자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 LyondellBasell보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
LyondellBasell Industries N.V., 월별 수익률
| LyondellBasell Industries N.V. (LYB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LYB,t1 | 피제수LYB,t1 | RLYB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2014. 1. 31. | $78.76 | 1,782.59 | ||||
| 1. | 2014. 2. 28. | $88.08 | $0.60 | 12.60% | 1,859.45 | 4.31% |
| 2. | 2014. 3. 31. | $88.94 | 0.98% | 1,872.34 | 0.69% | |
| 3. | 2014. 4. 30. | $92.50 | $0.70 | 4.79% | 1,883.95 | 0.62% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2018. 11. 30. | $93.31 | 4.53% | 2,760.17 | 1.79% | |
| 59. | 2018. 12. 31. | $83.16 | $1.00 | -9.81% | 2,506.85 | -9.18% |
| 평균의 (R): | 0.66% | 0.63% | ||||
| 표준 편차: | 7.34% | 3.13% | ||||
| LyondellBasell Industries N.V. (LYB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LYB,t1 | 피제수LYB,t1 | RLYB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2014. 1. 31. | $78.76 | 1,782.59 | ||||
| 1. | 2014. 2. 28. | $88.08 | $0.60 | 12.60% | 1,859.45 | 4.31% |
| 2. | 2014. 3. 31. | $88.94 | 0.98% | 1,872.34 | 0.69% | |
| 3. | 2014. 4. 30. | $92.50 | $0.70 | 4.79% | 1,883.95 | 0.62% |
| 4. | 2014. 5. 31. | $99.57 | 7.64% | 1,923.57 | 2.10% | |
| 5. | 2014. 6. 30. | $97.65 | -1.93% | 1,960.23 | 1.91% | |
| 6. | 2014. 7. 31. | $106.25 | 8.81% | 1,930.67 | -1.51% | |
| 7. | 2014. 8. 31. | $114.35 | $0.70 | 8.28% | 2,003.37 | 3.77% |
| 8. | 2014. 9. 30. | $108.66 | -4.98% | 1,972.29 | -1.55% | |
| 9. | 2014. 10. 31. | $91.63 | -15.67% | 2,018.05 | 2.32% | |
| 10. | 2014. 11. 30. | $78.86 | $0.70 | -13.17% | 2,067.56 | 2.45% |
| 11. | 2014. 12. 31. | $79.39 | 0.67% | 2,058.90 | -0.42% | |
| 12. | 2015. 1. 31. | $79.09 | -0.38% | 1,994.99 | -3.10% | |
| 13. | 2015. 2. 28. | $85.91 | $0.70 | 9.51% | 2,104.50 | 5.49% |
| 14. | 2015. 3. 31. | $87.80 | 2.20% | 2,067.89 | -1.74% | |
| 15. | 2015. 4. 30. | $103.52 | 17.90% | 2,085.51 | 0.85% | |
| 16. | 2015. 5. 31. | $101.10 | $0.78 | -1.58% | 2,107.39 | 1.05% |
| 17. | 2015. 6. 30. | $103.52 | 2.39% | 2,063.11 | -2.10% | |
| 18. | 2015. 7. 31. | $93.83 | -9.36% | 2,103.84 | 1.97% | |
| 19. | 2015. 8. 31. | $85.38 | $0.78 | -8.17% | 1,972.18 | -6.26% |
| 20. | 2015. 9. 30. | $83.36 | -2.37% | 1,920.03 | -2.64% | |
| 21. | 2015. 10. 31. | $92.91 | 11.46% | 2,079.36 | 8.30% | |
| 22. | 2015. 11. 30. | $95.82 | $0.78 | 3.97% | 2,080.41 | 0.05% |
| 23. | 2015. 12. 31. | $86.90 | -9.31% | 2,043.94 | -1.75% | |
| 24. | 2016. 1. 31. | $77.97 | -10.28% | 1,940.24 | -5.07% | |
