O modelo de precificação de ativos de capital (CAPM) indica qual deve ser a taxa de retorno esperada ou exigida sobre ativos de risco, como ações ordinárias de Dollar General.
Taxas de retorno
Dollar General Corp. (DG) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Data | PreçoDG,t1 | DividendoDG,t1 | RDG,t2 | PreçoS&P 500,t | RS&P 500,t3 |
28 de fev. de 2017 | $73.02 | 2,363.64 | ||||
1. | 31 de mar. de 2017 | $69.73 | -4.51% | 2,362.72 | -0.04% | |
2. | 30 de abr. de 2017 | $72.71 | $0.26 | 4.65% | 2,384.20 | 0.91% |
3. | 31 de mai. de 2017 | $73.39 | 0.94% | 2,411.80 | 1.16% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 de dez. de 2022 | $246.25 | $0.55 | -3.47% | 3,839.50 | -5.90% |
71. | 31 de jan. de 2023 | $233.60 | -5.14% | 4,076.60 | 6.18% | |
Média (R): | 1.91% | 0.90% | ||||
Desvio padrão: | 6.00% | 5.01% |
Dollar General Corp. (DG) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Data | PreçoDG,t1 | DividendoDG,t1 | RDG,t2 | PreçoS&P 500,t | RS&P 500,t3 |
