자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Roper보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Roper Technologies Inc., 월별 수익률
| Roper Technologies Inc. (ROP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ROP,t1 | 피제수ROP,t1 | RROP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $280.59 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $275.09 | -1.96% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $280.69 | 2.04% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $264.19 | $0.4125 | -5.73% | 2,648.05 | 0.27% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $438.89 | 5.87% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $432.09 | -1.55% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.04% | 0.67% | ||||
| 표준 편차: | 7.33% | 5.40% | ||||
| Roper Technologies Inc. (ROP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ROP,t1 | 피제수ROP,t1 | RROP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $280.59 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $275.09 | -1.96% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $280.69 | 2.04% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $264.19 | $0.4125 | -5.73% | 2,648.05 | 0.27% |
| 4. | 2018. 5. 31. | $275.79 | 4.39% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $275.91 | 0.04% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $301.90 | $0.4125 | 9.57% | 2,816.29 | 3.60% |
| 7. | 2018. 8. 31. | $298.37 | -1.17% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $296.21 | -0.72% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $282.90 | $0.4125 | -4.35% | 2,711.74 | -6.94% |
| 10. | 2018. 11. 30. | $297.59 | 5.19% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $266.52 | -10.44% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $283.26 | $0.4625 | 6.45% | 2,704.10 | 7.87% |
| 13. | 2019. 2. 28. | $323.65 | 14.26% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $341.97 | 5.66% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $359.70 | $0.4625 | 5.32% | 2,945.83 | 3.93% |
| 16. | 2019. 5. 31. | $343.92 | -4.39% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $366.26 | 6.50% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $363.65 | $0.4625 | -0.59% | 2,980.38 | 1.31% |
| 19. | 2019. 8. 31. | $366.76 | 0.86% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $356.60 | -2.77% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $336.96 | $0.4625 | -5.38% | 3,037.56 | 2.04% |
| 22. | 2019. 11. 30. | $360.37 | 6.95% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $354.23 | -1.70% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $381.66 | $0.5125 | 7.89% | 3,225.52 | -0.16% |
| 25. | 2020. 2. 29. | $351.70 | -7.85% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $311.81 | -11.34% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $341.03 | $0.5125 | 9.54% | 2,912.43 | 12.68% |
| 28. | 2020. 5. 31. | $393.80 | 15.47% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $388.26 | -1.41% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $432.45 | $0.5125 | 11.51% | 3,271.12 | 5.51% |
| 31. | 2020. 8. 31. | $427.19 | -1.22% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $395.11 | -7.51% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $371.34 | $0.5125 | -5.89% | 3,269.96 | -2.77% |
| 34. | 2020. 11. 30. | $427.00 | 14.99% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $431.09 | 0.96% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $392.91 | $0.5625 | -8.73% | 3,714.24 | -1.11% |
