자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 ADP보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Automatic Data Processing Inc., 월별 수익률
| Automatic Data Processing Inc. (ADP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ADP,t1 | 피제수ADP,t1 | RADP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 7. 31. | $79.77 | 2,103.84 | ||||
| 1. | 2015. 8. 31. | $77.32 | -3.07% | 1,972.18 | -6.26% | |
| 2. | 2015. 9. 30. | $80.36 | $0.49 | 4.57% | 1,920.03 | -2.64% |
| 3. | 2015. 10. 31. | $86.99 | 8.25% | 2,079.36 | 8.30% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2021. 5. 31. | $196.02 | 4.83% | 4,204.11 | 0.55% | |
| 71. | 2021. 6. 30. | $198.62 | $0.93 | 1.80% | 4,297.50 | 2.22% |
| 평균의 (R): | 1.63% | 1.10% | ||||
| 표준 편차: | 5.54% | 4.32% | ||||
| Automatic Data Processing Inc. (ADP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ADP,t1 | 피제수ADP,t1 | RADP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 7. 31. | $79.77 | 2,103.84 | ||||
| 1. | 2015. 8. 31. | $77.32 | -3.07% | 1,972.18 | -6.26% | |
| 2. | 2015. 9. 30. | $80.36 | $0.49 | 4.57% | 1,920.03 | -2.64% |
| 3. | 2015. 10. 31. | $86.99 | 8.25% | 2,079.36 | 8.30% | |
| 4. | 2015. 11. 30. | $86.26 | -0.84% | 2,080.41 | 0.05% | |
| 5. | 2015. 12. 31. | $84.72 | $0.53 | -1.17% | 2,043.94 | -1.75% |
| 6. | 2016. 1. 31. | $83.09 | -1.92% | 1,940.24 | -5.07% | |
| 7. | 2016. 2. 29. | $84.69 | 1.93% | 1,932.23 | -0.41% | |
| 8. | 2016. 3. 31. | $89.71 | $0.53 | 6.55% | 2,059.74 | 6.60% |
| 9. | 2016. 4. 30. | $88.44 | -1.42% | 2,065.30 | 0.27% | |
| 10. | 2016. 5. 31. | $87.84 | -0.68% | 2,096.95 | 1.53% | |
| 11. | 2016. 6. 30. | $91.87 | $0.53 | 5.19% | 2,098.86 | 0.09% |
| 12. | 2016. 7. 31. | $88.95 | -3.18% | 2,173.60 | 3.56% | |
| 13. | 2016. 8. 31. | $89.81 | 0.97% | 2,170.95 | -0.12% | |
| 14. | 2016. 9. 30. | $88.20 | $0.53 | -1.20% | 2,168.27 | -0.12% |
| 15. | 2016. 10. 31. | $87.06 | -1.29% | 2,126.15 | -1.94% | |
| 16. | 2016. 11. 30. | $96.02 | 10.29% | 2,198.81 | 3.42% | |
| 17. | 2016. 12. 31. | $102.78 | $0.57 | 7.63% | 2,238.83 | 1.82% |
| 18. | 2017. 1. 31. | $100.99 | -1.74% | 2,278.87 | 1.79% | |
| 19. | 2017. 2. 28. | $102.62 | 1.61% | 2,363.64 | 3.72% | |
| 20. | 2017. 3. 31. | $102.39 | $0.57 | 0.33% | 2,362.72 | -0.04% |
| 21. | 2017. 4. 30. | $104.49 | 2.05% | 2,384.20 | 0.91% | |
| 22. | 2017. 5. 31. | $102.37 | -2.03% | 2,411.80 | 1.16% | |
