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 Arista.
Tasas de retorno
Arista Networks Inc., tasas mensuales de retorno
| Arista Networks Inc. (ANET) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioANET,t1 | DividendoANET,t1 | RANET,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $53.70 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $71.31 | 32.79% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $78.61 | 10.24% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $78.07 | -0.69% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $219.71 | 9.65% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $235.51 | 7.19% | 4,769.83 | 4.42% | |
| Promedio (R): | 3.28% | 1.11% | ||||
| Desviación estándar: | 12.47% | 5.31% | ||||
| Arista Networks Inc. (ANET) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioANET,t1 | DividendoANET,t1 | RANET,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $53.70 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $71.31 | 32.79% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $78.61 | 10.24% | 2,834.40 | 1.79% | |
| 3. | 30 abr. 2019 | $78.07 | -0.69% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $61.15 | -21.67% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $64.90 | 6.13% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $68.36 | 5.33% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $56.65 | -17.13% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $59.73 | 5.44% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $61.14 | 2.36% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $48.78 | -20.22% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $50.85 | 4.24% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $55.83 | 9.79% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $48.28 | -13.52% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $50.64 | 4.89% | 2,584.59 | -12.51% | |
| 15. | 30 abr. 2020 | $54.83 | 8.27% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $58.37 | 6.46% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $52.51 | -10.04% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $64.94 | 23.67% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $55.86 | -13.98% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $51.73 | -7.39% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $52.22 | 0.95% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $67.68 | 29.61% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $72.64 | 7.33% | 3,756.07 | 3.71% | |
| 24. | 31 ene. 2021 | $76.89 | 5.85% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $69.96 | -9.01% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $75.47 | 7.88% | 3,972.89 | 4.24% | |
| 27. | 30 abr. 2021 | $78.79 | 4.40% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $84.85 | 7.69% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $90.58 | 6.75% | 4,297.50 | 2.22% | |
| 30. | 31 jul. 2021 | $95.10 | 4.99% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $92.38 | -2.86% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $85.91 | -7.00% | 4,307.54 | -4.76% | |
| 33. | 31 oct. 2021 | $102.42 | 19.22% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $124.06 | 21.13% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $143.75 | 15.87% | 4,766.18 | 4.36% | |
| 36. | 31 ene. 2022 | $124.31 | -13.52% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $122.73 | -1.27% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $138.98 | 13.24% | 4,530.41 | 3.58% | |
| 39. | 30 abr. 2022 | $115.57 | -16.84% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $102.28 | -11.50% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $93.74 | -8.35% | 3,785.38 | -8.39% | |
