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 Target.
Tasas de retorno
Target Corp., tasas mensuales de retorno
| Target Corp. (TGT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTGT,t1 | DividendoTGT,t1 | RTGT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 28 feb. 2018 | $75.41 | 2,713.83 | ||||
| 1. | 31 mar. 2018 | $69.43 | -7.93% | 2,640.87 | -2.69% | |
| 2. | 30 abr. 2018 | $72.60 | 4.57% | 2,648.05 | 0.27% | |
| 3. | 31 may. 2018 | $72.89 | $0.62 | 1.25% | 2,705.27 | 2.16% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2023 | $142.42 | 6.43% | 4,769.83 | 4.42% | |
| 71. | 31 ene. 2024 | $139.08 | -2.35% | 4,845.65 | 1.59% | |
| Promedio (R): | 1.55% | 0.95% | ||||
| Desviación estándar: | 9.86% | 5.18% | ||||
| Target Corp. (TGT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTGT,t1 | DividendoTGT,t1 | RTGT,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 28 feb. 2018 | $75.41 | 2,713.83 | ||||
| 1. | 31 mar. 2018 | $69.43 | -7.93% | 2,640.87 | -2.69% | |
| 2. | 30 abr. 2018 | $72.60 | 4.57% | 2,648.05 | 0.27% | |
| 3. | 31 may. 2018 | $72.89 | $0.62 | 1.25% | 2,705.27 | 2.16% |
| 4. | 30 jun. 2018 | $76.12 | 4.43% | 2,718.37 | 0.48% | |
| 5. | 31 jul. 2018 | $80.68 | 5.99% | 2,816.29 | 3.60% | |
| 6. | 31 ago. 2018 | $87.50 | $0.64 | 9.25% | 2,901.52 | 3.03% |
| 7. | 30 sept. 2018 | $88.21 | 0.81% | 2,913.98 | 0.43% | |
| 8. | 31 oct. 2018 | $83.63 | -5.19% | 2,711.74 | -6.94% | |
| 9. | 30 nov. 2018 | $70.96 | $0.64 | -14.38% | 2,760.17 | 1.79% |
| 10. | 31 dic. 2018 | $66.09 | -6.86% | 2,506.85 | -9.18% | |
| 11. | 31 ene. 2019 | $73.00 | 10.46% | 2,704.10 | 7.87% | |
| 12. | 28 feb. 2019 | $72.64 | $0.64 | 0.38% | 2,784.49 | 2.97% |
| 13. | 31 mar. 2019 | $80.26 | 10.49% | 2,834.40 | 1.79% | |
| 14. | 30 abr. 2019 | $77.42 | -3.54% | 2,945.83 | 3.93% | |
| 15. | 31 may. 2019 | $80.45 | $0.64 | 4.74% | 2,752.06 | -6.58% |
| 16. | 30 jun. 2019 | $86.61 | 7.66% | 2,941.76 | 6.89% | |
| 17. | 31 jul. 2019 | $86.40 | -0.24% | 2,980.38 | 1.31% | |
| 18. | 31 ago. 2019 | $107.04 | $0.66 | 24.65% | 2,926.46 | -1.81% |
| 19. | 30 sept. 2019 | $106.91 | -0.12% | 2,976.74 | 1.72% | |
| 20. | 31 oct. 2019 | $106.91 | 0.00% | 3,037.56 | 2.04% | |
| 21. | 30 nov. 2019 | $125.01 | $0.66 | 17.55% | 3,140.98 | 3.40% |
| 22. | 31 dic. 2019 | $128.21 | 2.56% | 3,230.78 | 2.86% | |
| 23. | 31 ene. 2020 | $110.74 | -13.63% | 3,225.52 | -0.16% | |
