Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Amazon.com Inc. common stock.
Rates of Return
Amazon.com Inc. (AMZN) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAMZN,t1 | DividendAMZN,t1 | RAMZN,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2018 | $72.54 | 2,823.81 | ||||
1. | Feb 28, 2018 | $75.62 | 4.25% | 2,713.83 | -3.89% | |
2. | Mar 31, 2018 | $72.37 | -4.30% | 2,640.87 | -2.69% | |
3. | Apr 30, 2018 | $78.31 | 8.21% | 2,648.05 | 0.27% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
58. | Nov 30, 2022 | $96.54 | -5.76% | 4,080.11 | 5.38% | |
59. | Dec 31, 2022 | $84.00 | -12.99% | 3,839.50 | -5.90% | |
Average (R): | 0.69% | 0.67% | ||||
Standard deviation: | 9.49% | 5.40% |
Amazon.com Inc. (AMZN) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAMZN,t1 | DividendAMZN,t1 | RAMZN,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2018 | $72.54 | 2,823.81 | ||||
1. | Feb 28, 2018 | $75.62 | 4.25% | 2,713.83 | -3.89% | |
2. | Mar 31, 2018 | $72.37 | -4.30% | 2,640.87 | -2.69% | |
3. | Apr 30, 2018 | $78.31 | 8.21% | 2,648.05 | 0.27% | |
4. | May 31, 2018 | $81.48 | 4.05% | 2,705.27 | 2.16% | |
5. | Jun 30, 2018 | $84.99 | 4.31% | 2,718.37 | 0.48% | |
6. | Jul 31, 2018 | $88.87 | 4.57% | 2,816.29 | 3.60% | |
7. | Aug 31, 2018 | $100.64 | 13.24% | 2,901.52 | 3.03% | |
8. | Sep 30, 2018 | $100.15 | -0.49% | 2,913.98 | 0.43% | |
9. | Oct 31, 2018 | $79.90 | -20.22% | 2,711.74 | -6.94% | |
10. | Nov 30, 2018 | $84.51 | 5.77% | 2,760.17 | 1.79% | |
11. | Dec 31, 2018 | $75.10 | -11.13% | 2,506.85 | -9.18% | |
12. | Jan 31, 2019 | $85.94 | 14.43% | 2,704.10 | 7.87% | |
13. | Feb 28, 2019 | $81.99 | -4.60% | 2,784.49 | 2.97% | |
14. | Mar 31, 2019 | $89.04 | 8.60% | 2,834.40 | 1.79% | |
15. | Apr 30, 2019 | $96.33 | 8.19% | 2,945.83 | 3.93% | |
16. | May 31, 2019 | $88.75 | -7.87% | 2,752.06 | -6.58% | |
17. | Jun 30, 2019 | $94.68 | 6.68% | 2,941.76 | 6.89% | |
18. | Jul 31, 2019 | $93.34 | -1.42% | 2,980.38 | 1.31% | |
19. | Aug 31, 2019 | $88.81 | -4.85% | 2,926.46 | -1.81% | |
20. | Sep 30, 2019 | $86.80 | -2.26% | 2,976.74 | 1.72% | |
21. | Oct 31, 2019 | $88.83 | 2.34% | 3,037.56 | 2.04% | |
22. | Nov 30, 2019 | $90.04 | 1.36% | 3,140.98 | 3.40% | |
23. | Dec 31, 2019 | $92.39 | 2.61% | 3,230.78 | 2.86% | |
24. | Jan 31, 2020 | $100.44 | 8.71% | 3,225.52 | -0.16% | |
25. | Feb 29, 2020 | $94.19 | -6.22% | 2,954.22 | -8.41% | |
26. | Mar 31, 2020 | $97.49 | 3.50% | 2,584.59 | -12.51% | |
27. | Apr 30, 2020 | $123.70 | 26.88% | 2,912.43 | 12.68% | |
