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 Sherwin-Williams Co. common stock.
Rates of Return
Sherwin-Williams Co., monthly rates of return
| Sherwin-Williams Co. (SHW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceSHW,t1 | DividendSHW,t1 | RSHW,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2020 | $185.66 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $172.25 | $0.4467 | -6.98% | 2,954.22 | -8.41% |
| 2. | Mar 31, 2020 | $153.17 | -11.08% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $178.79 | 16.73% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | $397.40 | $0.715 | 10.97% | 6,032.38 | 5.73% |
| 59. | Dec 31, 2024 | $339.93 | -14.46% | 5,881.63 | -2.50% | |
| Average (R): | 1.49% | 1.16% | ||||
| Standard deviation: | 8.85% | 5.28% | ||||
| Sherwin-Williams Co. (SHW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceSHW,t1 | DividendSHW,t1 | RSHW,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2020 | $185.66 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $172.25 | $0.4467 | -6.98% | 2,954.22 | -8.41% |
| 2. | Mar 31, 2020 | $153.17 | -11.08% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $178.79 | 16.73% | 2,912.43 | 12.68% | |
| 4. | May 31, 2020 | $197.95 | $0.4467 | 10.97% | 3,044.31 | 4.53% |
| 5. | Jun 30, 2020 | $192.62 | -2.69% | 3,100.29 | 1.84% | |
| 6. | Jul 31, 2020 | $215.97 | 12.12% | 3,271.12 | 5.51% | |
| 7. | Aug 31, 2020 | $223.68 | $0.4467 | 3.78% | 3,500.31 | 7.01% |
| 8. | Sep 30, 2020 | $232.25 | 3.83% | 3,363.00 | -3.92% | |
| 9. | Oct 31, 2020 | $229.33 | -1.26% | 3,269.96 | -2.77% | |
| 10. | Nov 30, 2020 | $249.21 | $0.4467 | 8.86% | 3,621.63 | 10.75% |
| 11. | Dec 31, 2020 | $244.97 | -1.70% | 3,756.07 | 3.71% | |
| 12. | Jan 31, 2021 | $230.60 | -5.87% | 3,714.24 | -1.11% | |
| 13. | Feb 28, 2021 | $226.78 | $0.55 | -1.42% | 3,811.15 | 2.61% |
| 14. | Mar 31, 2021 | $246.00 | 8.48% | 3,972.89 | 4.24% | |
| 15. | Apr 30, 2021 | $273.87 | 11.33% | 4,181.17 | 5.24% | |
| 16. | May 31, 2021 | $283.53 | $0.55 | 3.73% | 4,204.11 | 0.55% |
| 17. | Jun 30, 2021 | $272.45 | -3.91% | 4,297.50 | 2.22% | |
| 18. | Jul 31, 2021 | $291.03 | 6.82% | 4,395.26 | 2.27% | |
| 19. | Aug 31, 2021 | $303.67 | $0.55 | 4.53% | 4,522.68 | 2.90% |
| 20. | Sep 30, 2021 | $279.73 | -7.88% | 4,307.54 | -4.76% | |
| 21. | Oct 31, 2021 | $316.61 | 13.18% | 4,605.38 | 6.91% | |
| 22. | Nov 30, 2021 | $331.24 | $0.55 | 4.79% | 4,567.00 | -0.83% |
| 23. | Dec 31, 2021 | $352.16 | 6.32% | 4,766.18 | 4.36% | |
| 24. | Jan 31, 2022 | $286.51 | -18.64% | 4,515.55 | -5.26% | |
| 25. | Feb 28, 2022 | $263.13 | $0.60 | -7.95% | 4,373.94 | -3.14% |
| 26. | Mar 31, 2022 | $249.62 | -5.13% | 4,530.41 | 3.58% | |
