Stock Analysis on Net

Microsoft Corp. (NASDAQ:MSFT)

Modelo de precificação de ativos de capital (CAPM) 

Microsoft Excel

Taxas de retorno

Microsoft Corp., taxas mensais de retorno

Microsoft Excel
Microsoft Corp. (MSFT) Standard & Poor’s 500 (S&P 500)
t Data PreçoMSFT,t1 DividendoMSFT,t1 RMSFT,t2 PreçoS&P 500,t RS&P 500,t3
31 de jul. de 2017 $72.70 2,470.30
1. 31 de ago. de 2017 $74.77 $0.39 3.38% 2,471.65 0.05%
2. 30 de set. de 2017 $74.49 -0.37% 2,519.36 1.93%
3. 31 de out. de 2017 $83.18 11.67% 2,575.26 2.22%
. . . . . . .
. . . . . . .
. . . . . . .
70. 31 de mai. de 2023 $328.39 $0.68 7.10% 4,179.83 0.25%
71. 30 de jun. de 2023 $340.54 3.70% 4,376.86 4.71%
Média (R): 2.49% 0.94%
Desvio padrão: 6.15% 5.05%
Microsoft Corp. (MSFT) Standard & Poor’s 500 (S&P 500)
t Data PreçoMSFT,t1 DividendoMSFT,t1 RMSFT,t2 PreçoS&P 500,t RS&P 500,t3
31 de jul. de 2017 $72.70 2,470.30
1. 31 de ago. de 2017 $74.77 $0.39 3.38% 2,471.65 0.05%
2. 30 de set. de 2017 $74.49 -0.37% 2,519.36 1.93%
3. 31 de out. de 2017 $83.18 11.67% 2,575.26 2.22%
4. 30 de nov. de 2017 $84.17 $0.42 1.70% 2,647.58 2.81%
5. 31 de dez. de 2017 $85.54 1.63% 2,673.61 0.98%
6. 31 de jan. de 2018 $95.01 11.07% 2,823.81 5.62%
7. 28 de fev. de 2018 $93.77 $0.42 -0.86% 2,713.83 -3.89%
8. 31 de mar. de 2018 $91.27 -2.67% 2,640.87 -2.69%
9. 30 de abr. de 2018 $93.52 2.47% 2,648.05 0.27%
10. 31 de mai. de 2018 $98.84 $0.42 6.14% 2,705.27 2.16%
11. 30 de jun. de 2018 $98.61 -0.23% 2,718.37 0.48%
12. 31 de jul. de 2018 $106.08 7.58% 2,816.29 3.60%
13. 31 de ago. de 2018 $112.33 $0.42 6.29% 2,901.52 3.03%
14. 30 de set. de 2018 $114.37 1.82% 2,913.98 0.43%
15. 31 de out. de 2018 $106.81 -6.61% 2,711.74 -6.94%
16. 30 de nov. de 2018 $110.89 $0.46 4.25% 2,760.17 1.79%
17. 31 de dez. de 2018 $101.57 -8.40% 2,506.85 -9.18%
18. 31 de jan. de 2019 $104.43 2.82% 2,704.10 7.87%
19. 28 de fev. de 2019 $112.03 $0.46 7.72% 2,784.49 2.97%
20. 31 de mar. de 2019 $117.94 5.28% 2,834.40 1.79%
21. 30 de abr. de 2019 $130.60 10.73% 2,945.83 3.93%
22. 31 de mai. de 2019 $123.68 $0.46 -4.95% 2,752.06 -6.58%
23. 30 de jun. de 2019 $133.96 8.31% 2,941.76 6.89%
24. 31 de jul. de 2019 $136.27 1.72% 2,980.38 1.31%
25. 31 de ago. de 2019 $137.86 $0.46 1.50% 2,926.46 -1.81%
26. 30 de set. de 2019 $139.03 0.85% 2,976.74 1.72%
27. 31 de out. de 2019 $143.37 3.12% 3,037.56 2.04%
28. 30 de nov. de 2019 $151.38 $0.51 5.94% 3,140.98 3.40%
