資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Biogen普通株式などのリスク資産の期待収益率または必要な収益率を示します。
収益率
Biogen Inc.、月間収益率
| Biogen Inc. (BIIB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格BIIB,t1 | 配当BIIB,t1 | RBIIB,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2017/01/31 | $277.24 | 2,278.87 | ||||
| 1. | 2017/02/28 | $288.60 | 4.10% | 2,363.64 | 3.72% | |
| 2. | 2017/03/31 | $273.42 | -5.26% | 2,362.72 | -0.04% | |
| 3. | 2017/04/30 | $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% | |
| 平均 (R): | 0.23% | 1.36% | ||||
| 標準偏差： | 9.89% | 4.48% | ||||
| Biogen Inc. (BIIB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格BIIB,t1 | 配当BIIB,t1 | RBIIB,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2017/01/31 | $277.24 | 2,278.87 | ||||
| 1. | 2017/02/28 | $288.60 | 4.10% | 2,363.64 | 3.72% | |
| 2. | 2017/03/31 | $273.42 | -5.26% | 2,362.72 | -0.04% | |
| 3. | 2017/04/30 | $271.21 | -0.81% | 2,384.20 | 0.91% | |
| 4. | 2017/05/31 | $247.77 | -8.64% | 2,411.80 | 1.16% | |
| 5. | 2017/06/30 | $271.36 | 9.52% | 2,423.41 | 0.48% | |
| 6. | 2017/07/31 | $289.59 | 6.72% | 2,470.30 | 1.93% | |
| 7. | 2017/08/31 | $316.56 | 9.31% | 2,471.65 | 0.05% | |
| 8. | 2017/09/30 | $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. | 2018/01/31 | $347.81 | 9.18% | 2,823.81 | 5.62% | |
| 13. | 2018/02/28 | $288.99 | -16.91% | 2,713.83 | -3.89% | |
| 14. | 2018/03/31 | $273.82 | -5.25% | 2,640.87 | -2.69% | |
| 15. | 2018/04/30 | $273.60 | -0.08% | 2,648.05 | 0.27% | |
| 16. | 2018/05/31 | $293.96 | 7.44% | 2,705.27 | 2.16% | |
| 17. | 2018/06/30 | $290.24 | -1.27% | 2,718.37 | 0.48% | |
| 18. | 2018/07/31 | $334.37 | 15.20% | 2,816.29 | 3.60% | |
| 19. | 2018/08/31 | $353.49 | 5.72% | 2,901.52 | 3.03% | |
| 20. | 2018/09/30 | $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. | 2019/01/31 | $333.78 | 10.92% | 2,704.10 | 7.87% | |
| 25. | 2019/02/28 | $328.01 | -1.73% | 2,784.49 | 2.97% | |
| 26. | 2019/03/31 | $236.38 | -27.94% | 2,834.40 | 1.79% | |
| 27. | 2019/04/30 | $229.24 | -3.02% | 2,945.83 | 3.93% | |
| 28. | 2019/05/31 | $219.29 | -4.34% | 2,752.06 | -6.58% | |
| 29. | 2019/06/30 | $233.87 | 6.65% | 2,941.76 | 6.89% | |
| 30. | 2019/07/31 | $237.82 | 1.69% | 2,980.38 | 1.31% | |
| 31. | 2019/08/31 | $219.75 | -7.60% | 2,926.46 | -1.81% | |
| 32. | 2019/09/30 | $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. | 2020/01/31 | $268.85 | -9.40% | 3,225.52 | -0.16% | |
| 37. | 2020/02/29 | $308.39 | 14.71% | 2,954.22 | -8.41% | |
| 38. | 2020/03/31 | $316.38 | 2.59% | 2,584.59 | -12.51% | |
| 39. | 2020/04/30 | $296.83 | -6.18% | 2,912.43 | 12.68% | |