| 37. | 2021. 2. 28. | $377.62 | -3.89% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $403.34 | 6.81% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $446.44 | $0.5625 | 10.83% | 4,181.17 | 5.24% |
| 40. | 2021. 5. 31. | $450.01 | 0.80% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $470.20 | 4.49% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $491.34 | $0.5625 | 4.62% | 4,395.26 | 2.27% |
| 43. | 2021. 8. 31. | $483.28 | -1.64% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $446.13 | -7.69% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $487.87 | $0.5625 | 9.48% | 4,605.38 | 6.91% |
| 46. | 2021. 11. 30. | $464.15 | -4.86% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $491.86 | 5.97% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $437.16 | $0.62 | -10.99% | 4,515.55 | -5.26% |
| 49. | 2022. 2. 28. | $448.22 | 2.53% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $472.23 | 5.36% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $469.92 | $0.62 | -0.36% | 4,131.93 | -8.80% |
| 52. | 2022. 5. 31. | $442.44 | -5.85% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $394.65 | -10.80% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $436.67 | $0.62 | 10.80% | 4,130.29 | 9.11% |
| 55. | 2022. 8. 31. | $402.58 | -7.81% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $359.64 | -10.67% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $414.54 | $0.62 | 15.44% | 3,871.98 | 7.99% |
| 58. | 2022. 11. 30. | $438.89 | 5.87% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $432.09 | -1.55% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.04% | 0.67% | ||||
| 표준 편차: | 7.33% | 5.40% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 ROP의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Roper Technologies Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RROP,t | RS&P 500,t | (RROP,t–RROP)2 | (RS&P 500,t–RS&P 500)2 | (RROP,t–RROP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -1.96% | -3.89% | 9.00 | 20.81 | 13.68 |
| 2. | 2018. 3. 31. | 2.04% | -2.69% | 0.99 | 11.26 | -3.34 |
| 3. | 2018. 4. 30. | -5.73% | 0.27% | 45.84 | 0.16 | 2.67 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 5.87% | 5.38% | 23.37 | 22.17 | 22.76 |
| 59. | 2022. 12. 31. | -1.55% | -5.90% | 6.70 | 43.08 | 16.99 |
| 합계 (Σ): | 3,117.43 | 1,691.48 | 1,785.85 | |||
| t | 날짜 | RROP,t | RS&P 500,t | (RROP,t–RROP)2 | (RS&P 500,t–RS&P 500)2 | (RROP,t–RROP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -1.96% | -3.89% | 9.00 | 20.81 | 13.68 |
| 2. | 2018. 3. 31. | 2.04% | -2.69% | 0.99 | 11.26 | -3.34 |
| 3. | 2018. 4. 30. | -5.73% | 0.27% | 45.84 | 0.16 | 2.67 |
| 4. | 2018. 5. 31. | 4.39% | 2.16% | 11.23 | 2.23 | 5.01 |
| 5. | 2018. 6. 30. | 0.04% | 0.48% | 0.99 | 0.03 | 0.18 |
| 6. | 2018. 7. 31. | 9.57% | 3.60% | 72.76 | 8.62 | 25.04 |
| 7. | 2018. 8. 31. | -1.17% | 3.03% | 4.88 | 5.57 | -5.21 |
| 8. | 2018. 9. 30. | -0.72% | 0.43% | 3.11 | 0.06 | 0.42 |
| 9. | 2018. 10. 31. | -4.35% | -6.94% | 29.09 | 57.87 | 41.03 |
| 10. | 2018. 11. 30. | 5.19% | 1.79% | 17.25 | 1.25 | 4.65 |
| 11. | 2018. 12. 31. | -10.44% | -9.18% | 131.79 | 96.91 | 113.01 |
| 12. | 2019. 1. 31. | 6.45% | 7.87% | 29.32 | 51.87 | 39.00 |
| 13. | 2019. 2. 28. | 14.26% | 2.97% | 174.76 | 5.32 | 30.49 |
| 14. | 2019. 3. 31. | 5.66% | 1.79% | 21.35 | 1.27 | 5.20 |
| 15. | 2019. 4. 30. | 5.32% | 3.93% | 18.32 | 10.66 | 13.97 |
| 16. | 2019. 5. 31. | -4.39% | -6.58% | 29.45 | 52.48 | 39.31 |
| 17. | 2019. 6. 30. | 6.50% | 6.89% | 29.77 | 38.77 | 33.97 |
| 18. | 2019. 7. 31. | -0.59% | 1.31% | 2.64 | 0.42 | -1.05 |
| 19. | 2019. 8. 31. | 0.86% | -1.81% | 0.03 | 6.13 | 0.46 |
