자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Emerson보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Emerson Electric Co., 월별 수익률
| Emerson Electric Co. (EMR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값EMR,t1 | 피제수EMR,t1 | REMR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2013. 10. 31. | $66.97 | 1,756.54 | ||||
| 1. | 2013. 11. 30. | $66.99 | $0.43 | 0.67% | 1,805.81 | 2.80% |
| 2. | 2013. 12. 31. | $70.18 | 4.76% | 1,848.36 | 2.36% | |
| 3. | 2014. 1. 31. | $65.94 | -6.04% | 1,782.59 | -3.56% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2019. 8. 31. | $59.59 | $0.49 | -7.40% | 2,926.46 | -1.81% |
| 71. | 2019. 9. 30. | $66.86 | 12.20% | 2,976.74 | 1.72% | |
| 평균의 (R): | 0.42% | 0.80% | ||||
| 표준 편차: | 5.69% | 3.29% | ||||
| Emerson Electric Co. (EMR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값EMR,t1 | 피제수EMR,t1 | REMR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2013. 10. 31. | $66.97 | 1,756.54 | ||||
| 1. | 2013. 11. 30. | $66.99 | $0.43 | 0.67% | 1,805.81 | 2.80% |
| 2. | 2013. 12. 31. | $70.18 | 4.76% | 1,848.36 | 2.36% | |
| 3. | 2014. 1. 31. | $65.94 | -6.04% | 1,782.59 | -3.56% | |
| 4. | 2014. 2. 28. | $65.26 | $0.43 | -0.38% | 1,859.45 | 4.31% |
| 5. | 2014. 3. 31. | $66.80 | 2.36% | 1,872.34 | 0.69% | |
| 6. | 2014. 4. 30. | $68.18 | 2.07% | 1,883.95 | 0.62% | |
| 7. | 2014. 5. 31. | $66.73 | $0.43 | -1.50% | 1,923.57 | 2.10% |
| 8. | 2014. 6. 30. | $66.36 | -0.55% | 1,960.23 | 1.91% | |
| 9. | 2014. 7. 31. | $63.65 | -4.08% | 1,930.67 | -1.51% | |
| 10. | 2014. 8. 31. | $64.02 | $0.43 | 1.26% | 2,003.37 | 3.77% |
| 11. | 2014. 9. 30. | $62.58 | -2.25% | 1,972.29 | -1.55% | |
| 12. | 2014. 10. 31. | $64.06 | 2.36% | 2,018.05 | 2.32% | |
| 13. | 2014. 11. 30. | $63.75 | $0.47 | 0.25% | 2,067.56 | 2.45% |
| 14. | 2014. 12. 31. | $61.73 | -3.17% | 2,058.90 | -0.42% | |
| 15. | 2015. 1. 31. | $56.94 | -7.76% | 1,994.99 | -3.10% | |
| 16. | 2015. 2. 28. | $57.92 | $0.47 | 2.55% | 2,104.50 | 5.49% |
| 17. | 2015. 3. 31. | $56.62 | -2.24% | 2,067.89 | -1.74% | |
| 18. | 2015. 4. 30. | $58.83 | 3.90% | 2,085.51 | 0.85% | |
| 19. | 2015. 5. 31. | $60.31 | $0.47 | 3.31% | 2,107.39 | 1.05% |
| 20. | 2015. 6. 30. | $55.43 | -8.09% | 2,063.11 | -2.10% | |
| 21. | 2015. 7. 31. | $51.75 | -6.64% | 2,103.84 | 1.97% | |
| 22. | 2015. 8. 31. | $47.72 | $0.47 | -6.88% | 1,972.18 | -6.26% |
