Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Microsoft Corp. common stock.
Rates of Return
Microsoft Corp. (MSFT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceMSFT,t1 | DividendMSFT,t1 | RMSFT,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2017 | $72.70 | 2,470.30 | ||||
1. | Aug 31, 2017 | $74.77 | $0.39 | 3.38% | 2,471.65 | 0.05% |
2. | Sep 30, 2017 | $74.49 | -0.37% | 2,519.36 | 1.93% | |
3. | Oct 31, 2017 | $83.18 | 11.67% | 2,575.26 | 2.22% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | May 31, 2023 | $328.39 | $0.68 | 7.10% | 4,179.83 | 0.25% |
71. | Jun 30, 2023 | $340.54 | 3.70% | 4,376.86 | 4.71% | |
Average (R): | 2.49% | 0.94% | ||||
Standard deviation: | 6.15% | 5.05% |
Microsoft Corp. (MSFT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceMSFT,t1 | DividendMSFT,t1 | RMSFT,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2017 | $72.70 | 2,470.30 | ||||
1. | Aug 31, 2017 | $74.77 | $0.39 | 3.38% | 2,471.65 | 0.05% |
2. | Sep 30, 2017 | $74.49 | -0.37% | 2,519.36 | 1.93% | |
3. | Oct 31, 2017 | $83.18 | 11.67% | 2,575.26 | 2.22% | |
4. | Nov 30, 2017 | $84.17 | $0.42 | 1.70% | 2,647.58 | 2.81% |
5. | Dec 31, 2017 | $85.54 | 1.63% | 2,673.61 | 0.98% | |
6. | Jan 31, 2018 | $95.01 | 11.07% | 2,823.81 | 5.62% | |
7. | Feb 28, 2018 | $93.77 | $0.42 | -0.86% | 2,713.83 | -3.89% |
8. | Mar 31, 2018 | $91.27 | -2.67% | 2,640.87 | -2.69% | |
9. | Apr 30, 2018 | $93.52 | 2.47% | 2,648.05 | 0.27% | |
10. | May 31, 2018 | $98.84 | $0.42 | 6.14% | 2,705.27 | 2.16% |
11. | Jun 30, 2018 | $98.61 | -0.23% | 2,718.37 | 0.48% | |
12. | Jul 31, 2018 | $106.08 | 7.58% | 2,816.29 | 3.60% | |
13. | Aug 31, 2018 | $112.33 | $0.42 | 6.29% | 2,901.52 | 3.03% |
14. | Sep 30, 2018 | $114.37 | 1.82% | 2,913.98 | 0.43% | |
15. | Oct 31, 2018 | $106.81 | -6.61% | 2,711.74 | -6.94% | |
16. | Nov 30, 2018 | $110.89 | $0.46 | 4.25% | 2,760.17 | 1.79% |
17. | Dec 31, 2018 | $101.57 | -8.40% | 2,506.85 | -9.18% | |
18. | Jan 31, 2019 | $104.43 | 2.82% | 2,704.10 | 7.87% | |
19. | Feb 28, 2019 | $112.03 | $0.46 | 7.72% | 2,784.49 | 2.97% |
20. | Mar 31, 2019 | $117.94 | 5.28% | 2,834.40 | 1.79% | |
21. | Apr 30, 2019 | $130.60 | 10.73% | 2,945.83 | 3.93% | |
22. | May 31, 2019 | $123.68 | $0.46 | -4.95% | 2,752.06 | -6.58% |
23. | Jun 30, 2019 | $133.96 | 8.31% | 2,941.76 | 6.89% | |
