Stock Analysis on Net

Apple Inc. (NASDAQ:AAPL) 

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

Microsoft Excel LibreOffice Calc

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 Apple.


Tasas de retorno

Apple Inc., tasas de rendimiento mensuales

Microsoft Excel LibreOffice Calc
Apple Inc. (AAPL) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioAAPL,t1 DividendoAAPL,t1 RAAPL,t2 PrecioS&P 500,t RS&P 500,t3
31 oct. 2015 $29.88 2,079.36
1. 30 nov. 2015 $29.58 $0.13 -0.57% 2,080.41 0.05%
2. 31 dic. 2015 $26.32 -11.02% 2,043.94 -1.75%
3. 31 ene. 2016 $24.34 -7.52% 1,940.24 -5.07%
. . . . . . .
. . . . . . .
. . . . . . .
70. 31 ago. 2021 $151.83 $0.22 4.24% 4,522.68 2.90%
71. 30 sept. 2021 $141.50 -6.80% 4,307.54 -4.76%
Promedio (R): 2.69% 1.12%
Desviación estándar: 8.49% 4.19%
Apple Inc. (AAPL) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioAAPL,t1 DividendoAAPL,t1 RAAPL,t2 PrecioS&P 500,t RS&P 500,t3
31 oct. 2015 $29.88 2,079.36
1. 30 nov. 2015 $29.58 $0.13 -0.57% 2,080.41 0.05%
2. 31 dic. 2015 $26.32 -11.02% 2,043.94 -1.75%
3. 31 ene. 2016 $24.34 -7.52% 1,940.24 -5.07%
4. 29 feb. 2016 $24.17 $0.13 -0.16% 1,932.23 -0.41%
5. 31 mar. 2016 $27.25 12.74% 2,059.74 6.60%
6. 30 abr. 2016 $23.44 -13.98% 2,065.30 0.27%
7. 31 may. 2016 $24.97 $0.1425 7.14% 2,096.95 1.53%
8. 30 jun. 2016 $23.90 -4.29% 2,098.86 0.09%
9. 31 jul. 2016 $26.05 9.00% 2,173.60 3.56%
10. 31 ago. 2016 $26.53 $0.1425 2.39% 2,170.95 -0.12%
11. 30 sept. 2016 $28.26 6.52% 2,168.27 -0.12%
12. 31 oct. 2016 $28.39 0.46% 2,126.15 -1.94%
13. 30 nov. 2016 $27.63 $0.1425 -2.18% 2,198.81 3.42%
14. 31 dic. 2016 $28.96 4.81% 2,238.83 1.82%
15. 31 ene. 2017 $30.34 4.77% 2,278.87 1.79%
16. 28 feb. 2017 $34.25 $0.1425 13.36% 2,363.64 3.72%
17. 31 mar. 2017 $35.92 4.88% 2,362.72 -0.04%
18. 30 abr. 2017 $35.91 -0.03% 2,384.20 0.91%
19. 31 may. 2017 $38.19 $0.1575 6.79% 2,411.80 1.16%
20. 30 jun. 2017 $36.01 -5.71% 2,423.41 0.48%
21. 31 jul. 2017 $37.18 3.25% 2,470.30 1.93%
22. 31 ago. 2017 $41.00 $0.1575 10.70% 2,471.65 0.05%
23. 30 sept. 2017 $38.53 -6.02% 2,519.36 1.93%
24. 31 oct. 2017 $42.26 9.68% 2,575.26 2.22%
25. 30 nov. 2017 $42.96 $0.1575 2.03% 2,647.58 2.81%
26. 31 dic. 2017 $42.31 -1.51% 2,673.61 0.98%
