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 ida e volta
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 |
29 de fev. de 2016 | $74.25 | 1,932.23 | ||||
1. | 31 de mar. de 2016 | $85.60 | $0.25 | 15.62% | 2,059.74 | 6.60% |
2. | 30 de abr. de 2016 | $81.91 | -4.31% | 2,065.30 | 0.27% | |
3. | 31 de mai. de 2016 | $89.90 | 9.75% | 2,096.95 | 1.53% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 de dez. de 2021 | $235.83 | 6.57% | 4,766.18 | 4.36% | |
71. | 31 de jan. de 2022 | $208.48 | $0.42 | -11.42% | 4,515.55 | -5.26% |
Média (R): | 1.77% | 1.29% | ||||
Desvio padrão: | 6.67% | 4.25% |
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 |
29 de fev. de 2016 | $74.25 | 1,932.23 | ||||
1. | 31 de mar. de 2016 | $85.60 | $0.25 | 15.62% | 2,059.74 | 6.60% |
2. | 30 de abr. de 2016 | $81.91 | -4.31% | 2,065.30 | 0.27% | |
3. | 31 de mai. de 2016 | $89.90 | 9.75% | 2,096.95 | 1.53% | |
4. | 30 de jun. de 2016 | $94.00 | $0.25 | 4.84% | 2,098.86 | 0.09% |
5. | 31 de jul. de 2016 | $94.74 | 0.79% | 2,173.60 | 3.56% | |
6. | 31 de ago. de 2016 | $73.41 | -22.51% | 2,170.95 | -0.12% | |
7. | 30 de set. de 2016 | $69.99 | $0.25 | -4.32% | 2,168.27 | -0.12% |
8. | 31 de out. de 2016 | $69.09 | -1.29% | 2,126.15 | -1.94% | |
9. | 30 de nov. de 2016 | $77.32 | 11.91% | 2,198.81 | 3.42% | |
10. | 31 de dez. de 2016 | $74.07 | $0.25 | -3.88% | 2,238.83 | 1.82% |
11. | 31 de jan. de 2017 | $73.82 | -0.34% | 2,278.87 | 1.79% | |
12. | 28 de fev. de 2017 | $73.02 | -1.08% | 2,363.64 | 3.72% | |
13. | 31 de mar. de 2017 | $69.73 | -4.51% | 2,362.72 | -0.04% | |
14. | 30 de abr. de 2017 | $72.71 | $0.26 | 4.65% | 2,384.20 | 0.91% |
15. | 31 de mai. de 2017 | $73.39 | 0.94% | 2,411.80 | 1.16% | |
16. | 30 de jun. de 2017 | $72.09 | -1.77% | 2,423.41 | 0.48% | |
17. | 31 de jul. de 2017 | $75.16 | $0.26 | 4.62% | 2,470.30 | 1.93% |
18. | 31 de ago. de 2017 | $72.56 | -3.46% | 2,471.65 | 0.05% | |
19. | 30 de set. de 2017 | $81.05 | 11.70% | 2,519.36 | 1.93% | |
20. | 31 de out. de 2017 | $80.84 | $0.26 | 0.06% | 2,575.26 | 2.22% |
21. | 30 de nov. de 2017 | $88.08 | 8.96% | 2,647.58 | 2.81% | |
22. | 31 de dez. de 2017 | $93.01 | 5.60% | 2,673.61 | 0.98% | |
23. | 31 de jan. de 2018 | $103.12 | $0.26 | 11.15% | 2,823.81 | 5.62% |
24. | 28 de fev. de 2018 | $94.59 | -8.27% | 2,713.83 | -3.89% | |
25. | 31 de mar. de 2018 | $93.55 | -1.10% | 2,640.87 | -2.69% | |
26. | 30 de abr. de 2018 | $96.53 | $0.29 | 3.50% | 2,648.05 | 0.27% |
