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, 2019 | $140.51 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $144.40 | $0.3767 | 3.04% | 2,784.49 | 2.97% |
| 2. | Mar 31, 2019 | $143.57 | -0.57% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $151.61 | 5.60% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | $278.80 | $0.61 | 17.30% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $311.90 | 11.87% | 4,769.83 | 4.42% | |
| Average (R): | 1.77% | 1.11% | ||||
| Standard deviation: | 8.16% | 5.31% | ||||
| 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, 2019 | $140.51 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $144.40 | $0.3767 | 3.04% | 2,784.49 | 2.97% |
| 2. | Mar 31, 2019 | $143.57 | -0.57% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $151.61 | 5.60% | 2,945.83 | 3.93% | |
| 4. | May 31, 2019 | $139.82 | $0.3767 | -7.53% | 2,752.06 | -6.58% |
| 5. | Jun 30, 2019 | $152.76 | 9.25% | 2,941.76 | 6.89% | |
| 6. | Jul 31, 2019 | $171.01 | 11.95% | 2,980.38 | 1.31% | |
| 7. | Aug 31, 2019 | $175.58 | $0.3767 | 2.89% | 2,926.46 | -1.81% |
| 8. | Sep 30, 2019 | $183.29 | 4.39% | 2,976.74 | 1.72% | |
| 9. | Oct 31, 2019 | $190.77 | 4.08% | 3,037.56 | 2.04% | |
| 10. | Nov 30, 2019 | $194.38 | $0.3767 | 2.09% | 3,140.98 | 3.40% |
| 11. | Dec 31, 2019 | $194.51 | 0.07% | 3,230.78 | 2.86% | |
| 12. | Jan 31, 2020 | $185.66 | -4.55% | 3,225.52 | -0.16% | |
| 13. | Feb 29, 2020 | $172.25 | $0.4467 | -6.98% | 2,954.22 | -8.41% |
| 14. | Mar 31, 2020 | $153.17 | -11.08% | 2,584.59 | -12.51% | |
| 15. | Apr 30, 2020 | $178.79 | 16.73% | 2,912.43 | 12.68% | |
| 16. | May 31, 2020 | $197.95 | $0.4467 | 10.97% | 3,044.31 | 4.53% |
| 17. | Jun 30, 2020 | $192.62 | -2.69% | 3,100.29 | 1.84% | |
| 18. | Jul 31, 2020 | $215.97 | 12.12% | 3,271.12 | 5.51% | |
| 19. | Aug 31, 2020 | $223.68 | $0.4467 | 3.78% | 3,500.31 | 7.01% |
| 20. | Sep 30, 2020 | $232.25 | 3.83% | 3,363.00 | -3.92% | |
| 21. | Oct 31, 2020 | $229.33 | -1.26% | 3,269.96 | -2.77% | |
| 22. | Nov 30, 2020 | $249.21 | $0.4467 | 8.86% | 3,621.63 | 10.75% |
| 23. | Dec 31, 2020 | $244.97 | -1.70% | 3,756.07 | 3.71% | |
| 24. | Jan 31, 2021 | $230.60 | -5.87% | 3,714.24 | -1.11% | |
| 25. | Feb 28, 2021 | $226.78 | $0.55 | -1.42% | 3,811.15 | 2.61% |
| 26. | Mar 31, 2021 | $246.00 | 8.48% | 3,972.89 | 4.24% | |
| 27. | Apr 30, 2021 | $273.87 | 11.33% | 4,181.17 | 5.24% | |
| 28. | May 31, 2021 | $283.53 | $0.55 | 3.73% | 4,204.11 | 0.55% |
