자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Accenture보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Accenture PLC, 월별 수익률
| Accenture PLC (ACN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ACN,t1 | 피제수ACN,t1 | RACN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 9. 30. | $135.07 | 2,519.36 | ||||
| 1. | 2017. 10. 31. | $142.36 | $1.33 | 6.38% | 2,575.26 | 2.22% |
| 2. | 2017. 11. 30. | $148.01 | 3.97% | 2,647.58 | 2.81% | |
| 3. | 2017. 12. 31. | $153.09 | 3.43% | 2,673.61 | 0.98% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 7. 31. | $316.35 | $1.12 | 2.88% | 4,588.96 | 4.85% |
| 71. | 2023. 8. 31. | $323.77 | 2.35% | 4,507.66 | -1.77% | |
| 평균의 (R): | 1.63% | 0.95% | ||||
| 표준 편차: | 7.17% | 5.08% | ||||
| Accenture PLC (ACN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ACN,t1 | 피제수ACN,t1 | RACN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 9. 30. | $135.07 | 2,519.36 | ||||
| 1. | 2017. 10. 31. | $142.36 | $1.33 | 6.38% | 2,575.26 | 2.22% |
| 2. | 2017. 11. 30. | $148.01 | 3.97% | 2,647.58 | 2.81% | |
| 3. | 2017. 12. 31. | $153.09 | 3.43% | 2,673.61 | 0.98% | |
| 4. | 2018. 1. 31. | $160.70 | 4.97% | 2,823.81 | 5.62% | |
| 5. | 2018. 2. 28. | $161.01 | 0.19% | 2,713.83 | -3.89% | |
| 6. | 2018. 3. 31. | $153.50 | -4.66% | 2,640.87 | -2.69% | |
| 7. | 2018. 4. 30. | $151.20 | $1.33 | -0.63% | 2,648.05 | 0.27% |
| 8. | 2018. 5. 31. | $155.74 | 3.00% | 2,705.27 | 2.16% | |
| 9. | 2018. 6. 30. | $163.59 | 5.04% | 2,718.37 | 0.48% | |
| 10. | 2018. 7. 31. | $159.33 | -2.60% | 2,816.29 | 3.60% | |
| 11. | 2018. 8. 31. | $169.07 | 6.11% | 2,901.52 | 3.03% | |
| 12. | 2018. 9. 30. | $170.20 | 0.67% | 2,913.98 | 0.43% | |
| 13. | 2018. 10. 31. | $157.62 | $1.46 | -6.53% | 2,711.74 | -6.94% |
| 14. | 2018. 11. 30. | $164.52 | 4.38% | 2,760.17 | 1.79% | |
| 15. | 2018. 12. 31. | $141.01 | -14.29% | 2,506.85 | -9.18% | |
| 16. | 2019. 1. 31. | $153.55 | 8.89% | 2,704.10 | 7.87% | |
| 17. | 2019. 2. 28. | $161.38 | 5.10% | 2,784.49 | 2.97% | |
| 18. | 2019. 3. 31. | $176.02 | 9.07% | 2,834.40 | 1.79% | |
| 19. | 2019. 4. 30. | $182.67 | $1.46 | 4.61% | 2,945.83 | 3.93% |
| 20. | 2019. 5. 31. | $178.07 | -2.52% | 2,752.06 | -6.58% | |
| 21. | 2019. 6. 30. | $184.77 | 3.76% | 2,941.76 | 6.89% | |
| 22. | 2019. 7. 31. | $192.58 | 4.23% | 2,980.38 | 1.31% | |
| 23. | 2019. 8. 31. | $198.17 | 2.90% | 2,926.46 | -1.81% | |