| 27. | Apr 30, 2022 | $274.96 | 10.15% | 4,131.93 | -8.80% | |
| 28. | May 31, 2022 | $268.04 | $0.60 | -2.30% | 4,132.15 | 0.01% |
| 29. | Jun 30, 2022 | $223.91 | -16.46% | 3,785.38 | -8.39% | |
| 30. | Jul 31, 2022 | $241.94 | 8.05% | 4,130.29 | 9.11% | |
| 31. | Aug 31, 2022 | $232.10 | $0.60 | -3.82% | 3,955.00 | -4.24% |
| 32. | Sep 30, 2022 | $204.75 | -11.78% | 3,585.62 | -9.34% | |
| 33. | Oct 31, 2022 | $225.03 | 9.90% | 3,871.98 | 7.99% | |
| 34. | Nov 30, 2022 | $249.18 | $0.60 | 11.00% | 4,080.11 | 5.38% |
| 35. | Dec 31, 2022 | $237.33 | -4.76% | 3,839.50 | -5.90% | |
| 36. | Jan 31, 2023 | $236.59 | -0.31% | 4,076.60 | 6.18% | |
| 37. | Feb 28, 2023 | $221.35 | $0.605 | -6.19% | 3,970.15 | -2.61% |
| 38. | Mar 31, 2023 | $224.77 | 1.55% | 4,109.31 | 3.51% | |
| 39. | Apr 30, 2023 | $237.54 | 5.68% | 4,169.48 | 1.46% | |
| 40. | May 31, 2023 | $227.78 | $0.605 | -3.85% | 4,179.83 | 0.25% |
| 41. | Jun 30, 2023 | $265.52 | 16.57% | 4,376.86 | 4.71% | |
| 42. | Jul 31, 2023 | $276.50 | 4.14% | 4,588.96 | 4.85% | |
| 43. | Aug 31, 2023 | $271.72 | $0.605 | -1.51% | 4,507.66 | -1.77% |
| 44. | Sep 30, 2023 | $255.05 | -6.13% | 4,288.05 | -4.87% | |
| 45. | Oct 31, 2023 | $238.21 | -6.60% | 4,193.80 | -2.20% | |
| 46. | Nov 30, 2023 | $278.80 | $0.605 | 17.29% | 4,567.80 | 8.92% |
| 47. | Dec 31, 2023 | $311.90 | 11.87% | 4,769.83 | 4.42% | |
| 48. | Jan 31, 2024 | $304.38 | -2.41% | 4,845.65 | 1.59% | |
| 49. | Feb 29, 2024 | $332.03 | $0.715 | 9.32% | 5,096.27 | 5.17% |
| 50. | Mar 31, 2024 | $347.33 | 4.61% | 5,254.35 | 3.10% | |
| 51. | Apr 30, 2024 | $299.61 | -13.74% | 5,035.69 | -4.16% | |
| 52. | May 31, 2024 | $303.80 | $0.715 | 1.64% | 5,277.51 | 4.80% |
| 53. | Jun 30, 2024 | $298.43 | -1.77% | 5,460.48 | 3.47% | |
| 54. | Jul 31, 2024 | $350.80 | 17.55% | 5,522.30 | 1.13% | |
| 55. | Aug 31, 2024 | $369.37 | $0.715 | 5.50% | 5,648.40 | 2.28% |
| 56. | Sep 30, 2024 | $381.67 | 3.33% | 5,762.48 | 2.02% | |
| 57. | Oct 31, 2024 | $358.77 | -6.00% | 5,705.45 | -0.99% | |
| 58. | Nov 30, 2024 | $397.40 | $0.715 | 10.97% | 6,032.38 | 5.73% |
| 59. | Dec 31, 2024 | $339.93 | -14.46% | 5,881.63 | -2.50% | |
| Average (R): | 1.49% | 1.16% | ||||
| Standard deviation: | 8.85% | 5.28% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of SHW during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Sherwin-Williams Co., calculation of variance and covariance of returns
| t | Date | RSHW,t | RS&P 500,t | (RSHW,t–RSHW)2 | (RS&P 500,t–RS&P 500)2 | (RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2020 | -6.98% | -8.41% | 71.79 | 91.63 | 81.11 |
| 2. | Mar 31, 2020 | -11.08% | -12.51% | 157.95 | 186.96 | 171.84 |