| 29. | Jun 30, 2021 | $272.45 | -3.91% | 4,297.50 | 2.22% | |
| 30. | Jul 31, 2021 | $291.03 | 6.82% | 4,395.26 | 2.27% | |
| 31. | Aug 31, 2021 | $303.67 | $0.55 | 4.53% | 4,522.68 | 2.90% |
| 32. | Sep 30, 2021 | $279.73 | -7.88% | 4,307.54 | -4.76% | |
| 33. | Oct 31, 2021 | $316.61 | 13.18% | 4,605.38 | 6.91% | |
| 34. | Nov 30, 2021 | $331.24 | $0.55 | 4.79% | 4,567.00 | -0.83% |
| 35. | Dec 31, 2021 | $352.16 | 6.32% | 4,766.18 | 4.36% | |
| 36. | Jan 31, 2022 | $286.51 | -18.64% | 4,515.55 | -5.26% | |
| 37. | Feb 28, 2022 | $263.13 | $0.60 | -7.95% | 4,373.94 | -3.14% |
| 38. | Mar 31, 2022 | $249.62 | -5.13% | 4,530.41 | 3.58% | |
| 39. | Apr 30, 2022 | $274.96 | 10.15% | 4,131.93 | -8.80% | |
| 40. | May 31, 2022 | $268.04 | $0.60 | -2.30% | 4,132.15 | 0.01% |
| 41. | Jun 30, 2022 | $223.91 | -16.46% | 3,785.38 | -8.39% | |
| 42. | Jul 31, 2022 | $241.94 | 8.05% | 4,130.29 | 9.11% | |
| 43. | Aug 31, 2022 | $232.10 | $0.60 | -3.82% | 3,955.00 | -4.24% |
| 44. | Sep 30, 2022 | $204.75 | -11.78% | 3,585.62 | -9.34% | |
| 45. | Oct 31, 2022 | $225.03 | 9.90% | 3,871.98 | 7.99% | |
| 46. | Nov 30, 2022 | $249.18 | $0.60 | 11.00% | 4,080.11 | 5.38% |
| 47. | Dec 31, 2022 | $237.33 | -4.76% | 3,839.50 | -5.90% | |
| 48. | Jan 31, 2023 | $236.59 | -0.31% | 4,076.60 | 6.18% | |
| 49. | Feb 28, 2023 | $221.35 | $0.61 | -6.18% | 3,970.15 | -2.61% |
| 50. | Mar 31, 2023 | $224.77 | 1.55% | 4,109.31 | 3.51% | |
| 51. | Apr 30, 2023 | $237.54 | 5.68% | 4,169.48 | 1.46% | |
| 52. | May 31, 2023 | $227.78 | $0.61 | -3.85% | 4,179.83 | 0.25% |
| 53. | Jun 30, 2023 | $265.52 | 16.57% | 4,376.86 | 4.71% | |
| 54. | Jul 31, 2023 | $276.50 | 4.14% | 4,588.96 | 4.85% | |
| 55. | Aug 31, 2023 | $271.72 | $0.61 | -1.51% | 4,507.66 | -1.77% |
| 56. | Sep 30, 2023 | $255.05 | -6.13% | 4,288.05 | -4.87% | |
| 57. | Oct 31, 2023 | $238.21 | -6.60% | 4,193.80 | -2.20% | |
| 58. | Nov 30, 2023 | $278.80 | $0.61 | 17.30% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $311.90 | 11.87% | 4,769.83 | 4.42% | |
| Average (R): | 1.77% | 1.11% | ||||
| Standard deviation: | 8.16% | 5.31% | ||||
Show all
1 Data in US$ 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, 2019 | 3.04% | 2.97% | 1.62 | 3.49 | 2.37 |
| 2. | Mar 31, 2019 | -0.57% | 1.79% | 5.48 | 0.47 | -1.61 |
| 3. | Apr 30, 2019 | 5.60% | 3.93% | 14.71 | 7.98 | 10.84 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | 17.30% | 8.92% | 241.19 | 61.03 | 121.32 |
| 59. | Dec 31, 2023 | 11.87% | 4.42% | 102.15 | 11.00 | 33.53 |
