자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Apache보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Apache Corp., 월별 수익률
| Apache Corp. (APA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값APA,t1 | 피제수APA,t1 | RAPA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $119.36 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $124.62 | 4.41% | 1,327.22 | 3.20% | |
| 2. | 2011. 3. 31. | $130.92 | 5.06% | 1,325.83 | -0.10% | |
| 3. | 2011. 4. 30. | $133.37 | $0.15 | 1.99% | 1,363.61 | 2.85% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | $49.18 | 4.35% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $44.47 | -9.58% | 2,043.94 | -1.75% | |
| 평균의 (R): | -1.14% | 0.84% | ||||
| 표준 편차: | 9.27% | 3.40% | ||||
| Apache Corp. (APA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값APA,t1 | 피제수APA,t1 | RAPA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $119.36 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $124.62 | 4.41% | 1,327.22 | 3.20% | |
| 2. | 2011. 3. 31. | $130.92 | 5.06% | 1,325.83 | -0.10% | |
| 3. | 2011. 4. 30. | $133.37 | $0.15 | 1.99% | 1,363.61 | 2.85% |
| 4. | 2011. 5. 31. | $124.60 | -6.58% | 1,345.20 | -1.35% | |
| 5. | 2011. 6. 30. | $123.39 | -0.97% | 1,320.64 | -1.83% | |
| 6. | 2011. 7. 31. | $123.72 | $0.15 | 0.39% | 1,292.28 | -2.15% |
| 7. | 2011. 8. 31. | $103.07 | -16.69% | 1,218.89 | -5.68% | |
| 8. | 2011. 9. 30. | $80.24 | -22.15% | 1,131.42 | -7.18% | |
| 9. | 2011. 10. 31. | $99.63 | $0.15 | 24.35% | 1,253.30 | 10.77% |
| 10. | 2011. 11. 30. | $99.44 | -0.19% | 1,246.96 | -0.51% | |
| 11. | 2011. 12. 31. | $90.58 | -8.91% | 1,257.60 | 0.85% | |
| 12. | 2012. 1. 31. | $98.88 | $0.15 | 9.33% | 1,312.41 | 4.36% |
| 13. | 2012. 2. 29. | $107.93 | 9.15% | 1,365.68 | 4.06% | |
| 14. | 2012. 3. 31. | $100.44 | -6.94% | 1,408.47 | 3.13% | |
| 15. | 2012. 4. 30. | $95.94 | $0.17 | -4.31% | 1,397.91 | -0.75% |
| 16. | 2012. 5. 31. | $81.38 | -15.18% | 1,310.33 | -6.27% | |
| 17. | 2012. 6. 30. | $87.89 | 8.00% | 1,362.16 | 3.96% | |
| 18. | 2012. 7. 31. | $86.12 | $0.17 | -1.82% | 1,379.32 | 1.26% |
| 19. | 2012. 8. 31. | $85.75 | -0.43% | 1,406.58 | 1.98% | |
| 20. | 2012. 9. 30. | $86.47 | 0.84% | 1,440.67 | 2.42% | |
| 21. | 2012. 10. 31. | $82.72 | $0.17 | -4.14% | 1,412.16 | -1.98% |
| 22. | 2012. 11. 30. | $77.09 | -6.81% | 1,416.18 | 0.28% | |
| 23. | 2012. 12. 31. | $78.50 | 1.83% | 1,426.19 | 0.71% | |
| 24. | 2013. 1. 31. | $83.76 | $0.17 | 6.92% | 1,498.11 | 5.04% |
| 25. | 2013. 2. 28. | $74.27 | -11.33% | 1,514.68 | 1.11% | |
