자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Biogen보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Biogen Inc., 월별 수익률
| Biogen Inc. (BIIB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BIIB,t1 | 피제수BIIB,t1 | RBIIB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $277.24 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $288.60 | 4.10% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $273.42 | -5.26% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $271.21 | -0.81% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $235.74 | -11.60% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $239.92 | 1.77% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.23% | 1.36% | ||||
| 표준 편차: | 9.89% | 4.48% | ||||
| Biogen Inc. (BIIB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BIIB,t1 | 피제수BIIB,t1 | RBIIB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $277.24 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $288.60 | 4.10% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $273.42 | -5.26% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $271.21 | -0.81% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $247.77 | -8.64% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $271.36 | 9.52% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $289.59 | 6.72% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $316.56 | 9.31% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $313.12 | -1.09% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $311.66 | -0.47% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $322.17 | 3.37% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $318.57 | -1.12% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $347.81 | 9.18% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $288.99 | -16.91% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $273.82 | -5.25% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $273.60 | -0.08% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $293.96 | 7.44% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $290.24 | -1.27% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $334.37 | 15.20% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $353.49 | 5.72% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $353.31 | -0.05% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $304.27 | -13.88% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $333.72 | 9.68% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $300.92 | -9.83% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $333.78 | 10.92% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $328.01 | -1.73% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $236.38 | -27.94% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $229.24 | -3.02% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $219.29 | -4.34% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $233.87 | 6.65% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $237.82 | 1.69% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $219.75 | -7.60% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $232.82 | 5.95% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $298.71 | 28.30% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $299.81 | 0.37% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $296.73 | -1.03% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $268.85 | -9.40% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $308.39 | 14.71% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $316.38 | 2.59% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $296.83 | -6.18% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $307.09 | 3.46% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $267.55 | -12.88% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $274.69 | 2.67% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $287.64 | 4.71% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $283.68 | -1.38% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $252.07 | -11.14% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $240.17 | -4.72% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $244.86 | 1.95% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $282.61 | 15.42% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $272.88 | -3.44% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $279.75 | 2.52% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $267.33 | -4.44% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $267.48 | 0.06% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $346.27 | 29.46% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $326.73 | -5.64% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $338.91 | 3.73% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $282.99 | -16.50% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $266.68 | -5.76% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $235.74 | -11.60% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $239.92 | 1.77% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.23% | 1.36% | ||||
| 표준 편차: | 9.89% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 BIIB의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Biogen Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RBIIB,t | RS&P 500,t | (RBIIB,t–RBIIB)2 | (RS&P 500,t–RS&P 500)2 | (RBIIB,t–RBIIB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 4.10% | 3.72% | 14.93 | 5.58 | 9.13 |
| 2. | 2017. 3. 31. | -5.26% | -0.04% | 30.18 | 1.95 | 7.67 |
| 3. | 2017. 4. 30. | -0.81% | 0.91% | 1.09 | 0.20 | 0.47 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -11.60% | -0.83% | 140.08 | 4.80 | 25.93 |
| 59. | 2021. 12. 31. | 1.77% | 4.36% | 2.37 | 9.02 | 4.62 |
| 합계 (Σ): | 5,668.53 | 1,164.17 | 487.91 | |||
| t | 날짜 | RBIIB,t | RS&P 500,t | (RBIIB,t–RBIIB)2 | (RS&P 500,t–RS&P 500)2 | (RBIIB,t–RBIIB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 4.10% | 3.72% | 14.93 | 5.58 | 9.13 |
| 2. | 2017. 3. 31. | -5.26% | -0.04% | 30.18 | 1.95 | 7.67 |
| 3. | 2017. 4. 30. | -0.81% | 0.91% | 1.09 | 0.20 | 0.47 |
| 4. | 2017. 5. 31. | -8.64% | 1.16% | 78.79 | 0.04 | 1.78 |
| 5. | 2017. 6. 30. | 9.52% | 0.48% | 86.26 | 0.77 | -8.14 |
| 6. | 2017. 7. 31. | 6.72% | 1.93% | 42.05 | 0.33 | 3.74 |
| 7. | 2017. 8. 31. | 9.31% | 0.05% | 82.44 | 1.70 | -11.83 |
| 8. | 2017. 9. 30. | -1.09% | 1.93% | 1.74 | 0.33 | -0.76 |
| 9. | 2017. 10. 31. | -0.47% | 2.22% | 0.49 | 0.74 | -0.60 |
| 10. | 2017. 11. 30. | 3.37% | 2.81% | 9.85 | 2.10 | 4.55 |
| 11. | 2017. 12. 31. | -1.12% | 0.98% | 1.82 | 0.14 | 0.51 |
| 12. | 2018. 1. 31. | 9.18% | 5.62% | 80.01 | 18.15 | 38.11 |
| 13. | 2018. 2. 28. | -16.91% | -3.89% | 293.95 | 27.59 | 90.06 |
| 14. | 2018. 3. 31. | -5.25% | -2.69% | 30.06 | 16.37 | 22.19 |
| 15. | 2018. 4. 30. | -0.08% | 0.27% | 0.10 | 1.18 | 0.34 |
| 16. | 2018. 5. 31. | 7.44% | 2.16% | 51.96 | 0.64 | 5.79 |
| 17. | 2018. 6. 30. | -1.27% | 0.48% | 2.25 | 0.76 | 1.31 |
| 18. | 2018. 7. 31. | 15.20% | 3.60% | 224.14 | 5.04 | 33.60 |
| 19. | 2018. 8. 31. | 5.72% | 3.03% | 30.08 | 2.78 | 9.15 |
