자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Cintas의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
Cintas Corp., 월별 수익률
| Cintas Corp. (CTAS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CTAS,t1 | 피제수CTAS,t1 | RCTAS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 6. 30. | $46.27 | 2,718.37 | ||||
| 1. | 2018. 7. 31. | $51.12 | 10.48% | 2,816.29 | 3.60% | |
| 2. | 2018. 8. 31. | $53.34 | 4.34% | 2,901.52 | 3.03% | |
| 3. | 2018. 9. 30. | $49.45 | -7.29% | 2,913.98 | 0.43% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 4. 30. | $164.59 | -4.17% | 5,035.69 | -4.16% | |
| 71. | 2024. 5. 31. | $169.49 | $0.338 | 3.18% | 5,277.51 | 4.80% |
| 평균의 (R): | 2.30% | 1.08% | ||||
| 표준 편차: | 8.40% | 5.24% | ||||
| Cintas Corp. (CTAS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CTAS,t1 | 피제수CTAS,t1 | RCTAS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 6. 30. | $46.27 | 2,718.37 | ||||
| 1. | 2018. 7. 31. | $51.12 | 10.48% | 2,816.29 | 3.60% | |
| 2. | 2018. 8. 31. | $53.34 | 4.34% | 2,901.52 | 3.03% | |
| 3. | 2018. 9. 30. | $49.45 | -7.29% | 2,913.98 | 0.43% | |
| 4. | 2018. 10. 31. | $45.47 | -8.05% | 2,711.74 | -6.94% | |
| 5. | 2018. 11. 30. | $46.85 | $0.513 | 4.16% | 2,760.17 | 1.79% |
| 6. | 2018. 12. 31. | $42.00 | -10.35% | 2,506.85 | -9.18% | |
| 7. | 2019. 1. 31. | $46.88 | 11.62% | 2,704.10 | 7.87% | |
| 8. | 2019. 2. 28. | $51.65 | 10.17% | 2,784.49 | 2.97% | |
| 9. | 2019. 3. 31. | $50.53 | -2.17% | 2,834.40 | 1.79% | |
| 10. | 2019. 4. 30. | $54.29 | 7.44% | 2,945.83 | 3.93% | |
| 11. | 2019. 5. 31. | $55.46 | 2.16% | 2,752.06 | -6.58% | |
| 12. | 2019. 6. 30. | $59.32 | 6.96% | 2,941.76 | 6.89% | |
| 13. | 2019. 7. 31. | $65.11 | 9.76% | 2,980.38 | 1.31% | |
| 14. | 2019. 8. 31. | $65.95 | 1.29% | 2,926.46 | -1.81% | |
| 15. | 2019. 9. 30. | $67.03 | 1.64% | 2,976.74 | 1.72% | |
| 16. | 2019. 10. 31. | $67.17 | 0.21% | 3,037.56 | 2.04% | |
| 17. | 2019. 11. 30. | $64.27 | $0.638 | -3.37% | 3,140.98 | 3.40% |
| 18. | 2019. 12. 31. | $67.27 | 4.67% | 3,230.78 | 2.86% | |
| 19. | 2020. 1. 31. | $69.74 | 3.67% | 3,225.52 | -0.16% | |
| 20. | 2020. 2. 29. | $66.69 | -4.37% | 2,954.22 | -8.41% | |
| 21. | 2020. 3. 31. | $43.31 | -35.06% | 2,584.59 | -12.51% | |
| 22. | 2020. 4. 30. | $55.46 | 28.05% | 2,912.43 | 12.68% | |
| 23. | 2020. 5. 31. | $61.99 | 11.77% | 3,044.31 | 4.53% | |
