자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Occidental보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Occidental Petroleum Corp., 월별 수익률
| Occidental Petroleum Corp. (OXY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값OXY,t1 | 피제수OXY,t1 | ROXY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $39.72 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $32.74 | -17.57% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $11.58 | $0.79 | -62.22% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $16.60 | 43.35% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $50.58 | 0.94% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $49.41 | $0.22 | -1.88% | 5,881.63 | -2.50% |
| 평균의 (R): | 2.41% | 1.16% | ||||
| 표준 편차: | 19.17% | 5.28% | ||||
| Occidental Petroleum Corp. (OXY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값OXY,t1 | 피제수OXY,t1 | ROXY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $39.72 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $32.74 | -17.57% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $11.58 | $0.79 | -62.22% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $16.60 | 43.35% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $12.95 | -21.99% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $18.30 | $0.01 | 41.39% | 3,100.29 | 1.84% |
| 6. | 2020. 7. 31. | $15.74 | -13.99% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $12.74 | -19.06% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $10.01 | $0.01 | -21.35% | 3,363.00 | -3.92% |
| 9. | 2020. 10. 31. | $9.13 | -8.79% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $15.76 | 72.62% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $17.31 | $0.01 | 9.90% | 3,756.07 | 3.71% |
| 12. | 2021. 1. 31. | $20.06 | 15.89% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $26.61 | 32.65% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $26.62 | $0.01 | 0.08% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $25.36 | -4.73% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $25.96 | 2.37% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $31.27 | $0.01 | 20.49% | 4,297.50 | 2.22% |
| 18. | 2021. 7. 31. | $26.10 | -16.53% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $25.69 | -1.57% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $29.58 | $0.01 | 15.18% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $33.53 | 13.35% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $29.65 | -11.57% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $28.99 | $0.01 | -2.19% | 4,766.18 | 4.36% |
| 24. | 2022. 1. 31. | $37.67 | 29.94% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $43.73 | 16.09% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $56.74 | $0.13 | 30.05% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $55.09 | -2.91% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $69.31 | 25.81% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $58.88 | $0.13 | -14.86% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $65.75 | 11.67% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $71.00 | 7.98% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $61.45 | $0.13 | -13.27% | 3,585.62 | -9.34% |
