Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de Palo Alto Networks.
Tasas de retorno
Palo Alto Networks Inc., tasas mensuales de retorno
| Palo Alto Networks Inc. (PANW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPANW,t1 | DividendoPANW,t1 | RPANW,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ago. 2018 | $77.05 | 2,901.52 | ||||
| 1. | 30 sept. 2018 | $75.09 | -2.54% | 2,913.98 | 0.43% | |
| 2. | 31 oct. 2018 | $61.01 | -18.75% | 2,711.74 | -6.94% | |
| 3. | 30 nov. 2018 | $57.65 | -5.51% | 2,760.17 | 1.79% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 jun. 2024 | $339.01 | 14.95% | 5,460.48 | 3.47% | |
| 71. | 31 jul. 2024 | $324.73 | -4.21% | 5,522.30 | 1.13% | |
| Promedio (R): | 2.63% | 1.05% | ||||
| Desviación estándar: | 11.00% | 5.24% | ||||
| Palo Alto Networks Inc. (PANW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPANW,t1 | DividendoPANW,t1 | RPANW,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ago. 2018 | $77.05 | 2,901.52 | ||||
| 1. | 30 sept. 2018 | $75.09 | -2.54% | 2,913.98 | 0.43% | |
| 2. | 31 oct. 2018 | $61.01 | -18.75% | 2,711.74 | -6.94% | |
| 3. | 30 nov. 2018 | $57.65 | -5.51% | 2,760.17 | 1.79% | |
| 4. | 31 dic. 2018 | $62.78 | 8.90% | 2,506.85 | -9.18% | |
| 5. | 31 ene. 2019 | $71.61 | 14.06% | 2,704.10 | 7.87% | |
| 6. | 28 feb. 2019 | $82.09 | 14.63% | 2,784.49 | 2.97% | |
| 7. | 31 mar. 2019 | $80.96 | -1.38% | 2,834.40 | 1.79% | |
| 8. | 30 abr. 2019 | $82.94 | 2.45% | 2,945.83 | 3.93% | |
| 9. | 31 may. 2019 | $66.71 | -19.57% | 2,752.06 | -6.58% | |
| 10. | 30 jun. 2019 | $67.92 | 1.81% | 2,941.76 | 6.89% | |
| 11. | 31 jul. 2019 | $75.51 | 11.17% | 2,980.38 | 1.31% | |
| 12. | 31 ago. 2019 | $67.87 | -10.12% | 2,926.46 | -1.81% | |
| 13. | 30 sept. 2019 | $67.94 | 0.10% | 2,976.74 | 1.72% | |
| 14. | 31 oct. 2019 | $75.80 | 11.57% | 3,037.56 | 2.04% | |
| 15. | 30 nov. 2019 | $75.74 | -0.08% | 3,140.98 | 3.40% | |
| 16. | 31 dic. 2019 | $77.08 | 1.77% | 3,230.78 | 2.86% | |
| 17. | 31 ene. 2020 | $78.26 | 1.53% | 3,225.52 | -0.16% | |
| 18. | 29 feb. 2020 | $61.54 | -21.36% | 2,954.22 | -8.41% | |
| 19. | 31 mar. 2020 | $54.65 | -11.20% | 2,584.59 | -12.51% | |
| 20. | 30 abr. 2020 | $65.50 | 19.85% | 2,912.43 | 12.68% | |
| 21. | 31 may. 2020 | $78.42 | 19.73% | 3,044.31 | 4.53% | |
| 22. | 30 jun. 2020 | $76.56 | -2.37% | 3,100.29 | 1.84% | |
| 23. | 31 jul. 2020 | $85.31 | 11.43% | 3,271.12 | 5.51% | |
