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 TJX.
Tasas de retorno
TJX Cos. Inc. (TJX) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioTJX,t1 | DividendoTJX,t1 | RTJX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
29 feb. 2016 | $37.05 | 1,932.23 | ||||
1. | 31 mar. 2016 | $39.18 | 5.75% | 2,059.74 | 6.60% | |
2. | 30 abr. 2016 | $37.91 | -3.24% | 2,065.30 | 0.27% | |
3. | 31 may. 2016 | $38.06 | $0.13 | 0.74% | 2,096.95 | 1.53% |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 dic. 2021 | $75.92 | 9.39% | 4,766.18 | 4.36% | |
71. | 31 ene. 2022 | $71.97 | -5.20% | 4,515.55 | -5.26% | |
Promedio (R): | 1.24% | 1.29% | ||||
Desviación estándar: | 6.31% | 4.25% |
TJX Cos. Inc. (TJX) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioTJX,t1 | DividendoTJX,t1 | RTJX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
29 feb. 2016 | $37.05 | 1,932.23 | ||||
1. | 31 mar. 2016 | $39.18 | 5.75% | 2,059.74 | 6.60% | |
2. | 30 abr. 2016 | $37.91 | -3.24% | 2,065.30 | 0.27% | |
3. | 31 may. 2016 | $38.06 | $0.13 | 0.74% | 2,096.95 | 1.53% |
4. | 30 jun. 2016 | $38.62 | 1.47% | 2,098.86 | 0.09% | |
5. | 31 jul. 2016 | $40.86 | 5.80% | 2,173.60 | 3.56% | |
6. | 31 ago. 2016 | $38.72 | $0.13 | -4.92% | 2,170.95 | -0.12% |
7. | 30 sept. 2016 | $37.39 | -3.43% | 2,168.27 | -0.12% | |
8. | 31 oct. 2016 | $36.88 | -1.36% | 2,126.15 | -1.94% | |
9. | 30 nov. 2016 | $39.17 | $0.13 | 6.56% | 2,198.81 | 3.42% |
10. | 31 dic. 2016 | $37.57 | -4.08% | 2,238.83 | 1.82% | |
11. | 31 ene. 2017 | $37.46 | -0.29% | 2,278.87 | 1.79% | |
12. | 28 feb. 2017 | $39.23 | $0.13 | 5.07% | 2,363.64 | 3.72% |
13. | 31 mar. 2017 | $39.54 | 0.79% | 2,362.72 | -0.04% | |
14. | 30 abr. 2017 | $39.32 | -0.56% | 2,384.20 | 0.91% | |
15. | 31 may. 2017 | $37.61 | $0.15625 | -3.95% | 2,411.80 | 1.16% |
16. | 30 jun. 2017 | $36.09 | -4.04% | 2,423.41 | 0.48% | |
17. | 31 jul. 2017 | $35.16 | -2.58% | 2,470.30 | 1.93% | |
18. | 31 ago. 2017 | $36.15 | $0.15625 | 3.26% | 2,471.65 | 0.05% |
19. | 30 sept. 2017 | $36.87 | 1.99% | 2,519.36 | 1.93% | |
20. | 31 oct. 2017 | $34.90 | -5.34% | 2,575.26 | 2.22% | |
21. | 30 nov. 2017 | $37.78 | $0.15625 | 8.70% | 2,647.58 | 2.81% |
22. | 31 dic. 2017 | $38.23 | 1.19% | 2,673.61 | 0.98% | |
23. | 31 ene. 2018 | $40.16 | 5.05% | 2,823.81 | 5.62% | |
24. | 28 feb. 2018 | $41.34 | $0.15625 | 3.33% | 2,713.83 | -3.89% |