24. | Jul 31, 2019 | $136.27 | 1.72% | 2,980.38 | 1.31% | |
25. | Aug 31, 2019 | $137.86 | $0.46 | 1.50% | 2,926.46 | -1.81% |
26. | Sep 30, 2019 | $139.03 | 0.85% | 2,976.74 | 1.72% | |
27. | Oct 31, 2019 | $143.37 | 3.12% | 3,037.56 | 2.04% | |
28. | Nov 30, 2019 | $151.38 | $0.51 | 5.94% | 3,140.98 | 3.40% |
29. | Dec 31, 2019 | $157.70 | 4.17% | 3,230.78 | 2.86% | |
30. | Jan 31, 2020 | $170.23 | 7.95% | 3,225.52 | -0.16% | |
31. | Feb 29, 2020 | $162.01 | $0.51 | -4.53% | 2,954.22 | -8.41% |
32. | Mar 31, 2020 | $157.71 | -2.65% | 2,584.59 | -12.51% | |
33. | Apr 30, 2020 | $179.21 | 13.63% | 2,912.43 | 12.68% | |
34. | May 31, 2020 | $183.25 | $0.51 | 2.54% | 3,044.31 | 4.53% |
35. | Jun 30, 2020 | $203.51 | 11.06% | 3,100.29 | 1.84% | |
36. | Jul 31, 2020 | $205.01 | 0.74% | 3,271.12 | 5.51% | |
37. | Aug 31, 2020 | $225.53 | $0.51 | 10.26% | 3,500.31 | 7.01% |
38. | Sep 30, 2020 | $210.33 | -6.74% | 3,363.00 | -3.92% | |
39. | Oct 31, 2020 | $202.47 | -3.74% | 3,269.96 | -2.77% | |
40. | Nov 30, 2020 | $214.07 | $0.56 | 6.01% | 3,621.63 | 10.75% |
41. | Dec 31, 2020 | $222.42 | 3.90% | 3,756.07 | 3.71% | |
42. | Jan 31, 2021 | $231.96 | 4.29% | 3,714.24 | -1.11% | |
43. | Feb 28, 2021 | $232.38 | $0.56 | 0.42% | 3,811.15 | 2.61% |
44. | Mar 31, 2021 | $235.77 | 1.46% | 3,972.89 | 4.24% | |
45. | Apr 30, 2021 | $252.18 | 6.96% | 4,181.17 | 5.24% | |
46. | May 31, 2021 | $249.68 | $0.56 | -0.77% | 4,204.11 | 0.55% |
47. | Jun 30, 2021 | $270.90 | 8.50% | 4,297.50 | 2.22% | |
48. | Jul 31, 2021 | $284.91 | 5.17% | 4,395.26 | 2.27% | |
49. | Aug 31, 2021 | $301.88 | $0.56 | 6.15% | 4,522.68 | 2.90% |
50. | Sep 30, 2021 | $281.92 | -6.61% | 4,307.54 | -4.76% | |
51. | Oct 31, 2021 | $331.62 | 17.63% | 4,605.38 | 6.91% | |
52. | Nov 30, 2021 | $330.59 | $0.62 | -0.12% | 4,567.00 | -0.83% |
53. | Dec 31, 2021 | $336.32 | 1.73% | 4,766.18 | 4.36% | |
54. | Jan 31, 2022 | $310.98 | -7.53% | 4,515.55 | -5.26% | |
55. | Feb 28, 2022 | $298.79 | $0.62 | -3.72% | 4,373.94 | -3.14% |
56. | Mar 31, 2022 | $308.31 | 3.19% | 4,530.41 | 3.58% | |
57. | Apr 30, 2022 | $277.52 | -9.99% | 4,131.93 | -8.80% | |
58. | May 31, 2022 | $271.87 | $0.62 | -1.81% | 4,132.15 | 0.01% |
59. | Jun 30, 2022 | $256.83 | -5.53% | 3,785.38 | -8.39% | |
60. | Jul 31, 2022 | $280.74 | 9.31% | 4,130.29 | 9.11% | |
61. | Aug 31, 2022 | $261.47 | $0.62 | -6.64% | 3,955.00 | -4.24% |
