자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Parker보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Parker-Hannifin Corp., 월별 수익률
| Parker-Hannifin Corp. (PH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PH,t1 | 피제수PH,t1 | RPH,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2016. 7. 31. | $114.19 | 2,173.60 | ||||
| 1. | 2016. 8. 31. | $122.53 | $0.63 | 7.86% | 2,170.95 | -0.12% |
| 2. | 2016. 9. 30. | $125.53 | 2.45% | 2,168.27 | -0.12% | |
| 3. | 2016. 10. 31. | $122.75 | -2.21% | 2,126.15 | -1.94% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2022. 5. 31. | $272.17 | $1.33 | 0.99% | 4,132.15 | 0.01% |
| 71. | 2022. 6. 30. | $246.05 | -9.60% | 3,785.38 | -8.39% | |
| 평균의 (R): | 1.61% | 0.89% | ||||
| 표준 편차: | 8.72% | 4.53% | ||||
| Parker-Hannifin Corp. (PH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PH,t1 | 피제수PH,t1 | RPH,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2016. 7. 31. | $114.19 | 2,173.60 | ||||
| 1. | 2016. 8. 31. | $122.53 | $0.63 | 7.86% | 2,170.95 | -0.12% |
| 2. | 2016. 9. 30. | $125.53 | 2.45% | 2,168.27 | -0.12% | |
| 3. | 2016. 10. 31. | $122.75 | -2.21% | 2,126.15 | -1.94% | |
| 4. | 2016. 11. 30. | $138.93 | $0.63 | 13.69% | 2,198.81 | 3.42% |
| 5. | 2016. 12. 31. | $140.00 | 0.77% | 2,238.83 | 1.82% | |
| 6. | 2017. 1. 31. | $147.13 | 5.09% | 2,278.87 | 1.79% | |
| 7. | 2017. 2. 28. | $154.84 | $0.66 | 5.69% | 2,363.64 | 3.72% |
| 8. | 2017. 3. 31. | $160.32 | 3.54% | 2,362.72 | -0.04% | |
| 9. | 2017. 4. 30. | $160.80 | 0.30% | 2,384.20 | 0.91% | |
| 10. | 2017. 5. 31. | $157.47 | $0.66 | -1.66% | 2,411.80 | 1.16% |
| 11. | 2017. 6. 30. | $159.82 | 1.49% | 2,423.41 | 0.48% | |
| 12. | 2017. 7. 31. | $165.98 | 3.85% | 2,470.30 | 1.93% | |
| 13. | 2017. 8. 31. | $160.89 | $0.66 | -2.67% | 2,471.65 | 0.05% |
| 14. | 2017. 9. 30. | $175.02 | 8.78% | 2,519.36 | 1.93% | |
| 15. | 2017. 10. 31. | $182.61 | 4.34% | 2,575.26 | 2.22% | |
| 16. | 2017. 11. 30. | $187.49 | $0.66 | 3.03% | 2,647.58 | 2.81% |
| 17. | 2017. 12. 31. | $199.58 | 6.45% | 2,673.61 | 0.98% | |
| 18. | 2018. 1. 31. | $201.42 | 0.92% | 2,823.81 | 5.62% | |
| 19. | 2018. 2. 28. | $178.47 | $0.66 | -11.07% | 2,713.83 | -3.89% |
| 20. | 2018. 3. 31. | $171.03 | -4.17% | 2,640.87 | -2.69% | |
| 21. | 2018. 4. 30. | $164.62 | -3.75% | 2,648.05 | 0.27% | |
| 22. | 2018. 5. 31. | $170.90 | $0.76 | 4.28% | 2,705.27 | 2.16% |
