Modelo de fijación de precios de activos de capital (CAPM)
El modelo de valoración 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 Cintas.
Tasas de retorno
Cintas Corp., tasas mensuales de retorno
| Cintas Corp. (CTAS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCTAS,t1 | DividendoCTAS,t1 | RCTAS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 jun. 2018 | $46.27 | 2,718.37 | ||||
| 1. | 31 jul. 2018 | $51.12 | 10.48% | 2,816.29 | 3.60% | |
| 2. | 31 ago. 2018 | $53.34 | 4.34% | 2,901.52 | 3.03% | |
| 3. | 30 sept. 2018 | $49.45 | -7.29% | 2,913.98 | 0.43% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 abr. 2024 | $164.59 | -4.17% | 5,035.69 | -4.16% | |
| 71. | 31 may. 2024 | $169.49 | $0.338 | 3.18% | 5,277.51 | 4.80% |
| Promedio (R): | 2.30% | 1.08% | ||||
| Desviación estándar: | 8.40% | 5.24% | ||||
| Cintas Corp. (CTAS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCTAS,t1 | DividendoCTAS,t1 | RCTAS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 jun. 2018 | $46.27 | 2,718.37 | ||||
| 1. | 31 jul. 2018 | $51.12 | 10.48% | 2,816.29 | 3.60% | |
| 2. | 31 ago. 2018 | $53.34 | 4.34% | 2,901.52 | 3.03% | |
| 3. | 30 sept. 2018 | $49.45 | -7.29% | 2,913.98 | 0.43% | |
| 4. | 31 oct. 2018 | $45.47 | -8.05% | 2,711.74 | -6.94% | |
| 5. | 30 nov. 2018 | $46.85 | $0.513 | 4.16% | 2,760.17 | 1.79% |
| 6. | 31 dic. 2018 | $42.00 | -10.35% | 2,506.85 | -9.18% | |
| 7. | 31 ene. 2019 | $46.88 | 11.62% | 2,704.10 | 7.87% | |
| 8. | 28 feb. 2019 | $51.65 | 10.17% | 2,784.49 | 2.97% | |
| 9. | 31 mar. 2019 | $50.53 | -2.17% | 2,834.40 | 1.79% | |
| 10. | 30 abr. 2019 | $54.29 | 7.44% | 2,945.83 | 3.93% | |
| 11. | 31 may. 2019 | $55.46 | 2.16% | 2,752.06 | -6.58% | |
| 12. | 30 jun. 2019 | $59.32 | 6.96% | 2,941.76 | 6.89% | |
| 13. | 31 jul. 2019 | $65.11 | 9.76% | 2,980.38 | 1.31% | |
| 14. | 31 ago. 2019 | $65.95 | 1.29% | 2,926.46 | -1.81% | |
| 15. | 30 sept. 2019 | $67.03 | 1.64% | 2,976.74 | 1.72% | |
| 16. | 31 oct. 2019 | $67.17 | 0.21% | 3,037.56 | 2.04% | |
| 17. | 30 nov. 2019 | $64.27 | $0.638 | -3.37% | 3,140.98 | 3.40% |
| 18. | 31 dic. 2019 | $67.27 | 4.67% | 3,230.78 | 2.86% | |
| 19. | 31 ene. 2020 | $69.74 | 3.67% | 3,225.52 | -0.16% | |
| 20. | 29 feb. 2020 | $66.69 | -4.37% | 2,954.22 | -8.41% | |
| 21. | 31 mar. 2020 | $43.31 | -35.06% | 2,584.59 | -12.51% | |
| 22. | 30 abr. 2020 | $55.46 | 28.05% | 2,912.43 | 12.68% | |
| 23. | 31 may. 2020 | $61.99 | 11.77% | 3,044.31 | 4.53% | |