| 20. | 2019. 9. 30. | -2.77% | 1.72% | 14.51 | 1.11 | -4.01 |
| 21. | 2019. 10. 31. | -5.38% | 2.04% | 41.18 | 1.89 | -8.83 |
| 22. | 2019. 11. 30. | 6.95% | 3.40% | 34.90 | 7.50 | 16.18 |
| 23. | 2019. 12. 31. | -1.70% | 2.86% | 7.53 | 4.81 | -6.01 |
| 24. | 2020. 1. 31. | 7.89% | -0.16% | 46.91 | 0.69 | -5.68 |
| 25. | 2020. 2. 29. | -7.85% | -8.41% | 79.02 | 82.40 | 80.70 |
| 26. | 2020. 3. 31. | -11.34% | -12.51% | 153.30 | 173.67 | 163.17 |
| 27. | 2020. 4. 30. | 9.54% | 12.68% | 72.18 | 144.43 | 102.10 |
| 28. | 2020. 5. 31. | 15.47% | 4.53% | 208.35 | 14.91 | 55.74 |
| 29. | 2020. 6. 30. | -1.41% | 1.84% | 5.98 | 1.37 | -2.87 |
| 30. | 2020. 7. 31. | 11.51% | 5.51% | 109.71 | 23.46 | 50.73 |
| 31. | 2020. 8. 31. | -1.22% | 7.01% | 5.09 | 40.19 | -14.30 |
| 32. | 2020. 9. 30. | -7.51% | -3.92% | 73.09 | 21.06 | 39.24 |
| 33. | 2020. 10. 31. | -5.89% | -2.77% | 47.97 | 11.79 | 23.78 |
| 34. | 2020. 11. 30. | 14.99% | 10.75% | 194.59 | 101.77 | 140.72 |
| 35. | 2020. 12. 31. | 0.96% | 3.71% | 0.01 | 9.28 | -0.25 |
| 36. | 2021. 1. 31. | -8.73% | -1.11% | 95.37 | 3.17 | 17.39 |
| 37. | 2021. 2. 28. | -3.89% | 2.61% | 24.31 | 3.77 | -9.58 |
| 38. | 2021. 3. 31. | 6.81% | 4.24% | 33.31 | 12.80 | 20.65 |
| 39. | 2021. 4. 30. | 10.83% | 5.24% | 95.76 | 20.94 | 44.78 |
| 40. | 2021. 5. 31. | 0.80% | 0.55% | 0.06 | 0.01 | 0.03 |
| 41. | 2021. 6. 30. | 4.49% | 2.22% | 11.88 | 2.42 | 5.36 |
| 42. | 2021. 7. 31. | 4.62% | 2.27% | 12.79 | 2.59 | 5.75 |
| 43. | 2021. 8. 31. | -1.64% | 2.90% | 7.18 | 4.98 | -5.98 |
| 44. | 2021. 9. 30. | -7.69% | -4.76% | 76.15 | 29.42 | 47.33 |
| 45. | 2021. 10. 31. | 9.48% | 6.91% | 71.28 | 39.03 | 52.75 |
| 46. | 2021. 11. 30. | -4.86% | -0.83% | 34.83 | 2.25 | 8.85 |
| 47. | 2021. 12. 31. | 5.97% | 4.36% | 24.31 | 13.65 | 18.22 |
| 48. | 2022. 1. 31. | -10.99% | -5.26% | 144.83 | 35.11 | 71.31 |
| 49. | 2022. 2. 28. | 2.53% | -3.14% | 2.22 | 14.46 | -5.67 |
| 50. | 2022. 3. 31. | 5.36% | 3.58% | 18.64 | 8.47 | 12.57 |
| 51. | 2022. 4. 30. | -0.36% | -8.80% | 1.95 | 89.54 | 13.22 |
| 52. | 2022. 5. 31. | -5.85% | 0.01% | 47.43 | 0.44 | 4.55 |
| 53. | 2022. 6. 30. | -10.80% | -8.39% | 140.21 | 82.06 | 107.26 |
| 54. | 2022. 7. 31. | 10.80% | 9.11% | 95.36 | 71.32 | 82.47 |
| 55. | 2022. 8. 31. | -7.81% | -4.24% | 78.26 | 24.11 | 43.44 |
| 56. | 2022. 9. 30. | -10.67% | -9.34% | 137.02 | 100.12 | 117.13 |
| 57. | 2022. 10. 31. | 15.44% | 7.99% | 207.31 | 53.58 | 105.39 |
| 58. | 2022. 11. 30. | 5.87% | 5.38% | 23.37 | 22.17 | 22.76 |
| 59. | 2022. 12. 31. | -1.55% | -5.90% | 6.70 | 43.08 | 16.99 |
| 합계 (Σ): | 3,117.43 | 1,691.48 | 1,785.85 | |||
모두 표시
분산ROP = Σ(RROP,t–RROP)2 ÷ (59 – 1)
= 3,117.43 ÷ (59 – 1)
= 53.75
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산ROP, S&P 500 = Σ(RROP,t–RROP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,785.85 ÷ (59 – 1)
= 30.79
체계적인 위험 추정 (β)
| 분산ROP | 53.75 |
| 분산S&P 500 | 29.16 |
| 공분산ROP, S&P 500 | 30.79 |
| 상관 계수ROP, S&P 5001 | 0.78 |
| βROP2 | 1.06 |
| αROP3 | 0.34% |
계산
1 상관 계수ROP, S&P 500
= 공분산ROP, S&P 500 ÷ (표준 편차ROP × 표준 편차S&P 500)
= 30.79 ÷ (7.33% × 5.40%)
= 0.78
2 βROP
= 공분산ROP, S&P 500 ÷ 분산S&P 500
= 30.79 ÷ 29.16
= 1.06
3 αROP
= 평균의ROP – βROP × 평균의S&P 500
= 1.04% – 1.06 × 0.67%
= 0.34%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.62% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.69% |
| 보통주의 체계적 위험 Roper | βROP | 1.06 |
| Roper 보통주에 대한 예상 수익률3 | E(RROP) | 14.19% |
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(RROP) = RF + βROP [E(RM) – RF]
= 4.62% + 1.06 [13.69% – 4.62%]
= 14.19%