자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 ONEOK의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
ONEOK Inc., 월별 수익률
| ONEOK Inc. (OKE) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값OKE,t1 | 피제수OKE,t1 | ROKE,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $58.86 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $56.33 | -4.30% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $56.92 | 1.05% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $60.22 | $0.795 | 7.19% | 2,648.05 | 0.27% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $66.92 | 12.81% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $65.70 | -1.82% | 3,839.50 | -5.90% | |
| 평균의 (R): | 2.03% | 0.67% | ||||
| 표준 편차: | 13.78% | 5.40% | ||||
| ONEOK Inc. (OKE) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값OKE,t1 | 피제수OKE,t1 | ROKE,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $58.86 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $56.33 | -4.30% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $56.92 | 1.05% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $60.22 | $0.795 | 7.19% | 2,648.05 | 0.27% |
| 4. | 2018. 5. 31. | $68.16 | 13.18% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $69.83 | 2.45% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $70.44 | 0.87% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $65.91 | $0.825 | -5.26% | 2,901.52 | 3.03% |
| 8. | 2018. 9. 30. | $67.79 | 2.85% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $65.60 | -3.23% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $61.43 | $0.855 | -5.05% | 2,760.17 | 1.79% |
| 11. | 2018. 12. 31. | $53.95 | -12.18% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $64.21 | $0.86 | 20.61% | 2,704.10 | 7.87% |
| 13. | 2019. 2. 28. | $64.26 | 0.08% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $69.84 | 8.68% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $67.93 | $0.865 | -1.50% | 2,945.83 | 3.93% |
| 16. | 2019. 5. 31. | $63.62 | -6.34% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $68.81 | 8.16% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $70.08 | 1.85% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $71.28 | $0.89 | 2.98% | 2,926.46 | -1.81% |
| 20. | 2019. 9. 30. | $73.69 | 3.38% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $69.83 | -5.24% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $71.05 | $0.915 | 3.06% | 3,140.98 | 3.40% |
| 23. | 2019. 12. 31. | $75.67 | 6.50% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $74.87 | $0.935 | 0.18% | 3,225.52 | -0.16% |
| 25. | 2020. 2. 29. | $66.72 | -10.89% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $21.81 | -67.31% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $29.93 | $0.935 | 41.52% | 2,912.43 | 12.68% |
| 28. | 2020. 5. 31. | $36.69 | 22.59% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $33.22 | -9.46% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $27.91 | $0.935 | -13.17% | 3,271.12 | 5.51% |
| 31. | 2020. 8. 31. | $27.48 | -1.54% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $25.98 | -5.46% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $29.00 | $0.935 | 15.22% | 3,269.96 | -2.77% |
| 34. | 2020. 11. 30. | $35.87 | 23.69% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $38.38 | 7.00% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $39.83 | $0.935 | 6.21% | 3,714.24 | -1.11% |
| 37. | 2021. 2. 28. | $44.29 | 11.20% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $50.66 | 14.38% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $52.34 | $0.935 | 5.16% | 4,181.17 | 5.24% |
