자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 ConocoPhillips보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
ConocoPhillips, 월별 수익률
| ConocoPhillips (COP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값COP,t1 | 피제수COP,t1 | RCOP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $67.69 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $67.85 | $0.305 | 0.69% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $66.74 | -1.64% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $63.12 | -5.42% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $115.57 | $0.58 | -2.23% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $116.07 | 0.43% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.03% | 1.11% | ||||
| 표준 편차: | 12.90% | 5.31% | ||||
| ConocoPhillips (COP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값COP,t1 | 피제수COP,t1 | RCOP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $67.69 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $67.85 | $0.305 | 0.69% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $66.74 | -1.64% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $63.12 | -5.42% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $58.96 | $0.305 | -6.11% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $61.00 | 3.46% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $59.08 | $0.305 | -2.65% | 2,980.38 | 1.31% |
| 7. | 2019. 8. 31. | $52.18 | -11.68% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $56.98 | 9.20% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $55.20 | $0.42 | -2.39% | 3,037.56 | 2.04% |
| 10. | 2019. 11. 30. | $59.94 | 8.59% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $65.03 | 8.49% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $59.43 | -8.61% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $48.42 | $0.42 | -17.82% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $30.80 | -36.39% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $42.10 | 36.69% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $42.18 | $0.42 | 1.19% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $42.02 | -0.38% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $37.39 | $0.42 | -10.02% | 3,271.12 | 5.51% |
| 19. | 2020. 8. 31. | $37.89 | 1.34% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $32.84 | -13.33% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $28.62 | $0.43 | -11.54% | 3,269.96 | -2.77% |
| 22. | 2020. 11. 30. | $39.56 | 38.23% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $39.99 | 1.09% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $40.03 | 0.10% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $52.01 | $0.43 | 31.00% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $52.97 | 1.85% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $51.14 | -3.45% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $55.74 | $0.43 | 9.84% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $60.90 | 9.26% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $56.06 | $0.43 | -7.24% | 4,395.26 | 2.27% |
| 31. | 2021. 8. 31. | $55.53 | -0.95% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $67.77 | 22.04% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $74.49 | $0.46 | 10.59% | 4,605.38 | 6.91% |
