Stock Analysis on Net

International Business Machines Corp. (NYSE:IBM)

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

Microsoft Excel

Tasas de retorno

International Business Machines Corp., tasas mensuales de retorno

Microsoft Excel
International Business Machines Corp. (IBM) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioIBM,t1 DividendoIBM,t1 RIBM,t2 PrecioS&P 500,t RS&P 500,t3
31 ene 2020 $143.73 3,225.52
1. 29 feb 2020 $130.15 $1.62 -8.32% 2,954.22 -8.41%
2. 31 mar 2020 $110.93 -14.77% 2,584.59 -12.51%
3. 30 abr 2020 $125.56 13.19% 2,912.43 12.68%
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov 2024 $227.41 $1.67 10.82% 6,032.38 5.73%
59. 31 dic 2024 $219.83 -3.33% 5,881.63 -2.50%
Promedio (R): 1.46% 1.16%
Desviación estándar: 6.87% 5.28%
International Business Machines Corp. (IBM) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioIBM,t1 DividendoIBM,t1 RIBM,t2 PrecioS&P 500,t RS&P 500,t3
31 ene 2020 $143.73 3,225.52
1. 29 feb 2020 $130.15 $1.62 -8.32% 2,954.22 -8.41%
2. 31 mar 2020 $110.93 -14.77% 2,584.59 -12.51%
3. 30 abr 2020 $125.56 13.19% 2,912.43 12.68%
4. 31 may 2020 $124.90 $1.63 0.77% 3,044.31 4.53%
5. 30 jun 2020 $120.77 -3.31% 3,100.29 1.84%
6. 31 jul 2020 $122.94 1.80% 3,271.12 5.51%
7. 31 ago 2020 $123.31 $1.63 1.63% 3,500.31 7.01%
8. 30 sept 2020 $121.67 -1.33% 3,363.00 -3.92%
9. 31 oct 2020 $111.66 -8.23% 3,269.96 -2.77%
10. 30 nov 2020 $123.52 $1.63 12.08% 3,621.63 10.75%
11. 31 dic 2020 $125.88 1.91% 3,756.07 3.71%
12. 31 ene 2021 $119.11 -5.38% 3,714.24 -1.11%
13. 28 feb 2021 $118.93 $1.63 1.22% 3,811.15 2.61%
14. 31 mar 2021 $133.26 12.05% 3,972.89 4.24%
15. 30 abr 2021 $141.88 6.47% 4,181.17 5.24%
16. 31 may 2021 $143.74 $1.64 2.47% 4,204.11 0.55%
17. 30 jun 2021 $146.59 1.98% 4,297.50 2.22%
18. 31 jul 2021 $140.96 -3.84% 4,395.26 2.27%
19. 31 ago 2021 $140.34 $1.64 0.72% 4,522.68 2.90%
20. 30 sept 2021 $138.93 -1.00% 4,307.54 -4.76%
21. 31 oct 2021 $125.10 $8.00 -4.20% 4,605.38 6.91%
22. 30 nov 2021 $117.10 $1.64 -5.08% 4,567.00 -0.83%
23. 31 dic 2021 $133.66 14.14% 4,766.18 4.36%
24. 31 ene 2022 $133.57 -0.07% 4,515.55 -5.26%
25. 28 feb 2022 $122.51 $1.64 -7.05% 4,373.94 -3.14%
26. 31 mar 2022 $130.02 6.13% 4,530.41 3.58%
27. 30 abr 2022 $132.21 1.68% 4,131.93 -8.80%
28. 31 may 2022 $138.84 $1.65 6.26% 4,132.15 0.01%
29. 30 jun 2022 $141.19 1.69% 3,785.38 -8.39%
30. 31 jul 2022 $130.79 -7.37% 4,130.29 9.11%
31. 31 ago 2022 $128.45 $1.65 -0.53% 3,955.00 -4.24%
32. 30 sept 2022 $118.81 -7.50% 3,585.62 -9.34%
33. 31 oct 2022 $138.29 16.40% 3,871.98 7.99%
34. 30 nov 2022 $148.90 $1.65 8.87% 4,080.11 5.38%
35. 31 dic 2022 $140.89 -5.38% 3,839.50 -5.90%
36. 31 ene 2023 $134.73 -4.37% 4,076.60 6.18%
37. 28 feb 2023 $129.30 $1.65 -2.81% 3,970.15 -2.61%
38. 31 mar 2023 $131.09 1.38% 4,109.31 3.51%
39. 30 abr 2023 $126.41 -3.57% 4,169.48 1.46%
40. 31 may 2023 $128.59 $1.66 3.04% 4,179.83 0.25%
41. 30 jun 2023 $133.81 4.06% 4,376.86 4.71%
42. 31 jul 2023 $144.18 7.75% 4,588.96 4.85%
43. 31 ago 2023 $146.83 $1.66 2.99% 4,507.66 -1.77%
44. 30 sept 2023 $140.30 -4.45% 4,288.05 -4.87%
45. 31 oct 2023 $144.64 3.09% 4,193.80 -2.20%
46. 30 nov 2023 $158.56 $1.66 10.77% 4,567.80 8.92%
47. 31 dic 2023 $163.55 3.15% 4,769.83 4.42%
48. 31 ene 2024 $183.66 12.30% 4,845.65 1.59%
49. 29 feb 2024 $185.03 $1.66 1.65% 5,096.27 5.17%
50. 31 mar 2024 $190.96 3.20% 5,254.35 3.10%
51. 30 abr 2024 $166.20 -12.97% 5,035.69 -4.16%
52. 31 may 2024 $166.85 $1.67 1.40% 5,277.51 4.80%
53. 30 jun 2024 $172.95 3.66% 5,460.48 3.47%
54. 31 jul 2024 $192.14 11.10% 5,522.30 1.13%
55. 31 ago 2024 $202.13 $1.67 6.07% 5,648.40 2.28%
56. 30 sept 2024 $221.08 9.38% 5,762.48 2.02%
57. 31 oct 2024 $206.72 -6.50% 5,705.45 -0.99%
58. 30 nov 2024 $227.41 $1.67 10.82% 6,032.38 5.73%
59. 31 dic 2024 $219.83 -3.33% 5,881.63 -2.50%
Promedio (R): 1.46% 1.16%
Desviación estándar: 6.87% 5.28%

