Stock Analysis on Net

International Business Machines Corp. (NYSE:IBM)

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

Microsoft Excel LibreOffice Calc

Tasas de retorno

International Business Machines Corp., tasas mensuales de retorno

Microsoft Excel LibreOffice Calc
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. 2017 $174.52 2,278.87
1. 28 feb. 2017 $179.82 $1.40 3.84% 2,363.64 3.72%
2. 31 mar. 2017 $174.14 -3.16% 2,362.72 -0.04%
3. 30 abr. 2017 $160.29 -7.95% 2,384.20 0.91%
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2021 $117.10 $1.64 -5.08% 4,567.00 -0.83%
59. 31 dic. 2021 $133.66 14.14% 4,766.18 4.36%
Promedio (R): 0.21% 1.36%
Desviación estándar: 7.27% 4.48%
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. 2017 $174.52 2,278.87
1. 28 feb. 2017 $179.82 $1.40 3.84% 2,363.64 3.72%
2. 31 mar. 2017 $174.14 -3.16% 2,362.72 -0.04%
3. 30 abr. 2017 $160.29 -7.95% 2,384.20 0.91%
4. 31 may. 2017 $152.63 $1.50 -3.84% 2,411.80 1.16%
5. 30 jun. 2017 $153.83 0.79% 2,423.41 0.48%
6. 31 jul. 2017 $144.67 -5.95% 2,470.30 1.93%
7. 31 ago. 2017 $143.03 $1.50 -0.10% 2,471.65 0.05%
8. 30 sept. 2017 $145.08 1.43% 2,519.36 1.93%
9. 31 oct. 2017 $154.06 6.19% 2,575.26 2.22%
10. 30 nov. 2017 $153.97 $1.50 0.92% 2,647.58 2.81%
11. 31 dic. 2017 $153.42 -0.36% 2,673.61 0.98%
12. 31 ene. 2018 $163.70 6.70% 2,823.81 5.62%
13. 28 feb. 2018 $155.83 $1.50 -3.89% 2,713.83 -3.89%
14. 31 mar. 2018 $153.43 -1.54% 2,640.87 -2.69%
15. 30 abr. 2018 $144.96 -5.52% 2,648.05 0.27%
16. 31 may. 2018 $141.31 $1.57 -1.43% 2,705.27 2.16%
17. 30 jun. 2018 $139.70 -1.14% 2,718.37 0.48%
18. 31 jul. 2018 $144.93 3.74% 2,816.29 3.60%
19. 31 ago. 2018 $146.48 $1.57 2.15% 2,901.52 3.03%
20. 30 sept. 2018 $151.21 3.23% 2,913.98 0.43%
21. 31 oct. 2018 $115.43 -23.66% 2,711.74 -6.94%
22. 30 nov. 2018 $124.27 $1.57 9.02% 2,760.17 1.79%
23. 31 dic. 2018 $113.67 -8.53% 2,506.85 -9.18%
24. 31 ene. 2019 $134.42 18.25% 2,704.10 7.87%
25. 28 feb. 2019 $138.13 $1.57 3.93% 2,784.49 2.97%
26. 31 mar. 2019 $141.10 2.15% 2,834.40 1.79%
27. 30 abr. 2019 $140.27 -0.59% 2,945.83 3.93%
28. 31 may. 2019 $126.99 $1.62 -8.31% 2,752.06 -6.58%
29. 30 jun. 2019 $137.90 8.59% 2,941.76 6.89%
30. 31 jul. 2019 $148.24 7.50% 2,980.38 1.31%
31. 31 ago. 2019 $135.53 $1.62 -7.48% 2,926.46 -1.81%
32. 30 sept. 2019 $145.42 7.30% 2,976.74 1.72%
33. 31 oct. 2019 $133.73 -8.04% 3,037.56 2.04%
34. 30 nov. 2019 $134.45 $1.62 1.75% 3,140.98 3.40%
35. 31 dic. 2019 $134.04 -0.30% 3,230.78 2.86%
36. 31 ene. 2020 $143.73 7.23% 3,225.52 -0.16%
37. 29 feb. 2020 $130.15 $1.62 -8.32% 2,954.22 -8.41%
38. 31 mar. 2020 $110.93 -14.77% 2,584.59 -12.51%
39. 30 abr. 2020 $125.56 13.19% 2,912.43 12.68%
40. 31 may. 2020 $124.90 $1.63 0.77% 3,044.31 4.53%
41. 30 jun. 2020 $120.77 -3.31% 3,100.29 1.84%
42. 31 jul. 2020 $122.94 1.80% 3,271.12 5.51%
43. 31 ago. 2020 $123.31 $1.63 1.63% 3,500.31 7.01%
44. 30 sept. 2020 $121.67 -1.33% 3,363.00 -3.92%
45. 31 oct. 2020 $111.66 -8.23% 3,269.96 -2.77%
46. 30 nov. 2020 $123.52 $1.63 12.08% 3,621.63 10.75%
47. 31 dic. 2020 $125.88 1.91% 3,756.07 3.71%
48. 31 ene. 2021 $119.11 -5.38% 3,714.24 -1.11%
49. 28 feb. 2021 $118.93 $1.63 1.22% 3,811.15 2.61%
50. 31 mar. 2021 $133.26 12.05% 3,972.89 4.24%
51. 30 abr. 2021 $141.88 6.47% 4,181.17 5.24%
52. 31 may. 2021 $143.74 $1.64 2.47% 4,204.11 0.55%
53. 30 jun. 2021 $146.59 1.98% 4,297.50 2.22%
54. 31 jul. 2021 $140.96 -3.84% 4,395.26 2.27%
55. 31 ago. 2021 $140.34 $1.64 0.72% 4,522.68 2.90%
56. 30 sept. 2021 $138.93 -1.00% 4,307.54 -4.76%
57. 31 oct. 2021 $125.10 -9.95% 4,605.38 6.91%
58. 30 nov. 2021 $117.10 $1.64 -5.08% 4,567.00 -0.83%
59. 31 dic. 2021 $133.66 14.14% 4,766.18 4.36%
Promedio (R): 0.21% 1.36%
Desviación estándar: 7.27% 4.48%

