Stock Analysis on Net

Microsoft Corp. (NASDAQ:MSFT)

Modelo de fijación de precios de activos de capital (CAPM) 

Microsoft Excel

Tasas de retorno

Microsoft Corp., tasas mensuales de retorno

Microsoft Excel
Microsoft Corp. (MSFT) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioMSFT,t1 DividendoMSFT,t1 RMSFT,t2 PrecioS&P 500,t RS&P 500,t3
31 jul. 2016 $56.68 2,173.60
1. 31 ago. 2016 $57.46 $0.36 2.01% 2,170.95 -0.12%
2. 30 sept. 2016 $57.60 0.24% 2,168.27 -0.12%
3. 31 oct. 2016 $59.92 4.03% 2,126.15 -1.94%
. . . . . . .
. . . . . . .
. . . . . . .
70. 31 may. 2022 $271.87 $0.62 -1.81% 4,132.15 0.01%
71. 30 jun. 2022 $256.83 -5.53% 3,785.38 -8.39%
Promedio (R): 2.42% 0.89%
Desviación estándar: 5.38% 4.53%
Microsoft Corp. (MSFT) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioMSFT,t1 DividendoMSFT,t1 RMSFT,t2 PrecioS&P 500,t RS&P 500,t3
31 jul. 2016 $56.68 2,173.60
1. 31 ago. 2016 $57.46 $0.36 2.01% 2,170.95 -0.12%
2. 30 sept. 2016 $57.60 0.24% 2,168.27 -0.12%
3. 31 oct. 2016 $59.92 4.03% 2,126.15 -1.94%
4. 30 nov. 2016 $60.26 $0.39 1.22% 2,198.81 3.42%
5. 31 dic. 2016 $62.14 3.12% 2,238.83 1.82%
6. 31 ene. 2017 $64.65 4.04% 2,278.87 1.79%
7. 28 feb. 2017 $63.98 $0.39 -0.43% 2,363.64 3.72%
8. 31 mar. 2017 $65.86 2.94% 2,362.72 -0.04%
9. 30 abr. 2017 $68.46 3.95% 2,384.20 0.91%
10. 31 may. 2017 $69.84 $0.39 2.59% 2,411.80 1.16%
11. 30 jun. 2017 $68.93 -1.30% 2,423.41 0.48%
12. 31 jul. 2017 $72.70 5.47% 2,470.30 1.93%
13. 31 ago. 2017 $74.77 $0.39 3.38% 2,471.65 0.05%
14. 30 sept. 2017 $74.49 -0.37% 2,519.36 1.93%
15. 31 oct. 2017 $83.18 11.67% 2,575.26 2.22%
16. 30 nov. 2017 $84.17 $0.42 1.70% 2,647.58 2.81%
17. 31 dic. 2017 $85.54 1.63% 2,673.61 0.98%
18. 31 ene. 2018 $95.01 11.07% 2,823.81 5.62%
19. 28 feb. 2018 $93.77 $0.42 -0.86% 2,713.83 -3.89%
20. 31 mar. 2018 $91.27 -2.67% 2,640.87 -2.69%
21. 30 abr. 2018 $93.52 2.47% 2,648.05 0.27%
22. 31 may. 2018 $98.84 $0.42 6.14% 2,705.27 2.16%
23. 30 jun. 2018 $98.61 -0.23% 2,718.37 0.48%
24. 31 jul. 2018 $106.08 7.58% 2,816.29 3.60%
25. 31 ago. 2018 $112.33 $0.42 6.29% 2,901.52 3.03%
26. 30 sept. 2018 $114.37 1.82% 2,913.98 0.43%
27. 31 oct. 2018 $106.81 -6.61% 2,711.74 -6.94%
