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 Cintas Corp. common stock.
Rates of Return
Cintas Corp., monthly rates of return
| Cintas Corp. (CTAS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCTAS,t1 | DividendCTAS,t1 | RCTAS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jun 30, 2018 | $46.27 | 2,718.37 | ||||
| 1. | Jul 31, 2018 | $51.12 | 10.48% | 2,816.29 | 3.60% | |
| 2. | Aug 31, 2018 | $53.34 | 4.34% | 2,901.52 | 3.03% | |
| 3. | Sep 30, 2018 | $49.45 | -7.29% | 2,913.98 | 0.43% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Apr 30, 2024 | $164.59 | -4.17% | 5,035.69 | -4.16% | |
| 71. | May 31, 2024 | $169.49 | $0.338 | 3.18% | 5,277.51 | 4.80% |
| Average (R): | 2.30% | 1.08% | ||||
| Standard deviation: | 8.40% | 5.24% | ||||
| Cintas Corp. (CTAS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCTAS,t1 | DividendCTAS,t1 | RCTAS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jun 30, 2018 | $46.27 | 2,718.37 | ||||
| 1. | Jul 31, 2018 | $51.12 | 10.48% | 2,816.29 | 3.60% | |
| 2. | Aug 31, 2018 | $53.34 | 4.34% | 2,901.52 | 3.03% | |
| 3. | Sep 30, 2018 | $49.45 | -7.29% | 2,913.98 | 0.43% | |
| 4. | Oct 31, 2018 | $45.47 | -8.05% | 2,711.74 | -6.94% | |
| 5. | Nov 30, 2018 | $46.85 | $0.513 | 4.16% | 2,760.17 | 1.79% |
| 6. | Dec 31, 2018 | $42.00 | -10.35% | 2,506.85 | -9.18% | |
| 7. | Jan 31, 2019 | $46.88 | 11.62% | 2,704.10 | 7.87% | |
| 8. | Feb 28, 2019 | $51.65 | 10.17% | 2,784.49 | 2.97% | |
| 9. | Mar 31, 2019 | $50.53 | -2.17% | 2,834.40 | 1.79% | |
| 10. | Apr 30, 2019 | $54.29 | 7.44% | 2,945.83 | 3.93% | |
| 11. | May 31, 2019 | $55.46 | 2.16% | 2,752.06 | -6.58% | |
| 12. | Jun 30, 2019 | $59.32 | 6.96% | 2,941.76 | 6.89% | |
| 13. | Jul 31, 2019 | $65.11 | 9.76% | 2,980.38 | 1.31% | |
| 14. | Aug 31, 2019 | $65.95 | 1.29% | 2,926.46 | -1.81% | |
| 15. | Sep 30, 2019 | $67.03 | 1.64% | 2,976.74 | 1.72% | |
| 16. | Oct 31, 2019 | $67.17 | 0.21% | 3,037.56 | 2.04% | |
| 17. | Nov 30, 2019 | $64.27 | $0.638 | -3.37% | 3,140.98 | 3.40% |
| 18. | Dec 31, 2019 | $67.27 | 4.67% | 3,230.78 | 2.86% | |
| 19. | Jan 31, 2020 | $69.74 | 3.67% | 3,225.52 | -0.16% | |
| 20. | Feb 29, 2020 | $66.69 | -4.37% | 2,954.22 | -8.41% | |
| 21. | Mar 31, 2020 | $43.31 | -35.06% | 2,584.59 | -12.51% | |
| 22. | Apr 30, 2020 | $55.46 | 28.05% | 2,912.43 | 12.68% | |
| 23. | May 31, 2020 | $61.99 | 11.77% | 3,044.31 | 4.53% | |
| 24. | Jun 30, 2020 | $66.59 | 7.42% | 3,100.29 | 1.84% | |