27. | 31 de mai. de 2018 | $87.48 | -9.38% | 2,705.27 | 2.16% | |
28. | 30 de jun. de 2018 | $98.60 | 12.71% | 2,718.37 | 0.48% | |
29. | 31 de jul. de 2018 | $98.15 | $0.29 | -0.16% | 2,816.29 | 3.60% |
30. | 31 de ago. de 2018 | $107.73 | 9.76% | 2,901.52 | 3.03% | |
31. | 30 de set. de 2018 | $109.30 | 1.46% | 2,913.98 | 0.43% | |
32. | 31 de out. de 2018 | $111.38 | $0.29 | 2.17% | 2,711.74 | -6.94% |
33. | 30 de nov. de 2018 | $110.99 | -0.35% | 2,760.17 | 1.79% | |
34. | 31 de dez. de 2018 | $108.08 | -2.62% | 2,506.85 | -9.18% | |
35. | 31 de jan. de 2019 | $115.43 | $0.29 | 7.07% | 2,704.10 | 7.87% |
36. | 28 de fev. de 2019 | $118.46 | 2.62% | 2,784.49 | 2.97% | |
37. | 31 de mar. de 2019 | $119.30 | 0.71% | 2,834.40 | 1.79% | |
38. | 30 de abr. de 2019 | $126.09 | $0.32 | 5.96% | 2,945.83 | 3.93% |
39. | 31 de mai. de 2019 | $127.28 | 0.94% | 2,752.06 | -6.58% | |
40. | 30 de jun. de 2019 | $135.16 | 6.19% | 2,941.76 | 6.89% | |
41. | 31 de jul. de 2019 | $134.02 | $0.32 | -0.61% | 2,980.38 | 1.31% |
42. | 31 de ago. de 2019 | $156.09 | 16.47% | 2,926.46 | -1.81% | |
43. | 30 de set. de 2019 | $158.94 | 1.83% | 2,976.74 | 1.72% | |
44. | 31 de out. de 2019 | $160.34 | $0.32 | 1.08% | 3,037.56 | 2.04% |
45. | 30 de nov. de 2019 | $157.36 | -1.86% | 3,140.98 | 3.40% | |
46. | 31 de dez. de 2019 | $155.98 | -0.88% | 3,230.78 | 2.86% | |
47. | 31 de jan. de 2020 | $153.41 | $0.32 | -1.44% | 3,225.52 | -0.16% |
48. | 29 de fev. de 2020 | $150.30 | -2.03% | 2,954.22 | -8.41% | |
49. | 31 de mar. de 2020 | $151.01 | 0.47% | 2,584.59 | -12.51% | |
50. | 30 de abr. de 2020 | $175.30 | $0.36 | 16.32% | 2,912.43 | 12.68% |
51. | 31 de mai. de 2020 | $191.51 | 9.25% | 3,044.31 | 4.53% | |
52. | 30 de jun. de 2020 | $190.51 | -0.52% | 3,100.29 | 1.84% | |
53. | 31 de jul. de 2020 | $190.40 | $0.36 | 0.13% | 3,271.12 | 5.51% |
54. | 31 de ago. de 2020 | $201.88 | 6.03% | 3,500.31 | 7.01% | |
55. | 30 de set. de 2020 | $209.62 | 3.83% | 3,363.00 | -3.92% | |
56. | 31 de out. de 2020 | $208.71 | $0.36 | -0.26% | 3,269.96 | -2.77% |
57. | 30 de nov. de 2020 | $218.58 | 4.73% | 3,621.63 | 10.75% | |
58. | 31 de dez. de 2020 | $210.30 | -3.79% | 3,756.07 | 3.71% | |
59. | 31 de jan. de 2021 | $194.61 | $0.36 | -7.29% | 3,714.24 | -1.11% |
60. | 28 de fev. de 2021 | $188.99 | -2.89% | 3,811.15 | 2.61% | |
61. | 31 de mar. de 2021 | $202.62 | 7.21% | 3,972.89 | 4.24% | |
62. | 30 de abr. de 2021 | $214.75 | $0.42 | 6.19% | 4,181.17 | 5.24% |