| 24. | 29 feb. 2020 | $103.00 | $0.66 | -6.39% | 2,954.22 | -8.41% |
| 25. | 31 mar. 2020 | $92.97 | -9.74% | 2,584.59 | -12.51% | |
| 26. | 30 abr. 2020 | $109.74 | 18.04% | 2,912.43 | 12.68% | |
| 27. | 31 may. 2020 | $122.33 | $0.66 | 12.07% | 3,044.31 | 4.53% |
| 28. | 30 jun. 2020 | $119.93 | -1.96% | 3,100.29 | 1.84% | |
| 29. | 31 jul. 2020 | $125.88 | 4.96% | 3,271.12 | 5.51% | |
| 30. | 31 ago. 2020 | $151.21 | $0.68 | 20.66% | 3,500.31 | 7.01% |
| 31. | 30 sept. 2020 | $157.42 | 4.11% | 3,363.00 | -3.92% | |
| 32. | 31 oct. 2020 | $152.22 | -3.30% | 3,269.96 | -2.77% | |
| 33. | 30 nov. 2020 | $179.53 | $0.68 | 18.39% | 3,621.63 | 10.75% |
| 34. | 31 dic. 2020 | $176.53 | -1.67% | 3,756.07 | 3.71% | |
| 35. | 31 ene. 2021 | $181.17 | 2.63% | 3,714.24 | -1.11% | |
| 36. | 28 feb. 2021 | $183.44 | $0.68 | 1.63% | 3,811.15 | 2.61% |
| 37. | 31 mar. 2021 | $198.07 | 7.98% | 3,972.89 | 4.24% | |
| 38. | 30 abr. 2021 | $207.26 | 4.64% | 4,181.17 | 5.24% | |
| 39. | 31 may. 2021 | $226.92 | $0.68 | 9.81% | 4,204.11 | 0.55% |
| 40. | 30 jun. 2021 | $241.74 | 6.53% | 4,297.50 | 2.22% | |
| 41. | 31 jul. 2021 | $261.05 | 7.99% | 4,395.26 | 2.27% | |
| 42. | 31 ago. 2021 | $246.98 | $0.90 | -5.05% | 4,522.68 | 2.90% |
| 43. | 30 sept. 2021 | $228.77 | -7.37% | 4,307.54 | -4.76% | |
| 44. | 31 oct. 2021 | $259.62 | 13.49% | 4,605.38 | 6.91% | |
| 45. | 30 nov. 2021 | $243.84 | $0.90 | -5.73% | 4,567.00 | -0.83% |
| 46. | 31 dic. 2021 | $231.44 | -5.09% | 4,766.18 | 4.36% | |
| 47. | 31 ene. 2022 | $220.43 | -4.76% | 4,515.55 | -5.26% | |
| 48. | 28 feb. 2022 | $199.77 | $0.90 | -8.96% | 4,373.94 | -3.14% |
| 49. | 31 mar. 2022 | $212.22 | 6.23% | 4,530.41 | 3.58% | |
| 50. | 30 abr. 2022 | $228.65 | 7.74% | 4,131.93 | -8.80% | |
| 51. | 31 may. 2022 | $161.88 | $0.90 | -28.81% | 4,132.15 | 0.01% |
| 52. | 30 jun. 2022 | $141.23 | -12.76% | 3,785.38 | -8.39% | |
| 53. | 31 jul. 2022 | $163.38 | 15.68% | 4,130.29 | 9.11% | |
| 54. | 31 ago. 2022 | $160.34 | $1.08 | -1.20% | 3,955.00 | -4.24% |
| 55. | 30 sept. 2022 | $148.39 | -7.45% | 3,585.62 | -9.34% | |
| 56. | 31 oct. 2022 | $164.25 | 10.69% | 3,871.98 | 7.99% | |
| 57. | 30 nov. 2022 | $167.07 | $1.08 | 2.37% | 4,080.11 | 5.38% |
| 58. | 31 dic. 2022 | $149.04 | -10.79% | 3,839.50 | -5.90% | |
| 59. | 31 ene. 2023 | $172.14 | 15.50% | 4,076.60 | 6.18% | |
| 60. | 28 feb. 2023 | $168.50 | $1.08 | -1.49% | 3,970.15 | -2.61% |
| 61. | 31 mar. 2023 | $165.63 | -1.70% | 4,109.31 | 3.51% | |
