자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Anadarko보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Anadarko Petroleum Corp., 월별 수익률
| Anadarko Petroleum Corp. (APC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값APC,t1 | 피제수APC,t1 | RAPC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2012. 1. 31. | $80.72 | 1,312.41 | ||||
| 1. | 2012. 2. 29. | $84.12 | 4.21% | 1,365.68 | 4.06% | |
| 2. | 2012. 3. 31. | $78.34 | $0.09 | -6.76% | 1,408.47 | 3.13% |
| 3. | 2012. 4. 30. | $73.21 | -6.55% | 1,397.91 | -0.75% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2016. 11. 30. | $69.15 | 16.34% | 2,198.81 | 3.42% | |
| 59. | 2016. 12. 31. | $69.73 | $0.05 | 0.91% | 2,238.83 | 1.82% |
| 평균의 (R): | 0.22% | 0.95% | ||||
| 표준 편차: | 8.95% | 2.98% | ||||
| Anadarko Petroleum Corp. (APC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값APC,t1 | 피제수APC,t1 | RAPC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2012. 1. 31. | $80.72 | 1,312.41 | ||||
| 1. | 2012. 2. 29. | $84.12 | 4.21% | 1,365.68 | 4.06% | |
| 2. | 2012. 3. 31. | $78.34 | $0.09 | -6.76% | 1,408.47 | 3.13% |
| 3. | 2012. 4. 30. | $73.21 | -6.55% | 1,397.91 | -0.75% | |
| 4. | 2012. 5. 31. | $61.00 | -16.68% | 1,310.33 | -6.27% | |
| 5. | 2012. 6. 30. | $66.20 | $0.09 | 8.67% | 1,362.16 | 3.96% |
| 6. | 2012. 7. 31. | $69.44 | 4.89% | 1,379.32 | 1.26% | |
| 7. | 2012. 8. 31. | $69.27 | -0.24% | 1,406.58 | 1.98% | |
| 8. | 2012. 9. 30. | $69.92 | $0.09 | 1.07% | 1,440.67 | 2.42% |
| 9. | 2012. 10. 31. | $68.81 | -1.59% | 1,412.16 | -1.98% | |
| 10. | 2012. 11. 30. | $73.19 | 6.37% | 1,416.18 | 0.28% | |
| 11. | 2012. 12. 31. | $74.31 | $0.09 | 1.65% | 1,426.19 | 0.71% |
| 12. | 2013. 1. 31. | $80.02 | 7.68% | 1,498.11 | 5.04% | |
| 13. | 2013. 2. 28. | $79.58 | -0.55% | 1,514.68 | 1.11% | |
| 14. | 2013. 3. 31. | $87.45 | $0.09 | 10.00% | 1,569.19 | 3.60% |
| 15. | 2013. 4. 30. | $84.76 | -3.08% | 1,597.57 | 1.81% | |
| 16. | 2013. 5. 31. | $87.47 | 3.20% | 1,630.74 | 2.08% | |
| 17. | 2013. 6. 30. | $85.93 | $0.09 | -1.66% | 1,606.28 | -1.50% |
| 18. | 2013. 7. 31. | $88.52 | 3.01% | 1,685.73 | 4.95% | |
| 19. | 2013. 8. 31. | $91.42 | 3.28% | 1,632.97 | -3.13% | |
| 20. | 2013. 9. 30. | $92.99 | $0.18 | 1.91% | 1,681.55 | 2.97% |
| 21. | 2013. 10. 31. | $95.29 | 2.47% | 1,756.54 | 4.46% | |
| 22. | 2013. 11. 30. | $88.82 | -6.79% | 1,805.81 | 2.80% | |
| 23. | 2013. 12. 31. | $79.32 | $0.18 | -10.49% | 1,848.36 | 2.36% |
| 24. | 2014. 1. 31. | $80.69 | 1.73% | 1,782.59 | -3.56% | |
| 25. | 2014. 2. 28. | $84.16 | 4.30% | 1,859.45 | 4.31% | |
