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 sobre activos de riesgo como las acciones ordinarias de GameStop.
Tasas de retorno
GameStop Corp., tasas mensuales de retorno
| GameStop Corp. (GME) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGME,t1 | DividendoGME,t1 | RGME,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 29 feb. 2016 | $7.71 | 1,932.23 | ||||
| 1. | 31 mar. 2016 | $7.93 | $0.0925 | 4.05% | 2,059.74 | 6.60% |
| 2. | 30 abr. 2016 | $8.20 | 3.40% | 2,065.30 | 0.27% | |
| 3. | 31 may. 2016 | $7.28 | -11.22% | 2,096.95 | 1.53% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2021 | $37.10 | -24.36% | 4,766.18 | 4.36% | |
| 71. | 31 ene. 2022 | $27.23 | -26.60% | 4,515.55 | -5.26% | |
| Promedio (R): | 23.78% | 1.29% | ||||
| Desviación estándar: | 194.23% | 4.25% | ||||
| GameStop Corp. (GME) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioGME,t1 | DividendoGME,t1 | RGME,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 29 feb. 2016 | $7.71 | 1,932.23 | ||||
| 1. | 31 mar. 2016 | $7.93 | $0.0925 | 4.05% | 2,059.74 | 6.60% |
| 2. | 30 abr. 2016 | $8.20 | 3.40% | 2,065.30 | 0.27% | |
| 3. | 31 may. 2016 | $7.28 | -11.22% | 2,096.95 | 1.53% | |
| 4. | 30 jun. 2016 | $6.65 | $0.0925 | -7.38% | 2,098.86 | 0.09% |
| 5. | 31 jul. 2016 | $7.74 | 16.39% | 2,173.60 | 3.56% | |
| 6. | 31 ago. 2016 | $7.10 | -8.27% | 2,170.95 | -0.12% | |
| 7. | 30 sept. 2016 | $6.90 | $0.0925 | -1.51% | 2,168.27 | -0.12% |
| 8. | 31 oct. 2016 | $6.01 | -12.90% | 2,126.15 | -1.94% | |
| 9. | 30 nov. 2016 | $6.17 | $0.0925 | 4.20% | 2,198.81 | 3.42% |
| 10. | 31 dic. 2016 | $6.32 | 2.43% | 2,238.83 | 1.82% | |
| 11. | 31 ene. 2017 | $6.12 | -3.16% | 2,278.87 | 1.79% | |
| 12. | 28 feb. 2017 | $6.11 | -0.16% | 2,363.64 | 3.72% | |
| 13. | 31 mar. 2017 | $5.64 | $0.095 | -6.14% | 2,362.72 | -0.04% |
| 14. | 30 abr. 2017 | $5.67 | 0.53% | 2,384.20 | 0.91% | |
| 15. | 31 may. 2017 | $5.54 | -2.29% | 2,411.80 | 1.16% | |
| 16. | 30 jun. 2017 | $5.40 | $0.095 | -0.81% | 2,423.41 | 0.48% |
| 17. | 31 jul. 2017 | $5.42 | 0.37% | 2,470.30 | 1.93% | |
| 18. | 31 ago. 2017 | $4.63 | -14.58% | 2,471.65 | 0.05% | |
| 19. | 30 sept. 2017 | $5.17 | $0.095 | 13.71% | 2,519.36 | 1.93% |
| 20. | 31 oct. 2017 | $4.67 | -9.67% | 2,575.26 | 2.22% | |
| 21. | 30 nov. 2017 | $4.69 | $0.095 | 2.46% | 2,647.58 | 2.81% |
| 22. | 31 dic. 2017 | $4.49 | -4.26% | 2,673.61 | 0.98% | |
| 23. | 31 ene. 2018 | $4.20 | -6.46% | 2,823.81 | 5.62% | |