| 23. | 2015. 9. 30. | $44.17 | -7.44% | 1,920.03 | -2.64% | |
| 24. | 2015. 10. 31. | $47.23 | 6.93% | 2,079.36 | 8.30% | |
| 25. | 2015. 11. 30. | $50.00 | $0.475 | 6.87% | 2,080.41 | 0.05% |
| 26. | 2015. 12. 31. | $47.83 | -4.34% | 2,043.94 | -1.75% | |
| 27. | 2016. 1. 31. | $45.98 | -3.87% | 1,940.24 | -5.07% | |
| 28. | 2016. 2. 29. | $48.83 | $0.475 | 7.23% | 1,932.23 | -0.41% |
| 29. | 2016. 3. 31. | $54.38 | 11.37% | 2,059.74 | 6.60% | |
| 30. | 2016. 4. 30. | $54.63 | 0.46% | 2,065.30 | 0.27% | |
| 31. | 2016. 5. 31. | $52.02 | $0.475 | -3.91% | 2,096.95 | 1.53% |
| 32. | 2016. 6. 30. | $52.16 | 0.27% | 2,098.86 | 0.09% | |
| 33. | 2016. 7. 31. | $55.90 | 7.17% | 2,173.60 | 3.56% | |
| 34. | 2016. 8. 31. | $52.68 | $0.475 | -4.91% | 2,170.95 | -0.12% |
| 35. | 2016. 9. 30. | $54.51 | 3.47% | 2,168.27 | -0.12% | |
| 36. | 2016. 10. 31. | $50.68 | -7.03% | 2,126.15 | -1.94% | |
| 37. | 2016. 11. 30. | $56.44 | $0.48 | 12.31% | 2,198.81 | 3.42% |
| 38. | 2016. 12. 31. | $55.75 | -1.22% | 2,238.83 | 1.82% | |
| 39. | 2017. 1. 31. | $58.66 | 5.22% | 2,278.87 | 1.79% | |
| 40. | 2017. 2. 28. | $60.10 | $0.48 | 3.27% | 2,363.64 | 3.72% |
| 41. | 2017. 3. 31. | $59.86 | -0.40% | 2,362.72 | -0.04% | |
| 42. | 2017. 4. 30. | $60.28 | 0.70% | 2,384.20 | 0.91% | |
| 43. | 2017. 5. 31. | $59.12 | $0.48 | -1.13% | 2,411.80 | 1.16% |
| 44. | 2017. 6. 30. | $59.62 | 0.85% | 2,423.41 | 0.48% | |
| 45. | 2017. 7. 31. | $59.61 | -0.02% | 2,470.30 | 1.93% | |
| 46. | 2017. 8. 31. | $59.04 | $0.48 | -0.15% | 2,471.65 | 0.05% |
| 47. | 2017. 9. 30. | $62.84 | 6.44% | 2,519.36 | 1.93% | |
| 48. | 2017. 10. 31. | $64.46 | 2.58% | 2,575.26 | 2.22% | |
| 49. | 2017. 11. 30. | $64.82 | $0.485 | 1.31% | 2,647.58 | 2.81% |
| 50. | 2017. 12. 31. | $69.69 | 7.51% | 2,673.61 | 0.98% | |
| 51. | 2018. 1. 31. | $72.23 | 3.64% | 2,823.81 | 5.62% | |
| 52. | 2018. 2. 28. | $71.06 | $0.485 | -0.95% | 2,713.83 | -3.89% |
| 53. | 2018. 3. 31. | $68.30 | -3.88% | 2,640.87 | -2.69% | |
| 54. | 2018. 4. 30. | $66.41 | -2.77% | 2,648.05 | 0.27% | |
| 55. | 2018. 5. 31. | $70.84 | $0.485 | 7.40% | 2,705.27 | 2.16% |
| 56. | 2018. 6. 30. | $69.14 | -2.40% | 2,718.37 | 0.48% | |
| 57. | 2018. 7. 31. | $72.28 | 4.54% | 2,816.29 | 3.60% | |
| 58. | 2018. 8. 31. | $76.73 | $0.485 | 6.83% | 2,901.52 | 3.03% |
| 59. | 2018. 9. 30. | $76.58 | -0.20% | 2,913.98 | 0.43% | |