| 26. | 2014. 3. 31. | $84.76 | $0.18 | 0.93% | 1,872.34 | 0.69% |
| 27. | 2014. 4. 30. | $99.02 | 16.82% | 1,883.95 | 0.62% | |
| 28. | 2014. 5. 31. | $102.86 | 3.88% | 1,923.57 | 2.10% | |
| 29. | 2014. 6. 30. | $109.47 | $0.27 | 6.69% | 1,960.23 | 1.91% |
| 30. | 2014. 7. 31. | $106.85 | -2.39% | 1,930.67 | -1.51% | |
| 31. | 2014. 8. 31. | $112.69 | 5.47% | 2,003.37 | 3.77% | |
| 32. | 2014. 9. 30. | $101.44 | $0.27 | -9.74% | 1,972.29 | -1.55% |
| 33. | 2014. 10. 31. | $91.78 | -9.52% | 2,018.05 | 2.32% | |
| 34. | 2014. 11. 30. | $79.15 | -13.76% | 2,067.56 | 2.45% | |
| 35. | 2014. 12. 31. | $82.50 | $0.27 | 4.57% | 2,058.90 | -0.42% |
| 36. | 2015. 1. 31. | $81.75 | -0.91% | 1,994.99 | -3.10% | |
| 37. | 2015. 2. 28. | $84.23 | 3.03% | 2,104.50 | 5.49% | |
| 38. | 2015. 3. 31. | $82.81 | $0.27 | -1.37% | 2,067.89 | -1.74% |
| 39. | 2015. 4. 30. | $94.10 | 13.63% | 2,085.51 | 0.85% | |
| 40. | 2015. 5. 31. | $83.61 | -11.15% | 2,107.39 | 1.05% | |
| 41. | 2015. 6. 30. | $78.06 | $0.27 | -6.32% | 2,063.11 | -2.10% |
| 42. | 2015. 7. 31. | $74.35 | -4.75% | 2,103.84 | 1.97% | |
| 43. | 2015. 8. 31. | $71.58 | -3.73% | 1,972.18 | -6.26% | |
| 44. | 2015. 9. 30. | $60.39 | $0.27 | -15.26% | 1,920.03 | -2.64% |
| 45. | 2015. 10. 31. | $66.88 | 10.75% | 2,079.36 | 8.30% | |
| 46. | 2015. 11. 30. | $59.90 | -10.44% | 2,080.41 | 0.05% | |
| 47. | 2015. 12. 31. | $48.58 | $0.27 | -18.45% | 2,043.94 | -1.75% |
| 48. | 2016. 1. 31. | $39.09 | -19.53% | 1,940.24 | -5.07% | |
| 49. | 2016. 2. 29. | $37.95 | -2.92% | 1,932.23 | -0.41% | |
| 50. | 2016. 3. 31. | $46.57 | $0.05 | 22.85% | 2,059.74 | 6.60% |
| 51. | 2016. 4. 30. | $52.76 | 13.29% | 2,065.30 | 0.27% | |
| 52. | 2016. 5. 31. | $51.86 | -1.71% | 2,096.95 | 1.53% | |
| 53. | 2016. 6. 30. | $53.25 | $0.05 | 2.78% | 2,098.86 | 0.09% |
| 54. | 2016. 7. 31. | $54.53 | 2.40% | 2,173.60 | 3.56% | |
| 55. | 2016. 8. 31. | $53.47 | -1.94% | 2,170.95 | -0.12% | |
| 56. | 2016. 9. 30. | $63.36 | $0.05 | 18.59% | 2,168.27 | -0.12% |
| 57. | 2016. 10. 31. | $59.44 | -6.19% | 2,126.15 | -1.94% | |
| 58. | 2016. 11. 30. | $69.15 | 16.34% | 2,198.81 | 3.42% | |
| 59. | 2016. 12. 31. | $69.73 | $0.05 | 0.91% | 2,238.83 | 1.82% |
| 평균의 (R): | 0.22% | 0.95% | ||||
| 표준 편차: | 8.95% | 2.98% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 APC의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Anadarko Petroleum Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RAPC,t | RS&P 500,t | (RAPC,t–RAPC)2 | (RS&P 500,t–RS&P 500)2 | (RAPC,t–RAPC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2012. 2. 29. | 4.21% | 4.06% | 15.94 | 9.65 | 12.40 |