28. | May 31, 2020 | $122.12 | -1.28% | 3,044.31 | 4.53% | |
29. | Jun 30, 2020 | $137.94 | 12.95% | 3,100.29 | 1.84% | |
30. | Jul 31, 2020 | $158.23 | 14.71% | 3,271.12 | 5.51% | |
31. | Aug 31, 2020 | $172.55 | 9.05% | 3,500.31 | 7.01% | |
32. | Sep 30, 2020 | $157.44 | -8.76% | 3,363.00 | -3.92% | |
33. | Oct 31, 2020 | $151.81 | -3.58% | 3,269.96 | -2.77% | |
34. | Nov 30, 2020 | $158.40 | 4.34% | 3,621.63 | 10.75% | |
35. | Dec 31, 2020 | $162.85 | 2.81% | 3,756.07 | 3.71% | |
36. | Jan 31, 2021 | $160.31 | -1.56% | 3,714.24 | -1.11% | |
37. | Feb 28, 2021 | $154.65 | -3.53% | 3,811.15 | 2.61% | |
38. | Mar 31, 2021 | $154.70 | 0.03% | 3,972.89 | 4.24% | |
39. | Apr 30, 2021 | $173.37 | 12.07% | 4,181.17 | 5.24% | |
40. | May 31, 2021 | $161.15 | -7.05% | 4,204.11 | 0.55% | |
41. | Jun 30, 2021 | $172.01 | 6.74% | 4,297.50 | 2.22% | |
42. | Jul 31, 2021 | $166.38 | -3.27% | 4,395.26 | 2.27% | |
43. | Aug 31, 2021 | $173.54 | 4.30% | 4,522.68 | 2.90% | |
44. | Sep 30, 2021 | $164.25 | -5.35% | 4,307.54 | -4.76% | |
45. | Oct 31, 2021 | $168.62 | 2.66% | 4,605.38 | 6.91% | |
46. | Nov 30, 2021 | $175.35 | 3.99% | 4,567.00 | -0.83% | |
47. | Dec 31, 2021 | $166.72 | -4.92% | 4,766.18 | 4.36% | |
48. | Jan 31, 2022 | $149.57 | -10.29% | 4,515.55 | -5.26% | |
49. | Feb 28, 2022 | $153.56 | 2.67% | 4,373.94 | -3.14% | |
50. | Mar 31, 2022 | $163.00 | 6.15% | 4,530.41 | 3.58% | |
51. | Apr 30, 2022 | $124.28 | -23.75% | 4,131.93 | -8.80% | |
52. | May 31, 2022 | $120.21 | -3.27% | 4,132.15 | 0.01% | |
53. | Jun 30, 2022 | $106.21 | -11.65% | 3,785.38 | -8.39% | |
54. | Jul 31, 2022 | $134.95 | 27.06% | 4,130.29 | 9.11% | |
55. | Aug 31, 2022 | $126.77 | -6.06% | 3,955.00 | -4.24% | |
56. | Sep 30, 2022 | $113.00 | -10.86% | 3,585.62 | -9.34% | |
57. | Oct 31, 2022 | $102.44 | -9.35% | 3,871.98 | 7.99% | |
58. | Nov 30, 2022 | $96.54 | -5.76% | 4,080.11 | 5.38% | |
59. | Dec 31, 2022 | $84.00 | -12.99% | 3,839.50 | -5.90% | |
Average (R): | 0.69% | 0.67% | ||||
Standard deviation: | 9.49% | 5.40% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of AMZN during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RAMZN,t | RS&P 500,t | (RAMZN,t–RAMZN)2 | (RS&P 500,t–RS&P 500)2 | (RAMZN,t–RAMZN)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2018 | 4.25% | -3.89% | 12.66 | 20.81 | -16.23 |
2. | Mar 31, 2018 | -4.30% | -2.69% | 24.86 | 11.26 | 16.73 |
3. | Apr 30, 2018 | 8.21% | 0.27% | 56.55 | 0.16 | -2.97 |
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58. | Nov 30, 2022 | -5.76% | 5.38% | 41.57 | 22.17 | -30.36 |
