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 Cadence.
Tasas de retorno
Cadence Design Systems Inc., tasas mensuales de retorno
| Cadence Design Systems Inc. (CDNS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCDNS,t1 | DividendoCDNS,t1 | RCDNS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $44.86 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $38.77 | -13.58% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $36.77 | -5.16% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $40.06 | 8.95% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $172.04 | 13.64% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $160.64 | -6.63% | 3,839.50 | -5.90% | |
| Promedio (R): | 2.55% | 0.67% | ||||
| Desviación estándar: | 8.79% | 5.40% | ||||
| Cadence Design Systems Inc. (CDNS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCDNS,t1 | DividendoCDNS,t1 | RCDNS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $44.86 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $38.77 | -13.58% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $36.77 | -5.16% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $40.06 | 8.95% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $42.45 | 5.97% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $43.31 | 2.03% | 2,718.37 | 0.48% | |
| 6. | 31 jul. 2018 | $44.09 | 1.80% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $47.04 | 6.69% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $45.32 | -3.66% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $44.57 | -1.65% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $45.04 | 1.05% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $43.48 | -3.46% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $48.03 | 10.46% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $57.25 | 19.20% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $63.51 | 10.93% | 2,834.40 | 1.79% | |
| 15. | 30 abr. 2019 | $69.38 | 9.24% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $63.57 | -8.37% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $70.81 | 11.39% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $73.91 | 4.38% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $68.48 | -7.35% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $66.08 | -3.50% | 2,976.74 | 1.72% | |
| 21. | 31 oct. 2019 | $65.35 | -1.10% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $70.25 | 7.50% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $69.36 | -1.27% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $72.11 | 3.96% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $66.14 | -8.28% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $66.04 | -0.15% | 2,584.59 | -12.51% | |
| 27. | 30 abr. 2020 | $81.13 | 22.85% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $91.29 | 12.52% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $95.96 | 5.12% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $109.25 | 13.85% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $110.91 | 1.52% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $106.63 | -3.86% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $109.37 | 2.57% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $116.30 | 6.34% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $136.43 | 17.31% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $130.39 | -4.43% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $141.09 | 8.21% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $136.99 | -2.91% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $131.77 | -3.81% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $126.99 | -3.63% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $136.82 | 7.74% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $147.65 | 7.92% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $163.48 | 10.72% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $151.44 | -7.36% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $173.11 | 14.31% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $177.46 | 2.51% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $186.35 | 5.01% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $152.14 | -18.36% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $151.43 | -0.47% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $164.46 | 8.60% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $150.85 | -8.28% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $153.73 | 1.91% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $150.03 | -2.41% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $186.08 | 24.03% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $173.77 | -6.62% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $163.43 | -5.95% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $151.39 | -7.37% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $172.04 | 13.64% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $160.64 | -6.63% | 3,839.50 | -5.90% | |
| Promedio (R): | 2.55% | 0.67% | ||||
| Desviación estándar: | 8.79% | 5.40% | ||||
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 CDNS 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
Cadence Design Systems Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RCDNS,t | RS&P 500,t | (RCDNS,t–RCDNS)2 | (RS&P 500,t–RS&P 500)2 | (RCDNS,t–RCDNS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -13.58% | -3.89% | 260.13 | 20.81 | 73.57 |
| 2. | 31 mar. 2018 | -5.16% | -2.69% | 59.47 | 11.26 | 25.87 |
| 3. | 30 abr. 2018 | 8.95% | 0.27% | 40.89 | 0.16 | -2.52 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | 13.64% | 5.38% | 122.93 | 22.17 | 52.21 |
| 59. | 31 dic. 2022 | -6.63% | -5.90% | 84.26 | 43.08 | 60.25 |
| Total (Σ): | 4,476.36 | 1,691.48 | 1,858.75 | |||
| t | Fecha | RCDNS,t | RS&P 500,t | (RCDNS,t–RCDNS)2 | (RS&P 500,t–RS&P 500)2 | (RCDNS,t–RCDNS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -13.58% | -3.89% | 260.13 | 20.81 | 73.57 |
| 2. | 31 mar. 2018 | -5.16% | -2.69% | 59.47 | 11.26 | 25.87 |
| 3. | 30 abr. 2018 | 8.95% | 0.27% | 40.89 | 0.16 | -2.52 |
| 4. | 31 may. 2018 | 5.97% | 2.16% | 11.65 | 2.23 | 5.10 |
| 5. | 30 jun. 2018 | 2.03% | 0.48% | 0.28 | 0.03 | 0.10 |
| 6. | 31 jul. 2018 | 1.80% | 3.60% | 0.57 | 8.62 | -2.21 |
| 7. | 31 ago. 2018 | 6.69% | 3.03% | 17.12 | 5.57 | 9.76 |
| 8. | 30 sept. 2018 | -3.66% | 0.43% | 38.56 | 0.06 | 1.47 |
| 9. | 31 oct. 2018 | -1.65% | -6.94% | 17.71 | 57.87 | 32.01 |
| 10. | 30 nov. 2018 | 1.05% | 1.79% | 2.25 | 1.25 | -1.68 |
| 11. | 31 dic. 2018 | -3.46% | -9.18% | 36.20 | 96.91 | 59.23 |
| 12. | 31 ene. 2019 | 10.46% | 7.87% | 62.59 | 51.87 | 56.98 |
| 13. | 28 feb. 2019 | 19.20% | 2.97% | 277.00 | 5.32 | 38.38 |
| 14. | 31 mar. 2019 | 10.93% | 1.79% | 70.25 | 1.27 | 9.44 |
| 15. | 30 abr. 2019 | 9.24% | 3.93% | 44.75 | 10.66 | 21.84 |
| 16. | 31 may. 2019 | -8.37% | -6.58% | 119.40 | 52.48 | 79.16 |
| 17. | 30 jun. 2019 | 11.39% | 6.89% | 78.08 | 38.77 | 55.02 |
| 18. | 31 jul. 2019 | 4.38% | 1.31% | 3.33 | 0.42 | 1.18 |
| 19. | 31 ago. 2019 | -7.35% | -1.81% | 98.01 | 6.13 | 24.51 |
| 20. | 30 sept. 2019 | -3.50% | 1.72% | 36.70 | 1.11 | -6.37 |
| 21. | 31 oct. 2019 | -1.10% | 2.04% | 13.38 | 1.89 | -5.03 |
| 22. | 30 nov. 2019 | 7.50% | 3.40% | 24.45 | 7.50 | 13.54 |
