자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Allergan보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Allergan Inc., 월별 수익률
| Allergan Inc. (AGN.) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AGN.,t1 | 피제수AGN.,t1 | RAGN.,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2010. 1. 31. | $57.50 | 1,073.87 | ||||
| 1. | 2010. 2. 28. | $58.43 | $0.05 | 1.70% | 1,104.49 | 2.85% |
| 2. | 2010. 3. 31. | $65.32 | 11.79% | 1,169.43 | 5.88% | |
| 3. | 2010. 4. 30. | $63.69 | -2.50% | 1,186.69 | 1.48% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2014. 11. 30. | $213.89 | $0.05 | 12.56% | 2,067.56 | 2.45% |
| 59. | 2014. 12. 31. | $212.59 | -0.61% | 2,058.90 | -0.42% | |
| 평균의 (R): | 2.51% | 1.18% | ||||
| 표준 편차: | 7.35% | 3.73% | ||||
| Allergan Inc. (AGN.) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AGN.,t1 | 피제수AGN.,t1 | RAGN.,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2010. 1. 31. | $57.50 | 1,073.87 | ||||
| 1. | 2010. 2. 28. | $58.43 | $0.05 | 1.70% | 1,104.49 | 2.85% |
| 2. | 2010. 3. 31. | $65.32 | 11.79% | 1,169.43 | 5.88% | |
| 3. | 2010. 4. 30. | $63.69 | -2.50% | 1,186.69 | 1.48% | |
| 4. | 2010. 5. 31. | $60.19 | $0.05 | -5.42% | 1,089.41 | -8.20% |
| 5. | 2010. 6. 30. | $58.26 | -3.21% | 1,030.71 | -5.39% | |
| 6. | 2010. 7. 31. | $61.06 | 4.81% | 1,101.60 | 6.88% | |
| 7. | 2010. 8. 31. | $61.42 | $0.05 | 0.67% | 1,049.33 | -4.74% |
| 8. | 2010. 9. 30. | $66.53 | 8.32% | 1,141.20 | 8.76% | |
| 9. | 2010. 10. 31. | $72.41 | 8.84% | 1,183.26 | 3.69% | |
| 10. | 2010. 11. 30. | $66.27 | $0.05 | -8.41% | 1,180.55 | -0.23% |
| 11. | 2010. 12. 31. | $68.67 | 3.62% | 1,257.64 | 6.53% | |
| 12. | 2011. 1. 31. | $70.61 | 2.83% | 1,286.12 | 2.26% | |
| 13. | 2011. 2. 28. | $74.17 | $0.05 | 5.11% | 1,327.22 | 3.20% |
| 14. | 2011. 3. 31. | $71.02 | -4.25% | 1,325.83 | -0.10% | |
| 15. | 2011. 4. 30. | $79.56 | 12.02% | 1,363.61 | 2.85% | |
| 16. | 2011. 5. 31. | $82.73 | $0.05 | 4.05% | 1,345.20 | -1.35% |
| 17. | 2011. 6. 30. | $83.25 | 0.63% | 1,320.64 | -1.83% | |
| 18. | 2011. 7. 31. | $81.31 | -2.33% | 1,292.28 | -2.15% | |
| 19. | 2011. 8. 31. | $81.81 | $0.05 | 0.68% | 1,218.89 | -5.68% |
| 20. | 2011. 9. 30. | $82.38 | 0.70% | 1,131.42 | -7.18% | |
| 21. | 2011. 10. 31. | $84.12 | 2.11% | 1,253.30 | 10.77% | |
| 22. | 2011. 11. 30. | $83.72 | $0.05 | -0.42% | 1,246.96 | -0.51% |
| 23. | 2011. 12. 31. | $87.74 | 4.80% | 1,257.60 | 0.85% | |
| 24. | 2012. 1. 31. | $87.91 | 0.19% | 1,312.41 | 4.36% | |
| 25. | 2012. 2. 29. | $89.59 | $0.05 | 1.97% | 1,365.68 | 4.06% |
| 26. | 2012. 3. 31. | $95.43 | 6.52% | 1,408.47 | 3.13% | |