| 2. | 2012. 3. 31. | -6.76% | 3.13% | 48.77 | 4.75 | -15.23 |
| 3. | 2012. 4. 30. | -6.55% | -0.75% | 45.80 | 2.90 | 11.52 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2016. 11. 30. | 16.34% | 3.42% | 259.75 | 6.07 | 39.72 |
| 59. | 2016. 12. 31. | 0.91% | 1.82% | 0.48 | 0.75 | 0.60 |
| 합계 (Σ): | 4,648.43 | 514.91 | 761.51 | |||
| t | 날짜 | RAPC,t | RS&P 500,t | (RAPC,t–RAPC)2 | (RS&P 500,t–RS&P 500)2 | (RAPC,t–RAPC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2012. 2. 29. | 4.21% | 4.06% | 15.94 | 9.65 | 12.40 |
| 2. | 2012. 3. 31. | -6.76% | 3.13% | 48.77 | 4.75 | -15.23 |
| 3. | 2012. 4. 30. | -6.55% | -0.75% | 45.80 | 2.90 | 11.52 |
| 4. | 2012. 5. 31. | -16.68% | -6.27% | 285.51 | 52.10 | 121.96 |
| 5. | 2012. 6. 30. | 8.67% | 3.96% | 71.45 | 9.02 | 25.38 |
| 6. | 2012. 7. 31. | 4.89% | 1.26% | 21.86 | 0.09 | 1.44 |
| 7. | 2012. 8. 31. | -0.24% | 1.98% | 0.22 | 1.05 | -0.47 |
| 8. | 2012. 9. 30. | 1.07% | 2.42% | 0.72 | 2.16 | 1.25 |
| 9. | 2012. 10. 31. | -1.59% | -1.98% | 3.26 | 8.60 | 5.30 |
| 10. | 2012. 11. 30. | 6.37% | 0.28% | 37.78 | 0.45 | -4.11 |
| 11. | 2012. 12. 31. | 1.65% | 0.71% | 2.06 | 0.06 | -0.35 |
| 12. | 2013. 1. 31. | 7.68% | 5.04% | 55.73 | 16.73 | 30.53 |
| 13. | 2013. 2. 28. | -0.55% | 1.11% | 0.59 | 0.02 | -0.12 |
| 14. | 2013. 3. 31. | 10.00% | 3.60% | 95.72 | 7.00 | 25.89 |
| 15. | 2013. 4. 30. | -3.08% | 1.81% | 10.86 | 0.73 | -2.82 |
| 16. | 2013. 5. 31. | 3.20% | 2.08% | 8.87 | 1.26 | 3.35 |
| 17. | 2013. 6. 30. | -1.66% | -1.50% | 3.52 | 6.02 | 4.60 |
| 18. | 2013. 7. 31. | 3.01% | 4.95% | 7.81 | 15.95 | 11.16 |
| 19. | 2013. 8. 31. | 3.28% | -3.13% | 9.35 | 16.67 | -12.48 |
| 20. | 2013. 9. 30. | 1.91% | 2.97% | 2.87 | 4.09 | 3.43 |
| 21. | 2013. 10. 31. | 2.47% | 4.46% | 5.08 | 12.30 | 7.91 |
| 22. | 2013. 11. 30. | -6.79% | 2.80% | 49.12 | 3.43 | -12.98 |
| 23. | 2013. 12. 31. | -10.49% | 2.36% | 114.75 | 1.97 | -15.03 |
| 24. | 2014. 1. 31. | 1.73% | -3.56% | 2.27 | 20.35 | -6.80 |
| 25. | 2014. 2. 28. | 4.30% | 4.31% | 16.66 | 11.28 | 13.71 |
| 26. | 2014. 3. 31. | 0.93% | 0.69% | 0.50 | 0.07 | -0.18 |
| 27. | 2014. 4. 30. | 16.82% | 0.62% | 275.72 | 0.11 | -5.53 |
| 28. | 2014. 5. 31. | 3.88% | 2.10% | 13.39 | 1.32 | 4.21 |
| 29. | 2014. 6. 30. | 6.69% | 1.91% | 41.86 | 0.91 | 6.17 |
| 30. | 2014. 7. 31. | -2.39% | -1.51% | 6.82 | 6.06 | 6.43 |
| 31. | 2014. 8. 31. | 5.47% | 3.77% | 27.53 | 7.91 | 14.76 |
| 32. | 2014. 9. 30. | -9.74% | -1.55% | 99.25 | 6.27 | 24.95 |
| 33. | 2014. 10. 31. | -9.52% | 2.32% | 94.91 | 1.87 | -13.32 |