62. | Sep 30, 2022 | $232.90 | -10.93% | 3,585.62 | -9.34% | |
63. | Oct 31, 2022 | $232.13 | -0.33% | 3,871.98 | 7.99% | |
64. | Nov 30, 2022 | $255.14 | $0.68 | 10.21% | 4,080.11 | 5.38% |
65. | Dec 31, 2022 | $239.82 | -6.00% | 3,839.50 | -5.90% | |
66. | Jan 31, 2023 | $247.81 | 3.33% | 4,076.60 | 6.18% | |
67. | Feb 28, 2023 | $249.42 | $0.68 | 0.92% | 3,970.15 | -2.61% |
68. | Mar 31, 2023 | $288.30 | 15.59% | 4,109.31 | 3.51% | |
69. | Apr 30, 2023 | $307.26 | 6.58% | 4,169.48 | 1.46% | |
70. | May 31, 2023 | $328.39 | $0.68 | 7.10% | 4,179.83 | 0.25% |
71. | Jun 30, 2023 | $340.54 | 3.70% | 4,376.86 | 4.71% | |
Average (R): | 2.49% | 0.94% | ||||
Standard deviation: | 6.15% | 5.05% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of MSFT during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RMSFT,t | RS&P 500,t | (RMSFT,t–RMSFT)2 | (RS&P 500,t–RS&P 500)2 | (RMSFT,t–RMSFT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2017 | 3.38% | 0.05% | 0.80 | 0.78 | -0.79 |
2. | Sep 30, 2017 | -0.37% | 1.93% | 8.20 | 0.99 | -2.85 |
3. | Oct 31, 2017 | 11.67% | 2.22% | 84.22 | 1.65 | 11.77 |
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. | . | . | . | . | . | . |
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70. | May 31, 2023 | 7.10% | 0.25% | 21.25 | 0.47 | -3.17 |
71. | Jun 30, 2023 | 3.70% | 4.71% | 1.47 | 14.27 | 4.58 |
Total (Σ): | 2,645.73 | 1,786.26 | 1,672.61 |
t | Date | RMSFT,t | RS&P 500,t | (RMSFT,t–RMSFT)2 | (RS&P 500,t–RS&P 500)2 | (RMSFT,t–RMSFT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2017 | 3.38% | 0.05% | 0.80 | 0.78 | -0.79 |
2. | Sep 30, 2017 | -0.37% | 1.93% | 8.20 | 0.99 | -2.85 |
3. | Oct 31, 2017 | 11.67% | 2.22% | 84.22 | 1.65 | 11.77 |
4. | Nov 30, 2017 | 1.70% | 2.81% | 0.63 | 3.51 | -1.49 |
5. | Dec 31, 2017 | 1.63% | 0.98% | 0.74 | 0.00 | -0.04 |
6. | Jan 31, 2018 | 11.07% | 5.62% | 73.65 | 21.92 | 40.18 |
7. | Feb 28, 2018 | -0.86% | -3.89% | 11.24 | 23.33 | 16.19 |
8. | Mar 31, 2018 | -2.67% | -2.69% | 26.57 | 13.14 | 18.68 |
9. | Apr 30, 2018 | 2.47% | 0.27% | 0.00 | 0.44 | 0.02 |
10. | May 31, 2018 | 6.14% | 2.16% | 13.31 | 1.50 | 4.47 |
11. | Jun 30, 2018 | -0.23% | 0.48% | 7.41 | 0.20 | 1.23 |
12. | Jul 31, 2018 | 7.58% | 3.60% | 25.87 | 7.11 | 13.56 |
13. | Aug 31, 2018 | 6.29% | 3.03% | 14.43 | 4.37 | 7.94 |
14. | Sep 30, 2018 | 1.82% | 0.43% | 0.45 | 0.26 | 0.34 |