25. | 31 mar. 2018 | $40.78 | -1.35% | 2,640.87 | -2.69% | |
26. | 30 abr. 2018 | $42.42 | 4.02% | 2,648.05 | 0.27% | |
27. | 31 may. 2018 | $45.16 | $0.195 | 6.92% | 2,705.27 | 2.16% |
28. | 30 jun. 2018 | $47.59 | 5.38% | 2,718.37 | 0.48% | |
29. | 31 jul. 2018 | $48.63 | 2.19% | 2,816.29 | 3.60% | |
30. | 31 ago. 2018 | $54.99 | $0.195 | 13.48% | 2,901.52 | 3.03% |
31. | 30 sept. 2018 | $56.01 | 1.85% | 2,913.98 | 0.43% | |
32. | 31 oct. 2018 | $54.94 | -1.91% | 2,711.74 | -6.94% | |
33. | 30 nov. 2018 | $48.85 | $0.195 | -10.73% | 2,760.17 | 1.79% |
34. | 31 dic. 2018 | $44.74 | -8.41% | 2,506.85 | -9.18% | |
35. | 31 ene. 2019 | $49.73 | 11.15% | 2,704.10 | 7.87% | |
36. | 28 feb. 2019 | $51.29 | $0.195 | 3.53% | 2,784.49 | 2.97% |
37. | 31 mar. 2019 | $53.21 | 3.74% | 2,834.40 | 1.79% | |
38. | 30 abr. 2019 | $54.88 | 3.14% | 2,945.83 | 3.93% | |
39. | 31 may. 2019 | $50.29 | $0.23 | -7.94% | 2,752.06 | -6.58% |
40. | 30 jun. 2019 | $52.88 | 5.15% | 2,941.76 | 6.89% | |
41. | 31 jul. 2019 | $54.56 | 3.18% | 2,980.38 | 1.31% | |
42. | 31 ago. 2019 | $54.97 | $0.23 | 1.17% | 2,926.46 | -1.81% |
43. | 30 sept. 2019 | $55.74 | 1.40% | 2,976.74 | 1.72% | |
44. | 31 oct. 2019 | $57.65 | 3.43% | 3,037.56 | 2.04% | |
45. | 30 nov. 2019 | $61.13 | $0.23 | 6.44% | 3,140.98 | 3.40% |
46. | 31 dic. 2019 | $61.06 | -0.11% | 3,230.78 | 2.86% | |
47. | 31 ene. 2020 | $59.04 | -3.31% | 3,225.52 | -0.16% | |
48. | 29 feb. 2020 | $59.80 | $0.23 | 1.68% | 2,954.22 | -8.41% |
49. | 31 mar. 2020 | $47.81 | -20.05% | 2,584.59 | -12.51% | |
50. | 30 abr. 2020 | $49.05 | 2.59% | 2,912.43 | 12.68% | |
51. | 31 may. 2020 | $52.76 | 7.56% | 3,044.31 | 4.53% | |
52. | 30 jun. 2020 | $50.56 | -4.17% | 3,100.29 | 1.84% | |
53. | 31 jul. 2020 | $51.99 | 2.83% | 3,271.12 | 5.51% | |
54. | 31 ago. 2020 | $54.79 | 5.39% | 3,500.31 | 7.01% | |
55. | 30 sept. 2020 | $55.65 | 1.57% | 3,363.00 | -3.92% | |
56. | 31 oct. 2020 | $50.80 | -8.72% | 3,269.96 | -2.77% | |
57. | 30 nov. 2020 | $63.51 | 25.02% | 3,621.63 | 10.75% | |
58. | 31 dic. 2020 | $68.29 | 7.53% | 3,756.07 | 3.71% | |
59. | 31 ene. 2021 | $64.04 | -6.22% | 3,714.24 | -1.11% | |
60. | 28 feb. 2021 | $65.99 | $0.26 | 3.45% | 3,811.15 | 2.61% |
61. | 31 mar. 2021 | $66.15 | 0.24% | 3,972.89 | 4.24% | |
62. | 30 abr. 2021 | $71.00 | 7.33% | 4,181.17 | 5.24% | |