| 3. | Apr 30, 2020 | 16.73% | 12.68% | 232.12 | 132.78 | 175.56 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | 10.97% | 5.73% | 89.79 | 20.87 | 43.29 |
| 59. | Dec 31, 2024 | -14.46% | -2.50% | 254.48 | 13.40 | 58.39 |
| Total (Σ): | 4,540.81 | 1,618.62 | 1,955.13 | |||
| t | Date | RSHW,t | RS&P 500,t | (RSHW,t–RSHW)2 | (RS&P 500,t–RS&P 500)2 | (RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2020 | -6.98% | -8.41% | 71.79 | 91.63 | 81.11 |
| 2. | Mar 31, 2020 | -11.08% | -12.51% | 157.95 | 186.96 | 171.84 |
| 3. | Apr 30, 2020 | 16.73% | 12.68% | 232.12 | 132.78 | 175.56 |
| 4. | May 31, 2020 | 10.97% | 4.53% | 89.78 | 11.34 | 31.90 |
| 5. | Jun 30, 2020 | -2.69% | 1.84% | 17.50 | 0.46 | -2.83 |
| 6. | Jul 31, 2020 | 12.12% | 5.51% | 113.03 | 18.91 | 46.23 |
| 7. | Aug 31, 2020 | 3.78% | 7.01% | 5.23 | 34.17 | 13.36 |
| 8. | Sep 30, 2020 | 3.83% | -3.92% | 5.48 | 25.85 | -11.90 |
| 9. | Oct 31, 2020 | -1.26% | -2.77% | 7.55 | 15.43 | 10.79 |
| 10. | Nov 30, 2020 | 8.86% | 10.75% | 54.36 | 92.03 | 70.73 |
| 11. | Dec 31, 2020 | -1.70% | 3.71% | 10.19 | 6.51 | -8.14 |
| 12. | Jan 31, 2021 | -5.87% | -1.11% | 54.12 | 5.18 | 16.74 |
| 13. | Feb 28, 2021 | -1.42% | 2.61% | 8.46 | 2.10 | -4.21 |
| 14. | Mar 31, 2021 | 8.48% | 4.24% | 48.78 | 9.50 | 21.53 |
| 15. | Apr 30, 2021 | 11.33% | 5.24% | 96.79 | 16.66 | 40.15 |
| 16. | May 31, 2021 | 3.73% | 0.55% | 5.00 | 0.38 | -1.37 |
| 17. | Jun 30, 2021 | -3.91% | 2.22% | 29.15 | 1.12 | -5.72 |
| 18. | Jul 31, 2021 | 6.82% | 2.27% | 28.40 | 1.24 | 5.93 |
| 19. | Aug 31, 2021 | 4.53% | 2.90% | 9.25 | 3.02 | 5.29 |
| 20. | Sep 30, 2021 | -7.88% | -4.76% | 87.88 | 35.02 | 55.48 |
| 21. | Oct 31, 2021 | 13.18% | 6.91% | 136.73 | 33.10 | 67.27 |
| 22. | Nov 30, 2021 | 4.79% | -0.83% | 10.91 | 3.98 | -6.59 |
| 23. | Dec 31, 2021 | 6.32% | 4.36% | 23.28 | 10.24 | 15.44 |
| 24. | Jan 31, 2022 | -18.64% | -5.26% | 405.34 | 41.21 | 129.25 |
| 25. | Feb 28, 2022 | -7.95% | -3.14% | 89.15 | 18.47 | 40.57 |
| 26. | Mar 31, 2022 | -5.13% | 3.58% | 43.89 | 5.84 | -16.01 |
| 27. | Apr 30, 2022 | 10.15% | -8.80% | 75.00 | 99.14 | -86.23 |
| 28. | May 31, 2022 | -2.30% | 0.01% | 14.36 | 1.34 | 4.38 |
| 29. | Jun 30, 2022 | -16.46% | -8.39% | 322.38 | 91.26 | 171.53 |
| 30. | Jul 31, 2022 | 8.05% | 9.11% | 43.05 | 63.21 | 52.17 |
| 31. | Aug 31, 2022 | -3.82% | -4.24% | 28.20 | 29.22 | 28.70 |
| 32. | Sep 30, 2022 | -11.78% | -9.34% | 176.22 | 110.27 | 139.39 |
| 33. | Oct 31, 2022 | 9.90% | 7.99% | 70.79 | 46.58 | 57.43 |
| 34. | Nov 30, 2022 | 11.00% | 5.38% | 90.40 | 17.76 | 40.07 |
| 35. | Dec 31, 2022 | -4.76% | -5.90% | 39.02 | 49.82 | 44.09 |
| 36. | Jan 31, 2023 | -0.31% | 6.18% | 3.25 | 25.14 | -9.04 |
