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, 2021 | $230.60 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $226.78 | $0.55 | -1.42% | 3,811.15 | 2.61% |
| 2. | Mar 31, 2021 | $246.00 | 8.48% | 3,972.89 | 4.24% | |
| 3. | Apr 30, 2021 | $273.87 | 11.33% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | $343.69 | $0.79 | -0.13% | 6,849.09 | 0.13% |
| 59. | Dec 31, 2025 | $324.03 | -5.72% | 6,845.50 | -0.05% | |
| Average (R): | 0.99% | 1.14% | ||||
| Standard deviation: | 8.30% | 4.37% | ||||
| 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, 2021 | $230.60 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $226.78 | $0.55 | -1.42% | 3,811.15 | 2.61% |
| 2. | Mar 31, 2021 | $246.00 | 8.48% | 3,972.89 | 4.24% | |
| 3. | Apr 30, 2021 | $273.87 | 11.33% | 4,181.17 | 5.24% | |
| 4. | May 31, 2021 | $283.53 | $0.55 | 3.73% | 4,204.11 | 0.55% |
| 5. | Jun 30, 2021 | $272.45 | -3.91% | 4,297.50 | 2.22% | |
| 6. | Jul 31, 2021 | $291.03 | 6.82% | 4,395.26 | 2.27% | |
| 7. | Aug 31, 2021 | $303.67 | $0.55 | 4.53% | 4,522.68 | 2.90% |
| 8. | Sep 30, 2021 | $279.73 | -7.88% | 4,307.54 | -4.76% | |
| 9. | Oct 31, 2021 | $316.61 | 13.18% | 4,605.38 | 6.91% | |
| 10. | Nov 30, 2021 | $331.24 | $0.55 | 4.79% | 4,567.00 | -0.83% |
| 11. | Dec 31, 2021 | $352.16 | 6.32% | 4,766.18 | 4.36% | |
| 12. | Jan 31, 2022 | $286.51 | -18.64% | 4,515.55 | -5.26% | |
| 13. | Feb 28, 2022 | $263.13 | $0.60 | -7.95% | 4,373.94 | -3.14% |
| 14. | Mar 31, 2022 | $249.62 | -5.13% | 4,530.41 | 3.58% | |
| 15. | Apr 30, 2022 | $274.96 | 10.15% | 4,131.93 | -8.80% | |
| 16. | May 31, 2022 | $268.04 | $0.60 | -2.30% | 4,132.15 | 0.01% |
| 17. | Jun 30, 2022 | $223.91 | -16.46% | 3,785.38 | -8.39% | |
| 18. | Jul 31, 2022 | $241.94 | 8.05% | 4,130.29 | 9.11% | |
| 19. | Aug 31, 2022 | $232.10 | $0.60 | -3.82% | 3,955.00 | -4.24% |
| 20. | Sep 30, 2022 | $204.75 | -11.78% | 3,585.62 | -9.34% | |
| 21. | Oct 31, 2022 | $225.03 | 9.90% | 3,871.98 | 7.99% | |
| 22. | Nov 30, 2022 | $249.18 | $0.60 | 11.00% | 4,080.11 | 5.38% |
| 23. | Dec 31, 2022 | $237.33 | -4.76% | 3,839.50 | -5.90% | |
| 24. | Jan 31, 2023 | $236.59 | -0.31% | 4,076.60 | 6.18% | |
| 25. | Feb 28, 2023 | $221.35 | $0.605 | -6.19% | 3,970.15 | -2.61% |
| 26. | Mar 31, 2023 | $224.77 | 1.55% | 4,109.31 | 3.51% | |
| 27. | Apr 30, 2023 | $237.54 | 5.68% | 4,169.48 | 1.46% | |
| 28. | May 31, 2023 | $227.78 | $0.605 | -3.85% | 4,179.83 | 0.25% |
| 29. | Jun 30, 2023 | $265.52 | 16.57% | 4,376.86 | 4.71% | |