28 de fev. de 2017 | $73.02 | 2,363.64 | ||||
1. | 31 de mar. de 2017 | $69.73 | -4.51% | 2,362.72 | -0.04% | |
2. | 30 de abr. de 2017 | $72.71 | $0.26 | 4.65% | 2,384.20 | 0.91% |
3. | 31 de mai. de 2017 | $73.39 | 0.94% | 2,411.80 | 1.16% | |
4. | 30 de jun. de 2017 | $72.09 | -1.77% | 2,423.41 | 0.48% | |
5. | 31 de jul. de 2017 | $75.16 | $0.26 | 4.62% | 2,470.30 | 1.93% |
6. | 31 de ago. de 2017 | $72.56 | -3.46% | 2,471.65 | 0.05% | |
7. | 30 de set. de 2017 | $81.05 | 11.70% | 2,519.36 | 1.93% | |
8. | 31 de out. de 2017 | $80.84 | $0.26 | 0.06% | 2,575.26 | 2.22% |
9. | 30 de nov. de 2017 | $88.08 | 8.96% | 2,647.58 | 2.81% | |
10. | 31 de dez. de 2017 | $93.01 | 5.60% | 2,673.61 | 0.98% | |
11. | 31 de jan. de 2018 | $103.12 | $0.26 | 11.15% | 2,823.81 | 5.62% |
12. | 28 de fev. de 2018 | $94.59 | -8.27% | 2,713.83 | -3.89% | |
13. | 31 de mar. de 2018 | $93.55 | -1.10% | 2,640.87 | -2.69% | |
14. | 30 de abr. de 2018 | $96.53 | $0.29 | 3.50% | 2,648.05 | 0.27% |
15. | 31 de mai. de 2018 | $87.48 | -9.38% | 2,705.27 | 2.16% | |
16. | 30 de jun. de 2018 | $98.60 | 12.71% | 2,718.37 | 0.48% | |
17. | 31 de jul. de 2018 | $98.15 | $0.29 | -0.16% | 2,816.29 | 3.60% |
18. | 31 de ago. de 2018 | $107.73 | 9.76% | 2,901.52 | 3.03% | |
19. | 30 de set. de 2018 | $109.30 | 1.46% | 2,913.98 | 0.43% | |
20. | 31 de out. de 2018 | $111.38 | $0.29 | 2.17% | 2,711.74 | -6.94% |
21. | 30 de nov. de 2018 | $110.99 | -0.35% | 2,760.17 | 1.79% | |
22. | 31 de dez. de 2018 | $108.08 | -2.62% | 2,506.85 | -9.18% | |
23. | 31 de jan. de 2019 | $115.43 | $0.29 | 7.07% | 2,704.10 | 7.87% |
24. | 28 de fev. de 2019 | $118.46 | 2.62% | 2,784.49 | 2.97% | |
25. | 31 de mar. de 2019 | $119.30 | 0.71% | 2,834.40 | 1.79% | |
26. | 30 de abr. de 2019 | $126.09 | $0.32 | 5.96% | 2,945.83 | 3.93% |
27. | 31 de mai. de 2019 | $127.28 | 0.94% | 2,752.06 | -6.58% | |
28. | 30 de jun. de 2019 | $135.16 | 6.19% | 2,941.76 | 6.89% | |
29. | 31 de jul. de 2019 | $134.02 | $0.32 | -0.61% | 2,980.38 | 1.31% |
30. | 31 de ago. de 2019 | $156.09 | 16.47% | 2,926.46 | -1.81% | |
31. | 30 de set. de 2019 | $158.94 | 1.83% | 2,976.74 | 1.72% | |
32. | 31 de out. de 2019 | $160.34 | $0.32 | 1.08% | 3,037.56 | 2.04% |
33. | 30 de nov. de 2019 | $157.36 | -1.86% | 3,140.98 | 3.40% | |
34. | 31 de dez. de 2019 | $155.98 | -0.88% | 3,230.78 | 2.86% | |
35. | 31 de jan. de 2020 | $153.41 | $0.32 | -1.44% | 3,225.52 | -0.16% |
36. | 29 de fev. de 2020 | $150.30 | -2.03% | 2,954.22 | -8.41% | |
37. | 31 de mar. de 2020 | $151.01 | 0.47% | 2,584.59 | -12.51% | |
38. | 30 de abr. de 2020 | $175.30 | $0.36 | 16.32% | 2,912.43 | 12.68% |
39. | 31 de mai. de 2020 | $191.51 | 9.25% | 3,044.31 | 4.53% | |
40. | 30 de jun. de 2020 | $190.51 | -0.52% | 3,100.29 | 1.84% | |
41. | 31 de jul. de 2020 | $190.40 | $0.36 | 0.13% | 3,271.12 | 5.51% |
42. | 31 de ago. de 2020 | $201.88 | 6.03% | 3,500.31 | 7.01% | |
43. | 30 de set. de 2020 | $209.62 | 3.83% | 3,363.00 | -3.92% | |
44. | 31 de out. de 2020 | $208.71 | $0.36 | -0.26% | 3,269.96 | -2.77% |
