Stock Analysis on Net

Boeing Co. (NYSE:BA)

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

Microsoft Excel

El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida de los activos de riesgo, como las acciones ordinarias de Boeing.


Tasas de retorno

Boeing Co., tasas mensuales de retorno

Microsoft Excel
Boeing Co. (BA) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioBA,t1 DividendoBA,t1 RBA,t2 PrecioS&P 500,t RS&P 500,t3
31 ene. 2017 $163.42 2,278.87
1. 28 feb. 2017 $180.23 $1.42 11.16% 2,363.64 3.72%
2. 31 mar. 2017 $176.86 -1.87% 2,362.72 -0.04%
3. 30 abr. 2017 $184.83 4.51% 2,384.20 0.91%
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2021 $197.85 -4.43% 4,567.00 -0.83%
59. 31 dic. 2021 $201.32 1.75% 4,766.18 4.36%
Promedio (R): 1.28% 1.36%
Desviación estándar: 12.54% 4.48%
Boeing Co. (BA) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioBA,t1 DividendoBA,t1 RBA,t2 PrecioS&P 500,t RS&P 500,t3
31 ene. 2017 $163.42 2,278.87
1. 28 feb. 2017 $180.23 $1.42 11.16% 2,363.64 3.72%
2. 31 mar. 2017 $176.86 -1.87% 2,362.72 -0.04%
3. 30 abr. 2017 $184.83 4.51% 2,384.20 0.91%
4. 31 may. 2017 $187.63 $1.42 2.28% 2,411.80 1.16%
5. 30 jun. 2017 $197.75 5.39% 2,423.41 0.48%
6. 31 jul. 2017 $242.46 22.61% 2,470.30 1.93%
7. 31 ago. 2017 $239.66 $1.42 -0.57% 2,471.65 0.05%
8. 30 sept. 2017 $254.21 6.07% 2,519.36 1.93%
9. 31 oct. 2017 $257.98 1.48% 2,575.26 2.22%
10. 30 nov. 2017 $276.80 $1.42 7.85% 2,647.58 2.81%
11. 31 dic. 2017 $294.91 6.54% 2,673.61 0.98%
12. 31 ene. 2018 $354.37 20.16% 2,823.81 5.62%
13. 28 feb. 2018 $362.21 $1.71 2.69% 2,713.83 -3.89%
14. 31 mar. 2018 $327.88 -9.48% 2,640.87 -2.69%
15. 30 abr. 2018 $333.56 1.73% 2,648.05 0.27%
16. 31 may. 2018 $352.16 $1.71 6.09% 2,705.27 2.16%
17. 30 jun. 2018 $335.51 -4.73% 2,718.37 0.48%
18. 31 jul. 2018 $356.30 6.20% 2,816.29 3.60%
19. 31 ago. 2018 $342.79 $1.71 -3.31% 2,901.52 3.03%
20. 30 sept. 2018 $371.90 8.49% 2,913.98 0.43%
21. 31 oct. 2018 $354.86 -4.58% 2,711.74 -6.94%
22. 30 nov. 2018 $346.76 $1.71 -1.80% 2,760.17 1.79%
23. 31 dic. 2018 $322.50 -7.00% 2,506.85 -9.18%
24. 31 ene. 2019 $385.62 19.57% 2,704.10 7.87%
25. 28 feb. 2019 $439.96 $2.055 14.62% 2,784.49 2.97%
26. 31 mar. 2019 $381.42 -13.31% 2,834.40 1.79%
27. 30 abr. 2019 $377.69 -0.98% 2,945.83 3.93%
28. 31 may. 2019 $341.61 $2.055 -9.01% 2,752.06 -6.58%
29. 30 jun. 2019 $364.01 6.56% 2,941.76 6.89%
30. 31 jul. 2019 $341.18 -6.27% 2,980.38 1.31%
31. 31 ago. 2019 $364.09 $2.055 7.32% 2,926.46 -1.81%
32. 30 sept. 2019 $380.47 4.50% 2,976.74 1.72%
33. 31 oct. 2019 $339.91 -10.66% 3,037.56 2.04%
34. 30 nov. 2019 $366.18 $2.055 8.33% 3,140.98 3.40%
35. 31 dic. 2019 $325.76 -11.04% 3,230.78 2.86%
36. 31 ene. 2020 $318.27 -2.30% 3,225.52 -0.16%
37. 29 feb. 2020 $275.11 $2.055 -12.92% 2,954.22 -8.41%
38. 31 mar. 2020 $149.14 -45.79% 2,584.59 -12.51%
39. 30 abr. 2020 $141.02 -5.44% 2,912.43 12.68%
40. 31 may. 2020 $145.85 3.43% 3,044.31 4.53%
41. 30 jun. 2020 $183.30 25.68% 3,100.29 1.84%
42. 31 jul. 2020 $158.00 -13.80% 3,271.12 5.51%
43. 31 ago. 2020 $171.82 8.75% 3,500.31 7.01%
44. 30 sept. 2020 $165.26 -3.82% 3,363.00 -3.92%
45. 31 oct. 2020 $144.39 -12.63% 3,269.96 -2.77%
46. 30 nov. 2020 $210.71 45.93% 3,621.63 10.75%
47. 31 dic. 2020 $214.06 1.59% 3,756.07 3.71%
48. 31 ene. 2021 $194.19 -9.28% 3,714.24 -1.11%
49. 28 feb. 2021 $212.01 9.18% 3,811.15 2.61%
50. 31 mar. 2021 $254.72 20.15% 3,972.89 4.24%
51. 30 abr. 2021 $234.31 -8.01% 4,181.17 5.24%
52. 31 may. 2021 $247.02 5.42% 4,204.11 0.55%
53. 30 jun. 2021 $239.56 -3.02% 4,297.50 2.22%
54. 31 jul. 2021 $226.48 -5.46% 4,395.26 2.27%
55. 31 ago. 2021 $219.50 -3.08% 4,522.68 2.90%
56. 30 sept. 2021 $219.94 0.20% 4,307.54 -4.76%
57. 31 oct. 2021 $207.03 -5.87% 4,605.38 6.91%
58. 30 nov. 2021 $197.85 -4.43% 4,567.00 -0.83%
59. 31 dic. 2021 $201.32 1.75% 4,766.18 4.36%
Promedio (R): 1.28% 1.36%
Desviación estándar: 12.54% 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 BA 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