| 40. | 2020/05/31 | $307.09 | 3.46% | 3,044.31 | 4.53% | |
| 41. | 2020/06/30 | $267.55 | -12.88% | 3,100.29 | 1.84% | |
| 42. | 2020/07/31 | $274.69 | 2.67% | 3,271.12 | 5.51% | |
| 43. | 2020/08/31 | $287.64 | 4.71% | 3,500.31 | 7.01% | |
| 44. | 2020/09/30 | $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. | 2021/01/31 | $282.61 | 15.42% | 3,714.24 | -1.11% | |
| 49. | 2021/02/28 | $272.88 | -3.44% | 3,811.15 | 2.61% | |
| 50. | 2021/03/31 | $279.75 | 2.52% | 3,972.89 | 4.24% | |
| 51. | 2021/04/30 | $267.33 | -4.44% | 4,181.17 | 5.24% | |
| 52. | 2021/05/31 | $267.48 | 0.06% | 4,204.11 | 0.55% | |
| 53. | 2021/06/30 | $346.27 | 29.46% | 4,297.50 | 2.22% | |
| 54. | 2021/07/31 | $326.73 | -5.64% | 4,395.26 | 2.27% | |
| 55. | 2021/08/31 | $338.91 | 3.73% | 4,522.68 | 2.90% | |
| 56. | 2021/09/30 | $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% | |
| 平均 (R): | 0.23% | 1.36% | ||||
| 標準偏差： | 9.89% | 4.48% | ||||
すべて表示
1 普通株式1株当たり米ドルのデータで、分割と株式配当を調整したものです。
2 期間 tにおけるBIIBの普通株式の収益率。
3 期間 tにおけるS&P 500(市場ポートフォリオの代理)の収益率。
分散と共分散
Biogen Inc.、分散の計算、および戻り値の共分散
| t | 日付 | 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. | 2017/02/28 | 4.10% | 3.72% | 14.93 | 5.58 | 9.13 |
| 2. | 2017/03/31 | -5.26% | -0.04% | 30.18 | 1.95 | 7.67 |
| 3. | 2017/04/30 | -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 |
| トータル (Σ): | 5,668.53 | 1,164.17 | 487.91 | |||
| t | 日付 | 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. | 2017/02/28 | 4.10% | 3.72% | 14.93 | 5.58 | 9.13 |
| 2. | 2017/03/31 | -5.26% | -0.04% | 30.18 | 1.95 | 7.67 |
| 3. | 2017/04/30 | -0.81% | 0.91% | 1.09 | 0.20 | 0.47 |
| 4. | 2017/05/31 | -8.64% | 1.16% | 78.79 | 0.04 | 1.78 |
| 5. | 2017/06/30 | 9.52% | 0.48% | 86.26 | 0.77 | -8.14 |
| 6. | 2017/07/31 | 6.72% | 1.93% | 42.05 | 0.33 | 3.74 |
| 7. | 2017/08/31 | 9.31% | 0.05% | 82.44 | 1.70 | -11.83 |
| 8. | 2017/09/30 | -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. | 2018/01/31 | 9.18% | 5.62% | 80.01 | 18.15 | 38.11 |
| 13. | 2018/02/28 | -16.91% | -3.89% | 293.95 | 27.59 | 90.06 |
| 14. | 2018/03/31 | -5.25% | -2.69% | 30.06 | 16.37 | 22.19 |
| 15. | 2018/04/30 | -0.08% | 0.27% | 0.10 | 1.18 | 0.34 |
| 16. | 2018/05/31 | 7.44% | 2.16% | 51.96 | 0.64 | 5.79 |
| 17. | 2018/06/30 | -1.27% | 0.48% | 2.25 | 0.76 | 1.31 |
| 18. | 2018/07/31 | 15.20% | 3.60% | 224.14 | 5.04 | 33.60 |
| 19. | 2018/08/31 | 5.72% | 3.03% | 30.08 | 2.78 | 9.15 |
| 20. | 2018/09/30 | -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. | 2019/01/31 | 10.92% | 7.87% | 114.20 | 42.39 | 69.57 |
| 25. | 2019/02/28 | -1.73% | 2.97% | 3.85 | 2.61 | -3.17 |