| 26. | 2013. 3. 31. | $77.16 | 3.89% | 1,569.19 | 3.60% | |
| 27. | 2013. 4. 30. | $73.88 | $0.20 | -3.99% | 1,597.57 | 1.81% |
| 28. | 2013. 5. 31. | $82.13 | 11.17% | 1,630.74 | 2.08% | |
| 29. | 2013. 6. 30. | $83.83 | 2.07% | 1,606.28 | -1.50% | |
| 30. | 2013. 7. 31. | $80.25 | $0.20 | -4.03% | 1,685.73 | 4.95% |
| 31. | 2013. 8. 31. | $85.68 | 6.77% | 1,632.97 | -3.13% | |
| 32. | 2013. 9. 30. | $85.14 | -0.63% | 1,681.55 | 2.97% | |
| 33. | 2013. 10. 31. | $88.80 | $0.20 | 4.53% | 1,756.54 | 4.46% |
| 34. | 2013. 11. 30. | $91.49 | 3.03% | 1,805.81 | 2.80% | |
| 35. | 2013. 12. 31. | $85.94 | -6.07% | 1,848.36 | 2.36% | |
| 36. | 2014. 1. 31. | $80.26 | $0.20 | -6.38% | 1,782.59 | -3.56% |
| 37. | 2014. 2. 28. | $79.29 | -1.21% | 1,859.45 | 4.31% | |
| 38. | 2014. 3. 31. | $82.95 | 4.62% | 1,872.34 | 0.69% | |
| 39. | 2014. 4. 30. | $86.80 | $0.25 | 4.94% | 1,883.95 | 0.62% |
| 40. | 2014. 5. 31. | $93.22 | 7.40% | 1,923.57 | 2.10% | |
| 41. | 2014. 6. 30. | $100.62 | 7.94% | 1,960.23 | 1.91% | |
| 42. | 2014. 7. 31. | $102.66 | $0.25 | 2.28% | 1,930.67 | -1.51% |
| 43. | 2014. 8. 31. | $101.83 | -0.81% | 2,003.37 | 3.77% | |
| 44. | 2014. 9. 30. | $93.87 | -7.82% | 1,972.29 | -1.55% | |
| 45. | 2014. 10. 31. | $77.20 | $0.25 | -17.49% | 2,018.05 | 2.32% |
| 46. | 2014. 11. 30. | $64.09 | -16.98% | 2,067.56 | 2.45% | |
| 47. | 2014. 12. 31. | $62.67 | -2.22% | 2,058.90 | -0.42% | |
| 48. | 2015. 1. 31. | $62.57 | $0.25 | 0.24% | 1,994.99 | -3.10% |
| 49. | 2015. 2. 28. | $65.84 | 5.23% | 2,104.50 | 5.49% | |
| 50. | 2015. 3. 31. | $60.33 | -8.37% | 2,067.89 | -1.74% | |
| 51. | 2015. 4. 30. | $68.40 | $0.25 | 13.79% | 2,085.51 | 0.85% |
| 52. | 2015. 5. 31. | $59.84 | -12.51% | 2,107.39 | 1.05% | |
| 53. | 2015. 6. 30. | $57.63 | -3.69% | 2,063.11 | -2.10% | |
| 54. | 2015. 7. 31. | $45.86 | $0.25 | -19.99% | 2,103.84 | 1.97% |
| 55. | 2015. 8. 31. | $45.24 | -1.35% | 1,972.18 | -6.26% | |
| 56. | 2015. 9. 30. | $39.16 | -13.44% | 1,920.03 | -2.64% | |
| 57. | 2015. 10. 31. | $47.13 | $0.25 | 20.99% | 2,079.36 | 8.30% |
| 58. | 2015. 11. 30. | $49.18 | 4.35% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $44.47 | -9.58% | 2,043.94 | -1.75% | |
| 평균의 (R): | -1.14% | 0.84% | ||||
| 표준 편차: | 9.27% | 3.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 APA의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Apache Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RAPA,t | RS&P 500,t | (RAPA,t–RAPA)2 | (RS&P 500,t–RS&P 500)2 | (RAPA,t–RAPA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 4.41% | 3.20% | 30.82 | 5.53 | 13.05 |