| 24. | 31 ago. 2020 | $85.80 | 0.57% | 3,500.31 | 7.01% | |
| 25. | 30 sept. 2020 | $81.58 | -4.92% | 3,363.00 | -3.92% | |
| 26. | 31 oct. 2020 | $73.73 | -9.62% | 3,269.96 | -2.77% | |
| 27. | 30 nov. 2020 | $97.97 | 32.88% | 3,621.63 | 10.75% | |
| 28. | 31 dic. 2020 | $118.46 | 20.91% | 3,756.07 | 3.71% | |
| 29. | 31 ene. 2021 | $116.92 | -1.30% | 3,714.24 | -1.11% | |
| 30. | 28 feb. 2021 | $119.44 | 2.16% | 3,811.15 | 2.61% | |
| 31. | 31 mar. 2021 | $107.35 | -10.12% | 3,972.89 | 4.24% | |
| 32. | 30 abr. 2021 | $117.80 | 9.73% | 4,181.17 | 5.24% | |
| 33. | 31 may. 2021 | $121.08 | 2.78% | 4,204.11 | 0.55% | |
| 34. | 30 jun. 2021 | $123.68 | 2.15% | 4,297.50 | 2.22% | |
| 35. | 31 jul. 2021 | $133.02 | 7.55% | 4,395.26 | 2.27% | |
| 36. | 31 ago. 2021 | $153.68 | 15.53% | 4,522.68 | 2.90% | |
| 37. | 30 sept. 2021 | $159.67 | 3.90% | 4,307.54 | -4.76% | |
| 38. | 31 oct. 2021 | $169.70 | 6.28% | 4,605.38 | 6.91% | |
| 39. | 30 nov. 2021 | $182.31 | 7.43% | 4,567.00 | -0.83% | |
| 40. | 31 dic. 2021 | $185.59 | 1.80% | 4,766.18 | 4.36% | |
| 41. | 31 ene. 2022 | $172.47 | -7.07% | 4,515.55 | -5.26% | |
| 42. | 28 feb. 2022 | $198.08 | 14.85% | 4,373.94 | -3.14% | |
| 43. | 31 mar. 2022 | $207.50 | 4.76% | 4,530.41 | 3.58% | |
| 44. | 30 abr. 2022 | $187.09 | -9.84% | 4,131.93 | -8.80% | |
| 45. | 31 may. 2022 | $167.59 | -10.42% | 4,132.15 | 0.01% | |
| 46. | 30 jun. 2022 | $164.65 | -1.75% | 3,785.38 | -8.39% | |
| 47. | 31 jul. 2022 | $166.37 | 1.04% | 4,130.29 | 9.11% | |
| 48. | 31 ago. 2022 | $185.60 | 11.56% | 3,955.00 | -4.24% | |
| 49. | 30 sept. 2022 | $163.79 | -11.75% | 3,585.62 | -9.34% | |
| 50. | 31 oct. 2022 | $171.59 | 4.76% | 3,871.98 | 7.99% | |
| 51. | 30 nov. 2022 | $169.90 | -0.98% | 4,080.11 | 5.38% | |
| 52. | 31 dic. 2022 | $139.54 | -17.87% | 3,839.50 | -5.90% | |
| 53. | 31 ene. 2023 | $158.64 | 13.69% | 4,076.60 | 6.18% | |
| 54. | 28 feb. 2023 | $188.37 | 18.74% | 3,970.15 | -2.61% | |
| 55. | 31 mar. 2023 | $199.74 | 6.04% | 4,109.31 | 3.51% | |
| 56. | 30 abr. 2023 | $182.46 | -8.65% | 4,169.48 | 1.46% | |
| 57. | 31 may. 2023 | $213.39 | 16.95% | 4,179.83 | 0.25% | |
| 58. | 30 jun. 2023 | $255.51 | 19.74% | 4,376.86 | 4.71% | |
| 59. | 31 jul. 2023 | $249.96 | -2.17% | 4,588.96 | 4.85% | |
| 60. | 31 ago. 2023 | $243.30 | -2.66% | 4,507.66 | -1.77% | |
| 61. | 30 sept. 2023 | $234.44 | -3.64% | 4,288.05 | -4.87% | |
| 62. | 31 oct. 2023 | $243.02 | 3.66% | 4,193.80 | -2.20% | |
