자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 KMI보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Kinder Morgan Inc., 월별 수익률
| Kinder Morgan Inc. (KMI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값KMI,t1 | 피제수KMI,t1 | RKMI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $41.05 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $41.01 | -0.10% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $42.06 | 2.56% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $42.95 | $0.48 | 3.26% | 2,085.51 | 0.85% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | $19.61 | -1.85% | 3,140.98 | 3.40% | |
| 59. | 2019. 12. 31. | $21.17 | 7.96% | 3,230.78 | 2.86% | |
| 평균의 (R): | -0.44% | 0.88% | ||||
| 표준 편차: | 8.13% | 3.45% | ||||
| Kinder Morgan Inc. (KMI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값KMI,t1 | 피제수KMI,t1 | RKMI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $41.05 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $41.01 | -0.10% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $42.06 | 2.56% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $42.95 | $0.48 | 3.26% | 2,085.51 | 0.85% |
| 4. | 2015. 5. 31. | $41.49 | -3.40% | 2,107.39 | 1.05% | |
| 5. | 2015. 6. 30. | $38.39 | -7.47% | 2,063.11 | -2.10% | |
| 6. | 2015. 7. 31. | $34.64 | $0.49 | -8.49% | 2,103.84 | 1.97% |
| 7. | 2015. 8. 31. | $32.41 | -6.44% | 1,972.18 | -6.26% | |
| 8. | 2015. 9. 30. | $27.68 | -14.59% | 1,920.03 | -2.64% | |
| 9. | 2015. 10. 31. | $27.35 | $0.51 | 0.65% | 2,079.36 | 8.30% |
| 10. | 2015. 11. 30. | $23.57 | -13.82% | 2,080.41 | 0.05% | |
| 11. | 2015. 12. 31. | $14.92 | -36.70% | 2,043.94 | -1.75% | |
| 12. | 2016. 1. 31. | $16.45 | $0.125 | 11.09% | 1,940.24 | -5.07% |
| 13. | 2016. 2. 29. | $18.09 | 9.97% | 1,932.23 | -0.41% | |
| 14. | 2016. 3. 31. | $17.86 | -1.27% | 2,059.74 | 6.60% | |
| 15. | 2016. 4. 30. | $17.76 | $0.125 | 0.14% | 2,065.30 | 0.27% |
| 16. | 2016. 5. 31. | $18.08 | 1.80% | 2,096.95 | 1.53% | |
| 17. | 2016. 6. 30. | $18.72 | 3.54% | 2,098.86 | 0.09% | |
| 18. | 2016. 7. 31. | $20.33 | $0.125 | 9.27% | 2,173.60 | 3.56% |
| 19. | 2016. 8. 31. | $21.85 | 7.48% | 2,170.95 | -0.12% | |
| 20. | 2016. 9. 30. | $23.13 | 5.86% | 2,168.27 | -0.12% | |
| 21. | 2016. 10. 31. | $20.43 | $0.125 | -11.13% | 2,126.15 | -1.94% |
| 22. | 2016. 11. 30. | $22.20 | 8.66% | 2,198.81 | 3.42% | |
| 23. | 2016. 12. 31. | $20.71 | -6.71% | 2,238.83 | 1.82% | |
| 24. | 2017. 1. 31. | $22.34 | $0.125 | 8.47% | 2,278.87 | 1.79% |
| 25. | 2017. 2. 28. | $21.31 | -4.61% | 2,363.64 | 3.72% | |