| 24. | 30 jun. 2020 | $66.59 | 7.42% | 3,100.29 | 1.84% | |
| 25. | 31 jul. 2020 | $75.47 | 13.34% | 3,271.12 | 5.51% | |
| 26. | 31 ago. 2020 | $83.31 | 10.39% | 3,500.31 | 7.01% | |
| 27. | 30 sept. 2020 | $83.21 | -0.12% | 3,363.00 | -3.92% | |
| 28. | 31 oct. 2020 | $78.64 | -5.49% | 3,269.96 | -2.77% | |
| 29. | 30 nov. 2020 | $88.83 | $0.878 | 14.07% | 3,621.63 | 10.75% |
| 30. | 31 dic. 2020 | $88.37 | -0.52% | 3,756.07 | 3.71% | |
| 31. | 31 ene. 2021 | $79.53 | -10.00% | 3,714.24 | -1.11% | |
| 32. | 28 feb. 2021 | $81.09 | $0.188 | 2.20% | 3,811.15 | 2.61% |
| 33. | 31 mar. 2021 | $85.33 | 5.23% | 3,972.89 | 4.24% | |
| 34. | 30 abr. 2021 | $86.29 | 1.13% | 4,181.17 | 5.24% | |
| 35. | 31 may. 2021 | $88.39 | $0.188 | 2.65% | 4,204.11 | 0.55% |
| 36. | 30 jun. 2021 | $95.50 | 8.04% | 4,297.50 | 2.22% | |
| 37. | 31 jul. 2021 | $98.55 | 3.19% | 4,395.26 | 2.27% | |
| 38. | 31 ago. 2021 | $98.94 | $0.238 | 0.64% | 4,522.68 | 2.90% |
| 39. | 30 sept. 2021 | $95.17 | -3.81% | 4,307.54 | -4.76% | |
| 40. | 31 oct. 2021 | $108.28 | 13.78% | 4,605.38 | 6.91% | |
| 41. | 30 nov. 2021 | $105.55 | $0.238 | -2.30% | 4,567.00 | -0.83% |
| 42. | 31 dic. 2021 | $110.79 | 4.96% | 4,766.18 | 4.36% | |
| 43. | 31 ene. 2022 | $97.88 | -11.65% | 4,515.55 | -5.26% | |
| 44. | 28 feb. 2022 | $93.83 | $0.238 | -3.89% | 4,373.94 | -3.14% |
| 45. | 31 mar. 2022 | $106.35 | 13.34% | 4,530.41 | 3.58% | |
| 46. | 30 abr. 2022 | $99.32 | -6.61% | 4,131.93 | -8.80% | |
| 47. | 31 may. 2022 | $99.58 | $0.238 | 0.50% | 4,132.15 | 0.01% |
| 48. | 30 jun. 2022 | $93.38 | -6.23% | 3,785.38 | -8.39% | |
| 49. | 31 jul. 2022 | $106.37 | 13.91% | 4,130.29 | 9.11% | |
| 50. | 31 ago. 2022 | $101.71 | $0.288 | -4.11% | 3,955.00 | -4.24% |
| 51. | 30 sept. 2022 | $97.05 | -4.58% | 3,585.62 | -9.34% | |
| 52. | 31 oct. 2022 | $106.89 | 10.14% | 3,871.98 | 7.99% | |
| 53. | 30 nov. 2022 | $115.45 | $0.288 | 8.28% | 4,080.11 | 5.38% |
| 54. | 31 dic. 2022 | $112.91 | -2.20% | 3,839.50 | -5.90% | |
| 55. | 31 ene. 2023 | $110.94 | -1.74% | 4,076.60 | 6.18% | |
| 56. | 28 feb. 2023 | $109.62 | $0.288 | -0.93% | 3,970.15 | -2.61% |
| 57. | 31 mar. 2023 | $115.67 | 5.52% | 4,109.31 | 3.51% | |
| 58. | 30 abr. 2023 | $113.94 | -1.50% | 4,169.48 | 1.46% | |
| 59. | 31 may. 2023 | $118.04 | $0.288 | 3.85% | 4,179.83 | 0.25% |
| 60. | 30 jun. 2023 | $124.27 | 5.28% | 4,376.86 | 4.71% | |
| 61. | 31 jul. 2023 | $125.51 | 1.00% | 4,588.96 | 4.85% | |