27. 31 ene. 2018 $41.86 -1.06% 2,823.81 5.62%
28. 28 feb. 2018 $44.53 $0.1575 6.75% 2,713.83 -3.89%
29. 31 mar. 2018 $41.95 -5.79% 2,640.87 -2.69%
30. 30 abr. 2018 $41.32 -1.50% 2,648.05 0.27%
31. 31 may. 2018 $46.72 $0.1825 13.51% 2,705.27 2.16%
32. 30 jun. 2018 $46.28 -0.94% 2,718.37 0.48%
33. 31 jul. 2018 $47.57 2.79% 2,816.29 3.60%
34. 31 ago. 2018 $56.91 $0.1825 20.02% 2,901.52 3.03%
35. 30 sept. 2018 $56.44 -0.83% 2,913.98 0.43%
36. 31 oct. 2018 $54.72 -3.05% 2,711.74 -6.94%
37. 30 nov. 2018 $44.65 $0.1825 -18.07% 2,760.17 1.79%
38. 31 dic. 2018 $39.44 -11.67% 2,506.85 -9.18%
39. 31 ene. 2019 $41.61 5.50% 2,704.10 7.87%
40. 28 feb. 2019 $43.29 $0.1825 4.48% 2,784.49 2.97%
41. 31 mar. 2019 $47.49 9.70% 2,834.40 1.79%
42. 30 abr. 2019 $50.17 5.64% 2,945.83 3.93%
43. 31 may. 2019 $43.77 $0.1925 -12.37% 2,752.06 -6.58%
44. 30 jun. 2019 $49.48 13.05% 2,941.76 6.89%
45. 31 jul. 2019 $53.26 7.64% 2,980.38 1.31%
46. 31 ago. 2019 $52.19 $0.1925 -1.65% 2,926.46 -1.81%
47. 30 sept. 2019 $55.99 7.28% 2,976.74 1.72%
48. 31 oct. 2019 $62.19 11.07% 3,037.56 2.04%
49. 30 nov. 2019 $66.81 $0.1925 7.74% 3,140.98 3.40%
50. 31 dic. 2019 $73.41 9.88% 3,230.78 2.86%
51. 31 ene. 2020 $77.38 5.41% 3,225.52 -0.16%
52. 29 feb. 2020 $68.34 $0.1925 -11.43% 2,954.22 -8.41%
53. 31 mar. 2020 $63.57 -6.98% 2,584.59 -12.51%
54. 30 abr. 2020 $73.45 15.54% 2,912.43 12.68%
55. 31 may. 2020 $79.49 $0.205 8.50% 3,044.31 4.53%
56. 30 jun. 2020 $91.20 14.73% 3,100.29 1.84%
57. 31 jul. 2020 $106.26 16.51% 3,271.12 5.51%
58. 31 ago. 2020 $129.04 $0.205 21.63% 3,500.31 7.01%
59. 30 sept. 2020 $115.81 -10.25% 3,363.00 -3.92%
60. 31 oct. 2020 $108.86 -6.00% 3,269.96 -2.77%
61. 30 nov. 2020 $119.05 $0.205 9.55% 3,621.63 10.75%
62. 31 dic. 2020 $132.69 11.46% 3,756.07 3.71%
63. 31 ene. 2021 $131.96 -0.55% 3,714.24 -1.11%
64. 28 feb. 2021 $121.26 $0.205 -7.95% 3,811.15 2.61%
65. 31 mar. 2021 $122.15 0.73% 3,972.89 4.24%
66. 30 abr. 2021 $131.46 7.62% 4,181.17 5.24%
67. 31 may. 2021 $124.61 $0.22 -5.04% 4,204.11 0.55%
68. 30 jun. 2021 $136.96 9.91% 4,297.50 2.22%
69. 31 jul. 2021 $145.86 6.50% 4,395.26 2.27%
70. 31 ago. 2021 $151.83 $0.22 4.24% 4,522.68 2.90%
71. 30 sept. 2021 $141.50 -6.80% 4,307.54 -4.76%
Promedio (R): 2.69% 1.12%
Desviación estándar: 8.49% 4.19%