| 62. | 30 abr. 2023 | $157.75 | -4.76% | 4,169.48 | 1.46% | |
| 63. | 31 may. 2023 | $130.93 | $1.08 | -16.32% | 4,179.83 | 0.25% |
| 64. | 30 jun. 2023 | $131.90 | 0.74% | 4,376.86 | 4.71% | |
| 65. | 31 jul. 2023 | $136.47 | 3.46% | 4,588.96 | 4.85% | |
| 66. | 31 ago. 2023 | $126.55 | $1.10 | -6.46% | 4,507.66 | -1.77% |
| 67. | 30 sept. 2023 | $110.57 | -12.63% | 4,288.05 | -4.87% | |
| 68. | 31 oct. 2023 | $110.79 | 0.20% | 4,193.80 | -2.20% | |
| 69. | 30 nov. 2023 | $133.81 | $1.10 | 21.77% | 4,567.80 | 8.92% |
| 70. | 31 dic. 2023 | $142.42 | 6.43% | 4,769.83 | 4.42% | |
| 71. | 31 ene. 2024 | $139.08 | -2.35% | 4,845.65 | 1.59% | |
| Promedio (R): | 1.55% | 0.95% | ||||
| Desviación estándar: | 9.86% | 5.18% | ||||
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 TGT 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
Target Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RTGT,t | RS&P 500,t | (RTGT,t–RTGT)2 | (RS&P 500,t–RS&P 500)2 | (RTGT,t–RTGT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2018 | -7.93% | -2.69% | 89.83 | 13.26 | 34.51 |
| 2. | 30 abr. 2018 | 4.57% | 0.27% | 9.11 | 0.46 | -2.06 |
| 3. | 31 may. 2018 | 1.25% | 2.16% | 0.09 | 1.46 | -0.36 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2023 | 6.43% | 4.42% | 23.88 | 12.04 | 16.96 |
| 71. | 31 ene. 2024 | -2.35% | 1.59% | 15.16 | 0.41 | -2.48 |
| Total (Σ): | 6,810.32 | 1,876.53 | 2,073.89 | |||
| t | Fecha | RTGT,t | RS&P 500,t | (RTGT,t–RTGT)2 | (RS&P 500,t–RS&P 500)2 | (RTGT,t–RTGT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2018 | -7.93% | -2.69% | 89.83 | 13.26 | 34.51 |
| 2. | 30 abr. 2018 | 4.57% | 0.27% | 9.11 | 0.46 | -2.06 |
| 3. | 31 may. 2018 | 1.25% | 2.16% | 0.09 | 1.46 | -0.36 |
| 4. | 30 jun. 2018 | 4.43% | 0.48% | 8.31 | 0.22 | -1.35 |
| 5. | 31 jul. 2018 | 5.99% | 3.60% | 19.74 | 7.02 | 11.77 |
| 6. | 31 ago. 2018 | 9.25% | 3.03% | 59.27 | 4.30 | 15.96 |
| 7. | 30 sept. 2018 | 0.81% | 0.43% | 0.54 | 0.27 | 0.39 |
| 8. | 31 oct. 2018 | -5.19% | -6.94% | 45.43 | 62.30 | 53.20 |
| 9. | 30 nov. 2018 | -14.38% | 1.79% | 253.85 | 0.69 | -13.27 |
| 10. | 31 dic. 2018 | -6.86% | -9.18% | 70.74 | 102.63 | 85.21 |
| 11. | 31 ene. 2019 | 10.46% | 7.87% | 79.34 | 47.82 | 61.60 |
| 12. | 28 feb. 2019 | 0.38% | 2.97% | 1.36 | 4.08 | -2.35 |
| 13. | 31 mar. 2019 | 10.49% | 1.79% | 79.96 | 0.70 | 7.51 |
| 14. | 30 abr. 2019 | -3.54% | 3.93% | 25.87 | 8.87 | -15.15 |
