Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Amgen Inc. common stock.
Rates of Return
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% | |
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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 | $260.64 | -7.86% | 5,881.63 | -2.50% | |
Average (R): | 0.83% | 1.16% | ||||
Standard deviation: | 7.07% | 5.28% |
Show all
1 Data in US$ 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
t | Date | RAMGN,t | RS&P 500,t | (RAMGN,t–RAMGN)2 | (RS&P 500,t–RS&P 500)2 | (RAMGN,t–RAMGN)×(RS&P 500,t–RS&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 |
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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,t–RAMGN)2 | (RS&P 500,t–RS&P 500)2 | (RAMGN,t–RAMGN)×(RS&P 500,t–RS&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 |
Show all
VarianceAMGN = Σ(RAMGN,t–RAMGN)2 ÷ (59 – 1)
= 2,899.31 ÷ (59 – 1)
= 49.99
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
CovarianceAMGN, S&P 500 = Σ(RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 912.04 ÷ (59 – 1)
= 15.72
Systematic Risk (β) Estimation
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
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).
3 E(RAMGN) = RF + βAMGN [E(RM) – RF]
= 4.94% + 0.56 [15.05% – 4.94%]
= 10.63%