| 25. | Jul 31, 2020 | $75.47 | 13.34% | 3,271.12 | 5.51% | |
| 26. | Aug 31, 2020 | $83.31 | 10.39% | 3,500.31 | 7.01% | |
| 27. | Sep 30, 2020 | $83.21 | -0.12% | 3,363.00 | -3.92% | |
| 28. | Oct 31, 2020 | $78.64 | -5.49% | 3,269.96 | -2.77% | |
| 29. | Nov 30, 2020 | $88.83 | $0.878 | 14.07% | 3,621.63 | 10.75% |
| 30. | Dec 31, 2020 | $88.37 | -0.52% | 3,756.07 | 3.71% | |
| 31. | Jan 31, 2021 | $79.53 | -10.00% | 3,714.24 | -1.11% | |
| 32. | Feb 28, 2021 | $81.09 | $0.188 | 2.20% | 3,811.15 | 2.61% |
| 33. | Mar 31, 2021 | $85.33 | 5.23% | 3,972.89 | 4.24% | |
| 34. | Apr 30, 2021 | $86.29 | 1.13% | 4,181.17 | 5.24% | |
| 35. | May 31, 2021 | $88.39 | $0.188 | 2.65% | 4,204.11 | 0.55% |
| 36. | Jun 30, 2021 | $95.50 | 8.04% | 4,297.50 | 2.22% | |
| 37. | Jul 31, 2021 | $98.55 | 3.19% | 4,395.26 | 2.27% | |
| 38. | Aug 31, 2021 | $98.94 | $0.238 | 0.64% | 4,522.68 | 2.90% |
| 39. | Sep 30, 2021 | $95.17 | -3.81% | 4,307.54 | -4.76% | |
| 40. | Oct 31, 2021 | $108.28 | 13.78% | 4,605.38 | 6.91% | |
| 41. | Nov 30, 2021 | $105.55 | $0.238 | -2.30% | 4,567.00 | -0.83% |
| 42. | Dec 31, 2021 | $110.79 | 4.96% | 4,766.18 | 4.36% | |
| 43. | Jan 31, 2022 | $97.88 | -11.65% | 4,515.55 | -5.26% | |
| 44. | Feb 28, 2022 | $93.83 | $0.238 | -3.89% | 4,373.94 | -3.14% |
| 45. | Mar 31, 2022 | $106.35 | 13.34% | 4,530.41 | 3.58% | |
| 46. | Apr 30, 2022 | $99.32 | -6.61% | 4,131.93 | -8.80% | |
| 47. | May 31, 2022 | $99.58 | $0.238 | 0.50% | 4,132.15 | 0.01% |
| 48. | Jun 30, 2022 | $93.38 | -6.23% | 3,785.38 | -8.39% | |
| 49. | Jul 31, 2022 | $106.37 | 13.91% | 4,130.29 | 9.11% | |
| 50. | Aug 31, 2022 | $101.71 | $0.288 | -4.11% | 3,955.00 | -4.24% |
| 51. | Sep 30, 2022 | $97.05 | -4.58% | 3,585.62 | -9.34% | |
| 52. | Oct 31, 2022 | $106.89 | 10.14% | 3,871.98 | 7.99% | |
| 53. | Nov 30, 2022 | $115.45 | $0.288 | 8.28% | 4,080.11 | 5.38% |
| 54. | Dec 31, 2022 | $112.91 | -2.20% | 3,839.50 | -5.90% | |
| 55. | Jan 31, 2023 | $110.94 | -1.74% | 4,076.60 | 6.18% | |
| 56. | Feb 28, 2023 | $109.62 | $0.288 | -0.93% | 3,970.15 | -2.61% |
| 57. | Mar 31, 2023 | $115.67 | 5.52% | 4,109.31 | 3.51% | |
| 58. | Apr 30, 2023 | $113.94 | -1.50% | 4,169.48 | 1.46% | |
| 59. | May 31, 2023 | $118.04 | $0.288 | 3.85% | 4,179.83 | 0.25% |
| 60. | Jun 30, 2023 | $124.27 | 5.28% | 4,376.86 | 4.71% | |
| 61. | Jul 31, 2023 | $125.51 | 1.00% | 4,588.96 | 4.85% | |