45. | 30 de nov. de 2020 | $218.58 | 4.73% | 3,621.63 | 10.75% | |
46. | 31 de dez. de 2020 | $210.30 | -3.79% | 3,756.07 | 3.71% | |
47. | 31 de jan. de 2021 | $194.61 | $0.36 | -7.29% | 3,714.24 | -1.11% |
48. | 28 de fev. de 2021 | $188.99 | -2.89% | 3,811.15 | 2.61% | |
49. | 31 de mar. de 2021 | $202.62 | 7.21% | 3,972.89 | 4.24% | |
50. | 30 de abr. de 2021 | $214.75 | $0.42 | 6.19% | 4,181.17 | 5.24% |
51. | 31 de mai. de 2021 | $202.96 | -5.49% | 4,204.11 | 0.55% | |
52. | 30 de jun. de 2021 | $216.39 | 6.62% | 4,297.50 | 2.22% | |
53. | 31 de jul. de 2021 | $232.64 | $0.42 | 7.70% | 4,395.26 | 2.27% |
54. | 31 de ago. de 2021 | $222.91 | -4.18% | 4,522.68 | 2.90% | |
55. | 30 de set. de 2021 | $212.14 | -4.83% | 4,307.54 | -4.76% | |
56. | 31 de out. de 2021 | $221.52 | $0.42 | 4.62% | 4,605.38 | 6.91% |
57. | 30 de nov. de 2021 | $221.30 | -0.10% | 4,567.00 | -0.83% | |
58. | 31 de dez. de 2021 | $235.83 | 6.57% | 4,766.18 | 4.36% | |
59. | 31 de jan. de 2022 | $208.48 | $0.42 | -11.42% | 4,515.55 | -5.26% |
60. | 28 de fev. de 2022 | $198.34 | -4.86% | 4,373.94 | -3.14% | |
61. | 31 de mar. de 2022 | $222.63 | 12.25% | 4,530.41 | 3.58% | |
62. | 30 de abr. de 2022 | $237.53 | $0.55 | 6.94% | 4,131.93 | -8.80% |
63. | 31 de mai. de 2022 | $220.34 | -7.24% | 4,132.15 | 0.01% | |
64. | 30 de jun. de 2022 | $245.44 | 11.39% | 3,785.38 | -8.39% | |
65. | 31 de jul. de 2022 | $248.43 | $0.55 | 1.44% | 4,130.29 | 9.11% |
66. | 31 de ago. de 2022 | $237.42 | -4.43% | 3,955.00 | -4.24% | |
67. | 30 de set. de 2022 | $239.86 | 1.03% | 3,585.62 | -9.34% | |
68. | 31 de out. de 2022 | $255.05 | $0.55 | 6.56% | 3,871.98 | 7.99% |
69. | 30 de nov. de 2022 | $255.68 | 0.25% | 4,080.11 | 5.38% | |
70. | 31 de dez. de 2022 | $246.25 | $0.55 | -3.47% | 3,839.50 | -5.90% |
71. | 31 de jan. de 2023 | $233.60 | -5.14% | 4,076.60 | 6.18% | |
Média (R): | 1.91% | 0.90% | ||||
Desvio padrão: | 6.00% | 5.01% |
Mostrar tudo
1 Dados em US$ por ação ordinária, ajustados por desdobramentos e dividendos das ações.
2 Taxa de rendibilidade das acções ordinárias da DG durante o período t.
3 Taxa de retorno do S&P 500 (proxy da carteira de mercado) durante o período t.
Variância e covariância
t | Data | RDG,t | RS&P 500,t | (RDG,t–RDG)2 | (RS&P 500,t–RS&P 500)2 | (RDG,t–RDG)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 de mar. de 2017 | -4.51% | -0.04% | 41.11 | 0.87 | 5.99 |
2. | 30 de abr. de 2017 | 4.65% | 0.91% | 7.51 | 0.00 | 0.04 |
3. | 31 de mai. de 2017 | 0.94% | 1.16% | 0.94 | 0.07 | -0.25 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 de dez. de 2022 | -3.47% | -5.90% | 28.93 | 46.14 | 36.54 |
71. | 31 de jan. de 2023 | -5.14% | 6.18% | 49.60 | 27.88 | -37.19 |
Total (Σ): | 2,522.48 | 1,754.14 | 675.21 |
t | Data | RDG,t | RS&P 500,t | (RDG,t–RDG)2 | (RS&P 500,t–RS&P 500)2 | (RDG,t–RDG)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 31 de mar. de 2017 | -4.51% | -0.04% | 41.11 | 0.87 | 5.99 |
2. | 30 de abr. de 2017 | 4.65% | 0.91% | 7.51 | 0.00 | 0.04 |