| 63. | 30 nov. 2023 | $295.09 | 21.43% | 4,567.80 | 8.92% | |
| 64. | 31 dic. 2023 | $294.88 | -0.07% | 4,769.83 | 4.42% | |
| 65. | 31 ene. 2024 | $338.51 | 14.80% | 4,845.65 | 1.59% | |
| 66. | 29 feb. 2024 | $310.55 | -8.26% | 5,096.27 | 5.17% | |
| 67. | 31 mar. 2024 | $284.13 | -8.51% | 5,254.35 | 3.10% | |
| 68. | 30 abr. 2024 | $290.89 | 2.38% | 5,035.69 | -4.16% | |
| 69. | 31 may. 2024 | $294.91 | 1.38% | 5,277.51 | 4.80% | |
| 70. | 30 jun. 2024 | $339.01 | 14.95% | 5,460.48 | 3.47% | |
| 71. | 31 jul. 2024 | $324.73 | -4.21% | 5,522.30 | 1.13% | |
| Promedio (R): | 2.63% | 1.05% | ||||
| Desviación estándar: | 11.00% | 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 PANW 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
Palo Alto Networks Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RPANW,t | RS&P 500,t | (RPANW,t–RPANW)2 | (RS&P 500,t–RS&P 500)2 | (RPANW,t–RPANW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 sept. 2018 | -2.54% | 0.43% | 26.76 | 0.38 | 3.19 |
| 2. | 31 oct. 2018 | -18.75% | -6.94% | 457.13 | 63.79 | 170.77 |
| 3. | 30 nov. 2018 | -5.51% | 1.79% | 66.21 | 0.55 | -6.02 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 jun. 2024 | 14.95% | 3.47% | 151.88 | 5.86 | 29.83 |
| 71. | 31 jul. 2024 | -4.21% | 1.13% | 46.81 | 0.01 | -0.58 |
| Total (Σ): | 8,463.36 | 1,918.93 | 2,168.23 | |||
| t | Fecha | RPANW,t | RS&P 500,t | (RPANW,t–RPANW)2 | (RS&P 500,t–RS&P 500)2 | (RPANW,t–RPANW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 30 sept. 2018 | -2.54% | 0.43% | 26.76 | 0.38 | 3.19 |
| 2. | 31 oct. 2018 | -18.75% | -6.94% | 457.13 | 63.79 | 170.77 |
| 3. | 30 nov. 2018 | -5.51% | 1.79% | 66.21 | 0.55 | -6.02 |
| 4. | 31 dic. 2018 | 8.90% | -9.18% | 39.30 | 104.54 | -64.10 |
| 5. | 31 ene. 2019 | 14.06% | 7.87% | 130.77 | 46.54 | 78.01 |
| 6. | 28 feb. 2019 | 14.63% | 2.97% | 144.12 | 3.71 | 23.12 |
| 7. | 31 mar. 2019 | -1.38% | 1.79% | 16.05 | 0.56 | -2.99 |
| 8. | 30 abr. 2019 | 2.45% | 3.93% | 0.03 | 8.32 | -0.53 |
| 9. | 31 may. 2019 | -19.57% | -6.58% | 492.75 | 58.13 | 169.25 |
| 10. | 30 jun. 2019 | 1.81% | 6.89% | 0.67 | 34.18 | -4.77 |
| 11. | 31 jul. 2019 | 11.17% | 1.31% | 73.02 | 0.07 | 2.27 |
| 12. | 31 ago. 2019 | -10.12% | -1.81% | 162.50 | 8.16 | 36.40 |
| 13. | 30 sept. 2019 | 0.10% | 1.72% | 6.38 | 0.45 | -1.70 |
| 14. | 31 oct. 2019 | 11.57% | 2.04% | 79.91 | 0.99 | 8.91 |
