Stock Analysis on Net

Amgen Inc. (NASDAQ:AMGN)

Capital Asset Pricing Model (CAPM) 

Microsoft Excel

Rates of Return

Amgen Inc., monthly rates of return

Microsoft Excel
Amgen Inc. (AMGN) Standard & Poor’s 500 (S&P 500)
t Date PriceAMGN,t1 DividendAMGN,t1 RAMGN,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2020 $216.05 3,225.52
1. Feb 29, 2020 $199.73 $1.60 -6.81% 2,954.22 -8.41%
2. Mar 31, 2020 $202.73 1.50% 2,584.59 -12.51%
3. Apr 30, 2020 $239.22 18.00% 2,912.43 12.68%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2024 $282.87 $2.25 -10.94% 6,032.38 5.73%
59. Dec 31, 2024 $260.64 -7.86% 5,881.63 -2.50%
Average (R): 0.83% 1.16%
Standard deviation: 7.07% 5.28%
Amgen Inc. (AMGN) Standard & Poor’s 500 (S&P 500)
t Date PriceAMGN,t1 DividendAMGN,t1 RAMGN,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2020 $216.05 3,225.52
1. Feb 29, 2020 $199.73 $1.60 -6.81% 2,954.22 -8.41%
2. Mar 31, 2020 $202.73 1.50% 2,584.59 -12.51%
3. Apr 30, 2020 $239.22 18.00% 2,912.43 12.68%
4. May 31, 2020 $229.70 $1.60 -3.31% 3,044.31 4.53%
5. Jun 30, 2020 $235.86 2.68% 3,100.29 1.84%
6. Jul 31, 2020 $244.67 3.74% 3,271.12 5.51%
7. Aug 31, 2020 $253.32 $1.60 4.19% 3,500.31 7.01%
8. Sep 30, 2020 $254.16 0.33% 3,363.00 -3.92%
9. Oct 31, 2020 $216.94 -14.64% 3,269.96 -2.77%
10. Nov 30, 2020 $222.04 $1.60 3.09% 3,621.63 10.75%
11. Dec 31, 2020 $229.92 3.55% 3,756.07 3.71%
12. Jan 31, 2021 $241.43 5.01% 3,714.24 -1.11%
13. Feb 28, 2021 $224.92 $1.76 -6.11% 3,811.15 2.61%
14. Mar 31, 2021 $248.81 10.62% 3,972.89 4.24%
15. Apr 30, 2021 $239.64 -3.69% 4,181.17 5.24%
16. May 31, 2021 $237.94 $1.76 0.03% 4,204.11 0.55%
17. Jun 30, 2021 $243.75 2.44% 4,297.50 2.22%
18. Jul 31, 2021 $241.54 -0.91% 4,395.26 2.27%
19. Aug 31, 2021 $225.53 $1.76 -5.90% 4,522.68 2.90%
20. Sep 30, 2021 $212.65 -5.71% 4,307.54 -4.76%
21. Oct 31, 2021 $206.97 -2.67% 4,605.38 6.91%
22. Nov 30, 2021 $198.88 $1.76 -3.06% 4,567.00 -0.83%
23. Dec 31, 2021 $224.97 13.12% 4,766.18 4.36%
24. Jan 31, 2022 $227.14 0.96% 4,515.55 -5.26%
25. Feb 28, 2022 $226.48 $1.94 0.56% 4,373.94 -3.14%
26. Mar 31, 2022 $241.82 6.77% 4,530.41 3.58%
27. Apr 30, 2022 $233.19 -3.57% 4,131.93 -8.80%
28. May 31, 2022 $256.74 $1.94 10.93% 4,132.15 0.01%
29. Jun 30, 2022 $243.30 -5.23% 3,785.38 -8.39%
30. Jul 31, 2022 $247.47 1.71% 4,130.29 9.11%
31. Aug 31, 2022 $240.30 $1.94 -2.11% 3,955.00 -4.24%
32. Sep 30, 2022 $225.40 -6.20% 3,585.62 -9.34%
33. Oct 31, 2022 $270.35 19.94% 3,871.98 7.99%
34. Nov 30, 2022 $286.40 $1.94 6.65% 4,080.11 5.38%
35. Dec 31, 2022 $262.64 -8.30% 3,839.50 -5.90%
36. Jan 31, 2023 $252.40 -3.90% 4,076.60 6.18%
37. Feb 28, 2023 $231.66 $2.13 -7.37% 3,970.15 -2.61%
38. Mar 31, 2023 $241.75 4.36% 4,109.31 3.51%
39. Apr 30, 2023 $239.74 -0.83% 4,169.48 1.46%
40. May 31, 2023 $220.65 $2.13 -7.07% 4,179.83 0.25%
41. Jun 30, 2023 $222.02 0.62% 4,376.86 4.71%
42. Jul 31, 2023 $234.15 5.46% 4,588.96 4.85%
43. Aug 31, 2023 $256.34 $2.13 10.39% 4,507.66 -1.77%
44. Sep 30, 2023 $268.76 4.85% 4,288.05 -4.87%
45. Oct 31, 2023 $255.70 -4.86% 4,193.80 -2.20%
46. Nov 30, 2023 $269.64 $2.13 6.28% 4,567.80 8.92%
47. Dec 31, 2023 $288.02 6.82% 4,769.83 4.42%
48. Jan 31, 2024 $314.26 9.11% 4,845.65 1.59%
49. Feb 29, 2024 $273.83 $2.25 -12.15% 5,096.27 5.17%
50. Mar 31, 2024 $284.32 3.83% 5,254.35 3.10%
51. Apr 30, 2024 $273.94 -3.65% 5,035.69 -4.16%
52. May 31, 2024 $305.85 $2.25 12.47% 5,277.51 4.80%
53. Jun 30, 2024 $312.45 2.16% 5,460.48 3.47%
54. Jul 31, 2024 $332.47 6.41% 5,522.30 1.13%
55. Aug 31, 2024 $333.83 $2.25 1.09% 5,648.40 2.28%
56. Sep 30, 2024 $322.21 -3.48% 5,762.48 2.02%
57. Oct 31, 2024 $320.16 -0.64% 5,705.45 -0.99%
58. Nov 30, 2024 $282.87 $2.25 -10.94% 6,032.38 5.73%
59. Dec 31, 2024 $260.64 -7.86% 5,881.63 -2.50%
Average (R): 0.83% 1.16%
Standard deviation: 7.07% 5.28%