| 40. | 2021. 5. 31. | $52.74 | 0.76% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $55.64 | 5.50% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $51.97 | $0.935 | -4.92% | 4,395.26 | 2.27% |
| 43. | 2021. 8. 31. | $52.52 | 1.06% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $57.99 | 10.42% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $63.62 | $0.935 | 11.32% | 4,605.38 | 6.91% |
| 46. | 2021. 11. 30. | $59.84 | -5.94% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $58.76 | -1.80% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $60.68 | $0.935 | 4.86% | 4,515.55 | -5.26% |
| 49. | 2022. 2. 28. | $65.30 | 7.61% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $70.63 | 8.16% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $63.33 | $0.935 | -9.01% | 4,131.93 | -8.80% |
| 52. | 2022. 5. 31. | $65.85 | 3.98% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $55.50 | -15.72% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $59.74 | $0.935 | 9.32% | 4,130.29 | 9.11% |
| 55. | 2022. 8. 31. | $61.23 | 2.49% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $51.24 | -16.32% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $59.32 | $0.935 | 17.59% | 3,871.98 | 7.99% |
| 58. | 2022. 11. 30. | $66.92 | 12.81% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $65.70 | -1.82% | 3,839.50 | -5.90% | |
| 평균의 (R): | 2.03% | 0.67% | ||||
| 표준 편차: | 13.78% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 OKE의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
ONEOK Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | ROKE,t | RS&P 500,t | (ROKE,t–ROKE)2 | (RS&P 500,t–RS&P 500)2 | (ROKE,t–ROKE)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -4.30% | -3.89% | 39.99 | 20.81 | 28.84 |
| 2. | 2018. 3. 31. | 1.05% | -2.69% | 0.96 | 11.26 | 3.28 |
| 3. | 2018. 4. 30. | 7.19% | 0.27% | 26.72 | 0.16 | -2.04 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 12.81% | 5.38% | 116.35 | 22.17 | 50.79 |
| 59. | 2022. 12. 31. | -1.82% | -5.90% | 14.81 | 43.08 | 25.26 |
| 합계 (Σ): | 11,019.64 | 1,691.48 | 2,871.18 | |||
| t | 날짜 | ROKE,t | RS&P 500,t | (ROKE,t–ROKE)2 | (RS&P 500,t–RS&P 500)2 | (ROKE,t–ROKE)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -4.30% | -3.89% | 39.99 | 20.81 | 28.84 |
| 2. | 2018. 3. 31. | 1.05% | -2.69% | 0.96 | 11.26 | 3.28 |
| 3. | 2018. 4. 30. | 7.19% | 0.27% | 26.72 | 0.16 | -2.04 |
| 4. | 2018. 5. 31. | 13.18% | 2.16% | 124.54 | 2.23 | 16.67 |
| 5. | 2018. 6. 30. | 2.45% | 0.48% | 0.18 | 0.03 | -0.08 |
| 6. | 2018. 7. 31. | 0.87% | 3.60% | 1.33 | 8.62 | -3.38 |
| 7. | 2018. 8. 31. | -5.26% | 3.03% | 53.07 | 5.57 | -17.19 |
| 8. | 2018. 9. 30. | 2.85% | 0.43% | 0.68 | 0.06 | -0.20 |
| 9. | 2018. 10. 31. | -3.23% | -6.94% | 27.62 | 57.87 | 39.98 |
| 10. | 2018. 11. 30. | -5.05% | 1.79% | 50.11 | 1.25 | -7.92 |
| 11. | 2018. 12. 31. | -12.18% | -9.18% | 201.69 | 96.91 | 139.81 |
| 12. | 2019. 1. 31. | 20.61% | 7.87% | 345.45 | 51.87 | 133.85 |
| 13. | 2019. 2. 28. | 0.08% | 2.97% | 3.79 | 5.32 | -4.49 |
| 14. | 2019. 3. 31. | 8.68% | 1.79% | 44.33 | 1.27 | 7.50 |
| 15. | 2019. 4. 30. | -1.50% | 3.93% | 12.40 | 10.66 | -11.50 |
| 16. | 2019. 5. 31. | -6.34% | -6.58% | 70.06 | 52.48 | 60.64 |
| 17. | 2019. 6. 30. | 8.16% | 6.89% | 37.61 | 38.77 | 38.18 |
| 18. | 2019. 7. 31. | 1.85% | 1.31% | 0.03 | 0.42 | -0.12 |
| 19. | 2019. 8. 31. | 2.98% | -1.81% | 0.92 | 6.13 | -2.37 |
| 20. | 2019. 9. 30. | 3.38% | 1.72% | 1.84 | 1.11 | 1.43 |
