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. (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, 2017 | $101.27 | 2,278.87 | ||||
1. | Feb 28, 2017 | $102.85 | $0.2833 | 1.84% | 2,363.64 | 3.72% |
2. | Mar 31, 2017 | $103.40 | 0.53% | 2,362.72 | -0.04% | |
3. | Apr 30, 2017 | $111.56 | 7.89% | 2,384.20 | 0.91% | |
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58. | Nov 30, 2021 | $331.24 | $0.55 | 4.79% | 4,567.00 | -0.83% |
59. | Dec 31, 2021 | $352.16 | 6.32% | 4,766.18 | 4.36% | |
Average (R): | 2.41% | 1.36% | ||||
Standard deviation: | 6.35% | 4.48% |
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, 2017 | $101.27 | 2,278.87 | ||||
1. | Feb 28, 2017 | $102.85 | $0.2833 | 1.84% | 2,363.64 | 3.72% |
2. | Mar 31, 2017 | $103.40 | 0.53% | 2,362.72 | -0.04% | |
3. | Apr 30, 2017 | $111.56 | 7.89% | 2,384.20 | 0.91% | |
4. | May 31, 2017 | $110.59 | $0.2833 | -0.62% | 2,411.80 | 1.16% |
5. | Jun 30, 2017 | $116.99 | 5.79% | 2,423.41 | 0.48% | |
6. | Jul 31, 2017 | $112.42 | -3.91% | 2,470.30 | 1.93% | |
7. | Aug 31, 2017 | $113.09 | $0.2833 | 0.85% | 2,471.65 | 0.05% |
8. | Sep 30, 2017 | $119.35 | 5.54% | 2,519.36 | 1.93% | |
9. | Oct 31, 2017 | $131.72 | 10.36% | 2,575.26 | 2.22% | |
10. | Nov 30, 2017 | $133.14 | $0.2833 | 1.29% | 2,647.58 | 2.81% |
11. | Dec 31, 2017 | $136.68 | 2.66% | 2,673.61 | 0.98% | |
12. | Jan 31, 2018 | $139.04 | 1.73% | 2,823.81 | 5.62% | |
13. | Feb 28, 2018 | $133.86 | $0.2867 | -3.52% | 2,713.83 | -3.89% |
14. | Mar 31, 2018 | $130.71 | -2.35% | 2,640.87 | -2.69% | |
15. | Apr 30, 2018 | $122.55 | -6.24% | 2,648.05 | 0.27% | |
16. | May 31, 2018 | $126.42 | $0.2867 | 3.39% | 2,705.27 | 2.16% |
17. | Jun 30, 2018 | $135.86 | 7.47% | 2,718.37 | 0.48% | |
18. | Jul 31, 2018 | $146.91 | 8.13% | 2,816.29 | 3.60% | |
19. | Aug 31, 2018 | $151.86 | $0.2867 | 3.56% | 2,901.52 | 3.03% |
20. | Sep 30, 2018 | $151.74 | -0.08% | 2,913.98 | 0.43% | |
21. | Oct 31, 2018 | $131.16 | -13.56% | 2,711.74 | -6.94% | |
22. | Nov 30, 2018 | $141.36 | $0.2867 | 8.00% | 2,760.17 | 1.79% |
23. | Dec 31, 2018 | $131.15 | -7.22% | 2,506.85 | -9.18% | |
24. | Jan 31, 2019 | $140.51 | 7.14% | 2,704.10 | 7.87% | |
25. | Feb 28, 2019 | $144.40 | $0.3767 | 3.04% | 2,784.49 | 2.97% |
26. | Mar 31, 2019 | $143.57 | -0.57% | 2,834.40 | 1.79% | |
27. | Apr 30, 2019 | $151.61 | 5.60% | 2,945.83 | 3.93% | |
28. | May 31, 2019 | $139.82 | $0.3767 | -7.53% | 2,752.06 | -6.58% |