| 24. | 28 feb. 2018 | $3.92 | -6.67% | 2,713.83 | -3.89% | |
| 25. | 31 mar. 2018 | $3.16 | $0.095 | -16.96% | 2,640.87 | -2.69% |
| 26. | 30 abr. 2018 | $3.41 | 7.91% | 2,648.05 | 0.27% | |
| 27. | 31 may. 2018 | $3.30 | -3.23% | 2,705.27 | 2.16% | |
| 28. | 30 jun. 2018 | $3.64 | $0.095 | 13.18% | 2,718.37 | 0.48% |
| 29. | 31 jul. 2018 | $3.60 | -1.10% | 2,816.29 | 3.60% | |
| 30. | 31 ago. 2018 | $3.32 | -7.78% | 2,901.52 | 3.03% | |
| 31. | 30 sept. 2018 | $3.82 | $0.095 | 17.92% | 2,913.98 | 0.43% |
| 32. | 31 oct. 2018 | $3.65 | -4.45% | 2,711.74 | -6.94% | |
| 33. | 30 nov. 2018 | $3.42 | -6.30% | 2,760.17 | 1.79% | |
| 34. | 31 dic. 2018 | $3.16 | $0.095 | -4.82% | 2,506.85 | -9.18% |
| 35. | 31 ene. 2019 | $2.84 | -10.13% | 2,704.10 | 7.87% | |
| 36. | 28 feb. 2019 | $2.93 | 3.17% | 2,784.49 | 2.97% | |
| 37. | 31 mar. 2019 | $2.54 | $0.095 | -10.07% | 2,834.40 | 1.79% |
| 38. | 30 abr. 2019 | $2.16 | -14.96% | 2,945.83 | 3.93% | |
| 39. | 31 may. 2019 | $1.90 | -12.04% | 2,752.06 | -6.58% | |
| 40. | 30 jun. 2019 | $1.37 | -27.89% | 2,941.76 | 6.89% | |
| 41. | 31 jul. 2019 | $1.01 | -26.28% | 2,980.38 | 1.31% | |
| 42. | 31 ago. 2019 | $0.99 | -1.98% | 2,926.46 | -1.81% | |
| 43. | 30 sept. 2019 | $1.38 | 39.39% | 2,976.74 | 1.72% | |
| 44. | 31 oct. 2019 | $1.36 | -1.45% | 3,037.56 | 2.04% | |
| 45. | 30 nov. 2019 | $1.59 | 16.91% | 3,140.98 | 3.40% | |
| 46. | 31 dic. 2019 | $1.52 | -4.40% | 3,230.78 | 2.86% | |
| 47. | 31 ene. 2020 | $0.96 | -36.84% | 3,225.52 | -0.16% | |
| 48. | 29 feb. 2020 | $0.90 | -6.25% | 2,954.22 | -8.41% | |
| 49. | 31 mar. 2020 | $0.88 | -2.22% | 2,584.59 | -12.51% | |
| 50. | 30 abr. 2020 | $1.43 | 62.50% | 2,912.43 | 12.68% | |
| 51. | 31 may. 2020 | $1.02 | -28.67% | 3,044.31 | 4.53% | |
| 52. | 30 jun. 2020 | $1.09 | 6.86% | 3,100.29 | 1.84% | |
| 53. | 31 jul. 2020 | $1.00 | -8.26% | 3,271.12 | 5.51% | |
| 54. | 31 ago. 2020 | $1.67 | 67.00% | 3,500.31 | 7.01% | |
| 55. | 30 sept. 2020 | $2.55 | 52.69% | 3,363.00 | -3.92% | |
| 56. | 31 oct. 2020 | $2.62 | 2.75% | 3,269.96 | -2.77% | |
| 57. | 30 nov. 2020 | $4.14 | 58.02% | 3,621.63 | 10.75% | |
| 58. | 31 dic. 2020 | $4.71 | 13.77% | 3,756.07 | 3.71% | |
| 59. | 31 ene. 2021 | $81.25 | 1,625.05% | 3,714.24 | -1.11% | |
| 60. | 28 feb. 2021 | $25.44 | -68.69% | 3,811.15 | 2.61% | |
| 61. | 31 mar. 2021 | $47.46 | 86.56% | 3,972.89 | 4.24% | |
| 62. | 30 abr. 2021 | $43.40 | -8.55% | 4,181.17 | 5.24% | |
| 63. | 31 may. 2021 | $55.50 | 27.88% | 4,204.11 | 0.55% | |
