자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 RH의 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
RH, 월별 수익률
| RH (RH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값RH,t1 | 피제수RH,t1 | RRH,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 2. 28. | $30.44 | 2,363.64 | ||||
| 1. | 2017. 3. 31. | $46.26 | 51.97% | 2,362.72 | -0.04% | |
| 2. | 2017. 4. 30. | $47.97 | 3.70% | 2,384.20 | 0.91% | |
| 3. | 2017. 5. 31. | $56.11 | 16.97% | 2,411.80 | 1.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2022. 12. 31. | $267.19 | -6.85% | 3,839.50 | -5.90% | |
| 71. | 2023. 1. 31. | $311.99 | 16.77% | 4,076.60 | 6.18% | |
| 평균의 (R): | 5.13% | 0.90% | ||||
| 표준 편차: | 19.44% | 5.01% | ||||
| RH (RH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값RH,t1 | 피제수RH,t1 | RRH,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 2. 28. | $30.44 | 2,363.64 | ||||
| 1. | 2017. 3. 31. | $46.26 | 51.97% | 2,362.72 | -0.04% | |
| 2. | 2017. 4. 30. | $47.97 | 3.70% | 2,384.20 | 0.91% | |
| 3. | 2017. 5. 31. | $56.11 | 16.97% | 2,411.80 | 1.16% | |
| 4. | 2017. 6. 30. | $64.52 | 14.99% | 2,423.41 | 0.48% | |
| 5. | 2017. 7. 31. | $65.13 | 0.95% | 2,470.30 | 1.93% | |
| 6. | 2017. 8. 31. | $46.79 | -28.16% | 2,471.65 | 0.05% | |
| 7. | 2017. 9. 30. | $70.32 | 50.29% | 2,519.36 | 1.93% | |
| 8. | 2017. 10. 31. | $89.92 | 27.87% | 2,575.26 | 2.22% | |
| 9. | 2017. 11. 30. | $101.39 | 12.76% | 2,647.58 | 2.81% | |
| 10. | 2017. 12. 31. | $86.21 | -14.97% | 2,673.61 | 0.98% | |
| 11. | 2018. 1. 31. | $93.99 | 9.02% | 2,823.81 | 5.62% | |
| 12. | 2018. 2. 28. | $84.88 | -9.69% | 2,713.83 | -3.89% | |
| 13. | 2018. 3. 31. | $95.28 | 12.25% | 2,640.87 | -2.69% | |
| 14. | 2018. 4. 30. | $95.45 | 0.18% | 2,648.05 | 0.27% | |
| 15. | 2018. 5. 31. | $97.73 | 2.39% | 2,705.27 | 2.16% | |
| 16. | 2018. 6. 30. | $139.70 | 42.94% | 2,718.37 | 0.48% | |
| 17. | 2018. 7. 31. | $135.86 | -2.75% | 2,816.29 | 3.60% | |
| 18. | 2018. 8. 31. | $159.00 | 17.03% | 2,901.52 | 3.03% | |
| 19. | 2018. 9. 30. | $131.01 | -17.60% | 2,913.98 | 0.43% | |
| 20. | 2018. 10. 31. | $115.71 | -11.68% | 2,711.74 | -6.94% | |
| 21. | 2018. 11. 30. | $116.14 | 0.37% | 2,760.17 | 1.79% | |
| 22. | 2018. 12. 31. | $119.82 | 3.17% | 2,506.85 | -9.18% | |
| 23. | 2019. 1. 31. | $135.87 | 13.40% | 2,704.10 | 7.87% | |