63. | 31 de mai. de 2021 | $202.96 | -5.49% | 4,204.11 | 0.55% | |
64. | 30 de jun. de 2021 | $216.39 | 6.62% | 4,297.50 | 2.22% | |
65. | 31 de jul. de 2021 | $232.64 | $0.42 | 7.70% | 4,395.26 | 2.27% |
66. | 31 de ago. de 2021 | $222.91 | -4.18% | 4,522.68 | 2.90% | |
67. | 30 de set. de 2021 | $212.14 | -4.83% | 4,307.54 | -4.76% | |
68. | 31 de out. de 2021 | $221.52 | $0.42 | 4.62% | 4,605.38 | 6.91% |
69. | 30 de nov. de 2021 | $221.30 | -0.10% | 4,567.00 | -0.83% | |
70. | 31 de dez. de 2021 | $235.83 | 6.57% | 4,766.18 | 4.36% | |
71. | 31 de jan. de 2022 | $208.48 | $0.42 | -11.42% | 4,515.55 | -5.26% |
Média (R): | 1.77% | 1.29% | ||||
Desvio padrão: | 6.67% | 4.25% |
Mostrar tudo
1 Dados em US$ por ação ordinária, ajustados por desdobramentos e dividendos de ações.
2 Taxa de retorno sobre as ações ordinárias de DG durante o período t.
3 Taxa de retorno do S&P 500 (o 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 2016 | 15.62% | 6.60% | 191.85 | 28.16 | 73.51 |
2. | 30 de abr. de 2016 | -4.31% | 0.27% | 37.00 | 1.05 | 6.22 |
3. | 31 de mai. de 2016 | 9.75% | 1.53% | 63.73 | 0.06 | 1.92 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | 31 de dez. de 2021 | 6.57% | 4.36% | 22.98 | 9.42 | 14.71 |
71. | 31 de jan. de 2022 | -11.42% | -5.26% | 174.00 | 42.91 | 86.41 |
Total (Σ): | 3,116.51 | 1,262.70 | 821.48 |
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 2016 | 15.62% | 6.60% | 191.85 | 28.16 | 73.51 |
2. | 30 de abr. de 2016 | -4.31% | 0.27% | 37.00 | 1.05 | 6.22 |
3. | 31 de mai. de 2016 | 9.75% | 1.53% | 63.73 | 0.06 | 1.92 |
4. | 30 de jun. de 2016 | 4.84% | 0.09% | 9.41 | 1.44 | -3.68 |
5. | 31 de jul. de 2016 | 0.79% | 3.56% | 0.97 | 5.15 | -2.23 |
6. | 31 de ago. de 2016 | -22.51% | -0.12% | 589.81 | 2.00 | 34.34 |
7. | 30 de set. de 2016 | -4.32% | -0.12% | 37.09 | 2.00 | 8.62 |
8. | 31 de out. de 2016 | -1.29% | -1.94% | 9.35 | 10.46 | 9.89 |
9. | 30 de nov. de 2016 | 11.91% | 3.42% | 102.82 | 4.52 | 21.55 |
10. | 31 de dez. de 2016 | -3.88% | 1.82% | 31.94 | 0.28 | -2.98 |
11. | 31 de jan. de 2017 | -0.34% | 1.79% | 4.45 | 0.25 | -1.05 |
12. | 28 de fev. de 2017 | -1.08% | 3.72% | 8.15 | 5.89 | -6.93 |
13. | 31 de mar. de 2017 | -4.51% | -0.04% | 39.41 | 1.77 | 8.36 |
14. | 30 de abr. de 2017 | 4.65% | 0.91% | 8.26 | 0.15 | -1.10 |
15. | 31 de mai. de 2017 | 0.94% | 1.16% | 0.70 | 0.02 | 0.11 |
16. | 30 de jun. de 2017 | -1.77% | 0.48% | 12.55 | 0.66 | 2.87 |
17. | 31 de jul. de 2017 | 4.62% | 1.93% | 8.11 | 0.41 | 1.83 |