| 60. | 2018. 10. 31. | $67.88 | -11.36% | 2,711.74 | -6.94% | |
| 61. | 2018. 11. 30. | $67.52 | $0.49 | 0.19% | 2,760.17 | 1.79% |
| 62. | 2018. 12. 31. | $59.75 | -11.51% | 2,506.85 | -9.18% | |
| 63. | 2019. 1. 31. | $65.47 | 9.57% | 2,704.10 | 7.87% | |
| 64. | 2019. 2. 28. | $68.15 | $0.49 | 4.84% | 2,784.49 | 2.97% |
| 65. | 2019. 3. 31. | $68.47 | 0.47% | 2,834.40 | 1.79% | |
| 66. | 2019. 4. 30. | $70.99 | 3.68% | 2,945.83 | 3.93% | |
| 67. | 2019. 5. 31. | $60.24 | $0.49 | -14.45% | 2,752.06 | -6.58% |
| 68. | 2019. 6. 30. | $66.72 | 10.76% | 2,941.76 | 6.89% | |
| 69. | 2019. 7. 31. | $64.88 | -2.76% | 2,980.38 | 1.31% | |
| 70. | 2019. 8. 31. | $59.59 | $0.49 | -7.40% | 2,926.46 | -1.81% |
| 71. | 2019. 9. 30. | $66.86 | 12.20% | 2,976.74 | 1.72% | |
| 평균의 (R): | 0.42% | 0.80% | ||||
| 표준 편차: | 5.69% | 3.29% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 EMR의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Emerson Electric Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | REMR,t | RS&P 500,t | (REMR,t–REMR)2 | (RS&P 500,t–RS&P 500)2 | (REMR,t–REMR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013. 11. 30. | 0.67% | 2.80% | 0.06 | 4.02 | 0.50 |
| 2. | 2013. 12. 31. | 4.76% | 2.36% | 18.84 | 2.42 | 6.76 |
| 3. | 2014. 1. 31. | -6.04% | -3.56% | 41.77 | 18.99 | 28.16 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2019. 8. 31. | -7.40% | -1.81% | 61.15 | 6.80 | 20.40 |
| 71. | 2019. 9. 30. | 12.20% | 1.72% | 138.74 | 0.84 | 10.82 |
| 합계 (Σ): | 2,262.58 | 758.73 | 1,001.26 | |||
| t | 날짜 | REMR,t | RS&P 500,t | (REMR,t–REMR)2 | (RS&P 500,t–RS&P 500)2 | (REMR,t–REMR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013. 11. 30. | 0.67% | 2.80% | 0.06 | 4.02 | 0.50 |
| 2. | 2013. 12. 31. | 4.76% | 2.36% | 18.84 | 2.42 | 6.76 |
| 3. | 2014. 1. 31. | -6.04% | -3.56% | 41.77 | 18.99 | 28.16 |
| 4. | 2014. 2. 28. | -0.38% | 4.31% | 0.64 | 12.34 | -2.81 |
| 5. | 2014. 3. 31. | 2.36% | 0.69% | 3.76 | 0.01 | -0.21 |
| 6. | 2014. 4. 30. | 2.07% | 0.62% | 2.70 | 0.03 | -0.29 |
| 7. | 2014. 5. 31. | -1.50% | 2.10% | 3.68 | 1.70 | -2.50 |
| 8. | 2014. 6. 30. | -0.55% | 1.91% | 0.95 | 1.22 | -1.08 |
| 9. | 2014. 7. 31. | -4.08% | -1.51% | 20.30 | 5.32 | 10.39 |
| 10. | 2014. 8. 31. | 1.26% | 3.77% | 0.70 | 8.80 | 2.48 |
| 11. | 2014. 9. 30. | -2.25% | -1.55% | 7.13 | 5.53 | 6.28 |