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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 AMGN during period t

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


Variance and Covariance

Amgen Inc., calculation of variance and covariance of returns

Microsoft Excel
t Date RAMGN,t RS&P 500,t (RAMGN,tRAMGN)2 (RS&P 500,tRS&P 500)2 (RAMGN,tRAMGN)×(RS&P 500,tRS&P 500)
1. Feb 29, 2020 -6.81% -8.41% 58.35 91.63 73.12
2. Mar 31, 2020 1.50% -12.51% 0.46 186.96 -9.25
3. Apr 30, 2020 18.00% 12.68% 294.95 132.78 197.90
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2024 -10.94% 5.73% 138.53 20.87 -53.77
59. Dec 31, 2024 -7.86% -2.50% 75.41 13.40 31.79
Total (Σ): 2,899.31 1,618.62 912.04
t Date RAMGN,t RS&P 500,t (RAMGN,tRAMGN)2 (RS&P 500,tRS&P 500)2 (RAMGN,tRAMGN)×(RS&P 500,tRS&P 500)
1. Feb 29, 2020 -6.81% -8.41% 58.35 91.63 73.12
2. Mar 31, 2020 1.50% -12.51% 0.46 186.96 -9.25
3. Apr 30, 2020 18.00% 12.68% 294.95 132.78 197.90
4. May 31, 2020 -3.31% 4.53% 17.11 11.34 -13.93
5. Jun 30, 2020 2.68% 1.84% 3.45 0.46 1.26
6. Jul 31, 2020 3.74% 5.51% 8.47 18.91 12.66
7. Aug 31, 2020 4.19% 7.01% 11.32 34.17 19.66
8. Sep 30, 2020 0.33% -3.92% 0.24 25.85 2.51
9. Oct 31, 2020 -14.64% -2.77% 239.31 15.43 60.76
10. Nov 30, 2020 3.09% 10.75% 5.12 92.03 21.71
11. Dec 31, 2020 3.55% 3.71% 7.42 6.51 6.95
12. Jan 31, 2021 5.01% -1.11% 17.48 5.18 -9.51
13. Feb 28, 2021 -6.11% 2.61% 48.09 2.10 -10.04
14. Mar 31, 2021 10.62% 4.24% 95.97 9.50 30.20
15. Apr 30, 2021 -3.69% 5.24% 20.35 16.66 -18.41
16. May 31, 2021 0.03% 0.55% 0.64 0.38 0.49
17. Jun 30, 2021 2.44% 2.22% 2.61 1.12 1.71
18. Jul 31, 2021 -0.91% 2.27% 3.00 1.24 -1.93
19. Aug 31, 2021 -5.90% 2.90% 45.22 3.02 -11.69
20. Sep 30, 2021 -5.71% -4.76% 42.72 35.02 38.68
21. Oct 31, 2021 -2.67% 6.91% 12.22 33.10 -20.11
22. Nov 30, 2021 -3.06% -0.83% 15.08 3.98 7.75
23. Dec 31, 2021 13.12% 4.36% 151.12 10.24 39.34
24. Jan 31, 2022 0.96% -5.26% 0.02 41.21 -0.89
25. Feb 28, 2022 0.56% -3.14% 0.07 18.47 1.12
26. Mar 31, 2022 6.77% 3.58% 35.38 5.84 14.37
27. Apr 30, 2022 -3.57% -8.80% 19.31 99.14 43.75
28. May 31, 2022 10.93% 0.01% 102.13 1.34 -11.68
29. Jun 30, 2022 -5.23% -8.39% 36.72 91.26 57.89
30. Jul 31, 2022 1.71% 9.11% 0.79 63.21 7.07
31. Aug 31, 2022 -2.11% -4.24% 8.64 29.22 15.88
32. Sep 30, 2022 -6.20% -9.34% 49.36 110.27 73.78
33. Oct 31, 2022 19.94% 7.99% 365.46 46.58 130.48
34. Nov 30, 2022 6.65% 5.38% 33.98 17.76 24.56