28. 30 nov. 2018 $110.89 $0.46 4.25% 2,760.17 1.79%
29. 31 dic. 2018 $101.57 -8.40% 2,506.85 -9.18%
30. 31 ene. 2019 $104.43 2.82% 2,704.10 7.87%
31. 28 feb. 2019 $112.03 $0.46 7.72% 2,784.49 2.97%
32. 31 mar. 2019 $117.94 5.28% 2,834.40 1.79%
33. 30 abr. 2019 $130.60 10.73% 2,945.83 3.93%
34. 31 may. 2019 $123.68 $0.46 -4.95% 2,752.06 -6.58%
35. 30 jun. 2019 $133.96 8.31% 2,941.76 6.89%
36. 31 jul. 2019 $136.27 1.72% 2,980.38 1.31%
37. 31 ago. 2019 $137.86 $0.46 1.50% 2,926.46 -1.81%
38. 30 sept. 2019 $139.03 0.85% 2,976.74 1.72%
39. 31 oct. 2019 $143.37 3.12% 3,037.56 2.04%
40. 30 nov. 2019 $151.38 $0.51 5.94% 3,140.98 3.40%
41. 31 dic. 2019 $157.70 4.17% 3,230.78 2.86%
42. 31 ene. 2020 $170.23 7.95% 3,225.52 -0.16%
43. 29 feb. 2020 $162.01 $0.51 -4.53% 2,954.22 -8.41%
44. 31 mar. 2020 $157.71 -2.65% 2,584.59 -12.51%
45. 30 abr. 2020 $179.21 13.63% 2,912.43 12.68%
46. 31 may. 2020 $183.25 $0.51 2.54% 3,044.31 4.53%
47. 30 jun. 2020 $203.51 11.06% 3,100.29 1.84%
48. 31 jul. 2020 $205.01 0.74% 3,271.12 5.51%
49. 31 ago. 2020 $225.53 $0.51 10.26% 3,500.31 7.01%
50. 30 sept. 2020 $210.33 -6.74% 3,363.00 -3.92%
51. 31 oct. 2020 $202.47 -3.74% 3,269.96 -2.77%
52. 30 nov. 2020 $214.07 $0.56 6.01% 3,621.63 10.75%
53. 31 dic. 2020 $222.42 3.90% 3,756.07 3.71%
54. 31 ene. 2021 $231.96 4.29% 3,714.24 -1.11%
55. 28 feb. 2021 $232.38 $0.56 0.42% 3,811.15 2.61%
56. 31 mar. 2021 $235.77 1.46% 3,972.89 4.24%
57. 30 abr. 2021 $252.18 6.96% 4,181.17 5.24%
58. 31 may. 2021 $249.68 $0.56 -0.77% 4,204.11 0.55%
59. 30 jun. 2021 $270.90 8.50% 4,297.50 2.22%
60. 31 jul. 2021 $284.91 5.17% 4,395.26 2.27%
61. 31 ago. 2021 $301.88 $0.56 6.15% 4,522.68 2.90%
62. 30 sept. 2021 $281.92 -6.61% 4,307.54 -4.76%
63. 31 oct. 2021 $331.62 17.63% 4,605.38 6.91%
64. 30 nov. 2021 $330.59 $0.62 -0.12% 4,567.00 -0.83%
65. 31 dic. 2021 $336.32 1.73% 4,766.18 4.36%
66. 31 ene. 2022 $310.98 -7.53% 4,515.55 -5.26%
67. 28 feb. 2022 $298.79 $0.62 -3.72% 4,373.94 -3.14%
68. 31 mar. 2022 $308.31 3.19% 4,530.41 3.58%
69. 30 abr. 2022 $277.52 -9.99% 4,131.93 -8.80%
70. 31 may. 2022 $271.87 $0.62 -1.81% 4,132.15 0.01%
71. 30 jun. 2022 $256.83 -5.53% 3,785.38 -8.39%
Promedio (R): 2.42% 0.89%
Desviación estándar: 5.38% 4.53%