| 24. | 2019. 2. 28. | $153.59 | 13.04% | 2,784.49 | 2.97% | |
| 25. | 2019. 3. 31. | $102.95 | -32.97% | 2,834.40 | 1.79% | |
| 26. | 2019. 4. 30. | $106.71 | 3.65% | 2,945.83 | 3.93% | |
| 27. | 2019. 5. 31. | $85.15 | -20.20% | 2,752.06 | -6.58% | |
| 28. | 2019. 6. 30. | $115.60 | 35.76% | 2,941.76 | 6.89% | |
| 29. | 2019. 7. 31. | $139.40 | 20.59% | 2,980.38 | 1.31% | |
| 30. | 2019. 8. 31. | $143.25 | 2.76% | 2,926.46 | -1.81% | |
| 31. | 2019. 9. 30. | $170.83 | 19.25% | 2,976.74 | 1.72% | |
| 32. | 2019. 10. 31. | $181.70 | 6.36% | 3,037.56 | 2.04% | |
| 33. | 2019. 11. 30. | $205.59 | 13.15% | 3,140.98 | 3.40% | |
| 34. | 2019. 12. 31. | $213.50 | 3.85% | 3,230.78 | 2.86% | |
| 35. | 2020. 1. 31. | $208.75 | -2.22% | 3,225.52 | -0.16% | |
| 36. | 2020. 2. 29. | $181.40 | -13.10% | 2,954.22 | -8.41% | |
| 37. | 2020. 3. 31. | $100.47 | -44.61% | 2,584.59 | -12.51% | |
| 38. | 2020. 4. 30. | $143.78 | 43.11% | 2,912.43 | 12.68% | |
| 39. | 2020. 5. 31. | $216.89 | 50.85% | 3,044.31 | 4.53% | |
| 40. | 2020. 6. 30. | $248.90 | 14.76% | 3,100.29 | 1.84% | |
| 41. | 2020. 7. 31. | $287.43 | 15.48% | 3,271.12 | 5.51% | |
| 42. | 2020. 8. 31. | $330.55 | 15.00% | 3,500.31 | 7.01% | |
| 43. | 2020. 9. 30. | $382.62 | 15.75% | 3,363.00 | -3.92% | |
| 44. | 2020. 10. 31. | $335.23 | -12.39% | 3,269.96 | -2.77% | |
| 45. | 2020. 11. 30. | $453.16 | 35.18% | 3,621.63 | 10.75% | |
| 46. | 2020. 12. 31. | $447.52 | -1.24% | 3,756.07 | 3.71% | |
| 47. | 2021. 1. 31. | $475.36 | 6.22% | 3,714.24 | -1.11% | |
| 48. | 2021. 2. 28. | $490.37 | 3.16% | 3,811.15 | 2.61% | |
| 49. | 2021. 3. 31. | $596.60 | 21.66% | 3,972.89 | 4.24% | |
| 50. | 2021. 4. 30. | $688.02 | 15.32% | 4,181.17 | 5.24% | |
| 51. | 2021. 5. 31. | $641.05 | -6.83% | 4,204.11 | 0.55% | |
| 52. | 2021. 6. 30. | $679.00 | 5.92% | 4,297.50 | 2.22% | |
| 53. | 2021. 7. 31. | $664.08 | -2.20% | 4,395.26 | 2.27% | |
| 54. | 2021. 8. 31. | $700.67 | 5.51% | 4,522.68 | 2.90% | |
| 55. | 2021. 9. 30. | $666.91 | -4.82% | 4,307.54 | -4.76% | |
| 56. | 2021. 10. 31. | $659.63 | -1.09% | 4,605.38 | 6.91% | |
| 57. | 2021. 11. 30. | $583.18 | -11.59% | 4,567.00 | -0.83% | |
| 58. | 2021. 12. 31. | $535.94 | -8.10% | 4,766.18 | 4.36% | |
| 59. | 2022. 1. 31. | $402.82 | -24.84% | 4,515.55 | -5.26% | |
| 60. | 2022. 2. 28. | $401.87 | -0.24% | 4,373.94 | -3.14% | |