| 26. | 2017. 3. 31. | $21.74 | 2.02% | 2,362.72 | -0.04% | |
| 27. | 2017. 4. 30. | $20.63 | $0.125 | -4.53% | 2,384.20 | 0.91% |
| 28. | 2017. 5. 31. | $18.76 | -9.06% | 2,411.80 | 1.16% | |
| 29. | 2017. 6. 30. | $19.16 | 2.13% | 2,423.41 | 0.48% | |
| 30. | 2017. 7. 31. | $20.43 | $0.125 | 7.28% | 2,470.30 | 1.93% |
| 31. | 2017. 8. 31. | $19.33 | -5.38% | 2,471.65 | 0.05% | |
| 32. | 2017. 9. 30. | $19.18 | -0.78% | 2,519.36 | 1.93% | |
| 33. | 2017. 10. 31. | $18.11 | $0.125 | -4.93% | 2,575.26 | 2.22% |
| 34. | 2017. 11. 30. | $17.23 | -4.86% | 2,647.58 | 2.81% | |
| 35. | 2017. 12. 31. | $18.07 | 4.88% | 2,673.61 | 0.98% | |
| 36. | 2018. 1. 31. | $17.98 | $0.125 | 0.19% | 2,823.81 | 5.62% |
| 37. | 2018. 2. 28. | $16.20 | -9.90% | 2,713.83 | -3.89% | |
| 38. | 2018. 3. 31. | $15.06 | -7.04% | 2,640.87 | -2.69% | |
| 39. | 2018. 4. 30. | $15.82 | $0.20 | 6.37% | 2,648.05 | 0.27% |
| 40. | 2018. 5. 31. | $16.68 | 5.44% | 2,705.27 | 2.16% | |
| 41. | 2018. 6. 30. | $17.67 | 5.94% | 2,718.37 | 0.48% | |
| 42. | 2018. 7. 31. | $17.78 | $0.20 | 1.75% | 2,816.29 | 3.60% |
| 43. | 2018. 8. 31. | $17.70 | -0.45% | 2,901.52 | 3.03% | |
| 44. | 2018. 9. 30. | $17.73 | 0.17% | 2,913.98 | 0.43% | |
| 45. | 2018. 10. 31. | $17.02 | $0.20 | -2.88% | 2,711.74 | -6.94% |
| 46. | 2018. 11. 30. | $17.07 | 0.29% | 2,760.17 | 1.79% | |
| 47. | 2018. 12. 31. | $15.38 | -9.90% | 2,506.85 | -9.18% | |
| 48. | 2019. 1. 31. | $18.10 | $0.20 | 18.99% | 2,704.10 | 7.87% |
| 49. | 2019. 2. 28. | $19.16 | 5.86% | 2,784.49 | 2.97% | |
| 50. | 2019. 3. 31. | $20.01 | 4.44% | 2,834.40 | 1.79% | |
| 51. | 2019. 4. 30. | $19.87 | $0.25 | 0.55% | 2,945.83 | 3.93% |
| 52. | 2019. 5. 31. | $19.95 | 0.40% | 2,752.06 | -6.58% | |
| 53. | 2019. 6. 30. | $20.88 | 4.66% | 2,941.76 | 6.89% | |
| 54. | 2019. 7. 31. | $20.62 | $0.25 | -0.05% | 2,980.38 | 1.31% |
| 55. | 2019. 8. 31. | $20.27 | -1.70% | 2,926.46 | -1.81% | |
| 56. | 2019. 9. 30. | $20.61 | 1.68% | 2,976.74 | 1.72% | |
| 57. | 2019. 10. 31. | $19.98 | $0.25 | -1.84% | 3,037.56 | 2.04% |
| 58. | 2019. 11. 30. | $19.61 | -1.85% | 3,140.98 | 3.40% | |
| 59. | 2019. 12. 31. | $21.17 | 7.96% | 3,230.78 | 2.86% | |
| 평균의 (R): | -0.44% | 0.88% | ||||
| 표준 편차: | 8.13% | 3.45% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 KMI의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Kinder Morgan Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RKMI,t | RS&P 500,t | (RKMI,t–RKMI)2 | (RS&P 500,t–RS&P 500)2 | (RKMI,t–RKMI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | -0.10% | 5.49% | 0.12 | 21.25 | 1.59 |