29. 31 de dez. de 2019 $157.70 4.17% 3,230.78 2.86%
30. 31 de jan. de 2020 $170.23 7.95% 3,225.52 -0.16%
31. 29 de fev. de 2020 $162.01 $0.51 -4.53% 2,954.22 -8.41%
32. 31 de mar. de 2020 $157.71 -2.65% 2,584.59 -12.51%
33. 30 de abr. de 2020 $179.21 13.63% 2,912.43 12.68%
34. 31 de mai. de 2020 $183.25 $0.51 2.54% 3,044.31 4.53%
35. 30 de jun. de 2020 $203.51 11.06% 3,100.29 1.84%
36. 31 de jul. de 2020 $205.01 0.74% 3,271.12 5.51%
37. 31 de ago. de 2020 $225.53 $0.51 10.26% 3,500.31 7.01%
38. 30 de set. de 2020 $210.33 -6.74% 3,363.00 -3.92%
39. 31 de out. de 2020 $202.47 -3.74% 3,269.96 -2.77%
40. 30 de nov. de 2020 $214.07 $0.56 6.01% 3,621.63 10.75%
41. 31 de dez. de 2020 $222.42 3.90% 3,756.07 3.71%
42. 31 de jan. de 2021 $231.96 4.29% 3,714.24 -1.11%
43. 28 de fev. de 2021 $232.38 $0.56 0.42% 3,811.15 2.61%
44. 31 de mar. de 2021 $235.77 1.46% 3,972.89 4.24%
45. 30 de abr. de 2021 $252.18 6.96% 4,181.17 5.24%
46. 31 de mai. de 2021 $249.68 $0.56 -0.77% 4,204.11 0.55%
47. 30 de jun. de 2021 $270.90 8.50% 4,297.50 2.22%
48. 31 de jul. de 2021 $284.91 5.17% 4,395.26 2.27%
49. 31 de ago. de 2021 $301.88 $0.56 6.15% 4,522.68 2.90%
50. 30 de set. de 2021 $281.92 -6.61% 4,307.54 -4.76%
51. 31 de out. de 2021 $331.62 17.63% 4,605.38 6.91%
52. 30 de nov. de 2021 $330.59 $0.62 -0.12% 4,567.00 -0.83%
53. 31 de dez. de 2021 $336.32 1.73% 4,766.18 4.36%
54. 31 de jan. de 2022 $310.98 -7.53% 4,515.55 -5.26%
55. 28 de fev. de 2022 $298.79 $0.62 -3.72% 4,373.94 -3.14%
56. 31 de mar. de 2022 $308.31 3.19% 4,530.41 3.58%
57. 30 de abr. de 2022 $277.52 -9.99% 4,131.93 -8.80%
58. 31 de mai. de 2022 $271.87 $0.62 -1.81% 4,132.15 0.01%
59. 30 de jun. de 2022 $256.83 -5.53% 3,785.38 -8.39%
60. 31 de jul. de 2022 $280.74 9.31% 4,130.29 9.11%
61. 31 de ago. de 2022 $261.47 $0.62 -6.64% 3,955.00 -4.24%
62. 30 de set. de 2022 $232.90 -10.93% 3,585.62 -9.34%
63. 31 de out. de 2022 $232.13 -0.33% 3,871.98 7.99%
64. 30 de nov. de 2022 $255.14 $0.68 10.21% 4,080.11 5.38%
65. 31 de dez. de 2022 $239.82 -6.00% 3,839.50 -5.90%
66. 31 de jan. de 2023 $247.81 3.33% 4,076.60 6.18%
67. 28 de fev. de 2023 $249.42 $0.68 0.92% 3,970.15 -2.61%
68. 31 de mar. de 2023 $288.30 15.59% 4,109.31 3.51%
69. 30 de abr. de 2023 $307.26 6.58% 4,169.48 1.46%
70. 31 de mai. de 2023 $328.39 $0.68 7.10% 4,179.83 0.25%
71. 30 de jun. de 2023 $340.54 3.70% 4,376.86 4.71%
Média (R): 2.49% 0.94%
Desvio padrão: 6.15% 5.05%