63. | 31 may. 2021 | $67.54 | $0.26 | -4.51% | 4,204.11 | 0.55% |
64. | 30 jun. 2021 | $67.42 | -0.18% | 4,297.50 | 2.22% | |
65. | 31 jul. 2021 | $68.81 | 2.06% | 4,395.26 | 2.27% | |
66. | 31 ago. 2021 | $72.72 | $0.26 | 6.06% | 4,522.68 | 2.90% |
67. | 30 sept. 2021 | $65.98 | -9.27% | 4,307.54 | -4.76% | |
68. | 31 oct. 2021 | $65.49 | -0.74% | 4,605.38 | 6.91% | |
69. | 30 nov. 2021 | $69.40 | $0.26 | 6.37% | 4,567.00 | -0.83% |
70. | 31 dic. 2021 | $75.92 | 9.39% | 4,766.18 | 4.36% | |
71. | 31 ene. 2022 | $71.97 | -5.20% | 4,515.55 | -5.26% | |
Promedio (R): | 1.24% | 1.29% | ||||
Desviación estándar: | 6.31% | 4.25% |
Mostrar todo
1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de TJX 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
t | Fecha | RTJX,t | RS&P 500,t | (RTJX,t–RTJX)2 | (RS&P 500,t–RS&P 500)2 | (RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 mar. 2016 | 5.75% | 6.60% | 20.30 | 28.16 | 23.91 |
2. | 30 abr. 2016 | -3.24% | 0.27% | 20.12 | 1.05 | 4.59 |
3. | 31 may. 2016 | 0.74% | 1.53% | 0.26 | 0.06 | -0.12 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 dic. 2021 | 9.39% | 4.36% | 66.44 | 9.42 | 25.02 |
71. | 31 ene. 2022 | -5.20% | -5.26% | 41.56 | 42.91 | 42.23 |
Total (Σ): | 2,784.34 | 1,262.70 | 1,226.01 |
t | Fecha | RTJX,t | RS&P 500,t | (RTJX,t–RTJX)2 | (RS&P 500,t–RS&P 500)2 | (RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 mar. 2016 | 5.75% | 6.60% | 20.30 | 28.16 | 23.91 |
2. | 30 abr. 2016 | -3.24% | 0.27% | 20.12 | 1.05 | 4.59 |
3. | 31 may. 2016 | 0.74% | 1.53% | 0.26 | 0.06 | -0.12 |
4. | 30 jun. 2016 | 1.47% | 0.09% | 0.05 | 1.44 | -0.27 |
5. | 31 jul. 2016 | 5.80% | 3.56% | 20.76 | 5.15 | 10.34 |
6. | 31 ago. 2016 | -4.92% | -0.12% | 37.98 | 2.00 | 8.72 |
7. | 30 sept. 2016 | -3.43% | -0.12% | 21.89 | 2.00 | 6.62 |
8. | 31 oct. 2016 | -1.36% | -1.94% | 6.80 | 10.46 | 8.44 |
9. | 30 nov. 2016 | 6.56% | 3.42% | 28.28 | 4.52 | 11.30 |
10. | 31 dic. 2016 | -4.08% | 1.82% | 28.39 | 0.28 | -2.81 |
11. | 31 ene. 2017 | -0.29% | 1.79% | 2.36 | 0.25 | -0.76 |
12. | 28 feb. 2017 | 5.07% | 3.72% | 14.66 | 5.89 | 9.29 |
13. | 31 mar. 2017 | 0.79% | -0.04% | 0.21 | 1.77 | 0.60 |
14. | 30 abr. 2017 | -0.56% | 0.91% | 3.24 | 0.15 | 0.69 |
15. | 31 may. 2017 | -3.95% | 1.16% | 26.99 | 0.02 | 0.70 |
16. | 30 jun. 2017 | -4.04% | 0.48% | 27.93 | 0.66 | 4.29 |