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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 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 varianza y covarianza de rendimientos

Microsoft Excel LibreOffice Calc
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. 28 feb. 2017 3.84% 3.72% 13.20 5.58 8.58
2. 31 mar. 2017 -3.16% -0.04% 11.32 1.95 4.70
3. 30 abr. 2017 -7.95% 0.91% 66.56 0.20 3.66
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2021 -5.08% -0.83% 27.98 4.80 11.59
59. 31 dic. 2021 14.14% 4.36% 194.23 9.02 41.86
Total (Σ): 3,065.40 1,164.17 1,320.75
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. 28 feb. 2017 3.84% 3.72% 13.20 5.58 8.58
2. 31 mar. 2017 -3.16% -0.04% 11.32 1.95 4.70
3. 30 abr. 2017 -7.95% 0.91% 66.56 0.20 3.66
4. 31 may. 2017 -3.84% 1.16% 16.39 0.04 0.81
5. 30 jun. 2017 0.79% 0.48% 0.34 0.77 -0.51
6. 31 jul. 2017 -5.95% 1.93% 37.94 0.33 -3.55
7. 31 ago. 2017 -0.10% 0.05% 0.09 1.70 0.39
8. 30 sept. 2017 1.43% 1.93% 1.51 0.33 0.70
9. 31 oct. 2017 6.19% 2.22% 35.81 0.74 5.15
10. 30 nov. 2017 0.92% 2.81% 0.50 2.10 1.03
11. 31 dic. 2017 -0.36% 0.98% 0.32 0.14 0.21
12. 31 ene. 2018 6.70% 5.62% 42.19 18.15 27.67
13. 28 feb. 2018 -3.89% -3.89% 16.78 27.59 21.52
14. 31 mar. 2018 -1.54% -2.69% 3.05 16.37 7.06
15. 30 abr. 2018 -5.52% 0.27% 32.78 1.18 6.22
16. 31 may. 2018 -1.43% 2.16% 2.69 0.64 -1.32
17. 30 jun. 2018 -1.14% 0.48% 1.81 0.76 1.17
18. 31 jul. 2018 3.74% 3.60% 12.52 5.04 7.94
19. 31 ago. 2018 2.15% 3.03% 3.79 2.78 3.25
20. 30 sept. 2018 3.23% 0.43% 9.14 0.86 -2.81
21. 31 oct. 2018 -23.66% -6.94% 569.67 68.86 198.06
22. 30 nov. 2018 9.02% 1.79% 77.67 0.18 3.77
23. 31 dic. 2018 -8.53% -9.18% 76.30 111.00 92.03
24. 31 ene. 2019 18.25% 7.87% 325.78 42.39 117.51
25. 28 feb. 2019 3.93% 2.97% 13.86 2.61 6.01
26. 31 mar. 2019 2.15% 1.79% 3.78 0.19 0.85
27. 30 abr. 2019 -0.59% 3.93% 0.63 6.62 -2.04
28. 31 may. 2019 -8.31% -6.58% 72.55 62.97 67.59
29. 30 jun. 2019 8.59% 6.89% 70.32 30.64 46.42
30. 31 jul. 2019 7.50% 1.31% 53.19 0.00 -0.33
31. 31 ago. 2019 -7.48% -1.81% 59.08 10.03 24.34
32. 30 sept. 2019 7.30% 1.72% 50.30 0.13 2.55
33. 31 oct. 2019 -8.04% 2.04% 67.96 0.47 -5.65
34. 30 nov. 2019 1.75% 3.40% 2.39 4.19 3.16
35. 31 dic. 2019 -0.30% 2.86% 0.26 2.25 -0.77
36. 31 ene. 2020 7.23% -0.16% 49.34 2.31 -10.68
37. 29 feb. 2020 -8.32% -8.41% 72.70 95.43 83.29
38. 31 mar. 2020 -14.77% -12.51% 224.19 192.37 207.67
39. 30 abr. 2020 13.19% 12.68% 168.56 128.29 147.05
40. 31 may. 2020 0.77% 4.53% 0.32 10.05 1.80
41. 30 jun. 2020 -3.31% 1.84% 12.33 0.23 -1.69
42. 31 jul. 2020 1.80% 5.51% 2.53 17.24 6.61
43. 31 ago. 2020 1.63% 7.01% 2.02 31.91 8.03
44. 30 sept. 2020 -1.33% -3.92% 2.36 27.89 8.11
45. 31 oct. 2020 -8.23% -2.77% 71.11 17.01 34.78
46. 30 nov. 2020 12.08% 10.75% 141.04 88.30 111.60
47. 31 dic. 2020 1.91% 3.71% 2.91 5.54 4.01
48. 31 ene. 2021 -5.38% -1.11% 31.17 6.11 13.80
49. 28 feb. 2021 1.22% 2.61% 1.02 1.57 1.27
50. 31 mar. 2021 12.05% 4.24% 140.28 8.33 34.18
51. 30 abr. 2021 6.47% 5.24% 39.23 15.09 24.33
52. 31 may. 2021 2.47% 0.55% 5.11 0.65 -1.83
53. 30 jun. 2021 1.98% 2.22% 3.16 0.75 1.53
54. 31 jul. 2021 -3.84% 2.27% 16.37 0.84 -3.71
55. 31 ago. 2021 0.72% 2.90% 0.27 2.38 0.80
56. 30 sept. 2021 -1.00% -4.76% 1.46 37.39 7.40
57. 31 oct. 2021 -9.95% 6.91% 103.22 30.87 -56.45
58. 30 nov. 2021 -5.08% -0.83% 27.98 4.80 11.59
59. 31 dic. 2021 14.14% 4.36% 194.23 9.02 41.86
Total (Σ): 3,065.40 1,164.17 1,320.75

