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. 2017 $72.70 2,470.30
1. 31 ago. 2017 $74.77 $0.39 3.38% 2,471.65 0.05%
2. 30 sept. 2017 $74.49 -0.37% 2,519.36 1.93%
3. 31 oct. 2017 $83.18 11.67% 2,575.26 2.22%
. . . . . . .
. . . . . . .
. . . . . . .
70. 31 may. 2023 $328.39 $0.68 7.10% 4,179.83 0.25%
71. 30 jun. 2023 $340.54 3.70% 4,376.86 4.71%
Promedio (R): 2.49% 0.94%
Desviación estándar: 6.15% 5.05%
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. 2017 $72.70 2,470.30
1. 31 ago. 2017 $74.77 $0.39 3.38% 2,471.65 0.05%
2. 30 sept. 2017 $74.49 -0.37% 2,519.36 1.93%
3. 31 oct. 2017 $83.18 11.67% 2,575.26 2.22%
4. 30 nov. 2017 $84.17 $0.42 1.70% 2,647.58 2.81%
5. 31 dic. 2017 $85.54 1.63% 2,673.61 0.98%
6. 31 ene. 2018 $95.01 11.07% 2,823.81 5.62%
7. 28 feb. 2018 $93.77 $0.42 -0.86% 2,713.83 -3.89%
8. 31 mar. 2018 $91.27 -2.67% 2,640.87 -2.69%
9. 30 abr. 2018 $93.52 2.47% 2,648.05 0.27%
10. 31 may. 2018 $98.84 $0.42 6.14% 2,705.27 2.16%
11. 30 jun. 2018 $98.61 -0.23% 2,718.37 0.48%
12. 31 jul. 2018 $106.08 7.58% 2,816.29 3.60%
13. 31 ago. 2018 $112.33 $0.42 6.29% 2,901.52 3.03%
14. 30 sept. 2018 $114.37 1.82% 2,913.98 0.43%
15. 31 oct. 2018 $106.81 -6.61% 2,711.74 -6.94%
16. 30 nov. 2018 $110.89 $0.46 4.25% 2,760.17 1.79%
17. 31 dic. 2018 $101.57 -8.40% 2,506.85 -9.18%
18. 31 ene. 2019 $104.43 2.82% 2,704.10 7.87%
19. 28 feb. 2019 $112.03 $0.46 7.72% 2,784.49 2.97%
20. 31 mar. 2019 $117.94 5.28% 2,834.40 1.79%
21. 30 abr. 2019 $130.60 10.73% 2,945.83 3.93%
22. 31 may. 2019 $123.68 $0.46 -4.95% 2,752.06 -6.58%
23. 30 jun. 2019 $133.96 8.31% 2,941.76 6.89%
24. 31 jul. 2019 $136.27 1.72% 2,980.38 1.31%
25. 31 ago. 2019 $137.86 $0.46 1.50% 2,926.46 -1.81%
26. 30 sept. 2019 $139.03 0.85% 2,976.74 1.72%
27. 31 oct. 2019 $143.37 3.12% 3,037.56 2.04%
28. 30 nov. 2019 $151.38 $0.51 5.94% 3,140.98 3.40%
29. 31 dic. 2019 $157.70 4.17% 3,230.78 2.86%
30. 31 ene. 2020 $170.23 7.95% 3,225.52 -0.16%
31. 29 feb. 2020 $162.01 $0.51 -4.53% 2,954.22 -8.41%
32. 31 mar. 2020 $157.71 -2.65% 2,584.59 -12.51%
33. 30 abr. 2020 $179.21 13.63% 2,912.43 12.68%
34. 31 may. 2020 $183.25 $0.51 2.54% 3,044.31 4.53%
35. 30 jun. 2020 $203.51 11.06% 3,100.29 1.84%
36. 31 jul. 2020 $205.01 0.74% 3,271.12 5.51%
37. 31 ago. 2020 $225.53 $0.51 10.26% 3,500.31 7.01%
38. 30 sept. 2020 $210.33 -6.74% 3,363.00 -3.92%
39. 31 oct. 2020 $202.47 -3.74% 3,269.96 -2.77%
40. 30 nov. 2020 $214.07 $0.56 6.01% 3,621.63 10.75%
41. 31 dic. 2020 $222.42 3.90% 3,756.07 3.71%
42. 31 ene. 2021 $231.96 4.29% 3,714.24 -1.11%
43. 28 feb. 2021 $232.38 $0.56 0.42% 3,811.15 2.61%
44. 31 mar. 2021 $235.77 1.46% 3,972.89 4.24%
45. 30 abr. 2021 $252.18 6.96% 4,181.17 5.24%
46. 31 may. 2021 $249.68 $0.56 -0.77% 4,204.11 0.55%
47. 30 jun. 2021 $270.90 8.50% 4,297.50 2.22%
48. 31 jul. 2021 $284.91 5.17% 4,395.26 2.27%
49. 31 ago. 2021 $301.88 $0.56 6.15% 4,522.68 2.90%
50. 30 sept. 2021 $281.92 -6.61% 4,307.54 -4.76%
51. 31 oct. 2021 $331.62 17.63% 4,605.38 6.91%
52. 30 nov. 2021 $330.59 $0.62 -0.12% 4,567.00 -0.83%
53. 31 dic. 2021 $336.32 1.73% 4,766.18 4.36%
54. 31 ene. 2022 $310.98 -7.53% 4,515.55 -5.26%
55. 28 feb. 2022 $298.79 $0.62 -3.72% 4,373.94 -3.14%
56. 31 mar. 2022 $308.31 3.19% 4,530.41 3.58%
57. 30 abr. 2022 $277.52 -9.99% 4,131.93 -8.80%
58. 31 may. 2022 $271.87 $0.62 -1.81% 4,132.15 0.01%
59. 30 jun. 2022 $256.83 -5.53% 3,785.38 -8.39%
60. 31 jul. 2022 $280.74 9.31% 4,130.29 9.11%
61. 31 ago. 2022 $261.47 $0.62 -6.64% 3,955.00 -4.24%
62. 30 sept. 2022 $232.90 -10.93% 3,585.62 -9.34%
63. 31 oct. 2022 $232.13 -0.33% 3,871.98 7.99%
64. 30 nov. 2022 $255.14 $0.68 10.21% 4,080.11 5.38%
65. 31 dic. 2022 $239.82 -6.00% 3,839.50 -5.90%
66. 31 ene. 2023 $247.81 3.33% 4,076.60 6.18%
67. 28 feb. 2023 $249.42 $0.68 0.92% 3,970.15 -2.61%
68. 31 mar. 2023 $288.30 15.59% 4,109.31 3.51%
69. 30 abr. 2023 $307.26 6.58% 4,169.48 1.46%
70. 31 may. 2023 $328.39 $0.68 7.10% 4,179.83 0.25%
71. 30 jun. 2023 $340.54 3.70% 4,376.86 4.71%
Promedio (R): 2.49% 0.94%
Desviación estándar: 6.15% 5.05%