3. | 31 de mai. de 2017 | 0.94% | 1.16% | 0.94 | 0.07 | -0.25 |
4. | 30 de jun. de 2017 | -1.77% | 0.48% | 13.52 | 0.17 | 1.52 |
5. | 31 de jul. de 2017 | 4.62% | 1.93% | 7.36 | 1.08 | 2.82 |
6. | 31 de ago. de 2017 | -3.46% | 0.05% | 28.79 | 0.71 | 4.51 |
7. | 30 de set. de 2017 | 11.70% | 1.93% | 95.94 | 1.07 | 10.14 |
8. | 31 de out. de 2017 | 0.06% | 2.22% | 3.40 | 1.75 | -2.44 |
9. | 30 de nov. de 2017 | 8.96% | 2.81% | 49.70 | 3.66 | 13.49 |
10. | 31 de dez. de 2017 | 5.60% | 0.98% | 13.63 | 0.01 | 0.32 |
11. | 31 de jan. de 2018 | 11.15% | 5.62% | 85.44 | 22.30 | 43.65 |
12. | 28 de fev. de 2018 | -8.27% | -3.89% | 103.59 | 22.94 | 48.75 |
13. | 31 de mar. de 2018 | -1.10% | -2.69% | 9.03 | 12.84 | 10.77 |
14. | 30 de abr. de 2018 | 3.50% | 0.27% | 2.53 | 0.39 | -0.99 |
15. | 31 de mai. de 2018 | -9.38% | 2.16% | 127.27 | 1.60 | -14.28 |
16. | 30 de jun. de 2018 | 12.71% | 0.48% | 116.76 | 0.17 | -4.44 |
17. | 31 de jul. de 2018 | -0.16% | 3.60% | 4.28 | 7.33 | -5.60 |
18. | 31 de ago. de 2018 | 9.76% | 3.03% | 61.69 | 4.54 | 16.74 |
19. | 30 de set. de 2018 | 1.46% | 0.43% | 0.20 | 0.22 | 0.21 |
20. | 31 de out. de 2018 | 2.17% | -6.94% | 0.07 | 61.40 | -2.06 |
21. | 30 de nov. de 2018 | -0.35% | 1.79% | 5.09 | 0.79 | -2.01 |
22. | 31 de dez. de 2018 | -2.62% | -9.18% | 20.50 | 101.46 | 45.61 |
23. | 31 de jan. de 2019 | 7.07% | 7.87% | 26.66 | 48.63 | 36.00 |
24. | 28 de fev. de 2019 | 2.62% | 2.97% | 0.52 | 4.32 | 1.49 |
25. | 31 de mar. de 2019 | 0.71% | 1.79% | 1.43 | 0.80 | -1.07 |
26. | 30 de abr. de 2019 | 5.96% | 3.93% | 16.43 | 9.22 | 12.31 |
27. | 31 de mai. de 2019 | 0.94% | -6.58% | 0.93 | 55.85 | 7.19 |
28. | 30 de jun. de 2019 | 6.19% | 6.89% | 18.36 | 35.97 | 25.70 |
29. | 31 de jul. de 2019 | -0.61% | 1.31% | 6.31 | 0.17 | -1.05 |
30. | 31 de ago. de 2019 | 16.47% | -1.81% | 212.04 | 7.31 | -39.38 |
31. | 30 de set. de 2019 | 1.83% | 1.72% | 0.01 | 0.68 | -0.07 |
32. | 31 de out. de 2019 | 1.08% | 2.04% | 0.68 | 1.32 | -0.95 |
33. | 30 de nov. de 2019 | -1.86% | 3.40% | 14.17 | 6.30 | -9.45 |
34. | 31 de dez. de 2019 | -0.88% | 2.86% | 7.74 | 3.86 | -5.46 |
35. | 31 de jan. de 2020 | -1.44% | -0.16% | 11.21 | 1.12 | 3.54 |
36. | 29 de fev. de 2020 | -2.03% | -8.41% | 15.47 | 86.61 | 36.60 |
37. | 31 de mar. de 2020 | 0.47% | -12.51% | 2.06 | 179.75 | 19.22 |
38. | 30 de abr. de 2020 | 16.32% | 12.68% | 207.86 | 138.98 | 169.97 |
39. | 31 de mai. de 2020 | 9.25% | 4.53% | 53.89 | 13.20 | 26.67 |
40. | 30 de jun. de 2020 | -0.52% | 1.84% | 5.90 | 0.89 | -2.29 |
41. | 31 de jul. de 2020 | 0.13% | 5.51% | 3.15 | 21.30 | -8.19 |
42. | 31 de ago. de 2020 | 6.03% | 7.01% | 17.00 | 37.35 | 25.20 |
43. | 30 de set. de 2020 | 3.83% | -3.92% | 3.72 | 23.21 | -9.29 |
44. | 31 de out. de 2020 | -0.26% | -2.77% | 4.70 | 13.41 | 7.94 |
45. | 30 de nov. de 2020 | 4.73% | 10.75% | 7.97 | 97.21 | 27.83 |
46. | 31 de dez. de 2020 | -3.79% | 3.71% | 32.42 | 7.93 | -16.04 |
47. | 31 de jan. de 2021 | -7.29% | -1.11% | 84.56 | 4.04 | 18.47 |