| 33. | 2022. 10. 31. | $72.60 | 18.14% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $69.49 | -4.28% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $62.99 | $0.13 | -9.17% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $64.79 | 2.86% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $58.56 | -9.62% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $62.43 | $0.18 | 6.92% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $61.53 | -1.44% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $57.66 | -6.29% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $58.80 | $0.18 | 2.29% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $63.13 | 7.36% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $62.79 | -0.54% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $64.88 | $0.18 | 3.62% | 4,288.05 | -4.87% |
| 45. | 2023. 10. 31. | $61.81 | -4.73% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $59.15 | -4.30% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $59.71 | $0.18 | 1.25% | 4,769.83 | 4.42% |
| 48. | 2024. 1. 31. | $57.57 | -3.58% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $60.61 | 5.28% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $64.99 | $0.22 | 7.59% | 5,254.35 | 3.10% |
| 51. | 2024. 4. 30. | $66.14 | 1.77% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $62.50 | -5.50% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $63.03 | $0.22 | 1.20% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $60.82 | -3.51% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $56.98 | -6.31% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $51.54 | $0.22 | -9.16% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $50.11 | -2.77% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $50.58 | 0.94% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $49.41 | $0.22 | -1.88% | 5,881.63 | -2.50% |
| 평균의 (R): | 2.41% | 1.16% | ||||
| 표준 편차: | 19.17% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 OXY의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Occidental Petroleum Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | ROXY,t | RS&P 500,t | (ROXY,t–ROXY)2 | (RS&P 500,t–RS&P 500)2 | (ROXY,t–ROXY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -17.57% | -8.41% | 399.41 | 91.63 | 191.31 |
| 2. | 2020. 3. 31. | -62.22% | -12.51% | 4,177.00 | 186.96 | 883.70 |
| 3. | 2020. 4. 30. | 43.35% | 12.68% | 1,675.95 | 132.78 | 471.74 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 0.94% | 5.73% | 2.17 | 20.87 | -6.74 |
| 59. | 2024. 12. 31. | -1.88% | -2.50% | 18.41 | 13.40 | 15.70 |
| 합계 (Σ): | 21,313.66 | 1,618.62 | 2,554.89 | |||
| t | 날짜 | ROXY,t | RS&P 500,t | (ROXY,t–ROXY)2 | (RS&P 500,t–RS&P 500)2 | (ROXY,t–ROXY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -17.57% | -8.41% | 399.41 | 91.63 | 191.31 |
| 2. | 2020. 3. 31. | -62.22% | -12.51% | 4,177.00 | 186.96 | 883.70 |
| 3. | 2020. 4. 30. | 43.35% | 12.68% | 1,675.95 | 132.78 | 471.74 |
| 4. | 2020. 5. 31. | -21.99% | 4.53% | 595.37 | 11.34 | -82.15 |
| 5. | 2020. 6. 30. | 41.39% | 1.84% | 1,519.26 | 0.46 | 26.41 |
| 6. | 2020. 7. 31. | -13.99% | 5.51% | 269.00 | 18.91 | -71.33 |
| 7. | 2020. 8. 31. | -19.06% | 7.01% | 461.04 | 34.17 | -125.51 |
| 8. | 2020. 9. 30. | -21.35% | -3.92% | 564.65 | 25.85 | 120.81 |
| 9. | 2020. 10. 31. | -8.79% | -2.77% | 125.52 | 15.43 | 44.01 |
| 10. | 2020. 11. 30. | 72.62% | 10.75% | 4,928.81 | 92.03 | 673.50 |
| 11. | 2020. 12. 31. | 9.90% | 3.71% | 56.04 | 6.51 | 19.10 |
| 12. | 2021. 1. 31. | 15.89% | -1.11% | 181.56 | 5.18 | -30.65 |
| 13. | 2021. 2. 28. | 32.65% | 2.61% | 914.45 | 2.10 | 43.78 |
| 14. | 2021. 3. 31. | 0.08% | 4.24% | 5.46 | 9.50 | -7.20 |
| 15. | 2021. 4. 30. | -4.73% | 5.24% | 51.06 | 16.66 | -29.16 |
| 16. | 2021. 5. 31. | 2.37% | 0.55% | 0.00 | 0.38 | 0.03 |
| 17. | 2021. 6. 30. | 20.49% | 2.22% | 326.92 | 1.12 | 19.17 |
| 18. | 2021. 7. 31. | -16.53% | 2.27% | 358.94 | 1.24 | -21.10 |