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 MSFT 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

Microsoft Corp., cálculo de varianza y covarianza de rendimientos

Microsoft Excel
t Fecha 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 ago. 2016 2.01% -0.12% 0.17 1.02 0.41
2. 30 sept. 2016 0.24% -0.12% 4.73 1.02 2.20
3. 31 oct. 2016 4.03% -1.94% 2.59 8.00 -4.55
. . . . . . .
. . . . . . .
. . . . . . .
70. 31 may. 2022 -1.81% 0.01% 17.90 0.78 3.73
71. 30 jun. 2022 -5.53% -8.39% 63.22 86.09 73.77
Total (Σ): 2,027.88 1,437.21 1,305.14
t Fecha 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 ago. 2016 2.01% -0.12% 0.17 1.02 0.41
2. 30 sept. 2016 0.24% -0.12% 4.73 1.02 2.20
3. 31 oct. 2016 4.03% -1.94% 2.59 8.00 -4.55
4. 30 nov. 2016 1.22% 3.42% 1.44 6.40 -3.04
5. 31 dic. 2016 3.12% 1.82% 0.49 0.87 0.65
6. 31 ene. 2017 4.04% 1.79% 2.63 0.81 1.46
7. 28 feb. 2017 -0.43% 3.72% 8.13 8.03 -8.08
8. 31 mar. 2017 2.94% -0.04% 0.27 0.86 -0.48
9. 30 abr. 2017 3.95% 0.91% 2.34 0.00 0.03
10. 31 may. 2017 2.59% 1.16% 0.03 0.07 0.05
11. 30 jun. 2017 -1.30% 0.48% 13.85 0.16 1.51
12. 31 jul. 2017 5.47% 1.93% 9.31 1.10 3.20
13. 31 ago. 2017 3.38% 0.05% 0.93 0.69 -0.80
14. 30 sept. 2017 -0.37% 1.93% 7.80 1.09 -2.92
15. 31 oct. 2017 11.67% 2.22% 85.51 1.77 12.32
16. 30 nov. 2017 1.70% 2.81% 0.52 3.69 -1.39
17. 31 dic. 2017 1.63% 0.98% 0.63 0.01 -0.08
18. 31 ene. 2018 11.07% 5.62% 74.86 22.38 40.93
19. 28 feb. 2018 -0.86% -3.89% 10.77 22.86 15.69
20. 31 mar. 2018 -2.67% -2.69% 25.86 12.78 18.18
21. 30 abr. 2018 2.47% 0.27% 0.00 0.38 -0.03
22. 31 may. 2018 6.14% 2.16% 13.83 1.62 4.74
23. 30 jun. 2018 -0.23% 0.48% 7.03 0.16 1.07
24. 31 jul. 2018 7.58% 3.60% 26.59 7.37 14.00
25. 31 ago. 2018 6.29% 3.03% 14.97 4.58 8.28
26. 30 sept. 2018 1.82% 0.43% 0.36 0.21 0.28
27. 31 oct. 2018 -6.61% -6.94% 81.52 61.26 70.67
28. 30 nov. 2018 4.25% 1.79% 3.35 0.81 1.65
29. 31 dic. 2018 -8.40% -9.18% 117.15 101.29 108.93
30. 31 ene. 2019 2.82% 7.87% 0.16 48.74 2.77
31. 28 feb. 2019 7.72% 2.97% 28.08 4.35 11.06
32. 31 mar. 2019 5.28% 1.79% 8.16 0.82 2.59
33. 30 abr. 2019 10.73% 3.93% 69.15 9.27 25.32
34. 31 may. 2019 -4.95% -6.58% 54.25 55.72 54.98
35. 30 jun. 2019 8.31% 6.89% 34.73 36.08 35.39
36. 31 jul. 2019 1.72% 1.31% 0.48 0.18 -0.30
37. 31 ago. 2019 1.50% -1.81% 0.84 7.27 2.47
38. 30 sept. 2019 0.85% 1.72% 2.47 0.69 -1.31
39. 31 oct. 2019 3.12% 2.04% 0.49 1.34 0.81
40. 30 nov. 2019 5.94% 3.40% 12.42 6.34 8.87
41. 31 dic. 2019 4.17% 2.86% 3.08 3.89 3.46
42. 31 ene. 2020 7.95% -0.16% 30.54 1.10 -5.80
43. 29 feb. 2020 -4.53% -8.41% 48.28 86.45 64.60
44. 31 mar. 2020 -2.65% -12.51% 25.74 179.52 67.97
45. 30 abr. 2020 13.63% 12.68% 125.75 139.19 132.30
46. 31 may. 2020 2.54% 4.53% 0.01 13.26 0.44
47. 30 jun. 2020 11.06% 1.84% 74.60 0.91 8.22
48. 31 jul. 2020 0.74% 5.51% 2.83 21.38 -7.78
49. 31 ago. 2020 10.26% 7.01% 61.45 37.45 47.97
50. 30 sept. 2020 -6.74% -3.92% 83.88 23.13 44.05
51. 31 oct. 2020 -3.74% -2.77% 37.89 13.35 22.49
52. 30 nov. 2020 6.01% 10.75% 12.87 97.38 35.40
53. 31 dic. 2020 3.90% 3.71% 2.20 7.98 4.19
54. 31 ene. 2021 4.29% -1.11% 3.50 4.00 -3.74
55. 28 feb. 2021 0.42% 2.61% 3.99 2.97 -3.44
56. 31 mar. 2021 1.46% 4.24% 0.92 11.27 -3.22
57. 30 abr. 2021 6.96% 5.24% 20.62 18.97 19.78
58. 31 may. 2021 -0.77% 0.55% 10.16 0.11 1.08
59. 30 jun. 2021 8.50% 2.22% 36.97 1.78 8.12
60. 31 jul. 2021 5.17% 2.27% 7.58 1.93 3.82
61. 31 ago. 2021 6.15% 2.90% 13.94 4.05 7.51
62. 30 sept. 2021 -6.61% -4.76% 81.56 31.85 50.97
63. 31 oct. 2021 17.63% 6.91% 231.35 36.33 91.68
64. 30 nov. 2021 -0.12% -0.83% 6.46 2.96 4.37
65. 31 dic. 2021 1.73% 4.36% 0.47 12.07 -2.38
66. 31 ene. 2022 -7.53% -5.26% 99.07 37.76 61.17
67. 28 feb. 2022 -3.72% -3.14% 37.69 16.18 24.70
68. 31 mar. 2022 3.19% 3.58% 0.59 7.24 2.06
69. 30 abr. 2022 -9.99% -8.80% 153.90 93.75 120.12
70. 31 may. 2022 -1.81% 0.01% 17.90 0.78 3.73
71. 30 jun. 2022 -5.53% -8.39% 63.22 86.09 73.77
Total (Σ): 2,027.88 1,437.21 1,305.14