29. | Jun 30, 2019 | $152.76 | 9.25% | 2,941.76 | 6.89% | |
30. | Jul 31, 2019 | $171.01 | 11.95% | 2,980.38 | 1.31% | |
31. | Aug 31, 2019 | $175.58 | $0.3767 | 2.89% | 2,926.46 | -1.81% |
32. | Sep 30, 2019 | $183.29 | 4.39% | 2,976.74 | 1.72% | |
33. | Oct 31, 2019 | $190.77 | 4.08% | 3,037.56 | 2.04% | |
34. | Nov 30, 2019 | $194.38 | $0.3767 | 2.09% | 3,140.98 | 3.40% |
35. | Dec 31, 2019 | $194.51 | 0.07% | 3,230.78 | 2.86% | |
36. | Jan 31, 2020 | $185.66 | -4.55% | 3,225.52 | -0.16% | |
37. | Feb 29, 2020 | $172.25 | $0.4467 | -6.98% | 2,954.22 | -8.41% |
38. | Mar 31, 2020 | $153.17 | -11.08% | 2,584.59 | -12.51% | |
39. | Apr 30, 2020 | $178.79 | 16.73% | 2,912.43 | 12.68% | |
40. | May 31, 2020 | $197.95 | $0.4467 | 10.97% | 3,044.31 | 4.53% |
41. | Jun 30, 2020 | $192.62 | -2.69% | 3,100.29 | 1.84% | |
42. | Jul 31, 2020 | $215.97 | 12.12% | 3,271.12 | 5.51% | |
43. | Aug 31, 2020 | $223.68 | $0.4467 | 3.78% | 3,500.31 | 7.01% |
44. | Sep 30, 2020 | $232.25 | 3.83% | 3,363.00 | -3.92% | |
45. | Oct 31, 2020 | $229.33 | -1.26% | 3,269.96 | -2.77% | |
46. | Nov 30, 2020 | $249.21 | $0.4467 | 8.86% | 3,621.63 | 10.75% |
47. | Dec 31, 2020 | $244.97 | -1.70% | 3,756.07 | 3.71% | |
48. | Jan 31, 2021 | $230.60 | -5.87% | 3,714.24 | -1.11% | |
49. | Feb 28, 2021 | $226.78 | $0.55 | -1.42% | 3,811.15 | 2.61% |
50. | Mar 31, 2021 | $246.00 | 8.48% | 3,972.89 | 4.24% | |
51. | Apr 30, 2021 | $273.87 | 11.33% | 4,181.17 | 5.24% | |
52. | May 31, 2021 | $283.53 | $0.55 | 3.73% | 4,204.11 | 0.55% |
53. | Jun 30, 2021 | $272.45 | -3.91% | 4,297.50 | 2.22% | |
54. | Jul 31, 2021 | $291.03 | 6.82% | 4,395.26 | 2.27% | |
55. | Aug 31, 2021 | $303.67 | $0.55 | 4.53% | 4,522.68 | 2.90% |
56. | Sep 30, 2021 | $279.73 | -7.88% | 4,307.54 | -4.76% | |
57. | Oct 31, 2021 | $316.61 | 13.18% | 4,605.38 | 6.91% | |
58. | Nov 30, 2021 | $331.24 | $0.55 | 4.79% | 4,567.00 | -0.83% |
59. | Dec 31, 2021 | $352.16 | 6.32% | 4,766.18 | 4.36% | |
Average (R): | 2.41% | 1.36% | ||||
Standard deviation: | 6.35% | 4.48% |
Show all
1 Data in US$ 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
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, 2017 | 1.84% | 3.72% | 0.32 | 5.58 | -1.34 |
2. | Mar 31, 2017 | 0.53% | -0.04% | 3.51 | 1.95 | 2.62 |
3. | Apr 30, 2017 | 7.89% | 0.91% | 30.07 | 0.20 | -2.46 |
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58. | Nov 30, 2021 | 4.79% | -0.83% | 5.70 | 4.80 | -5.23 |