Mostrar tudo

1 Dados em US$ por ação ordinária, ajustados por desdobramentos e dividendos das ações.

2 Taxa de retorno das ações ordinárias da MSFT durante o período t.

3 Taxa de retorno do S&P 500 (proxy da carteira de mercado) durante o período t.


Variância e covariância

Microsoft Corp., cálculo da variância e covariância dos retornos

Microsoft Excel
t Data RMSFT,t RS&P 500,t (RMSFT,tRMSFT)2 (RS&P 500,tRS&P 500)2 (RMSFT,tRMSFT)×(RS&P 500,tRS&P 500)
1. 31 de ago. de 2017 3.38% 0.05% 0.80 0.78 -0.79
2. 30 de set. de 2017 -0.37% 1.93% 8.20 0.99 -2.85
3. 31 de out. de 2017 11.67% 2.22% 84.22 1.65 11.77
. . . . . . .
. . . . . . .
. . . . . . .
70. 31 de mai. de 2023 7.10% 0.25% 21.25 0.47 -3.17
71. 30 de jun. de 2023 3.70% 4.71% 1.47 14.27 4.58
Total (Σ): 2,645.73 1,786.26 1,672.61
t Data RMSFT,t RS&P 500,t (RMSFT,tRMSFT)2 (RS&P 500,tRS&P 500)2 (RMSFT,tRMSFT)×(RS&P 500,tRS&P 500)
1. 31 de ago. de 2017 3.38% 0.05% 0.80 0.78 -0.79
2. 30 de set. de 2017 -0.37% 1.93% 8.20 0.99 -2.85
3. 31 de out. de 2017 11.67% 2.22% 84.22 1.65 11.77
4. 30 de nov. de 2017 1.70% 2.81% 0.63 3.51 -1.49
5. 31 de dez. de 2017 1.63% 0.98% 0.74 0.00 -0.04
6. 31 de jan. de 2018 11.07% 5.62% 73.65 21.92 40.18
7. 28 de fev. de 2018 -0.86% -3.89% 11.24 23.33 16.19
8. 31 de mar. de 2018 -2.67% -2.69% 26.57 13.14 18.68
9. 30 de abr. de 2018 2.47% 0.27% 0.00 0.44 0.02
10. 31 de mai. de 2018 6.14% 2.16% 13.31 1.50 4.47
11. 30 de jun. de 2018 -0.23% 0.48% 7.41 0.20 1.23
12. 31 de jul. de 2018 7.58% 3.60% 25.87 7.11 13.56
13. 31 de ago. de 2018 6.29% 3.03% 14.43 4.37 7.94
14. 30 de set. de 2018 1.82% 0.43% 0.45 0.26 0.34
15. 31 de out. de 2018 -6.61% -6.94% 82.79 62.03 71.66
16. 30 de nov. de 2018 4.25% 1.79% 3.10 0.72 1.50
17. 31 de dez. de 2018 -8.40% -9.18% 118.67 102.28 110.17
18. 31 de jan. de 2019 2.82% 7.87% 0.11 48.06 2.27
19. 28 de fev. de 2019 7.72% 2.97% 27.35 4.15 10.65
20. 31 de mar. de 2019 5.28% 1.79% 7.76 0.73 2.39
21. 30 de abr. de 2019 10.73% 3.93% 67.99 8.97 24.70
22. 31 de mai. de 2019 -4.95% -6.58% 55.28 56.45 55.86
23. 30 de jun. de 2019 8.31% 6.89% 33.91 35.49 34.69
24. 31 de jul. de 2019 1.72% 1.31% 0.58 0.14 -0.29
25. 31 de ago. de 2019 1.50% -1.81% 0.97 7.53 2.70
26. 30 de set. de 2019 0.85% 1.72% 2.69 0.61 -1.28
27. 31 de out. de 2019 3.12% 2.04% 0.40 1.23 0.70
28. 30 de nov. de 2019 5.94% 3.40% 11.93 6.10 8.53
29. 31 de dez. de 2019 4.17% 2.86% 2.84 3.70 3.24
30. 31 de jan. de 2020 7.95% -0.16% 29.78 1.21 -5.99
31. 29 de fev. de 2020 -4.53% -8.41% 49.25 87.36 65.60
32. 31 de mar. de 2020 -2.65% -12.51% 26.45 180.84 69.16
33. 30 de abr. de 2020 13.63% 12.68% 124.18 138.03 130.92
34. 31 de mai. de 2020 2.54% 4.53% 0.00 12.91 0.18
35. 30 de jun. de 2020 11.06% 1.84% 73.40 0.82 7.74
36. 31 de jul. de 2020 0.74% 5.51% 3.07 20.92 -8.01
37. 31 de ago. de 2020 10.26% 7.01% 60.36 36.85 47.16
38. 30 de set. de 2020 -6.74% -3.92% 85.16 23.61 44.84
39. 31 de out. de 2020 -3.74% -2.77% 38.76 13.71 23.05
40. 30 de nov. de 2020 6.01% 10.75% 12.37 96.41 34.53
41. 31 de dez. de 2020 3.90% 3.71% 1.99 7.71 3.92
42. 31 de jan. de 2021 4.29% -1.11% 3.24 4.20 -3.69
43. 28 de fev. de 2021 0.42% 2.61% 4.27 2.80 -3.46
44. 31 de mar. de 2021 1.46% 4.24% 1.06 10.94 -3.41
45. 30 de abr. de 2021 6.96% 5.24% 19.99 18.55 19.26
46. 31 de mai. de 2021 -0.77% 0.55% 10.62 0.15 1.26
47. 30 de jun. de 2021 8.50% 2.22% 36.12 1.65 7.73
48. 31 de jul. de 2021 5.17% 2.27% 7.20 1.79 3.59
49. 31 de ago. de 2021 6.15% 2.90% 13.43 3.85 7.19
50. 30 de set. de 2021 -6.61% -4.76% 82.82 32.41 51.81
51. 31 de out. de 2021 17.63% 6.91% 229.23 35.74 90.52
52. 30 de nov. de 2021 -0.12% -0.83% 6.82 3.13 4.62
53. 31 de dez. de 2021 1.73% 4.36% 0.57 11.73 -2.59
54. 31 de jan. de 2022 -7.53% -5.26% 100.47 38.37 62.09
55. 28 de fev. de 2022 -3.72% -3.14% 38.56 16.58 25.28
56. 31 de mar. de 2022 3.19% 3.58% 0.49 6.98 1.84
57. 30 de abr. de 2022 -9.99% -8.80% 155.64 94.70 121.40
58. 31 de mai. de 2022 -1.81% 0.01% 18.50 0.87 4.00
59. 30 de jun. de 2022 -5.53% -8.39% 64.33 87.01 74.82
60. 31 de jul. de 2022 9.31% 9.11% 46.52 66.84 55.77
61. 31 de ago. de 2022 -6.64% -4.24% 83.39 26.83 47.30
62. 30 de set. de 2022 -10.93% -9.34% 179.98 105.58 137.85
63. 31 de out. de 2022 -0.33% 7.99% 7.95 49.71 -19.88
64. 30 de nov. de 2022 10.21% 5.38% 59.55 19.71 34.26
65. 31 de dez. de 2022 -6.00% -5.90% 72.14 46.69 58.03
66. 31 de jan. de 2023 3.33% 6.18% 0.71 27.45 4.42
67. 28 de fev. de 2023 0.92% -2.61% 2.45 12.58 5.55
68. 31 de mar. de 2023 15.59% 3.51% 171.59 6.60 33.66
69. 30 de abr. de 2023 6.58% 1.46% 16.71 0.28 2.16
70. 31 de mai. de 2023 7.10% 0.25% 21.25 0.47 -3.17
71. 30 de jun. de 2023 3.70% 4.71% 1.47 14.27 4.58
Total (Σ): 2,645.73 1,786.26 1,672.61