| 12. | 2014. 10. 31. | 2.36% | 2.32% | 3.78 | 2.31 | 2.96 |
| 13. | 2014. 11. 30. | 0.25% | 2.45% | 0.03 | 2.74 | -0.28 |
| 14. | 2014. 12. 31. | -3.17% | -0.42% | 12.89 | 1.48 | 4.37 |
| 15. | 2015. 1. 31. | -7.76% | -3.10% | 66.93 | 15.24 | 31.93 |
| 16. | 2015. 2. 28. | 2.55% | 5.49% | 4.52 | 22.00 | 9.97 |
| 17. | 2015. 3. 31. | -2.24% | -1.74% | 7.11 | 6.45 | 6.77 |
| 18. | 2015. 4. 30. | 3.90% | 0.85% | 12.12 | 0.00 | 0.18 |
| 19. | 2015. 5. 31. | 3.31% | 1.05% | 8.37 | 0.06 | 0.72 |
| 20. | 2015. 6. 30. | -8.09% | -2.10% | 72.47 | 8.41 | 24.69 |
| 21. | 2015. 7. 31. | -6.64% | 1.97% | 49.85 | 1.38 | -8.29 |
| 22. | 2015. 8. 31. | -6.88% | -6.26% | 53.30 | 49.81 | 51.52 |
| 23. | 2015. 9. 30. | -7.44% | -2.64% | 61.79 | 11.86 | 27.07 |
| 24. | 2015. 10. 31. | 6.93% | 8.30% | 42.33 | 56.23 | 48.79 |
| 25. | 2015. 11. 30. | 6.87% | 0.05% | 41.59 | 0.56 | -4.83 |
| 26. | 2015. 12. 31. | -4.34% | -1.75% | 22.67 | 6.51 | 12.15 |
| 27. | 2016. 1. 31. | -3.87% | -5.07% | 18.40 | 34.49 | 25.19 |
| 28. | 2016. 2. 29. | 7.23% | -0.41% | 46.38 | 1.47 | -8.26 |
| 29. | 2016. 3. 31. | 11.37% | 6.60% | 119.78 | 33.64 | 63.48 |
| 30. | 2016. 4. 30. | 0.46% | 0.27% | 0.00 | 0.28 | -0.02 |
| 31. | 2016. 5. 31. | -3.91% | 1.53% | 18.74 | 0.54 | -3.17 |
| 32. | 2016. 6. 30. | 0.27% | 0.09% | 0.02 | 0.50 | 0.11 |
| 33. | 2016. 7. 31. | 7.17% | 3.56% | 45.55 | 7.63 | 18.64 |
| 34. | 2016. 8. 31. | -4.91% | -0.12% | 28.43 | 0.85 | 4.91 |
| 35. | 2016. 9. 30. | 3.47% | -0.12% | 9.32 | 0.85 | -2.82 |
| 36. | 2016. 10. 31. | -7.03% | -1.94% | 55.47 | 7.52 | 20.42 |
| 37. | 2016. 11. 30. | 12.31% | 3.42% | 141.40 | 6.85 | 31.13 |
| 38. | 2016. 12. 31. | -1.22% | 1.82% | 2.70 | 1.04 | -1.68 |
| 39. | 2017. 1. 31. | 5.22% | 1.79% | 23.02 | 0.98 | 4.75 |
| 40. | 2017. 2. 28. | 3.27% | 3.72% | 8.13 | 8.53 | 8.33 |
| 41. | 2017. 3. 31. | -0.40% | -0.04% | 0.67 | 0.70 | 0.69 |
| 42. | 2017. 4. 30. | 0.70% | 0.91% | 0.08 | 0.01 | 0.03 |
| 43. | 2017. 5. 31. | -1.13% | 1.16% | 2.40 | 0.13 | -0.56 |
| 44. | 2017. 6. 30. | 0.85% | 0.48% | 0.18 | 0.10 | -0.13 |
| 45. | 2017. 7. 31. | -0.02% | 1.93% | 0.19 | 1.29 | -0.50 |
| 46. | 2017. 8. 31. | -0.15% | 0.05% | 0.33 | 0.55 | 0.43 |
| 47. | 2017. 9. 30. | 6.44% | 1.93% | 36.18 | 1.28 | 6.80 |
| 48. | 2017. 10. 31. | 2.58% | 2.22% | 4.65 | 2.01 | 3.06 |
| 49. | 2017. 11. 30. | 1.31% | 2.81% | 0.79 | 4.04 | 1.79 |
