Stock Analysis on Net
Stock Analysis on Net

Apple Inc. (NASDAQ:AAPL)

Capital Asset Pricing Model (CAPM)

Microsoft Excel LibreOffice Calc

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Apple Inc.’s common stock.


Rates of Return

Apple Inc., monthly rates of return

Microsoft Excel LibreOffice Calc
Apple Inc. (AAPL) Standard & Poor’s 500 (S&P 500)
t Date PriceAAPL,t1 DividendAAPL,t1 RAAPL,t2 PriceS&P 500,t RS&P 500,t3
Oct 31, 2014 $27.00 2,018.05
1. Nov 30, 2014 $29.73 $0.1175 10.55% 2,067.56 2.45%
2. Dec 31, 2014 $27.60 -7.16% 2,058.90 -0.42%
3. Jan 31, 2015 $29.29 6.12% 1,994.99 -3.10%
. . . . . . .
. . . . . . .
. . . . . . .
70. Aug 31, 2020 $129.04 $0.205 21.63% 3,500.31 7.01%
71. Sep 30, 2020 $115.81 -10.25% 3,363.00 -3.92%
Average (R): 2.55% 0.81%
Standard deviation: 8.42% 4.16%
Apple Inc. (AAPL) Standard & Poor’s 500 (S&P 500)
t Date PriceAAPL,t1 DividendAAPL,t1 RAAPL,t2 PriceS&P 500,t RS&P 500,t3
Oct 31, 2014 $27.00 2,018.05
1. Nov 30, 2014 $29.73 $0.1175 10.55% 2,067.56 2.45%
2. Dec 31, 2014 $27.60 -7.16% 2,058.90 -0.42%
3. Jan 31, 2015 $29.29 6.12% 1,994.99 -3.10%
4. Feb 28, 2015 $32.12 $0.1175 10.06% 2,104.50 5.49%
5. Mar 31, 2015 $31.11 -3.14% 2,067.89 -1.74%
6. Apr 30, 2015 $31.29 0.58% 2,085.51 0.85%
7. May 31, 2015 $32.57 $0.13 4.51% 2,107.39 1.05%
8. Jun 30, 2015 $31.36 -3.72% 2,063.11 -2.10%
9. Jul 31, 2015 $30.33 -3.28% 2,103.84 1.97%
10. Aug 31, 2015 $28.19 $0.13 -6.63% 1,972.18 -6.26%
11. Sep 30, 2015 $27.58 -2.16% 1,920.03 -2.64%
12. Oct 31, 2015 $29.88 8.34% 2,079.36 8.30%
13. Nov 30, 2015 $29.58 $0.13 -0.57% 2,080.41 0.05%
14. Dec 31, 2015 $26.32 -11.02% 2,043.94 -1.75%
15. Jan 31, 2016 $24.34 -7.52% 1,940.24 -5.07%
16. Feb 29, 2016 $24.17 $0.13 -0.16% 1,932.23 -0.41%
17. Mar 31, 2016 $27.25 12.74% 2,059.74 6.60%
18. Apr 30, 2016 $23.44 -13.98% 2,065.30 0.27%
19. May 31, 2016 $24.97 $0.1425 7.14% 2,096.95 1.53%
20. Jun 30, 2016 $23.90 -4.29% 2,098.86 0.09%
21. Jul 31, 2016 $26.05 9.00% 2,173.60 3.56%
22. Aug 31, 2016 $26.53 $0.1425 2.39% 2,170.95 -0.12%
23. Sep 30, 2016 $28.26 6.52% 2,168.27 -0.12%
24. Oct 31, 2016 $28.39 0.46% 2,126.15 -1.94%
25. Nov 30, 2016 $27.63 $0.1425 -2.18% 2,198.81 3.42%
26. Dec 31, 2016 $28.96 4.81% 2,238.83 1.82%