| 23. | 2017. 6. 30. | $102.46 | $0.57 | 0.64% | 2,423.41 | 0.48% |
| 24. | 2017. 7. 31. | $118.91 | 16.06% | 2,470.30 | 1.93% | |
| 25. | 2017. 8. 31. | $106.47 | -10.46% | 2,471.65 | 0.05% | |
| 26. | 2017. 9. 30. | $109.32 | $0.57 | 3.21% | 2,519.36 | 1.93% |
| 27. | 2017. 10. 31. | $116.26 | 6.35% | 2,575.26 | 2.22% | |
| 28. | 2017. 11. 30. | $114.46 | -1.55% | 2,647.58 | 2.81% | |
| 29. | 2017. 12. 31. | $117.19 | $0.63 | 2.94% | 2,673.61 | 0.98% |
| 30. | 2018. 1. 31. | $123.63 | 5.50% | 2,823.81 | 5.62% | |
| 31. | 2018. 2. 28. | $115.32 | -6.72% | 2,713.83 | -3.89% | |
| 32. | 2018. 3. 31. | $113.48 | $0.63 | -1.05% | 2,640.87 | -2.69% |
| 33. | 2018. 4. 30. | $118.08 | 4.05% | 2,648.05 | 0.27% | |
| 34. | 2018. 5. 31. | $130.02 | 10.11% | 2,705.27 | 2.16% | |
| 35. | 2018. 6. 30. | $134.14 | $0.69 | 3.70% | 2,718.37 | 0.48% |
| 36. | 2018. 7. 31. | $134.99 | 0.63% | 2,816.29 | 3.60% | |
| 37. | 2018. 8. 31. | $146.75 | 8.71% | 2,901.52 | 3.03% | |
| 38. | 2018. 9. 30. | $150.66 | $0.69 | 3.13% | 2,913.98 | 0.43% |
| 39. | 2018. 10. 31. | $144.08 | -4.37% | 2,711.74 | -6.94% | |
| 40. | 2018. 11. 30. | $147.42 | 2.32% | 2,760.17 | 1.79% | |
| 41. | 2018. 12. 31. | $131.12 | $0.79 | -10.52% | 2,506.85 | -9.18% |
| 42. | 2019. 1. 31. | $139.84 | 6.65% | 2,704.10 | 7.87% | |
| 43. | 2019. 2. 28. | $153.03 | 9.43% | 2,784.49 | 2.97% | |
| 44. | 2019. 3. 31. | $159.74 | $0.79 | 4.90% | 2,834.40 | 1.79% |
| 45. | 2019. 4. 30. | $164.39 | 2.91% | 2,945.83 | 3.93% | |
| 46. | 2019. 5. 31. | $160.12 | -2.60% | 2,752.06 | -6.58% | |
| 47. | 2019. 6. 30. | $165.33 | $0.79 | 3.75% | 2,941.76 | 6.89% |
| 48. | 2019. 7. 31. | $166.52 | 0.72% | 2,980.38 | 1.31% | |
| 49. | 2019. 8. 31. | $169.84 | 1.99% | 2,926.46 | -1.81% | |
| 50. | 2019. 9. 30. | $161.42 | $0.79 | -4.49% | 2,976.74 | 1.72% |
| 51. | 2019. 10. 31. | $162.23 | 0.50% | 3,037.56 | 2.04% | |
| 52. | 2019. 11. 30. | $170.78 | 5.27% | 3,140.98 | 3.40% | |
| 53. | 2019. 12. 31. | $170.50 | $0.91 | 0.37% | 3,230.78 | 2.86% |
| 54. | 2020. 1. 31. | $171.39 | 0.52% | 3,225.52 | -0.16% | |
| 55. | 2020. 2. 29. | $154.74 | -9.71% | 2,954.22 | -8.41% | |
| 56. | 2020. 3. 31. | $136.68 | $0.91 | -11.08% | 2,584.59 | -12.51% |
| 57. | 2020. 4. 30. | $146.69 | 7.32% | 2,912.43 | 12.68% | |
| 58. | 2020. 5. 31. | $146.49 | -0.14% | 3,044.31 | 4.53% | |
| 59. | 2020. 6. 30. | $148.89 | $0.91 | 2.26% | 3,100.29 | 1.84% |