| 42. | 31 jul. 2022 | $116.63 | 24.42% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $119.88 | 2.79% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $112.89 | -5.83% | 3,585.62 | -9.34% | |
| 45. | 31 oct. 2022 | $120.86 | 7.06% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $139.30 | 15.26% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $121.35 | -12.89% | 3,839.50 | -5.90% | |
| 48. | 31 ene. 2023 | $126.02 | 3.85% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $138.70 | 10.06% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $167.86 | 21.02% | 4,109.31 | 3.51% | |
| 51. | 30 abr. 2023 | $160.16 | -4.59% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $166.34 | 3.86% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $162.06 | -2.57% | 4,376.86 | 4.71% | |
| 54. | 31 jul. 2023 | $155.09 | -4.30% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $195.23 | 25.88% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $183.93 | -5.79% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $200.37 | 8.94% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $219.71 | 9.65% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $235.51 | 7.19% | 4,769.83 | 4.42% | |
| Promedio (R): | 3.28% | 1.11% | ||||
| Desviación estándar: | 12.47% | 5.31% | ||||
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 ANET 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
Arista Networks Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RANET,t | RS&P 500,t | (RANET,t–RANET)2 | (RS&P 500,t–RS&P 500)2 | (RANET,t–RANET)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 32.79% | 2.97% | 871.03 | 3.49 | 55.10 |
| 2. | 31 mar. 2019 | 10.24% | 1.79% | 48.40 | 0.47 | 4.78 |
| 3. | 30 abr. 2019 | -0.69% | 3.93% | 15.74 | 7.98 | -11.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 9.65% | 8.92% | 40.60 | 61.03 | 49.78 |
| 59. | 31 dic. 2023 | 7.19% | 4.42% | 15.30 | 11.00 | 12.97 |
| Total (Σ): | 9,022.94 | 1,634.30 | 1,850.30 | |||
| t | Fecha | RANET,t | RS&P 500,t | (RANET,t–RANET)2 | (RS&P 500,t–RS&P 500)2 | (RANET,t–RANET)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 32.79% | 2.97% | 871.03 | 3.49 | 55.10 |
| 2. | 31 mar. 2019 | 10.24% | 1.79% | 48.40 | 0.47 | 4.78 |
| 3. | 30 abr. 2019 | -0.69% | 3.93% | 15.74 | 7.98 | -11.21 |
| 4. | 31 may. 2019 | -21.67% | -6.58% | 622.65 | 59.04 | 191.73 |
| 5. | 30 jun. 2019 | 6.13% | 6.89% | 8.14 | 33.49 | 16.51 |
| 6. | 31 jul. 2019 | 5.33% | 1.31% | 4.21 | 0.04 | 0.42 |
| 7. | 31 ago. 2019 | -17.13% | -1.81% | 416.57 | 8.50 | 59.50 |
| 8. | 30 sept. 2019 | 5.44% | 1.72% | 4.65 | 0.37 | 1.32 |
| 9. | 31 oct. 2019 | 2.36% | 2.04% | 0.85 | 0.88 | -0.86 |
| 10. | 30 nov. 2019 | -20.22% | 3.40% | 552.06 | 5.28 | -54.01 |
| 11. | 31 dic. 2019 | 4.24% | 2.86% | 0.93 | 3.07 | 1.69 |
| 12. | 31 ene. 2020 | 9.79% | -0.16% | 42.43 | 1.61 | -8.26 |
| 13. | 29 feb. 2020 | -13.52% | -8.41% | 282.35 | 90.57 | 159.91 |
| 14. | 31 mar. 2020 | 4.89% | -12.51% | 2.59 | 185.44 | -21.90 |
| 15. | 30 abr. 2020 | 8.27% | 12.68% | 24.94 | 134.06 | 57.82 |
| 16. | 31 may. 2020 | 6.46% | 4.53% | 10.09 | 11.71 | 10.87 |
| 17. | 30 jun. 2020 | -10.04% | 1.84% | 177.41 | 0.54 | -9.76 |
| 18. | 31 jul. 2020 | 23.67% | 5.51% | 415.82 | 19.40 | 89.81 |
| 19. | 31 ago. 2020 | -13.98% | 7.01% | 297.98 | 34.82 | -101.86 |
| 20. | 30 sept. 2020 | -7.39% | -3.92% | 113.92 | 25.29 | 53.67 |
| 21. | 31 oct. 2020 | 0.95% | -2.77% | 5.44 | 15.00 | 9.03 |
| 22. | 30 nov. 2020 | 29.61% | 10.75% | 693.03 | 93.10 | 254.01 |