18. | 31 de ago. de 2017 | -3.46% | 0.05% | 27.36 | 1.53 | 6.47 |
19. | 30 de set. de 2017 | 11.70% | 1.93% | 98.58 | 0.41 | 6.34 |
20. | 31 de out. de 2017 | 0.06% | 2.22% | 2.92 | 0.86 | -1.58 |
21. | 30 de nov. de 2017 | 8.96% | 2.81% | 51.61 | 2.30 | 10.89 |
22. | 31 de dez. de 2017 | 5.60% | 0.98% | 14.63 | 0.10 | -1.18 |
23. | 31 de jan. de 2018 | 11.15% | 5.62% | 87.94 | 18.71 | 40.56 |
24. | 28 de fev. de 2018 | -8.27% | -3.89% | 100.88 | 26.90 | 52.10 |
25. | 31 de mar. de 2018 | -1.10% | -2.69% | 8.24 | 15.85 | 11.43 |
26. | 30 de abr. de 2018 | 3.50% | 0.27% | 2.97 | 1.04 | -1.76 |
27. | 31 de mai. de 2018 | -9.38% | 2.16% | 124.26 | 0.75 | -9.68 |
28. | 30 de jun. de 2018 | 12.71% | 0.48% | 119.68 | 0.65 | -8.84 |
29. | 31 de jul. de 2018 | -0.16% | 3.60% | 3.74 | 5.34 | -4.47 |
30. | 31 de ago. de 2018 | 9.76% | 3.03% | 63.82 | 3.01 | 13.85 |
31. | 30 de set. de 2018 | 1.46% | 0.43% | 0.10 | 0.74 | 0.27 |
32. | 31 de out. de 2018 | 2.17% | -6.94% | 0.16 | 67.78 | -3.27 |
33. | 30 de nov. de 2018 | -0.35% | 1.79% | 4.50 | 0.24 | -1.05 |
34. | 31 de dez. de 2018 | -2.62% | -9.18% | 19.30 | 109.62 | 46.00 |
35. | 31 de jan. de 2019 | 7.07% | 7.87% | 28.06 | 43.25 | 34.83 |
36. | 28 de fev. de 2019 | 2.62% | 2.97% | 0.73 | 2.82 | 1.43 |
37. | 31 de mar. de 2019 | 0.71% | 1.79% | 1.13 | 0.25 | -0.53 |
38. | 30 de abr. de 2019 | 5.96% | 3.93% | 17.54 | 6.96 | 11.05 |
39. | 31 de mai. de 2019 | 0.94% | -6.58% | 0.69 | 61.94 | 6.52 |
40. | 30 de jun. de 2019 | 6.19% | 6.89% | 19.53 | 31.37 | 24.75 |
41. | 31 de jul. de 2019 | -0.61% | 1.31% | 5.66 | 0.00 | -0.05 |
42. | 31 de ago. de 2019 | 16.47% | -1.81% | 215.97 | 9.62 | -45.58 |
43. | 30 de set. de 2019 | 1.83% | 1.72% | 0.00 | 0.18 | 0.02 |
44. | 31 de out. de 2019 | 1.08% | 2.04% | 0.48 | 0.56 | -0.52 |
45. | 30 de nov. de 2019 | -1.86% | 3.40% | 13.18 | 4.46 | -7.67 |
46. | 31 de dez. de 2019 | -0.88% | 2.86% | 7.02 | 2.45 | -4.15 |
47. | 31 de jan. de 2020 | -1.44% | -0.16% | 10.33 | 2.12 | 4.68 |
48. | 29 de fev. de 2020 | -2.03% | -8.41% | 14.43 | 94.15 | 36.86 |
49. | 31 de mar. de 2020 | 0.47% | -12.51% | 1.69 | 190.56 | 17.94 |
50. | 30 de abr. de 2020 | 16.32% | 12.68% | 211.75 | 129.78 | 165.78 |
51. | 31 de mai. de 2020 | 9.25% | 4.53% | 55.88 | 10.47 | 24.19 |
52. | 30 de jun. de 2020 | -0.52% | 1.84% | 5.26 | 0.30 | -1.25 |
53. | 31 de jul. de 2020 | 0.13% | 5.51% | 2.69 | 17.79 | -6.92 |
54. | 31 de ago. de 2020 | 6.03% | 7.01% | 18.13 | 32.65 | 24.33 |