Mostrar todo

VarianzaIBM = Σ(RIBM,tRIBM)2 ÷ (59 – 1)
= 3,065.40 ÷ (59 – 1)
= 52.85

VarianzaS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07

CovarianzaIBM, S&P 500 = Σ(RIBM,tRIBM)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,320.75 ÷ (59 – 1)
= 22.77


Estimación sistemática del riesgo (β)

Microsoft Excel LibreOffice Calc
VarianzaIBM 52.85
VarianzaS&P 500 20.07
CovarianzaIBM, S&P 500 22.77
Coeficiente de correlaciónIBM, S&P 5001 0.70
βIBM2 1.13
αIBM3 -1.34%

Cálculos

1 Coeficiente de correlaciónIBM, S&P 500
= CovarianzaIBM, S&P 500 ÷ (Desviación estándarIBM × Desviación estándarS&P 500)
= 22.77 ÷ (7.27% × 4.48%)
= 0.70

2 βIBM
= CovarianzaIBM, S&P 500 ÷ VarianzaS&P 500
= 22.77 ÷ 20.07
= 1.13

3 αIBM
= PromedioIBM – βIBM × PromedioS&P 500
= 0.21%1.13 × 1.36%
= -1.34%


Tasa de rendimiento esperada

Microsoft Excel LibreOffice Calc
Suposiciones
Tasa de rendimiento de LT Treasury Composite1 RF 3.20%
Tasa de rendimiento esperada de la cartera de mercado2 E(RM) 12.23%
Riesgo sistemático de acciones ordinarias IBM βIBM 1.13
 
Tasa de rendimiento esperada de las acciones ordinarias de IBM3 E(RIBM) 13.44%

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(RIBM) = RF + βIBM [E(RM) – RF]
= 3.20% + 1.13 [12.23%3.20%]
= 13.44%