27. Jan 31, 2017 $30.34 4.77% 2,278.87 1.79%
28. Feb 28, 2017 $34.25 $0.1425 13.36% 2,363.64 3.72%
29. Mar 31, 2017 $35.92 4.88% 2,362.72 -0.04%
30. Apr 30, 2017 $35.91 -0.03% 2,384.20 0.91%
31. May 31, 2017 $38.19 $0.1575 6.79% 2,411.80 1.16%
32. Jun 30, 2017 $36.01 -5.71% 2,423.41 0.48%
33. Jul 31, 2017 $37.18 3.25% 2,470.30 1.93%
34. Aug 31, 2017 $41.00 $0.1575 10.70% 2,471.65 0.05%
35. Sep 30, 2017 $38.53 -6.02% 2,519.36 1.93%
36. Oct 31, 2017 $42.26 9.68% 2,575.26 2.22%
37. Nov 30, 2017 $42.96 $0.1575 2.03% 2,647.58 2.81%
38. Dec 31, 2017 $42.31 -1.51% 2,673.61 0.98%
39. Jan 31, 2018 $41.86 -1.06% 2,823.81 5.62%
40. Feb 28, 2018 $44.53 $0.1575 6.75% 2,713.83 -3.89%
41. Mar 31, 2018 $41.95 -5.79% 2,640.87 -2.69%
42. Apr 30, 2018 $41.32 -1.50% 2,648.05 0.27%
43. May 31, 2018 $46.72 $0.1825 13.51% 2,705.27 2.16%
44. Jun 30, 2018 $46.28 -0.94% 2,718.37 0.48%
45. Jul 31, 2018 $47.57 2.79% 2,816.29 3.60%
46. Aug 31, 2018 $56.91 $0.1825 20.02% 2,901.52 3.03%
47. Sep 30, 2018 $56.44 -0.83% 2,913.98 0.43%
48. Oct 31, 2018 $54.72 -3.05% 2,711.74 -6.94%
49. Nov 30, 2018 $44.65 $0.1825 -18.07% 2,760.17 1.79%
50. Dec 31, 2018 $39.44 -11.67% 2,506.85 -9.18%
51. Jan 31, 2019 $41.61 5.50% 2,704.10 7.87%
52. Feb 28, 2019 $43.29 $0.1825 4.48% 2,784.49 2.97%
53. Mar 31, 2019 $47.49 9.70% 2,834.40 1.79%
54. Apr 30, 2019 $50.17 5.64% 2,945.83 3.93%
55. May 31, 2019 $43.77 $0.1925 -12.37% 2,752.06 -6.58%
56. Jun 30, 2019 $49.48 13.05% 2,941.76 6.89%
57. Jul 31, 2019 $53.26 7.64% 2,980.38 1.31%
58. Aug 31, 2019 $52.19 $0.1925 -1.65% 2,926.46 -1.81%
59. Sep 30, 2019 $55.99 7.28% 2,976.74 1.72%
60. Oct 31, 2019 $62.19 11.07% 3,037.56 2.04%
61. Nov 30, 2019 $66.81 $0.1925 7.74% 3,140.98 3.40%
62. Dec 31, 2019 $73.41 9.88% 3,230.78 2.86%
63. Jan 31, 2020 $77.38 5.41% 3,225.52 -0.16%
64. Feb 29, 2020 $68.34 $0.1925 -11.43% 2,954.22 -8.41%
65. Mar 31, 2020 $63.57 -6.98% 2,584.59 -12.51%
66. Apr 30, 2020 $73.45 15.54% 2,912.43 12.68%
67. May 31, 2020 $79.49 $0.205 8.50% 3,044.31 4.53%
68. Jun 30, 2020 $91.20 14.73% 3,100.29 1.84%
69. Jul 31, 2020 $106.26 16.51% 3,271.12 5.51%
70. Aug 31, 2020 $129.04 $0.205 21.63% 3,500.31 7.01%
71. Sep 30, 2020 $115.81 -10.25% 3,363.00 -3.92%
Average (R): 2.55% 0.81%
Standard deviation: 8.42% 4.16%