| 27. | 2012. 4. 30. | $96.00 | 0.60% | 1,397.91 | -0.75% | |
| 28. | 2012. 5. 31. | $90.25 | $0.05 | -5.94% | 1,310.33 | -6.27% |
| 29. | 2012. 6. 30. | $92.57 | 2.57% | 1,362.16 | 3.96% | |
| 30. | 2012. 7. 31. | $82.07 | -11.34% | 1,379.32 | 1.26% | |
| 31. | 2012. 8. 31. | $86.13 | $0.05 | 5.01% | 1,406.58 | 1.98% |
| 32. | 2012. 9. 30. | $91.58 | 6.33% | 1,440.67 | 2.42% | |
| 33. | 2012. 10. 31. | $89.92 | -1.81% | 1,412.16 | -1.98% | |
| 34. | 2012. 11. 30. | $92.75 | $0.05 | 3.20% | 1,416.18 | 0.28% |
| 35. | 2012. 12. 31. | $91.73 | -1.10% | 1,426.19 | 0.71% | |
| 36. | 2013. 1. 31. | $105.01 | 14.48% | 1,498.11 | 5.04% | |
| 37. | 2013. 2. 28. | $108.42 | $0.05 | 3.29% | 1,514.68 | 1.11% |
| 38. | 2013. 3. 31. | $111.63 | 2.96% | 1,569.19 | 3.60% | |
| 39. | 2013. 4. 30. | $113.55 | 1.72% | 1,597.57 | 1.81% | |
| 40. | 2013. 5. 31. | $99.49 | $0.05 | -12.34% | 1,630.74 | 2.08% |
| 41. | 2013. 6. 30. | $84.24 | -15.33% | 1,606.28 | -1.50% | |
| 42. | 2013. 7. 31. | $91.12 | 8.17% | 1,685.73 | 4.95% | |
| 43. | 2013. 8. 31. | $88.38 | $0.05 | -2.95% | 1,632.97 | -3.13% |
| 44. | 2013. 9. 30. | $90.45 | 2.34% | 1,681.55 | 2.97% | |
| 45. | 2013. 10. 31. | $90.61 | 0.18% | 1,756.54 | 4.46% | |
| 46. | 2013. 11. 30. | $97.05 | $0.05 | 7.16% | 1,805.81 | 2.80% |
| 47. | 2013. 12. 31. | $111.08 | 14.46% | 1,848.36 | 2.36% | |
| 48. | 2014. 1. 31. | $114.60 | 3.17% | 1,782.59 | -3.56% | |
| 49. | 2014. 2. 28. | $127.00 | $0.05 | 10.86% | 1,859.45 | 4.31% |
| 50. | 2014. 3. 31. | $124.10 | -2.28% | 1,872.34 | 0.69% | |
| 51. | 2014. 4. 30. | $165.84 | 33.63% | 1,883.95 | 0.62% | |
| 52. | 2014. 5. 31. | $167.46 | $0.05 | 1.01% | 1,923.57 | 2.10% |
| 53. | 2014. 6. 30. | $169.22 | 1.05% | 1,960.23 | 1.91% | |
| 54. | 2014. 7. 31. | $165.86 | -1.99% | 1,930.67 | -1.51% | |
| 55. | 2014. 8. 31. | $163.68 | $0.05 | -1.28% | 2,003.37 | 3.77% |
| 56. | 2014. 9. 30. | $178.19 | 8.86% | 1,972.29 | -1.55% | |
| 57. | 2014. 10. 31. | $190.06 | 6.66% | 2,018.05 | 2.32% | |
| 58. | 2014. 11. 30. | $213.89 | $0.05 | 12.56% | 2,067.56 | 2.45% |
| 59. | 2014. 12. 31. | $212.59 | -0.61% | 2,058.90 | -0.42% | |
| 평균의 (R): | 2.51% | 1.18% | ||||
| 표준 편차: | 7.35% | 3.73% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 AGN의 보통주 수익률. 기간 t.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Allergan Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RAGN.,t | RS&P 500,t | (RAGN.,t–RAGN.)2 | (RS&P 500,t–RS&P 500)2 | (RAGN.,t–RAGN.)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2010. 2. 28. | 1.70% | 2.85% | 0.65 | 2.80 | -1.35 |