| Total (Σ): | 3,860.35 | 1,634.30 | 1,858.19 | |||
| 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, 2019 | 3.04% | 2.97% | 1.62 | 3.49 | 2.37 |
| 2. | Mar 31, 2019 | -0.57% | 1.79% | 5.48 | 0.47 | -1.61 |
| 3. | Apr 30, 2019 | 5.60% | 3.93% | 14.71 | 7.98 | 10.84 |
| 4. | May 31, 2019 | -7.53% | -6.58% | 86.37 | 59.04 | 71.41 |
| 5. | Jun 30, 2019 | 9.25% | 6.89% | 56.09 | 33.49 | 43.34 |
| 6. | Jul 31, 2019 | 11.95% | 1.31% | 103.66 | 0.04 | 2.11 |
| 7. | Aug 31, 2019 | 2.89% | -1.81% | 1.27 | 8.50 | -3.29 |
| 8. | Sep 30, 2019 | 4.39% | 1.72% | 6.90 | 0.37 | 1.61 |
| 9. | Oct 31, 2019 | 4.08% | 2.04% | 5.36 | 0.88 | 2.17 |
| 10. | Nov 30, 2019 | 2.09% | 3.40% | 0.11 | 5.28 | 0.75 |
| 11. | Dec 31, 2019 | 0.07% | 2.86% | 2.88 | 3.07 | -2.98 |
| 12. | Jan 31, 2020 | -4.55% | -0.16% | 39.88 | 1.61 | 8.01 |
| 13. | Feb 29, 2020 | -6.98% | -8.41% | 76.52 | 90.57 | 83.25 |
| 14. | Mar 31, 2020 | -11.08% | -12.51% | 164.92 | 185.44 | 174.88 |
| 15. | Apr 30, 2020 | 16.73% | 12.68% | 223.84 | 134.06 | 173.23 |
| 16. | May 31, 2020 | 10.97% | 4.53% | 84.66 | 11.71 | 31.49 |
| 17. | Jun 30, 2020 | -2.69% | 1.84% | 19.87 | 0.54 | -3.27 |
| 18. | Jul 31, 2020 | 12.12% | 5.51% | 107.27 | 19.40 | 45.62 |
| 19. | Aug 31, 2020 | 3.78% | 7.01% | 4.05 | 34.82 | 11.87 |
| 20. | Sep 30, 2020 | 3.83% | -3.92% | 4.27 | 25.29 | -10.39 |
| 21. | Oct 31, 2020 | -1.26% | -2.77% | 9.14 | 15.00 | 11.70 |
| 22. | Nov 30, 2020 | 8.86% | 10.75% | 50.39 | 93.10 | 68.49 |
| 23. | Dec 31, 2020 | -1.70% | 3.71% | 12.02 | 6.79 | -9.04 |
| 24. | Jan 31, 2021 | -5.87% | -1.11% | 58.24 | 4.93 | 16.94 |
| 25. | Feb 28, 2021 | -1.42% | 2.61% | 10.13 | 2.26 | -4.79 |
| 26. | Mar 31, 2021 | 8.48% | 4.24% | 45.02 | 9.85 | 21.06 |
| 27. | Apr 30, 2021 | 11.33% | 5.24% | 91.47 | 17.11 | 39.56 |
| 28. | May 31, 2021 | 3.73% | 0.55% | 3.85 | 0.31 | -1.09 |
| 29. | Jun 30, 2021 | -3.91% | 2.22% | 32.18 | 1.24 | -6.33 |
| 30. | Jul 31, 2021 | 6.82% | 2.27% | 25.55 | 1.37 | 5.91 |
| 31. | Aug 31, 2021 | 4.53% | 2.90% | 7.66 | 3.22 | 4.96 |
| 32. | Sep 30, 2021 | -7.88% | -4.76% | 93.10 | 34.37 | 56.57 |
| 33. | Oct 31, 2021 | 13.18% | 6.91% | 130.39 | 33.74 | 66.33 |
| 34. | Nov 30, 2021 | 4.79% | -0.83% | 9.18 | 3.76 | -5.87 |
| 35. | Dec 31, 2021 | 6.32% | 4.36% | 20.71 | 10.60 | 14.81 |
| 36. | Jan 31, 2022 | -18.64% | -5.26% | 416.46 | 40.51 | 129.88 |
| 37. | Feb 28, 2022 | -7.95% | -3.14% | 94.40 | 17.99 | 41.21 |
| 38. | Mar 31, 2022 | -5.13% | 3.58% | 47.60 | 6.11 | -17.05 |
