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 |
| 2019. 1. 31. | $66.78 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $66.15 | -0.94% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $66.20 | $0.78 | 1.25% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $58.88 | -11.06% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $59.15 | -4.30% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $59.71 | $0.18 | 1.25% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.99% | 1.11% | ||||
| 표준 편차: | 19.46% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $66.78 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $66.15 | -0.94% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $66.20 | $0.78 | 1.25% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $58.88 | -11.06% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $49.77 | -15.47% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $50.28 | $0.78 | 2.59% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $51.36 | 2.15% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $43.48 | -15.34% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $44.47 | $0.79 | 4.09% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $40.50 | -8.93% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $38.57 | -4.77% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $41.21 | $0.79 | 8.89% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $39.72 | -3.62% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $32.74 | -17.57% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $11.58 | $0.79 | -62.22% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $16.60 | 43.35% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $12.95 | -21.99% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $18.30 | $0.01 | 41.39% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $15.74 | -13.99% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $12.74 | -19.06% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $10.01 | $0.01 | -21.35% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $9.13 | -8.79% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $15.76 | 72.62% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $17.31 | $0.01 | 9.90% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $20.06 | 15.89% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $26.61 | 32.65% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $26.62 | $0.01 | 0.08% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $25.36 | -4.73% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $25.96 | 2.37% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $31.27 | $0.01 | 20.49% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $26.10 | -16.53% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $25.69 | -1.57% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $29.58 | $0.01 | 15.18% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $33.53 | 13.35% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $29.65 | -11.57% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $28.99 | $0.01 | -2.19% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $37.67 | 29.94% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $43.73 | 16.09% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $56.74 | $0.13 | 30.05% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $55.09 | -2.91% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $69.31 | 25.81% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $58.88 | $0.13 | -14.86% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $65.75 | 11.67% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $71.00 | 7.98% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $61.45 | $0.13 | -13.27% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $72.60 | 18.14% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $69.49 | -4.28% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $62.99 | $0.13 | -9.17% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $64.79 | 2.86% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $58.56 | -9.62% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $62.43 | $0.18 | 6.92% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $61.53 | -1.44% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $57.66 | -6.29% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $58.80 | $0.18 | 2.29% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $63.13 | 7.36% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $62.79 | -0.54% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $64.88 | $0.18 | 3.62% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $61.81 | -4.73% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $59.15 | -4.30% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $59.71 | $0.18 | 1.25% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.99% | 1.11% | ||||
| 표준 편차: | 19.46% | 5.31% | ||||
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. | 2019. 2. 28. | -0.94% | 2.97% | 8.58 | 3.49 | -5.47 |
| 2. | 2019. 3. 31. | 1.25% | 1.79% | 0.53 | 0.47 | -0.50 |
| 3. | 2019. 4. 30. | -11.06% | 3.93% | 170.11 | 7.98 | -36.85 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -4.30% | 8.92% | 39.55 | 61.03 | -49.13 |
| 59. | 2023. 12. 31. | 1.25% | 4.42% | 0.54 | 11.00 | -2.44 |
| 합계 (Σ): | 21,965.27 | 1,634.30 | 2,703.97 | |||
| 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. | 2019. 2. 28. | -0.94% | 2.97% | 8.58 | 3.49 | -5.47 |
| 2. | 2019. 3. 31. | 1.25% | 1.79% | 0.53 | 0.47 | -0.50 |
| 3. | 2019. 4. 30. | -11.06% | 3.93% | 170.11 | 7.98 | -36.85 |
| 4. | 2019. 5. 31. | -15.47% | -6.58% | 304.76 | 59.04 | 134.14 |
| 5. | 2019. 6. 30. | 2.59% | 6.89% | 0.37 | 33.49 | 3.51 |
| 6. | 2019. 7. 31. | 2.15% | 1.31% | 0.03 | 0.04 | 0.03 |
| 7. | 2019. 8. 31. | -15.34% | -1.81% | 300.25 | 8.50 | 50.51 |
| 8. | 2019. 9. 30. | 4.09% | 1.72% | 4.45 | 0.37 | 1.29 |
| 9. | 2019. 10. 31. | -8.93% | 2.04% | 119.08 | 0.88 | -10.23 |
| 10. | 2019. 11. 30. | -4.77% | 3.40% | 45.57 | 5.28 | -15.52 |
| 11. | 2019. 12. 31. | 8.89% | 2.86% | 47.72 | 3.07 | 12.11 |
| 12. | 2020. 1. 31. | -3.62% | -0.16% | 31.37 | 1.61 | 7.11 |
| 13. | 2020. 2. 29. | -17.57% | -8.41% | 382.52 | 90.57 | 186.13 |
| 14. | 2020. 3. 31. | -62.22% | -12.51% | 4,121.98 | 185.44 | 874.30 |
| 15. | 2020. 4. 30. | 43.35% | 12.68% | 1,711.10 | 134.06 | 478.95 |
| 16. | 2020. 5. 31. | -21.99% | 4.53% | 574.71 | 11.71 | -82.04 |
| 17. | 2020. 6. 30. | 41.39% | 1.84% | 1,552.74 | 0.54 | 28.88 |
| 18. | 2020. 7. 31. | -13.99% | 5.51% | 255.18 | 19.40 | -70.35 |
| 19. | 2020. 8. 31. | -19.06% | 7.01% | 442.89 | 34.82 | -124.18 |
| 20. | 2020. 9. 30. | -21.35% | -3.92% | 544.53 | 25.29 | 117.34 |
| 21. | 2020. 10. 31. | -8.79% | -2.77% | 116.13 | 15.00 | 41.73 |
| 22. | 2020. 11. 30. | 72.62% | 10.75% | 4,988.96 | 93.10 | 681.51 |