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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 AAPL 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

Apple Inc., cálculo de varianza y covarianza de rendimientos

Microsoft Excel LibreOffice Calc
t Fecha RAAPL,t RS&P 500,t (RAAPL,tRAAPL)2 (RS&P 500,tRS&P 500)2 (RAAPL,tRAAPL)×(RS&P 500,tRS&P 500)
1. 30 nov. 2015 -0.57% 0.05% 10.62 1.14 3.48
2. 31 dic. 2015 -11.02% -1.75% 187.98 8.24 39.36
3. 31 ene. 2016 -7.52% -5.07% 104.29 38.33 63.23
. . . . . . .
. . . . . . .
. . . . . . .
70. 31 ago. 2021 4.24% 2.90% 2.42 3.17 2.77
71. 30 sept. 2021 -6.80% -4.76% 90.12 34.51 55.77
Total (Σ): 5,051.17 1,226.33 1,589.97
t Fecha RAAPL,t RS&P 500,t (RAAPL,tRAAPL)2 (RS&P 500,tRS&P 500)2 (RAAPL,tRAAPL)×(RS&P 500,tRS&P 500)
1. 30 nov. 2015 -0.57% 0.05% 10.62 1.14 3.48
2. 31 dic. 2015 -11.02% -1.75% 187.98 8.24 39.36
3. 31 ene. 2016 -7.52% -5.07% 104.29 38.33 63.23
4. 29 feb. 2016 -0.16% -0.41% 8.14 2.34 4.37
5. 31 mar. 2016 12.74% 6.60% 101.08 30.04 55.11
6. 30 abr. 2016 -13.98% 0.27% 277.93 0.72 14.14
7. 31 may. 2016 7.14% 1.53% 19.77 0.17 1.84
8. 30 jun. 2016 -4.29% 0.09% 48.64 1.05 7.16
9. 31 jul. 2016 9.00% 3.56% 39.77 5.97 15.41
10. 31 ago. 2016 2.39% -0.12% 0.09 1.54 0.37
11. 30 sept. 2016 6.52% -0.12% 14.68 1.54 -4.76
12. 31 oct. 2016 0.46% -1.94% 4.97 9.37 6.82
13. 30 nov. 2016 -2.18% 3.42% 23.66 5.29 -11.19
14. 31 dic. 2016 4.81% 1.82% 4.51 0.49 1.49
15. 31 ene. 2017 4.77% 1.79% 4.31 0.45 1.39
16. 28 feb. 2017 13.36% 3.72% 113.80 6.77 27.76
17. 31 mar. 2017 4.88% -0.04% 4.78 1.34 -2.53
18. 30 abr. 2017 -0.03% 0.91% 7.38 0.04 0.57
19. 31 may. 2017 6.79% 1.16% 16.80 0.00 0.16
20. 30 jun. 2017 -5.71% 0.48% 70.52 0.41 5.35
21. 31 jul. 2017 3.25% 1.93% 0.31 0.67 0.46
22. 31 ago. 2017 10.70% 0.05% 64.14 1.13 -8.52
23. 30 sept. 2017 -6.02% 1.93% 75.93 0.66 -7.08
24. 31 oct. 2017 9.68% 2.22% 48.88 1.21 7.70
25. 30 nov. 2017 2.03% 2.81% 0.44 2.86 -1.12
26. 31 dic. 2017 -1.51% 0.98% 17.66 0.02 0.57
27. 31 ene. 2018 -1.06% 5.62% 14.09 20.25 -16.89
28. 28 feb. 2018 6.75% -3.89% 16.53 25.13 -20.38
29. 31 mar. 2018 -5.79% -2.69% 71.97 14.49 32.29
30. 30 abr. 2018 -1.50% 0.27% 17.57 0.72 3.55
31. 31 may. 2018 13.51% 2.16% 117.09 1.09 11.28
32. 30 jun. 2018 -0.94% 0.48% 13.19 0.40 2.30
33. 31 jul. 2018 2.79% 3.60% 0.01 6.17 0.24
34. 31 ago. 2018 20.02% 3.03% 300.27 3.64 33.07
35. 30 sept. 2018 -0.83% 0.43% 12.36 0.47 2.42
36. 31 oct. 2018 -3.05% -6.94% 32.91 64.94 46.23
37. 30 nov. 2018 -18.07% 1.79% 430.92 0.45 -13.87
38. 31 dic. 2018 -11.67% -9.18% 206.15 106.00 147.83
39. 31 ene. 2019 5.50% 7.87% 7.91 45.57 18.99
40. 28 feb. 2019 4.48% 2.97% 3.19 3.44 3.31
41. 31 mar. 2019 9.70% 1.79% 49.18 0.45 4.73
42. 30 abr. 2019 5.64% 3.93% 8.73 7.92 8.31
43. 31 may. 2019 -12.37% -6.58% 226.88 59.22 115.92
44. 30 jun. 2019 13.05% 6.89% 107.25 33.35 59.81
45. 31 jul. 2019 7.64% 1.31% 24.50 0.04 0.96
46. 31 ago. 2019 -1.65% -1.81% 18.81 8.57 12.70
47. 30 sept. 2019 7.28% 1.72% 21.08 0.36 2.76
48. 31 oct. 2019 11.07% 2.04% 70.29 0.86 7.76
49. 30 nov. 2019 7.74% 3.40% 25.49 5.23 11.55
50. 31 dic. 2019 9.88% 2.86% 51.69 3.03 12.52
51. 31 ene. 2020 5.41% -0.16% 7.39 1.64 -3.48
52. 29 feb. 2020 -11.43% -8.41% 199.47 90.80 134.58
53. 31 mar. 2020 -6.98% -12.51% 93.49 185.77 131.79
54. 30 abr. 2020 15.54% 12.68% 165.19 133.78 148.66
55. 31 may. 2020 8.50% 4.53% 33.79 11.63 19.82
56. 30 jun. 2020 14.73% 1.84% 145.01 0.52 8.68
57. 31 jul. 2020 16.51% 5.51% 191.09 19.29 60.72
58. 31 ago. 2020 21.63% 7.01% 358.78 34.67 111.54
59. 30 sept. 2020 -10.25% -3.92% 167.50 25.41 65.24
60. 31 oct. 2020 -6.00% -2.77% 75.53 15.09 33.76
61. 30 nov. 2020 9.55% 10.75% 47.05 92.86 66.10
62. 31 dic. 2020 11.46% 3.71% 76.88 6.73 22.75
63. 31 ene. 2021 -0.55% -1.11% 10.50 4.98 7.23
64. 28 feb. 2021 -7.95% 2.61% 113.27 2.22 -15.87
65. 31 mar. 2021 0.73% 4.24% 3.82 9.77 -6.11
66. 30 abr. 2021 7.62% 5.24% 24.33 17.01 20.34
67. 31 may. 2021 -5.04% 0.55% 59.80 0.32 4.40
68. 30 jun. 2021 9.91% 2.22% 52.15 1.22 7.97
69. 31 jul. 2021 6.50% 2.27% 14.51 1.34 4.41
70. 31 ago. 2021 4.24% 2.90% 2.42 3.17 2.77
71. 30 sept. 2021 -6.80% -4.76% 90.12 34.51 55.77
Total (Σ): 5,051.17 1,226.33 1,589.97

