자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다 MPC.
수익률
Marathon Petroleum Corp., 월별 수익률
| Marathon Petroleum Corp. (MPC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MPC,t1 | 피제수MPC,t1 | RMPC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $66.26 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $62.01 | $0.53 | -5.61% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $59.85 | -3.48% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $60.87 | 1.70% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $149.19 | $0.825 | -0.82% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $148.36 | -0.56% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.70% | 1.11% | ||||
| 표준 편차: | 13.63% | 5.31% | ||||
| Marathon Petroleum Corp. (MPC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MPC,t1 | 피제수MPC,t1 | RMPC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $66.26 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $62.01 | $0.53 | -5.61% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $59.85 | -3.48% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $60.87 | 1.70% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $45.99 | $0.53 | -23.57% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $55.88 | 21.50% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $56.39 | 0.91% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $49.21 | $0.53 | -11.79% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $60.75 | 23.45% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $63.95 | 5.27% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $60.64 | $0.53 | -4.35% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $60.25 | -0.64% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $54.50 | -9.54% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $47.42 | $0.58 | -11.93% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $23.62 | -50.19% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $32.08 | 35.82% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $35.14 | $0.58 | 11.35% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $37.38 | 6.37% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $38.20 | 2.19% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $35.46 | $0.58 | -5.65% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $29.34 | -17.26% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $29.50 | 0.55% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $38.88 | $0.58 | 33.76% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $41.36 | 6.38% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $43.16 | 4.35% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $54.62 | $0.58 | 27.90% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $53.49 | -2.07% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $55.65 | 4.04% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $61.80 | $0.58 | 12.09% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $60.42 | -2.23% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $55.22 | -8.61% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $59.27 | $0.58 | 8.38% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $61.81 | 4.29% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $65.93 | 6.67% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $60.85 | $0.58 | -6.83% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $63.99 | 5.16% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $71.75 | 12.13% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $77.87 | $0.58 | 9.34% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $85.50 | 9.80% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $87.26 | 2.06% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $101.79 | $0.58 | 17.32% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $82.21 | -19.24% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $91.66 | 11.49% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $100.75 | $0.58 | 10.55% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $99.33 | -1.41% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $113.62 | 14.39% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $121.81 | $0.75 | 7.87% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $116.39 | -4.45% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $128.52 | 10.42% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $123.60 | $0.75 | -3.24% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $134.83 | 9.09% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $122.00 | -9.52% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $104.91 | $0.75 | -13.39% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $116.60 | 11.14% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $133.02 | 14.08% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $142.77 | $0.75 | 7.89% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $151.34 | 6.00% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $151.25 | -0.06% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $149.19 | $0.825 | -0.82% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $148.36 | -0.56% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.70% | 1.11% | ||||
| 표준 편차: | 13.63% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 MPC의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Marathon Petroleum Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMPC,t | RS&P 500,t | (RMPC,t–RMPC)2 | (RS&P 500,t–RS&P 500)2 | (RMPC,t–RMPC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -5.61% | 2.97% | 69.11 | 3.49 | -15.52 |
| 2. | 2019. 3. 31. | -3.48% | 1.79% | 38.22 | 0.47 | -4.24 |
| 3. | 2019. 4. 30. | 1.70% | 3.93% | 0.99 | 7.98 | -2.81 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -0.82% | 8.92% | 12.36 | 61.03 | -27.47 |
| 59. | 2023. 12. 31. | -0.56% | 4.42% | 10.60 | 11.00 | -10.80 |
| 합계 (Σ): | 10,773.16 | 1,634.30 | 2,478.55 | |||
| t | 날짜 | RMPC,t | RS&P 500,t | (RMPC,t–RMPC)2 | (RS&P 500,t–RS&P 500)2 | (RMPC,t–RMPC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -5.61% | 2.97% | 69.11 | 3.49 | -15.52 |
| 2. | 2019. 3. 31. | -3.48% | 1.79% | 38.22 | 0.47 | -4.24 |
| 3. | 2019. 4. 30. | 1.70% | 3.93% | 0.99 | 7.98 | -2.81 |
| 4. | 2019. 5. 31. | -23.57% | -6.58% | 690.33 | 59.04 | 201.88 |
| 5. | 2019. 6. 30. | 21.50% | 6.89% | 353.64 | 33.49 | 108.83 |
| 6. | 2019. 7. 31. | 0.91% | 1.31% | 3.19 | 0.04 | -0.37 |
| 7. | 2019. 8. 31. | -11.79% | -1.81% | 210.02 | 8.50 | 42.24 |
| 8. | 2019. 9. 30. | 23.45% | 1.72% | 430.61 | 0.37 | 12.71 |
| 9. | 2019. 10. 31. | 5.27% | 2.04% | 6.60 | 0.88 | 2.41 |
| 10. | 2019. 11. 30. | -4.35% | 3.40% | 49.65 | 5.28 | -16.20 |
| 11. | 2019. 12. 31. | -0.64% | 2.86% | 11.17 | 3.07 | -5.86 |
| 12. | 2020. 1. 31. | -9.54% | -0.16% | 149.89 | 1.61 | 15.53 |
| 13. | 2020. 2. 29. | -11.93% | -8.41% | 213.92 | 90.57 | 139.19 |
| 14. | 2020. 3. 31. | -50.19% | -12.51% | 2,797.25 | 185.44 | 720.23 |
| 15. | 2020. 4. 30. | 35.82% | 12.68% | 1,096.79 | 134.06 | 383.46 |
| 16. | 2020. 5. 31. | 11.35% | 4.53% | 74.78 | 11.71 | 29.59 |
| 17. | 2020. 6. 30. | 6.37% | 1.84% | 13.51 | 0.54 | 2.69 |
| 18. | 2020. 7. 31. | 2.19% | 5.51% | 0.26 | 19.40 | -2.23 |
