자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Marathon Oil보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Marathon Oil Corp., 월별 수익률
| Marathon Oil Corp. (MRO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MRO,t1 | 피제수MRO,t1 | RMRO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $16.75 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $16.00 | $0.05 | -4.18% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $15.80 | -1.25% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $14.87 | -5.89% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $15.49 | $0.06 | -4.72% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $16.42 | 6.00% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.04% | 1.36% | ||||
| 표준 편차: | 20.26% | 4.48% | ||||
| Marathon Oil Corp. (MRO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MRO,t1 | 피제수MRO,t1 | RMRO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $16.75 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $16.00 | $0.05 | -4.18% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $15.80 | -1.25% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $14.87 | -5.89% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $13.02 | $0.05 | -12.10% | 2,411.80 | 1.16% |
| 5. | 2017. 6. 30. | $11.85 | -8.99% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $12.23 | 3.21% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $11.12 | $0.05 | -8.67% | 2,471.65 | 0.05% |
| 8. | 2017. 9. 30. | $13.56 | 21.94% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $14.22 | 4.87% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $14.84 | $0.05 | 4.71% | 2,647.58 | 2.81% |
| 11. | 2017. 12. 31. | $16.93 | 14.08% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $18.19 | 7.44% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $14.52 | $0.05 | -19.90% | 2,713.83 | -3.89% |
| 14. | 2018. 3. 31. | $16.13 | 11.09% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $18.25 | 13.14% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $21.43 | $0.05 | 17.70% | 2,705.27 | 2.16% |
| 17. | 2018. 6. 30. | $20.86 | -2.66% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $21.12 | 1.25% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $21.51 | $0.05 | 2.08% | 2,901.52 | 3.03% |
| 20. | 2018. 9. 30. | $23.28 | 8.23% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $18.99 | -18.43% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $16.69 | $0.05 | -11.85% | 2,760.17 | 1.79% |
| 23. | 2018. 12. 31. | $14.34 | -14.08% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $15.79 | 10.11% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $16.60 | $0.05 | 5.45% | 2,784.49 | 2.97% |
| 26. | 2019. 3. 31. | $16.71 | 0.66% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $17.04 | 1.97% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $13.15 | $0.05 | -22.54% | 2,752.06 | -6.58% |
| 29. | 2019. 6. 30. | $14.21 | 8.06% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $14.07 | -0.99% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $11.84 | $0.05 | -15.49% | 2,926.46 | -1.81% |
| 32. | 2019. 9. 30. | $12.27 | 3.63% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $11.53 | -6.03% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $11.65 | $0.05 | 1.47% | 3,140.98 | 3.40% |
| 35. | 2019. 12. 31. | $13.58 | 16.57% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $11.37 | -16.27% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $8.28 | $0.05 | -26.74% | 2,954.22 | -8.41% |