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1 Data in US$ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of AAPL during period t

3 Rate of return on S&P 500 (the market portfolio proxy) during period t


Variance and Covariance

Apple Inc., calculation of variance and covariance of returns

Microsoft Excel LibreOffice Calc
t Date 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. Nov 30, 2014 10.55% 2.45% 63.87 2.71 13.15
2. Dec 31, 2014 -7.16% -0.42% 94.45 1.50 11.92
3. Jan 31, 2015 6.12% -3.10% 12.74 15.30 -13.96
. . . . . . .
. . . . . . .
. . . . . . .
70. Aug 31, 2020 21.63% 7.01% 363.92 38.42 118.25
71. Sep 30, 2020 -10.25% -3.92% 164.01 22.38 60.58
Total (Σ): 4,965.28 1,210.80 1,587.01
t Date 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. Nov 30, 2014 10.55% 2.45% 63.87 2.71 13.15
2. Dec 31, 2014 -7.16% -0.42% 94.45 1.50 11.92
3. Jan 31, 2015 6.12% -3.10% 12.74 15.30 -13.96
4. Feb 28, 2015 10.06% 5.49% 56.39 21.92 35.15
5. Mar 31, 2015 -3.14% -1.74% 32.47 6.49 14.52
6. Apr 30, 2015 0.58% 0.85% 3.90 0.00 -0.09
7. May 31, 2015 4.51% 1.05% 3.81 0.06 0.47
8. Jun 30, 2015 -3.72% -2.10% 39.30 8.46 18.24
9. Jul 31, 2015 -3.28% 1.97% 34.09 1.36 -6.81
10. Aug 31, 2015 -6.63% -6.26% 84.30 49.93 64.87
11. Sep 30, 2015 -2.16% -2.64% 22.26 11.92 16.29
12. Oct 31, 2015 8.34% 8.30% 33.47 56.11 43.33
13. Nov 30, 2015 -0.57% 0.05% 9.75 0.57 2.37
14. Dec 31, 2015 -11.02% -1.75% 184.28 6.56 34.76
15. Jan 31, 2016 -7.52% -5.07% 101.54 34.59 59.27
16. Feb 29, 2016 -0.16% -0.41% 7.39 1.49 3.32
17. Mar 31, 2016 12.74% 6.60% 103.81 33.54 59.01
18. Apr 30, 2016 -13.98% 0.27% 273.43 0.29 8.89
19. May 31, 2016 7.14% 1.53% 20.99 0.53 3.32
20. Jun 30, 2016 -4.29% 0.09% 46.78 0.51 4.90
21. Jul 31, 2016 9.00% 3.56% 41.49 7.58 17.73
22. Aug 31, 2016 2.39% -0.12% 0.03 0.86 0.15
23. Sep 30, 2016 6.52% -0.12% 15.74 0.87 -3.69
24. Oct 31, 2016 0.46% -1.94% 4.39 7.56 5.76
25. Nov 30, 2016 -2.18% 3.42% 22.37 6.81 -12.34
26. Dec 31, 2016 4.81% 1.82% 5.11 1.02 2.29
27. Jan 31, 2017 4.77% 1.79% 4.89 0.96 2.17
28. Feb 28, 2017 13.36% 3.72% 116.70 8.48 31.46
29. Mar 31, 2017 4.88% -0.04% 5.39 0.72 -1.97
30. Apr 30, 2017 -0.03% 0.91% 6.67 0.01 -0.26
31. May 31, 2017 6.79% 1.16% 17.92 0.12 1.48
32. Jun 30, 2017 -5.71% 0.48% 68.27 0.11 2.70
33. Jul 31, 2017 3.25% 1.93% 0.48 1.27 0.78
34. Aug 31, 2017 10.70% 0.05% 66.32 0.57 -6.13
35. Sep 30, 2017 -6.02% 1.93% 73.59 1.26 -9.63
36. Oct 31, 2017 9.68% 2.22% 50.79 1.99 10.06
37. Nov 30, 2017 2.03% 2.81% 0.28 4.00 -1.05
38. Dec 31, 2017 -1.51% 0.98% 16.54 0.03 -0.71
39. Jan 31, 2018 -1.06% 5.62% 13.09 23.14 -17.40
40. Feb 28, 2018 6.75% -3.89% 17.64 22.11 -19.75
41. Mar 31, 2018 -5.79% -2.69% 69.69 12.22 29.19
42. Apr 30, 2018 -1.50% 0.27% 16.45 0.29 2.17
43. May 31, 2018 13.51% 2.16% 120.04 1.83 14.82
44. Jun 30, 2018 -0.94% 0.48% 12.22 0.10 1.13
45. Jul 31, 2018 2.79% 3.60% 0.05 7.81 0.65
46. Aug 31, 2018 20.02% 3.03% 304.98 4.92 38.74
47. Sep 30, 2018 -0.83% 0.43% 11.42 0.14 1.28
48. Oct 31, 2018 -3.05% -6.94% 31.38 60.03 43.40
49. Nov 30, 2018 -18.07% 1.79% 425.33 0.96 -20.17
50. Dec 31, 2018 -11.67% -9.18% 202.28 99.71 142.02
51. Jan 31, 2019 5.50% 7.87% 8.69 49.85 20.81
52. Feb 28, 2019 4.48% 2.97% 3.69 4.69 4.16
53. Mar 31, 2019 9.70% 1.79% 51.09 0.97 7.04
54. Apr 30, 2019 5.64% 3.93% 9.54 9.76 9.65
55. May 31, 2019 -12.37% -6.58% 222.82 54.55 110.25
56. Jun 30, 2019 13.05% 6.89% 110.07 37.03 63.84
57. Jul 31, 2019 7.64% 1.31% 25.86 0.25 2.57
58. Aug 31, 2019 -1.65% -1.81% 17.65 6.85 11.00
59. Sep 30, 2019 7.28% 1.72% 22.34 0.83 4.30
60. Oct 31, 2019 11.07% 2.04% 72.58 1.53 10.52
61. Nov 30, 2019 7.74% 3.40% 26.88 6.74 13.46
62. Dec 31, 2019 9.88% 2.86% 53.65 4.21 15.02
63. Jan 31, 2020 5.41% -0.16% 8.14 0.94 -2.77
64. Feb 29, 2020 -11.43% -8.41% 195.66 84.99 128.95
65. Mar 31, 2020 -6.98% -12.51% 90.90 177.42 126.99
66. Apr 30, 2020 15.54% 12.68% 168.68 141.05 154.25
67. May 31, 2020 8.50% 4.53% 35.38 13.84 22.13
68. Jun 30, 2020 14.73% 1.84% 148.29 1.06 12.55
69. Jul 31, 2020 16.51% 5.51% 194.85 22.11 65.64
70. Aug 31, 2020 21.63% 7.01% 363.92 38.42 118.25
71. Sep 30, 2020 -10.25% -3.92% 164.01 22.38 60.58
Total (Σ): 4,965.28 1,210.80 1,587.01