17. | 31 jul. 2017 | -2.58% | 1.93% | 14.60 | 0.41 | -2.46 |
18. | 31 ago. 2017 | 3.26% | 0.05% | 4.07 | 1.53 | -2.50 |
19. | 30 sept. 2017 | 1.99% | 1.93% | 0.56 | 0.41 | 0.48 |
20. | 31 oct. 2017 | -5.34% | 2.22% | 43.39 | 0.86 | -6.10 |
21. | 30 nov. 2017 | 8.70% | 2.81% | 55.59 | 2.30 | 11.30 |
22. | 31 dic. 2017 | 1.19% | 0.98% | 0.00 | 0.10 | 0.02 |
23. | 31 ene. 2018 | 5.05% | 5.62% | 14.48 | 18.71 | 16.46 |
24. | 28 feb. 2018 | 3.33% | -3.89% | 4.34 | 26.90 | -10.81 |
25. | 31 mar. 2018 | -1.35% | -2.69% | 6.75 | 15.85 | 10.34 |
26. | 30 abr. 2018 | 4.02% | 0.27% | 7.72 | 1.04 | -2.83 |
27. | 31 may. 2018 | 6.92% | 2.16% | 32.21 | 0.75 | 4.93 |
28. | 30 jun. 2018 | 5.38% | 0.48% | 17.12 | 0.65 | -3.34 |
29. | 31 jul. 2018 | 2.19% | 3.60% | 0.89 | 5.34 | 2.18 |
30. | 31 ago. 2018 | 13.48% | 3.03% | 149.71 | 3.01 | 21.22 |
31. | 30 sept. 2018 | 1.85% | 0.43% | 0.37 | 0.74 | -0.53 |
32. | 31 oct. 2018 | -1.91% | -6.94% | 9.95 | 67.78 | 25.97 |
33. | 30 nov. 2018 | -10.73% | 1.79% | 143.37 | 0.24 | -5.91 |
34. | 31 dic. 2018 | -8.41% | -9.18% | 93.26 | 109.62 | 101.11 |
35. | 31 ene. 2019 | 11.15% | 7.87% | 98.20 | 43.25 | 65.17 |
36. | 28 feb. 2019 | 3.53% | 2.97% | 5.22 | 2.82 | 3.84 |
37. | 31 mar. 2019 | 3.74% | 1.79% | 6.25 | 0.25 | 1.25 |
38. | 30 abr. 2019 | 3.14% | 3.93% | 3.59 | 6.96 | 5.00 |
39. | 31 may. 2019 | -7.94% | -6.58% | 84.43 | 61.94 | 72.31 |
40. | 30 jun. 2019 | 5.15% | 6.89% | 15.26 | 31.37 | 21.88 |
41. | 31 jul. 2019 | 3.18% | 1.31% | 3.74 | 0.00 | 0.04 |
42. | 31 ago. 2019 | 1.17% | -1.81% | 0.00 | 9.62 | 0.22 |
43. | 30 sept. 2019 | 1.40% | 1.72% | 0.02 | 0.18 | 0.07 |
44. | 31 oct. 2019 | 3.43% | 2.04% | 4.77 | 0.56 | 1.64 |
45. | 30 nov. 2019 | 6.44% | 3.40% | 26.95 | 4.46 | 10.97 |
46. | 31 dic. 2019 | -0.11% | 2.86% | 1.84 | 2.45 | -2.13 |
47. | 31 ene. 2020 | -3.31% | -0.16% | 20.72 | 2.12 | 6.62 |
48. | 29 feb. 2020 | 1.68% | -8.41% | 0.19 | 94.15 | -4.20 |
49. | 31 mar. 2020 | -20.05% | -12.51% | 453.43 | 190.56 | 293.94 |
50. | 30 abr. 2020 | 2.59% | 12.68% | 1.82 | 129.78 | 15.38 |
51. | 31 may. 2020 | 7.56% | 4.53% | 39.94 | 10.47 | 20.45 |
52. | 30 jun. 2020 | -4.17% | 1.84% | 29.31 | 0.30 | -2.96 |
53. | 31 jul. 2020 | 2.83% | 5.51% | 2.51 | 17.79 | 6.68 |
54. | 31 ago. 2020 | 5.39% | 7.01% | 17.16 | 32.65 | 23.67 |
55. | 30 sept. 2020 | 1.57% | -3.92% | 0.11 | 27.20 | -1.70 |