| 20. | 2018. 9. 30. | -0.05% | 0.43% | 0.08 | 0.86 | 0.26 |
| 21. | 2018. 10. 31. | -13.88% | -6.94% | 199.20 | 68.86 | 117.12 |
| 22. | 2018. 11. 30. | 9.68% | 1.79% | 89.22 | 0.18 | 4.04 |
| 23. | 2018. 12. 31. | -9.83% | -9.18% | 101.25 | 111.00 | 106.01 |
| 24. | 2019. 1. 31. | 10.92% | 7.87% | 114.20 | 42.39 | 69.57 |
| 25. | 2019. 2. 28. | -1.73% | 2.97% | 3.85 | 2.61 | -3.17 |
| 26. | 2019. 3. 31. | -27.94% | 1.79% | 793.47 | 0.19 | -12.24 |
| 27. | 2019. 4. 30. | -3.02% | 3.93% | 10.59 | 6.62 | -8.37 |
| 28. | 2019. 5. 31. | -4.34% | -6.58% | 20.92 | 62.97 | 36.30 |
| 29. | 2019. 6. 30. | 6.65% | 6.89% | 41.16 | 30.64 | 35.51 |
| 30. | 2019. 7. 31. | 1.69% | 1.31% | 2.12 | 0.00 | -0.07 |
| 31. | 2019. 8. 31. | -7.60% | -1.81% | 61.34 | 10.03 | 24.80 |
| 32. | 2019. 9. 30. | 5.95% | 1.72% | 32.65 | 0.13 | 2.06 |
| 33. | 2019. 10. 31. | 28.30% | 2.04% | 787.78 | 0.47 | 19.23 |
| 34. | 2019. 11. 30. | 0.37% | 3.40% | 0.02 | 4.19 | 0.28 |
| 35. | 2019. 12. 31. | -1.03% | 2.86% | 1.59 | 2.25 | -1.89 |
| 36. | 2020. 1. 31. | -9.40% | -0.16% | 92.72 | 2.31 | 14.64 |
| 37. | 2020. 2. 29. | 14.71% | -8.41% | 209.48 | 95.43 | -141.39 |
| 38. | 2020. 3. 31. | 2.59% | -12.51% | 5.56 | 192.37 | -32.70 |
| 39. | 2020. 4. 30. | -6.18% | 12.68% | 41.12 | 128.29 | -72.63 |
| 40. | 2020. 5. 31. | 3.46% | 4.53% | 10.39 | 10.05 | 10.22 |
| 41. | 2020. 6. 30. | -12.88% | 1.84% | 171.85 | 0.23 | -6.30 |
| 42. | 2020. 7. 31. | 2.67% | 5.51% | 5.93 | 17.24 | 10.11 |
| 43. | 2020. 8. 31. | 4.71% | 7.01% | 20.08 | 31.91 | 25.31 |
| 44. | 2020. 9. 30. | -1.38% | -3.92% | 2.59 | 27.89 | 8.50 |
| 45. | 2020. 10. 31. | -11.14% | -2.77% | 129.42 | 17.01 | 46.92 |
| 46. | 2020. 11. 30. | -4.72% | 10.75% | 24.55 | 88.30 | -46.55 |
| 47. | 2020. 12. 31. | 1.95% | 3.71% | 2.96 | 5.54 | 4.05 |
| 48. | 2021. 1. 31. | 15.42% | -1.11% | 230.54 | 6.11 | -37.53 |
| 49. | 2021. 2. 28. | -3.44% | 2.61% | 13.52 | 1.57 | -4.60 |
| 50. | 2021. 3. 31. | 2.52% | 4.24% | 5.22 | 8.33 | 6.59 |
| 51. | 2021. 4. 30. | -4.44% | 5.24% | 21.84 | 15.09 | -18.15 |
| 52. | 2021. 5. 31. | 0.06% | 0.55% | 0.03 | 0.65 | 0.14 |
| 53. | 2021. 6. 30. | 29.46% | 2.22% | 853.98 | 0.75 | 25.23 |
| 54. | 2021. 7. 31. | -5.64% | 2.27% | 34.53 | 0.84 | -5.39 |
| 55. | 2021. 8. 31. | 3.73% | 2.90% | 12.21 | 2.38 | 5.39 |
| 56. | 2021. 9. 30. | -16.50% | -4.76% | 280.01 | 37.39 | 102.32 |
| 57. | 2021. 10. 31. | -5.76% | 6.91% | 35.96 | 30.87 | -33.32 |
| 58. | 2021. 11. 30. | -11.60% | -0.83% | 140.08 | 4.80 | 25.93 |
| 59. | 2021. 12. 31. | 1.77% | 4.36% | 2.37 | 9.02 | 4.62 |
| 합계 (Σ): | 5,668.53 | 1,164.17 | 487.91 | |||
모두 보기
분산BIIB = Σ(RBIIB,t–RBIIB)2 ÷ (59 – 1)
= 5,668.53 ÷ (59 – 1)
= 97.73
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산BIIB, S&P 500 = Σ(RBIIB,t–RBIIB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 487.91 ÷ (59 – 1)
= 8.41
체계적인 위험 추정 (β)
| 분산BIIB | 97.73 |
| 분산S&P 500 | 20.07 |
| 공분산BIIB, S&P 500 | 8.41 |
| 상관 계수BIIB, S&P 5001 | 0.19 |
| βBIIB2 | 0.42 |
| αBIIB3 | -0.34% |
계산
1 상관 계수BIIB, S&P 500
= 공분산BIIB, S&P 500 ÷ (표준 편차BIIB × 표준 편차S&P 500)
= 8.41 ÷ (9.89% × 4.48%)
= 0.19
2 βBIIB
= 공분산BIIB, S&P 500 ÷ 분산S&P 500
= 8.41 ÷ 20.07
= 0.42
3 αBIIB
= 평균의BIIB – βBIIB × 평균의S&P 500
= 0.23% – 0.42 × 1.36%
= -0.34%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험Biogen | βBIIB | 0.42 |
| 바이오젠 보통주 기대수익률3 | E(RBIIB) | 9.07% |
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(RBIIB) = RF + βBIIB [E(RM) – RF]
= 4.91% + 0.42 [14.84% – 4.91%]
= 9.07%