| 15. | 30 nov. 2019 | -0.08% | 3.40% | 7.34 | 5.56 | -6.39 |
| 16. | 31 dic. 2019 | 1.77% | 2.86% | 0.74 | 3.28 | -1.56 |
| 17. | 31 ene. 2020 | 1.53% | -0.16% | 1.21 | 1.46 | 1.33 |
| 18. | 29 feb. 2020 | -21.36% | -8.41% | 575.73 | 89.45 | 226.93 |
| 19. | 31 mar. 2020 | -11.20% | -12.51% | 191.15 | 183.84 | 187.46 |
| 20. | 30 abr. 2020 | 19.85% | 12.68% | 296.66 | 135.44 | 200.45 |
| 21. | 31 may. 2020 | 19.73% | 4.53% | 292.26 | 12.12 | 59.52 |
| 22. | 30 jun. 2020 | -2.37% | 1.84% | 25.02 | 0.63 | -3.96 |
| 23. | 31 jul. 2020 | 11.43% | 5.51% | 77.43 | 19.92 | 39.28 |
| 24. | 31 ago. 2020 | 0.57% | 7.01% | 4.22 | 35.52 | -12.25 |
| 25. | 30 sept. 2020 | -4.92% | -3.92% | 56.97 | 24.70 | 37.51 |
| 26. | 31 oct. 2020 | -9.62% | -2.77% | 150.11 | 14.54 | 46.72 |
| 27. | 30 nov. 2020 | 32.88% | 10.75% | 914.88 | 94.24 | 293.63 |
| 28. | 31 dic. 2020 | 20.91% | 3.71% | 334.34 | 7.10 | 48.74 |
| 29. | 31 ene. 2021 | -1.30% | -1.11% | 15.44 | 4.67 | 8.49 |
| 30. | 28 feb. 2021 | 2.16% | 2.61% | 0.23 | 2.44 | -0.74 |
| 31. | 31 mar. 2021 | -10.12% | 4.24% | 162.61 | 10.22 | -40.77 |
| 32. | 30 abr. 2021 | 9.73% | 5.24% | 50.48 | 17.61 | 29.81 |
| 33. | 31 may. 2021 | 2.78% | 0.55% | 0.02 | 0.25 | -0.08 |
| 34. | 30 jun. 2021 | 2.15% | 2.22% | 0.23 | 1.38 | -0.57 |
| 35. | 31 jul. 2021 | 7.55% | 2.27% | 24.23 | 1.51 | 6.04 |
| 36. | 31 ago. 2021 | 15.53% | 2.90% | 166.46 | 3.43 | 23.90 |
| 37. | 30 sept. 2021 | 3.90% | -4.76% | 1.61 | 33.68 | -7.36 |
| 38. | 31 oct. 2021 | 6.28% | 6.91% | 13.34 | 34.43 | 21.43 |
| 39. | 30 nov. 2021 | 7.43% | -0.83% | 23.05 | 3.53 | -9.03 |
| 40. | 31 dic. 2021 | 1.80% | 4.36% | 0.69 | 10.99 | -2.75 |
| 41. | 31 ene. 2022 | -7.07% | -5.26% | 94.07 | 39.76 | 61.15 |
| 42. | 28 feb. 2022 | 14.85% | -3.14% | 149.31 | 17.50 | -51.11 |
| 43. | 31 mar. 2022 | 4.76% | 3.58% | 4.52 | 6.40 | 5.38 |
| 44. | 30 abr. 2022 | -9.84% | -8.80% | 155.40 | 96.87 | 122.69 |
| 45. | 31 may. 2022 | -10.42% | 0.01% | 170.37 | 1.08 | 13.59 |
| 46. | 30 jun. 2022 | -1.75% | -8.39% | 19.22 | 89.09 | 41.38 |
| 47. | 31 jul. 2022 | 1.04% | 9.11% | 2.51 | 65.04 | -12.78 |
| 48. | 31 ago. 2022 | 11.56% | -4.24% | 79.73 | 27.99 | -47.24 |
| 49. | 30 sept. 2022 | -11.75% | -9.34% | 206.81 | 107.87 | 149.36 |
| 50. | 31 oct. 2022 | 4.76% | 7.99% | 4.55 | 48.16 | 14.80 |
| 51. | 30 nov. 2022 | -0.98% | 5.38% | 13.07 | 18.74 | -15.65 |
| 52. | 31 dic. 2022 | -17.87% | -5.90% | 420.21 | 48.22 | 142.34 |