| 26. | 2019/03/31 | -27.94% | 1.79% | 793.47 | 0.19 | -12.24 |
| 27. | 2019/04/30 | -3.02% | 3.93% | 10.59 | 6.62 | -8.37 |
| 28. | 2019/05/31 | -4.34% | -6.58% | 20.92 | 62.97 | 36.30 |
| 29. | 2019/06/30 | 6.65% | 6.89% | 41.16 | 30.64 | 35.51 |
| 30. | 2019/07/31 | 1.69% | 1.31% | 2.12 | 0.00 | -0.07 |
| 31. | 2019/08/31 | -7.60% | -1.81% | 61.34 | 10.03 | 24.80 |
| 32. | 2019/09/30 | 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. | 2020/01/31 | -9.40% | -0.16% | 92.72 | 2.31 | 14.64 |
| 37. | 2020/02/29 | 14.71% | -8.41% | 209.48 | 95.43 | -141.39 |
| 38. | 2020/03/31 | 2.59% | -12.51% | 5.56 | 192.37 | -32.70 |
| 39. | 2020/04/30 | -6.18% | 12.68% | 41.12 | 128.29 | -72.63 |
| 40. | 2020/05/31 | 3.46% | 4.53% | 10.39 | 10.05 | 10.22 |
| 41. | 2020/06/30 | -12.88% | 1.84% | 171.85 | 0.23 | -6.30 |
| 42. | 2020/07/31 | 2.67% | 5.51% | 5.93 | 17.24 | 10.11 |
| 43. | 2020/08/31 | 4.71% | 7.01% | 20.08 | 31.91 | 25.31 |
| 44. | 2020/09/30 | -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. | 2021/01/31 | 15.42% | -1.11% | 230.54 | 6.11 | -37.53 |
| 49. | 2021/02/28 | -3.44% | 2.61% | 13.52 | 1.57 | -4.60 |
| 50. | 2021/03/31 | 2.52% | 4.24% | 5.22 | 8.33 | 6.59 |
| 51. | 2021/04/30 | -4.44% | 5.24% | 21.84 | 15.09 | -18.15 |
| 52. | 2021/05/31 | 0.06% | 0.55% | 0.03 | 0.65 | 0.14 |
| 53. | 2021/06/30 | 29.46% | 2.22% | 853.98 | 0.75 | 25.23 |
| 54. | 2021/07/31 | -5.64% | 2.27% | 34.53 | 0.84 | -5.39 |
| 55. | 2021/08/31 | 3.73% | 2.90% | 12.21 | 2.38 | 5.39 |
| 56. | 2021/09/30 | -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 |
| トータル (Σ): | 5,668.53 | 1,164.17 | 487.91 | |||
すべて表示
分散BIIB = Σ(RBIIB,t–RBIIB)2 ÷ (59 – 1)
= 5,668.53 ÷ (59 – 1)
= 97.73
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
共 分散BIIB, S&P 500 = Σ(RBIIB,t–RBIIB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 487.91 ÷ (59 – 1)
= 8.41
システマティックなリスク推定 (β)
| 分散BIIB | 97.73 |
| 分散S&P 500 | 20.07 |
| 共 分散BIIB, S&P 500 | 8.41 |
| 相関係数BIIB, S&P 5001 | 0.19 |
| βBIIB2 | 0.42 |
| αBIIB3 | -0.34% |
計算
1 相関係数BIIB, S&P 500
= 共 分散BIIB, S&P 500 ÷ (標準偏差BIIB × 標準偏差S&P 500)
= 8.41 ÷ (9.89% × 4.48%)
= 0.19
2 βBIIB
= 共 分散BIIB, S&P 500 ÷ 分散S&P 500
= 8.41 ÷ 20.07
= 0.42
3 αBIIB
= 平均BIIB – βBIIB × 平均S&P 500
= 0.23% – 0.42 × 1.36%
= -0.34%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.91% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.84% |
| 普通株式 Biogen システマティックリスク | βBIIB | 0.42 |
| バイオジェンの普通株式の期待収益率3 | E(RBIIB) | 9.07% |
1 10年以内に期限が到来しない、または償還不能となるすべての発行済み固定利回り米国債の入札利回りの加重平均(リスクフリー・リターン・プロキシ)。
2 詳しく見る »
3 E(RBIIB) = RF + βBIIB [E(RM) – RF]
= 4.91% + 0.42 [14.84% – 4.91%]
= 9.07%