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 PLC, 월별 수익률
| Allergan PLC (AGN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AGN,t1 | 피제수AGN,t1 | RAGN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $266.54 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $291.36 | 9.31% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $297.62 | 2.15% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $282.86 | -4.96% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | $184.94 | $0.74 | 5.43% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $191.17 | 3.37% | 3,230.78 | 2.86% | |
| 평균의 (R): | -0.03% | 0.88% | ||||
| 표준 편차: | 9.66% | 3.45% | ||||
| Allergan PLC (AGN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AGN,t1 | 피제수AGN,t1 | RAGN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $266.54 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $291.36 | 9.31% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $297.62 | 2.15% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $282.86 | -4.96% | 2,085.51 | 0.85% | |
| 4. | 2015. 5. 31. | $306.81 | 8.47% | 2,107.39 | 1.05% | |
| 5. | 2015. 6. 30. | $303.46 | -1.09% | 2,063.11 | -2.10% | |
| 6. | 2015. 7. 31. | $331.15 | 9.12% | 2,103.84 | 1.97% | |
| 7. | 2015. 8. 31. | $303.74 | -8.28% | 1,972.18 | -6.26% | |
| 8. | 2015. 9. 30. | $271.81 | -10.51% | 1,920.03 | -2.64% | |
| 9. | 2015. 10. 31. | $308.47 | 13.49% | 2,079.36 | 8.30% | |
| 10. | 2015. 11. 30. | $313.89 | 1.76% | 2,080.41 | 0.05% | |
| 11. | 2015. 12. 31. | $312.50 | -0.44% | 2,043.94 | -1.75% | |
| 12. | 2016. 1. 31. | $284.43 | -8.98% | 1,940.24 | -5.07% | |
| 13. | 2016. 2. 29. | $290.11 | 2.00% | 1,932.23 | -0.41% | |
| 14. | 2016. 3. 31. | $268.03 | -7.61% | 2,059.74 | 6.60% | |
| 15. | 2016. 4. 30. | $216.56 | -19.20% | 2,065.30 | 0.27% | |
| 16. | 2016. 5. 31. | $235.75 | 8.86% | 2,096.95 | 1.53% | |
| 17. | 2016. 6. 30. | $231.09 | -1.98% | 2,098.86 | 0.09% | |
| 18. | 2016. 7. 31. | $252.95 | 9.46% | 2,173.60 | 3.56% | |
| 19. | 2016. 8. 31. | $234.54 | -7.28% | 2,170.95 | -0.12% | |
| 20. | 2016. 9. 30. | $230.31 | -1.80% | 2,168.27 | -0.12% | |
| 21. | 2016. 10. 31. | $208.94 | -9.28% | 2,126.15 | -1.94% | |
| 22. | 2016. 11. 30. | $194.30 | -7.01% | 2,198.81 | 3.42% | |
| 23. | 2016. 12. 31. | $210.01 | 8.09% | 2,238.83 | 1.82% | |
| 24. | 2017. 1. 31. | $218.89 | 4.23% | 2,278.87 | 1.79% | |
| 25. | 2017. 2. 28. | $244.82 | $0.70 | 12.17% | 2,363.64 | 3.72% |
| 26. | 2017. 3. 31. | $238.92 | -2.41% | 2,362.72 | -0.04% | |