Mostrar todo

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

Mostrar todo

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

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

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


Estimación sistemática del riesgo (β)

Microsoft Excel
VarianzaMSFT 37.80
VarianzaS&P 500 25.52
CovarianzaMSFT, S&P 500 23.89
Coeficiente de correlaciónMSFT, S&P 5001 0.77
βMSFT2 0.94
αMSFT3 1.61%

Cálculos

1 Coeficiente de correlaciónMSFT, S&P 500
= CovarianzaMSFT, S&P 500 ÷ (Desviación estándarMSFT × Desviación estándarS&P 500)
= 23.89 ÷ (6.15% × 5.05%)
= 0.77

2 βMSFT
= CovarianzaMSFT, S&P 500 ÷ VarianzaS&P 500
= 23.89 ÷ 25.52
= 0.94

3 αMSFT
= PromedioMSFT – βMSFT × PromedioS&P 500
= 2.49%0.94 × 0.94%
= 1.61%


Tasa de rendimiento esperada

Microsoft Excel
Suposiciones
Tasa de rendimiento del LT Treasury Composite1 RF 4.53%
Tasa de rendimiento esperada de la cartera de mercado2 E(RM) 13.63%
Riesgo sistemático de Microsoft acciones ordinarias βMSFT 0.94
 
Tasa de rendimiento esperada de las acciones ordinarias de Microsoft3 E(RMSFT) 13.05%

1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. con cupón fijo en circulación que no vencen ni son rescatables en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).

2 Ver detalles »

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