59. | Dec 31, 2022 | -12.99% | -5.90% | 187.08 | 43.08 | 89.78 |
Total (Σ): | 5,227.22 | 1,691.48 | 1,977.60 |
t | Date | RAMZN,t | RS&P 500,t | (RAMZN,t–RAMZN)2 | (RS&P 500,t–RS&P 500)2 | (RAMZN,t–RAMZN)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2018 | 4.25% | -3.89% | 12.66 | 20.81 | -16.23 |
2. | Mar 31, 2018 | -4.30% | -2.69% | 24.86 | 11.26 | 16.73 |
3. | Apr 30, 2018 | 8.21% | 0.27% | 56.55 | 0.16 | -2.97 |
4. | May 31, 2018 | 4.05% | 2.16% | 11.29 | 2.23 | 5.02 |
5. | Jun 30, 2018 | 4.31% | 0.48% | 13.10 | 0.03 | -0.66 |
6. | Jul 31, 2018 | 4.57% | 3.60% | 15.03 | 8.62 | 11.38 |
7. | Aug 31, 2018 | 13.24% | 3.03% | 157.65 | 5.57 | 29.63 |
8. | Sep 30, 2018 | -0.49% | 0.43% | 1.38 | 0.06 | 0.28 |
9. | Oct 31, 2018 | -20.22% | -6.94% | 437.14 | 57.87 | 159.05 |
10. | Nov 30, 2018 | 5.77% | 1.79% | 25.82 | 1.25 | 5.69 |
11. | Dec 31, 2018 | -11.13% | -9.18% | 139.78 | 96.91 | 116.39 |
12. | Jan 31, 2019 | 14.43% | 7.87% | 188.95 | 51.87 | 99.00 |
13. | Feb 28, 2019 | -4.60% | 2.97% | 27.92 | 5.32 | -12.19 |
14. | Mar 31, 2019 | 8.60% | 1.79% | 62.58 | 1.27 | 8.91 |
15. | Apr 30, 2019 | 8.19% | 3.93% | 56.24 | 10.66 | 24.48 |
16. | May 31, 2019 | -7.87% | -6.58% | 73.22 | 52.48 | 61.99 |
17. | Jun 30, 2019 | 6.68% | 6.89% | 35.92 | 38.77 | 37.32 |
18. | Jul 31, 2019 | -1.42% | 1.31% | 4.42 | 0.42 | -1.36 |
19. | Aug 31, 2019 | -4.85% | -1.81% | 30.71 | 6.13 | 13.72 |
20. | Sep 30, 2019 | -2.26% | 1.72% | 8.71 | 1.11 | -3.10 |
21. | Oct 31, 2019 | 2.34% | 2.04% | 2.72 | 1.89 | 2.27 |
22. | Nov 30, 2019 | 1.36% | 3.40% | 0.45 | 7.50 | 1.85 |
23. | Dec 31, 2019 | 2.61% | 2.86% | 3.69 | 4.81 | 4.21 |
24. | Jan 31, 2020 | 8.71% | -0.16% | 64.40 | 0.69 | -6.66 |
25. | Feb 29, 2020 | -6.22% | -8.41% | 47.76 | 82.40 | 62.73 |
26. | Mar 31, 2020 | 3.50% | -12.51% | 7.93 | 173.67 | -37.10 |
27. | Apr 30, 2020 | 26.88% | 12.68% | 686.26 | 144.43 | 314.83 |
28. | May 31, 2020 | -1.28% | 4.53% | 3.86 | 14.91 | -7.59 |
29. | Jun 30, 2020 | 12.95% | 1.84% | 150.46 | 1.37 | 14.38 |
30. | Jul 31, 2020 | 14.71% | 5.51% | 196.59 | 23.46 | 67.91 |
31. | Aug 31, 2020 | 9.05% | 7.01% | 69.92 | 40.19 | 53.01 |
32. | Sep 30, 2020 | -8.76% | -3.92% | 89.21 | 21.06 | 43.35 |
33. | Oct 31, 2020 | -3.58% | -2.77% | 18.18 | 11.79 | 14.64 |
34. | Nov 30, 2020 | 4.34% | 10.75% | 13.34 | 101.77 | 36.85 |
35. | Dec 31, 2020 | 2.81% | 3.71% | 4.50 | 9.28 | 6.46 |
36. | Jan 31, 2021 | -1.56% | -1.11% | 5.05 | 3.17 | 4.00 |
37. | Feb 28, 2021 | -3.53% | 2.61% | 17.80 | 3.77 | -8.20 |
38. | Mar 31, 2021 | 0.03% | 4.24% | 0.43 | 12.80 | -2.35 |