| 30. | Jul 31, 2023 | $276.50 | 4.14% | 4,588.96 | 4.85% | |
| 31. | Aug 31, 2023 | $271.72 | $0.605 | -1.51% | 4,507.66 | -1.77% |
| 32. | Sep 30, 2023 | $255.05 | -6.13% | 4,288.05 | -4.87% | |
| 33. | Oct 31, 2023 | $238.21 | -6.60% | 4,193.80 | -2.20% | |
| 34. | Nov 30, 2023 | $278.80 | $0.605 | 17.29% | 4,567.80 | 8.92% |
| 35. | Dec 31, 2023 | $311.90 | 11.87% | 4,769.83 | 4.42% | |
| 36. | Jan 31, 2024 | $304.38 | -2.41% | 4,845.65 | 1.59% | |
| 37. | Feb 29, 2024 | $332.03 | $0.715 | 9.32% | 5,096.27 | 5.17% |
| 38. | Mar 31, 2024 | $347.33 | 4.61% | 5,254.35 | 3.10% | |
| 39. | Apr 30, 2024 | $299.61 | -13.74% | 5,035.69 | -4.16% | |
| 40. | May 31, 2024 | $303.80 | $0.715 | 1.64% | 5,277.51 | 4.80% |
| 41. | Jun 30, 2024 | $298.43 | -1.77% | 5,460.48 | 3.47% | |
| 42. | Jul 31, 2024 | $350.80 | 17.55% | 5,522.30 | 1.13% | |
| 43. | Aug 31, 2024 | $369.37 | $0.715 | 5.50% | 5,648.40 | 2.28% |
| 44. | Sep 30, 2024 | $381.67 | 3.33% | 5,762.48 | 2.02% | |
| 45. | Oct 31, 2024 | $358.77 | -6.00% | 5,705.45 | -0.99% | |
| 46. | Nov 30, 2024 | $397.40 | $0.715 | 10.97% | 6,032.38 | 5.73% |
| 47. | Dec 31, 2024 | $339.93 | -14.46% | 5,881.63 | -2.50% | |
| 48. | Jan 31, 2025 | $358.16 | 5.36% | 6,040.53 | 2.70% | |
| 49. | Feb 28, 2025 | $362.27 | 1.15% | 5,954.50 | -1.42% | |
| 50. | Mar 31, 2025 | $349.19 | $0.79 | -3.39% | 5,611.85 | -5.75% |
| 51. | Apr 30, 2025 | $352.92 | 1.07% | 5,569.06 | -0.76% | |
| 52. | May 31, 2025 | $358.81 | $0.79 | 1.89% | 5,911.69 | 6.15% |
| 53. | Jun 30, 2025 | $343.36 | -4.31% | 6,204.95 | 4.96% | |
| 54. | Jul 31, 2025 | $330.88 | -3.63% | 6,339.39 | 2.17% | |
| 55. | Aug 31, 2025 | $365.83 | $0.79 | 10.80% | 6,460.26 | 1.91% |
| 56. | Sep 30, 2025 | $346.26 | -5.35% | 6,688.46 | 3.53% | |
| 57. | Oct 31, 2025 | $344.94 | -0.38% | 6,840.20 | 2.27% | |
| 58. | Nov 30, 2025 | $343.69 | $0.79 | -0.13% | 6,849.09 | 0.13% |
| 59. | Dec 31, 2025 | $324.03 | -5.72% | 6,845.50 | -0.05% | |
| Average (R): | 0.99% | 1.14% | ||||
| Standard deviation: | 8.30% | 4.37% | ||||
Show all
1 Data in US$ 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 28, 2021 | -1.42% | 2.61% | 5.81 | 2.17 | -3.55 |
| 2. | Mar 31, 2021 | 8.48% | 4.24% | 55.98 | 9.66 | 23.25 |
| 3. | Apr 30, 2021 | 11.33% | 5.24% | 106.83 | 16.86 | 42.44 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | -0.13% | 0.13% | 1.27 | 1.01 | 1.13 |
| 59. | Dec 31, 2025 | -5.72% | -0.05% | 45.07 | 1.41 | 7.98 |
| Total (Σ): | 3,997.90 | 1,108.23 | 1,374.34 | |||