| 53. | 31 ene. 2023 | 13.69% | 6.18% | 122.28 | 26.30 | 56.71 |
| 54. | 28 feb. 2023 | 18.74% | -2.61% | 259.56 | 13.38 | -58.93 |
| 55. | 31 mar. 2023 | 6.04% | 3.51% | 11.60 | 6.04 | 8.37 |
| 56. | 30 abr. 2023 | -8.65% | 1.46% | 127.26 | 0.17 | -4.71 |
| 57. | 31 may. 2023 | 16.95% | 0.25% | 205.12 | 0.64 | -11.44 |
| 58. | 30 jun. 2023 | 19.74% | 4.71% | 292.71 | 13.45 | 62.74 |
| 59. | 31 jul. 2023 | -2.17% | 4.85% | 23.06 | 14.43 | -18.24 |
| 60. | 31 ago. 2023 | -2.66% | -1.77% | 28.03 | 7.94 | 14.92 |
| 61. | 30 sept. 2023 | -3.64% | -4.87% | 39.33 | 35.03 | 37.12 |
| 62. | 31 oct. 2023 | 3.66% | -2.20% | 1.06 | 10.53 | -3.34 |
| 63. | 30 nov. 2023 | 21.43% | 8.92% | 353.31 | 61.96 | 147.95 |
| 64. | 31 dic. 2023 | -0.07% | 4.42% | 7.29 | 11.40 | -9.12 |
| 65. | 31 ene. 2024 | 14.80% | 1.59% | 148.02 | 0.29 | 6.61 |
| 66. | 29 feb. 2024 | -8.26% | 5.17% | 118.58 | 17.02 | -44.92 |
| 67. | 31 mar. 2024 | -8.51% | 3.10% | 124.04 | 4.22 | -22.89 |
| 68. | 30 abr. 2024 | 2.38% | -4.16% | 0.06 | 27.13 | 1.30 |
| 69. | 31 may. 2024 | 1.38% | 4.80% | 1.56 | 14.10 | -4.69 |
| 70. | 30 jun. 2024 | 14.95% | 3.47% | 151.88 | 5.86 | 29.83 |
| 71. | 31 jul. 2024 | -4.21% | 1.13% | 46.81 | 0.01 | -0.58 |
| Total (Σ): | 8,463.36 | 1,918.93 | 2,168.23 | |||
Mostrar todo
VarianzaPANW = Σ(RPANW,t–RPANW)2 ÷ (71 – 1)
= 8,463.36 ÷ (71 – 1)
= 120.91
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,918.93 ÷ (71 – 1)
= 27.41
CovarianzaPANW, S&P 500 = Σ(RPANW,t–RPANW)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,168.23 ÷ (71 – 1)
= 30.97
Estimación sistemática del riesgo (β)
| VarianzaPANW | 120.91 |
| VarianzaS&P 500 | 27.41 |
| CovarianzaPANW, S&P 500 | 30.97 |
| Coeficiente de correlaciónPANW, S&P 5001 | 0.54 |
| βPANW2 | 1.13 |
| αPANW3 | 1.45% |
Cálculos
1 Coeficiente de correlaciónPANW, S&P 500
= CovarianzaPANW, S&P 500 ÷ (Desviación estándarPANW × Desviación estándarS&P 500)
= 30.97 ÷ (11.00% × 5.24%)
= 0.54
2 βPANW
= CovarianzaPANW, S&P 500 ÷ VarianzaS&P 500
= 30.97 ÷ 27.41
= 1.13
3 αPANW
= PromedioPANW – βPANW × PromedioS&P 500
= 2.63% – 1.13 × 1.05%
= 1.45%
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 Palo Alto Networks acciones ordinarias | βPANW | 1.13 |
| Tasa de rendimiento esperada de las acciones ordinarias de Palo Alto Networks3 | E(RPANW) | 14.97% |
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(RPANW) = RF + βPANW [E(RM) – RF]
= 4.67% + 1.13 [13.79% – 4.67%]
= 14.97%