| 23. | 2018. 6. 30. | $155.85 | -8.81% | 2,718.37 | 0.48% | |
| 24. | 2018. 7. 31. | $169.05 | 8.47% | 2,816.29 | 3.60% | |
| 25. | 2018. 8. 31. | $175.60 | $0.76 | 4.32% | 2,901.52 | 3.03% |
| 26. | 2018. 9. 30. | $183.93 | 4.74% | 2,913.98 | 0.43% | |
| 27. | 2018. 10. 31. | $151.63 | -17.56% | 2,711.74 | -6.94% | |
| 28. | 2018. 11. 30. | $172.04 | $0.76 | 13.96% | 2,760.17 | 1.79% |
| 29. | 2018. 12. 31. | $149.14 | -13.31% | 2,506.85 | -9.18% | |
| 30. | 2019. 1. 31. | $164.81 | 10.51% | 2,704.10 | 7.87% | |
| 31. | 2019. 2. 28. | $176.16 | $0.76 | 7.35% | 2,784.49 | 2.97% |
| 32. | 2019. 3. 31. | $171.62 | -2.58% | 2,834.40 | 1.79% | |
| 33. | 2019. 4. 30. | $181.08 | 5.51% | 2,945.83 | 3.93% | |
| 34. | 2019. 5. 31. | $152.32 | $0.88 | -15.40% | 2,752.06 | -6.58% |
| 35. | 2019. 6. 30. | $170.01 | 11.61% | 2,941.76 | 6.89% | |
| 36. | 2019. 7. 31. | $175.08 | 2.98% | 2,980.38 | 1.31% | |
| 37. | 2019. 8. 31. | $165.77 | $0.88 | -4.81% | 2,926.46 | -1.81% |
| 38. | 2019. 9. 30. | $180.61 | 8.95% | 2,976.74 | 1.72% | |
| 39. | 2019. 10. 31. | $183.49 | 1.59% | 3,037.56 | 2.04% | |
| 40. | 2019. 11. 30. | $198.79 | $0.88 | 8.82% | 3,140.98 | 3.40% |
| 41. | 2019. 12. 31. | $205.82 | 3.54% | 3,230.78 | 2.86% | |
| 42. | 2020. 1. 31. | $195.69 | -4.92% | 3,225.52 | -0.16% | |
| 43. | 2020. 2. 29. | $184.77 | $0.88 | -5.13% | 2,954.22 | -8.41% |
| 44. | 2020. 3. 31. | $129.73 | -29.79% | 2,584.59 | -12.51% | |
| 45. | 2020. 4. 30. | $158.12 | 21.88% | 2,912.43 | 12.68% | |
| 46. | 2020. 5. 31. | $179.97 | $0.88 | 14.38% | 3,044.31 | 4.53% |
| 47. | 2020. 6. 30. | $183.27 | 1.83% | 3,100.29 | 1.84% | |
| 48. | 2020. 7. 31. | $178.92 | -2.37% | 3,271.12 | 5.51% | |
| 49. | 2020. 8. 31. | $206.01 | $0.88 | 15.63% | 3,500.31 | 7.01% |
| 50. | 2020. 9. 30. | $202.34 | -1.78% | 3,363.00 | -3.92% | |
| 51. | 2020. 10. 31. | $208.36 | 2.98% | 3,269.96 | -2.77% | |
| 52. | 2020. 11. 30. | $267.26 | $0.88 | 28.69% | 3,621.63 | 10.75% |
| 53. | 2020. 12. 31. | $272.41 | 1.93% | 3,756.07 | 3.71% | |
| 54. | 2021. 1. 31. | $264.61 | -2.86% | 3,714.24 | -1.11% | |
| 55. | 2021. 2. 28. | $286.96 | $0.88 | 8.78% | 3,811.15 | 2.61% |
| 56. | 2021. 3. 31. | $315.43 | 9.92% | 3,972.89 | 4.24% | |
| 57. | 2021. 4. 30. | $313.81 | -0.51% | 4,181.17 | 5.24% | |
| 58. | 2021. 5. 31. | $308.15 | $1.03 | -1.48% | 4,204.11 | 0.55% |