| 19. | 2020. 8. 31. | -5.65% | 7.01% | 69.78 | 34.82 | -49.29 |
| 20. | 2020. 9. 30. | -17.26% | -3.92% | 398.33 | 25.29 | 100.36 |
| 21. | 2020. 10. 31. | 0.55% | -2.77% | 4.64 | 15.00 | 8.34 |
| 22. | 2020. 11. 30. | 33.76% | 10.75% | 964.94 | 93.10 | 299.72 |
| 23. | 2020. 12. 31. | 6.38% | 3.71% | 13.54 | 6.79 | 9.59 |
| 24. | 2021. 1. 31. | 4.35% | -1.11% | 2.73 | 4.93 | -3.67 |
| 25. | 2021. 2. 28. | 27.90% | 2.61% | 634.89 | 2.26 | 37.88 |
| 26. | 2021. 3. 31. | -2.07% | 4.24% | 22.73 | 9.85 | -14.96 |
| 27. | 2021. 4. 30. | 4.04% | 5.24% | 1.79 | 17.11 | 5.54 |
| 28. | 2021. 5. 31. | 12.09% | 0.55% | 88.25 | 0.31 | -5.23 |
| 29. | 2021. 6. 30. | -2.23% | 2.22% | 24.33 | 1.24 | -5.50 |
| 30. | 2021. 7. 31. | -8.61% | 2.27% | 127.82 | 1.37 | -13.22 |
| 31. | 2021. 8. 31. | 8.38% | 2.90% | 32.32 | 3.22 | 10.19 |
| 32. | 2021. 9. 30. | 4.29% | -4.76% | 2.52 | 34.37 | -9.30 |
| 33. | 2021. 10. 31. | 6.67% | 6.91% | 15.73 | 33.74 | 23.04 |
| 34. | 2021. 11. 30. | -6.83% | -0.83% | 90.72 | 3.76 | 18.47 |
| 35. | 2021. 12. 31. | 5.16% | 4.36% | 6.06 | 10.60 | 8.01 |
| 36. | 2022. 1. 31. | 12.13% | -5.26% | 88.88 | 40.51 | -60.00 |
| 37. | 2022. 2. 28. | 9.34% | -3.14% | 44.07 | 17.99 | -28.16 |
| 38. | 2022. 3. 31. | 9.80% | 3.58% | 50.40 | 6.11 | 17.55 |
| 39. | 2022. 4. 30. | 2.06% | -8.80% | 0.41 | 98.04 | 6.34 |
| 40. | 2022. 5. 31. | 17.32% | 0.01% | 213.65 | 1.21 | -16.09 |
| 41. | 2022. 6. 30. | -19.24% | -8.39% | 481.14 | 90.21 | 208.33 |
| 42. | 2022. 7. 31. | 11.49% | 9.11% | 77.36 | 64.09 | 70.42 |
| 43. | 2022. 8. 31. | 10.55% | -4.24% | 61.63 | 28.62 | -42.00 |
| 44. | 2022. 9. 30. | -1.41% | -9.34% | 16.88 | 109.11 | 42.92 |
| 45. | 2022. 10. 31. | 14.39% | 7.99% | 136.59 | 47.34 | 80.41 |
| 46. | 2022. 11. 30. | 7.87% | 5.38% | 26.72 | 18.23 | 22.07 |
| 47. | 2022. 12. 31. | -4.45% | -5.90% | 51.11 | 49.04 | 50.06 |
| 48. | 2023. 1. 31. | 10.42% | 6.18% | 59.64 | 25.70 | 39.15 |
| 49. | 2023. 2. 28. | -3.24% | -2.61% | 35.33 | 13.82 | 22.09 |
| 50. | 2023. 3. 31. | 9.09% | 3.51% | 40.79 | 5.76 | 15.32 |
| 51. | 2023. 4. 30. | -9.52% | 1.46% | 149.21 | 0.13 | -4.38 |
| 52. | 2023. 5. 31. | -13.39% | 0.25% | 258.98 | 0.74 | 13.80 |
| 53. | 2023. 6. 30. | 11.14% | 4.71% | 71.29 | 13.02 | 30.46 |
| 54. | 2023. 7. 31. | 14.08% | 4.85% | 129.57 | 13.99 | 42.57 |
| 55. | 2023. 8. 31. | 7.89% | -1.77% | 26.98 | 8.28 | -14.95 |
| 56. | 2023. 9. 30. | 6.00% | -4.87% | 10.91 | 35.73 | -19.75 |
| 57. | 2023. 10. 31. | -0.06% | -2.20% | 7.61 | 10.92 | 9.11 |
| 58. | 2023. 11. 30. | -0.82% | 8.92% | 12.36 | 61.03 | -27.47 |
| 59. | 2023. 12. 31. | -0.56% | 4.42% | 10.60 | 11.00 | -10.80 |
| 합계 (Σ): | 10,773.16 | 1,634.30 | 2,478.55 | |||
모두 표시
분산MPC = Σ(RMPC,t–RMPC)2 ÷ (59 – 1)
= 10,773.16 ÷ (59 – 1)
= 185.74
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산MPC, S&P 500 = Σ(RMPC,t–RMPC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,478.55 ÷ (59 – 1)
= 42.73
체계적인 위험 추정 (β)
| 분산MPC | 185.74 |
| 분산S&P 500 | 28.18 |
| 공분산MPC, S&P 500 | 42.73 |
| 상관 계수MPC, S&P 5001 | 0.59 |
| βMPC2 | 1.52 |
| αMPC3 | 1.02% |
계산
1 상관 계수MPC, S&P 500
= 공분산MPC, S&P 500 ÷ (표준 편차MPC × 표준 편차S&P 500)
= 42.73 ÷ (13.63% × 5.31%)
= 0.59
2 βMPC
= 공분산MPC, S&P 500 ÷ 분산S&P 500
= 42.73 ÷ 28.18
= 1.52
3 αMPC
= 평균의MPC – βMPC × 평균의S&P 500
= 2.70% – 1.52 × 1.11%
= 1.02%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주 MPC 의 체계적인 리스크 | βMPC | 1.52 |
| MPC 보통주에 대한 예상 수익률3 | E(RMPC) | 18.52% |
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(RMPC) = RF + βMPC [E(RM) – RF]
= 4.56% + 1.52 [13.77% – 4.56%]
= 18.52%