55. | 30 de set. de 2020 | 3.83% | -3.92% | 4.25 | 27.20 | -10.75 |
56. | 31 de out. de 2020 | -0.26% | -2.77% | 4.14 | 16.47 | 8.26 |
57. | 30 de nov. de 2020 | 4.73% | 10.75% | 8.75 | 89.54 | 27.98 |
58. | 31 de dez. de 2020 | -3.79% | 3.71% | 30.91 | 5.86 | -13.45 |
59. | 31 de jan. de 2021 | -7.29% | -1.11% | 82.11 | 5.79 | 21.80 |
60. | 28 de fev. de 2021 | -2.89% | 2.61% | 21.71 | 1.73 | -6.14 |
61. | 31 de mar. de 2021 | 7.21% | 4.24% | 29.60 | 8.71 | 16.06 |
62. | 30 de abr. de 2021 | 6.19% | 5.24% | 19.56 | 15.60 | 17.47 |
63. | 31 de mai. de 2021 | -5.49% | 0.55% | 52.73 | 0.55 | 5.40 |
64. | 30 de jun. de 2021 | 6.62% | 2.22% | 23.48 | 0.86 | 4.50 |
65. | 31 de jul. de 2021 | 7.70% | 2.27% | 35.19 | 0.97 | 5.83 |
66. | 31 de ago. de 2021 | -4.18% | 2.90% | 35.45 | 2.58 | -9.57 |
67. | 30 de set. de 2021 | -4.83% | -4.76% | 43.60 | 36.59 | 39.94 |
68. | 31 de out. de 2021 | 4.62% | 6.91% | 8.11 | 31.61 | 16.01 |
69. | 30 de nov. de 2021 | -0.10% | -0.83% | 3.50 | 4.52 | 3.98 |
70. | 31 de dez. de 2021 | 6.57% | 4.36% | 22.98 | 9.42 | 14.71 |
71. | 31 de jan. de 2022 | -11.42% | -5.26% | 174.00 | 42.91 | 86.41 |
Total (Σ): | 3,116.51 | 1,262.70 | 821.48 |
Mostrar tudo
VariaçãoDG = Σ(RDG,t–RDG)2 ÷ (71 – 1)
= 3,116.51 ÷ (71 – 1)
= 44.52
VariaçãoS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04
CovariânciaDG, S&P 500 = Σ(RDG,t–RDG)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 821.48 ÷ (71 – 1)
= 11.74
Estimativa sistemática de risco (β)
VariaçãoDG | 44.52 |
VariaçãoS&P 500 | 18.04 |
CovariânciaDG, S&P 500 | 11.74 |
Coeficiente de correlaçãoDG, S&P 5001 | 0.41 |
βDG2 | 0.65 |
αDG3 | 0.93% |
Cálculos
1 Coeficiente de correlaçãoDG, S&P 500
= CovariânciaDG, S&P 500 ÷ (Desvio padrãoDG × Desvio padrãoS&P 500)
= 11.74 ÷ (6.67% × 4.25%)
= 0.41
2 βDG
= CovariânciaDG, S&P 500 ÷ VariaçãoS&P 500
= 11.74 ÷ 18.04
= 0.65
3 αDG
= MédiaDG – βDG × MédiaS&P 500
= 1.77% – 0.65 × 1.29%
= 0.93%
Taxa de retorno esperada
Suposições | ||
Taxa de retorno do LT Treasury Composite1 | RF | 3.70% |
Taxa esperada de retorno da carteira de mercado2 | E(RM) | 13.67% |
Risco sistemático de Dollar General ações ordinárias | βDG | 0.65 |
Taxa de retorno esperada das ações ordinárias da Dollar General3 | E(RDG) | 10.18% |
1 Média não ponderada dos rendimentos das ofertas em todos os títulos do Tesouro dos EUA de cupom fixo em circulação, nem vencidos ou exigíveis em menos de 10 anos (proxy de taxa de retorno sem risco).
3 E(RDG) = RF + βDG [E(RM) – RF]
= 3.70% + 0.65 [13.67% – 3.70%]
= 10.18%