| 34. | 2021. 11. 30. | $70.13 | -5.85% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $72.18 | $0.20 | 3.21% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $88.62 | 22.78% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $94.86 | $0.46 | 7.56% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $100.00 | $0.30 | 5.73% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $95.52 | -4.48% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $112.36 | $0.46 | 18.11% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $89.81 | $0.70 | -19.45% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $97.43 | 8.48% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $109.45 | $0.46 | 12.81% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $102.34 | $1.40 | -5.22% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $126.09 | 23.21% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $123.51 | $0.51 | -1.64% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $118.00 | $0.70 | -3.89% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $121.87 | 3.28% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $103.35 | $0.51 | -14.78% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $99.21 | $0.60 | -3.43% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $102.89 | 3.71% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $99.30 | $0.51 | -2.99% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $103.61 | $0.60 | 4.94% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $117.72 | 13.62% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $119.03 | $0.51 | 1.55% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $119.80 | $0.60 | 1.15% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $118.80 | -0.83% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $115.57 | $0.58 | -2.23% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $116.07 | 0.43% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.03% | 1.11% | ||||
| 표준 편차: | 12.90% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 COP의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
ConocoPhillips, 수익률의 분산 및 공분산 계산
| t | 날짜 | RCOP,t | RS&P 500,t | (RCOP,t–RCOP)2 | (RS&P 500,t–RS&P 500)2 | (RCOP,t–RCOP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 0.69% | 2.97% | 1.80 | 3.49 | -2.51 |
| 2. | 2019. 3. 31. | -1.64% | 1.79% | 13.44 | 0.47 | -2.52 |
| 3. | 2019. 4. 30. | -5.42% | 3.93% | 55.57 | 7.98 | -21.06 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -2.23% | 8.92% | 18.16 | 61.03 | -33.29 |
| 59. | 2023. 12. 31. | 0.43% | 4.42% | 2.55 | 11.00 | -5.30 |
| 합계 (Σ): | 9,649.74 | 1,634.30 | 2,053.31 | |||
| t | 날짜 | RCOP,t | RS&P 500,t | (RCOP,t–RCOP)2 | (RS&P 500,t–RS&P 500)2 | (RCOP,t–RCOP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 0.69% | 2.97% | 1.80 | 3.49 | -2.51 |
| 2. | 2019. 3. 31. | -1.64% | 1.79% | 13.44 | 0.47 | -2.52 |
| 3. | 2019. 4. 30. | -5.42% | 3.93% | 55.57 | 7.98 | -21.06 |
| 4. | 2019. 5. 31. | -6.11% | -6.58% | 66.22 | 59.04 | 62.53 |
| 5. | 2019. 6. 30. | 3.46% | 6.89% | 2.04 | 33.49 | 8.27 |
| 6. | 2019. 7. 31. | -2.65% | 1.31% | 21.88 | 0.04 | -0.97 |
| 7. | 2019. 8. 31. | -11.68% | -1.81% | 187.95 | 8.50 | 39.96 |
| 8. | 2019. 9. 30. | 9.20% | 1.72% | 51.39 | 0.37 | 4.39 |
| 9. | 2019. 10. 31. | -2.39% | 2.04% | 19.51 | 0.88 | -4.14 |
| 10. | 2019. 11. 30. | 8.59% | 3.40% | 42.99 | 5.28 | 15.07 |
| 11. | 2019. 12. 31. | 8.49% | 2.86% | 41.75 | 3.07 | 11.33 |
| 12. | 2020. 1. 31. | -8.61% | -0.16% | 113.25 | 1.61 | 13.50 |
| 13. | 2020. 2. 29. | -17.82% | -8.41% | 394.01 | 90.57 | 188.91 |
| 14. | 2020. 3. 31. | -36.39% | -12.51% | 1,476.12 | 185.44 | 523.20 |
| 15. | 2020. 4. 30. | 36.69% | 12.68% | 1,201.17 | 134.06 | 401.29 |
| 16. | 2020. 5. 31. | 1.19% | 4.53% | 0.71 | 11.71 | -2.88 |
| 17. | 2020. 6. 30. | -0.38% | 1.84% | 5.81 | 0.54 | -1.77 |
| 18. | 2020. 7. 31. | -10.02% | 5.51% | 145.19 | 19.40 | -53.07 |