| 2. | 2015. 3. 31. | 2.56% | -1.74% | 9.02 | 6.86 | -7.87 |
| 3. | 2015. 4. 30. | 3.26% | 0.85% | 13.69 | 0.00 | -0.10 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | -1.85% | 3.40% | 1.98 | 6.38 | -3.56 |
| 59. | 2019. 12. 31. | 7.96% | 2.86% | 70.53 | 3.92 | 16.63 |
| 합계 (Σ): | 3,831.54 | 688.77 | 561.88 | |||
| t | 날짜 | RKMI,t | RS&P 500,t | (RKMI,t–RKMI)2 | (RS&P 500,t–RS&P 500)2 | (RKMI,t–RKMI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | -0.10% | 5.49% | 0.12 | 21.25 | 1.59 |
| 2. | 2015. 3. 31. | 2.56% | -1.74% | 9.02 | 6.86 | -7.87 |
| 3. | 2015. 4. 30. | 3.26% | 0.85% | 13.69 | 0.00 | -0.10 |
| 4. | 2015. 5. 31. | -3.40% | 1.05% | 8.74 | 0.03 | -0.50 |
| 5. | 2015. 6. 30. | -7.47% | -2.10% | 49.40 | 8.88 | 20.95 |
| 6. | 2015. 7. 31. | -8.49% | 1.97% | 64.78 | 1.20 | -8.81 |
| 7. | 2015. 8. 31. | -6.44% | -6.26% | 35.93 | 50.94 | 42.78 |
| 8. | 2015. 9. 30. | -14.59% | -2.64% | 200.25 | 12.41 | 49.86 |
| 9. | 2015. 10. 31. | 0.65% | 8.30% | 1.20 | 55.04 | 8.11 |
| 10. | 2015. 11. 30. | -13.82% | 0.05% | 178.96 | 0.69 | 11.09 |
| 11. | 2015. 12. 31. | -36.70% | -1.75% | 1,314.50 | 6.93 | 95.43 |
| 12. | 2016. 1. 31. | 11.09% | -5.07% | 133.07 | 35.43 | -68.67 |
| 13. | 2016. 2. 29. | 9.97% | -0.41% | 108.42 | 1.67 | -13.45 |
| 14. | 2016. 3. 31. | -1.27% | 6.60% | 0.69 | 32.72 | -4.74 |
| 15. | 2016. 4. 30. | 0.14% | 0.27% | 0.34 | 0.37 | -0.36 |
| 16. | 2016. 5. 31. | 1.80% | 1.53% | 5.04 | 0.43 | 1.47 |
| 17. | 2016. 6. 30. | 3.54% | 0.09% | 15.86 | 0.62 | -3.14 |
| 18. | 2016. 7. 31. | 9.27% | 3.56% | 94.31 | 7.19 | 26.04 |
| 19. | 2016. 8. 31. | 7.48% | -0.12% | 62.72 | 1.00 | -7.93 |
| 20. | 2016. 9. 30. | 5.86% | -0.12% | 39.71 | 1.01 | -6.32 |
| 21. | 2016. 10. 31. | -11.13% | -1.94% | 114.27 | 7.96 | 30.16 |
| 22. | 2016. 11. 30. | 8.66% | 3.42% | 82.93 | 6.44 | 23.12 |
| 23. | 2016. 12. 31. | -6.71% | 1.82% | 39.30 | 0.89 | -5.90 |
| 24. | 2017. 1. 31. | 8.47% | 1.79% | 79.52 | 0.83 | 8.11 |
| 25. | 2017. 2. 28. | -4.61% | 3.72% | 17.37 | 8.07 | -11.84 |
| 26. | 2017. 3. 31. | 2.02% | -0.04% | 6.06 | 0.84 | -2.26 |
| 27. | 2017. 4. 30. | -4.53% | 0.91% | 16.71 | 0.00 | -0.12 |
| 28. | 2017. 5. 31. | -9.06% | 1.16% | 74.33 | 0.08 | -2.40 |
| 29. | 2017. 6. 30. | 2.13% | 0.48% | 6.63 | 0.16 | -1.02 |
| 30. | 2017. 7. 31. | 7.28% | 1.93% | 59.66 | 1.11 | 8.15 |
| 31. | 2017. 8. 31. | -5.38% | 0.05% | 24.41 | 0.68 | 4.07 |
| 32. | 2017. 9. 30. | -0.78% | 1.93% | 0.11 | 1.10 | -0.35 |
| 33. | 2017. 10. 31. | -4.93% | 2.22% | 20.11 | 1.79 | -6.01 |