| 64. | 30 jun. 2021 | $53.54 | -3.53% | 4,297.50 | 2.22% | |
| 65. | 31 jul. 2021 | $40.28 | -24.77% | 4,395.26 | 2.27% | |
| 66. | 31 ago. 2021 | $54.56 | 35.45% | 4,522.68 | 2.90% | |
| 67. | 30 sept. 2021 | $43.87 | -19.59% | 4,307.54 | -4.76% | |
| 68. | 31 oct. 2021 | $45.88 | 4.58% | 4,605.38 | 6.91% | |
| 69. | 30 nov. 2021 | $49.05 | 6.91% | 4,567.00 | -0.83% | |
| 70. | 31 dic. 2021 | $37.10 | -24.36% | 4,766.18 | 4.36% | |
| 71. | 31 ene. 2022 | $27.23 | -26.60% | 4,515.55 | -5.26% | |
| Promedio (R): | 23.78% | 1.29% | ||||
| Desviación estándar: | 194.23% | 4.25% | ||||
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 GME 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
GameStop Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RGME,t | RS&P 500,t | (RGME,t–RGME)2 | (RS&P 500,t–RS&P 500)2 | (RGME,t–RGME)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2016 | 4.05% | 6.60% | 389.16 | 28.16 | -104.69 |
| 2. | 30 abr. 2016 | 3.40% | 0.27% | 415.16 | 1.05 | 20.83 |
| 3. | 31 may. 2016 | -11.22% | 1.53% | 1,224.98 | 0.06 | -8.41 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2021 | -24.36% | 4.36% | 2,317.76 | 9.42 | -147.75 |
| 71. | 31 ene. 2022 | -26.60% | -5.26% | 2,538.54 | 42.91 | 330.05 |
| Total (Σ): | 2,640,729.02 | 1,262.70 | -1,983.24 | |||
| t | Fecha | RGME,t | RS&P 500,t | (RGME,t–RGME)2 | (RS&P 500,t–RS&P 500)2 | (RGME,t–RGME)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2016 | 4.05% | 6.60% | 389.16 | 28.16 | -104.69 |
| 2. | 30 abr. 2016 | 3.40% | 0.27% | 415.16 | 1.05 | 20.83 |
| 3. | 31 may. 2016 | -11.22% | 1.53% | 1,224.98 | 0.06 | -8.41 |
| 4. | 30 jun. 2016 | -7.38% | 0.09% | 971.16 | 1.44 | 37.43 |
| 5. | 31 jul. 2016 | 16.39% | 3.56% | 54.60 | 5.15 | -16.76 |
| 6. | 31 ago. 2016 | -8.27% | -0.12% | 1,027.13 | 2.00 | 45.32 |
| 7. | 30 sept. 2016 | -1.51% | -0.12% | 639.80 | 2.00 | 35.81 |
| 8. | 31 oct. 2016 | -12.90% | -1.94% | 1,345.33 | 10.46 | 118.65 |
| 9. | 30 nov. 2016 | 4.20% | 3.42% | 383.33 | 4.52 | -41.61 |
| 10. | 31 dic. 2016 | 2.43% | 1.82% | 455.78 | 0.28 | -11.27 |
| 11. | 31 ene. 2017 | -3.16% | 1.79% | 726.02 | 0.25 | -13.37 |
| 12. | 28 feb. 2017 | -0.16% | 3.72% | 573.30 | 5.89 | -58.13 |
| 13. | 31 mar. 2017 | -6.14% | -0.04% | 895.07 | 1.77 | 39.83 |
| 14. | 30 abr. 2017 | 0.53% | 0.91% | 540.48 | 0.15 | 8.91 |
| 15. | 31 may. 2017 | -2.29% | 1.16% | 679.80 | 0.02 | 3.51 |
| 16. | 30 jun. 2017 | -0.81% | 0.48% | 604.79 | 0.66 | 19.94 |