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 IBM 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

International Business Machines Corp., cálculo de la varianza y covarianza de los rendimientos

Microsoft Excel
t Fecha RIBM,t RS&P 500,t (RIBM,tRIBM)2 (RS&P 500,tRS&P 500)2 (RIBM,tRIBM)×(RS&P 500,tRS&P 500)
1. 29 feb 2020 -8.32% -8.41% 95.59 91.63 93.59
2. 31 mar 2020 -14.77% -12.51% 263.20 186.96 221.83
3. 30 abr 2020 13.19% 12.68% 137.65 132.78 135.19
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov 2024 10.82% 5.73% 87.62 20.87 42.77
59. 31 dic 2024 -3.33% -2.50% 22.94 13.40 17.53
Total (Σ): 2,736.67 1,618.62 1,262.36
t Fecha RIBM,t RS&P 500,t (RIBM,tRIBM)2 (RS&P 500,tRS&P 500)2 (RIBM,tRIBM)×(RS&P 500,tRS&P 500)
1. 29 feb 2020 -8.32% -8.41% 95.59 91.63 93.59
2. 31 mar 2020 -14.77% -12.51% 263.20 186.96 221.83
3. 30 abr 2020 13.19% 12.68% 137.65 132.78 135.19
4. 31 may 2020 0.77% 4.53% 0.47 11.34 -2.30
5. 30 jun 2020 -3.31% 1.84% 22.68 0.46 -3.23
6. 31 jul 2020 1.80% 5.51% 0.12 18.91 1.48
7. 31 ago 2020 1.63% 7.01% 0.03 34.17 1.00
8. 30 sept 2020 -1.33% -3.92% 7.76 25.85 14.16
9. 31 oct 2020 -8.23% -2.77% 93.76 15.43 38.03
10. 30 nov 2020 12.08% 10.75% 112.90 92.03 101.93
11. 31 dic 2020 1.91% 3.71% 0.21 6.51 1.16
12. 31 ene 2021 -5.38% -1.11% 46.71 5.18 15.55
13. 28 feb 2021 1.22% 2.61% 0.06 2.10 -0.35
14. 31 mar 2021 12.05% 4.24% 112.21 9.50 32.65
15. 30 abr 2021 6.47% 5.24% 25.13 16.66 20.46
16. 31 may 2021 2.47% 0.55% 1.02 0.38 -0.62
17. 30 jun 2021 1.98% 2.22% 0.28 1.12 0.56
18. 31 jul 2021 -3.84% 2.27% 28.05 1.24 -5.90
19. 31 ago 2021 0.72% 2.90% 0.54 3.02 -1.27
20. 30 sept 2021 -1.00% -4.76% 6.06 35.02 14.56
21. 31 oct 2021 -4.20% 6.91% 31.95 33.10 -32.52
22. 30 nov 2021 -5.08% -0.83% 42.77 3.98 13.04
23. 31 dic 2021 14.14% 4.36% 160.93 10.24 40.59
24. 31 ene 2022 -0.07% -5.26% 2.32 41.21 9.78
25. 28 feb 2022 -7.05% -3.14% 72.39 18.47 36.56
26. 31 mar 2022 6.13% 3.58% 21.85 5.84 11.29
27. 30 abr 2022 1.68% -8.80% 0.05 99.14 -2.27
28. 31 may 2022 6.26% 0.01% 23.10 1.34 -5.56
29. 30 jun 2022 1.69% -8.39% 0.06 91.26 -2.26
30. 31 jul 2022 -7.37% 9.11% 77.83 63.21 -70.14
31. 31 ago 2022 -0.53% -4.24% 3.93 29.22 10.72
32. 30 sept 2022 -7.50% -9.34% 80.30 110.27 94.10
33. 31 oct 2022 16.40% 7.99% 223.20 46.58 101.97
34. 30 nov 2022 8.87% 5.38% 54.90 17.76 31.22
35. 31 dic 2022 -5.38% -5.90% 46.72 49.82 48.25
36. 31 ene 2023 -4.37% 6.18% 33.97 25.14 -29.22
37. 28 feb 2023 -2.81% -2.61% 18.16 14.23 16.08
38. 31 mar 2023 1.38% 3.51% 0.01 5.49 -0.17
39. 30 abr 2023 -3.57% 1.46% 25.26 0.09 -1.52
40. 31 may 2023 3.04% 0.25% 2.50 0.83 -1.44
41. 30 jun 2023 4.06% 4.71% 6.78 12.62 9.25
42. 31 jul 2023 7.75% 4.85% 39.61 13.58 23.19
43. 31 ago 2023 2.99% -1.77% 2.35 8.60 -4.50
44. 30 sept 2023 -4.45% -4.87% 34.85 36.40 35.62
45. 31 oct 2023 3.09% -2.20% 2.68 11.28 -5.50
46. 30 nov 2023 10.77% 8.92% 86.78 60.17 72.26
47. 31 dic 2023 3.15% 4.42% 2.86 10.64 5.52
48. 31 ene 2024 12.30% 1.59% 117.50 0.18 4.64
49. 29 feb 2024 1.65% 5.17% 0.04 16.09 0.78
50. 31 mar 2024 3.20% 3.10% 3.06 3.77 3.39
51. 30 abr 2024 -12.97% -4.16% 208.00 28.33 76.77
52. 31 may 2024 1.40% 4.80% 0.00 13.26 -0.22
53. 30 jun 2024 3.66% 3.47% 4.84 5.32 5.07
54. 31 jul 2024 11.10% 1.13% 92.92 0.00 -0.28
55. 31 ago 2024 6.07% 2.28% 21.27 1.26 5.18
56. 30 sept 2024 9.38% 2.02% 62.71 0.74 6.80
57. 31 oct 2024 -6.50% -0.99% 63.22 4.63 17.10
58. 30 nov 2024 10.82% 5.73% 87.62 20.87 42.77
59. 31 dic 2024 -3.33% -2.50% 22.94 13.40 17.53
Total (Σ): 2,736.67 1,618.62 1,262.36