| 21. | 2019. 10. 31. | -5.24% | 2.04% | 52.76 | 1.89 | -10.00 |
| 22. | 2019. 11. 30. | 3.06% | 3.40% | 1.07 | 7.50 | 2.83 |
| 23. | 2019. 12. 31. | 6.50% | 2.86% | 20.04 | 4.81 | 9.82 |
| 24. | 2020. 1. 31. | 0.18% | -0.16% | 3.41 | 0.69 | 1.53 |
| 25. | 2020. 2. 29. | -10.89% | -8.41% | 166.69 | 82.40 | 117.20 |
| 26. | 2020. 3. 31. | -67.31% | -12.51% | 4,807.55 | 173.67 | 913.76 |
| 27. | 2020. 4. 30. | 41.52% | 12.68% | 1,559.64 | 144.43 | 474.61 |
| 28. | 2020. 5. 31. | 22.59% | 4.53% | 422.74 | 14.91 | 79.40 |
| 29. | 2020. 6. 30. | -9.46% | 1.84% | 131.86 | 1.37 | -13.46 |
| 30. | 2020. 7. 31. | -13.17% | 5.51% | 230.89 | 23.46 | -73.60 |
| 31. | 2020. 8. 31. | -1.54% | 7.01% | 12.72 | 40.19 | -22.61 |
| 32. | 2020. 9. 30. | -5.46% | -3.92% | 56.01 | 21.06 | 34.35 |
| 33. | 2020. 10. 31. | 15.22% | -2.77% | 174.18 | 11.79 | -45.31 |
| 34. | 2020. 11. 30. | 23.69% | 10.75% | 469.34 | 101.77 | 218.55 |
| 35. | 2020. 12. 31. | 7.00% | 3.71% | 24.72 | 9.28 | 15.14 |
| 36. | 2021. 1. 31. | 6.21% | -1.11% | 17.55 | 3.17 | -7.46 |
| 37. | 2021. 2. 28. | 11.20% | 2.61% | 84.13 | 3.77 | 17.82 |
| 38. | 2021. 3. 31. | 14.38% | 4.24% | 152.70 | 12.80 | 44.20 |
| 39. | 2021. 4. 30. | 5.16% | 5.24% | 9.84 | 20.94 | 14.35 |
| 40. | 2021. 5. 31. | 0.76% | 0.55% | 1.59 | 0.01 | 0.15 |
| 41. | 2021. 6. 30. | 5.50% | 2.22% | 12.06 | 2.42 | 5.40 |
| 42. | 2021. 7. 31. | -4.92% | 2.27% | 48.18 | 2.59 | -11.16 |
| 43. | 2021. 8. 31. | 1.06% | 2.90% | 0.94 | 4.98 | -2.16 |
| 44. | 2021. 9. 30. | 10.42% | -4.76% | 70.39 | 29.42 | -45.50 |
| 45. | 2021. 10. 31. | 11.32% | 6.91% | 86.41 | 39.03 | 58.08 |
| 46. | 2021. 11. 30. | -5.94% | -0.83% | 63.47 | 2.25 | 11.95 |
| 47. | 2021. 12. 31. | -1.80% | 4.36% | 14.67 | 13.65 | -14.15 |
| 48. | 2022. 1. 31. | 4.86% | -5.26% | 8.03 | 35.11 | -16.79 |
| 49. | 2022. 2. 28. | 7.61% | -3.14% | 31.23 | 14.46 | -21.25 |
| 50. | 2022. 3. 31. | 8.16% | 3.58% | 37.66 | 8.47 | 17.86 |
| 51. | 2022. 4. 30. | -9.01% | -8.80% | 121.82 | 89.54 | 104.44 |
| 52. | 2022. 5. 31. | 3.98% | 0.01% | 3.82 | 0.44 | -1.29 |
| 53. | 2022. 6. 30. | -15.72% | -8.39% | 314.81 | 82.06 | 160.73 |
| 54. | 2022. 7. 31. | 9.32% | 9.11% | 53.28 | 71.32 | 61.64 |
| 55. | 2022. 8. 31. | 2.49% | -4.24% | 0.22 | 24.11 | -2.30 |
| 56. | 2022. 9. 30. | -16.32% | -9.34% | 336.39 | 100.12 | 183.52 |
| 57. | 2022. 10. 31. | 17.59% | 7.99% | 242.37 | 53.58 | 113.96 |
| 58. | 2022. 11. 30. | 12.81% | 5.38% | 116.35 | 22.17 | 50.79 |
| 59. | 2022. 12. 31. | -1.82% | -5.90% | 14.81 | 43.08 | 25.26 |
| 합계 (Σ): | 11,019.64 | 1,691.48 | 2,871.18 | |||
모두 보기
분산OKE = Σ(ROKE,t–ROKE)2 ÷ (59 – 1)
= 11,019.64 ÷ (59 – 1)
= 189.99
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산OKE, S&P 500 = Σ(ROKE,t–ROKE)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,871.18 ÷ (59 – 1)
= 49.50
체계적인 위험 추정 (β)
| 분산OKE | 189.99 |
| 분산S&P 500 | 29.16 |
| 공분산OKE, S&P 500 | 49.50 |
| 상관 계수OKE, S&P 5001 | 0.67 |
| βOKE2 | 1.70 |
| αOKE3 | 0.89% |
계산
1 상관 계수OKE, S&P 500
= 공분산OKE, S&P 500 ÷ (표준 편차OKE × 표준 편차S&P 500)
= 49.50 ÷ (13.78% × 5.40%)
= 0.67
2 βOKE
= 공분산OKE, S&P 500 ÷ 분산S&P 500
= 49.50 ÷ 29.16
= 1.70
3 αOKE
= 평균의OKE – βOKE × 평균의S&P 500
= 2.03% – 1.70 × 0.67%
= 0.89%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.89% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.83% |
| 보통주의 체계적 위험ONEOK | βOKE | 1.70 |
| ONEOK 보통주의 예상 수익률3 | E(ROKE) | 21.77% |
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(ROKE) = RF + βOKE [E(RM) – RF]
= 4.89% + 1.70 [14.83% – 4.89%]
= 21.77%