| 59. | 2021. 6. 30. | $307.11 | -0.34% | 4,297.50 | 2.22% | |
| 60. | 2021. 7. 31. | $312.03 | 1.60% | 4,395.26 | 2.27% | |
| 61. | 2021. 8. 31. | $296.67 | $1.03 | -4.59% | 4,522.68 | 2.90% |
| 62. | 2021. 9. 30. | $279.62 | -5.75% | 4,307.54 | -4.76% | |
| 63. | 2021. 10. 31. | $296.59 | 6.07% | 4,605.38 | 6.91% | |
| 64. | 2021. 11. 30. | $302.06 | $1.03 | 2.19% | 4,567.00 | -0.83% |
| 65. | 2021. 12. 31. | $318.12 | 5.32% | 4,766.18 | 4.36% | |
| 66. | 2022. 1. 31. | $310.01 | -2.55% | 4,515.55 | -5.26% | |
| 67. | 2022. 2. 28. | $296.39 | $1.03 | -4.06% | 4,373.94 | -3.14% |
| 68. | 2022. 3. 31. | $283.76 | -4.26% | 4,530.41 | 3.58% | |
| 69. | 2022. 4. 30. | $270.82 | -4.56% | 4,131.93 | -8.80% | |
| 70. | 2022. 5. 31. | $272.17 | $1.33 | 0.99% | 4,132.15 | 0.01% |
| 71. | 2022. 6. 30. | $246.05 | -9.60% | 3,785.38 | -8.39% | |
| 평균의 (R): | 1.61% | 0.89% | ||||
| 표준 편차: | 8.72% | 4.53% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 PH의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Parker-Hannifin Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RPH,t | RS&P 500,t | (RPH,t–RPH)2 | (RS&P 500,t–RS&P 500)2 | (RPH,t–RPH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2016. 8. 31. | 7.86% | -0.12% | 38.96 | 1.02 | -6.30 |
| 2. | 2016. 9. 30. | 2.45% | -0.12% | 0.70 | 1.02 | -0.84 |
| 3. | 2016. 10. 31. | -2.21% | -1.94% | 14.65 | 8.00 | 10.83 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2022. 5. 31. | 0.99% | 0.01% | 0.39 | 0.78 | 0.55 |
| 71. | 2022. 6. 30. | -9.60% | -8.39% | 125.67 | 86.09 | 104.02 |
| 합계 (Σ): | 5,326.54 | 1,437.21 | 2,230.11 | |||
| t | 날짜 | RPH,t | RS&P 500,t | (RPH,t–RPH)2 | (RS&P 500,t–RS&P 500)2 | (RPH,t–RPH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2016. 8. 31. | 7.86% | -0.12% | 38.96 | 1.02 | -6.30 |
| 2. | 2016. 9. 30. | 2.45% | -0.12% | 0.70 | 1.02 | -0.84 |
| 3. | 2016. 10. 31. | -2.21% | -1.94% | 14.65 | 8.00 | 10.83 |
| 4. | 2016. 11. 30. | 13.69% | 3.42% | 145.96 | 6.40 | 30.57 |
| 5. | 2016. 12. 31. | 0.77% | 1.82% | 0.71 | 0.87 | -0.79 |
| 6. | 2017. 1. 31. | 5.09% | 1.79% | 12.11 | 0.81 | 3.14 |
| 7. | 2017. 2. 28. | 5.69% | 3.72% | 16.61 | 8.03 | 11.55 |
| 8. | 2017. 3. 31. | 3.54% | -0.04% | 3.71 | 0.86 | -1.78 |
| 9. | 2017. 4. 30. | 0.30% | 0.91% | 1.73 | 0.00 | -0.03 |
| 10. | 2017. 5. 31. | -1.66% | 1.16% | 10.72 | 0.07 | -0.89 |
| 11. | 2017. 6. 30. | 1.49% | 0.48% | 0.01 | 0.16 | 0.05 |