| 24. | 2019. 9. 30. | $192.35 | -2.94% | 2,976.74 | 1.72% | |
| 25. | 2019. 10. 31. | $185.42 | $0.80 | -3.19% | 3,037.56 | 2.04% |
| 26. | 2019. 11. 30. | $201.16 | 8.49% | 3,140.98 | 3.40% | |
| 27. | 2019. 12. 31. | $210.57 | 4.68% | 3,230.78 | 2.86% | |
| 28. | 2020. 1. 31. | $205.21 | $0.80 | -2.17% | 3,225.52 | -0.16% |
| 29. | 2020. 2. 29. | $180.59 | -12.00% | 2,954.22 | -8.41% | |
| 30. | 2020. 3. 31. | $163.26 | -9.60% | 2,584.59 | -12.51% | |
| 31. | 2020. 4. 30. | $185.19 | $0.80 | 13.92% | 2,912.43 | 12.68% |
| 32. | 2020. 5. 31. | $201.62 | 8.87% | 3,044.31 | 4.53% | |
| 33. | 2020. 6. 30. | $214.72 | 6.50% | 3,100.29 | 1.84% | |
| 34. | 2020. 7. 31. | $224.78 | $0.80 | 5.06% | 3,271.12 | 5.51% |
| 35. | 2020. 8. 31. | $239.93 | 6.74% | 3,500.31 | 7.01% | |
| 36. | 2020. 9. 30. | $225.99 | -5.81% | 3,363.00 | -3.92% | |
| 37. | 2020. 10. 31. | $216.91 | $0.88 | -3.63% | 3,269.96 | -2.77% |
| 38. | 2020. 11. 30. | $249.09 | 14.84% | 3,621.63 | 10.75% | |
| 39. | 2020. 12. 31. | $261.21 | 4.87% | 3,756.07 | 3.71% | |
| 40. | 2021. 1. 31. | $241.92 | $0.88 | -7.05% | 3,714.24 | -1.11% |
| 41. | 2021. 2. 28. | $250.90 | 3.71% | 3,811.15 | 2.61% | |
| 42. | 2021. 3. 31. | $276.25 | 10.10% | 3,972.89 | 4.24% | |
| 43. | 2021. 4. 30. | $289.97 | $0.88 | 5.29% | 4,181.17 | 5.24% |
| 44. | 2021. 5. 31. | $282.16 | -2.69% | 4,204.11 | 0.55% | |
| 45. | 2021. 6. 30. | $294.79 | 4.48% | 4,297.50 | 2.22% | |
| 46. | 2021. 7. 31. | $317.68 | $0.88 | 8.06% | 4,395.26 | 2.27% |
| 47. | 2021. 8. 31. | $336.56 | 5.94% | 4,522.68 | 2.90% | |
| 48. | 2021. 9. 30. | $319.92 | -4.94% | 4,307.54 | -4.76% | |
| 49. | 2021. 10. 31. | $358.79 | $0.97 | 12.45% | 4,605.38 | 6.91% |
| 50. | 2021. 11. 30. | $357.40 | -0.39% | 4,567.00 | -0.83% | |
| 51. | 2021. 12. 31. | $414.55 | 15.99% | 4,766.18 | 4.36% | |
| 52. | 2022. 1. 31. | $353.58 | $0.97 | -14.47% | 4,515.55 | -5.26% |
| 53. | 2022. 2. 28. | $316.02 | -10.62% | 4,373.94 | -3.14% | |
| 54. | 2022. 3. 31. | $337.23 | 6.71% | 4,530.41 | 3.58% | |
| 55. | 2022. 4. 30. | $300.36 | $0.97 | -10.65% | 4,131.93 | -8.80% |
| 56. | 2022. 5. 31. | $298.46 | -0.63% | 4,132.15 | 0.01% | |
| 57. | 2022. 6. 30. | $277.65 | -6.97% | 3,785.38 | -8.39% | |
| 58. | 2022. 7. 31. | $306.26 | $0.97 | 10.65% | 4,130.29 | 9.11% |
| 59. | 2022. 8. 31. | $288.46 | -5.81% | 3,955.00 | -4.24% | |
