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.
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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, 2018 | ||||||
| 1. | Aug 31, 2018 | |||||
| 2. | Sep 30, 2018 | |||||
| 3. | Oct 31, 2018 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | May 31, 2024 | |||||
| 71. | Jun 30, 2024 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
| 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, 2018 | ||||||
| 1. | Aug 31, 2018 | |||||
| 2. | Sep 30, 2018 | |||||
| 3. | Oct 31, 2018 | |||||
| 4. | Nov 30, 2018 | |||||
| 5. | Dec 31, 2018 | |||||
| 6. | Jan 31, 2019 | |||||
| 7. | Feb 28, 2019 | |||||
| 8. | Mar 31, 2019 | |||||
| 9. | Apr 30, 2019 | |||||
| 10. | May 31, 2019 | |||||
| 11. | Jun 30, 2019 | |||||
| 12. | Jul 31, 2019 | |||||
| 13. | Aug 31, 2019 | |||||
| 14. | Sep 30, 2019 | |||||
| 15. | Oct 31, 2019 | |||||
| 16. | Nov 30, 2019 | |||||
| 17. | Dec 31, 2019 | |||||
| 18. | Jan 31, 2020 | |||||
| 19. | Feb 29, 2020 | |||||
| 20. | Mar 31, 2020 | |||||
| 21. | Apr 30, 2020 | |||||
| 22. | May 31, 2020 | |||||
| 23. | Jun 30, 2020 | |||||
| 24. | Jul 31, 2020 | |||||
| 25. | Aug 31, 2020 | |||||
| 26. | Sep 30, 2020 | |||||
| 27. | Oct 31, 2020 | |||||
| 28. | Nov 30, 2020 | |||||
| 29. | Dec 31, 2020 | |||||
| 30. | Jan 31, 2021 | |||||
| 31. | Feb 28, 2021 | |||||
| 32. | Mar 31, 2021 | |||||
| 33. | Apr 30, 2021 | |||||
| 34. | May 31, 2021 | |||||
| 35. | Jun 30, 2021 | |||||
| 36. | Jul 31, 2021 | |||||
| 37. | Aug 31, 2021 | |||||
| 38. | Sep 30, 2021 | |||||
| 39. | Oct 31, 2021 | |||||
| 40. | Nov 30, 2021 | |||||
| 41. | Dec 31, 2021 | |||||
| 42. | Jan 31, 2022 | |||||
| 43. | Feb 28, 2022 | |||||
| 44. | Mar 31, 2022 | |||||
| 45. | Apr 30, 2022 | |||||
| 46. | May 31, 2022 | |||||
| 47. | Jun 30, 2022 | |||||
| 48. | Jul 31, 2022 | |||||
| 49. | Aug 31, 2022 | |||||
| 50. | Sep 30, 2022 | |||||
| 51. | Oct 31, 2022 | |||||
| 52. | Nov 30, 2022 | |||||
| 53. | Dec 31, 2022 | |||||
| 54. | Jan 31, 2023 | |||||
| 55. | Feb 28, 2023 | |||||
| 56. | Mar 31, 2023 | |||||
| 57. | Apr 30, 2023 | |||||
| 58. | May 31, 2023 | |||||
| 59. | Jun 30, 2023 | |||||
| 60. | Jul 31, 2023 | |||||
| 61. | Aug 31, 2023 | |||||
| 62. | Sep 30, 2023 | |||||
| 63. | Oct 31, 2023 | |||||
| 64. | Nov 30, 2023 | |||||
| 65. | Dec 31, 2023 | |||||
| 66. | Jan 31, 2024 | |||||
| 67. | Feb 29, 2024 | |||||
| 68. | Mar 31, 2024 | |||||
| 69. | Apr 30, 2024 | |||||
| 70. | May 31, 2024 | |||||
| 71. | Jun 30, 2024 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
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, 2018 | |||||
| 2. | Sep 30, 2018 | |||||
| 3. | Oct 31, 2018 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | May 31, 2024 | |||||
| 71. | Jun 30, 2024 | |||||
| Total (Σ): | ||||||
| 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, 2018 | |||||
| 2. | Sep 30, 2018 | |||||
| 3. | Oct 31, 2018 | |||||