| 2. | 2010. 3. 31. | 11.79% | 5.88% | 86.14 | 22.11 | 43.64 |
| 3. | 2010. 4. 30. | -2.50% | 1.48% | 25.06 | 0.09 | -1.49 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2014. 11. 30. | 12.56% | 2.45% | 101.07 | 1.63 | 12.82 |
| 59. | 2014. 12. 31. | -0.61% | -0.42% | 9.73 | 2.55 | 4.98 |
| 합계 (Σ): | 3,129.33 | 809.11 | 572.71 | |||
| t | 날짜 | RAGN.,t | RS&P 500,t | (RAGN.,t–RAGN.)2 | (RS&P 500,t–RS&P 500)2 | (RAGN.,t–RAGN.)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2010. 2. 28. | 1.70% | 2.85% | 0.65 | 2.80 | -1.35 |
| 2. | 2010. 3. 31. | 11.79% | 5.88% | 86.14 | 22.11 | 43.64 |
| 3. | 2010. 4. 30. | -2.50% | 1.48% | 25.06 | 0.09 | -1.49 |
| 4. | 2010. 5. 31. | -5.42% | -8.20% | 62.85 | 87.90 | 74.33 |
| 5. | 2010. 6. 30. | -3.21% | -5.39% | 32.69 | 43.11 | 37.54 |
| 6. | 2010. 7. 31. | 4.81% | 6.88% | 5.27 | 32.49 | 13.08 |
| 7. | 2010. 8. 31. | 0.67% | -4.74% | 3.38 | 35.08 | 10.89 |
| 8. | 2010. 9. 30. | 8.32% | 8.76% | 33.74 | 57.42 | 44.02 |
| 9. | 2010. 10. 31. | 8.84% | 3.69% | 40.03 | 6.29 | 15.87 |
| 10. | 2010. 11. 30. | -8.41% | -0.23% | 119.28 | 1.98 | 15.36 |
| 11. | 2010. 12. 31. | 3.62% | 6.53% | 1.23 | 28.65 | 5.94 |
| 12. | 2011. 1. 31. | 2.83% | 2.26% | 0.10 | 1.18 | 0.34 |
| 13. | 2011. 2. 28. | 5.11% | 3.20% | 6.77 | 4.07 | 5.25 |
| 14. | 2011. 3. 31. | -4.25% | -0.10% | 45.67 | 1.64 | 8.67 |
| 15. | 2011. 4. 30. | 12.02% | 2.85% | 90.51 | 2.79 | 15.91 |
| 16. | 2011. 5. 31. | 4.05% | -1.35% | 2.36 | 6.39 | -3.88 |
| 17. | 2011. 6. 30. | 0.63% | -1.83% | 3.54 | 9.02 | 5.65 |
| 18. | 2011. 7. 31. | -2.33% | -2.15% | 23.44 | 11.06 | 16.10 |
| 19. | 2011. 8. 31. | 0.68% | -5.68% | 3.37 | 47.02 | 12.58 |
| 20. | 2011. 9. 30. | 0.70% | -7.18% | 3.29 | 69.79 | 15.16 |
| 21. | 2011. 10. 31. | 2.11% | 10.77% | 0.16 | 92.06 | -3.83 |
| 22. | 2011. 11. 30. | -0.42% | -0.51% | 8.57 | 2.83 | 4.93 |
| 23. | 2011. 12. 31. | 4.80% | 0.85% | 5.25 | 0.11 | -0.74 |
| 24. | 2012. 1. 31. | 0.19% | 4.36% | 5.37 | 10.12 | -7.37 |
| 25. | 2012. 2. 29. | 1.97% | 4.06% | 0.29 | 8.30 | -1.56 |
| 26. | 2012. 3. 31. | 6.52% | 3.13% | 16.06 | 3.82 | 7.84 |
| 27. | 2012. 4. 30. | 0.60% | -0.75% | 3.66 | 3.72 | 3.69 |
| 28. | 2012. 5. 31. | -5.94% | -6.27% | 71.38 | 55.40 | 62.88 |
| 29. | 2012. 6. 30. | 2.57% | 3.96% | 0.00 | 7.72 | 0.17 |
| 30. | 2012. 7. 31. | -11.34% | 1.26% | 191.92 | 0.01 | -1.14 |
| 31. | 2012. 8. 31. | 5.01% | 1.98% | 6.24 | 0.64 | 1.99 |
| 32. | 2012. 9. 30. | 6.33% | 2.42% | 14.57 | 1.55 | 4.76 |
| 33. | 2012. 10. 31. | -1.81% | -1.98% | 18.69 | 9.96 | 13.65 |
| 34. | 2012. 11. 30. | 3.20% | 0.28% | 0.48 | 0.80 | -0.62 |