| 24. | 2020. 6. 30. | $66.59 | 7.42% | 3,100.29 | 1.84% | |
| 25. | 2020. 7. 31. | $75.47 | 13.34% | 3,271.12 | 5.51% | |
| 26. | 2020. 8. 31. | $83.31 | 10.39% | 3,500.31 | 7.01% | |
| 27. | 2020. 9. 30. | $83.21 | -0.12% | 3,363.00 | -3.92% | |
| 28. | 2020. 10. 31. | $78.64 | -5.49% | 3,269.96 | -2.77% | |
| 29. | 2020. 11. 30. | $88.83 | $0.878 | 14.07% | 3,621.63 | 10.75% |
| 30. | 2020. 12. 31. | $88.37 | -0.52% | 3,756.07 | 3.71% | |
| 31. | 2021. 1. 31. | $79.53 | -10.00% | 3,714.24 | -1.11% | |
| 32. | 2021. 2. 28. | $81.09 | $0.188 | 2.20% | 3,811.15 | 2.61% |
| 33. | 2021. 3. 31. | $85.33 | 5.23% | 3,972.89 | 4.24% | |
| 34. | 2021. 4. 30. | $86.29 | 1.13% | 4,181.17 | 5.24% | |
| 35. | 2021. 5. 31. | $88.39 | $0.188 | 2.65% | 4,204.11 | 0.55% |
| 36. | 2021. 6. 30. | $95.50 | 8.04% | 4,297.50 | 2.22% | |
| 37. | 2021. 7. 31. | $98.55 | 3.19% | 4,395.26 | 2.27% | |
| 38. | 2021. 8. 31. | $98.94 | $0.238 | 0.64% | 4,522.68 | 2.90% |
| 39. | 2021. 9. 30. | $95.17 | -3.81% | 4,307.54 | -4.76% | |
| 40. | 2021. 10. 31. | $108.28 | 13.78% | 4,605.38 | 6.91% | |
| 41. | 2021. 11. 30. | $105.55 | $0.238 | -2.30% | 4,567.00 | -0.83% |
| 42. | 2021. 12. 31. | $110.79 | 4.96% | 4,766.18 | 4.36% | |
| 43. | 2022. 1. 31. | $97.88 | -11.65% | 4,515.55 | -5.26% | |
| 44. | 2022. 2. 28. | $93.83 | $0.238 | -3.89% | 4,373.94 | -3.14% |
| 45. | 2022. 3. 31. | $106.35 | 13.34% | 4,530.41 | 3.58% | |
| 46. | 2022. 4. 30. | $99.32 | -6.61% | 4,131.93 | -8.80% | |
| 47. | 2022. 5. 31. | $99.58 | $0.238 | 0.50% | 4,132.15 | 0.01% |
| 48. | 2022. 6. 30. | $93.38 | -6.23% | 3,785.38 | -8.39% | |
| 49. | 2022. 7. 31. | $106.37 | 13.91% | 4,130.29 | 9.11% | |
| 50. | 2022. 8. 31. | $101.71 | $0.288 | -4.11% | 3,955.00 | -4.24% |
| 51. | 2022. 9. 30. | $97.05 | -4.58% | 3,585.62 | -9.34% | |
| 52. | 2022. 10. 31. | $106.89 | 10.14% | 3,871.98 | 7.99% | |
| 53. | 2022. 11. 30. | $115.45 | $0.288 | 8.28% | 4,080.11 | 5.38% |
| 54. | 2022. 12. 31. | $112.91 | -2.20% | 3,839.50 | -5.90% | |
| 55. | 2023. 1. 31. | $110.94 | -1.74% | 4,076.60 | 6.18% | |
| 56. | 2023. 2. 28. | $109.62 | $0.288 | -0.93% | 3,970.15 | -2.61% |
| 57. | 2023. 3. 31. | $115.67 | 5.52% | 4,109.31 | 3.51% | |
| 58. | 2023. 4. 30. | $113.94 | -1.50% | 4,169.48 | 1.46% | |
| 59. | 2023. 5. 31. | $118.04 | $0.288 | 3.85% | 4,179.83 | 0.25% |