| 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 28, 2021 | -1.42% | 2.61% | 5.81 | 2.17 | -3.55 |
| 2. | Mar 31, 2021 | 8.48% | 4.24% | 55.98 | 9.66 | 23.25 |
| 3. | Apr 30, 2021 | 11.33% | 5.24% | 106.83 | 16.86 | 42.44 |
| 4. | May 31, 2021 | 3.73% | 0.55% | 7.48 | 0.35 | -1.61 |
| 5. | Jun 30, 2021 | -3.91% | 2.22% | 24.02 | 1.18 | -5.32 |
| 6. | Jul 31, 2021 | 6.82% | 2.27% | 33.95 | 1.30 | 6.63 |
| 7. | Aug 31, 2021 | 4.53% | 2.90% | 12.52 | 3.11 | 6.24 |
| 8. | Sep 30, 2021 | -7.88% | -4.76% | 78.80 | 34.73 | 52.31 |
| 9. | Oct 31, 2021 | 13.18% | 6.91% | 148.62 | 33.39 | 70.44 |
| 10. | Nov 30, 2021 | 4.79% | -0.83% | 14.45 | 3.88 | -7.49 |
| 11. | Dec 31, 2021 | 6.32% | 4.36% | 28.33 | 10.40 | 17.17 |
| 12. | Jan 31, 2022 | -18.64% | -5.26% | 385.55 | 40.89 | 125.56 |
| 13. | Feb 28, 2022 | -7.95% | -3.14% | 80.00 | 18.25 | 38.21 |
| 14. | Mar 31, 2022 | -5.13% | 3.58% | 37.55 | 5.96 | -14.96 |
| 15. | Apr 30, 2022 | 10.15% | -8.80% | 83.87 | 98.64 | -90.96 |
| 16. | May 31, 2022 | -2.30% | 0.01% | 10.84 | 1.28 | 3.72 |
| 17. | Jun 30, 2022 | -16.46% | -8.39% | 304.76 | 90.79 | 166.34 |
| 18. | Jul 31, 2022 | 8.05% | 9.11% | 49.83 | 63.61 | 56.30 |
| 19. | Aug 31, 2022 | -3.82% | -4.24% | 23.16 | 28.95 | 25.89 |
| 20. | Sep 30, 2022 | -11.78% | -9.34% | 163.25 | 109.74 | 133.85 |
| 21. | Oct 31, 2022 | 9.90% | 7.99% | 79.41 | 46.93 | 61.05 |
| 22. | Nov 30, 2022 | 11.00% | 5.38% | 100.10 | 17.97 | 42.41 |
| 23. | Dec 31, 2022 | -4.76% | -5.90% | 33.05 | 49.47 | 40.43 |
| 24. | Jan 31, 2023 | -0.31% | 6.18% | 1.70 | 25.39 | -6.58 |
| 25. | Feb 28, 2023 | -6.19% | -2.61% | 51.54 | 14.04 | 26.90 |
| 26. | Mar 31, 2023 | 1.55% | 3.51% | 0.30 | 5.61 | 1.31 |
| 27. | Apr 30, 2023 | 5.68% | 1.46% | 21.98 | 0.11 | 1.54 |
| 28. | May 31, 2023 | -3.85% | 0.25% | 23.50 | 0.79 | 4.30 |
| 29. | Jun 30, 2023 | 16.57% | 4.71% | 242.59 | 12.80 | 55.72 |
| 30. | Jul 31, 2023 | 4.14% | 4.85% | 9.87 | 13.76 | 11.66 |
| 31. | Aug 31, 2023 | -1.51% | -1.77% | 6.27 | 8.46 | 7.28 |
| 32. | Sep 30, 2023 | -6.13% | -4.87% | 50.81 | 36.10 | 42.83 |
| 33. | Oct 31, 2023 | -6.60% | -2.20% | 57.70 | 11.12 | 25.33 |
| 34. | Nov 30, 2023 | 17.29% | 8.92% | 265.70 | 60.56 | 126.84 |
| 35. | Dec 31, 2023 | 11.87% | 4.42% | 118.35 | 10.80 | 35.76 |
| 36. | Jan 31, 2024 | -2.41% | 1.59% | 11.59 | 0.21 | -1.54 |
| 37. | Feb 29, 2024 | 9.32% | 5.17% | 69.32 | 16.29 | 33.60 |
| 38. | Mar 31, 2024 | 4.61% | 3.10% | 13.07 | 3.86 | 7.11 |