15. | Oct 31, 2018 | -6.61% | -6.94% | 82.79 | 62.03 | 71.66 |
16. | Nov 30, 2018 | 4.25% | 1.79% | 3.10 | 0.72 | 1.50 |
17. | Dec 31, 2018 | -8.40% | -9.18% | 118.67 | 102.28 | 110.17 |
18. | Jan 31, 2019 | 2.82% | 7.87% | 0.11 | 48.06 | 2.27 |
19. | Feb 28, 2019 | 7.72% | 2.97% | 27.35 | 4.15 | 10.65 |
20. | Mar 31, 2019 | 5.28% | 1.79% | 7.76 | 0.73 | 2.39 |
21. | Apr 30, 2019 | 10.73% | 3.93% | 67.99 | 8.97 | 24.70 |
22. | May 31, 2019 | -4.95% | -6.58% | 55.28 | 56.45 | 55.86 |
23. | Jun 30, 2019 | 8.31% | 6.89% | 33.91 | 35.49 | 34.69 |
24. | Jul 31, 2019 | 1.72% | 1.31% | 0.58 | 0.14 | -0.29 |
25. | Aug 31, 2019 | 1.50% | -1.81% | 0.97 | 7.53 | 2.70 |
26. | Sep 30, 2019 | 0.85% | 1.72% | 2.69 | 0.61 | -1.28 |
27. | Oct 31, 2019 | 3.12% | 2.04% | 0.40 | 1.23 | 0.70 |
28. | Nov 30, 2019 | 5.94% | 3.40% | 11.93 | 6.10 | 8.53 |
29. | Dec 31, 2019 | 4.17% | 2.86% | 2.84 | 3.70 | 3.24 |
30. | Jan 31, 2020 | 7.95% | -0.16% | 29.78 | 1.21 | -5.99 |
31. | Feb 29, 2020 | -4.53% | -8.41% | 49.25 | 87.36 | 65.60 |
32. | Mar 31, 2020 | -2.65% | -12.51% | 26.45 | 180.84 | 69.16 |
33. | Apr 30, 2020 | 13.63% | 12.68% | 124.18 | 138.03 | 130.92 |
34. | May 31, 2020 | 2.54% | 4.53% | 0.00 | 12.91 | 0.18 |
35. | Jun 30, 2020 | 11.06% | 1.84% | 73.40 | 0.82 | 7.74 |
36. | Jul 31, 2020 | 0.74% | 5.51% | 3.07 | 20.92 | -8.01 |
37. | Aug 31, 2020 | 10.26% | 7.01% | 60.36 | 36.85 | 47.16 |
38. | Sep 30, 2020 | -6.74% | -3.92% | 85.16 | 23.61 | 44.84 |
39. | Oct 31, 2020 | -3.74% | -2.77% | 38.76 | 13.71 | 23.05 |
40. | Nov 30, 2020 | 6.01% | 10.75% | 12.37 | 96.41 | 34.53 |
41. | Dec 31, 2020 | 3.90% | 3.71% | 1.99 | 7.71 | 3.92 |
42. | Jan 31, 2021 | 4.29% | -1.11% | 3.24 | 4.20 | -3.69 |
43. | Feb 28, 2021 | 0.42% | 2.61% | 4.27 | 2.80 | -3.46 |
44. | Mar 31, 2021 | 1.46% | 4.24% | 1.06 | 10.94 | -3.41 |
45. | Apr 30, 2021 | 6.96% | 5.24% | 19.99 | 18.55 | 19.26 |
46. | May 31, 2021 | -0.77% | 0.55% | 10.62 | 0.15 | 1.26 |
47. | Jun 30, 2021 | 8.50% | 2.22% | 36.12 | 1.65 | 7.73 |
48. | Jul 31, 2021 | 5.17% | 2.27% | 7.20 | 1.79 | 3.59 |
49. | Aug 31, 2021 | 6.15% | 2.90% | 13.43 | 3.85 | 7.19 |
50. | Sep 30, 2021 | -6.61% | -4.76% | 82.82 | 32.41 | 51.81 |
51. | Oct 31, 2021 | 17.63% | 6.91% | 229.23 | 35.74 | 90.52 |
52. | Nov 30, 2021 | -0.12% | -0.83% | 6.82 | 3.13 | 4.62 |
53. | Dec 31, 2021 | 1.73% | 4.36% | 0.57 | 11.73 | -2.59 |
