98% | 70.05 | 0.04 | -1.69 |
| 2. | 31 ene. 2018 | 8.65% | 5.62% | 35.57 | 23.40 | 28.85 |
| 3. | 28 feb. 2018 | -8.57% | -3.89% | 126.70 | 21.86 | 52.63 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 sept. 2023 | 0.02% | -4.87% | 7.10 | 31.95 | 15.06 |
| 71. | 31 oct. 2023 | 2.28% | -2.20% | 0.16 | 8.87 | 1.20 |
| Total (Σ): | 4,909.89 | 1,843.80 | 2,089.57 | |||
| t | Fecha | RSNPS,t | RS&P 500,t | (RSNPS,t–RSNPS)2 | (RS&P 500,t–RS&P 500)2 | (RSNPS,t–RSNPS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 dic. 2017 | -5.69% | 0.98% | 70.05 | 0.04 | -1.69 |
| 2. | 31 ene. 2018 | 8.65% | 5.62% | 35.57 | 23.40 | 28.85 |
| 3. | 28 feb. 2018 | -8.57% | -3.89% | 126.70 | 21.86 | 52.63 |
| 4. | 31 mar. 2018 | -1.69% | -2.69% | 19.11 | 12.04 | 15.17 |
| 5. | 30 abr. 2018 | 2.73% | 0.27% | 0.00 | 0.26 | -0.02 |
| 6. | 31 may. 2018 | 2.99% | 2.16% | 0.10 | 1.90 | 0.43 |
| 7. | 30 jun. 2018 | -2.84% | 0.48% | 30.48 | 0.09 | 1.64 |
| 8. | 31 jul. 2018 | 4.51% | 3.60% | 3.34 | 7.96 | 5.16 |
| 9. | 31 ago. 2018 | 14.21% | 3.03% | 132.93 | 5.04 | 25.89 |
| 10. | 30 sept. 2018 | -3.46% | 0.43% | 37.68 | 0.12 | 2.16 |
| 11. | 31 oct. 2018 | -9.21% | -6.94% | 141.38 | 59.62 | 91.81 |
| 12. | 30 nov. 2018 | 2.69% | 1.79% | 0.00 | 1.01 | 0.01 |
| 13. | 31 dic. 2018 | -8.38% | -9.18% | 122.27 | 99.17 | 110.12 |
| 14. | 31 ene. 2019 | 10.81% | 7.87% | 66.13 | 50.24 | 57.64 |
| 15. | 28 feb. 2019 | 8.92% | 2.97% | 38.95 | 4.81 | 13.68 |
| 16. | 31 mar. 2019 | 13.25% | 1.79% | 111.62 | 1.02 | 10.69 |
| 17. | 30 abr. 2019 | 5.15% | 3.93% | 6.09 | 9.93 | 7.77 |
| 18. | 31 may. 2019 | -3.83% | -6.58% | 42.44 | 54.15 | 47.94 |
| 19. | 30 jun. 2019 | 10.52% | 6.89% | 61.43 | 37.36 | 47.91 |
| 20. | 31 jul. 2019 | 3.16% | 1.31% | 0.23 | 0.28 | 0.26 |
| 21. | 31 ago. 2019 | 6.82% | -1.81% | 17.09 | 6.71 | -10.71 |
| 22. | 30 sept. 2019 | -3.22% | 1.72% | 34.79 | 0.88 | -5.53 |
| 23. | 31 oct. 2019 | -1.09% | 2.04% | 14.25 | 1.59 | -4.77 |
| 24. | 30 nov. 2019 | 3.90% | 3.40% | 1.47 | 6.89 | 3.19 |
| 25. | 31 dic. 2019 | -1.30% | 2.86% | 15.90 | 4.32 | -8.29 |
| 26. | 31 ene. 2020 | 5.97% | -0.16% | 10.81 | 0.89 | -3.10 |
| 27. | 29 feb. 2020 | -6.49% | -8.41% | 84.22 | 84.49 | 84.35 |
| 28. | 31 mar. 2020 | -6.63% | -12.51% | 86.66 | 176.70 | 123.74 |
| 29. | 30 abr. 2020 | 22.00% | 12.68% | 373.05 | 141.70 | 229.91 |
| 30. | 31 may. 2020 | 15.14% | 4.53% | 155.22 | 14.04 | 46.69 |
| 31. | 30 jun. 2020 | 7.79% | 1.84% | 26.07 | 1.12 | 5.40 |
| 32. | 31 jul. 2020 | 2.16% | 5.51% | 0.27 | 22.37 | -2.45 |
| 33. | 31 ago. 2020 | 11.08% | 7.01% | 70.57 | 38.76 | 52.30 |
| 34. | 30 sept. 2020 | -3.31% | -3.92% | 35.88 | 22.12 | 28.18 |
| 35. | 31 oct. 2020 | -0.06% | -2.77% | 7.50 | 12.58 | 9.71 |
| 36. | 30 nov. 2020 | 6.38% | 10.75% | 13.66 | 99.48 | 36.86 |
| 37. | 31 dic. 2020 | 13.95% | 3.71% | 126.99 | 8.59 | 33.03 |
| 38. | 31 ene. 2021 | -1.46% | -1.11% | 17.18 | 3.59 | 7.85 |
| 39. | 28 feb. 2021 | -4.01% | 2.61% | 44.77 | 3.34 | -12.23 |
| 40. | 31 mar. 2021 | 1.05% | 4.24% | 2.67 | 11.99 | -5.66 |
| 41. | 30 abr. 2021 | -0.29% | 5.24% | 8.84 | 19.91 | -13.27 |
| 42. | 31 may. 2021 | 2.95% | 0.55% | 0.07 | 0.05 | -0.06 |