| 60. | 2022. 9. 30. | $257.30 | -10.80% | 3,585.62 | -9.34% | |
| 61. | 2022. 10. 31. | $283.90 | $1.12 | 10.77% | 3,871.98 | 7.99% |
| 62. | 2022. 11. 30. | $300.93 | 6.00% | 4,080.11 | 5.38% | |
| 63. | 2022. 12. 31. | $266.84 | -11.33% | 3,839.50 | -5.90% | |
| 64. | 2023. 1. 31. | $279.05 | $1.12 | 5.00% | 4,076.60 | 6.18% |
| 65. | 2023. 2. 28. | $265.55 | -4.84% | 3,970.15 | -2.61% | |
| 66. | 2023. 3. 31. | $285.81 | 7.63% | 4,109.31 | 3.51% | |
| 67. | 2023. 4. 30. | $280.29 | $1.12 | -1.54% | 4,169.48 | 1.46% |
| 68. | 2023. 5. 31. | $305.92 | 9.14% | 4,179.83 | 0.25% | |
| 69. | 2023. 6. 30. | $308.58 | 0.87% | 4,376.86 | 4.71% | |
| 70. | 2023. 7. 31. | $316.35 | $1.12 | 2.88% | 4,588.96 | 4.85% |
| 71. | 2023. 8. 31. | $323.77 | 2.35% | 4,507.66 | -1.77% | |
| 평균의 (R): | 1.63% | 0.95% | ||||
| 표준 편차: | 7.17% | 5.08% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 ACN의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Accenture PLC, 수익률의 분산 및 공분산 계산
| t | 날짜 | RACN,t | RS&P 500,t | (RACN,t–RACN)2 | (RS&P 500,t–RS&P 500)2 | (RACN,t–RACN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 10. 31. | 6.38% | 2.22% | 22.63 | 1.61 | 6.03 |
| 2. | 2017. 11. 30. | 3.97% | 2.81% | 5.49 | 3.45 | 4.35 |
| 3. | 2017. 12. 31. | 3.43% | 0.98% | 3.26 | 0.00 | 0.06 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 7. 31. | 2.88% | 4.85% | 1.58 | 15.17 | 4.89 |
| 71. | 2023. 8. 31. | 2.35% | -1.77% | 0.52 | 7.41 | -1.96 |
| 합계 (Σ): | 3,595.64 | 1,807.09 | 2,179.01 | |||
| t | 날짜 | RACN,t | RS&P 500,t | (RACN,t–RACN)2 | (RS&P 500,t–RS&P 500)2 | (RACN,t–RACN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 10. 31. | 6.38% | 2.22% | 22.63 | 1.61 | 6.03 |
| 2. | 2017. 11. 30. | 3.97% | 2.81% | 5.49 | 3.45 | 4.35 |
| 3. | 2017. 12. 31. | 3.43% | 0.98% | 3.26 | 0.00 | 0.06 |
| 4. | 2018. 1. 31. | 4.97% | 5.62% | 11.19 | 21.78 | 15.61 |
| 5. | 2018. 2. 28. | 0.19% | -3.89% | 2.05 | 23.48 | 6.94 |
| 6. | 2018. 3. 31. | -4.66% | -2.69% | 39.56 | 13.25 | 22.89 |
| 7. | 2018. 4. 30. | -0.63% | 0.27% | 5.10 | 0.46 | 1.53 |
| 8. | 2018. 5. 31. | 3.00% | 2.16% | 1.90 | 1.46 | 1.67 |
| 9. | 2018. 6. 30. | 5.04% | 0.48% | 11.66 | 0.22 | -1.59 |
| 10. | 2018. 7. 31. | -2.60% | 3.60% | 17.89 | 7.03 | -11.21 |
| 11. | 2018. 8. 31. | 6.11% | 3.03% | 20.14 | 4.31 | 9.31 |
| 12. | 2018. 9. 30. | 0.67% | 0.43% | 0.92 | 0.27 | 0.50 |