| 39. | Apr 30, 2024 | -13.74% | -4.16% | 217.05 | 28.06 | 78.05 |
| 40. | May 31, 2024 | 1.64% | 4.80% | 0.41 | 13.44 | 2.36 |
| 41. | Jun 30, 2024 | -1.77% | 3.47% | 7.62 | 5.43 | -6.44 |
| 42. | Jul 31, 2024 | 17.55% | 1.13% | 274.07 | 0.00 | -0.07 |
| 43. | Aug 31, 2024 | 5.50% | 2.28% | 20.29 | 1.32 | 5.17 |
| 44. | Sep 30, 2024 | 3.33% | 2.02% | 5.46 | 0.78 | 2.06 |
| 45. | Oct 31, 2024 | -6.00% | -0.99% | 48.91 | 4.52 | 14.87 |
| 46. | Nov 30, 2024 | 10.97% | 5.73% | 99.47 | 21.10 | 45.82 |
| 47. | Dec 31, 2024 | -14.46% | -2.50% | 238.85 | 13.21 | 56.18 |
| 48. | Jan 31, 2025 | 5.36% | 2.70% | 19.09 | 2.45 | 6.84 |
| 49. | Feb 28, 2025 | 1.15% | -1.42% | 0.02 | 6.56 | -0.39 |
| 50. | Mar 31, 2025 | -3.39% | -5.75% | 19.24 | 47.48 | 30.22 |
| 51. | Apr 30, 2025 | 1.07% | -0.76% | 0.01 | 3.60 | -0.14 |
| 52. | May 31, 2025 | 1.89% | 6.15% | 0.81 | 25.16 | 4.51 |
| 53. | Jun 30, 2025 | -4.31% | 4.96% | 28.08 | 14.63 | -20.27 |
| 54. | Jul 31, 2025 | -3.63% | 2.17% | 21.42 | 1.06 | -4.77 |
| 55. | Aug 31, 2025 | 10.80% | 1.91% | 96.20 | 0.59 | 7.56 |
| 56. | Sep 30, 2025 | -5.35% | 3.53% | 40.23 | 5.74 | -15.20 |
| 57. | Oct 31, 2025 | -0.38% | 2.27% | 1.89 | 1.28 | -1.56 |
| 58. | Nov 30, 2025 | -0.13% | 0.13% | 1.27 | 1.01 | 1.13 |
| 59. | Dec 31, 2025 | -5.72% | -0.05% | 45.07 | 1.41 | 7.98 |
| Total (Σ): | 3,997.90 | 1,108.23 | 1,374.34 | |||
Show all
VarianceSHW = Σ(RSHW,t–RSHW)2 ÷ (59 – 1)
= 3,997.90 ÷ (59 – 1)
= 68.93
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
CovarianceSHW, S&P 500 = Σ(RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,374.34 ÷ (59 – 1)
= 23.70
Systematic Risk (β) Estimation
| VarianceSHW | 68.93 |
| VarianceS&P 500 | 19.11 |
| CovarianceSHW, S&P 500 | 23.70 |
| Correlation coefficientSHW, S&P 5001 | 0.65 |
| βSHW2 | 1.24 |
| αSHW3 | -0.42% |
Calculations
1 Correlation coefficientSHW, S&P 500
= CovarianceSHW, S&P 500 ÷ (Standard deviationSHW × Standard deviationS&P 500)
= 23.70 ÷ (8.30% × 4.37%)
= 0.65
2 βSHW
= CovarianceSHW, S&P 500 ÷ VarianceS&P 500
= 23.70 ÷ 19.11
= 1.24
3 αSHW
= AverageSHW – βSHW × AverageS&P 500
= 0.99% – 1.24 × 1.14%
= -0.42%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.94% |
| Expected rate of return on market portfolio2 | E(RM) | 17.36% |
| Systematic risk (β) of Sherwin-Williams Co. common stock | βSHW | 1.24 |
| Expected rate of return on Sherwin-Williams Co. common stock3 | E(RSHW) | 20.34% |
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% + 1.24 [17.36% – 4.94%]
= 20.34%