자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Phillips 66보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Phillips 66, 월별 수익률
| Phillips 66 (PSX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PSX,t1 | 피제수PSX,t1 | RPSX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $70.32 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $78.46 | $0.50 | 12.29% | 2,104.50 | 5.49% |
| 2. | 2015. 3. 31. | $78.60 | 0.18% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $79.31 | 0.90% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | $114.72 | $0.90 | -1.03% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $111.41 | -2.89% | 3,230.78 | 2.86% | |
| 평균의 (R): | 1.26% | 0.88% | ||||
| 표준 편차: | 6.69% | 3.45% | ||||
| Phillips 66 (PSX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PSX,t1 | 피제수PSX,t1 | RPSX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $70.32 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $78.46 | $0.50 | 12.29% | 2,104.50 | 5.49% |
| 2. | 2015. 3. 31. | $78.60 | 0.18% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $79.31 | 0.90% | 2,085.51 | 0.85% | |
| 4. | 2015. 5. 31. | $79.12 | $0.56 | 0.47% | 2,107.39 | 1.05% |
| 5. | 2015. 6. 30. | $80.56 | 1.82% | 2,063.11 | -2.10% | |
| 6. | 2015. 7. 31. | $79.50 | -1.32% | 2,103.84 | 1.97% | |
| 7. | 2015. 8. 31. | $79.07 | $0.56 | 0.16% | 1,972.18 | -6.26% |
| 8. | 2015. 9. 30. | $76.84 | -2.82% | 1,920.03 | -2.64% | |
| 9. | 2015. 10. 31. | $89.05 | 15.89% | 2,079.36 | 8.30% | |
| 10. | 2015. 11. 30. | $91.53 | $0.56 | 3.41% | 2,080.41 | 0.05% |
| 11. | 2015. 12. 31. | $81.80 | -10.63% | 2,043.94 | -1.75% | |
| 12. | 2016. 1. 31. | $80.15 | -2.02% | 1,940.24 | -5.07% | |
| 13. | 2016. 2. 29. | $79.39 | $0.56 | -0.25% | 1,932.23 | -0.41% |
| 14. | 2016. 3. 31. | $86.59 | 9.07% | 2,059.74 | 6.60% | |
| 15. | 2016. 4. 30. | $82.11 | -5.17% | 2,065.30 | 0.27% | |
| 16. | 2016. 5. 31. | $80.36 | $0.63 | -1.36% | 2,096.95 | 1.53% |
| 17. | 2016. 6. 30. | $79.34 | -1.27% | 2,098.86 | 0.09% | |
| 18. | 2016. 7. 31. | $76.06 | -4.13% | 2,173.60 | 3.56% | |
| 19. | 2016. 8. 31. | $78.45 | $0.63 | 3.97% | 2,170.95 | -0.12% |
| 20. | 2016. 9. 30. | $80.55 | 2.68% | 2,168.27 | -0.12% | |
| 21. | 2016. 10. 31. | $81.15 | 0.74% | 2,126.15 | -1.94% | |
| 22. | 2016. 11. 30. | $83.08 | $0.63 | 3.15% | 2,198.81 | 3.42% |
| 23. | 2016. 12. 31. | $86.41 | 4.01% | 2,238.83 | 1.82% | |
| 24. | 2017. 1. 31. | $81.62 | -5.54% | 2,278.87 | 1.79% | |
| 25. | 2017. 2. 28. | $78.19 | $0.63 | -3.43% | 2,363.64 | 3.72% |