| 34. | 2014. 11. 30. | -13.76% | 2.45% | 195.45 | 2.25 | -20.98 |
| 35. | 2014. 12. 31. | 4.57% | -0.42% | 18.96 | 1.88 | -5.97 |
| 36. | 2015. 1. 31. | -0.91% | -3.10% | 1.27 | 16.46 | 4.58 |
| 37. | 2015. 2. 28. | 3.03% | 5.49% | 7.92 | 20.58 | 12.77 |
| 38. | 2015. 3. 31. | -1.37% | -1.74% | 2.51 | 7.25 | 4.27 |
| 39. | 2015. 4. 30. | 13.63% | 0.85% | 179.95 | 0.01 | -1.35 |
| 40. | 2015. 5. 31. | -11.15% | 1.05% | 129.20 | 0.01 | -1.09 |
| 41. | 2015. 6. 30. | -6.32% | -2.10% | 42.69 | 9.33 | 19.96 |
| 42. | 2015. 7. 31. | -4.75% | 1.97% | 24.72 | 1.04 | -5.08 |
| 43. | 2015. 8. 31. | -3.73% | -6.26% | 15.56 | 52.00 | 28.44 |
| 44. | 2015. 9. 30. | -15.26% | -2.64% | 239.47 | 12.94 | 55.66 |
| 45. | 2015. 10. 31. | 10.75% | 8.30% | 110.83 | 53.96 | 77.33 |
| 46. | 2015. 11. 30. | -10.44% | 0.05% | 113.54 | 0.81 | 9.61 |
| 47. | 2015. 12. 31. | -18.45% | -1.75% | 348.44 | 7.32 | 50.51 |
| 48. | 2016. 1. 31. | -19.53% | -5.07% | 390.22 | 36.32 | 119.04 |
| 49. | 2016. 2. 29. | -2.92% | -0.41% | 9.83 | 1.87 | 4.28 |
| 50. | 2016. 3. 31. | 22.85% | 6.60% | 511.97 | 31.88 | 127.76 |
| 51. | 2016. 4. 30. | 13.29% | 0.27% | 170.90 | 0.47 | -8.93 |
| 52. | 2016. 5. 31. | -1.71% | 1.53% | 3.71 | 0.34 | -1.12 |
| 53. | 2016. 6. 30. | 2.78% | 0.09% | 6.54 | 0.74 | -2.20 |
| 54. | 2016. 7. 31. | 2.40% | 3.56% | 4.77 | 6.80 | 5.70 |
| 55. | 2016. 8. 31. | -1.94% | -0.12% | 4.68 | 1.16 | 2.32 |
| 56. | 2016. 9. 30. | 18.59% | -0.12% | 337.48 | 1.16 | -19.77 |
| 57. | 2016. 10. 31. | -6.19% | -1.94% | 41.04 | 8.38 | 18.55 |
| 58. | 2016. 11. 30. | 16.34% | 3.42% | 259.75 | 6.07 | 39.72 |
| 59. | 2016. 12. 31. | 0.91% | 1.82% | 0.48 | 0.75 | 0.60 |
| 합계 (Σ): | 4,648.43 | 514.91 | 761.51 | |||
모두 보기
분산APC = Σ(RAPC,t–RAPC)2 ÷ (59 – 1)
= 4,648.43 ÷ (59 – 1)
= 80.15
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 514.91 ÷ (59 – 1)
= 8.88
공분산APC, S&P 500 = Σ(RAPC,t–RAPC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 761.51 ÷ (59 – 1)
= 13.13
체계적인 위험 추정 (β)
| 분산APC | 80.15 |
| 분산S&P 500 | 8.88 |
| 공분산APC, S&P 500 | 13.13 |
| 상관 계수APC, S&P 5001 | 0.49 |
| βAPC2 | 1.48 |
| αAPC3 | -1.19% |
계산
1 상관 계수APC, S&P 500
= 공분산APC, S&P 500 ÷ (표준 편차APC × 표준 편차S&P 500)
= 13.13 ÷ (8.95% × 2.98%)
= 0.49
2 βAPC
= 공분산APC, S&P 500 ÷ 분산S&P 500
= 13.13 ÷ 8.88
= 1.48
3 αAPC
= 평균의APC – βAPC × 평균의S&P 500
= 0.22% – 1.48 × 0.95%
= -1.19%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Anadarko | βAPC | 1.48 |
| Anadarko 보통주의 예상 수익률3 | E(RAPC) | 18.15% |
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(RAPC) = RF + βAPC [E(RM) – RF]
= 4.67% + 1.48 [13.79% – 4.67%]
= 18.15%