| 25. | 2016. 2. 29. | $80.21 | $0.78 | 3.87% | 1,932.23 | -0.41% |
| 26. | 2016. 3. 31. | $85.58 | 6.69% | 2,059.74 | 6.60% | |
| 27. | 2016. 4. 30. | $82.67 | -3.40% | 2,065.30 | 0.27% | |
| 28. | 2016. 5. 31. | $81.36 | $0.85 | -0.56% | 2,096.95 | 1.53% |
| 29. | 2016. 6. 30. | $74.42 | -8.53% | 2,098.86 | 0.09% | |
| 30. | 2016. 7. 31. | $75.26 | 1.13% | 2,173.60 | 3.56% | |
| 31. | 2016. 8. 31. | $78.89 | $0.85 | 5.95% | 2,170.95 | -0.12% |
| 32. | 2016. 9. 30. | $80.66 | 2.24% | 2,168.27 | -0.12% | |
| 33. | 2016. 10. 31. | $79.55 | -1.38% | 2,126.15 | -1.94% | |
| 34. | 2016. 11. 30. | $90.32 | $0.85 | 14.61% | 2,198.81 | 3.42% |
| 35. | 2016. 12. 31. | $85.78 | -5.03% | 2,238.83 | 1.82% | |
| 36. | 2017. 1. 31. | $93.27 | 8.73% | 2,278.87 | 1.79% | |
| 37. | 2017. 2. 28. | $91.24 | -2.18% | 2,363.64 | 3.72% | |
| 38. | 2017. 3. 31. | $91.19 | $0.85 | 0.88% | 2,362.72 | -0.04% |
| 39. | 2017. 4. 30. | $84.76 | -7.05% | 2,384.20 | 0.91% | |
| 40. | 2017. 5. 31. | $80.52 | -5.00% | 2,411.80 | 1.16% | |
| 41. | 2017. 6. 30. | $84.39 | $0.90 | 5.92% | 2,423.41 | 0.48% |
| 42. | 2017. 7. 31. | $90.09 | 6.75% | 2,470.30 | 1.93% | |
| 43. | 2017. 8. 31. | $90.59 | 0.56% | 2,471.65 | 0.05% | |
| 44. | 2017. 9. 30. | $99.05 | $0.90 | 10.33% | 2,519.36 | 1.93% |
| 45. | 2017. 10. 31. | $103.53 | 4.52% | 2,575.26 | 2.22% | |
| 46. | 2017. 11. 30. | $104.70 | 1.13% | 2,647.58 | 2.81% | |
| 47. | 2017. 12. 31. | $110.32 | $0.90 | 6.23% | 2,673.61 | 0.98% |
| 48. | 2018. 1. 31. | $119.84 | 8.63% | 2,823.81 | 5.62% | |
| 49. | 2018. 2. 28. | $108.22 | -9.70% | 2,713.83 | -3.89% | |
| 50. | 2018. 3. 31. | $105.68 | $1.00 | -1.42% | 2,640.87 | -2.69% |
| 51. | 2018. 4. 30. | $105.73 | 0.05% | 2,648.05 | 0.27% | |
| 52. | 2018. 5. 31. | $112.12 | 6.04% | 2,705.27 | 2.16% | |
| 53. | 2018. 6. 30. | $109.85 | $1.00 | -1.13% | 2,718.37 | 0.48% |
| 54. | 2018. 7. 31. | $110.79 | 0.86% | 2,816.29 | 3.60% | |
| 55. | 2018. 8. 31. | $112.78 | 1.80% | 2,901.52 | 3.03% | |
| 56. | 2018. 9. 30. | $102.51 | $1.00 | -8.22% | 2,913.98 | 0.43% |
| 57. | 2018. 10. 31. | $89.27 | -12.92% | 2,711.74 | -6.94% | |
| 58. | 2018. 11. 30. | $93.31 | 4.53% | 2,760.17 | 1.79% | |
| 59. | 2018. 12. 31. | $83.16 | $1.00 | -9.81% | 2,506.85 | -9.18% |
| 평균의 (R): | 0.66% | 0.63% | ||||
| 표준 편차: | 7.34% | 3.13% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 LYB의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
LyondellBasell Industries N.V., 수익률의 분산 및 공분산 계산
| t | 날짜 | RLYB,t | RS&P 500,t | (RLYB,t–RLYB)2 | (RS&P 500,t–RS&P 500)2 | (RLYB,t–RLYB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2014. 2. 28. | 12.60% | 4.31% | 142.37 | 13.57 | 43.95 |