| 62. | Aug 31, 2023 | $126.04 | $0.338 | 0.69% | 4,507.66 | -1.77% |
| 63. | Sep 30, 2023 | $120.25 | -4.59% | 4,288.05 | -4.87% | |
| 64. | Oct 31, 2023 | $126.78 | 5.43% | 4,193.80 | -2.20% | |
| 65. | Nov 30, 2023 | $138.31 | $0.338 | 9.36% | 4,567.80 | 8.92% |
| 66. | Dec 31, 2023 | $150.67 | 8.94% | 4,769.83 | 4.42% | |
| 67. | Jan 31, 2024 | $151.14 | 0.31% | 4,845.65 | 1.59% | |
| 68. | Feb 29, 2024 | $157.15 | $0.338 | 4.20% | 5,096.27 | 5.17% |
| 69. | Mar 31, 2024 | $171.76 | 9.30% | 5,254.35 | 3.10% | |
| 70. | Apr 30, 2024 | $164.59 | -4.17% | 5,035.69 | -4.16% | |
| 71. | May 31, 2024 | $169.49 | $0.338 | 3.18% | 5,277.51 | 4.80% |
| Average (R): | 2.30% | 1.08% | ||||
| Standard deviation: | 8.40% | 5.24% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of CTAS during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Cintas Corp., calculation of variance and covariance of returns
| t | Date | RCTAS,t | RS&P 500,t | (RCTAS,t–RCTAS)2 | (RS&P 500,t–RS&P 500)2 | (RCTAS,t–RCTAS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Jul 31, 2018 | 10.48% | 3.60% | 66.89 | 6.39 | 20.67 |
| 2. | Aug 31, 2018 | 4.34% | 3.03% | 4.16 | 3.81 | 3.98 |
| 3. | Sep 30, 2018 | -7.29% | 0.43% | 92.09 | 0.42 | 6.20 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Apr 30, 2024 | -4.17% | -4.16% | 41.96 | 27.42 | 33.92 |
| 71. | May 31, 2024 | 3.18% | 4.80% | 0.77 | 13.89 | 3.28 |
| Total (Σ): | 4,935.48 | 1,923.46 | 2,458.46 | |||
| t | Date | RCTAS,t | RS&P 500,t | (RCTAS,t–RCTAS)2 | (RS&P 500,t–RS&P 500)2 | (RCTAS,t–RCTAS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Jul 31, 2018 | 10.48% | 3.60% | 66.89 | 6.39 | 20.67 |
| 2. | Aug 31, 2018 | 4.34% | 3.03% | 4.16 | 3.81 | 3.98 |
| 3. | Sep 30, 2018 | -7.29% | 0.43% | 92.09 | 0.42 | 6.20 |
| 4. | Oct 31, 2018 | -8.05% | -6.94% | 107.16 | 64.25 | 82.98 |
| 5. | Nov 30, 2018 | 4.16% | 1.79% | 3.46 | 0.51 | 1.32 |
| 6. | Dec 31, 2018 | -10.35% | -9.18% | 160.17 | 105.12 | 129.76 |
| 7. | Jan 31, 2019 | 11.62% | 7.87% | 86.78 | 46.15 | 63.28 |
| 8. | Feb 28, 2019 | 10.17% | 2.97% | 61.96 | 3.60 | 14.94 |
| 9. | Mar 31, 2019 | -2.17% | 1.79% | 20.00 | 0.51 | -3.21 |
| 10. | Apr 30, 2019 | 7.44% | 3.93% | 26.40 | 8.16 | 14.67 |
| 11. | May 31, 2019 | 2.16% | -6.58% | 0.02 | 58.57 | 1.14 |
| 12. | Jun 30, 2019 | 6.96% | 6.89% | 21.68 | 33.85 | 27.09 |
| 13. | Jul 31, 2019 | 9.76% | 1.31% | 55.61 | 0.06 | 1.77 |
| 14. | Aug 31, 2019 | 1.29% | -1.81% | 1.03 | 8.32 | 2.92 |