59. | Dec 31, 2021 | 6.32% | 4.36% | 15.27 | 9.02 | 11.74 |
Total (Σ): | 2,342.23 | 1,164.17 | 1,240.51 |
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, 2017 | 1.84% | 3.72% | 0.32 | 5.58 | -1.34 |
2. | Mar 31, 2017 | 0.53% | -0.04% | 3.51 | 1.95 | 2.62 |
3. | Apr 30, 2017 | 7.89% | 0.91% | 30.07 | 0.20 | -2.46 |
4. | May 31, 2017 | -0.62% | 1.16% | 9.14 | 0.04 | 0.61 |
5. | Jun 30, 2017 | 5.79% | 0.48% | 11.42 | 0.77 | -2.96 |
6. | Jul 31, 2017 | -3.91% | 1.93% | 39.87 | 0.33 | -3.64 |
7. | Aug 31, 2017 | 0.85% | 0.05% | 2.43 | 1.70 | 2.03 |
8. | Sep 30, 2017 | 5.54% | 1.93% | 9.78 | 0.33 | 1.79 |
9. | Oct 31, 2017 | 10.36% | 2.22% | 63.31 | 0.74 | 6.85 |
10. | Nov 30, 2017 | 1.29% | 2.81% | 1.24 | 2.10 | -1.62 |
11. | Dec 31, 2017 | 2.66% | 0.98% | 0.06 | 0.14 | -0.09 |
12. | Jan 31, 2018 | 1.73% | 5.62% | 0.46 | 18.15 | -2.90 |
13. | Feb 28, 2018 | -3.52% | -3.89% | 35.13 | 27.59 | 31.13 |
14. | Mar 31, 2018 | -2.35% | -2.69% | 22.67 | 16.37 | 19.26 |
15. | Apr 30, 2018 | -6.24% | 0.27% | 74.83 | 1.18 | 9.39 |
16. | May 31, 2018 | 3.39% | 2.16% | 0.97 | 0.64 | 0.79 |
17. | Jun 30, 2018 | 7.47% | 0.48% | 25.60 | 0.76 | -4.42 |
18. | Jul 31, 2018 | 8.13% | 3.60% | 32.78 | 5.04 | 12.85 |
19. | Aug 31, 2018 | 3.56% | 3.03% | 1.34 | 2.78 | 1.93 |
20. | Sep 30, 2018 | -0.08% | 0.43% | 6.18 | 0.86 | 2.31 |
21. | Oct 31, 2018 | -13.56% | -6.94% | 255.05 | 68.86 | 132.53 |
22. | Nov 30, 2018 | 8.00% | 1.79% | 31.22 | 0.18 | 2.39 |
23. | Dec 31, 2018 | -7.22% | -9.18% | 92.74 | 111.00 | 101.46 |
24. | Jan 31, 2019 | 7.14% | 7.87% | 22.37 | 42.39 | 30.79 |
25. | Feb 28, 2019 | 3.04% | 2.97% | 0.40 | 2.61 | 1.02 |
26. | Mar 31, 2019 | -0.57% | 1.79% | 8.90 | 0.19 | -1.30 |
27. | Apr 30, 2019 | 5.60% | 3.93% | 10.19 | 6.62 | 8.22 |
28. | May 31, 2019 | -7.53% | -6.58% | 98.72 | 62.97 | 78.85 |
29. | Jun 30, 2019 | 9.25% | 6.89% | 46.88 | 30.64 | 37.90 |
30. | Jul 31, 2019 | 11.95% | 1.31% | 91.00 | 0.00 | -0.43 |
31. | Aug 31, 2019 | 2.89% | -1.81% | 0.24 | 10.03 | -1.54 |
32. | Sep 30, 2019 | 4.39% | 1.72% | 3.93 | 0.13 | 0.71 |
33. | Oct 31, 2019 | 4.08% | 2.04% | 2.80 | 0.47 | 1.15 |
34. | Nov 30, 2019 | 2.09% | 3.40% | 0.10 | 4.19 | -0.65 |
35. | Dec 31, 2019 | 0.07% | 2.86% | 5.48 | 2.25 | -3.51 |
36. | Jan 31, 2020 | -4.55% | -0.16% | 48.41 | 2.31 | 10.58 |
37. | Feb 29, 2020 | -6.98% | -8.41% | 88.17 | 95.43 | 91.73 |
38. | Mar 31, 2020 | -11.08% | -12.51% | 181.83 | 192.37 | 187.03 |