| 38. | 2020. 3. 31. | $3.29 | -60.27% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $6.12 | 86.02% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $5.34 | -12.75% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $6.12 | 14.61% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $5.49 | -10.29% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $5.28 | -3.83% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $4.09 | -22.54% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $3.96 | -3.18% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $5.92 | $0.03 | 50.25% | 3,621.63 | 10.75% |
| 47. | 2020. 12. 31. | $6.67 | 12.67% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $7.24 | 8.55% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $11.10 | $0.03 | 53.73% | 3,811.15 | 2.61% |
| 50. | 2021. 3. 31. | $10.68 | -3.78% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $11.26 | 5.43% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $12.11 | $0.04 | 7.90% | 4,204.11 | 0.55% |
| 53. | 2021. 6. 30. | $13.62 | 12.47% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $11.59 | -14.90% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $11.75 | $0.05 | 1.81% | 4,522.68 | 2.90% |
| 56. | 2021. 9. 30. | $13.67 | 16.34% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $16.32 | 19.39% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $15.49 | $0.06 | -4.72% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $16.42 | 6.00% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.04% | 1.36% | ||||
| 표준 편차: | 20.26% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MRO의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Marathon Oil Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMRO,t | RS&P 500,t | (RMRO,t–RMRO)2 | (RS&P 500,t–RS&P 500)2 | (RMRO,t–RMRO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | -4.18% | 3.72% | 38.71 | 5.58 | -14.70 |
| 2. | 2017. 3. 31. | -1.25% | -0.04% | 10.84 | 1.95 | 4.60 |
| 3. | 2017. 4. 30. | -5.89% | 0.91% | 62.87 | 0.20 | 3.56 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -4.72% | -0.83% | 45.71 | 4.80 | 14.82 |
| 59. | 2021. 12. 31. | 6.00% | 4.36% | 15.69 | 9.02 | 11.90 |
| 합계 (Σ): | 23,800.60 | 1,164.17 | 3,520.83 | |||
| t | 날짜 | RMRO,t | RS&P 500,t | (RMRO,t–RMRO)2 | (RS&P 500,t–RS&P 500)2 | (RMRO,t–RMRO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | -4.18% | 3.72% | 38.71 | 5.58 | -14.70 |
| 2. | 2017. 3. 31. | -1.25% | -0.04% | 10.84 | 1.95 | 4.60 |
| 3. | 2017. 4. 30. | -5.89% | 0.91% | 62.87 | 0.20 | 3.56 |
| 4. | 2017. 5. 31. | -12.10% | 1.16% | 200.16 | 0.04 | 2.83 |
| 5. | 2017. 6. 30. | -8.99% | 0.48% | 121.64 | 0.77 | 9.67 |
| 6. | 2017. 7. 31. | 3.21% | 1.93% | 1.35 | 0.33 | 0.67 |
| 7. | 2017. 8. 31. | -8.67% | 0.05% | 114.71 | 1.70 | 13.96 |
| 8. | 2017. 9. 30. | 21.94% | 1.93% | 395.99 | 0.33 | 11.39 |
| 9. | 2017. 10. 31. | 4.87% | 2.22% | 7.98 | 0.74 | 2.43 |
| 10. | 2017. 11. 30. | 4.71% | 2.81% | 7.12 | 2.10 | 3.87 |
| 11. | 2017. 12. 31. | 14.08% | 0.98% | 144.97 | 0.14 | -4.51 |
| 12. | 2018. 1. 31. | 7.44% | 5.62% | 29.15 | 18.15 | 23.00 |
| 13. | 2018. 2. 28. | -19.90% | -3.89% | 481.54 | 27.59 | 115.26 |
| 14. | 2018. 3. 31. | 11.09% | -2.69% | 81.81 | 16.37 | -36.60 |
| 15. | 2018. 4. 30. | 13.14% | 0.27% | 123.21 | 1.18 | -12.06 |
| 16. | 2018. 5. 31. | 17.70% | 2.16% | 245.10 | 0.64 | 12.57 |
| 17. | 2018. 6. 30. | -2.66% | 0.48% | 22.12 | 0.76 | 4.11 |
| 18. | 2018. 7. 31. | 1.25% | 3.60% | 0.63 | 5.04 | -1.79 |
| 19. | 2018. 8. 31. | 2.08% | 3.03% | 0.00 | 2.78 | 0.07 |