| 27. | 2017. 4. 30. | $243.86 | 2.07% | 2,384.20 | 0.91% | |
| 28. | 2017. 5. 31. | $223.75 | $0.70 | -7.96% | 2,411.80 | 1.16% |
| 29. | 2017. 6. 30. | $243.09 | 8.64% | 2,423.41 | 0.48% | |
| 30. | 2017. 7. 31. | $252.33 | 3.80% | 2,470.30 | 1.93% | |
| 31. | 2017. 8. 31. | $229.48 | $0.70 | -8.78% | 2,471.65 | 0.05% |
| 32. | 2017. 9. 30. | $204.95 | -10.69% | 2,519.36 | 1.93% | |
| 33. | 2017. 10. 31. | $177.23 | -13.53% | 2,575.26 | 2.22% | |
| 34. | 2017. 11. 30. | $173.83 | $0.70 | -1.52% | 2,647.58 | 2.81% |
| 35. | 2017. 12. 31. | $163.58 | -5.90% | 2,673.61 | 0.98% | |
| 36. | 2018. 1. 31. | $180.26 | 10.20% | 2,823.81 | 5.62% | |
| 37. | 2018. 2. 28. | $154.22 | $0.72 | -14.05% | 2,713.83 | -3.89% |
| 38. | 2018. 3. 31. | $168.29 | 9.12% | 2,640.87 | -2.69% | |
| 39. | 2018. 4. 30. | $153.65 | -8.70% | 2,648.05 | 0.27% | |
| 40. | 2018. 5. 31. | $150.80 | $0.72 | -1.39% | 2,705.27 | 2.16% |
| 41. | 2018. 6. 30. | $166.72 | 10.56% | 2,718.37 | 0.48% | |
| 42. | 2018. 7. 31. | $184.09 | 10.42% | 2,816.29 | 3.60% | |
| 43. | 2018. 8. 31. | $191.71 | $0.72 | 4.53% | 2,901.52 | 3.03% |
| 44. | 2018. 9. 30. | $190.48 | -0.64% | 2,913.98 | 0.43% | |
| 45. | 2018. 10. 31. | $158.01 | -17.05% | 2,711.74 | -6.94% | |
| 46. | 2018. 11. 30. | $156.60 | $0.72 | -0.44% | 2,760.17 | 1.79% |
| 47. | 2018. 12. 31. | $133.66 | -14.65% | 2,506.85 | -9.18% | |
| 48. | 2019. 1. 31. | $143.98 | 7.72% | 2,704.10 | 7.87% | |
| 49. | 2019. 2. 28. | $137.71 | $0.74 | -3.84% | 2,784.49 | 2.97% |
| 50. | 2019. 3. 31. | $146.41 | 6.32% | 2,834.40 | 1.79% | |
| 51. | 2019. 4. 30. | $147.00 | 0.40% | 2,945.83 | 3.93% | |
| 52. | 2019. 5. 31. | $121.91 | $0.74 | -16.56% | 2,752.06 | -6.58% |
| 53. | 2019. 6. 30. | $167.43 | 37.34% | 2,941.76 | 6.89% | |
| 54. | 2019. 7. 31. | $160.50 | -4.14% | 2,980.38 | 1.31% | |
| 55. | 2019. 8. 31. | $159.72 | $0.74 | -0.02% | 2,926.46 | -1.81% |
| 56. | 2019. 9. 30. | $168.29 | 5.37% | 2,976.74 | 1.72% | |
| 57. | 2019. 10. 31. | $176.11 | 4.65% | 3,037.56 | 2.04% | |
| 58. | 2019. 11. 30. | $184.94 | $0.74 | 5.43% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $191.17 | 3.37% | 3,230.78 | 2.86% | |
| 평균의 (R): | -0.03% | 0.88% | ||||
| 표준 편차: | 9.66% | 3.45% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 AGN의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Allergan PLC, 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. | 2015. 2. 28. | 9.31% | 5.49% | 87.23 | 21.25 | 43.06 |