| 35. | 2012. 12. 31. | -1.10% | 0.71% | 13.04 | 0.22 | 1.70 |
| 36. | 2013. 1. 31. | 14.48% | 5.04% | 143.19 | 14.94 | 46.25 |
| 37. | 2013. 2. 28. | 3.29% | 1.11% | 0.61 | 0.01 | -0.06 |
| 38. | 2013. 3. 31. | 2.96% | 3.60% | 0.20 | 5.86 | 1.09 |
| 39. | 2013. 4. 30. | 1.72% | 1.81% | 0.63 | 0.40 | -0.50 |
| 40. | 2013. 5. 31. | -12.34% | 2.08% | 220.50 | 0.81 | -13.34 |
| 41. | 2013. 6. 30. | -15.33% | -1.50% | 318.23 | 7.17 | 47.77 |
| 42. | 2013. 7. 31. | 8.17% | 4.95% | 31.99 | 14.20 | 21.32 |
| 43. | 2013. 8. 31. | -2.95% | -3.13% | 29.85 | 18.55 | 23.53 |
| 44. | 2013. 9. 30. | 2.34% | 2.97% | 0.03 | 3.23 | -0.30 |
| 45. | 2013. 10. 31. | 0.18% | 4.46% | 5.45 | 10.77 | -7.66 |
| 46. | 2013. 11. 30. | 7.16% | 2.80% | 21.64 | 2.65 | 7.57 |
| 47. | 2013. 12. 31. | 14.46% | 2.36% | 142.70 | 1.39 | 14.08 |
| 48. | 2014. 1. 31. | 3.17% | -3.56% | 0.43 | 22.43 | -3.12 |
| 49. | 2014. 2. 28. | 10.86% | 4.31% | 69.77 | 9.82 | 26.18 |
| 50. | 2014. 3. 31. | -2.28% | 0.69% | 22.99 | 0.23 | 2.32 |
| 51. | 2014. 4. 30. | 33.63% | 0.62% | 968.66 | 0.31 | -17.36 |
| 52. | 2014. 5. 31. | 1.01% | 2.10% | 2.26 | 0.86 | -1.39 |
| 53. | 2014. 6. 30. | 1.05% | 1.91% | 2.13 | 0.53 | -1.06 |
| 54. | 2014. 7. 31. | -1.99% | -1.51% | 20.22 | 7.21 | 12.08 |
| 55. | 2014. 8. 31. | -1.28% | 3.77% | 14.40 | 6.70 | -9.82 |
| 56. | 2014. 9. 30. | 8.86% | -1.55% | 40.37 | 7.45 | -17.34 |
| 57. | 2014. 10. 31. | 6.66% | 2.32% | 17.23 | 1.31 | 4.74 |
| 58. | 2014. 11. 30. | 12.56% | 2.45% | 101.07 | 1.63 | 12.82 |
| 59. | 2014. 12. 31. | -0.61% | -0.42% | 9.73 | 2.55 | 4.98 |
| 합계 (Σ): | 3,129.33 | 809.11 | 572.71 | |||
모두 보기
분산AGN. = Σ(RAGN.,t–RAGN.)2 ÷ (59 – 1)
= 3,129.33 ÷ (59 – 1)
= 53.95
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 809.11 ÷ (59 – 1)
= 13.95
공분산AGN., S&P 500 = Σ(RAGN.,t–RAGN.)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 572.71 ÷ (59 – 1)
= 9.87
체계적인 위험 추정 (β)
| 분산AGN. | 53.95 |
| 분산S&P 500 | 13.95 |
| 공분산AGN., S&P 500 | 9.87 |
| 상관 계수AGN., S&P 5001 | 0.36 |
| βAGN.2 | 0.71 |
| αAGN.3 | 1.68% |
계산
1 상관 계수AGN., S&P 500
= 공분산AGN., S&P 500 ÷ (표준 편차AGN. × 표준 편차S&P 500)
= 9.87 ÷ (7.35% × 3.73%)
= 0.36
2 βAGN.
= 공분산AGN., S&P 500 ÷ 분산S&P 500
= 9.87 ÷ 13.95
= 0.71
3 αAGN.
= 평균의AGN. – βAGN. × 평균의S&P 500
= 2.51% – 0.71 × 1.18%
= 1.68%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 5.07% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.86% |
| 보통주의 체계적 위험Allergan | βAGN. | 0.71 |
| Allergan 보통주에 대한 기대 수익률3 | E(RAGN.) | 12.00% |
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(RAGN.) = RF + βAGN. [E(RM) – RF]
= 5.07% + 0.71 [14.86% – 5.07%]
= 12.00%