| 15. | 31 may. 2019 | 4.74% | -6.58% | 10.19 | 56.71 | -24.04 |
| 16. | 30 jun. 2019 | 7.66% | 6.89% | 37.32 | 35.28 | 36.29 |
| 17. | 31 jul. 2019 | -0.24% | 1.31% | 3.21 | 0.13 | -0.64 |
| 18. | 31 ago. 2019 | 24.65% | -1.81% | 533.83 | 7.63 | -63.82 |
| 19. | 30 sept. 2019 | -0.12% | 1.72% | 2.79 | 0.59 | -1.28 |
| 20. | 31 oct. 2019 | 0.00% | 2.04% | 2.40 | 1.19 | -1.69 |
| 21. | 30 nov. 2019 | 17.55% | 3.40% | 255.99 | 6.01 | 39.23 |
| 22. | 31 dic. 2019 | 2.56% | 2.86% | 1.02 | 3.63 | 1.93 |
| 23. | 31 ene. 2020 | -13.63% | -0.16% | 230.25 | 1.24 | 16.93 |
| 24. | 29 feb. 2020 | -6.39% | -8.41% | 63.06 | 87.68 | 74.36 |
| 25. | 31 mar. 2020 | -9.74% | -12.51% | 127.37 | 181.30 | 151.96 |
| 26. | 30 abr. 2020 | 18.04% | 12.68% | 271.92 | 137.63 | 193.45 |
| 27. | 31 may. 2020 | 12.07% | 4.53% | 110.80 | 12.78 | 37.63 |
| 28. | 30 jun. 2020 | -1.96% | 1.84% | 12.32 | 0.78 | -3.11 |
| 29. | 31 jul. 2020 | 4.96% | 5.51% | 11.65 | 20.77 | 15.56 |
| 30. | 31 ago. 2020 | 20.66% | 7.01% | 365.37 | 36.65 | 115.71 |
| 31. | 30 sept. 2020 | 4.11% | -3.92% | 6.55 | 23.77 | -12.48 |
| 32. | 31 oct. 2020 | -3.30% | -2.77% | 23.53 | 13.83 | 18.04 |
| 33. | 30 nov. 2020 | 18.39% | 10.75% | 283.58 | 96.07 | 165.06 |
| 34. | 31 dic. 2020 | -1.67% | 3.71% | 10.36 | 7.61 | -8.88 |
| 35. | 31 ene. 2021 | 2.63% | -1.11% | 1.17 | 4.27 | -2.23 |
| 36. | 28 feb. 2021 | 1.63% | 2.61% | 0.01 | 2.74 | 0.13 |
| 37. | 31 mar. 2021 | 7.98% | 4.24% | 41.31 | 10.83 | 21.15 |
| 38. | 30 abr. 2021 | 4.64% | 5.24% | 9.56 | 18.40 | 13.26 |
| 39. | 31 may. 2021 | 9.81% | 0.55% | 68.32 | 0.16 | -3.34 |
| 40. | 30 jun. 2021 | 6.53% | 2.22% | 24.83 | 1.61 | 6.32 |
| 41. | 31 jul. 2021 | 7.99% | 2.27% | 41.47 | 1.75 | 8.51 |
| 42. | 31 ago. 2021 | -5.05% | 2.90% | 43.47 | 3.79 | -12.83 |
| 43. | 30 sept. 2021 | -7.37% | -4.76% | 79.58 | 32.60 | 50.94 |
| 44. | 31 oct. 2021 | 13.49% | 6.91% | 142.50 | 35.54 | 71.16 |
| 45. | 30 nov. 2021 | -5.73% | -0.83% | 52.99 | 3.19 | 13.00 |
| 46. | 31 dic. 2021 | -5.09% | 4.36% | 44.00 | 11.62 | -22.61 |
| 47. | 31 ene. 2022 | -4.76% | -5.26% | 39.75 | 38.58 | 39.16 |
| 48. | 28 feb. 2022 | -8.96% | -3.14% | 110.51 | 16.72 | 42.98 |
| 49. | 31 mar. 2022 | 6.23% | 3.58% | 21.94 | 6.89 | 12.29 |
| 50. | 30 abr. 2022 | 7.74% | -8.80% | 38.37 | 95.04 | -60.38 |
| 51. | 31 may. 2022 | -28.81% | 0.01% | 921.50 | 0.90 | 28.77 |
| 52. | 30 jun. 2022 | -12.76% | -8.39% | 204.61 | 87.33 | 133.67 |