| 60. | 2023. 6. 30. | $124.27 | 5.28% | 4,376.86 | 4.71% | |
| 61. | 2023. 7. 31. | $125.51 | 1.00% | 4,588.96 | 4.85% | |
| 62. | 2023. 8. 31. | $126.04 | $0.338 | 0.69% | 4,507.66 | -1.77% |
| 63. | 2023. 9. 30. | $120.25 | -4.59% | 4,288.05 | -4.87% | |
| 64. | 2023. 10. 31. | $126.78 | 5.43% | 4,193.80 | -2.20% | |
| 65. | 2023. 11. 30. | $138.31 | $0.338 | 9.36% | 4,567.80 | 8.92% |
| 66. | 2023. 12. 31. | $150.67 | 8.94% | 4,769.83 | 4.42% | |
| 67. | 2024. 1. 31. | $151.14 | 0.31% | 4,845.65 | 1.59% | |
| 68. | 2024. 2. 29. | $157.15 | $0.338 | 4.20% | 5,096.27 | 5.17% |
| 69. | 2024. 3. 31. | $171.76 | 9.30% | 5,254.35 | 3.10% | |
| 70. | 2024. 4. 30. | $164.59 | -4.17% | 5,035.69 | -4.16% | |
| 71. | 2024. 5. 31. | $169.49 | $0.338 | 3.18% | 5,277.51 | 4.80% |
| 평균의 (R): | 2.30% | 1.08% | ||||
| 표준 편차: | 8.40% | 5.24% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 CTAS의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Cintas Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | 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. | 2018. 7. 31. | 10.48% | 3.60% | 66.89 | 6.39 | 20.67 |
| 2. | 2018. 8. 31. | 4.34% | 3.03% | 4.16 | 3.81 | 3.98 |
| 3. | 2018. 9. 30. | -7.29% | 0.43% | 92.09 | 0.42 | 6.20 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 4. 30. | -4.17% | -4.16% | 41.96 | 27.42 | 33.92 |
| 71. | 2024. 5. 31. | 3.18% | 4.80% | 0.77 | 13.89 | 3.28 |
| 합계 (Σ): | 4,935.48 | 1,923.46 | 2,458.46 | |||
| t | 날짜 | 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. | 2018. 7. 31. | 10.48% | 3.60% | 66.89 | 6.39 | 20.67 |
| 2. | 2018. 8. 31. | 4.34% | 3.03% | 4.16 | 3.81 | 3.98 |
| 3. | 2018. 9. 30. | -7.29% | 0.43% | 92.09 | 0.42 | 6.20 |
| 4. | 2018. 10. 31. | -8.05% | -6.94% | 107.16 | 64.25 | 82.98 |
| 5. | 2018. 11. 30. | 4.16% | 1.79% | 3.46 | 0.51 | 1.32 |
| 6. | 2018. 12. 31. | -10.35% | -9.18% | 160.17 | 105.12 | 129.76 |
| 7. | 2019. 1. 31. | 11.62% | 7.87% | 86.78 | 46.15 | 63.28 |
| 8. | 2019. 2. 28. | 10.17% | 2.97% | 61.96 | 3.60 | 14.94 |
| 9. | 2019. 3. 31. | -2.17% | 1.79% | 20.00 | 0.51 | -3.21 |
| 10. | 2019. 4. 30. | 7.44% | 3.93% | 26.40 | 8.16 | 14.67 |
| 11. | 2019. 5. 31. | 2.16% | -6.58% | 0.02 | 58.57 | 1.14 |
| 12. | 2019. 6. 30. | 6.96% | 6.89% | 21.68 | 33.85 | 27.09 |
| 13. | 2019. 7. 31. | 9.76% | 1.31% | 55.61 | 0.06 | 1.77 |
| 14. | 2019. 8. 31. | 1.29% | -1.81% | 1.03 | 8.32 | 2.92 |