| 60. | 2020. 7. 31. | $132.91 | -10.73% | 3,271.12 | 5.51% | |
| 61. | 2020. 8. 31. | $139.09 | 4.65% | 3,500.31 | 7.01% | |
| 62. | 2020. 9. 30. | $139.49 | $0.91 | 0.94% | 3,363.00 | -3.92% |
| 63. | 2020. 10. 31. | $157.96 | 13.24% | 3,269.96 | -2.77% | |
| 64. | 2020. 11. 30. | $173.88 | 10.08% | 3,621.63 | 10.75% | |
| 65. | 2020. 12. 31. | $176.20 | $0.93 | 1.87% | 3,756.07 | 3.71% |
| 66. | 2021. 1. 31. | $165.12 | -6.29% | 3,714.24 | -1.11% | |
| 67. | 2021. 2. 28. | $174.02 | 5.39% | 3,811.15 | 2.61% | |
| 68. | 2021. 3. 31. | $188.47 | $0.93 | 8.84% | 3,972.89 | 4.24% |
| 69. | 2021. 4. 30. | $186.99 | -0.79% | 4,181.17 | 5.24% | |
| 70. | 2021. 5. 31. | $196.02 | 4.83% | 4,204.11 | 0.55% | |
| 71. | 2021. 6. 30. | $198.62 | $0.93 | 1.80% | 4,297.50 | 2.22% |
| 평균의 (R): | 1.63% | 1.10% | ||||
| 표준 편차: | 5.54% | 4.32% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 ADP의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Automatic Data Processing Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RADP,t | RS&P 500,t | (RADP,t–RADP)2 | (RS&P 500,t–RS&P 500)2 | (RADP,t–RADP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 8. 31. | -3.07% | -6.26% | 22.13 | 54.19 | 34.63 |
| 2. | 2015. 9. 30. | 4.57% | -2.64% | 8.60 | 14.05 | -10.99 |
| 3. | 2015. 10. 31. | 8.25% | 8.30% | 43.79 | 51.76 | 47.61 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2021. 5. 31. | 4.83% | 0.55% | 10.22 | 0.31 | -1.77 |
| 71. | 2021. 6. 30. | 1.80% | 2.22% | 0.03 | 1.25 | 0.19 |
| 합계 (Σ): | 2,150.24 | 1,307.41 | 918.31 | |||
| t | 날짜 | RADP,t | RS&P 500,t | (RADP,t–RADP)2 | (RS&P 500,t–RS&P 500)2 | (RADP,t–RADP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 8. 31. | -3.07% | -6.26% | 22.13 | 54.19 | 34.63 |
| 2. | 2015. 9. 30. | 4.57% | -2.64% | 8.60 | 14.05 | -10.99 |
| 3. | 2015. 10. 31. | 8.25% | 8.30% | 43.79 | 51.76 | 47.61 |
| 4. | 2015. 11. 30. | -0.84% | 0.05% | 6.11 | 1.11 | 2.60 |
| 5. | 2015. 12. 31. | -1.17% | -1.75% | 7.86 | 8.16 | 8.01 |
| 6. | 2016. 1. 31. | -1.92% | -5.07% | 12.65 | 38.16 | 21.97 |
| 7. | 2016. 2. 29. | 1.93% | -0.41% | 0.09 | 2.30 | -0.44 |
| 8. | 2016. 3. 31. | 6.55% | 6.60% | 24.21 | 30.20 | 27.04 |
| 9. | 2016. 4. 30. | -1.42% | 0.27% | 9.29 | 0.69 | 2.54 |
| 10. | 2016. 5. 31. | -0.68% | 1.53% | 5.34 | 0.18 | -0.99 |
| 11. | 2016. 6. 30. | 5.19% | 0.09% | 12.66 | 1.03 | -3.60 |