| 50. | 2017. 12. 31. | 7.51% | 0.98% | 50.29 | 0.03 | 1.30 |
| 51. | 2018. 1. 31. | 3.64% | 5.62% | 10.39 | 23.22 | 15.53 |
| 52. | 2018. 2. 28. | -0.95% | -3.89% | 1.88 | 22.03 | 6.43 |
| 53. | 2018. 3. 31. | -3.88% | -2.69% | 18.54 | 12.16 | 15.02 |
| 54. | 2018. 4. 30. | -2.77% | 0.27% | 10.17 | 0.28 | 1.68 |
| 55. | 2018. 5. 31. | 7.40% | 2.16% | 48.72 | 1.85 | 9.50 |
| 56. | 2018. 6. 30. | -2.40% | 0.48% | 7.96 | 0.10 | 0.89 |
| 57. | 2018. 7. 31. | 4.54% | 3.60% | 16.98 | 7.86 | 11.55 |
| 58. | 2018. 8. 31. | 6.83% | 3.03% | 41.04 | 4.96 | 14.27 |
| 59. | 2018. 9. 30. | -0.20% | 0.43% | 0.38 | 0.14 | 0.23 |
| 60. | 2018. 10. 31. | -11.36% | -6.94% | 138.82 | 59.90 | 91.19 |
| 61. | 2018. 11. 30. | 0.19% | 1.79% | 0.05 | 0.97 | -0.23 |
| 62. | 2018. 12. 31. | -11.51% | -9.18% | 142.30 | 99.54 | 119.02 |
| 63. | 2019. 1. 31. | 9.57% | 7.87% | 83.76 | 49.97 | 64.70 |
| 64. | 2019. 2. 28. | 4.84% | 2.97% | 19.54 | 4.72 | 9.61 |
| 65. | 2019. 3. 31. | 0.47% | 1.79% | 0.00 | 0.99 | 0.05 |
| 66. | 2019. 4. 30. | 3.68% | 3.93% | 10.62 | 9.81 | 10.21 |
| 67. | 2019. 5. 31. | -14.45% | -6.58% | 221.24 | 54.42 | 109.73 |
| 68. | 2019. 6. 30. | 10.76% | 6.89% | 106.83 | 37.13 | 62.98 |
| 69. | 2019. 7. 31. | -2.76% | 1.31% | 10.11 | 0.26 | -1.63 |
| 70. | 2019. 8. 31. | -7.40% | -1.81% | 61.15 | 6.80 | 20.40 |
| 71. | 2019. 9. 30. | 12.20% | 1.72% | 138.74 | 0.84 | 10.82 |
| 합계 (Σ): | 2,262.58 | 758.73 | 1,001.26 | |||
모두 표시
분산EMR = Σ(REMR,t–REMR)2 ÷ (71 – 1)
= 2,262.58 ÷ (71 – 1)
= 32.32
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 758.73 ÷ (71 – 1)
= 10.84
공분산EMR, S&P 500 = Σ(REMR,t–REMR)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,001.26 ÷ (71 – 1)
= 14.30
체계적인 위험 추정 (β)
| 분산EMR | 32.32 |
| 분산S&P 500 | 10.84 |
| 공분산EMR, S&P 500 | 14.30 |
| 상관 계수EMR, S&P 5001 | 0.76 |
| βEMR2 | 1.32 |
| αEMR3 | -0.63% |
계산
1 상관 계수EMR, S&P 500
= 공분산EMR, S&P 500 ÷ (표준 편차EMR × 표준 편차S&P 500)
= 14.30 ÷ (5.69% × 3.29%)
= 0.76
2 βEMR
= 공분산EMR, S&P 500 ÷ 분산S&P 500
= 14.30 ÷ 10.84
= 1.32
3 αEMR
= 평균의EMR – βEMR × 평균의S&P 500
= 0.42% – 1.32 × 0.80%
= -0.63%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.72% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.44% |
| 보통주의 체계적 위험Emerson | βEMR | 1.32 |
| 에머슨 보통주의 예상 수익률3 | E(REMR) | 16.22% |
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(REMR) = RF + βEMR [E(RM) – RF]
= 4.72% + 1.32 [13.44% – 4.72%]
= 16.22%