| 26. | 2017. 3. 31. | $79.22 | 1.32% | 2,362.72 | -0.04% | |
| 27. | 2017. 4. 30. | $79.56 | 0.43% | 2,384.20 | 0.91% | |
| 28. | 2017. 5. 31. | $76.11 | $0.70 | -3.46% | 2,411.80 | 1.16% |
| 29. | 2017. 6. 30. | $82.69 | 8.65% | 2,423.41 | 0.48% | |
| 30. | 2017. 7. 31. | $83.75 | 1.28% | 2,470.30 | 1.93% | |
| 31. | 2017. 8. 31. | $83.81 | $0.70 | 0.91% | 2,471.65 | 0.05% |
| 32. | 2017. 9. 30. | $91.61 | 9.31% | 2,519.36 | 1.93% | |
| 33. | 2017. 10. 31. | $91.08 | -0.58% | 2,575.26 | 2.22% | |
| 34. | 2017. 11. 30. | $97.56 | $0.70 | 7.88% | 2,647.58 | 2.81% |
| 35. | 2017. 12. 31. | $101.15 | 3.68% | 2,673.61 | 0.98% | |
| 36. | 2018. 1. 31. | $102.40 | 1.24% | 2,823.81 | 5.62% | |
| 37. | 2018. 2. 28. | $90.37 | $0.70 | -11.06% | 2,713.83 | -3.89% |
| 38. | 2018. 3. 31. | $95.92 | 6.14% | 2,640.87 | -2.69% | |
| 39. | 2018. 4. 30. | $111.31 | 16.04% | 2,648.05 | 0.27% | |
| 40. | 2018. 5. 31. | $116.49 | $0.80 | 5.37% | 2,705.27 | 2.16% |
| 41. | 2018. 6. 30. | $112.31 | -3.59% | 2,718.37 | 0.48% | |
| 42. | 2018. 7. 31. | $123.34 | 9.82% | 2,816.29 | 3.60% | |
| 43. | 2018. 8. 31. | $118.51 | $0.80 | -3.27% | 2,901.52 | 3.03% |
| 44. | 2018. 9. 30. | $112.72 | -4.89% | 2,913.98 | 0.43% | |
| 45. | 2018. 10. 31. | $102.82 | -8.78% | 2,711.74 | -6.94% | |
| 46. | 2018. 11. 30. | $93.52 | $0.80 | -8.27% | 2,760.17 | 1.79% |
| 47. | 2018. 12. 31. | $86.15 | -7.88% | 2,506.85 | -9.18% | |
| 48. | 2019. 1. 31. | $95.41 | 10.75% | 2,704.10 | 7.87% | |
| 49. | 2019. 2. 28. | $96.36 | $0.80 | 1.83% | 2,784.49 | 2.97% |
| 50. | 2019. 3. 31. | $95.17 | -1.23% | 2,834.40 | 1.79% | |
| 51. | 2019. 4. 30. | $94.27 | -0.95% | 2,945.83 | 3.93% | |
| 52. | 2019. 5. 31. | $80.80 | $0.90 | -13.33% | 2,752.06 | -6.58% |
| 53. | 2019. 6. 30. | $93.54 | 15.77% | 2,941.76 | 6.89% | |
| 54. | 2019. 7. 31. | $102.56 | 9.64% | 2,980.38 | 1.31% | |
| 55. | 2019. 8. 31. | $98.63 | $0.90 | -2.95% | 2,926.46 | -1.81% |
| 56. | 2019. 9. 30. | $102.40 | 3.82% | 2,976.74 | 1.72% | |
| 57. | 2019. 10. 31. | $116.82 | 14.08% | 3,037.56 | 2.04% | |
| 58. | 2019. 11. 30. | $114.72 | $0.90 | -1.03% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $111.41 | -2.89% | 3,230.78 | 2.86% | |
| 평균의 (R): | 1.26% | 0.88% | ||||
| 표준 편차: | 6.69% | 3.45% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 PSX의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Phillips 66, 수익률의 분산 및 공분산 계산
| t | 날짜 | RPSX,t | RS&P 500,t | (RPSX,t–RPSX)2 | (RS&P 500,t–RS&P 500)2 | (RPSX,t–RPSX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 12.29% | 5.49% | 121.49 | 21.25 | 50.81 |