| 37. | Feb 28, 2023 | -6.19% | -2.61% | 58.93 | 14.23 | 28.96 |
| 38. | Mar 31, 2023 | 1.55% | 3.51% | 0.00 | 5.49 | 0.13 |
| 39. | Apr 30, 2023 | 5.68% | 1.46% | 17.56 | 0.09 | 1.27 |
| 40. | May 31, 2023 | -3.85% | 0.25% | 28.57 | 0.83 | 4.88 |
| 41. | Jun 30, 2023 | 16.57% | 4.71% | 227.34 | 12.62 | 53.56 |
| 42. | Jul 31, 2023 | 4.14% | 4.85% | 6.99 | 13.58 | 9.74 |
| 43. | Aug 31, 2023 | -1.51% | -1.77% | 9.01 | 8.60 | 8.80 |
| 44. | Sep 30, 2023 | -6.13% | -4.87% | 58.15 | 36.40 | 46.01 |
| 45. | Oct 31, 2023 | -6.60% | -2.20% | 65.51 | 11.28 | 27.19 |
| 46. | Nov 30, 2023 | 17.29% | 8.92% | 249.72 | 60.17 | 122.58 |
| 47. | Dec 31, 2023 | 11.87% | 4.42% | 107.77 | 10.64 | 33.86 |
| 48. | Jan 31, 2024 | -2.41% | 1.59% | 15.23 | 0.18 | -1.67 |
| 49. | Feb 29, 2024 | 9.32% | 5.17% | 61.28 | 16.09 | 31.40 |
| 50. | Mar 31, 2024 | 4.61% | 3.10% | 9.72 | 3.77 | 6.05 |
| 51. | Apr 30, 2024 | -13.74% | -4.16% | 231.95 | 28.33 | 81.07 |
| 52. | May 31, 2024 | 1.64% | 4.80% | 0.02 | 13.26 | 0.53 |
| 53. | Jun 30, 2024 | -1.77% | 3.47% | 10.62 | 5.32 | -7.51 |
| 54. | Jul 31, 2024 | 17.55% | 1.13% | 257.85 | 0.00 | -0.47 |
| 55. | Aug 31, 2024 | 5.50% | 2.28% | 16.05 | 1.26 | 4.50 |
| 56. | Sep 30, 2024 | 3.33% | 2.02% | 3.38 | 0.74 | 1.58 |
| 57. | Oct 31, 2024 | -6.00% | -0.99% | 56.11 | 4.63 | 16.11 |
| 58. | Nov 30, 2024 | 10.97% | 5.73% | 89.79 | 20.87 | 43.29 |
| 59. | Dec 31, 2024 | -14.46% | -2.50% | 254.48 | 13.40 | 58.39 |
| Total (Σ): | 4,540.81 | 1,618.62 | 1,955.13 | |||
Show all
VarianceSHW = Σ(RSHW,t–RSHW)2 ÷ (59 – 1)
= 4,540.81 ÷ (59 – 1)
= 78.29
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
CovarianceSHW, S&P 500 = Σ(RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,955.13 ÷ (59 – 1)
= 33.71
Systematic Risk (β) Estimation
| VarianceSHW | 78.29 |
| VarianceS&P 500 | 27.91 |
| CovarianceSHW, S&P 500 | 33.71 |
| Correlation coefficientSHW, S&P 5001 | 0.72 |
| βSHW2 | 1.21 |
| αSHW3 | 0.09% |
Calculations
1 Correlation coefficientSHW, S&P 500
= CovarianceSHW, S&P 500 ÷ (Standard deviationSHW × Standard deviationS&P 500)
= 33.71 ÷ (8.85% × 5.28%)
= 0.72
2 βSHW
= CovarianceSHW, S&P 500 ÷ VarianceS&P 500
= 33.71 ÷ 27.91
= 1.21
3 αSHW
= AverageSHW – βSHW × AverageS&P 500
= 1.49% – 1.21 × 1.16%
= 0.09%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.94% |
| Expected rate of return on market portfolio2 | E(RM) | 15.05% |
| Systematic risk (β) of Sherwin-Williams Co. common stock | βSHW | 1.21 |
| Expected rate of return on Sherwin-Williams Co. common stock3 | E(RSHW) | 17.15% |
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(RSHW) = RF + βSHW [E(RM) – RF]
= 4.94% + 1.21 [15.05% – 4.94%]
= 17.15%