| 19. | 2020. 8. 31. | 1.34% | 7.01% | 0.48 | 34.82 | -4.09 |
| 20. | 2020. 9. 30. | -13.33% | -3.92% | 235.88 | 25.29 | 77.23 |
| 21. | 2020. 10. 31. | -11.54% | -2.77% | 184.18 | 15.00 | 52.55 |
| 22. | 2020. 11. 30. | 38.23% | 10.75% | 1,310.05 | 93.10 | 349.23 |
| 23. | 2020. 12. 31. | 1.09% | 3.71% | 0.89 | 6.79 | -2.46 |
| 24. | 2021. 1. 31. | 0.10% | -1.11% | 3.73 | 4.93 | 4.28 |
| 25. | 2021. 2. 28. | 31.00% | 2.61% | 839.34 | 2.26 | 43.55 |
| 26. | 2021. 3. 31. | 1.85% | 4.24% | 0.03 | 9.85 | -0.58 |
| 27. | 2021. 4. 30. | -3.45% | 5.24% | 30.09 | 17.11 | -22.69 |
| 28. | 2021. 5. 31. | 9.84% | 0.55% | 60.92 | 0.31 | -4.35 |
| 29. | 2021. 6. 30. | 9.26% | 2.22% | 52.23 | 1.24 | 8.06 |
| 30. | 2021. 7. 31. | -7.24% | 2.27% | 85.97 | 1.37 | -10.84 |
| 31. | 2021. 8. 31. | -0.95% | 2.90% | 8.86 | 3.22 | -5.34 |
| 32. | 2021. 9. 30. | 22.04% | -4.76% | 400.47 | 34.37 | -117.32 |
| 33. | 2021. 10. 31. | 10.59% | 6.91% | 73.35 | 33.74 | 49.75 |
| 34. | 2021. 11. 30. | -5.85% | -0.83% | 62.15 | 3.76 | 15.29 |
| 35. | 2021. 12. 31. | 3.21% | 4.36% | 1.39 | 10.60 | 3.83 |
| 36. | 2022. 1. 31. | 22.78% | -5.26% | 430.39 | 40.51 | -132.03 |
| 37. | 2022. 2. 28. | 7.56% | -3.14% | 30.58 | 17.99 | -23.46 |
| 38. | 2022. 3. 31. | 5.73% | 3.58% | 13.72 | 6.11 | 9.16 |
| 39. | 2022. 4. 30. | -4.48% | -8.80% | 42.39 | 98.04 | 64.46 |
| 40. | 2022. 5. 31. | 18.11% | 0.01% | 258.60 | 1.21 | -17.70 |
| 41. | 2022. 6. 30. | -19.45% | -8.39% | 461.26 | 90.21 | 203.98 |
| 42. | 2022. 7. 31. | 8.48% | 9.11% | 41.66 | 64.09 | 51.67 |
| 43. | 2022. 8. 31. | 12.81% | -4.24% | 116.18 | 28.62 | -57.66 |
| 44. | 2022. 9. 30. | -5.22% | -9.34% | 52.53 | 109.11 | 75.70 |
| 45. | 2022. 10. 31. | 23.21% | 7.99% | 448.45 | 47.34 | 145.71 |
| 46. | 2022. 11. 30. | -1.64% | 5.38% | 13.48 | 18.23 | -15.68 |
| 47. | 2022. 12. 31. | -3.89% | -5.90% | 35.10 | 49.04 | 41.49 |
| 48. | 2023. 1. 31. | 3.28% | 6.18% | 1.56 | 25.70 | 6.33 |
| 49. | 2023. 2. 28. | -14.78% | -2.61% | 282.52 | 13.82 | 62.48 |
| 50. | 2023. 3. 31. | -3.43% | 3.51% | 29.76 | 5.76 | -13.09 |
| 51. | 2023. 4. 30. | 3.71% | 1.46% | 2.82 | 0.13 | 0.60 |
| 52. | 2023. 5. 31. | -2.99% | 0.25% | 25.24 | 0.74 | 4.31 |
| 53. | 2023. 6. 30. | 4.94% | 4.71% | 8.49 | 13.02 | 10.51 |
| 54. | 2023. 7. 31. | 13.62% | 4.85% | 134.28 | 13.99 | 43.34 |
| 55. | 2023. 8. 31. | 1.55% | -1.77% | 0.23 | 8.28 | 1.39 |
| 56. | 2023. 9. 30. | 1.15% | -4.87% | 0.77 | 35.73 | 5.26 |
| 57. | 2023. 10. 31. | -0.83% | -2.20% | 8.21 | 10.92 | 9.47 |
| 58. | 2023. 11. 30. | -2.23% | 8.92% | 18.16 | 61.03 | -33.29 |
| 59. | 2023. 12. 31. | 0.43% | 4.42% | 2.55 | 11.00 | -5.30 |
| 합계 (Σ): | 9,649.74 | 1,634.30 | 2,053.31 | |||
모두 표시
분산COP = Σ(RCOP,t–RCOP)2 ÷ (59 – 1)
= 9,649.74 ÷ (59 – 1)
= 166.37
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산COP, S&P 500 = Σ(RCOP,t–RCOP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,053.31 ÷ (59 – 1)
= 35.40
체계적인 위험 추정 (β)
| 분산COP | 166.37 |
| 분산S&P 500 | 28.18 |
| 공분산COP, S&P 500 | 35.40 |
| 상관 계수COP, S&P 5001 | 0.52 |
| βCOP2 | 1.26 |
| αCOP3 | 0.64% |
계산
1 상관 계수COP, S&P 500
= 공분산COP, S&P 500 ÷ (표준 편차COP × 표준 편차S&P 500)
= 35.40 ÷ (12.90% × 5.31%)
= 0.52
2 βCOP
= 공분산COP, S&P 500 ÷ 분산S&P 500
= 35.40 ÷ 28.18
= 1.26
3 αCOP
= 평균의COP – βCOP × 평균의S&P 500
= 2.03% – 1.26 × 1.11%
= 0.64%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주의 체계적 위험ConocoPhillips | βCOP | 1.26 |
| ConocoPhillips 보통주의 예상 수익률3 | E(RCOP) | 16.12% |
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(RCOP) = RF + βCOP [E(RM) – RF]
= 4.56% + 1.26 [13.77% – 4.56%]
= 16.12%