| 17. | 31 jul. 2017 | 0.37% | 1.93% | 548.02 | 0.41 | -15.04 |
| 18. | 31 ago. 2017 | -14.58% | 0.05% | 1,471.17 | 1.53 | 47.47 |
| 19. | 30 sept. 2017 | 13.71% | 1.93% | 101.31 | 0.41 | -6.42 |
| 20. | 31 oct. 2017 | -9.67% | 2.22% | 1,118.99 | 0.86 | -31.00 |
| 21. | 30 nov. 2017 | 2.46% | 2.81% | 454.44 | 2.30 | -32.32 |
| 22. | 31 dic. 2017 | -4.26% | 0.98% | 786.50 | 0.10 | 8.67 |
| 23. | 31 ene. 2018 | -6.46% | 5.62% | 914.40 | 18.71 | -130.80 |
| 24. | 28 feb. 2018 | -6.67% | -3.89% | 927.01 | 26.90 | 157.93 |
| 25. | 31 mar. 2018 | -16.96% | -2.69% | 1,660.11 | 15.85 | 162.19 |
| 26. | 30 abr. 2018 | 7.91% | 0.27% | 251.82 | 1.04 | 16.19 |
| 27. | 31 may. 2018 | -3.23% | 2.16% | 729.32 | 0.75 | -23.46 |
| 28. | 30 jun. 2018 | 13.18% | 0.48% | 112.33 | 0.65 | 8.56 |
| 29. | 31 jul. 2018 | -1.10% | 3.60% | 618.97 | 5.34 | -57.47 |
| 30. | 31 ago. 2018 | -7.78% | 3.03% | 995.91 | 3.01 | -54.72 |
| 31. | 30 sept. 2018 | 17.92% | 0.43% | 34.32 | 0.74 | 5.05 |
| 32. | 31 oct. 2018 | -4.45% | -6.94% | 796.96 | 67.78 | 232.41 |
| 33. | 30 nov. 2018 | -6.30% | 1.79% | 904.90 | 0.24 | -14.85 |
| 34. | 31 dic. 2018 | -4.82% | -9.18% | 818.23 | 109.62 | 299.49 |
| 35. | 31 ene. 2019 | -10.13% | 7.87% | 1,149.67 | 43.25 | -222.98 |
| 36. | 28 feb. 2019 | 3.17% | 2.97% | 424.82 | 2.82 | -34.64 |
| 37. | 31 mar. 2019 | -10.07% | 1.79% | 1,145.72 | 0.25 | -16.93 |
| 38. | 30 abr. 2019 | -14.96% | 3.93% | 1,500.85 | 6.96 | -102.24 |
| 39. | 31 may. 2019 | -12.04% | -6.58% | 1,282.87 | 61.94 | 281.88 |
| 40. | 30 jun. 2019 | -27.89% | 6.89% | 2,670.30 | 31.37 | -289.42 |
| 41. | 31 jul. 2019 | -26.28% | 1.31% | 2,505.76 | 0.00 | -1.03 |
| 42. | 31 ago. 2019 | -1.98% | -1.81% | 663.60 | 9.62 | 79.89 |
| 43. | 30 sept. 2019 | 39.39% | 1.72% | 243.79 | 0.18 | 6.65 |
| 44. | 31 oct. 2019 | -1.45% | 2.04% | 636.53 | 0.56 | -18.95 |
| 45. | 30 nov. 2019 | 16.91% | 3.40% | 47.18 | 4.46 | -14.51 |
| 46. | 31 dic. 2019 | -4.40% | 2.86% | 794.27 | 2.45 | -44.15 |
| 47. | 31 ene. 2020 | -36.84% | -0.16% | 3,675.06 | 2.12 | 88.21 |
| 48. | 29 feb. 2020 | -6.25% | -8.41% | 901.81 | 94.15 | 291.39 |
| 49. | 31 mar. 2020 | -2.22% | -12.51% | 676.13 | 190.56 | 358.94 |
| 50. | 30 abr. 2020 | 62.50% | 12.68% | 1,499.22 | 129.78 | 441.10 |
| 51. | 31 may. 2020 | -28.67% | 4.53% | 2,751.16 | 10.47 | -169.73 |
| 52. | 30 jun. 2020 | 6.86% | 1.84% | 286.20 | 0.30 | -9.25 |
| 53. | 31 jul. 2020 | -8.26% | 5.51% | 1,026.37 | 17.79 | -135.13 |