| 2. | 2014. 3. 31. | 0.98% | 0.69% | 0.10 | 0.00 | 0.02 |
| 3. | 2014. 4. 30. | 4.79% | 0.62% | 17.03 | 0.00 | -0.03 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2018. 11. 30. | 4.53% | 1.79% | 14.92 | 1.34 | 4.47 |
| 59. | 2018. 12. 31. | -9.81% | -9.18% | 109.61 | 96.15 | 102.66 |
| 합계 (Σ): | 3,127.55 | 566.60 | 695.50 | |||
| t | 날짜 | RLYB,t | RS&P 500,t | (RLYB,t–RLYB)2 | (RS&P 500,t–RS&P 500)2 | (RLYB,t–RLYB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2014. 2. 28. | 12.60% | 4.31% | 142.37 | 13.57 | 43.95 |
| 2. | 2014. 3. 31. | 0.98% | 0.69% | 0.10 | 0.00 | 0.02 |
| 3. | 2014. 4. 30. | 4.79% | 0.62% | 17.03 | 0.00 | -0.03 |
| 4. | 2014. 5. 31. | 7.64% | 2.10% | 48.72 | 2.18 | 10.30 |
| 5. | 2014. 6. 30. | -1.93% | 1.91% | 6.72 | 1.63 | -3.31 |
| 6. | 2014. 7. 31. | 8.81% | -1.51% | 66.32 | 4.56 | -17.39 |
| 7. | 2014. 8. 31. | 8.28% | 3.77% | 58.05 | 9.84 | 23.90 |
| 8. | 2014. 9. 30. | -4.98% | -1.55% | 31.80 | 4.75 | 12.29 |
| 9. | 2014. 10. 31. | -15.67% | 2.32% | 266.87 | 2.86 | -27.64 |
| 10. | 2014. 11. 30. | -13.17% | 2.45% | 191.43 | 3.33 | -25.26 |
| 11. | 2014. 12. 31. | 0.67% | -0.42% | 0.00 | 1.10 | -0.01 |
| 12. | 2015. 1. 31. | -0.38% | -3.10% | 1.08 | 13.93 | 3.89 |
| 13. | 2015. 2. 28. | 9.51% | 5.49% | 78.23 | 23.63 | 43.00 |
| 14. | 2015. 3. 31. | 2.20% | -1.74% | 2.36 | 5.61 | -3.64 |
| 15. | 2015. 4. 30. | 17.90% | 0.85% | 297.25 | 0.05 | 3.86 |
| 16. | 2015. 5. 31. | -1.58% | 1.05% | 5.05 | 0.18 | -0.95 |
| 17. | 2015. 6. 30. | 2.39% | -2.10% | 2.99 | 7.45 | -4.72 |
| 18. | 2015. 7. 31. | -9.36% | 1.97% | 100.48 | 1.81 | -13.49 |
| 19. | 2015. 8. 31. | -8.17% | -6.26% | 78.11 | 47.42 | 60.86 |
| 20. | 2015. 9. 30. | -2.37% | -2.64% | 9.18 | 10.71 | 9.91 |
| 21. | 2015. 10. 31. | 11.46% | 8.30% | 116.49 | 58.83 | 82.79 |
| 22. | 2015. 11. 30. | 3.97% | 0.05% | 10.94 | 0.33 | -1.91 |
| 23. | 2015. 12. 31. | -9.31% | -1.75% | 99.45 | 5.67 | 23.74 |
| 24. | 2016. 1. 31. | -10.28% | -5.07% | 119.68 | 32.51 | 62.37 |
| 25. | 2016. 2. 29. | 3.87% | -0.41% | 10.30 | 1.08 | -3.34 |
| 26. | 2016. 3. 31. | 6.69% | 6.60% | 36.38 | 35.65 | 36.01 |
| 27. | 2016. 4. 30. | -3.40% | 0.27% | 16.51 | 0.13 | 1.45 |
| 28. | 2016. 5. 31. | -0.56% | 1.53% | 1.49 | 0.82 | -1.10 |
| 29. | 2016. 6. 30. | -8.53% | 0.09% | 84.52 | 0.29 | 4.94 |
| 30. | 2016. 7. 31. | 1.13% | 3.56% | 0.22 | 8.60 | 1.36 |
| 31. | 2016. 8. 31. | 5.95% | -0.12% | 27.98 | 0.56 | -3.97 |
| 32. | 2016. 9. 30. | 2.24% | -0.12% | 2.50 | 0.56 | -1.19 |
| 33. | 2016. 10. 31. | -1.38% | -1.94% | 4.16 | 6.61 | 5.24 |