Boeing Co., cálculo de varianza y covarianza de rendimientos

Microsoft Excel
t Fecha RBA,t RS&P 500,t (RBA,tRBA)2 (RS&P 500,tRS&P 500)2 (RBA,tRBA)×(RS&P 500,tRS&P 500)
1. 28 feb. 2017 11.16% 3.72% 97.44 5.58 23.31
2. 31 mar. 2017 -1.87% -0.04% 9.95 1.95 4.41
3. 30 abr. 2017 4.51% 0.91% 10.38 0.20 -1.45
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2021 -4.43% -0.83% 32.70 4.80 12.53
59. 31 dic. 2021 1.75% 4.36% 0.22 9.02 1.41
Total (Σ): 9,116.17 1,164.17 1,752.14
t Fecha RBA,t RS&P 500,t (RBA,tRBA)2 (RS&P 500,tRS&P 500)2 (RBA,tRBA)×(RS&P 500,tRS&P 500)
1. 28 feb. 2017 11.16% 3.72% 97.44 5.58 23.31
2. 31 mar. 2017 -1.87% -0.04% 9.95 1.95 4.41
3. 30 abr. 2017 4.51% 0.91% 10.38 0.20 -1.45
4. 31 may. 2017 2.28% 1.16% 1.00 0.04 -0.20
5. 30 jun. 2017 5.39% 0.48% 16.89 0.77 -3.60
6. 31 jul. 2017 22.61% 1.93% 454.76 0.33 12.30
7. 31 ago. 2017 -0.57% 0.05% 3.44 1.70 2.42
8. 30 sept. 2017 6.07% 1.93% 22.91 0.33 2.74
9. 31 oct. 2017 1.48% 2.22% 0.04 0.74 0.17
10. 30 nov. 2017 7.85% 2.81% 43.05 2.10 9.52
11. 31 dic. 2017 6.54% 0.98% 27.65 0.14 -1.97
12. 31 ene. 2018 20.16% 5.62% 356.37 18.15 80.42
13. 28 feb. 2018 2.69% -3.89% 1.99 27.59 -7.41
14. 31 mar. 2018 -9.48% -2.69% 115.83 16.37 43.55
15. 30 abr. 2018 1.73% 0.27% 0.20 1.18 -0.49
16. 31 may. 2018 6.09% 2.16% 23.08 0.64 3.86
17. 30 jun. 2018 -4.73% 0.48% 36.15 0.76 5.25
18. 31 jul. 2018 6.20% 3.60% 24.13 5.04 11.02
19. 31 ago. 2018 -3.31% 3.03% 21.12 2.78 -7.67
20. 30 sept. 2018 8.49% 0.43% 51.95 0.86 -6.69
21. 31 oct. 2018 -4.58% -6.94% 34.41 68.86 48.68
22. 30 nov. 2018 -1.80% 1.79% 9.52 0.18 -1.32
23. 31 dic. 2018 -7.00% -9.18% 68.57 111.00 87.24
24. 31 ene. 2019 19.57% 7.87% 334.44 42.39 119.06
25. 28 feb. 2019 14.62% 2.97% 177.96 2.61 21.54
26. 31 mar. 2019 -13.31% 1.79% 212.87 0.19 -6.34
27. 30 abr. 2019 -0.98% 3.93% 5.12 6.62 -5.82
28. 31 may. 2019 -9.01% -6.58% 105.95 62.97 81.68
29. 30 jun. 2019 6.56% 6.89% 27.80 30.64 29.19
30. 31 jul. 2019 -6.27% 1.31% 57.09 0.00 0.34
31. 31 ago. 2019 7.32% -1.81% 36.40 10.03 -19.11
32. 30 sept. 2019 4.50% 1.72% 10.33 0.13 1.16
33. 31 oct. 2019 -10.66% 2.04% 142.68 0.47 -8.19
34. 30 nov. 2019 8.33% 3.40% 49.69 4.19 14.43
35. 31 dic. 2019 -11.04% 2.86% 151.85 2.25 -18.50
36. 31 ene. 2020 -2.30% -0.16% 12.84 2.31 5.45