| 61. | 2022. 3. 31. | $326.09 | -18.86% | 4,530.41 | 3.58% | |
| 62. | 2022. 4. 30. | $336.12 | 3.08% | 4,131.93 | -8.80% | |
| 63. | 2022. 5. 31. | $290.08 | -13.70% | 4,132.15 | 0.01% | |
| 64. | 2022. 6. 30. | $212.26 | -26.83% | 3,785.38 | -8.39% | |
| 65. | 2022. 7. 31. | $279.43 | 31.65% | 4,130.29 | 9.11% | |
| 66. | 2022. 8. 31. | $255.91 | -8.42% | 3,955.00 | -4.24% | |
| 67. | 2022. 9. 30. | $246.07 | -3.85% | 3,585.62 | -9.34% | |
| 68. | 2022. 10. 31. | $253.93 | 3.19% | 3,871.98 | 7.99% | |
| 69. | 2022. 11. 30. | $286.83 | 12.96% | 4,080.11 | 5.38% | |
| 70. | 2022. 12. 31. | $267.19 | -6.85% | 3,839.50 | -5.90% | |
| 71. | 2023. 1. 31. | $311.99 | 16.77% | 4,076.60 | 6.18% | |
| 평균의 (R): | 5.13% | 0.90% | ||||
| 표준 편차: | 19.44% | 5.01% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 RH의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
RH, 수익률의 분산 및 공분산 계산
| t | 날짜 | RRH,t | RS&P 500,t | (RRH,t–RRH)2 | (RS&P 500,t–RS&P 500)2 | (RRH,t–RRH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 3. 31. | 51.97% | -0.04% | 2,193.82 | 0.87 | -43.76 |
| 2. | 2017. 4. 30. | 3.70% | 0.91% | 2.06 | 0.00 | -0.02 |
| 3. | 2017. 5. 31. | 16.97% | 1.16% | 140.09 | 0.07 | 3.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2022. 12. 31. | -6.85% | -5.90% | 143.52 | 46.14 | 81.37 |
| 71. | 2023. 1. 31. | 16.77% | 6.18% | 135.36 | 27.88 | 61.43 |
| 합계 (Σ): | 26,450.59 | 1,754.14 | 3,707.33 | |||
| t | 날짜 | RRH,t | RS&P 500,t | (RRH,t–RRH)2 | (RS&P 500,t–RS&P 500)2 | (RRH,t–RRH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 3. 31. | 51.97% | -0.04% | 2,193.82 | 0.87 | -43.76 |
| 2. | 2017. 4. 30. | 3.70% | 0.91% | 2.06 | 0.00 | -0.02 |
| 3. | 2017. 5. 31. | 16.97% | 1.16% | 140.09 | 0.07 | 3.11 |
| 4. | 2017. 6. 30. | 14.99% | 0.48% | 97.13 | 0.17 | -4.08 |
| 5. | 2017. 7. 31. | 0.95% | 1.93% | 17.53 | 1.08 | -4.35 |
| 6. | 2017. 8. 31. | -28.16% | 0.05% | 1,108.35 | 0.71 | 27.99 |
| 7. | 2017. 9. 30. | 50.29% | 1.93% | 2,039.04 | 1.07 | 46.74 |
| 8. | 2017. 10. 31. | 27.87% | 2.22% | 517.10 | 1.75 | 30.10 |
| 9. | 2017. 11. 30. | 12.76% | 2.81% | 58.11 | 3.66 | 14.58 |
| 10. | 2017. 12. 31. | -14.97% | 0.98% | 404.20 | 0.01 | -1.77 |
| 11. | 2018. 1. 31. | 9.02% | 5.62% | 15.14 | 22.30 | 18.38 |
| 12. | 2018. 2. 28. | -9.69% | -3.89% | 219.79 | 22.94 | 71.01 |
| 13. | 2018. 3. 31. | 12.25% | -2.69% | 50.69 | 12.84 | -25.52 |