| 23. | 31 dic. 2019 | -1.27% | 2.86% | 14.59 | 4.81 | -8.37 |
| 24. | 31 ene. 2020 | 3.96% | -0.16% | 1.99 | 0.69 | -1.17 |
| 25. | 29 feb. 2020 | -8.28% | -8.41% | 117.33 | 82.40 | 98.33 |
| 26. | 31 mar. 2020 | -0.15% | -12.51% | 7.31 | 173.67 | 35.64 |
| 27. | 30 abr. 2020 | 22.85% | 12.68% | 411.96 | 144.43 | 243.92 |
| 28. | 31 may. 2020 | 12.52% | 4.53% | 99.40 | 14.91 | 38.50 |
| 29. | 30 jun. 2020 | 5.12% | 1.84% | 6.57 | 1.37 | 3.00 |
| 30. | 31 jul. 2020 | 13.85% | 5.51% | 127.61 | 23.46 | 54.71 |
| 31. | 31 ago. 2020 | 1.52% | 7.01% | 1.07 | 40.19 | -6.55 |
| 32. | 30 sept. 2020 | -3.86% | -3.92% | 41.11 | 21.06 | 29.43 |
| 33. | 31 oct. 2020 | 2.57% | -2.77% | 0.00 | 11.79 | -0.06 |
| 34. | 30 nov. 2020 | 6.34% | 10.75% | 14.31 | 101.77 | 38.17 |
| 35. | 31 dic. 2020 | 17.31% | 3.71% | 217.73 | 9.28 | 44.94 |
| 36. | 31 ene. 2021 | -4.43% | -1.11% | 48.72 | 3.17 | 12.43 |
| 37. | 28 feb. 2021 | 8.21% | 2.61% | 31.96 | 3.77 | 10.98 |
| 38. | 31 mar. 2021 | -2.91% | 4.24% | 29.80 | 12.80 | -19.53 |
| 39. | 30 abr. 2021 | -3.81% | 5.24% | 40.49 | 20.94 | -29.12 |
| 40. | 31 may. 2021 | -3.63% | 0.55% | 38.20 | 0.01 | 0.73 |
| 41. | 30 jun. 2021 | 7.74% | 2.22% | 26.91 | 2.42 | 8.07 |
| 42. | 31 jul. 2021 | 7.92% | 2.27% | 28.76 | 2.59 | 8.62 |
| 43. | 31 ago. 2021 | 10.72% | 2.90% | 66.72 | 4.98 | 18.23 |
| 44. | 30 sept. 2021 | -7.36% | -4.76% | 98.36 | 29.42 | 53.79 |
| 45. | 31 oct. 2021 | 14.31% | 6.91% | 138.21 | 39.03 | 73.45 |
| 46. | 30 nov. 2021 | 2.51% | -0.83% | 0.00 | 2.25 | 0.06 |
| 47. | 31 dic. 2021 | 5.01% | 4.36% | 6.03 | 13.65 | 9.08 |
| 48. | 31 ene. 2022 | -18.36% | -5.26% | 437.27 | 35.11 | 123.90 |
| 49. | 28 feb. 2022 | -0.47% | -3.14% | 9.12 | 14.46 | 11.48 |
| 50. | 31 mar. 2022 | 8.60% | 3.58% | 36.62 | 8.47 | 17.61 |
| 51. | 30 abr. 2022 | -8.28% | -8.80% | 117.26 | 89.54 | 102.46 |
| 52. | 31 may. 2022 | 1.91% | 0.01% | 0.41 | 0.44 | 0.43 |
| 53. | 30 jun. 2022 | -2.41% | -8.39% | 24.60 | 82.06 | 44.93 |
| 54. | 31 jul. 2022 | 24.03% | 9.11% | 461.20 | 71.32 | 181.36 |
| 55. | 31 ago. 2022 | -6.62% | -4.24% | 84.06 | 24.11 | 45.02 |
| 56. | 30 sept. 2022 | -5.95% | -9.34% | 72.31 | 100.12 | 85.09 |
| 57. | 31 oct. 2022 | -7.37% | 7.99% | 98.41 | 53.58 | -72.61 |
| 58. | 30 nov. 2022 | 13.64% | 5.38% | 122.93 | 22.17 | 52.21 |
| 59. | 31 dic. 2022 | -6.63% | -5.90% | 84.26 | 43.08 | 60.25 |
| Total (Σ): | 4,476.36 | 1,691.48 | 1,858.75 | |||
Mostrar todo
VarianzaCDNS = Σ(RCDNS,t–RCDNS)2 ÷ (59 – 1)
= 4,476.36 ÷ (59 – 1)
= 77.18
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaCDNS, S&P 500 = Σ(RCDNS,t–RCDNS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,858.75 ÷ (59 – 1)
= 32.05
Estimación sistemática del riesgo (β)
| VarianzaCDNS | 77.18 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaCDNS, S&P 500 | 32.05 |
| Coeficiente de correlaciónCDNS, S&P 5001 | 0.68 |
| βCDNS2 | 1.10 |
| αCDNS3 | 1.82% |
Cálculos
1 Coeficiente de correlaciónCDNS, S&P 500
= CovarianzaCDNS, S&P 500 ÷ (Desviación estándarCDNS × Desviación estándarS&P 500)
= 32.05 ÷ (8.79% × 5.40%)
= 0.68
2 βCDNS
= CovarianzaCDNS, S&P 500 ÷ VarianzaS&P 500
= 32.05 ÷ 29.16
= 1.10
3 αCDNS
= PromedioCDNS – βCDNS × PromedioS&P 500
= 2.55% – 1.10 × 0.67%
= 1.82%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.62% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.69% |
| Riesgo sistemático de Cadence acciones ordinarias | βCDNS | 1.10 |
| Tasa de rendimiento esperada de las acciones ordinarias de Cadence3 | E(RCDNS) | 14.58% |
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(RCDNS) = RF + βCDNS [E(RM) – RF]
= 4.62% + 1.10 [13.69% – 4.62%]
= 14.58%