| 19. | 2021. 8. 31. | -1.57% | 2.90% | 15.87 | 3.02 | -6.92 |
| 20. | 2021. 9. 30. | 15.18% | -4.76% | 163.04 | 35.02 | -75.57 |
| 21. | 2021. 10. 31. | 13.35% | 6.91% | 119.71 | 33.10 | 62.95 |
| 22. | 2021. 11. 30. | -11.57% | -0.83% | 195.55 | 3.98 | 27.89 |
| 23. | 2021. 12. 31. | -2.19% | 4.36% | 21.20 | 10.24 | -14.73 |
| 24. | 2022. 1. 31. | 29.94% | -5.26% | 757.85 | 41.21 | -176.73 |
| 25. | 2022. 2. 28. | 16.09% | -3.14% | 187.00 | 18.47 | -58.77 |
| 26. | 2022. 3. 31. | 30.05% | 3.58% | 763.74 | 5.84 | 66.77 |
| 27. | 2022. 4. 30. | -2.91% | -8.80% | 28.30 | 99.14 | 52.97 |
| 28. | 2022. 5. 31. | 25.81% | 0.01% | 547.56 | 1.34 | -27.05 |
| 29. | 2022. 6. 30. | -14.86% | -8.39% | 298.36 | 91.26 | 165.01 |
| 30. | 2022. 7. 31. | 11.67% | 9.11% | 85.67 | 63.21 | 73.59 |
| 31. | 2022. 8. 31. | 7.98% | -4.24% | 31.05 | 29.22 | -30.12 |
| 32. | 2022. 9. 30. | -13.27% | -9.34% | 245.86 | 110.27 | 164.65 |
| 33. | 2022. 10. 31. | 18.14% | 7.99% | 247.51 | 46.58 | 107.38 |
| 34. | 2022. 11. 30. | -4.28% | 5.38% | 44.84 | 17.76 | -28.22 |
| 35. | 2022. 12. 31. | -9.17% | -5.90% | 134.07 | 49.82 | 81.73 |
| 36. | 2023. 1. 31. | 2.86% | 6.18% | 0.20 | 25.14 | 2.23 |
| 37. | 2023. 2. 28. | -9.62% | -2.61% | 144.67 | 14.23 | 45.38 |
| 38. | 2023. 3. 31. | 6.92% | 3.51% | 20.28 | 5.49 | 10.56 |
| 39. | 2023. 4. 30. | -1.44% | 1.46% | 14.85 | 0.09 | -1.17 |
| 40. | 2023. 5. 31. | -6.29% | 0.25% | 75.72 | 0.83 | 7.95 |
| 41. | 2023. 6. 30. | 2.29% | 4.71% | 0.02 | 12.62 | -0.44 |
| 42. | 2023. 7. 31. | 7.36% | 4.85% | 24.52 | 13.58 | 18.25 |
| 43. | 2023. 8. 31. | -0.54% | -1.77% | 8.71 | 8.60 | 8.65 |
| 44. | 2023. 9. 30. | 3.62% | -4.87% | 1.45 | 36.40 | -7.26 |
| 45. | 2023. 10. 31. | -4.73% | -2.20% | 51.04 | 11.28 | 24.00 |
| 46. | 2023. 11. 30. | -4.30% | 8.92% | 45.10 | 60.17 | -52.09 |
| 47. | 2023. 12. 31. | 1.25% | 4.42% | 1.35 | 10.64 | -3.79 |
| 48. | 2024. 1. 31. | -3.58% | 1.59% | 35.95 | 0.18 | -2.57 |
| 49. | 2024. 2. 29. | 5.28% | 5.17% | 8.23 | 16.09 | 11.50 |
| 50. | 2024. 3. 31. | 7.59% | 3.10% | 26.80 | 3.77 | 10.05 |
| 51. | 2024. 4. 30. | 1.77% | -4.16% | 0.41 | 28.33 | 3.42 |
| 52. | 2024. 5. 31. | -5.50% | 4.80% | 62.66 | 13.26 | -28.82 |
| 53. | 2024. 6. 30. | 1.20% | 3.47% | 1.47 | 5.32 | -2.80 |
| 54. | 2024. 7. 31. | -3.51% | 1.13% | 35.03 | 0.00 | 0.17 |
| 55. | 2024. 8. 31. | -6.31% | 2.28% | 76.14 | 1.26 | -9.79 |
| 56. | 2024. 9. 30. | -9.16% | 2.02% | 133.94 | 0.74 | -9.93 |
| 57. | 2024. 10. 31. | -2.77% | -0.99% | 26.90 | 4.63 | 11.16 |
| 58. | 2024. 11. 30. | 0.94% | 5.73% | 2.17 | 20.87 | -6.74 |
| 59. | 2024. 12. 31. | -1.88% | -2.50% | 18.41 | 13.40 | 15.70 |
| 합계 (Σ): | 21,313.66 | 1,618.62 | 2,554.89 | |||
모두 보기
분산OXY = Σ(ROXY,t–ROXY)2 ÷ (59 – 1)
= 21,313.66 ÷ (59 – 1)
= 367.48
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산OXY, S&P 500 = Σ(ROXY,t–ROXY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,554.89 ÷ (59 – 1)
= 44.05
체계적인 위험 추정 (β)
| 분산OXY | 367.48 |
| 분산S&P 500 | 27.91 |
| 공분산OXY, S&P 500 | 44.05 |
| 상관 계수OXY, S&P 5001 | 0.43 |
| βOXY2 | 1.58 |
| αOXY3 | 0.58% |
계산
1 상관 계수OXY, S&P 500
= 공분산OXY, S&P 500 ÷ (표준 편차OXY × 표준 편차S&P 500)
= 44.05 ÷ (19.17% × 5.28%)
= 0.43
2 βOXY
= 공분산OXY, S&P 500 ÷ 분산S&P 500
= 44.05 ÷ 27.91
= 1.58
3 αOXY
= 평균의OXY – βOXY × 평균의S&P 500
= 2.41% – 1.58 × 1.16%
= 0.58%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.91% |
| 보통주의 체계적 위험Occidental | βOXY | 1.58 |
| 옥시덴탈 보통주의 예상 수익률3 | E(ROXY) | 20.83% |
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(ROXY) = RF + βOXY [E(RM) – RF]
= 4.67% + 1.58 [14.91% – 4.67%]
= 20.83%