| 23. | 31 dic. 2020 | 7.33% | 3.71% | 16.39 | 6.79 | 10.55 |
| 24. | 31 ene. 2021 | 5.85% | -1.11% | 6.61 | 4.93 | -5.71 |
| 25. | 28 feb. 2021 | -9.01% | 2.61% | 151.12 | 2.26 | -18.48 |
| 26. | 31 mar. 2021 | 7.88% | 4.24% | 21.12 | 9.85 | 14.42 |
| 27. | 30 abr. 2021 | 4.40% | 5.24% | 1.25 | 17.11 | 4.63 |
| 28. | 31 may. 2021 | 7.69% | 0.55% | 19.46 | 0.31 | -2.46 |
| 29. | 30 jun. 2021 | 6.75% | 2.22% | 12.06 | 1.24 | 3.87 |
| 30. | 31 jul. 2021 | 4.99% | 2.27% | 2.92 | 1.37 | 2.00 |
| 31. | 31 ago. 2021 | -2.86% | 2.90% | 37.70 | 3.22 | -11.01 |
| 32. | 30 sept. 2021 | -7.00% | -4.76% | 105.76 | 34.37 | 60.29 |
| 33. | 31 oct. 2021 | 19.22% | 6.91% | 254.01 | 33.74 | 92.57 |
| 34. | 30 nov. 2021 | 21.13% | -0.83% | 318.57 | 3.76 | -34.61 |
| 35. | 31 dic. 2021 | 15.87% | 4.36% | 158.54 | 10.60 | 40.99 |
| 36. | 31 ene. 2022 | -13.52% | -5.26% | 282.36 | 40.51 | 106.94 |
| 37. | 28 feb. 2022 | -1.27% | -3.14% | 20.71 | 17.99 | 19.31 |
| 38. | 31 mar. 2022 | 13.24% | 3.58% | 99.21 | 6.11 | 24.62 |
| 39. | 30 abr. 2022 | -16.84% | -8.80% | 404.98 | 98.04 | 199.26 |
| 40. | 31 may. 2022 | -11.50% | 0.01% | 218.44 | 1.21 | 16.27 |
| 41. | 30 jun. 2022 | -8.35% | -8.39% | 135.25 | 90.21 | 110.46 |
| 42. | 31 jul. 2022 | 24.42% | 9.11% | 446.84 | 64.09 | 169.23 |
| 43. | 31 ago. 2022 | 2.79% | -4.24% | 0.24 | 28.62 | 2.64 |
| 44. | 30 sept. 2022 | -5.83% | -9.34% | 83.01 | 109.11 | 95.17 |
| 45. | 31 oct. 2022 | 7.06% | 7.99% | 14.29 | 47.34 | 26.01 |
| 46. | 30 nov. 2022 | 15.26% | 5.38% | 143.45 | 18.23 | 51.14 |
| 47. | 31 dic. 2022 | -12.89% | -5.90% | 261.34 | 49.04 | 113.21 |
| 48. | 31 ene. 2023 | 3.85% | 6.18% | 0.32 | 25.70 | 2.88 |
| 49. | 28 feb. 2023 | 10.06% | -2.61% | 45.99 | 13.82 | -25.21 |
| 50. | 31 mar. 2023 | 21.02% | 3.51% | 314.84 | 5.76 | 42.57 |
| 51. | 30 abr. 2023 | -4.59% | 1.46% | 61.89 | 0.13 | -2.82 |
| 52. | 31 may. 2023 | 3.86% | 0.25% | 0.33 | 0.74 | -0.50 |
| 53. | 30 jun. 2023 | -2.57% | 4.71% | 34.26 | 13.02 | -21.12 |
| 54. | 31 jul. 2023 | -4.30% | 4.85% | 57.47 | 13.99 | -28.35 |
| 55. | 31 ago. 2023 | 25.88% | -1.77% | 510.84 | 8.28 | -65.04 |
| 56. | 30 sept. 2023 | -5.79% | -4.87% | 82.23 | 35.73 | 54.21 |
| 57. | 31 oct. 2023 | 8.94% | -2.20% | 32.01 | 10.92 | -18.69 |
| 58. | 30 nov. 2023 | 9.65% | 8.92% | 40.60 | 61.03 | 49.78 |
| 59. | 31 dic. 2023 | 7.19% | 4.42% | 15.30 | 11.00 | 12.97 |
| Total (Σ): | 9,022.94 | 1,634.30 | 1,850.30 | |||
Mostrar todo
VarianzaANET = Σ(RANET,t–RANET)2 ÷ (59 – 1)
= 9,022.94 ÷ (59 – 1)
= 155.57
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaANET, S&P 500 = Σ(RANET,t–RANET)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,850.30 ÷ (59 – 1)
= 31.90
Estimación sistemática del riesgo (β)
| VarianzaANET | 155.57 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaANET, S&P 500 | 31.90 |
| Coeficiente de correlaciónANET, S&P 5001 | 0.48 |
| βANET2 | 1.13 |
| αANET3 | 2.03% |
Cálculos
1 Coeficiente de correlaciónANET, S&P 500
= CovarianzaANET, S&P 500 ÷ (Desviación estándarANET × Desviación estándarS&P 500)
= 31.90 ÷ (12.47% × 5.31%)
= 0.48
2 βANET
= CovarianzaANET, S&P 500 ÷ VarianzaS&P 500
= 31.90 ÷ 28.18
= 1.13
3 αANET
= PromedioANET – βANET × PromedioS&P 500
= 3.28% – 1.13 × 1.11%
= 2.03%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.80% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.50% |
| Riesgo sistemático de Arista acciones ordinarias | βANET | 1.13 |
| Tasa de rendimiento esperada de las acciones ordinarias de Arista3 | E(RANET) | 14.65% |
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(RANET) = RF + βANET [E(RM) – RF]
= 4.80% + 1.13 [13.50% – 4.80%]
= 14.65%