Mostrar tudo

VariaçãoMSFT = Σ(RMSFT,tRMSFT)2 ÷ (71 – 1)
= 2,645.73 ÷ (71 – 1)
= 37.80

VariaçãoS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (71 – 1)
= 1,786.26 ÷ (71 – 1)
= 25.52

CovariânciaMSFT, S&P 500 = Σ(RMSFT,tRMSFT)×(RS&P 500,tRS&P 500) ÷ (71 – 1)
= 1,672.61 ÷ (71 – 1)
= 23.89


Estimativa sistemática de risco (β)

Microsoft Excel
VariaçãoMSFT 37.80
VariaçãoS&P 500 25.52
CovariânciaMSFT, S&P 500 23.89
Coeficiente de correlaçãoMSFT, S&P 5001 0.77
βMSFT2 0.94
αMSFT3 1.61%

Cálculos

1 Coeficiente de correlaçãoMSFT, S&P 500
= CovariânciaMSFT, S&P 500 ÷ (Desvio padrãoMSFT × Desvio padrãoS&P 500)
= 23.89 ÷ (6.15% × 5.05%)
= 0.77

2 βMSFT
= CovariânciaMSFT, S&P 500 ÷ VariaçãoS&P 500
= 23.89 ÷ 25.52
= 0.94

3 αMSFT
= MédiaMSFT – βMSFT × MédiaS&P 500
= 2.49%0.94 × 0.94%
= 1.61%


Taxa de retorno esperada

Microsoft Excel
Suposições
Taxa de retorno do LT Treasury Composite1 RF 4.53%
Taxa esperada de retorno da carteira de mercado2 E(RM) 13.63%
Risco sistemático de Microsoft ações ordinárias βMSFT 0.94
 
Taxa de retorno esperada sobre as ações ordinárias da Microsoft3 E(RMSFT) 13.05%

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).

2 Ver Detalhes »

3 E(RMSFT) = RF + βMSFT [E(RM) – RF]
= 4.53% + 0.94 [13.63%4.53%]
= 13.05%