| 43. | 30 jun. 2021 | 8.43% | 2.22% | 33.08 | 2.08 | 8.29 |
| 44. | 31 jul. 2021 | 4.42% | 2.27% | 3.03 | 2.23 | 2.60 |
| 45. | 31 ago. 2021 | 15.37% | 2.90% | 160.85 | 4.49 | 26.87 |
| 46. | 30 sept. 2021 | -9.88% | -4.76% | 157.85 | 30.67 | 69.57 |
| 47. | 31 oct. 2021 | 11.28% | 6.91% | 73.90 | 37.62 | 52.73 |
| 48. | 30 nov. 2021 | 2.35% | -0.83% | 0.11 | 2.61 | 0.54 |
| 49. | 31 dic. 2021 | 8.06% | 4.36% | 28.97 | 12.82 | 19.27 |
| 50. | 31 ene. 2022 | -15.74% | -5.26% | 339.37 | 36.47 | 111.26 |
| 51. | 28 feb. 2022 | 0.61% | -3.14% | 4.30 | 15.34 | 8.12 |
| 52. | 31 mar. 2022 | 6.68% | 3.58% | 16.01 | 7.82 | 11.19 |
| 53. | 30 abr. 2022 | -13.95% | -8.80% | 276.53 | 91.71 | 159.25 |
| 54. | 31 may. 2022 | 11.30% | 0.01% | 74.28 | 0.60 | -6.68 |
| 55. | 30 jun. 2022 | -4.86% | -8.39% | 56.83 | 84.14 | 69.15 |
| 56. | 31 jul. 2022 | 21.01% | 9.11% | 335.81 | 69.40 | 152.66 |
| 57. | 31 ago. 2022 | -5.84% | -4.24% | 72.72 | 25.25 | 42.85 |
| 58. | 30 sept. 2022 | -11.71% | -9.34% | 207.07 | 102.42 | 145.63 |
| 59. | 31 oct. 2022 | -4.24% | 7.99% | 47.95 | 51.92 | -49.90 |
| 60. | 30 nov. 2022 | 16.06% | 5.38% | 179.02 | 21.11 | 61.47 |
| 61. | 31 dic. 2022 | -5.96% | -5.90% | 74.76 | 44.59 | 57.74 |
| 62. | 31 ene. 2023 | 10.79% | 6.18% | 65.78 | 29.10 | 43.75 |
| 63. | 28 feb. 2023 | 2.83% | -2.61% | 0.02 | 11.51 | -0.50 |
| 64. | 31 mar. 2023 | 6.18% | 3.51% | 12.25 | 7.42 | 9.54 |
| 65. | 30 abr. 2023 | -3.87% | 1.46% | 42.87 | 0.47 | -4.48 |
| 66. | 31 may. 2023 | 22.53% | 0.25% | 393.73 | 0.28 | -10.57 |
| 67. | 30 jun. 2023 | -4.30% | 4.71% | 48.71 | 15.47 | -27.45 |
| 68. | 31 jul. 2023 | 3.76% | 4.85% | 1.17 | 16.53 | 4.40 |
| 69. | 31 ago. 2023 | 1.57% | -1.77% | 1.24 | 6.51 | 2.84 |
| 70. | 30 sept. 2023 | 0.02% | -4.87% | 7.10 | 31.95 | 15.06 |
| 71. | 31 oct. 2023 | 2.28% | -2.20% | 0.16 | 8.87 | 1.20 |
| Total (Σ): | 4,909.89 | 1,843.80 | 2,089.57 | |||
Mostrar todo
VarianzaSNPS = Σ(RSNPS,t–RSNPS)2 ÷ (71 – 1)
= 4,909.89 ÷ (71 – 1)
= 70.14
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,843.80 ÷ (71 – 1)
= 26.34
CovarianzaSNPS, S&P 500 = Σ(RSNPS,t–RSNPS)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,089.57 ÷ (71 – 1)
= 29.85
Estimación sistemática del riesgo (β)
| VarianzaSNPS | 70.14 |
| VarianzaS&P 500 | 26.34 |
| CovarianzaSNPS, S&P 500 | 29.85 |
| Coeficiente de correlaciónSNPS, S&P 5001 | 0.69 |
| βSNPS2 | 1.13 |
| αSNPS3 | 1.80% |
Cálculos
1 Coeficiente de correlaciónSNPS, S&P 500
= CovarianzaSNPS, S&P 500 ÷ (Desviación estándarSNPS × Desviación estándarS&P 500)
= 29.85 ÷ (8.38% × 5.13%)
= 0.69
2 βSNPS
= CovarianzaSNPS, S&P 500 ÷ VarianzaS&P 500
= 29.85 ÷ 26.34
= 1.13
3 αSNPS
= PromedioSNPS – βSNPS × PromedioS&P 500
= 2.68% – 1.13 × 0.78%
= 1.80%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.56% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.77% |
| Riesgo sistemático de Synopsys acciones ordinarias | βSNPS | 1.13 |
| Tasa de rendimiento esperada de las acciones ordinarias de Synopsys3 | E(RSNPS) | 14.99% |
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(RSNPS) = RF + βSNPS [E(RM) – RF]
= 4.56% + 1.13 [13.77% – 4.56%]
= 14.99%