| 12. | 2016. 7. 31. | -3.18% | 3.56% | 23.15 | 6.04 | -11.82 |
| 13. | 2016. 8. 31. | 0.97% | -0.12% | 0.44 | 1.50 | 0.82 |
| 14. | 2016. 9. 30. | -1.20% | -0.12% | 8.04 | 1.51 | 3.48 |
| 15. | 2016. 10. 31. | -1.29% | -1.94% | 8.56 | 9.28 | 8.91 |
| 16. | 2016. 11. 30. | 10.29% | 3.42% | 74.98 | 5.35 | 20.04 |
| 17. | 2016. 12. 31. | 7.63% | 1.82% | 36.01 | 0.51 | 4.30 |
| 18. | 2017. 1. 31. | -1.74% | 1.79% | 11.39 | 0.47 | -2.31 |
| 19. | 2017. 2. 28. | 1.61% | 3.72% | 0.00 | 6.84 | -0.05 |
| 20. | 2017. 3. 31. | 0.33% | -0.04% | 1.69 | 1.31 | 1.49 |
| 21. | 2017. 4. 30. | 2.05% | 0.91% | 0.17 | 0.04 | -0.08 |
| 22. | 2017. 5. 31. | -2.03% | 1.16% | 13.41 | 0.00 | -0.20 |
| 23. | 2017. 6. 30. | 0.64% | 0.48% | 0.98 | 0.39 | 0.61 |
| 24. | 2017. 7. 31. | 16.06% | 1.93% | 208.00 | 0.69 | 11.99 |
| 25. | 2017. 8. 31. | -10.46% | 0.05% | 146.28 | 1.10 | 12.69 |
| 26. | 2017. 9. 30. | 3.21% | 1.93% | 2.49 | 0.68 | 1.31 |
| 27. | 2017. 10. 31. | 6.35% | 2.22% | 22.24 | 1.24 | 5.26 |
| 28. | 2017. 11. 30. | -1.55% | 2.81% | 10.12 | 2.91 | -5.42 |
| 29. | 2017. 12. 31. | 2.94% | 0.98% | 1.70 | 0.01 | -0.16 |
| 30. | 2018. 1. 31. | 5.50% | 5.62% | 14.92 | 20.38 | 17.44 |
| 31. | 2018. 2. 28. | -6.72% | -3.89% | 69.80 | 24.98 | 41.76 |
| 32. | 2018. 3. 31. | -1.05% | -2.69% | 7.19 | 14.38 | 10.17 |
| 33. | 2018. 4. 30. | 4.05% | 0.27% | 5.86 | 0.69 | -2.01 |
| 34. | 2018. 5. 31. | 10.11% | 2.16% | 71.89 | 1.12 | 8.96 |
| 35. | 2018. 6. 30. | 3.70% | 0.48% | 4.27 | 0.38 | -1.28 |
| 36. | 2018. 7. 31. | 0.63% | 3.60% | 1.00 | 6.24 | -2.50 |
| 37. | 2018. 8. 31. | 8.71% | 3.03% | 50.11 | 3.70 | 13.61 |
| 38. | 2018. 9. 30. | 3.13% | 0.43% | 2.26 | 0.45 | -1.01 |
| 39. | 2018. 10. 31. | -4.37% | -6.94% | 36.00 | 64.70 | 48.27 |
| 40. | 2018. 11. 30. | 2.32% | 1.79% | 0.47 | 0.47 | 0.47 |
| 41. | 2018. 12. 31. | -10.52% | -9.18% | 147.71 | 105.71 | 124.96 |
| 42. | 2019. 1. 31. | 6.65% | 7.87% | 25.18 | 45.76 | 33.94 |
| 43. | 2019. 2. 28. | 9.43% | 2.97% | 60.83 | 3.49 | 14.58 |
| 44. | 2019. 3. 31. | 4.90% | 1.79% | 10.68 | 0.47 | 2.25 |
| 45. | 2019. 4. 30. | 2.91% | 3.93% | 1.63 | 8.00 | 3.61 |
| 46. | 2019. 5. 31. | -2.60% | -6.58% | 17.89 | 59.00 | 32.49 |
| 47. | 2019. 6. 30. | 3.75% | 6.89% | 4.47 | 33.52 | 12.24 |
| 48. | 2019. 7. 31. | 0.72% | 1.31% | 0.83 | 0.04 | -0.19 |
| 49. | 2019. 8. 31. | 1.99% | -1.81% | 0.13 | 8.48 | -1.05 |