48. | 28 de fev. de 2021 | -2.89% | 2.61% | 22.98 | 2.94 | -8.22 |
49. | 31 de mar. de 2021 | 7.21% | 4.24% | 28.15 | 11.21 | 17.77 |
50. | 30 de abr. de 2021 | 6.19% | 5.24% | 18.39 | 18.90 | 18.64 |
51. | 31 de mai. de 2021 | -5.49% | 0.55% | 54.70 | 0.12 | 2.56 |
52. | 30 de jun. de 2021 | 6.62% | 2.22% | 22.19 | 1.76 | 6.25 |
53. | 31 de jul. de 2021 | 7.70% | 2.27% | 33.61 | 1.90 | 8.00 |
54. | 31 de ago. de 2021 | -4.18% | 2.90% | 37.07 | 4.02 | -12.20 |
55. | 30 de set. de 2021 | -4.83% | -4.76% | 45.39 | 31.95 | 38.08 |
56. | 31 de out. de 2021 | 4.62% | 6.91% | 7.36 | 36.23 | 16.33 |
57. | 30 de nov. de 2021 | -0.10% | -0.83% | 4.02 | 2.99 | 3.47 |
58. | 31 de dez. de 2021 | 6.57% | 4.36% | 21.71 | 12.01 | 16.15 |
59. | 31 de jan. de 2022 | -11.42% | -5.26% | 177.56 | 37.87 | 82.00 |
60. | 28 de fev. de 2022 | -4.86% | -3.14% | 45.83 | 16.25 | 27.29 |
61. | 31 de mar. de 2022 | 12.25% | 3.58% | 106.93 | 7.19 | 27.73 |
62. | 30 de abr. de 2022 | 6.94% | -8.80% | 25.34 | 93.91 | -48.78 |
63. | 31 de mai. de 2022 | -7.24% | 0.01% | 83.59 | 0.79 | 8.14 |
64. | 30 de jun. de 2022 | 11.39% | -8.39% | 89.98 | 86.25 | -88.09 |
65. | 31 de jul. de 2022 | 1.44% | 9.11% | 0.21 | 67.51 | -3.81 |
66. | 31 de ago. de 2022 | -4.43% | -4.24% | 40.17 | 26.41 | 32.57 |
67. | 30 de set. de 2022 | 1.03% | -9.34% | 0.77 | 104.75 | 8.99 |
68. | 31 de out. de 2022 | 6.56% | 7.99% | 21.68 | 50.28 | 33.02 |
69. | 30 de nov. de 2022 | 0.25% | 5.38% | 2.75 | 20.07 | -7.43 |
70. | 31 de dez. de 2022 | -3.47% | -5.90% | 28.93 | 46.14 | 36.54 |
71. | 31 de jan. de 2023 | -5.14% | 6.18% | 49.60 | 27.88 | -37.19 |
Total (Σ): | 2,522.48 | 1,754.14 | 675.21 |
Mostrar tudo
VariaçãoDG = Σ(RDG,t–RDG)2 ÷ (71 – 1)
= 2,522.48 ÷ (71 – 1)
= 36.04
VariaçãoS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,754.14 ÷ (71 – 1)
= 25.06
CovariânciaDG, S&P 500 = Σ(RDG,t–RDG)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 675.21 ÷ (71 – 1)
= 9.65
Estimativa sistemática de risco (β)
VariaçãoDG | 36.04 |
VariaçãoS&P 500 | 25.06 |
CovariânciaDG, S&P 500 | 9.65 |
Coeficiente de correlaçãoDG, S&P 5001 | 0.32 |
βDG2 | 0.38 |
αDG3 | 1.56% |
Cálculos
1 Coeficiente de correlaçãoDG, S&P 500
= CovariânciaDG, S&P 500 ÷ (Desvio padrãoDG × Desvio padrãoS&P 500)
= 9.65 ÷ (6.00% × 5.01%)
= 0.32
2 βDG
= CovariânciaDG, S&P 500 ÷ VariaçãoS&P 500
= 9.65 ÷ 25.06
= 0.38
3 αDG
= MédiaDG – βDG × MédiaS&P 500
= 1.91% – 0.38 × 0.90%
= 1.56%
Taxa de retorno esperada
Suposições | ||
Taxa de retorno do LT Treasury Composite1 | RF | 4.56% |
Taxa esperada de retorno da carteira de mercado2 | E(RM) | 13.77% |
Risco sistemático de Dollar General ações ordinárias | βDG | 0.38 |
Taxa de retorno esperada sobre as ações ordinárias da Dollar General3 | E(RDG) | 8.10% |
1 Média não ponderada dos rendimentos de oferta de todos os títulos do Tesouro dos EUA com cupom fixo em circulação, vencidos ou exigíveis em menos de 10 anos (proxy de taxa de retorno livre de risco).
3 E(RDG) = RF + βDG [E(RM) – RF]
= 4.56% + 0.38 [13.77% – 4.56%]
= 8.10%