| 12. | 2017. 7. 31. | 3.85% | 1.93% | 5.02 | 1.10 | 2.35 |
| 13. | 2017. 8. 31. | -2.67% | 0.05% | 18.34 | 0.69 | 3.56 |
| 14. | 2017. 9. 30. | 8.78% | 1.93% | 51.40 | 1.09 | 7.48 |
| 15. | 2017. 10. 31. | 4.34% | 2.22% | 7.42 | 1.77 | 3.63 |
| 16. | 2017. 11. 30. | 3.03% | 2.81% | 2.02 | 3.69 | 2.73 |
| 17. | 2017. 12. 31. | 6.45% | 0.98% | 23.38 | 0.01 | 0.47 |
| 18. | 2018. 1. 31. | 0.92% | 5.62% | 0.48 | 22.38 | -3.27 |
| 19. | 2018. 2. 28. | -11.07% | -3.89% | 160.77 | 22.86 | 60.63 |
| 20. | 2018. 3. 31. | -4.17% | -2.69% | 33.43 | 12.78 | 20.67 |
| 21. | 2018. 4. 30. | -3.75% | 0.27% | 28.74 | 0.38 | 3.30 |
| 22. | 2018. 5. 31. | 4.28% | 2.16% | 7.09 | 1.62 | 3.39 |
| 23. | 2018. 6. 30. | -8.81% | 0.48% | 108.57 | 0.16 | 4.19 |
| 24. | 2018. 7. 31. | 8.47% | 3.60% | 47.01 | 7.37 | 18.62 |
| 25. | 2018. 8. 31. | 4.32% | 3.03% | 7.35 | 4.58 | 5.80 |
| 26. | 2018. 9. 30. | 4.74% | 0.43% | 9.80 | 0.21 | -1.43 |
| 27. | 2018. 10. 31. | -17.56% | -6.94% | 367.65 | 61.26 | 150.08 |
| 28. | 2018. 11. 30. | 13.96% | 1.79% | 152.48 | 0.81 | 11.10 |
| 29. | 2018. 12. 31. | -13.31% | -9.18% | 222.73 | 101.29 | 150.20 |
| 30. | 2019. 1. 31. | 10.51% | 7.87% | 79.10 | 48.74 | 62.09 |
| 31. | 2019. 2. 28. | 7.35% | 2.97% | 32.89 | 4.35 | 11.96 |
| 32. | 2019. 3. 31. | -2.58% | 1.79% | 17.56 | 0.82 | -3.80 |
| 33. | 2019. 4. 30. | 5.51% | 3.93% | 15.20 | 9.27 | 11.87 |
| 34. | 2019. 5. 31. | -15.40% | -6.58% | 289.33 | 55.72 | 126.97 |
| 35. | 2019. 6. 30. | 11.61% | 6.89% | 100.01 | 36.08 | 60.07 |
| 36. | 2019. 7. 31. | 2.98% | 1.31% | 1.87 | 0.18 | 0.58 |
| 37. | 2019. 8. 31. | -4.81% | -1.81% | 41.32 | 7.27 | 17.33 |
| 38. | 2019. 9. 30. | 8.95% | 1.72% | 53.86 | 0.69 | 6.10 |
| 39. | 2019. 10. 31. | 1.59% | 2.04% | 0.00 | 1.34 | -0.02 |
| 40. | 2019. 11. 30. | 8.82% | 3.40% | 51.91 | 6.34 | 18.14 |
| 41. | 2019. 12. 31. | 3.54% | 2.86% | 3.70 | 3.89 | 3.79 |
| 42. | 2020. 1. 31. | -4.92% | -0.16% | 42.71 | 1.10 | 6.86 |
| 43. | 2020. 2. 29. | -5.13% | -8.41% | 45.48 | 86.45 | 62.70 |
| 44. | 2020. 3. 31. | -29.79% | -12.51% | 986.06 | 179.52 | 420.74 |
| 45. | 2020. 4. 30. | 21.88% | 12.68% | 410.90 | 139.19 | 239.15 |
| 46. | 2020. 5. 31. | 14.38% | 4.53% | 162.87 | 13.26 | 46.47 |
| 47. | 2020. 6. 30. | 1.83% | 1.84% | 0.05 | 0.91 | 0.21 |
| 48. | 2020. 7. 31. | -2.37% | 5.51% | 15.89 | 21.38 | -18.43 |