Mostrar todo

VarianzaIBM = Σ(RIBM,tRIBM)2 ÷ (59 – 1)
= 2,736.67 ÷ (59 – 1)
= 47.18

VarianzaS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91

CovarianzaIBM, S&P 500 = Σ(RIBM,tRIBM)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,262.36 ÷ (59 – 1)
= 21.76


Estimación sistemática del riesgo (β)

Microsoft Excel
VarianzaIBM 47.18
VarianzaS&P 500 27.91
CovarianzaIBM, S&P 500 21.76
Coeficiente de correlaciónIBM, S&P 5001 0.60
βIBM2 0.78
αIBM3 0.55%

Cálculos

1 Coeficiente de correlaciónIBM, S&P 500
= CovarianzaIBM, S&P 500 ÷ (Desviación estándarIBM × Desviación estándarS&P 500)
= 21.76 ÷ (6.87% × 5.28%)
= 0.60

2 βIBM
= CovarianzaIBM, S&P 500 ÷ VarianzaS&P 500
= 21.76 ÷ 27.91
= 0.78

3 αIBM
= PromedioIBM – βIBM × PromedioS&P 500
= 1.46%0.78 × 1.16%
= 0.55%


Tasa de rendimiento esperada

Microsoft Excel
Suposiciones
Tasa de rendimiento del LT Treasury Composite1 RF 4.95%
Tasa de rendimiento esperada de la cartera de mercado2 E(RM) 14.71%
Riesgo sistemático de IBM acciones ordinarias βIBM 0.78
 
Tasa de rendimiento esperada de las acciones ordinarias de IBM3 E(RIBM) 12.56%

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(RIBM) = RF + βIBM [E(RM) – RF]
= 4.95% + 0.78 [14.71%4.95%]
= 12.56%