Capital Asset Pricing Model (CAPM)

Difficulty: Intermediate


Rates of Return

Amazon.com Inc., monthly 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, 2013 265.50 1,498.11
1. Feb 28, 2013 264.27 -0.46% 1,514.68 1.11%
2. Mar 31, 2013 266.49 0.84% 1,569.19 3.60%
3. Apr 30, 2013 253.81 -4.76% 1,597.57 1.81%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2017 1,176.75 6.47% 2,647.58 2.81%
59. Dec 31, 2017 1,169.47 -0.62% 2,673.61 0.98%
Average: 2.83% 1.02%
Standard Deviation: 7.72% 2.71%
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, 2013 265.50 1,498.11
1. Feb 28, 2013 264.27 -0.46% 1,514.68 1.11%
2. Mar 31, 2013 266.49 0.84% 1,569.19 3.60%
3. Apr 30, 2013 253.81 -4.76% 1,597.57 1.81%
4. May 31, 2013 269.20 6.06% 1,630.74 2.08%
5. Jun 30, 2013 277.69 3.15% 1,606.28 -1.50%
6. Jul 31, 2013 301.22 8.47% 1,685.73 4.95%
7. Aug 31, 2013 280.98 -6.72% 1,632.97 -3.13%
8. Sep 30, 2013 312.64 11.27% 1,681.55 2.97%
9. Oct 31, 2013 364.03 16.44% 1,756.54 4.46%
10. Nov 30, 2013 393.62 8.13% 1,805.81 2.80%
11. Dec 31, 2013 398.79 1.31% 1,848.36 2.36%
12. Jan 31, 2014 358.69 -10.06% 1,782.59 -3.56%
13. Feb 28, 2014 362.10 0.95% 1,859.45 4.31%
14. Mar 31, 2014 336.37 -7.11% 1,872.34 0.69%
15. Apr 30, 2014 304.13 -9.58% 1,883.95 0.62%
16. May 31, 2014 312.55 2.77% 1,923.57 2.10%
17. Jun 30, 2014 324.78 3.91% 1,960.23 1.91%
18. Jul 31, 2014 312.99 -3.63% 1,930.67 -1.51%
19. Aug 31, 2014 339.04 8.32% 2,003.37 3.77%
20. Sep 30, 2014 322.44 -4.90% 1,972.29 -1.55%
21. Oct 31, 2014 305.46 -5.27% 2,018.05 2.32%
22. Nov 30, 2014 338.64 10.86% 2,067.56 2.45%
23. Dec 31, 2014 310.35 -8.35% 2,058.90 -0.42%
24. Jan 31, 2015 354.53 14.24% 1,994.99 -3.10%
25. Feb 28, 2015 380.16 7.23% 2,104.50 5.49%
26. Mar 31, 2015 372.10 -2.12% 2,067.89 -1.74%
27. Apr 30, 2015 421.78 13.35% 2,085.51 0.85%
28. May 31, 2015 429.23 1.77% 2,107.39 1.05%
29. Jun 30, 2015 434.09 1.13% 2,063.11 -2.10%
30. Jul 31, 2015 536.15 23.51% 2,103.84 1.97%
31. Aug 31, 2015 512.89 -4.34% 1,972.18 -6.26%
32. Sep 30, 2015 511.89 -0.19% 1,920.03 -2.64%
33. Oct 31, 2015 625.90 22.27% 2,079.36 8.30%
34. Nov 30, 2015 664.80 6.22% 2,080.41 0.05%
35. Dec 31, 2015 675.89 1.67% 2,043.94 -1.75%
36. Jan 31, 2016 587.00 -13.15% 1,940.24 -5.07%
37. Feb 29, 2016 552.52 -5.87% 1,932.23 -0.41%
38. Mar 31, 2016 593.64 7.44% 2,059.74 6.60%
39. Apr 30, 2016 659.59 11.11% 2,065.30 0.27%
40. May 31, 2016 722.79 9.58% 2,096.95 1.53%
41. Jun 30, 2016 715.62 -0.99% 2,098.86 0.09%
42. Jul 31, 2016 758.81 6.04% 2,173.60 3.56%
43. Aug 31, 2016 769.16 1.36% 2,170.95 -0.12%
44. Sep 30, 2016 837.31 8.86% 2,168.27 -0.12%
45. Oct 31, 2016 789.82 -5.67% 2,126.15 -1.94%
46. Nov 30, 2016 750.57 -4.97% 2,198.81 3.42%
47. Dec 31, 2016 749.87 -0.09% 2,238.83 1.82%
48. Jan 31, 2017 823.48 9.82% 2,278.87 1.79%
49. Feb 28, 2017 845.04 2.62% 2,363.64 3.72%
50. Mar 31, 2017 886.54 4.91% 2,362.72 -0.04%
51. Apr 30, 2017 924.99 4.34% 2,384.20 0.91%
52. May 31, 2017 994.62 7.53% 2,411.80 1.16%
53. Jun 30, 2017 968.00 -2.68% 2,423.41 0.48%
54. Jul 31, 2017 987.78 2.04% 2,470.30 1.93%
55. Aug 31, 2017 980.60 -0.73% 2,471.65 0.05%
56. Sep 30, 2017 961.35 -1.96% 2,519.36 1.93%
57. Oct 31, 2017 1,105.28 14.97% 2,575.26 2.22%
58. Nov 30, 2017 1,176.75 6.47% 2,647.58 2.81%
59. Dec 31, 2017 1,169.47 -0.62% 2,673.61 0.98%
Average: 2.83% 1.02%
Standard Deviation: 7.72% 2.71%

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1 Data in USD $ 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

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Systematic Risk (β) Estimation

 
VarianceAMZN 59.64
VarianceS&P 500 7.32
CovarianceAMZN, S&P 500 10.99
Correlation CoefficientAMZN, S&P 5001 0.53
βAMZN2 1.50
αAMZN3 1.29

Calculations

1 CovarianceAMZN, S&P 500 ÷ (Standard DeviationAMZN × Standard DeviationS&P 500)
= 10.99 ÷ (7.72 × 2.71)

2 CovarianceAMZN, S&P 500 ÷ VarianceS&P 500
= 10.99 ÷ 7.32

3 AverageAMZN – βAMZN × AverageS&P 500
= 2.83 – 1.50 × 1.02

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Expected Rate of Return

 
Assumptions
Rate of return on LT Treasury Composite1 RF 3.00%
Expected rate of return on market portfolio2 E(RM) 12.42%
Systematic risk (β) of Amazon.com's common stock βAMZN 1.50
Expected rate of return on Amazon.com's common stock3 E(RAMZN) 17.14%

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).

Calculations

2 See Details »

3 E(RAMZN) = RF + βAMZN [E(RM) – RF]
= 3.00% + 1.50 [12.42% – 3.00%]
= 17.14%

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