| 53. | 31 jul. 2022 | 15.68% | 9.11% | 199.82 | 66.56 | 115.33 |
| 54. | 31 ago. 2022 | -1.20% | -4.24% | 7.55 | 27.01 | 14.28 |
| 55. | 30 sept. 2022 | -7.45% | -9.34% | 81.02 | 105.94 | 92.64 |
| 56. | 31 oct. 2022 | 10.69% | 7.99% | 83.54 | 49.47 | 64.29 |
| 57. | 30 nov. 2022 | 2.37% | 5.38% | 0.68 | 19.56 | 3.66 |
| 58. | 31 dic. 2022 | -10.79% | -5.90% | 152.27 | 46.92 | 84.53 |
| 59. | 31 ene. 2023 | 15.50% | 6.18% | 194.64 | 27.27 | 72.86 |
| 60. | 28 feb. 2023 | -1.49% | -2.61% | 9.21 | 12.70 | 10.82 |
| 61. | 31 mar. 2023 | -1.70% | 3.51% | 10.57 | 6.51 | -8.30 |
| 62. | 30 abr. 2023 | -4.76% | 1.46% | 39.76 | 0.26 | -3.22 |
| 63. | 31 may. 2023 | -16.32% | 0.25% | 319.15 | 0.50 | 12.59 |
| 64. | 30 jun. 2023 | 0.74% | 4.71% | 0.65 | 14.14 | -3.04 |
| 65. | 31 jul. 2023 | 3.46% | 4.85% | 3.67 | 15.16 | 7.46 |
| 66. | 31 ago. 2023 | -6.46% | -1.77% | 64.17 | 7.42 | 21.83 |
| 67. | 30 sept. 2023 | -12.63% | -4.87% | 200.94 | 33.93 | 82.57 |
| 68. | 31 oct. 2023 | 0.20% | -2.20% | 1.82 | 9.93 | 4.25 |
| 69. | 30 nov. 2023 | 21.77% | 8.92% | 408.97 | 63.44 | 161.08 |
| 70. | 31 dic. 2023 | 6.43% | 4.42% | 23.88 | 12.04 | 16.96 |
| 71. | 31 ene. 2024 | -2.35% | 1.59% | 15.16 | 0.41 | -2.48 |
| Total (Σ): | 6,810.32 | 1,876.53 | 2,073.89 | |||
Mostrar todo
VarianzaTGT = Σ(RTGT,t–RTGT)2 ÷ (71 – 1)
= 6,810.32 ÷ (71 – 1)
= 97.29
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,876.53 ÷ (71 – 1)
= 26.81
CovarianzaTGT, S&P 500 = Σ(RTGT,t–RTGT)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,073.89 ÷ (71 – 1)
= 29.63
Estimación sistemática del riesgo (β)
| VarianzaTGT | 97.29 |
| VarianzaS&P 500 | 26.81 |
| CovarianzaTGT, S&P 500 | 29.63 |
| Coeficiente de correlaciónTGT, S&P 5001 | 0.58 |
| βTGT2 | 1.11 |
| αTGT3 | 0.49% |
Cálculos
1 Coeficiente de correlaciónTGT, S&P 500
= CovarianzaTGT, S&P 500 ÷ (Desviación estándarTGT × Desviación estándarS&P 500)
= 29.63 ÷ (9.86% × 5.18%)
= 0.58
2 βTGT
= CovarianzaTGT, S&P 500 ÷ VarianzaS&P 500
= 29.63 ÷ 26.81
= 1.11
3 αTGT
= PromedioTGT – βTGT × PromedioS&P 500
= 1.55% – 1.11 × 0.95%
= 0.49%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.83% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.48% |
| Riesgo sistemático de Target acciones ordinarias | βTGT | 1.11 |
| Tasa de rendimiento esperada de las acciones ordinarias de Target3 | E(RTGT) | 14.38% |
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(RTGT) = RF + βTGT [E(RM) – RF]
= 4.83% + 1.11 [13.48% – 4.83%]
= 14.38%