| 2. | 2011. 3. 31. | 5.06% | -0.10% | 38.44 | 0.90 | -5.89 |
| 3. | 2011. 4. 30. | 1.99% | 2.85% | 9.80 | 4.02 | 6.28 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | 4.35% | 0.05% | 30.18 | 0.63 | -4.36 |
| 59. | 2015. 12. 31. | -9.58% | -1.75% | 71.11 | 6.75 | 21.91 |
| 합계 (Σ): | 4,988.66 | 670.89 | 1,031.10 | |||
| t | 날짜 | RAPA,t | RS&P 500,t | (RAPA,t–RAPA)2 | (RS&P 500,t–RS&P 500)2 | (RAPA,t–RAPA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 4.41% | 3.20% | 30.82 | 5.53 | 13.05 |
| 2. | 2011. 3. 31. | 5.06% | -0.10% | 38.44 | 0.90 | -5.89 |
| 3. | 2011. 4. 30. | 1.99% | 2.85% | 9.80 | 4.02 | 6.28 |
| 4. | 2011. 5. 31. | -6.58% | -1.35% | 29.50 | 4.82 | 11.92 |
| 5. | 2011. 6. 30. | -0.97% | -1.83% | 0.03 | 7.13 | -0.46 |
| 6. | 2011. 7. 31. | 0.39% | -2.15% | 2.35 | 8.95 | -4.59 |
| 7. | 2011. 8. 31. | -16.69% | -5.68% | 241.70 | 42.56 | 101.42 |
| 8. | 2011. 9. 30. | -22.15% | -7.18% | 441.24 | 64.34 | 168.48 |
| 9. | 2011. 10. 31. | 24.35% | 10.77% | 650.06 | 98.56 | 253.12 |
| 10. | 2011. 11. 30. | -0.19% | -0.51% | 0.91 | 1.82 | -1.29 |
| 11. | 2011. 12. 31. | -8.91% | 0.85% | 60.30 | 0.00 | -0.07 |
| 12. | 2012. 1. 31. | 9.33% | 4.36% | 109.69 | 12.35 | 36.80 |
| 13. | 2012. 2. 29. | 9.15% | 4.06% | 106.03 | 10.33 | 33.10 |
| 14. | 2012. 3. 31. | -6.94% | 3.13% | 33.59 | 5.24 | -13.26 |
| 15. | 2012. 4. 30. | -4.31% | -0.75% | 10.03 | 2.54 | 5.05 |
| 16. | 2012. 5. 31. | -15.18% | -6.27% | 196.89 | 50.55 | 99.76 |
| 17. | 2012. 6. 30. | 8.00% | 3.96% | 83.61 | 9.68 | 28.44 |
| 18. | 2012. 7. 31. | -1.82% | 1.26% | 0.46 | 0.17 | -0.28 |
| 19. | 2012. 8. 31. | -0.43% | 1.98% | 0.51 | 1.28 | 0.81 |
| 20. | 2012. 9. 30. | 0.84% | 2.42% | 3.94 | 2.49 | 3.13 |
| 21. | 2012. 10. 31. | -4.14% | -1.98% | 8.97 | 7.97 | 8.46 |
| 22. | 2012. 11. 30. | -6.81% | 0.28% | 32.06 | 0.31 | 3.17 |
| 23. | 2012. 12. 31. | 1.83% | 0.71% | 8.84 | 0.02 | -0.41 |
| 24. | 2013. 1. 31. | 6.92% | 5.04% | 64.99 | 17.62 | 33.84 |
| 25. | 2013. 2. 28. | -11.33% | 1.11% | 103.75 | 0.07 | -2.66 |
| 26. | 2013. 3. 31. | 3.89% | 3.60% | 25.36 | 7.58 | 13.87 |
| 27. | 2013. 4. 30. | -3.99% | 1.81% | 8.11 | 0.93 | -2.74 |
| 28. | 2013. 5. 31. | 11.17% | 2.08% | 151.56 | 1.52 | 15.16 |
| 29. | 2013. 6. 30. | 2.07% | -1.50% | 10.33 | 5.50 | -7.54 |
| 30. | 2013. 7. 31. | -4.03% | 4.95% | 8.34 | 16.82 | -11.84 |
| 31. | 2013. 8. 31. | 6.77% | -3.13% | 62.58 | 15.80 | -31.44 |
| 32. | 2013. 9. 30. | -0.63% | 2.97% | 0.26 | 4.54 | 1.10 |
| 33. | 2013. 10. 31. | 4.53% | 4.46% | 32.24 | 13.07 | 20.53 |