| 13. | 2018. 10. 31. | -6.53% | -6.94% | 66.57 | 62.28 | 64.38 |
| 14. | 2018. 11. 30. | 4.38% | 1.79% | 7.58 | 0.70 | 2.30 |
| 15. | 2018. 12. 31. | -14.29% | -9.18% | 253.30 | 102.59 | 161.20 |
| 16. | 2019. 1. 31. | 8.89% | 7.87% | 52.82 | 47.85 | 50.27 |
| 17. | 2019. 2. 28. | 5.10% | 2.97% | 12.07 | 4.09 | 7.02 |
| 18. | 2019. 3. 31. | 9.07% | 1.79% | 55.45 | 0.71 | 6.26 |
| 19. | 2019. 4. 30. | 4.61% | 3.93% | 8.89 | 8.88 | 8.89 |
| 20. | 2019. 5. 31. | -2.52% | -6.58% | 17.17 | 56.68 | 31.20 |
| 21. | 2019. 6. 30. | 3.76% | 6.89% | 4.57 | 35.31 | 12.70 |
| 22. | 2019. 7. 31. | 4.23% | 1.31% | 6.77 | 0.13 | 0.94 |
| 23. | 2019. 8. 31. | 2.90% | -1.81% | 1.63 | 7.62 | -3.53 |
| 24. | 2019. 9. 30. | -2.94% | 1.72% | 20.81 | 0.59 | -3.50 |
| 25. | 2019. 10. 31. | -3.19% | 2.04% | 23.16 | 1.19 | -5.26 |
| 26. | 2019. 11. 30. | 8.49% | 3.40% | 47.11 | 6.02 | 16.84 |
| 27. | 2019. 12. 31. | 4.68% | 2.86% | 9.32 | 3.64 | 5.82 |
| 28. | 2020. 1. 31. | -2.17% | -0.16% | 14.37 | 1.24 | 4.22 |
| 29. | 2020. 2. 29. | -12.00% | -8.41% | 185.58 | 87.65 | 127.54 |
| 30. | 2020. 3. 31. | -9.60% | -12.51% | 125.92 | 181.25 | 151.08 |
| 31. | 2020. 4. 30. | 13.92% | 12.68% | 151.22 | 137.67 | 144.29 |
| 32. | 2020. 5. 31. | 8.87% | 4.53% | 52.51 | 12.80 | 25.92 |
| 33. | 2020. 6. 30. | 6.50% | 1.84% | 23.74 | 0.79 | 4.32 |
| 34. | 2020. 7. 31. | 5.06% | 5.51% | 11.78 | 20.78 | 15.65 |
| 35. | 2020. 8. 31. | 6.74% | 7.01% | 26.16 | 36.67 | 30.97 |
| 36. | 2020. 9. 30. | -5.81% | -3.92% | 55.28 | 23.76 | 36.24 |
| 37. | 2020. 10. 31. | -3.63% | -2.77% | 27.60 | 13.82 | 19.53 |
| 38. | 2020. 11. 30. | 14.84% | 10.75% | 174.51 | 96.11 | 129.51 |
| 39. | 2020. 12. 31. | 4.87% | 3.71% | 10.50 | 7.62 | 8.95 |
| 40. | 2021. 1. 31. | -7.05% | -1.11% | 75.23 | 4.26 | 17.91 |
| 41. | 2021. 2. 28. | 3.71% | 2.61% | 4.35 | 2.75 | 3.46 |
| 42. | 2021. 3. 31. | 10.10% | 4.24% | 71.88 | 10.84 | 27.92 |
| 43. | 2021. 4. 30. | 5.29% | 5.24% | 13.39 | 18.42 | 15.71 |
| 44. | 2021. 5. 31. | -2.69% | 0.55% | 18.65 | 0.16 | 1.74 |
| 45. | 2021. 6. 30. | 4.48% | 2.22% | 8.13 | 1.61 | 3.62 |
| 46. | 2021. 7. 31. | 8.06% | 2.27% | 41.45 | 1.75 | 8.52 |
| 47. | 2021. 8. 31. | 5.94% | 2.90% | 18.64 | 3.79 | 8.41 |
| 48. | 2021. 9. 30. | -4.94% | -4.76% | 43.16 | 32.58 | 37.50 |
| 49. | 2021. 10. 31. | 12.45% | 6.91% | 117.24 | 35.56 | 64.57 |
| 50. | 2021. 11. 30. | -0.39% | -0.83% | 4.05 | 3.18 | 3.59 |