35. Dec 31, 2022 -8.30% -5.90% 83.20 49.82 64.38
36. Jan 31, 2023 -3.90% 6.18% 22.32 25.14 -23.69
37. Feb 28, 2023 -7.37% -2.61% 67.21 14.23 30.93
38. Mar 31, 2023 4.36% 3.51% 12.46 5.49 8.27
39. Apr 30, 2023 -0.83% 1.46% 2.74 0.09 -0.50
40. May 31, 2023 -7.07% 0.25% 62.40 0.83 7.21
41. Jun 30, 2023 0.62% 4.71% 0.04 12.62 -0.73
42. Jul 31, 2023 5.46% 4.85% 21.51 13.58 17.09
43. Aug 31, 2023 10.39% -1.77% 91.42 8.60 -28.04
44. Sep 30, 2023 4.85% -4.87% 16.16 36.40 -24.25
45. Oct 31, 2023 -4.86% -2.20% 32.31 11.28 19.10
46. Nov 30, 2023 6.28% 8.92% 29.81 60.17 42.35
47. Dec 31, 2023 6.82% 4.42% 35.90 10.64 19.54
48. Jan 31, 2024 9.11% 1.59% 68.65 0.18 3.55
49. Feb 29, 2024 -12.15% 5.17% 168.33 16.09 -52.04
50. Mar 31, 2024 3.83% 3.10% 9.03 3.77 5.83
51. Apr 30, 2024 -3.65% -4.16% 20.03 28.33 23.82
52. May 31, 2024 12.47% 4.80% 135.60 13.26 42.40
53. Jun 30, 2024 2.16% 3.47% 1.78 5.32 3.07
54. Jul 31, 2024 6.41% 1.13% 31.16 0.00 -0.16
55. Aug 31, 2024 1.09% 2.28% 0.07 1.26 0.29
56. Sep 30, 2024 -3.48% 2.02% 18.54 0.74 -3.70
57. Oct 31, 2024 -0.64% -0.99% 2.14 4.63 3.14
58. Nov 30, 2024 -10.94% 5.73% 138.53 20.87 -53.77
59. Dec 31, 2024 -7.86% -2.50% 75.41 13.40 31.79
Total (Σ): 2,899.31 1,618.62 912.04

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VarianceAMGN = Σ(RAMGN,tRAMGN)2 ÷ (59 – 1)
= 2,899.31 ÷ (59 – 1)
= 49.99

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

CovarianceAMGN, S&P 500 = Σ(RAMGN,tRAMGN)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 912.04 ÷ (59 – 1)
= 15.72


Systematic Risk (β) Estimation

Microsoft Excel
VarianceAMGN 49.99
VarianceS&P 500 27.91
CovarianceAMGN, S&P 500 15.72
Correlation coefficientAMGN, S&P 5001 0.42
βAMGN2 0.56
αAMGN3 0.17%

Calculations

1 Correlation coefficientAMGN, S&P 500
= CovarianceAMGN, S&P 500 ÷ (Standard deviationAMGN × Standard deviationS&P 500)
= 15.72 ÷ (7.07% × 5.28%)
= 0.42

2 βAMGN
= CovarianceAMGN, S&P 500 ÷ VarianceS&P 500
= 15.72 ÷ 27.91
= 0.56

3 αAMGN
= AverageAMGN – βAMGN × AverageS&P 500
= 0.83%0.56 × 1.16%
= 0.17%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.94%
Expected rate of return on market portfolio2 E(RM) 15.05%
Systematic risk (β) of Amgen Inc. common stock βAMGN 0.56
 
Expected rate of return on Amgen Inc. common stock3 E(RAMGN) 10.63%

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(RAMGN) = RF + βAMGN [E(RM) – RF]
= 4.94% + 0.56 [15.05%4.94%]
= 10.63%