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VarianzaMSFT = Σ(RMSFT,tRMSFT)2 ÷ (71 – 1)
= 2,027.88 ÷ (71 – 1)
= 28.97

VarianzaS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (71 – 1)
= 1,437.21 ÷ (71 – 1)
= 20.53

CovarianzaMSFT, S&P 500 = Σ(RMSFT,tRMSFT)×(RS&P 500,tRS&P 500) ÷ (71 – 1)
= 1,305.14 ÷ (71 – 1)
= 18.64


Estimación sistemática del riesgo (β)

Microsoft Excel
VarianzaMSFT 28.97
VarianzaS&P 500 20.53
CovarianzaMSFT, S&P 500 18.64
Coeficiente de correlaciónMSFT, S&P 5001 0.76
βMSFT2 0.91
αMSFT3 1.61%

Cálculos

1 Coeficiente de correlaciónMSFT, S&P 500
= CovarianzaMSFT, S&P 500 ÷ (Desviación estándarMSFT × Desviación estándarS&P 500)
= 18.64 ÷ (5.38% × 4.53%)
= 0.76

2 βMSFT
= CovarianzaMSFT, S&P 500 ÷ VarianzaS&P 500
= 18.64 ÷ 20.53
= 0.91

3 αMSFT
= PromedioMSFT – βMSFT × PromedioS&P 500
= 2.42%0.91 × 0.89%
= 1.61%


Tasa de rendimiento esperada

Microsoft Excel
Suposiciones
Tasa de rendimiento de LT Treasury Composite1 RF 3.24%
Tasa de rendimiento esperada de la cartera de mercado2 E(RM) 12.24%
Riesgo sistemático de acciones ordinarias Microsoft βMSFT 0.91
 
Tasa de rendimiento esperada de las acciones ordinarias de Microsoft3 E(RMSFT) 11.42%

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).

2 Ver detalles »

3 E(RMSFT) = RF + βMSFT [E(RM) – RF]
= 3.24% + 0.91 [12.24%3.24%]
= 11.42%