| 2. | 2015. 3. 31. | 2.15% | -1.74% | 4.74 | 6.86 | -5.70 |
| 3. | 2015. 4. 30. | -4.96% | 0.85% | 24.32 | 0.00 | 0.13 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | 5.43% | 3.40% | 29.83 | 6.38 | 13.80 |
| 59. | 2019. 12. 31. | 3.37% | 2.86% | 11.54 | 3.92 | 6.72 |
| 합계 (Σ): | 5,415.95 | 688.77 | 1,168.59 | |||
| 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. | 2015. 2. 28. | 9.31% | 5.49% | 87.23 | 21.25 | 43.06 |
| 2. | 2015. 3. 31. | 2.15% | -1.74% | 4.74 | 6.86 | -5.70 |
| 3. | 2015. 4. 30. | -4.96% | 0.85% | 24.32 | 0.00 | 0.13 |
| 4. | 2015. 5. 31. | 8.47% | 1.05% | 72.17 | 0.03 | 1.44 |
| 5. | 2015. 6. 30. | -1.09% | -2.10% | 1.13 | 8.88 | 3.17 |
| 6. | 2015. 7. 31. | 9.12% | 1.97% | 83.77 | 1.20 | 10.02 |
| 7. | 2015. 8. 31. | -8.28% | -6.26% | 68.05 | 50.94 | 58.88 |
| 8. | 2015. 9. 30. | -10.51% | -2.64% | 109.92 | 12.41 | 36.94 |
| 9. | 2015. 10. 31. | 13.49% | 8.30% | 182.67 | 55.04 | 100.27 |
| 10. | 2015. 11. 30. | 1.76% | 0.05% | 3.19 | 0.69 | -1.48 |
| 11. | 2015. 12. 31. | -0.44% | -1.75% | 0.17 | 6.93 | 1.09 |
| 12. | 2016. 1. 31. | -8.98% | -5.07% | 80.18 | 35.43 | 53.30 |
| 13. | 2016. 2. 29. | 2.00% | -0.41% | 4.10 | 1.67 | -2.62 |
| 14. | 2016. 3. 31. | -7.61% | 6.60% | 57.50 | 32.72 | -43.37 |
| 15. | 2016. 4. 30. | -19.20% | 0.27% | 367.68 | 0.37 | 11.68 |
| 16. | 2016. 5. 31. | 8.86% | 1.53% | 79.02 | 0.43 | 5.81 |
| 17. | 2016. 6. 30. | -1.98% | 0.09% | 3.80 | 0.62 | 1.54 |
| 18. | 2016. 7. 31. | 9.46% | 3.56% | 90.01 | 7.19 | 25.44 |
| 19. | 2016. 8. 31. | -7.28% | -0.12% | 52.56 | 1.00 | 7.26 |
| 20. | 2016. 9. 30. | -1.80% | -0.12% | 3.15 | 1.01 | 1.78 |
| 21. | 2016. 10. 31. | -9.28% | -1.94% | 85.58 | 7.96 | 26.10 |
| 22. | 2016. 11. 30. | -7.01% | 3.42% | 48.70 | 6.44 | -17.71 |
| 23. | 2016. 12. 31. | 8.09% | 1.82% | 65.83 | 0.89 | 7.63 |
| 24. | 2017. 1. 31. | 4.23% | 1.79% | 18.12 | 0.83 | 3.87 |
| 25. | 2017. 2. 28. | 12.17% | 3.72% | 148.69 | 8.07 | 34.64 |
| 26. | 2017. 3. 31. | -2.41% | -0.04% | 5.67 | 0.84 | 2.19 |
| 27. | 2017. 4. 30. | 2.07% | 0.91% | 4.39 | 0.00 | 0.06 |
| 28. | 2017. 5. 31. | -7.96% | 1.16% | 62.91 | 0.08 | -2.21 |
| 29. | 2017. 6. 30. | 8.64% | 0.48% | 75.20 | 0.16 | -3.45 |
| 30. | 2017. 7. 31. | 3.80% | 1.93% | 14.66 | 1.11 | 4.04 |
| 31. | 2017. 8. 31. | -8.78% | 0.05% | 76.57 | 0.68 | 7.21 |
| 32. | 2017. 9. 30. | -10.69% | 1.93% | 113.67 | 1.10 | -11.21 |
| 33. | 2017. 10. 31. | -13.53% | 2.22% | 182.18 | 1.79 | -18.08 |
| 34. | 2017. 11. 30. | -1.52% | 2.81% | 2.24 | 3.72 | -2.88 |