| 4. | Nov 30, 2018 | |||||
| 5. | Dec 31, 2018 | |||||
| 6. | Jan 31, 2019 | |||||
| 7. | Feb 28, 2019 | |||||
| 8. | Mar 31, 2019 | |||||
| 9. | Apr 30, 2019 | |||||
| 10. | May 31, 2019 | |||||
| 11. | Jun 30, 2019 | |||||
| 12. | Jul 31, 2019 | |||||
| 13. | Aug 31, 2019 | |||||
| 14. | Sep 30, 2019 | |||||
| 15. | Oct 31, 2019 | |||||
| 16. | Nov 30, 2019 | |||||
| 17. | Dec 31, 2019 | |||||
| 18. | Jan 31, 2020 | |||||
| 19. | Feb 29, 2020 | |||||
| 20. | Mar 31, 2020 | |||||
| 21. | Apr 30, 2020 | |||||
| 22. | May 31, 2020 | |||||
| 23. | Jun 30, 2020 | |||||
| 24. | Jul 31, 2020 | |||||
| 25. | Aug 31, 2020 | |||||
| 26. | Sep 30, 2020 | |||||
| 27. | Oct 31, 2020 | |||||
| 28. | Nov 30, 2020 | |||||
| 29. | Dec 31, 2020 | |||||
| 30. | Jan 31, 2021 | |||||
| 31. | Feb 28, 2021 | |||||
| 32. | Mar 31, 2021 | |||||
| 33. | Apr 30, 2021 | |||||
| 34. | May 31, 2021 | |||||
| 35. | Jun 30, 2021 | |||||
| 36. | Jul 31, 2021 | |||||
| 37. | Aug 31, 2021 | |||||
| 38. | Sep 30, 2021 | |||||
| 39. | Oct 31, 2021 | |||||
| 40. | Nov 30, 2021 | |||||
| 41. | Dec 31, 2021 | |||||
| 42. | Jan 31, 2022 | |||||
| 43. | Feb 28, 2022 | |||||
| 44. | Mar 31, 2022 | |||||
| 45. | Apr 30, 2022 | |||||
| 46. | May 31, 2022 | |||||
| 47. | Jun 30, 2022 | |||||
| 48. | Jul 31, 2022 | |||||
| 49. | Aug 31, 2022 | |||||
| 50. | Sep 30, 2022 | |||||
| 51. | Oct 31, 2022 | |||||
| 52. | Nov 30, 2022 | |||||
| 53. | Dec 31, 2022 | |||||
| 54. | Jan 31, 2023 | |||||
| 55. | Feb 28, 2023 | |||||
| 56. | Mar 31, 2023 | |||||
| 57. | Apr 30, 2023 | |||||
| 58. | May 31, 2023 | |||||
| 59. | Jun 30, 2023 | |||||
| 60. | Jul 31, 2023 | |||||
| 61. | Aug 31, 2023 | |||||
| 62. | Sep 30, 2023 | |||||
| 63. | Oct 31, 2023 | |||||
| 64. | Nov 30, 2023 | |||||
| 65. | Dec 31, 2023 | |||||
| 66. | Jan 31, 2024 | |||||
| 67. | Feb 29, 2024 | |||||
| 68. | Mar 31, 2024 | |||||
| 69. | Apr 30, 2024 | |||||
| 70. | May 31, 2024 | |||||
| 71. | Jun 30, 2024 | |||||
| Total (Σ): | ||||||
Show all
VarianceMSFT = Σ(RMSFT,t–RMSFT)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
CovarianceMSFT, S&P 500 = Σ(RMSFT,t–RMSFT)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= ÷ (71 – 1)
=
Systematic Risk (β) Estimation
| VarianceMSFT | |
| VarianceS&P 500 | |
| CovarianceMSFT, S&P 500 | |
| Correlation coefficientMSFT, S&P 5001 | |
| βMSFT2 | |
| αMSFT3 |
Calculations
1 Correlation coefficientMSFT, S&P 500
= CovarianceMSFT, S&P 500 ÷ (Standard deviationMSFT × Standard deviationS&P 500)
= ÷ ( × )
=
2 βMSFT
= CovarianceMSFT, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αMSFT
= AverageMSFT – βMSFT × AverageS&P 500
= – ×
=
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | |
| Expected rate of return on market portfolio2 | E(RM) | |
| Systematic risk (β) of Microsoft Corp. common stock | βMSFT | |
| Expected rate of return on Microsoft Corp. common stock3 | E(RMSFT) | |
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]
= + [ – ]
=