| 20. | 2018. 9. 30. | 8.23% | 0.43% | 38.26 | 0.86 | -5.74 |
| 21. | 2018. 10. 31. | -18.43% | -6.94% | 419.06 | 68.86 | 169.87 |
| 22. | 2018. 11. 30. | -11.85% | 1.79% | 192.97 | 0.18 | -5.95 |
| 23. | 2018. 12. 31. | -14.08% | -9.18% | 259.96 | 111.00 | 169.87 |
| 24. | 2019. 1. 31. | 10.11% | 7.87% | 65.10 | 42.39 | 52.53 |
| 25. | 2019. 2. 28. | 5.45% | 2.97% | 11.58 | 2.61 | 5.50 |
| 26. | 2019. 3. 31. | 0.66% | 1.79% | 1.91 | 0.19 | -0.60 |
| 27. | 2019. 4. 30. | 1.97% | 3.93% | 0.00 | 6.62 | -0.18 |
| 28. | 2019. 5. 31. | -22.54% | -6.58% | 604.09 | 62.97 | 195.04 |
| 29. | 2019. 6. 30. | 8.06% | 6.89% | 36.21 | 30.64 | 33.31 |
| 30. | 2019. 7. 31. | -0.99% | 1.31% | 9.17 | 0.00 | 0.14 |
| 31. | 2019. 8. 31. | -15.49% | -1.81% | 307.55 | 10.03 | 55.54 |
| 32. | 2019. 9. 30. | 3.63% | 1.72% | 2.52 | 0.13 | 0.57 |
| 33. | 2019. 10. 31. | -6.03% | 2.04% | 65.19 | 0.47 | -5.53 |
| 34. | 2019. 11. 30. | 1.47% | 3.40% | 0.32 | 4.19 | -1.16 |
| 35. | 2019. 12. 31. | 16.57% | 2.86% | 210.93 | 2.25 | 21.80 |
| 36. | 2020. 1. 31. | -16.27% | -0.16% | 335.51 | 2.31 | 27.85 |
| 37. | 2020. 2. 29. | -26.74% | -8.41% | 828.29 | 95.43 | 281.15 |
| 38. | 2020. 3. 31. | -60.27% | -12.51% | 3,882.38 | 192.37 | 864.21 |
| 39. | 2020. 4. 30. | 86.02% | 12.68% | 7,051.84 | 128.29 | 951.15 |
| 40. | 2020. 5. 31. | -12.75% | 4.53% | 218.69 | 10.05 | -46.88 |
| 41. | 2020. 6. 30. | 14.61% | 1.84% | 157.85 | 0.23 | 6.04 |
| 42. | 2020. 7. 31. | -10.29% | 5.51% | 152.21 | 17.24 | -51.23 |
| 43. | 2020. 8. 31. | -3.83% | 7.01% | 34.44 | 31.91 | -33.15 |
| 44. | 2020. 9. 30. | -22.54% | -3.92% | 604.22 | 27.89 | 129.80 |
| 45. | 2020. 10. 31. | -3.18% | -2.77% | 27.26 | 17.01 | 21.54 |
| 46. | 2020. 11. 30. | 50.25% | 10.75% | 2,324.16 | 88.30 | 453.01 |
| 47. | 2020. 12. 31. | 12.67% | 3.71% | 112.91 | 5.54 | 25.02 |
| 48. | 2021. 1. 31. | 8.55% | -1.11% | 42.29 | 6.11 | -16.07 |
| 49. | 2021. 2. 28. | 53.73% | 2.61% | 2,671.47 | 1.57 | 64.67 |
| 50. | 2021. 3. 31. | -3.78% | 4.24% | 33.95 | 8.33 | -16.82 |
| 51. | 2021. 4. 30. | 5.43% | 5.24% | 11.48 | 15.09 | 13.16 |
| 52. | 2021. 5. 31. | 7.90% | 0.55% | 34.35 | 0.65 | -4.74 |
| 53. | 2021. 6. 30. | 12.47% | 2.22% | 108.70 | 0.75 | 9.00 |
| 54. | 2021. 7. 31. | -14.90% | 2.27% | 287.22 | 0.84 | -15.54 |
| 55. | 2021. 8. 31. | 1.81% | 2.90% | 0.05 | 2.38 | -0.36 |
| 56. | 2021. 9. 30. | 16.34% | -4.76% | 204.42 | 37.39 | -87.43 |
| 57. | 2021. 10. 31. | 19.39% | 6.91% | 300.76 | 30.87 | 96.36 |
| 58. | 2021. 11. 30. | -4.72% | -0.83% | 45.71 | 4.80 | 14.82 |
| 59. | 2021. 12. 31. | 6.00% | 4.36% | 15.69 | 9.02 | 11.90 |
| 합계 (Σ): | 23,800.60 | 1,164.17 | 3,520.83 | |||
모두 보기
분산MRO = Σ(RMRO,t–RMRO)2 ÷ (59 – 1)
= 23,800.60 ÷ (59 – 1)
= 410.36
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산MRO, S&P 500 = Σ(RMRO,t–RMRO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,520.83 ÷ (59 – 1)
= 60.70
체계적인 위험 추정 (β)
| 분산MRO | 410.36 |
| 분산S&P 500 | 20.07 |
| 공분산MRO, S&P 500 | 60.70 |
| 상관 계수MRO, S&P 5001 | 0.67 |
| βMRO2 | 3.02 |
| αMRO3 | -2.06% |
계산
1 상관 계수MRO, S&P 500
= 공분산MRO, S&P 500 ÷ (표준 편차MRO × 표준 편차S&P 500)
= 60.70 ÷ (20.26% × 4.48%)
= 0.67
2 βMRO
= 공분산MRO, S&P 500 ÷ 분산S&P 500
= 60.70 ÷ 20.07
= 3.02
3 αMRO
= 평균의MRO – βMRO × 평균의S&P 500
= 2.04% – 3.02 × 1.36%
= -2.06%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Marathon Oil | βMRO | 3.02 |
| Marathon Oil 보통주 예상 수익률3 | E(RMRO) | 32.24% |
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(RMRO) = RF + βMRO [E(RM) – RF]
= 4.67% + 3.02 [13.79% – 4.67%]
= 32.24%