Capital Asset Pricing Model (CAPM)
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., monthly 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
Microsoft Corp., calculation of variance and covariance of returns
| 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 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 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%