37. 29 feb. 2020 -12.92% -8.41% 201.62 95.43 138.71
38. 31 mar. 2020 -45.79% -12.51% 2,215.89 192.37 652.90
39. 30 abr. 2020 -5.44% 12.68% 45.28 128.29 -76.21
40. 31 may. 2020 3.43% 4.53% 4.58 10.05 6.79
41. 30 jun. 2020 25.68% 1.84% 595.01 0.23 11.73
42. 31 jul. 2020 -13.80% 5.51% 227.61 17.24 -62.64
43. 31 ago. 2020 8.75% 7.01% 55.69 31.91 42.15
44. 30 sept. 2020 -3.82% -3.92% 26.03 27.89 26.94
45. 31 oct. 2020 -12.63% -2.77% 193.57 17.01 57.38
46. 30 nov. 2020 45.93% 10.75% 1,993.34 88.30 419.53
47. 31 dic. 2020 1.59% 3.71% 0.09 5.54 0.72
48. 31 ene. 2021 -9.28% -1.11% 111.66 6.11 26.12
49. 28 feb. 2021 9.18% 2.61% 62.29 1.57 9.88
50. 31 mar. 2021 20.15% 4.24% 355.74 8.33 54.43
51. 30 abr. 2021 -8.01% 5.24% 86.43 15.09 -36.12
52. 31 may. 2021 5.42% 0.55% 17.14 0.65 -3.35
53. 30 jun. 2021 -3.02% 2.22% 18.53 0.75 -3.72
54. 31 jul. 2021 -5.46% 2.27% 45.49 0.84 -6.18
55. 31 ago. 2021 -3.08% 2.90% 19.06 2.38 -6.73
56. 30 sept. 2021 0.20% -4.76% 1.17 37.39 6.63
57. 31 oct. 2021 -5.87% 6.91% 51.18 30.87 -39.75
58. 30 nov. 2021 -4.43% -0.83% 32.70 4.80 12.53
59. 31 dic. 2021 1.75% 4.36% 0.22 9.02 1.41
Total (Σ): 9,116.17 1,164.17 1,752.14

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VarianzaBA = Σ(RBA,tRBA)2 ÷ (59 – 1)
= 9,116.17 ÷ (59 – 1)
= 157.18

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

CovarianzaBA, S&P 500 = Σ(RBA,tRBA)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,752.14 ÷ (59 – 1)
= 30.21


Estimación sistemática del riesgo (β)

Microsoft Excel
VarianzaBA 157.18
VarianzaS&P 500 20.07
CovarianzaBA, S&P 500 30.21
Coeficiente de correlaciónBA, S&P 5001 0.54
βBA2 1.51
αBA3 -0.76%

Cálculos

1 Coeficiente de correlaciónBA, S&P 500
= CovarianzaBA, S&P 500 ÷ (Desviación estándarBA × Desviación estándarS&P 500)
= 30.21 ÷ (12.54% × 4.48%)
= 0.54

2 βBA
= CovarianzaBA, S&P 500 ÷ VarianzaS&P 500
= 30.21 ÷ 20.07
= 1.51

3 αBA
= PromedioBA – βBA × PromedioS&P 500
= 1.28%1.51 × 1.36%
= -0.76%


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 Boeing βBA 1.51
 
Tasa de rendimiento esperada de las acciones ordinarias de Boeing3 E(RBA) 16.79%

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(RBA) = RF + βBA [E(RM) – RF]
= 3.24% + 1.51 [12.24%3.24%]
= 16.79%