| 62. | 31 ago. 2023 | $126.04 | $0.338 | 0.69% | 4,507.66 | -1.77% |
| 63. | 30 sept. 2023 | $120.25 | -4.59% | 4,288.05 | -4.87% | |
| 64. | 31 oct. 2023 | $126.78 | 5.43% | 4,193.80 | -2.20% | |
| 65. | 30 nov. 2023 | $138.31 | $0.338 | 9.36% | 4,567.80 | 8.92% |
| 66. | 31 dic. 2023 | $150.67 | 8.94% | 4,769.83 | 4.42% | |
| 67. | 31 ene. 2024 | $151.14 | 0.31% | 4,845.65 | 1.59% | |
| 68. | 29 feb. 2024 | $157.15 | $0.338 | 4.20% | 5,096.27 | 5.17% |
| 69. | 31 mar. 2024 | $171.76 | 9.30% | 5,254.35 | 3.10% | |
| 70. | 30 abr. 2024 | $164.59 | -4.17% | 5,035.69 | -4.16% | |
| 71. | 31 may. 2024 | $169.49 | $0.338 | 3.18% | 5,277.51 | 4.80% |
| Promedio (R): | 2.30% | 1.08% | ||||
| Desviación estándar: | 8.40% | 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 CTAS 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
Cintas Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RCTAS,t | RS&P 500,t | (RCTAS,t–RCTAS)2 | (RS&P 500,t–RS&P 500)2 | (RCTAS,t–RCTAS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 jul. 2018 | 10.48% | 3.60% | 66.89 | 6.39 | 20.67 |
| 2. | 31 ago. 2018 | 4.34% | 3.03% | 4.16 | 3.81 | 3.98 |
| 3. | 30 sept. 2018 | -7.29% | 0.43% | 92.09 | 0.42 | 6.20 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 30 abr. 2024 | -4.17% | -4.16% | 41.96 | 27.42 | 33.92 |
| 71. | 31 may. 2024 | 3.18% | 4.80% | 0.77 | 13.89 | 3.28 |
| Total (Σ): | 4,935.48 | 1,923.46 | 2,458.46 | |||
| t | Fecha | RCTAS,t | RS&P 500,t | (RCTAS,t–RCTAS)2 | (RS&P 500,t–RS&P 500)2 | (RCTAS,t–RCTAS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 jul. 2018 | 10.48% | 3.60% | 66.89 | 6.39 | 20.67 |
| 2. | 31 ago. 2018 | 4.34% | 3.03% | 4.16 | 3.81 | 3.98 |
| 3. | 30 sept. 2018 | -7.29% | 0.43% | 92.09 | 0.42 | 6.20 |
| 4. | 31 oct. 2018 | -8.05% | -6.94% | 107.16 | 64.25 | 82.98 |
| 5. | 30 nov. 2018 | 4.16% | 1.79% | 3.46 | 0.51 | 1.32 |
| 6. | 31 dic. 2018 | -10.35% | -9.18% | 160.17 | 105.12 | 129.76 |
| 7. | 31 ene. 2019 | 11.62% | 7.87% | 86.78 | 46.15 | 63.28 |
| 8. | 28 feb. 2019 | 10.17% | 2.97% | 61.96 | 3.60 | 14.94 |
| 9. | 31 mar. 2019 | -2.17% | 1.79% | 20.00 | 0.51 | -3.21 |
| 10. | 30 abr. 2019 | 7.44% | 3.93% | 26.40 | 8.16 | 14.67 |
| 11. | 31 may. 2019 | 2.16% | -6.58% | 0.02 | 58.57 | 1.14 |
| 12. | 30 jun. 2019 | 6.96% | 6.89% | 21.68 | 33.85 | 27.09 |
| 13. | 31 jul. 2019 | 9.76% | 1.31% | 55.61 | 0.06 | 1.77 |
| 14. | 31 ago. 2019 | 1.29% | -1.81% | 1.03 | 8.32 | 2.92 |