39. | Apr 30, 2021 | 12.07% | 5.24% | 129.51 | 20.94 | 52.08 |
40. | May 31, 2021 | -7.05% | 0.55% | 59.86 | 0.01 | 0.91 |
41. | Jun 30, 2021 | 6.74% | 2.22% | 36.61 | 2.42 | 9.41 |
42. | Jul 31, 2021 | -3.27% | 2.27% | 15.69 | 2.59 | -6.37 |
43. | Aug 31, 2021 | 4.30% | 2.90% | 13.07 | 4.98 | 8.07 |
44. | Sep 30, 2021 | -5.35% | -4.76% | 36.50 | 29.42 | 32.77 |
45. | Oct 31, 2021 | 2.66% | 6.91% | 3.89 | 39.03 | 12.32 |
46. | Nov 30, 2021 | 3.99% | -0.83% | 10.91 | 2.25 | -4.95 |
47. | Dec 31, 2021 | -4.92% | 4.36% | 31.47 | 13.65 | -20.73 |
48. | Jan 31, 2022 | -10.29% | -5.26% | 120.45 | 35.11 | 65.03 |
49. | Feb 28, 2022 | 2.67% | -3.14% | 3.92 | 14.46 | -7.53 |
50. | Mar 31, 2022 | 6.15% | 3.58% | 29.80 | 8.47 | 15.89 |
51. | Apr 30, 2022 | -23.75% | -8.80% | 597.45 | 89.54 | 231.29 |
52. | May 31, 2022 | -3.27% | 0.01% | 15.71 | 0.44 | 2.62 |
53. | Jun 30, 2022 | -11.65% | -8.39% | 152.14 | 82.06 | 111.73 |
54. | Jul 31, 2022 | 27.06% | 9.11% | 695.45 | 71.32 | 222.71 |
55. | Aug 31, 2022 | -6.06% | -4.24% | 45.56 | 24.11 | 33.15 |
56. | Sep 30, 2022 | -10.86% | -9.34% | 133.41 | 100.12 | 115.58 |
57. | Oct 31, 2022 | -9.35% | 7.99% | 100.67 | 53.58 | -73.44 |
58. | Nov 30, 2022 | -5.76% | 5.38% | 41.57 | 22.17 | -30.36 |
59. | Dec 31, 2022 | -12.99% | -5.90% | 187.08 | 43.08 | 89.78 |
Total (Σ): | 5,227.22 | 1,691.48 | 1,977.60 |
Show all
VarianceAMZN = Σ(RAMZN,t–RAMZN)2 ÷ (59 – 1)
= 5,227.22 ÷ (59 – 1)
= 90.12
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianceAMZN, S&P 500 = Σ(RAMZN,t–RAMZN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,977.60 ÷ (59 – 1)
= 34.10
Systematic Risk (β) Estimation
VarianceAMZN | 90.12 |
VarianceS&P 500 | 29.16 |
CovarianceAMZN, S&P 500 | 34.10 |
Correlation coefficientAMZN, S&P 5001 | 0.67 |
βAMZN2 | 1.17 |
αAMZN3 | -0.09% |
Calculations
1 Correlation coefficientAMZN, S&P 500
= CovarianceAMZN, S&P 500 ÷ (Standard deviationAMZN × Standard deviationS&P 500)
= 34.10 ÷ (9.49% × 5.40%)
= 0.67
2 βAMZN
= CovarianceAMZN, S&P 500 ÷ VarianceS&P 500
= 34.10 ÷ 29.16
= 1.17
3 αAMZN
= AverageAMZN – βAMZN × AverageS&P 500
= 0.69% – 1.17 × 0.67%
= -0.09%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.46% |
Expected rate of return on market portfolio2 | E(RM) | 13.29% |
Systematic risk (β) of Amazon.com Inc. common stock | βAMZN | 1.17 |
Expected rate of return on Amazon.com Inc. common stock3 | E(RAMZN) | 14.78% |
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(RAMZN) = RF + βAMZN [E(RM) – RF]
= 4.46% + 1.17 [13.29% – 4.46%]
= 14.78%