| 2. | 2015. 3. 31. | 0.18% | -1.74% | 1.18 | 6.86 | 2.84 |
| 3. | 2015. 4. 30. | 0.90% | 0.85% | 0.13 | 0.00 | 0.01 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | -1.03% | 3.40% | 5.25 | 6.38 | -5.79 |
| 59. | 2019. 12. 31. | -2.89% | 2.86% | 17.22 | 3.92 | -8.22 |
| 합계 (Σ): | 2,598.43 | 688.77 | 755.71 | |||
| t | 날짜 | RPSX,t | RS&P 500,t | (RPSX,t–RPSX)2 | (RS&P 500,t–RS&P 500)2 | (RPSX,t–RPSX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 12.29% | 5.49% | 121.49 | 21.25 | 50.81 |
| 2. | 2015. 3. 31. | 0.18% | -1.74% | 1.18 | 6.86 | 2.84 |
| 3. | 2015. 4. 30. | 0.90% | 0.85% | 0.13 | 0.00 | 0.01 |
| 4. | 2015. 5. 31. | 0.47% | 1.05% | 0.64 | 0.03 | -0.14 |
| 5. | 2015. 6. 30. | 1.82% | -2.10% | 0.31 | 8.88 | -1.66 |
| 6. | 2015. 7. 31. | -1.32% | 1.97% | 6.66 | 1.20 | -2.83 |
| 7. | 2015. 8. 31. | 0.16% | -6.26% | 1.21 | 50.94 | 7.86 |
| 8. | 2015. 9. 30. | -2.82% | -2.64% | 16.69 | 12.41 | 14.39 |
| 9. | 2015. 10. 31. | 15.89% | 8.30% | 213.91 | 55.04 | 108.51 |
| 10. | 2015. 11. 30. | 3.41% | 0.05% | 4.62 | 0.69 | -1.78 |
| 11. | 2015. 12. 31. | -10.63% | -1.75% | 141.49 | 6.93 | 31.31 |
| 12. | 2016. 1. 31. | -2.02% | -5.07% | 10.77 | 35.43 | 19.53 |
| 13. | 2016. 2. 29. | -0.25% | -0.41% | 2.29 | 1.67 | 1.96 |
| 14. | 2016. 3. 31. | 9.07% | 6.60% | 60.91 | 32.72 | 44.64 |
| 15. | 2016. 4. 30. | -5.17% | 0.27% | 41.45 | 0.37 | 3.92 |
| 16. | 2016. 5. 31. | -1.36% | 1.53% | 6.91 | 0.43 | -1.72 |
| 17. | 2016. 6. 30. | -1.27% | 0.09% | 6.42 | 0.62 | 2.00 |
| 18. | 2016. 7. 31. | -4.13% | 3.56% | 29.15 | 7.19 | -14.48 |
| 19. | 2016. 8. 31. | 3.97% | -0.12% | 7.32 | 1.00 | -2.71 |
| 20. | 2016. 9. 30. | 2.68% | -0.12% | 1.99 | 1.01 | -1.42 |
| 21. | 2016. 10. 31. | 0.74% | -1.94% | 0.27 | 7.96 | 1.47 |
| 22. | 2016. 11. 30. | 3.15% | 3.42% | 3.57 | 6.44 | 4.80 |
| 23. | 2016. 12. 31. | 4.01% | 1.82% | 7.53 | 0.89 | 2.58 |
| 24. | 2017. 1. 31. | -5.54% | 1.79% | 46.35 | 0.83 | -6.19 |
| 25. | 2017. 2. 28. | -3.43% | 3.72% | 22.04 | 8.07 | -13.34 |
| 26. | 2017. 3. 31. | 1.32% | -0.04% | 0.00 | 0.84 | -0.05 |
| 27. | 2017. 4. 30. | 0.43% | 0.91% | 0.70 | 0.00 | -0.03 |
| 28. | 2017. 5. 31. | -3.46% | 1.16% | 22.29 | 0.08 | -1.31 |
| 29. | 2017. 6. 30. | 8.65% | 0.48% | 54.48 | 0.16 | -2.94 |
| 30. | 2017. 7. 31. | 1.28% | 1.93% | 0.00 | 1.11 | 0.02 |
| 31. | 2017. 8. 31. | 0.91% | 0.05% | 0.13 | 0.68 | 0.29 |
| 32. | 2017. 9. 30. | 9.31% | 1.93% | 64.68 | 1.10 | 8.45 |
| 33. | 2017. 10. 31. | -0.58% | 2.22% | 3.40 | 1.79 | -2.47 |