| 15. | 30 sept. 2019 | 1.64% | 1.72% | 0.44 | 0.41 | -0.43 |
| 16. | 31 oct. 2019 | 0.21% | 2.04% | 4.39 | 0.94 | -2.03 |
| 17. | 30 nov. 2019 | -3.37% | 3.40% | 32.16 | 5.43 | -13.21 |
| 18. | 31 dic. 2019 | 4.67% | 2.86% | 5.59 | 3.18 | 4.22 |
| 19. | 31 ene. 2020 | 3.67% | -0.16% | 1.87 | 1.53 | -1.69 |
| 20. | 29 feb. 2020 | -4.37% | -8.41% | 44.58 | 89.99 | 63.34 |
| 21. | 31 mar. 2020 | -35.06% | -12.51% | 1,395.86 | 184.61 | 507.63 |
| 22. | 30 abr. 2020 | 28.05% | 12.68% | 663.07 | 134.77 | 298.94 |
| 23. | 31 may. 2020 | 11.77% | 4.53% | 89.70 | 11.92 | 32.70 |
| 24. | 30 jun. 2020 | 7.42% | 1.84% | 26.18 | 0.58 | 3.91 |
| 25. | 31 jul. 2020 | 13.34% | 5.51% | 121.70 | 19.67 | 48.92 |
| 26. | 31 ago. 2020 | 10.39% | 7.01% | 65.36 | 35.18 | 47.95 |
| 27. | 30 sept. 2020 | -0.12% | -3.92% | 5.87 | 24.98 | 12.11 |
| 28. | 31 oct. 2020 | -5.49% | -2.77% | 60.77 | 14.76 | 29.95 |
| 29. | 30 nov. 2020 | 14.07% | 10.75% | 138.55 | 93.69 | 113.93 |
| 30. | 31 dic. 2020 | -0.52% | 3.71% | 7.96 | 6.95 | -7.44 |
| 31. | 31 ene. 2021 | -10.00% | -1.11% | 151.46 | 4.79 | 26.94 |
| 32. | 28 feb. 2021 | 2.20% | 2.61% | 0.01 | 2.35 | -0.16 |
| 33. | 31 mar. 2021 | 5.23% | 4.24% | 8.56 | 10.04 | 9.27 |
| 34. | 30 abr. 2021 | 1.13% | 5.24% | 1.39 | 17.37 | -4.91 |
| 35. | 31 may. 2021 | 2.65% | 0.55% | 0.12 | 0.28 | -0.18 |
| 36. | 30 jun. 2021 | 8.04% | 2.22% | 32.95 | 1.31 | 6.58 |
| 37. | 31 jul. 2021 | 3.19% | 2.27% | 0.79 | 1.44 | 1.07 |
| 38. | 31 ago. 2021 | 0.64% | 2.90% | 2.78 | 3.33 | -3.04 |
| 39. | 30 sept. 2021 | -3.81% | -4.76% | 37.38 | 34.01 | 35.66 |
| 40. | 31 oct. 2021 | 13.78% | 6.91% | 131.60 | 34.10 | 66.99 |
| 41. | 30 nov. 2021 | -2.30% | -0.83% | 21.21 | 3.64 | 8.79 |
| 42. | 31 dic. 2021 | 4.96% | 4.36% | 7.08 | 10.80 | 8.74 |
| 43. | 31 ene. 2022 | -11.65% | -5.26% | 194.77 | 40.12 | 88.40 |
| 44. | 28 feb. 2022 | -3.89% | -3.14% | 38.42 | 17.74 | 26.10 |
| 45. | 31 mar. 2022 | 13.34% | 3.58% | 121.88 | 6.26 | 27.62 |
| 46. | 30 abr. 2022 | -6.61% | -8.80% | 79.45 | 97.44 | 87.99 |
| 47. | 31 may. 2022 | 0.50% | 0.01% | 3.25 | 1.14 | 1.93 |
| 48. | 30 jun. 2022 | -6.23% | -8.39% | 72.75 | 89.63 | 80.75 |
| 49. | 31 jul. 2022 | 13.91% | 9.11% | 134.73 | 64.58 | 93.28 |
| 50. | 31 ago. 2022 | -4.11% | -4.24% | 41.14 | 28.29 | 34.12 |
| 51. | 30 sept. 2022 | -4.58% | -9.34% | 47.41 | 108.47 | 71.71 |
| 52. | 31 oct. 2022 | 10.14% | 7.99% | 61.40 | 47.76 | 54.15 |