| 50. | 2019. 9. 30. | -4.49% | 1.72% | 37.52 | 0.38 | -3.76 |
| 51. | 2019. 10. 31. | 0.50% | 2.04% | 1.28 | 0.88 | -1.06 |
| 52. | 2019. 11. 30. | 5.27% | 3.40% | 13.23 | 5.30 | 8.37 |
| 53. | 2019. 12. 31. | 0.37% | 2.86% | 1.60 | 3.08 | -2.22 |
| 54. | 2020. 1. 31. | 0.52% | -0.16% | 1.23 | 1.60 | 1.41 |
| 55. | 2020. 2. 29. | -9.71% | -8.41% | 128.76 | 90.53 | 107.97 |
| 56. | 2020. 3. 31. | -11.08% | -12.51% | 161.69 | 185.38 | 173.13 |
| 57. | 2020. 4. 30. | 7.32% | 12.68% | 32.39 | 134.12 | 65.91 |
| 58. | 2020. 5. 31. | -0.14% | 4.53% | 3.13 | 11.73 | -6.06 |
| 59. | 2020. 6. 30. | 2.26% | 1.84% | 0.39 | 0.54 | 0.46 |
| 60. | 2020. 7. 31. | -10.73% | 5.51% | 152.91 | 19.42 | -54.49 |
| 61. | 2020. 8. 31. | 4.65% | 7.01% | 9.10 | 34.84 | 17.81 |
| 62. | 2020. 9. 30. | 0.94% | -3.92% | 0.48 | 25.26 | 3.47 |
| 63. | 2020. 10. 31. | 13.24% | -2.77% | 134.75 | 14.98 | -44.93 |
| 64. | 2020. 11. 30. | 10.08% | 10.75% | 71.33 | 93.14 | 81.51 |
| 65. | 2020. 12. 31. | 1.87% | 3.71% | 0.06 | 6.80 | 0.62 |
| 66. | 2021. 1. 31. | -6.29% | -1.11% | 62.74 | 4.92 | 17.56 |
| 67. | 2021. 2. 28. | 5.39% | 2.61% | 14.12 | 2.27 | 5.66 |
| 68. | 2021. 3. 31. | 8.84% | 4.24% | 51.92 | 9.86 | 22.63 |
| 69. | 2021. 4. 30. | -0.79% | 5.24% | 5.85 | 17.13 | -10.01 |
| 70. | 2021. 5. 31. | 4.83% | 0.55% | 10.22 | 0.31 | -1.77 |
| 71. | 2021. 6. 30. | 1.80% | 2.22% | 0.03 | 1.25 | 0.19 |
| 합계 (Σ): | 2,150.24 | 1,307.41 | 918.31 | |||
모두 보기
분산ADP = Σ(RADP,t–RADP)2 ÷ (71 – 1)
= 2,150.24 ÷ (71 – 1)
= 30.72
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,307.41 ÷ (71 – 1)
= 18.68
공분산ADP, S&P 500 = Σ(RADP,t–RADP)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 918.31 ÷ (71 – 1)
= 13.12
체계적인 위험 추정 (β)
| 분산ADP | 30.72 |
| 분산S&P 500 | 18.68 |
| 공분산ADP, S&P 500 | 13.12 |
| 상관 계수ADP, S&P 5001 | 0.55 |
| βADP2 | 0.70 |
| αADP3 | 0.86% |
계산
1 상관 계수ADP, S&P 500
= 공분산ADP, S&P 500 ÷ (표준 편차ADP × 표준 편차S&P 500)
= 13.12 ÷ (5.54% × 4.32%)
= 0.55
2 βADP
= 공분산ADP, S&P 500 ÷ 분산S&P 500
= 13.12 ÷ 18.68
= 0.70
3 αADP
= 평균의ADP – βADP × 평균의S&P 500
= 1.63% – 0.70 × 1.10%
= 0.86%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.94% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.36% |
| 보통주의 체계적 위험ADP | βADP | 0.70 |
| ADP 보통주 예상 수익률3 | E(RADP) | 13.66% |
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(RADP) = RF + βADP [E(RM) – RF]
= 4.94% + 0.70 [17.36% – 4.94%]
= 13.66%