| 34. | 2017. 11. 30. | 7.88% | 2.81% | 43.81 | 3.72 | 12.77 |
| 35. | 2017. 12. 31. | 3.68% | 0.98% | 5.83 | 0.01 | 0.25 |
| 36. | 2018. 1. 31. | 1.24% | 5.62% | 0.00 | 22.46 | -0.14 |
| 37. | 2018. 2. 28. | -11.06% | -3.89% | 152.00 | 22.79 | 58.86 |
| 38. | 2018. 3. 31. | 6.14% | -2.69% | 23.78 | 12.73 | -17.40 |
| 39. | 2018. 4. 30. | 16.04% | 0.27% | 218.45 | 0.37 | -8.98 |
| 40. | 2018. 5. 31. | 5.37% | 2.16% | 16.87 | 1.64 | 5.27 |
| 41. | 2018. 6. 30. | -3.59% | 0.48% | 23.55 | 0.16 | 1.92 |
| 42. | 2018. 7. 31. | 9.82% | 3.60% | 73.21 | 7.41 | 23.30 |
| 43. | 2018. 8. 31. | -3.27% | 3.03% | 20.54 | 4.61 | -9.73 |
| 44. | 2018. 9. 30. | -4.89% | 0.43% | 37.83 | 0.20 | 2.77 |
| 45. | 2018. 10. 31. | -8.78% | -6.94% | 100.95 | 61.14 | 78.57 |
| 46. | 2018. 11. 30. | -8.27% | 1.79% | 90.85 | 0.82 | -8.64 |
| 47. | 2018. 12. 31. | -7.88% | -9.18% | 83.64 | 101.14 | 91.97 |
| 48. | 2019. 1. 31. | 10.75% | 7.87% | 89.95 | 48.85 | 66.29 |
| 49. | 2019. 2. 28. | 1.83% | 2.97% | 0.32 | 4.38 | 1.19 |
| 50. | 2019. 3. 31. | -1.23% | 1.79% | 6.25 | 0.83 | -2.28 |
| 51. | 2019. 4. 30. | -0.95% | 3.93% | 4.89 | 9.32 | -6.75 |
| 52. | 2019. 5. 31. | -13.33% | -6.58% | 213.12 | 55.61 | 108.86 |
| 53. | 2019. 6. 30. | 15.77% | 6.89% | 210.33 | 36.17 | 87.22 |
| 54. | 2019. 7. 31. | 9.64% | 1.31% | 70.20 | 0.19 | 3.63 |
| 55. | 2019. 8. 31. | -2.95% | -1.81% | 17.80 | 7.23 | 11.34 |
| 56. | 2019. 9. 30. | 3.82% | 1.72% | 6.54 | 0.70 | 2.15 |
| 57. | 2019. 10. 31. | 14.08% | 2.04% | 164.29 | 1.36 | 14.92 |
| 58. | 2019. 11. 30. | -1.03% | 3.40% | 5.25 | 6.38 | -5.79 |
| 59. | 2019. 12. 31. | -2.89% | 2.86% | 17.22 | 3.92 | -8.22 |
| 합계 (Σ): | 2,598.43 | 688.77 | 755.71 | |||
모두 보기
분산PSX = Σ(RPSX,t–RPSX)2 ÷ (59 – 1)
= 2,598.43 ÷ (59 – 1)
= 44.80
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
공분산PSX, S&P 500 = Σ(RPSX,t–RPSX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 755.71 ÷ (59 – 1)
= 13.03
체계적인 위험 추정 (β)
| 분산PSX | 44.80 |
| 분산S&P 500 | 11.88 |
| 공분산PSX, S&P 500 | 13.03 |
| 상관 계수PSX, S&P 5001 | 0.56 |
| βPSX2 | 1.10 |
| αPSX3 | 0.30% |
계산
1 상관 계수PSX, S&P 500
= 공분산PSX, S&P 500 ÷ (표준 편차PSX × 표준 편차S&P 500)
= 13.03 ÷ (6.69% × 3.45%)
= 0.56
2 βPSX
= 공분산PSX, S&P 500 ÷ 분산S&P 500
= 13.03 ÷ 11.88
= 1.10
3 αPSX
= 평균의PSX – βPSX × 평균의S&P 500
= 1.26% – 1.10 × 0.88%
= 0.30%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Phillips 66 | βPSX | 1.10 |
| Phillips 66 보통주의 예상 수익률3 | E(RPSX) | 15.89% |
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(RPSX) = RF + βPSX [E(RM) – RF]
= 4.60% + 1.10 [14.89% – 4.60%]
= 15.89%