| 54. | 31 ago. 2020 | 67.00% | 7.01% | 1,867.95 | 32.65 | 246.97 |
| 55. | 30 sept. 2020 | 52.69% | -3.92% | 836.04 | 27.20 | -150.79 |
| 56. | 31 oct. 2020 | 2.75% | -2.77% | 442.48 | 16.47 | 85.38 |
| 57. | 30 nov. 2020 | 58.02% | 10.75% | 1,172.04 | 89.54 | 323.94 |
| 58. | 31 dic. 2020 | 13.77% | 3.71% | 100.24 | 5.86 | -24.23 |
| 59. | 31 ene. 2021 | 1,625.05% | -1.11% | 2,564,074.83 | 5.79 | -3,852.52 |
| 60. | 28 feb. 2021 | -68.69% | 2.61% | 8,550.60 | 1.73 | -121.77 |
| 61. | 31 mar. 2021 | 86.56% | 4.24% | 3,940.88 | 8.71 | 185.29 |
| 62. | 30 abr. 2021 | -8.55% | 5.24% | 1,045.54 | 15.60 | -127.73 |
| 63. | 31 may. 2021 | 27.88% | 0.55% | 16.81 | 0.55 | -3.05 |
| 64. | 30 jun. 2021 | -3.53% | 2.22% | 745.93 | 0.86 | -25.38 |
| 65. | 31 jul. 2021 | -24.77% | 2.27% | 2,356.79 | 0.97 | -47.70 |
| 66. | 31 ago. 2021 | 35.45% | 2.90% | 136.23 | 2.58 | 18.75 |
| 67. | 30 sept. 2021 | -19.59% | -4.76% | 1,881.24 | 36.59 | 262.37 |
| 68. | 31 oct. 2021 | 4.58% | 6.91% | 368.58 | 31.61 | -107.94 |
| 69. | 30 nov. 2021 | 6.91% | -0.83% | 284.63 | 4.52 | 35.86 |
| 70. | 31 dic. 2021 | -24.36% | 4.36% | 2,317.76 | 9.42 | -147.75 |
| 71. | 31 ene. 2022 | -26.60% | -5.26% | 2,538.54 | 42.91 | 330.05 |
| Total (Σ): | 2,640,729.02 | 1,262.70 | -1,983.24 | |||
Mostrar todo
VarianzaGME = Σ(RGME,t–RGME)2 ÷ (71 – 1)
= 2,640,729.02 ÷ (71 – 1)
= 37,724.70
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04
CovarianzaGME, S&P 500 = Σ(RGME,t–RGME)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= -1,983.24 ÷ (71 – 1)
= -28.33
Estimación sistemática del riesgo (β)
| VarianzaGME | 37,724.70 |
| VarianzaS&P 500 | 18.04 |
| CovarianzaGME, S&P 500 | -28.33 |
| Coeficiente de correlaciónGME, S&P 5001 | -0.03 |
| βGME2 | -1.57 |
| αGME3 | 25.81% |
Cálculos
1 Coeficiente de correlaciónGME, S&P 500
= CovarianzaGME, S&P 500 ÷ (Desviación estándarGME × Desviación estándarS&P 500)
= -28.33 ÷ (194.23% × 4.25%)
= -0.03
2 βGME
= CovarianzaGME, S&P 500 ÷ VarianzaS&P 500
= -28.33 ÷ 18.04
= -1.57
3 αGME
= PromedioGME – βGME × PromedioS&P 500
= 23.78% – -1.57 × 1.29%
= 25.81%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.85% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.46% |
| Riesgo sistemático de GameStop acciones ordinarias | βGME | -1.57 |
| Tasa de rendimiento esperada de las acciones ordinarias de GameStop3 | E(RGME) | -8.68% |
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(RGME) = RF + βGME [E(RM) – RF]
= 4.85% + -1.57 [13.46% – 4.85%]
= -8.68%