| 15. | 2019. 9. 30. | 1.64% | 1.72% | 0.44 | 0.41 | -0.43 |
| 16. | 2019. 10. 31. | 0.21% | 2.04% | 4.39 | 0.94 | -2.03 |
| 17. | 2019. 11. 30. | -3.37% | 3.40% | 32.16 | 5.43 | -13.21 |
| 18. | 2019. 12. 31. | 4.67% | 2.86% | 5.59 | 3.18 | 4.22 |
| 19. | 2020. 1. 31. | 3.67% | -0.16% | 1.87 | 1.53 | -1.69 |
| 20. | 2020. 2. 29. | -4.37% | -8.41% | 44.58 | 89.99 | 63.34 |
| 21. | 2020. 3. 31. | -35.06% | -12.51% | 1,395.86 | 184.61 | 507.63 |
| 22. | 2020. 4. 30. | 28.05% | 12.68% | 663.07 | 134.77 | 298.94 |
| 23. | 2020. 5. 31. | 11.77% | 4.53% | 89.70 | 11.92 | 32.70 |
| 24. | 2020. 6. 30. | 7.42% | 1.84% | 26.18 | 0.58 | 3.91 |
| 25. | 2020. 7. 31. | 13.34% | 5.51% | 121.70 | 19.67 | 48.92 |
| 26. | 2020. 8. 31. | 10.39% | 7.01% | 65.36 | 35.18 | 47.95 |
| 27. | 2020. 9. 30. | -0.12% | -3.92% | 5.87 | 24.98 | 12.11 |
| 28. | 2020. 10. 31. | -5.49% | -2.77% | 60.77 | 14.76 | 29.95 |
| 29. | 2020. 11. 30. | 14.07% | 10.75% | 138.55 | 93.69 | 113.93 |
| 30. | 2020. 12. 31. | -0.52% | 3.71% | 7.96 | 6.95 | -7.44 |
| 31. | 2021. 1. 31. | -10.00% | -1.11% | 151.46 | 4.79 | 26.94 |
| 32. | 2021. 2. 28. | 2.20% | 2.61% | 0.01 | 2.35 | -0.16 |
| 33. | 2021. 3. 31. | 5.23% | 4.24% | 8.56 | 10.04 | 9.27 |
| 34. | 2021. 4. 30. | 1.13% | 5.24% | 1.39 | 17.37 | -4.91 |
| 35. | 2021. 5. 31. | 2.65% | 0.55% | 0.12 | 0.28 | -0.18 |
| 36. | 2021. 6. 30. | 8.04% | 2.22% | 32.95 | 1.31 | 6.58 |
| 37. | 2021. 7. 31. | 3.19% | 2.27% | 0.79 | 1.44 | 1.07 |
| 38. | 2021. 8. 31. | 0.64% | 2.90% | 2.78 | 3.33 | -3.04 |
| 39. | 2021. 9. 30. | -3.81% | -4.76% | 37.38 | 34.01 | 35.66 |
| 40. | 2021. 10. 31. | 13.78% | 6.91% | 131.60 | 34.10 | 66.99 |
| 41. | 2021. 11. 30. | -2.30% | -0.83% | 21.21 | 3.64 | 8.79 |
| 42. | 2021. 12. 31. | 4.96% | 4.36% | 7.08 | 10.80 | 8.74 |
| 43. | 2022. 1. 31. | -11.65% | -5.26% | 194.77 | 40.12 | 88.40 |
| 44. | 2022. 2. 28. | -3.89% | -3.14% | 38.42 | 17.74 | 26.10 |
| 45. | 2022. 3. 31. | 13.34% | 3.58% | 121.88 | 6.26 | 27.62 |
| 46. | 2022. 4. 30. | -6.61% | -8.80% | 79.45 | 97.44 | 87.99 |
| 47. | 2022. 5. 31. | 0.50% | 0.01% | 3.25 | 1.14 | 1.93 |
| 48. | 2022. 6. 30. | -6.23% | -8.39% | 72.75 | 89.63 | 80.75 |
| 49. | 2022. 7. 31. | 13.91% | 9.11% | 134.73 | 64.58 | 93.28 |
| 50. | 2022. 8. 31. | -4.11% | -4.24% | 41.14 | 28.29 | 34.12 |
| 51. | 2022. 9. 30. | -4.58% | -9.34% | 47.41 | 108.47 | 71.71 |