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VarianzaAAPL = Σ(RAAPL,tRAAPL)2 ÷ (71 – 1)
= 5,051.17 ÷ (71 – 1)
= 72.16

VarianzaS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (71 – 1)
= 1,226.33 ÷ (71 – 1)
= 17.52

CovarianzaAAPL, S&P 500 = Σ(RAAPL,tRAAPL)×(RS&P 500,tRS&P 500) ÷ (71 – 1)
= 1,589.97 ÷ (71 – 1)
= 22.71


Estimación sistemática del riesgo (β)

Microsoft Excel LibreOffice Calc
VarianzaAAPL 72.16
VarianzaS&P 500 17.52
CovarianzaAAPL, S&P 500 22.71
Coeficiente de correlaciónAAPL, S&P 5001 0.64
βAAPL2 1.30
αAAPL3 1.24%

Cálculos

1 Coeficiente de correlaciónAAPL, S&P 500
= CovarianzaAAPL, S&P 500 ÷ (Desviación estándarAAPL × Desviación estándarS&P 500)
= 22.71 ÷ (8.49% × 4.19%)
= 0.64

2 βAAPL
= CovarianzaAAPL, S&P 500 ÷ VarianzaS&P 500
= 22.71 ÷ 17.52
= 1.30

3 αAAPL
= PromedioAAPL – βAAPL × PromedioS&P 500
= 2.69%1.30 × 1.12%
= 1.24%


Tasa de rendimiento esperada

Microsoft Excel LibreOffice Calc
Suposiciones
Tasa de rendimiento de LT Treasury Composite1 RF 3.26%
Tasa de rendimiento esperada de la cartera de mercado2 E(RM) 13.05%
Riesgo sistemático de acciones ordinarias Apple βAAPL 1.30
 
Tasa de rendimiento esperada de las acciones ordinarias de Apple3 E(RAAPL) 15.96%

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(RAAPL) = RF + βAAPL [E(RM) – RF]
= 3.26% + 1.30 [13.05%3.26%]
= 15.96%