| 14. | 2018. 4. 30. | 0.18% | 0.27% | 24.55 | 0.39 | 3.09 |
| 15. | 2018. 5. 31. | 2.39% | 2.16% | 7.53 | 1.60 | -3.47 |
| 16. | 2018. 6. 30. | 42.94% | 0.48% | 1,429.75 | 0.17 | -15.54 |
| 17. | 2018. 7. 31. | -2.75% | 3.60% | 62.12 | 7.33 | -21.33 |
| 18. | 2018. 8. 31. | 17.03% | 3.03% | 141.60 | 4.54 | 25.36 |
| 19. | 2018. 9. 30. | -17.60% | 0.43% | 516.95 | 0.22 | 10.59 |
| 20. | 2018. 10. 31. | -11.68% | -6.94% | 282.62 | 61.40 | 131.73 |
| 21. | 2018. 11. 30. | 0.37% | 1.79% | 22.67 | 0.79 | -4.24 |
| 22. | 2018. 12. 31. | 3.17% | -9.18% | 3.86 | 101.46 | 19.79 |
| 23. | 2019. 1. 31. | 13.40% | 7.87% | 68.26 | 48.63 | 57.61 |
| 24. | 2019. 2. 28. | 13.04% | 2.97% | 62.55 | 4.32 | 16.43 |
| 25. | 2019. 3. 31. | -32.97% | 1.79% | 1,451.89 | 0.80 | -34.18 |
| 26. | 2019. 4. 30. | 3.65% | 3.93% | 2.19 | 9.22 | -4.50 |
| 27. | 2019. 5. 31. | -20.20% | -6.58% | 641.97 | 55.85 | 189.35 |
| 28. | 2019. 6. 30. | 35.76% | 6.89% | 938.05 | 35.97 | 183.70 |
| 29. | 2019. 7. 31. | 20.59% | 1.31% | 238.87 | 0.17 | 6.45 |
| 30. | 2019. 8. 31. | 2.76% | -1.81% | 5.62 | 7.31 | 6.41 |
| 31. | 2019. 9. 30. | 19.25% | 1.72% | 199.38 | 0.68 | 11.62 |
| 32. | 2019. 10. 31. | 6.36% | 2.04% | 1.51 | 1.32 | 1.41 |
| 33. | 2019. 11. 30. | 13.15% | 3.40% | 64.24 | 6.30 | 20.11 |
| 34. | 2019. 12. 31. | 3.85% | 2.86% | 1.65 | 3.86 | -2.52 |
| 35. | 2020. 1. 31. | -2.22% | -0.16% | 54.14 | 1.12 | 7.79 |
| 36. | 2020. 2. 29. | -13.10% | -8.41% | 332.50 | 86.61 | 169.70 |
| 37. | 2020. 3. 31. | -44.61% | -12.51% | 2,474.76 | 179.75 | 666.97 |
| 38. | 2020. 4. 30. | 43.11% | 12.68% | 1,442.07 | 138.98 | 447.69 |
| 39. | 2020. 5. 31. | 50.85% | 4.53% | 2,089.92 | 13.20 | 166.08 |
| 40. | 2020. 6. 30. | 14.76% | 1.84% | 92.66 | 0.89 | 9.08 |
| 41. | 2020. 7. 31. | 15.48% | 5.51% | 107.07 | 21.30 | 47.75 |
| 42. | 2020. 8. 31. | 15.00% | 7.01% | 97.40 | 37.35 | 60.31 |
| 43. | 2020. 9. 30. | 15.75% | -3.92% | 112.78 | 23.21 | -51.17 |
| 44. | 2020. 10. 31. | -12.39% | -2.77% | 306.90 | 13.41 | 64.15 |
| 45. | 2020. 11. 30. | 35.18% | 10.75% | 902.76 | 97.21 | 296.23 |
| 46. | 2020. 12. 31. | -1.24% | 3.71% | 40.67 | 7.93 | -17.96 |
| 47. | 2021. 1. 31. | 6.22% | -1.11% | 1.18 | 4.04 | -2.19 |
| 48. | 2021. 2. 28. | 3.16% | 2.61% | 3.90 | 2.94 | -3.39 |
| 49. | 2021. 3. 31. | 21.66% | 4.24% | 273.25 | 11.21 | 55.35 |