| 23. | 2020. 12. 31. | 9.90% | 3.71% | 62.62 | 6.79 | 20.62 |
| 24. | 2021. 1. 31. | 15.89% | -1.11% | 193.26 | 4.93 | -30.85 |
| 25. | 2021. 2. 28. | 32.65% | 2.61% | 940.46 | 2.26 | 46.10 |
| 26. | 2021. 3. 31. | 0.08% | 4.24% | 3.65 | 9.85 | -5.99 |
| 27. | 2021. 4. 30. | -4.73% | 5.24% | 45.14 | 17.11 | -27.79 |
| 28. | 2021. 5. 31. | 2.37% | 0.55% | 0.15 | 0.31 | -0.21 |
| 29. | 2021. 6. 30. | 20.49% | 2.22% | 342.54 | 1.24 | 20.65 |
| 30. | 2021. 7. 31. | -16.53% | 2.27% | 342.94 | 1.37 | -21.65 |
| 31. | 2021. 8. 31. | -1.57% | 2.90% | 12.65 | 3.22 | -6.38 |
| 32. | 2021. 9. 30. | 15.18% | -4.76% | 174.13 | 34.37 | -77.36 |
| 33. | 2021. 10. 31. | 13.35% | 6.91% | 129.24 | 33.74 | 66.03 |
| 34. | 2021. 11. 30. | -11.57% | -0.83% | 183.79 | 3.76 | 26.29 |
| 35. | 2021. 12. 31. | -2.19% | 4.36% | 17.45 | 10.60 | -13.60 |
| 36. | 2022. 1. 31. | 29.94% | -5.26% | 781.55 | 40.51 | -177.92 |
| 37. | 2022. 2. 28. | 16.09% | -3.14% | 198.86 | 17.99 | -59.82 |
| 38. | 2022. 3. 31. | 30.05% | 3.58% | 787.53 | 6.11 | 69.36 |
| 39. | 2022. 4. 30. | -2.91% | -8.80% | 23.94 | 98.04 | 48.45 |
| 40. | 2022. 5. 31. | 25.81% | 0.01% | 567.73 | 1.21 | -26.22 |
| 41. | 2022. 6. 30. | -14.86% | -8.39% | 283.78 | 90.21 | 160.00 |
| 42. | 2022. 7. 31. | 11.67% | 9.11% | 93.75 | 64.09 | 77.52 |
| 43. | 2022. 8. 31. | 7.98% | -4.24% | 36.00 | 28.62 | -32.10 |
| 44. | 2022. 9. 30. | -13.27% | -9.34% | 232.65 | 109.11 | 159.32 |
| 45. | 2022. 10. 31. | 18.14% | 7.99% | 261.14 | 47.34 | 111.19 |
| 46. | 2022. 11. 30. | -4.28% | 5.38% | 39.30 | 18.23 | -26.76 |
| 47. | 2022. 12. 31. | -9.17% | -5.90% | 124.37 | 49.04 | 78.10 |
| 48. | 2023. 1. 31. | 2.86% | 6.18% | 0.76 | 25.70 | 4.42 |
| 49. | 2023. 2. 28. | -9.62% | -2.61% | 134.58 | 13.82 | 43.12 |
| 50. | 2023. 3. 31. | 6.92% | 3.51% | 24.31 | 5.76 | 11.83 |
| 51. | 2023. 4. 30. | -1.44% | 1.46% | 11.74 | 0.13 | -1.23 |
| 52. | 2023. 5. 31. | -6.29% | 0.25% | 68.47 | 0.74 | 7.10 |
| 53. | 2023. 6. 30. | 2.29% | 4.71% | 0.09 | 13.02 | 1.10 |
| 54. | 2023. 7. 31. | 7.36% | 4.85% | 28.93 | 13.99 | 20.12 |
| 55. | 2023. 8. 31. | -0.54% | -1.77% | 6.37 | 8.28 | 7.26 |
| 56. | 2023. 9. 30. | 3.62% | -4.87% | 2.66 | 35.73 | -9.74 |
| 57. | 2023. 10. 31. | -4.73% | -2.20% | 45.12 | 10.92 | 22.19 |
| 58. | 2023. 11. 30. | -4.30% | 8.92% | 39.55 | 61.03 | -49.13 |
| 59. | 2023. 12. 31. | 1.25% | 4.42% | 0.54 | 11.00 | -2.44 |
| 합계 (Σ): | 21,965.27 | 1,634.30 | 2,703.97 | |||
모두 보기
분산OXY = Σ(ROXY,t–ROXY)2 ÷ (59 – 1)
= 21,965.27 ÷ (59 – 1)
= 378.71
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산OXY, S&P 500 = Σ(ROXY,t–ROXY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,703.97 ÷ (59 – 1)
= 46.62
체계적인 위험 추정 (β)
| 분산OXY | 378.71 |
| 분산S&P 500 | 28.18 |
| 공분산OXY, S&P 500 | 46.62 |
| 상관 계수OXY, S&P 5001 | 0.45 |
| βOXY2 | 1.65 |
| αOXY3 | 0.16% |
계산
1 상관 계수OXY, S&P 500
= 공분산OXY, S&P 500 ÷ (표준 편차OXY × 표준 편차S&P 500)
= 46.62 ÷ (19.46% × 5.31%)
= 0.45
2 βOXY
= 공분산OXY, S&P 500 ÷ 분산S&P 500
= 46.62 ÷ 28.18
= 1.65
3 αOXY
= 평균의OXY – βOXY × 평균의S&P 500
= 1.99% – 1.65 × 1.11%
= 0.16%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 3.99% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.81% |
| 보통주의 체계적 위험Occidental | βOXY | 1.65 |
| 옥시덴탈 보통주의 예상 수익률3 | E(ROXY) | 20.23% |
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]
= 3.99% + 1.65 [13.81% – 3.99%]
= 20.23%