39. | Apr 30, 2020 | 16.73% | 12.68% | 205.03 | 128.29 | 162.18 |
40. | May 31, 2020 | 10.97% | 4.53% | 73.25 | 10.05 | 27.13 |
41. | Jun 30, 2020 | -2.69% | 1.84% | 26.01 | 0.23 | -2.45 |
42. | Jul 31, 2020 | 12.12% | 5.51% | 94.37 | 17.24 | 40.34 |
43. | Aug 31, 2020 | 3.78% | 7.01% | 1.87 | 31.91 | 7.73 |
44. | Sep 30, 2020 | 3.83% | -3.92% | 2.03 | 27.89 | -7.52 |
45. | Oct 31, 2020 | -1.26% | -2.77% | 13.43 | 17.01 | 15.12 |
46. | Nov 30, 2020 | 8.86% | 10.75% | 41.68 | 88.30 | 60.66 |
47. | Dec 31, 2020 | -1.70% | 3.71% | 16.88 | 5.54 | -9.67 |
48. | Jan 31, 2021 | -5.87% | -1.11% | 68.45 | 6.11 | 20.45 |
49. | Feb 28, 2021 | -1.42% | 2.61% | 14.64 | 1.57 | -4.79 |
50. | Mar 31, 2021 | 8.48% | 4.24% | 36.81 | 8.33 | 17.51 |
51. | Apr 30, 2021 | 11.33% | 5.24% | 79.59 | 15.09 | 34.66 |
52. | May 31, 2021 | 3.73% | 0.55% | 1.74 | 0.65 | -1.07 |
53. | Jun 30, 2021 | -3.91% | 2.22% | 39.89 | 0.75 | -5.45 |
54. | Jul 31, 2021 | 6.82% | 2.27% | 19.46 | 0.84 | 4.05 |
55. | Aug 31, 2021 | 4.53% | 2.90% | 4.51 | 2.38 | 3.27 |
56. | Sep 30, 2021 | -7.88% | -4.76% | 105.91 | 37.39 | 62.93 |
57. | Oct 31, 2021 | 13.18% | 6.91% | 116.13 | 30.87 | 59.88 |
58. | Nov 30, 2021 | 4.79% | -0.83% | 5.70 | 4.80 | -5.23 |
59. | Dec 31, 2021 | 6.32% | 4.36% | 15.27 | 9.02 | 11.74 |
Total (Σ): | 2,342.23 | 1,164.17 | 1,240.51 |
Show all
VarianceSHW = Σ(RSHW,t–RSHW)2 ÷ (59 – 1)
= 2,342.23 ÷ (59 – 1)
= 40.38
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
CovarianceSHW, S&P 500 = Σ(RSHW,t–RSHW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,240.51 ÷ (59 – 1)
= 21.39
Systematic Risk (β) Estimation
VarianceSHW | 40.38 |
VarianceS&P 500 | 20.07 |
CovarianceSHW, S&P 500 | 21.39 |
Correlation coefficientSHW, S&P 5001 | 0.75 |
βSHW2 | 1.07 |
αSHW3 | 0.96% |
Calculations
1 Correlation coefficientSHW, S&P 500
= CovarianceSHW, S&P 500 ÷ (Standard deviationSHW × Standard deviationS&P 500)
= 21.39 ÷ (6.35% × 4.48%)
= 0.75
2 βSHW
= CovarianceSHW, S&P 500 ÷ VarianceS&P 500
= 21.39 ÷ 20.07
= 1.07
3 αSHW
= AverageSHW – βSHW × AverageS&P 500
= 2.41% – 1.07 × 1.36%
= 0.96%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.79% |
Expected rate of return on market portfolio2 | E(RM) | 13.48% |
Systematic risk (β) of Sherwin-Williams Co. common stock | βSHW | 1.07 |
Expected rate of return on Sherwin-Williams Co. common stock3 | E(RSHW) | 14.04% |
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% + 1.07 [13.48% – 4.79%]
= 14.04%