| 52. | 2022. 10. 31. | 10.14% | 7.99% | 61.40 | 47.76 | 54.15 |
| 53. | 2022. 11. 30. | 8.28% | 5.38% | 35.69 | 18.49 | 25.69 |
| 54. | 2022. 12. 31. | -2.20% | -5.90% | 20.28 | 48.61 | 31.40 |
| 55. | 2023. 1. 31. | -1.74% | 6.18% | 16.39 | 26.01 | -20.65 |
| 56. | 2023. 2. 28. | -0.93% | -2.61% | 10.46 | 13.59 | 11.92 |
| 57. | 2023. 3. 31. | 5.52% | 3.51% | 10.34 | 5.90 | 7.81 |
| 58. | 2023. 4. 30. | -1.50% | 1.46% | 14.43 | 0.15 | -1.48 |
| 59. | 2023. 5. 31. | 3.85% | 0.25% | 2.40 | 0.68 | -1.28 |
| 60. | 2023. 6. 30. | 5.28% | 4.71% | 8.85 | 13.24 | 10.82 |
| 61. | 2023. 7. 31. | 1.00% | 4.85% | 1.70 | 14.22 | -4.92 |
| 62. | 2023. 8. 31. | 0.69% | -1.77% | 2.60 | 8.10 | 4.59 |
| 63. | 2023. 9. 30. | -4.59% | -4.87% | 47.57 | 35.37 | 41.02 |
| 64. | 2023. 10. 31. | 5.43% | -2.20% | 9.78 | 10.71 | -10.23 |
| 65. | 2023. 11. 30. | 9.36% | 8.92% | 49.81 | 61.51 | 55.35 |
| 66. | 2023. 12. 31. | 8.94% | 4.42% | 44.00 | 11.21 | 22.20 |
| 67. | 2024. 1. 31. | 0.31% | 1.59% | 3.97 | 0.26 | -1.02 |
| 68. | 2024. 2. 29. | 4.20% | 5.17% | 3.60 | 16.78 | 7.77 |
| 69. | 2024. 3. 31. | 9.30% | 3.10% | 48.91 | 4.11 | 14.17 |
| 70. | 2024. 4. 30. | -4.17% | -4.16% | 41.96 | 27.42 | 33.92 |
| 71. | 2024. 5. 31. | 3.18% | 4.80% | 0.77 | 13.89 | 3.28 |
| 합계 (Σ): | 4,935.48 | 1,923.46 | 2,458.46 | |||
모두 보기
분산CTAS = Σ(RCTAS,t–RCTAS)2 ÷ (71 – 1)
= 4,935.48 ÷ (71 – 1)
= 70.51
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,923.46 ÷ (71 – 1)
= 27.48
공분산CTAS, S&P 500 = Σ(RCTAS,t–RCTAS)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,458.46 ÷ (71 – 1)
= 35.12
체계적인 위험 추정 (β)
| 분산CTAS | 70.51 |
| 분산S&P 500 | 27.48 |
| 공분산CTAS, S&P 500 | 35.12 |
| 상관 계수CTAS, S&P 5001 | 0.80 |
| βCTAS2 | 1.28 |
| αCTAS3 | 0.93% |
계산
1 상관 계수CTAS, S&P 500
= 공분산CTAS, S&P 500 ÷ (표준 편차CTAS × 표준 편차S&P 500)
= 35.12 ÷ (8.40% × 5.24%)
= 0.80
2 βCTAS
= 공분산CTAS, S&P 500 ÷ 분산S&P 500
= 35.12 ÷ 27.48
= 1.28
3 αCTAS
= 평균의CTAS – βCTAS × 평균의S&P 500
= 2.30% – 1.28 × 1.08%
= 0.93%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.90% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.94% |
| 보통주의 체계적 위험Cintas | βCTAS | 1.28 |
| Cintas 보통주에 대한 예상 수익률3 | E(RCTAS) | 16.46% |
1 10년 이내에 만기가 도래하거나 콜링할 수 없는 모든 미결제 고정 쿠폰 미국 국채에 대한 입찰 수익률의 비가중 평균(무위험 수익률 대리).
2 자세히 보기 »
3 E(RCTAS) = RF + βCTAS [E(RM) – RF]
= 4.90% + 1.28 [13.94% – 4.90%]
= 16.46%