| 50. | 2021. 4. 30. | 15.32% | 5.24% | 103.85 | 18.90 | 44.30 |
| 51. | 2021. 5. 31. | -6.83% | 0.55% | 143.03 | 0.12 | 4.15 |
| 52. | 2021. 6. 30. | 5.92% | 2.22% | 0.62 | 1.76 | 1.04 |
| 53. | 2021. 7. 31. | -2.20% | 2.27% | 53.73 | 1.90 | -10.11 |
| 54. | 2021. 8. 31. | 5.51% | 2.90% | 0.14 | 4.02 | 0.76 |
| 55. | 2021. 9. 30. | -4.82% | -4.76% | 99.02 | 31.95 | 56.25 |
| 56. | 2021. 10. 31. | -1.09% | 6.91% | 38.74 | 36.23 | -37.47 |
| 57. | 2021. 11. 30. | -11.59% | -0.83% | 279.65 | 2.99 | 28.91 |
| 58. | 2021. 12. 31. | -8.10% | 4.36% | 175.12 | 12.01 | -45.87 |
| 59. | 2022. 1. 31. | -24.84% | -5.26% | 898.29 | 37.87 | 184.44 |
| 60. | 2022. 2. 28. | -0.24% | -3.14% | 28.82 | 16.25 | 21.64 |
| 61. | 2022. 3. 31. | -18.86% | 3.58% | 575.50 | 7.19 | -64.34 |
| 62. | 2022. 4. 30. | 3.08% | -8.80% | 4.23 | 93.91 | 19.93 |
| 63. | 2022. 5. 31. | -13.70% | 0.01% | 354.58 | 0.79 | 16.76 |
| 64. | 2022. 6. 30. | -26.83% | -8.39% | 1,021.44 | 86.25 | 296.82 |
| 65. | 2022. 7. 31. | 31.65% | 9.11% | 702.90 | 67.51 | 217.83 |
| 66. | 2022. 8. 31. | -8.42% | -4.24% | 183.60 | 26.41 | 69.64 |
| 67. | 2022. 9. 30. | -3.85% | -9.34% | 80.60 | 104.75 | 91.89 |
| 68. | 2022. 10. 31. | 3.19% | 7.99% | 3.76 | 50.28 | -13.75 |
| 69. | 2022. 11. 30. | 12.96% | 5.38% | 61.21 | 20.07 | 35.05 |
| 70. | 2022. 12. 31. | -6.85% | -5.90% | 143.52 | 46.14 | 81.37 |
| 71. | 2023. 1. 31. | 16.77% | 6.18% | 135.36 | 27.88 | 61.43 |
| 합계 (Σ): | 26,450.59 | 1,754.14 | 3,707.33 | |||
모두 보기
분산RH = Σ(RRH,t–RRH)2 ÷ (71 – 1)
= 26,450.59 ÷ (71 – 1)
= 377.87
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,754.14 ÷ (71 – 1)
= 25.06
공분산RH, S&P 500 = Σ(RRH,t–RRH)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 3,707.33 ÷ (71 – 1)
= 52.96
체계적인 위험 추정 (β)
| 분산RH | 377.87 |
| 분산S&P 500 | 25.06 |
| 공분산RH, S&P 500 | 52.96 |
| 상관 계수RH, S&P 5001 | 0.54 |
| βRH2 | 2.11 |
| αRH3 | 3.24% |
계산
1 상관 계수RH, S&P 500
= 공분산RH, S&P 500 ÷ (표준 편차RH × 표준 편차S&P 500)
= 52.96 ÷ (19.44% × 5.01%)
= 0.54
2 βRH
= 공분산RH, S&P 500 ÷ 분산S&P 500
= 52.96 ÷ 25.06
= 2.11
3 αRH
= 평균의RH – βRH × 평균의S&P 500
= 5.13% – 2.11 × 0.90%
= 3.24%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험RH | βRH | 2.11 |
| RH 보통주에 대한 예상 수익률3 | E(RRH) | 26.34% |
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(RRH) = RF + βRH [E(RM) – RF]
= 4.60% + 2.11 [14.89% – 4.60%]
= 26.34%