| 34. | 2017. 11. 30. | -4.86% | 2.81% | 19.50 | 3.72 | -8.52 |
| 35. | 2017. 12. 31. | 4.88% | 0.98% | 28.28 | 0.01 | 0.55 |
| 36. | 2018. 1. 31. | 0.19% | 5.62% | 0.41 | 22.46 | 3.02 |
| 37. | 2018. 2. 28. | -9.90% | -3.89% | 89.43 | 22.79 | 45.15 |
| 38. | 2018. 3. 31. | -7.04% | -2.69% | 43.48 | 12.73 | 23.52 |
| 39. | 2018. 4. 30. | 6.37% | 0.27% | 46.48 | 0.37 | -4.14 |
| 40. | 2018. 5. 31. | 5.44% | 2.16% | 34.57 | 1.64 | 7.54 |
| 41. | 2018. 6. 30. | 5.94% | 0.48% | 40.68 | 0.16 | -2.52 |
| 42. | 2018. 7. 31. | 1.75% | 3.60% | 4.83 | 7.41 | 5.98 |
| 43. | 2018. 8. 31. | -0.45% | 3.03% | 0.00 | 4.61 | -0.01 |
| 44. | 2018. 9. 30. | 0.17% | 0.43% | 0.38 | 0.20 | -0.28 |
| 45. | 2018. 10. 31. | -2.88% | -6.94% | 5.92 | 61.14 | 19.03 |
| 46. | 2018. 11. 30. | 0.29% | 1.79% | 0.54 | 0.82 | 0.67 |
| 47. | 2018. 12. 31. | -9.90% | -9.18% | 89.44 | 101.14 | 95.11 |
| 48. | 2019. 1. 31. | 18.99% | 7.87% | 377.48 | 48.85 | 135.79 |
| 49. | 2019. 2. 28. | 5.86% | 2.97% | 39.68 | 4.38 | 13.19 |
| 50. | 2019. 3. 31. | 4.44% | 1.79% | 23.81 | 0.83 | 4.46 |
| 51. | 2019. 4. 30. | 0.55% | 3.93% | 0.99 | 9.32 | 3.03 |
| 52. | 2019. 5. 31. | 0.40% | -6.58% | 0.72 | 55.61 | -6.31 |
| 53. | 2019. 6. 30. | 4.66% | 6.89% | 26.06 | 36.17 | 30.70 |
| 54. | 2019. 7. 31. | -0.05% | 1.31% | 0.16 | 0.19 | 0.17 |
| 55. | 2019. 8. 31. | -1.70% | -1.81% | 1.57 | 7.23 | 3.37 |
| 56. | 2019. 9. 30. | 1.68% | 1.72% | 4.50 | 0.70 | 1.78 |
| 57. | 2019. 10. 31. | -1.84% | 2.04% | 1.96 | 1.36 | -1.63 |
| 58. | 2019. 11. 30. | -1.85% | 3.40% | 1.98 | 6.38 | -3.56 |
| 59. | 2019. 12. 31. | 7.96% | 2.86% | 70.53 | 3.92 | 16.63 |
| 합계 (Σ): | 3,831.54 | 688.77 | 561.88 | |||
모두 보기
분산KMI = Σ(RKMI,t–RKMI)2 ÷ (59 – 1)
= 3,831.54 ÷ (59 – 1)
= 66.06
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
공분산KMI, S&P 500 = Σ(RKMI,t–RKMI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 561.88 ÷ (59 – 1)
= 9.69
체계적인 위험 추정 (β)
| 분산KMI | 66.06 |
| 분산S&P 500 | 11.88 |
| 공분산KMI, S&P 500 | 9.69 |
| 상관 계수KMI, S&P 5001 | 0.35 |
| βKMI2 | 0.82 |
| αKMI3 | -1.16% |
계산
1 상관 계수KMI, S&P 500
= 공분산KMI, S&P 500 ÷ (표준 편차KMI × 표준 편차S&P 500)
= 9.69 ÷ (8.13% × 3.45%)
= 0.35
2 βKMI
= 공분산KMI, S&P 500 ÷ 분산S&P 500
= 9.69 ÷ 11.88
= 0.82
3 αKMI
= 평균의KMI – βKMI × 평균의S&P 500
= -0.44% – 0.82 × 0.88%
= -1.16%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험KMI | βKMI | 0.82 |
| KMI 보통주 예상 수익률3 | E(RKMI) | 12.11% |
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(RKMI) = RF + βKMI [E(RM) – RF]
= 4.67% + 0.82 [13.79% – 4.67%]
= 12.11%