54. | Jan 31, 2022 | -7.53% | -5.26% | 100.47 | 38.37 | 62.09 |
55. | Feb 28, 2022 | -3.72% | -3.14% | 38.56 | 16.58 | 25.28 |
56. | Mar 31, 2022 | 3.19% | 3.58% | 0.49 | 6.98 | 1.84 |
57. | Apr 30, 2022 | -9.99% | -8.80% | 155.64 | 94.70 | 121.40 |
58. | May 31, 2022 | -1.81% | 0.01% | 18.50 | 0.87 | 4.00 |
59. | Jun 30, 2022 | -5.53% | -8.39% | 64.33 | 87.01 | 74.82 |
60. | Jul 31, 2022 | 9.31% | 9.11% | 46.52 | 66.84 | 55.77 |
61. | Aug 31, 2022 | -6.64% | -4.24% | 83.39 | 26.83 | 47.30 |
62. | Sep 30, 2022 | -10.93% | -9.34% | 179.98 | 105.58 | 137.85 |
63. | Oct 31, 2022 | -0.33% | 7.99% | 7.95 | 49.71 | -19.88 |
64. | Nov 30, 2022 | 10.21% | 5.38% | 59.55 | 19.71 | 34.26 |
65. | Dec 31, 2022 | -6.00% | -5.90% | 72.14 | 46.69 | 58.03 |
66. | Jan 31, 2023 | 3.33% | 6.18% | 0.71 | 27.45 | 4.42 |
67. | Feb 28, 2023 | 0.92% | -2.61% | 2.45 | 12.58 | 5.55 |
68. | Mar 31, 2023 | 15.59% | 3.51% | 171.59 | 6.60 | 33.66 |
69. | Apr 30, 2023 | 6.58% | 1.46% | 16.71 | 0.28 | 2.16 |
70. | May 31, 2023 | 7.10% | 0.25% | 21.25 | 0.47 | -3.17 |
71. | Jun 30, 2023 | 3.70% | 4.71% | 1.47 | 14.27 | 4.58 |
Total (Σ): | 2,645.73 | 1,786.26 | 1,672.61 |
Show all
VarianceMSFT = Σ(RMSFT,t–RMSFT)2 ÷ (71 – 1)
= 2,645.73 ÷ (71 – 1)
= 37.80
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,786.26 ÷ (71 – 1)
= 25.52
CovarianceMSFT, S&P 500 = Σ(RMSFT,t–RMSFT)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,672.61 ÷ (71 – 1)
= 23.89
Systematic Risk (β) Estimation
VarianceMSFT | 37.80 |
VarianceS&P 500 | 25.52 |
CovarianceMSFT, S&P 500 | 23.89 |
Correlation coefficientMSFT, S&P 5001 | 0.77 |
βMSFT2 | 0.94 |
αMSFT3 | 1.61% |
Calculations
1 Correlation coefficientMSFT, S&P 500
= CovarianceMSFT, S&P 500 ÷ (Standard deviationMSFT × Standard deviationS&P 500)
= 23.89 ÷ (6.15% × 5.05%)
= 0.77
2 βMSFT
= CovarianceMSFT, S&P 500 ÷ VarianceS&P 500
= 23.89 ÷ 25.52
= 0.94
3 αMSFT
= AverageMSFT – βMSFT × AverageS&P 500
= 2.49% – 0.94 × 0.94%
= 1.61%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.88% |
Expected rate of return on market portfolio2 | E(RM) | 13.53% |
Systematic risk (β) of Microsoft Corp. common stock | βMSFT | 0.94 |
Expected rate of return on Microsoft Corp. common stock3 | E(RMSFT) | 12.98% |
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(RMSFT) = RF + βMSFT [E(RM) – RF]
= 4.88% + 0.94 [13.53% – 4.88%]
= 12.98%