| 53. | 30 nov. 2022 | 8.28% | 5.38% | 35.69 | 18.49 | 25.69 |
| 54. | 31 dic. 2022 | -2.20% | -5.90% | 20.28 | 48.61 | 31.40 |
| 55. | 31 ene. 2023 | -1.74% | 6.18% | 16.39 | 26.01 | -20.65 |
| 56. | 28 feb. 2023 | -0.93% | -2.61% | 10.46 | 13.59 | 11.92 |
| 57. | 31 mar. 2023 | 5.52% | 3.51% | 10.34 | 5.90 | 7.81 |
| 58. | 30 abr. 2023 | -1.50% | 1.46% | 14.43 | 0.15 | -1.48 |
| 59. | 31 may. 2023 | 3.85% | 0.25% | 2.40 | 0.68 | -1.28 |
| 60. | 30 jun. 2023 | 5.28% | 4.71% | 8.85 | 13.24 | 10.82 |
| 61. | 31 jul. 2023 | 1.00% | 4.85% | 1.70 | 14.22 | -4.92 |
| 62. | 31 ago. 2023 | 0.69% | -1.77% | 2.60 | 8.10 | 4.59 |
| 63. | 30 sept. 2023 | -4.59% | -4.87% | 47.57 | 35.37 | 41.02 |
| 64. | 31 oct. 2023 | 5.43% | -2.20% | 9.78 | 10.71 | -10.23 |
| 65. | 30 nov. 2023 | 9.36% | 8.92% | 49.81 | 61.51 | 55.35 |
| 66. | 31 dic. 2023 | 8.94% | 4.42% | 44.00 | 11.21 | 22.20 |
| 67. | 31 ene. 2024 | 0.31% | 1.59% | 3.97 | 0.26 | -1.02 |
| 68. | 29 feb. 2024 | 4.20% | 5.17% | 3.60 | 16.78 | 7.77 |
| 69. | 31 mar. 2024 | 9.30% | 3.10% | 48.91 | 4.11 | 14.17 |
| 70. | 30 abr. 2024 | -4.17% | -4.16% | 41.96 | 27.42 | 33.92 |
| 71. | 31 may. 2024 | 3.18% | 4.80% | 0.77 | 13.89 | 3.28 |
| Total (Σ): | 4,935.48 | 1,923.46 | 2,458.46 | |||
Mostrar todo
VarianzaCTAS = Σ(RCTAS,t–RCTAS)2 ÷ (71 – 1)
= 4,935.48 ÷ (71 – 1)
= 70.51
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,923.46 ÷ (71 – 1)
= 27.48
CovarianzaCTAS, S&P 500 = Σ(RCTAS,t–RCTAS)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,458.46 ÷ (71 – 1)
= 35.12
Estimación sistemática del riesgo (β)
| VarianzaCTAS | 70.51 |
| VarianzaS&P 500 | 27.48 |
| CovarianzaCTAS, S&P 500 | 35.12 |
| Coeficiente de correlaciónCTAS, S&P 5001 | 0.80 |
| βCTAS2 | 1.28 |
| αCTAS3 | 0.93% |
Cálculos
1 Coeficiente de correlaciónCTAS, S&P 500
= CovarianzaCTAS, S&P 500 ÷ (Desviación estándarCTAS × Desviación estándarS&P 500)
= 35.12 ÷ (8.40% × 5.24%)
= 0.80
2 βCTAS
= CovarianzaCTAS, S&P 500 ÷ VarianzaS&P 500
= 35.12 ÷ 27.48
= 1.28
3 αCTAS
= PromedioCTAS – βCTAS × PromedioS&P 500
= 2.30% – 1.28 × 1.08%
= 0.93%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.90% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.94% |
| Riesgo sistemático de Cintas acciones ordinarias | βCTAS | 1.28 |
| Tasa de rendimiento esperada de las acciones ordinarias de Cintas3 | E(RCTAS) | 16.46% |
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(RCTAS) = RF + βCTAS [E(RM) – RF]
= 4.90% + 1.28 [13.94% – 4.90%]
= 16.46%