56. | 31 oct. 2020 | -8.72% | -2.77% | 99.18 | 16.47 | 40.42 |
57. | 30 nov. 2020 | 25.02% | 10.75% | 565.30 | 89.54 | 224.98 |
58. | 31 dic. 2020 | 7.53% | 3.71% | 39.47 | 5.86 | 15.20 |
59. | 31 ene. 2021 | -6.22% | -1.11% | 55.76 | 5.79 | 17.97 |
60. | 28 feb. 2021 | 3.45% | 2.61% | 4.87 | 1.73 | 2.91 |
61. | 31 mar. 2021 | 0.24% | 4.24% | 1.00 | 8.71 | -2.96 |
62. | 30 abr. 2021 | 7.33% | 5.24% | 37.07 | 15.60 | 24.05 |
63. | 31 may. 2021 | -4.51% | 0.55% | 33.07 | 0.55 | 4.28 |
64. | 30 jun. 2021 | -0.18% | 2.22% | 2.02 | 0.86 | -1.32 |
65. | 31 jul. 2021 | 2.06% | 2.27% | 0.67 | 0.97 | 0.80 |
66. | 31 ago. 2021 | 6.06% | 2.90% | 23.20 | 2.58 | 7.74 |
67. | 30 sept. 2021 | -9.27% | -4.76% | 110.50 | 36.59 | 63.59 |
68. | 31 oct. 2021 | -0.74% | 6.91% | 3.95 | 31.61 | -11.17 |
69. | 30 nov. 2021 | 6.37% | -0.83% | 26.25 | 4.52 | -10.89 |
70. | 31 dic. 2021 | 9.39% | 4.36% | 66.44 | 9.42 | 25.02 |
71. | 31 ene. 2022 | -5.20% | -5.26% | 41.56 | 42.91 | 42.23 |
Total (Σ): | 2,784.34 | 1,262.70 | 1,226.01 |
Mostrar todo
VarianzaTJX = Σ(RTJX,t–RTJX)2 ÷ (71 – 1)
= 2,784.34 ÷ (71 – 1)
= 39.78
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04
CovarianzaTJX, S&P 500 = Σ(RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,226.01 ÷ (71 – 1)
= 17.51
Estimación sistemática del riesgo (β)
VarianzaTJX | 39.78 |
VarianzaS&P 500 | 18.04 |
CovarianzaTJX, S&P 500 | 17.51 |
Coeficiente de correlaciónTJX, S&P 5001 | 0.65 |
βTJX2 | 0.97 |
αTJX3 | -0.01% |
Cálculos
1 Coeficiente de correlaciónTJX, S&P 500
= CovarianzaTJX, S&P 500 ÷ (Desviación estándarTJX × Desviación estándarS&P 500)
= 17.51 ÷ (6.31% × 4.25%)
= 0.65
2 βTJX
= CovarianzaTJX, S&P 500 ÷ VarianzaS&P 500
= 17.51 ÷ 18.04
= 0.97
3 αTJX
= PromedioTJX – βTJX × PromedioS&P 500
= 1.24% – 0.97 × 1.29%
= -0.01%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento de LT Treasury Composite1 | RF | 3.77% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 12.52% |
Riesgo sistemático de TJX acciones ordinarias | βTJX | 0.97 |
Tasa de rendimiento esperada de las acciones ordinarias de TJX3 | E(RTJX) | 12.27% |
1 Promedio no ponderado de los rendimientos de las ofertas en todos los bonos del Tesoro de los Estados Unidos con cupón fijo pendientes, ni vencidos ni exigibles en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RTJX) = RF + βTJX [E(RM) – RF]
= 3.77% + 0.97 [12.52% – 3.77%]
= 12.27%