| 35. | 2017. 12. 31. | -5.90% | 0.98% | 34.44 | 0.01 | -0.61 |
| 36. | 2018. 1. 31. | 10.20% | 5.62% | 104.55 | 22.46 | 48.45 |
| 37. | 2018. 2. 28. | -14.05% | -3.89% | 196.51 | 22.79 | 66.92 |
| 38. | 2018. 3. 31. | 9.12% | -2.69% | 83.75 | 12.73 | -32.65 |
| 39. | 2018. 4. 30. | -8.70% | 0.27% | 75.19 | 0.37 | 5.27 |
| 40. | 2018. 5. 31. | -1.39% | 2.16% | 1.84 | 1.64 | -1.74 |
| 41. | 2018. 6. 30. | 10.56% | 0.48% | 112.04 | 0.16 | -4.18 |
| 42. | 2018. 7. 31. | 10.42% | 3.60% | 109.13 | 7.41 | 28.45 |
| 43. | 2018. 8. 31. | 4.53% | 3.03% | 20.78 | 4.61 | 9.79 |
| 44. | 2018. 9. 30. | -0.64% | 0.43% | 0.38 | 0.20 | 0.28 |
| 45. | 2018. 10. 31. | -17.05% | -6.94% | 289.63 | 61.14 | 133.07 |
| 46. | 2018. 11. 30. | -0.44% | 1.79% | 0.17 | 0.82 | -0.37 |
| 47. | 2018. 12. 31. | -14.65% | -9.18% | 213.77 | 101.14 | 147.04 |
| 48. | 2019. 1. 31. | 7.72% | 7.87% | 60.05 | 48.85 | 54.16 |
| 49. | 2019. 2. 28. | -3.84% | 2.97% | 14.54 | 4.38 | -7.98 |
| 50. | 2019. 3. 31. | 6.32% | 1.79% | 40.27 | 0.83 | 5.80 |
| 51. | 2019. 4. 30. | 0.40% | 3.93% | 0.19 | 9.32 | 1.32 |
| 52. | 2019. 5. 31. | -16.56% | -6.58% | 273.46 | 55.61 | 123.31 |
| 53. | 2019. 6. 30. | 37.34% | 6.89% | 1,396.29 | 36.17 | 224.72 |
| 54. | 2019. 7. 31. | -4.14% | 1.31% | 16.90 | 0.19 | -1.78 |
| 55. | 2019. 8. 31. | -0.02% | -1.81% | 0.00 | 7.23 | -0.01 |
| 56. | 2019. 9. 30. | 5.37% | 1.72% | 29.09 | 0.70 | 4.53 |
| 57. | 2019. 10. 31. | 4.65% | 2.04% | 21.85 | 1.36 | 5.44 |
| 58. | 2019. 11. 30. | 5.43% | 3.40% | 29.83 | 6.38 | 13.80 |
| 59. | 2019. 12. 31. | 3.37% | 2.86% | 11.54 | 3.92 | 6.72 |
| 합계 (Σ): | 5,415.95 | 688.77 | 1,168.59 | |||
모두 보기
분산AGN = Σ(RAGN,t–RAGN)2 ÷ (59 – 1)
= 5,415.95 ÷ (59 – 1)
= 93.38
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
공분산AGN, S&P 500 = Σ(RAGN,t–RAGN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,168.59 ÷ (59 – 1)
= 20.15
체계적인 위험 추정 (β)
| 분산AGN | 93.38 |
| 분산S&P 500 | 11.88 |
| 공분산AGN, S&P 500 | 20.15 |
| 상관 계수AGN, S&P 5001 | 0.61 |
| βAGN2 | 1.70 |
| αAGN3 | -1.52% |
계산
1 상관 계수AGN, S&P 500
= 공분산AGN, S&P 500 ÷ (표준 편차AGN × 표준 편차S&P 500)
= 20.15 ÷ (9.66% × 3.45%)
= 0.61
2 βAGN
= 공분산AGN, S&P 500 ÷ 분산S&P 500
= 20.15 ÷ 11.88
= 1.70
3 αAGN
= 평균의AGN – βAGN × 평균의S&P 500
= -0.03% – 1.70 × 0.88%
= -1.52%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 15.13% |
| 보통주의 체계적 위험Allergan | βAGN | 1.70 |
| Allergan 보통주에 대한 기대 수익률3 | E(RAGN) | 22.47% |
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]
= 4.60% + 1.70 [15.13% – 4.60%]
= 22.47%