| 15. | Sep 30, 2019 | 1.64% | 1.72% | 0.44 | 0.41 | -0.43 |
| 16. | Oct 31, 2019 | 0.21% | 2.04% | 4.39 | 0.94 | -2.03 |
| 17. | Nov 30, 2019 | -3.37% | 3.40% | 32.16 | 5.43 | -13.21 |
| 18. | Dec 31, 2019 | 4.67% | 2.86% | 5.59 | 3.18 | 4.22 |
| 19. | Jan 31, 2020 | 3.67% | -0.16% | 1.87 | 1.53 | -1.69 |
| 20. | Feb 29, 2020 | -4.37% | -8.41% | 44.58 | 89.99 | 63.34 |
| 21. | Mar 31, 2020 | -35.06% | -12.51% | 1,395.86 | 184.61 | 507.63 |
| 22. | Apr 30, 2020 | 28.05% | 12.68% | 663.07 | 134.77 | 298.94 |
| 23. | May 31, 2020 | 11.77% | 4.53% | 89.70 | 11.92 | 32.70 |
| 24. | Jun 30, 2020 | 7.42% | 1.84% | 26.18 | 0.58 | 3.91 |
| 25. | Jul 31, 2020 | 13.34% | 5.51% | 121.70 | 19.67 | 48.92 |
| 26. | Aug 31, 2020 | 10.39% | 7.01% | 65.36 | 35.18 | 47.95 |
| 27. | Sep 30, 2020 | -0.12% | -3.92% | 5.87 | 24.98 | 12.11 |
| 28. | Oct 31, 2020 | -5.49% | -2.77% | 60.77 | 14.76 | 29.95 |
| 29. | Nov 30, 2020 | 14.07% | 10.75% | 138.55 | 93.69 | 113.93 |
| 30. | Dec 31, 2020 | -0.52% | 3.71% | 7.96 | 6.95 | -7.44 |
| 31. | Jan 31, 2021 | -10.00% | -1.11% | 151.46 | 4.79 | 26.94 |
| 32. | Feb 28, 2021 | 2.20% | 2.61% | 0.01 | 2.35 | -0.16 |
| 33. | Mar 31, 2021 | 5.23% | 4.24% | 8.56 | 10.04 | 9.27 |
| 34. | Apr 30, 2021 | 1.13% | 5.24% | 1.39 | 17.37 | -4.91 |
| 35. | May 31, 2021 | 2.65% | 0.55% | 0.12 | 0.28 | -0.18 |
| 36. | Jun 30, 2021 | 8.04% | 2.22% | 32.95 | 1.31 | 6.58 |
| 37. | Jul 31, 2021 | 3.19% | 2.27% | 0.79 | 1.44 | 1.07 |
| 38. | Aug 31, 2021 | 0.64% | 2.90% | 2.78 | 3.33 | -3.04 |
| 39. | Sep 30, 2021 | -3.81% | -4.76% | 37.38 | 34.01 | 35.66 |
| 40. | Oct 31, 2021 | 13.78% | 6.91% | 131.60 | 34.10 | 66.99 |
| 41. | Nov 30, 2021 | -2.30% | -0.83% | 21.21 | 3.64 | 8.79 |
| 42. | Dec 31, 2021 | 4.96% | 4.36% | 7.08 | 10.80 | 8.74 |
| 43. | Jan 31, 2022 | -11.65% | -5.26% | 194.77 | 40.12 | 88.40 |
| 44. | Feb 28, 2022 | -3.89% | -3.14% | 38.42 | 17.74 | 26.10 |
| 45. | Mar 31, 2022 | 13.34% | 3.58% | 121.88 | 6.26 | 27.62 |
| 46. | Apr 30, 2022 | -6.61% | -8.80% | 79.45 | 97.44 | 87.99 |
| 47. | May 31, 2022 | 0.50% | 0.01% | 3.25 | 1.14 | 1.93 |
| 48. | Jun 30, 2022 | -6.23% | -8.39% | 72.75 | 89.63 | 80.75 |
| 49. | Jul 31, 2022 | 13.91% | 9.11% | 134.73 | 64.58 | 93.28 |
| 50. | Aug 31, 2022 | -4.11% | -4.24% | 41.14 | 28.29 | 34.12 |
| 51. | Sep 30, 2022 | -4.58% | -9.34% | 47.41 | 108.47 | 71.71 |
| 52. | Oct 31, 2022 | 10.14% | 7.99% | 61.40 | 47.76 | 54.15 |