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VarianceAAPL = Σ(RAAPL,tRAAPL)2 ÷ (71 – 1)
= 4,965.28 ÷ (71 – 1)
= 70.93

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (71 – 1)
= 1,210.80 ÷ (71 – 1)
= 17.30

CovarianceAAPL, S&P 500 = Σ(RAAPL,tRAAPL)×(RS&P 500,tRS&P 500) ÷ (71 – 1)
= 1,587.01 ÷ (71 – 1)
= 22.67


Systematic Risk (β) Estimation

Microsoft Excel LibreOffice Calc
VarianceAAPL 70.93
VarianceS&P 500 17.30
CovarianceAAPL, S&P 500 22.67
Correlation coefficientAAPL, S&P 5001 0.65
βAAPL2 1.31
αAAPL3 1.50%

Calculations

1 Correlation coefficientAAPL, S&P 500
= CovarianceAAPL, S&P 500 ÷ (Standard deviationAAPL × Standard deviationS&P 500)
= 22.67 ÷ (8.42% × 4.16%)
= 0.65

2 βAAPL
= CovarianceAAPL, S&P 500 ÷ VarianceS&P 500
= 22.67 ÷ 17.30
= 1.31

3 αAAPL
= AverageAAPL – βAAPL × AverageS&P 500
= 2.55%1.31 × 0.81%
= 1.50%


Expected Rate of Return

Microsoft Excel LibreOffice Calc
Assumptions
Rate of return on LT Treasury Composite1 RF 1.76%
Expected rate of return on market portfolio2 E(RM) 11.84%
Systematic risk (β) of Apple Inc.’s common stock βAAPL 1.31
 
Expected rate of return on Apple Inc.’s common stock3 E(RAAPL) 14.97%

1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).

2 See details »

3 E(RAAPL) = RF + βAAPL [E(RM) – RF]
= 1.76% + 1.31 [11.84%1.76%]
= 14.97%