| 34. | 2016. 11. 30. | 14.61% | 3.42% | 194.43 | 7.78 | 38.90 |
| 35. | 2016. 12. 31. | -5.03% | 1.82% | 32.38 | 1.42 | -6.78 |
| 36. | 2017. 1. 31. | 8.73% | 1.79% | 65.10 | 1.35 | 9.36 |
| 37. | 2017. 2. 28. | -2.18% | 3.72% | 8.07 | 9.56 | -8.78 |
| 38. | 2017. 3. 31. | 0.88% | -0.04% | 0.05 | 0.44 | -0.14 |
| 39. | 2017. 4. 30. | -7.05% | 0.91% | 59.52 | 0.08 | -2.17 |
| 40. | 2017. 5. 31. | -5.00% | 1.16% | 32.10 | 0.28 | -3.00 |
| 41. | 2017. 6. 30. | 5.92% | 0.48% | 27.67 | 0.02 | -0.77 |
| 42. | 2017. 7. 31. | 6.75% | 1.93% | 37.10 | 1.71 | 7.96 |
| 43. | 2017. 8. 31. | 0.56% | 0.05% | 0.01 | 0.33 | 0.06 |
| 44. | 2017. 9. 30. | 10.33% | 1.93% | 93.49 | 1.70 | 12.59 |
| 45. | 2017. 10. 31. | 4.52% | 2.22% | 14.90 | 2.53 | 6.14 |
| 46. | 2017. 11. 30. | 1.13% | 2.81% | 0.22 | 4.75 | 1.02 |
| 47. | 2017. 12. 31. | 6.23% | 0.98% | 30.96 | 0.13 | 1.98 |
| 48. | 2018. 1. 31. | 8.63% | 5.62% | 63.46 | 24.90 | 39.75 |
| 49. | 2018. 2. 28. | -9.70% | -3.89% | 107.32 | 20.45 | 46.85 |
| 50. | 2018. 3. 31. | -1.42% | -2.69% | 4.35 | 11.00 | 6.92 |
| 51. | 2018. 4. 30. | 0.05% | 0.27% | 0.38 | 0.13 | 0.22 |
| 52. | 2018. 5. 31. | 6.04% | 2.16% | 28.95 | 2.35 | 8.25 |
| 53. | 2018. 6. 30. | -1.13% | 0.48% | 3.23 | 0.02 | 0.26 |
| 54. | 2018. 7. 31. | 0.86% | 3.60% | 0.04 | 8.85 | 0.57 |
| 55. | 2018. 8. 31. | 1.80% | 3.03% | 1.28 | 5.75 | 2.72 |
| 56. | 2018. 9. 30. | -8.22% | 0.43% | 78.91 | 0.04 | 1.76 |
| 57. | 2018. 10. 31. | -12.92% | -6.94% | 184.40 | 57.28 | 102.77 |
| 58. | 2018. 11. 30. | 4.53% | 1.79% | 14.92 | 1.34 | 4.47 |
| 59. | 2018. 12. 31. | -9.81% | -9.18% | 109.61 | 96.15 | 102.66 |
| 합계 (Σ): | 3,127.55 | 566.60 | 695.50 | |||
모두 보기
분산LYB = Σ(RLYB,t–RLYB)2 ÷ (59 – 1)
= 3,127.55 ÷ (59 – 1)
= 53.92
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 566.60 ÷ (59 – 1)
= 9.77
공분산LYB, S&P 500 = Σ(RLYB,t–RLYB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 695.50 ÷ (59 – 1)
= 11.99
체계적인 위험 추정 (β)
| 분산LYB | 53.92 |
| 분산S&P 500 | 9.77 |
| 공분산LYB, S&P 500 | 11.99 |
| 상관 계수LYB, S&P 5001 | 0.52 |
| βLYB2 | 1.23 |
| αLYB3 | -0.11% |
계산
1 상관 계수LYB, S&P 500
= 공분산LYB, S&P 500 ÷ (표준 편차LYB × 표준 편차S&P 500)
= 11.99 ÷ (7.34% × 3.13%)
= 0.52
2 βLYB
= 공분산LYB, S&P 500 ÷ 분산S&P 500
= 11.99 ÷ 9.77
= 1.23
3 αLYB
= 평균의LYB – βLYB × 평균의S&P 500
= 0.66% – 1.23 × 0.63%
= -0.11%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험LyondellBasell | βLYB | 1.23 |
| LyondellBasell 보통주의 예상 수익률3 | E(RLYB) | 15.86% |
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(RLYB) = RF + βLYB [E(RM) – RF]
= 4.67% + 1.23 [13.79% – 4.67%]
= 15.86%