| 53. | Nov 30, 2022 | 8.28% | 5.38% | 35.69 | 18.49 | 25.69 |
| 54. | Dec 31, 2022 | -2.20% | -5.90% | 20.28 | 48.61 | 31.40 |
| 55. | Jan 31, 2023 | -1.74% | 6.18% | 16.39 | 26.01 | -20.65 |
| 56. | Feb 28, 2023 | -0.93% | -2.61% | 10.46 | 13.59 | 11.92 |
| 57. | Mar 31, 2023 | 5.52% | 3.51% | 10.34 | 5.90 | 7.81 |
| 58. | Apr 30, 2023 | -1.50% | 1.46% | 14.43 | 0.15 | -1.48 |
| 59. | May 31, 2023 | 3.85% | 0.25% | 2.40 | 0.68 | -1.28 |
| 60. | Jun 30, 2023 | 5.28% | 4.71% | 8.85 | 13.24 | 10.82 |
| 61. | Jul 31, 2023 | 1.00% | 4.85% | 1.70 | 14.22 | -4.92 |
| 62. | Aug 31, 2023 | 0.69% | -1.77% | 2.60 | 8.10 | 4.59 |
| 63. | Sep 30, 2023 | -4.59% | -4.87% | 47.57 | 35.37 | 41.02 |
| 64. | Oct 31, 2023 | 5.43% | -2.20% | 9.78 | 10.71 | -10.23 |
| 65. | Nov 30, 2023 | 9.36% | 8.92% | 49.81 | 61.51 | 55.35 |
| 66. | Dec 31, 2023 | 8.94% | 4.42% | 44.00 | 11.21 | 22.20 |
| 67. | Jan 31, 2024 | 0.31% | 1.59% | 3.97 | 0.26 | -1.02 |
| 68. | Feb 29, 2024 | 4.20% | 5.17% | 3.60 | 16.78 | 7.77 |
| 69. | Mar 31, 2024 | 9.30% | 3.10% | 48.91 | 4.11 | 14.17 |
| 70. | Apr 30, 2024 | -4.17% | -4.16% | 41.96 | 27.42 | 33.92 |
| 71. | May 31, 2024 | 3.18% | 4.80% | 0.77 | 13.89 | 3.28 |
| Total (Σ): | 4,935.48 | 1,923.46 | 2,458.46 | |||
Show all
VarianceCTAS = Σ(RCTAS,t–RCTAS)2 ÷ (71 – 1)
= 4,935.48 ÷ (71 – 1)
= 70.51
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,923.46 ÷ (71 – 1)
= 27.48
CovarianceCTAS, S&P 500 = Σ(RCTAS,t–RCTAS)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,458.46 ÷ (71 – 1)
= 35.12
Systematic Risk (β) Estimation
| VarianceCTAS | 70.51 |
| VarianceS&P 500 | 27.48 |
| CovarianceCTAS, S&P 500 | 35.12 |
| Correlation coefficientCTAS, S&P 5001 | 0.80 |
| βCTAS2 | 1.28 |
| αCTAS3 | 0.93% |
Calculations
1 Correlation coefficientCTAS, S&P 500
= CovarianceCTAS, S&P 500 ÷ (Standard deviationCTAS × Standard deviationS&P 500)
= 35.12 ÷ (8.40% × 5.24%)
= 0.80
2 βCTAS
= CovarianceCTAS, S&P 500 ÷ VarianceS&P 500
= 35.12 ÷ 27.48
= 1.28
3 αCTAS
= AverageCTAS – βCTAS × AverageS&P 500
= 2.30% – 1.28 × 1.08%
= 0.93%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.90% |
| Expected rate of return on market portfolio2 | E(RM) | 13.94% |
| Systematic risk (β) of Cintas Corp. common stock | βCTAS | 1.28 |
| Expected rate of return on Cintas Corp. common stock3 | E(RCTAS) | 16.46% |
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(RCTAS) = RF + βCTAS [E(RM) – RF]
= 4.90% + 1.28 [13.94% – 4.90%]
= 16.46%