| 34. | 2013. 11. 30. | 3.03% | 2.80% | 17.42 | 3.84 | 8.18 |
| 35. | 2013. 12. 31. | -6.07% | 2.36% | 24.22 | 2.28 | -7.44 |
| 36. | 2014. 1. 31. | -6.38% | -3.56% | 27.38 | 19.39 | 23.04 |
| 37. | 2014. 2. 28. | -1.21% | 4.31% | 0.00 | 12.02 | -0.22 |
| 38. | 2014. 3. 31. | 4.62% | 0.69% | 33.18 | 0.02 | -0.87 |
| 39. | 2014. 4. 30. | 4.94% | 0.62% | 37.05 | 0.05 | -1.37 |
| 40. | 2014. 5. 31. | 7.40% | 2.10% | 72.94 | 1.58 | 10.75 |
| 41. | 2014. 6. 30. | 7.94% | 1.91% | 82.49 | 1.13 | 9.64 |
| 42. | 2014. 7. 31. | 2.28% | -1.51% | 11.70 | 5.54 | -8.05 |
| 43. | 2014. 8. 31. | -0.81% | 3.77% | 0.11 | 8.53 | 0.98 |
| 44. | 2014. 9. 30. | -7.82% | -1.55% | 44.52 | 5.74 | 15.99 |
| 45. | 2014. 10. 31. | -17.49% | 2.32% | 267.25 | 2.18 | -24.12 |
| 46. | 2014. 11. 30. | -16.98% | 2.45% | 250.83 | 2.59 | -25.48 |
| 47. | 2014. 12. 31. | -2.22% | -0.42% | 1.15 | 1.60 | 1.35 |
| 48. | 2015. 1. 31. | 0.24% | -3.10% | 1.91 | 15.59 | -5.46 |
| 49. | 2015. 2. 28. | 5.23% | 5.49% | 40.58 | 21.57 | 29.59 |
| 50. | 2015. 3. 31. | -8.37% | -1.74% | 52.19 | 6.68 | 18.67 |
| 51. | 2015. 4. 30. | 13.79% | 0.85% | 223.06 | 0.00 | 0.11 |
| 52. | 2015. 5. 31. | -12.51% | 1.05% | 129.28 | 0.04 | -2.32 |
| 53. | 2015. 6. 30. | -3.69% | -2.10% | 6.50 | 8.68 | 7.51 |
| 54. | 2015. 7. 31. | -19.99% | 1.97% | 355.14 | 1.28 | -21.29 |
| 55. | 2015. 8. 31. | -1.35% | -6.26% | 0.04 | 50.45 | 1.47 |
| 56. | 2015. 9. 30. | -13.44% | -2.64% | 151.17 | 12.17 | 42.90 |
| 57. | 2015. 10. 31. | 20.99% | 8.30% | 489.97 | 55.56 | 164.99 |
| 58. | 2015. 11. 30. | 4.35% | 0.05% | 30.18 | 0.63 | -4.36 |
| 59. | 2015. 12. 31. | -9.58% | -1.75% | 71.11 | 6.75 | 21.91 |
| 합계 (Σ): | 4,988.66 | 670.89 | 1,031.10 | |||
모두 보기
분산APA = Σ(RAPA,t–RAPA)2 ÷ (59 – 1)
= 4,988.66 ÷ (59 – 1)
= 86.01
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 670.89 ÷ (59 – 1)
= 11.57
공분산APA, S&P 500 = Σ(RAPA,t–RAPA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,031.10 ÷ (59 – 1)
= 17.78
체계적인 위험 추정 (β)
| 분산APA | 86.01 |
| 분산S&P 500 | 11.57 |
| 공분산APA, S&P 500 | 17.78 |
| 상관 계수APA, S&P 5001 | 0.56 |
| βAPA2 | 1.54 |
| αAPA3 | -2.44% |
계산
1 상관 계수APA, S&P 500
= 공분산APA, S&P 500 ÷ (표준 편차APA × 표준 편차S&P 500)
= 17.78 ÷ (9.27% × 3.40%)
= 0.56
2 βAPA
= 공분산APA, S&P 500 ÷ 분산S&P 500
= 17.78 ÷ 11.57
= 1.54
3 αAPA
= 평균의APA – βAPA × 평균의S&P 500
= -1.14% – 1.54 × 0.84%
= -2.44%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Apache | βAPA | 1.54 |
| Apache 보통주에 대한 예상 수익률3 | E(RAPA) | 20.41% |
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(RAPA) = RF + βAPA [E(RM) – RF]
= 4.60% + 1.54 [14.89% – 4.60%]
= 20.41%