| 49. | 2020. 8. 31. | 15.63% | 7.01% | 196.55 | 37.45 | 85.80 |
| 50. | 2020. 9. 30. | -1.78% | -3.92% | 11.52 | 23.13 | 16.33 |
| 51. | 2020. 10. 31. | 2.98% | -2.77% | 1.86 | 13.35 | -4.98 |
| 52. | 2020. 11. 30. | 28.69% | 10.75% | 733.19 | 97.38 | 267.20 |
| 53. | 2020. 12. 31. | 1.93% | 3.71% | 0.10 | 7.98 | 0.89 |
| 54. | 2021. 1. 31. | -2.86% | -1.11% | 20.04 | 4.00 | 8.95 |
| 55. | 2021. 2. 28. | 8.78% | 2.61% | 51.35 | 2.97 | 12.34 |
| 56. | 2021. 3. 31. | 9.92% | 4.24% | 69.02 | 11.27 | 27.89 |
| 57. | 2021. 4. 30. | -0.51% | 5.24% | 4.52 | 18.97 | -9.26 |
| 58. | 2021. 5. 31. | -1.48% | 0.55% | 9.54 | 0.11 | 1.04 |
| 59. | 2021. 6. 30. | -0.34% | 2.22% | 3.81 | 1.78 | -2.60 |
| 60. | 2021. 7. 31. | 1.60% | 2.27% | 0.00 | 1.93 | -0.02 |
| 61. | 2021. 8. 31. | -4.59% | 2.90% | 38.51 | 4.05 | -12.49 |
| 62. | 2021. 9. 30. | -5.75% | -4.76% | 54.17 | 31.85 | 41.54 |
| 63. | 2021. 10. 31. | 6.07% | 6.91% | 19.85 | 36.33 | 26.86 |
| 64. | 2021. 11. 30. | 2.19% | -0.83% | 0.33 | 2.96 | -0.99 |
| 65. | 2021. 12. 31. | 5.32% | 4.36% | 13.72 | 12.07 | 12.87 |
| 66. | 2022. 1. 31. | -2.55% | -5.26% | 17.33 | 37.76 | 25.58 |
| 67. | 2022. 2. 28. | -4.06% | -3.14% | 32.20 | 16.18 | 22.83 |
| 68. | 2022. 3. 31. | -4.26% | 3.58% | 34.51 | 7.24 | -15.81 |
| 69. | 2022. 4. 30. | -4.56% | -8.80% | 38.11 | 93.75 | 59.77 |
| 70. | 2022. 5. 31. | 0.99% | 0.01% | 0.39 | 0.78 | 0.55 |
| 71. | 2022. 6. 30. | -9.60% | -8.39% | 125.67 | 86.09 | 104.02 |
| 합계 (Σ): | 5,326.54 | 1,437.21 | 2,230.11 | |||
모두 보기
분산PH = Σ(RPH,t–RPH)2 ÷ (71 – 1)
= 5,326.54 ÷ (71 – 1)
= 76.09
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,437.21 ÷ (71 – 1)
= 20.53
공분산PH, S&P 500 = Σ(RPH,t–RPH)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,230.11 ÷ (71 – 1)
= 31.86
체계적인 위험 추정 (β)
| 분산PH | 76.09 |
| 분산S&P 500 | 20.53 |
| 공분산PH, S&P 500 | 31.86 |
| 상관 계수PH, S&P 5001 | 0.81 |
| βPH2 | 1.55 |
| αPH3 | 0.24% |
계산
1 상관 계수PH, S&P 500
= 공분산PH, S&P 500 ÷ (표준 편차PH × 표준 편차S&P 500)
= 31.86 ÷ (8.72% × 4.53%)
= 0.81
2 βPH
= 공분산PH, S&P 500 ÷ 분산S&P 500
= 31.86 ÷ 20.53
= 1.55
3 αPH
= 평균의PH – βPH × 평균의S&P 500
= 1.61% – 1.55 × 0.89%
= 0.24%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험Parker | βPH | 1.55 |
| Parker 보통주에 대한 기대 수익률3 | E(RPH) | 20.32% |
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(RPH) = RF + βPH [E(RM) – RF]
= 4.91% + 1.55 [14.84% – 4.91%]
= 20.32%