| 51. | 2021. 12. 31. | 15.99% | 4.36% | 206.36 | 11.63 | 48.99 |
| 52. | 2022. 1. 31. | -14.47% | -5.26% | 259.17 | 38.56 | 99.97 |
| 53. | 2022. 2. 28. | -10.62% | -3.14% | 150.02 | 16.71 | 50.06 |
| 54. | 2022. 3. 31. | 6.71% | 3.58% | 25.87 | 6.90 | 13.36 |
| 55. | 2022. 4. 30. | -10.65% | -8.80% | 150.57 | 95.00 | 119.60 |
| 56. | 2022. 5. 31. | -0.63% | 0.01% | 5.10 | 0.89 | 2.14 |
| 57. | 2022. 6. 30. | -6.97% | -8.39% | 73.92 | 87.29 | 80.33 |
| 58. | 2022. 7. 31. | 10.65% | 9.11% | 81.51 | 66.59 | 73.68 |
| 59. | 2022. 8. 31. | -5.81% | -4.24% | 55.31 | 26.99 | 38.64 |
| 60. | 2022. 9. 30. | -10.80% | -9.34% | 154.44 | 105.90 | 127.89 |
| 61. | 2022. 10. 31. | 10.77% | 7.99% | 83.69 | 49.49 | 64.36 |
| 62. | 2022. 11. 30. | 6.00% | 5.38% | 19.13 | 19.57 | 19.35 |
| 63. | 2022. 12. 31. | -11.33% | -5.90% | 167.79 | 46.90 | 88.71 |
| 64. | 2023. 1. 31. | 5.00% | 6.18% | 11.36 | 27.29 | 17.61 |
| 65. | 2023. 2. 28. | -4.84% | -2.61% | 41.77 | 12.69 | 23.02 |
| 66. | 2023. 3. 31. | 7.63% | 3.51% | 36.05 | 6.52 | 15.33 |
| 67. | 2023. 4. 30. | -1.54% | 1.46% | 10.02 | 0.26 | -1.62 |
| 68. | 2023. 5. 31. | 9.14% | 0.25% | 56.53 | 0.49 | -5.28 |
| 69. | 2023. 6. 30. | 0.87% | 4.71% | 0.57 | 14.16 | -2.84 |
| 70. | 2023. 7. 31. | 2.88% | 4.85% | 1.58 | 15.17 | 4.89 |
| 71. | 2023. 8. 31. | 2.35% | -1.77% | 0.52 | 7.41 | -1.96 |
| 합계 (Σ): | 3,595.64 | 1,807.09 | 2,179.01 | |||
모두 표시
분산ACN = Σ(RACN,t–RACN)2 ÷ (71 – 1)
= 3,595.64 ÷ (71 – 1)
= 51.37
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,807.09 ÷ (71 – 1)
= 25.82
공분산ACN, S&P 500 = Σ(RACN,t–RACN)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,179.01 ÷ (71 – 1)
= 31.13
체계적인 위험 추정 (β)
| 분산ACN | 51.37 |
| 분산S&P 500 | 25.82 |
| 공분산ACN, S&P 500 | 31.13 |
| 상관 계수ACN, S&P 5001 | 0.85 |
| βACN2 | 1.21 |
| αACN3 | 0.48% |
계산
1 상관 계수ACN, S&P 500
= 공분산ACN, S&P 500 ÷ (표준 편차ACN × 표준 편차S&P 500)
= 31.13 ÷ (7.17% × 5.08%)
= 0.85
2 βACN
= 공분산ACN, S&P 500 ÷ 분산S&P 500
= 31.13 ÷ 25.82
= 1.21
3 αACN
= 평균의ACN – βACN × 평균의S&P 500
= 1.63% – 1.21 × 0.95%
= 0.48%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.79% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.48% |
| 보통주의 체계적 위험Accenture | βACN | 1.21 |
| Accenture 보통주에 대한 예상 수익률3 | E(RACN) | 15.26% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RACN) = RF + βACN [E(RM) – RF]
= 4.79% + 1.21 [13.48% – 4.79%]
= 15.26%