| 39. | Apr 30, 2022 | 10.15% | -8.80% | 70.33 | 98.04 | -83.04 |
| 40. | May 31, 2022 | -2.30% | 0.01% | 16.51 | 1.21 | 4.47 |
| 41. | Jun 30, 2022 | -16.46% | -8.39% | 332.30 | 90.21 | 173.14 |
| 42. | Jul 31, 2022 | 8.05% | 9.11% | 39.53 | 64.09 | 50.33 |
| 43. | Aug 31, 2022 | -3.82% | -4.24% | 31.19 | 28.62 | 29.88 |
| 44. | Sep 30, 2022 | -11.78% | -9.34% | 183.57 | 109.11 | 141.52 |
| 45. | Oct 31, 2022 | 9.90% | 7.99% | 66.25 | 47.34 | 56.00 |
| 46. | Nov 30, 2022 | 11.00% | 5.38% | 85.25 | 18.23 | 39.42 |
| 47. | Dec 31, 2022 | -4.76% | -5.90% | 42.52 | 49.04 | 45.67 |
| 48. | Jan 31, 2023 | -0.31% | 6.18% | 4.31 | 25.70 | -10.53 |
| 49. | Feb 28, 2023 | -6.18% | -2.61% | 63.19 | 13.82 | 29.55 |
| 50. | Mar 31, 2023 | 1.55% | 3.51% | 0.05 | 5.76 | -0.53 |
| 51. | Apr 30, 2023 | 5.68% | 1.46% | 15.34 | 0.13 | 1.40 |
| 52. | May 31, 2023 | -3.85% | 0.25% | 31.55 | 0.74 | 4.82 |
| 53. | Jun 30, 2023 | 16.57% | 4.71% | 219.14 | 13.02 | 53.41 |
| 54. | Jul 31, 2023 | 4.14% | 4.85% | 5.62 | 13.99 | 8.86 |
| 55. | Aug 31, 2023 | -1.51% | -1.77% | 10.72 | 8.28 | 9.42 |
| 56. | Sep 30, 2023 | -6.13% | -4.87% | 62.41 | 35.73 | 47.23 |
| 57. | Oct 31, 2023 | -6.60% | -2.20% | 70.02 | 10.92 | 27.65 |
| 58. | Nov 30, 2023 | 17.30% | 8.92% | 241.19 | 61.03 | 121.32 |
| 59. | Dec 31, 2023 | 11.87% | 4.42% | 102.15 | 11.00 | 33.53 |
| Total (Σ): | 3,860.35 | 1,634.30 | 1,858.19 | |||
Show all
VarianceSHW = Σ(RSHW,t–RSHW)2 ÷ (59 – 1)
= 3,860.35 ÷ (59 – 1)
= 66.56
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceSHW, S&P 500 = Σ(RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,858.19 ÷ (59 – 1)
= 32.04
Systematic Risk (β) Estimation
| VarianceSHW | 66.56 |
| VarianceS&P 500 | 28.18 |
| CovarianceSHW, S&P 500 | 32.04 |
| Correlation coefficientSHW, S&P 5001 | 0.74 |
| βSHW2 | 1.14 |
| αSHW3 | 0.51% |
Calculations
1 Correlation coefficientSHW, S&P 500
= CovarianceSHW, S&P 500 ÷ (Standard deviationSHW × Standard deviationS&P 500)
= 32.04 ÷ (8.16% × 5.31%)
= 0.74
2 βSHW
= CovarianceSHW, S&P 500 ÷ VarianceS&P 500
= 32.04 ÷ 28.18
= 1.14
3 αSHW
= AverageSHW – βSHW × AverageS&P 500
= 1.77% – 1.14 × 1.11%
= 0.51%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.79% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk (β) of Sherwin-Williams Co. common stock | βSHW | 1.14 |
| Expected rate of return on Sherwin-Williams Co. common stock3 | E(RSHW) | 15.03% |
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]
= 4.79% + 1.14 [13.79% – 4.79%]
= 15.03%