資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Abbott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
Abbott Laboratories、月間収益率
| Abbott Laboratories (ABT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格ABT,t1 | 配当ABT,t1 | RABT,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $72.98 | 2,704.10 | ||||
| 1. | 2019/02/28 | $77.62 | 6.36% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $79.94 | 2.99% | 2,834.40 | 1.79% | |
| 3. | 2019/04/30 | $79.56 | $0.32 | -0.08% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | $104.29 | 10.30% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $110.07 | 5.54% | 4,769.83 | 4.42% | |
| 平均 (R): | 1.01% | 1.11% | ||||
| 標準偏差： | 6.14% | 5.31% | ||||
| Abbott Laboratories (ABT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格ABT,t1 | 配当ABT,t1 | RABT,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $72.98 | 2,704.10 | ||||
| 1. | 2019/02/28 | $77.62 | 6.36% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $79.94 | 2.99% | 2,834.40 | 1.79% | |
| 3. | 2019/04/30 | $79.56 | $0.32 | -0.08% | 2,945.83 | 3.93% |
| 4. | 2019/05/31 | $76.13 | -4.31% | 2,752.06 | -6.58% | |
| 5. | 2019/06/30 | $84.10 | 10.47% | 2,941.76 | 6.89% | |
| 6. | 2019/07/31 | $87.10 | $0.32 | 3.95% | 2,980.38 | 1.31% |
| 7. | 2019/08/31 | $85.32 | -2.04% | 2,926.46 | -1.81% | |
| 8. | 2019/09/30 | $83.67 | -1.93% | 2,976.74 | 1.72% | |
| 9. | 2019/10/31 | $83.61 | $0.32 | 0.31% | 3,037.56 | 2.04% |
| 10. | 2019/11/30 | $85.45 | 2.20% | 3,140.98 | 3.40% | |
| 11. | 2019/12/31 | $86.86 | 1.65% | 3,230.78 | 2.86% | |
| 12. | 2020/01/31 | $87.14 | $0.36 | 0.74% | 3,225.52 | -0.16% |
| 13. | 2020/02/29 | $77.03 | -11.60% | 2,954.22 | -8.41% | |
| 14. | 2020/03/31 | $78.91 | 2.44% | 2,584.59 | -12.51% | |
| 15. | 2020/04/30 | $92.09 | $0.36 | 17.16% | 2,912.43 | 12.68% |
| 16. | 2020/05/31 | $94.92 | 3.07% | 3,044.31 | 4.53% | |
| 17. | 2020/06/30 | $91.43 | -3.68% | 3,100.29 | 1.84% | |
| 18. | 2020/07/31 | $100.64 | $0.36 | 10.47% | 3,271.12 | 5.51% |
| 19. | 2020/08/31 | $109.47 | 8.77% | 3,500.31 | 7.01% | |
| 20. | 2020/09/30 | $108.83 | -0.58% | 3,363.00 | -3.92% | |
| 21. | 2020/10/31 | $105.11 | $0.36 | -3.09% | 3,269.96 | -2.77% |
| 22. | 2020/11/30 | $108.22 | 2.96% | 3,621.63 | 10.75% | |
| 23. | 2020/12/31 | $109.49 | 1.17% | 3,756.07 | 3.71% | |
| 24. | 2021/01/31 | $123.59 | $0.45 | 13.29% | 3,714.24 | -1.11% |
| 25. | 2021/02/28 | $119.78 | -3.08% | 3,811.15 | 2.61% | |
| 26. | 2021/03/31 | $119.84 | 0.05% | 3,972.89 | 4.24% | |
| 27. | 2021/04/30 | $120.08 | $0.45 | 0.58% | 4,181.17 | 5.24% |
| 28. | 2021/05/31 | $116.65 | -2.86% | 4,204.11 | 0.55% | |
| 29. | 2021/06/30 | $115.93 | -0.62% | 4,297.50 | 2.22% | |
| 30. | 2021/07/31 | $120.98 | $0.45 | 4.74% | 4,395.26 | 2.27% |
| 31. | 2021/08/31 | $126.37 | 4.46% | 4,522.68 | 2.90% | |
| 32. | 2021/09/30 | $118.13 | -6.52% | 4,307.54 | -4.76% | |
| 33. | 2021/10/31 | $128.89 | $0.45 | 9.49% | 4,605.38 | 6.91% |
| 34. | 2021/11/30 | $125.77 | -2.42% | 4,567.00 | -0.83% | |
| 35. | 2021/12/31 | $140.74 | 11.90% | 4,766.18 | 4.36% | |
| 36. | 2022/01/31 | $127.46 | $0.47 | -9.10% | 4,515.55 | -5.26% |
| 37. | 2022/02/28 | $120.62 | -5.37% | 4,373.94 | -3.14% | |
| 38. | 2022/03/31 | $118.36 | -1.87% | 4,530.41 | 3.58% | |
| 39. | 2022/04/30 | $113.50 | $0.47 | -3.71% | 4,131.93 | -8.80% |
| 40. | 2022/05/31 | $117.46 | 3.49% | 4,132.15 | 0.01% | |
| 41. | 2022/06/30 | $108.65 | -7.50% | 3,785.38 | -8.39% | |
| 42. | 2022/07/31 | $108.84 | $0.47 | 0.61% | 4,130.29 | 9.11% |
| 43. | 2022/08/31 | $102.65 | -5.69% | 3,955.00 | -4.24% | |
| 44. | 2022/09/30 | $96.76 | -5.74% | 3,585.62 | -9.34% | |
| 45. | 2022/10/31 | $98.94 | $0.47 | 2.74% | 3,871.98 | 7.99% |
| 46. | 2022/11/30 | $107.58 | 8.73% | 4,080.11 | 5.38% | |
| 47. | 2022/12/31 | $109.79 | 2.05% | 3,839.50 | -5.90% | |
| 48. | 2023/01/31 | $110.55 | $0.51 | 1.16% | 4,076.60 | 6.18% |
| 49. | 2023/02/28 | $101.72 | -7.99% | 3,970.15 | -2.61% | |
| 50. | 2023/03/31 | $101.26 | -0.45% | 4,109.31 | 3.51% | |
| 51. | 2023/04/30 | $110.47 | $0.51 | 9.60% | 4,169.48 | 1.46% |
| 52. | 2023/05/31 | $102.00 | -7.67% | 4,179.83 | 0.25% | |
| 53. | 2023/06/30 | $109.02 | 6.88% | 4,376.86 | 4.71% | |
| 54. | 2023/07/31 | $111.33 | $0.51 | 2.59% | 4,588.96 | 4.85% |
| 55. | 2023/08/31 | $102.90 | -7.57% | 4,507.66 | -1.77% | |
| 56. | 2023/09/30 | $96.85 | -5.88% | 4,288.05 | -4.87% | |
| 57. | 2023/10/31 | $94.55 | $0.51 | -1.85% | 4,193.80 | -2.20% |
| 58. | 2023/11/30 | $104.29 | 10.30% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $110.07 | 5.54% | 4,769.83 | 4.42% | |
| 平均 (R): | 1.01% | 1.11% | ||||
| 標準偏差： | 6.14% | 5.31% | ||||
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ABT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
Abbott Laboratories、分散の計算、および戻り値の共分散
| t | 日付 | RABT,t | RS&P 500,t | (RABT,t–RABT)2 | (RS&P 500,t–RS&P 500)2 | (RABT,t–RABT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 6.36% | 2.97% | 28.58 | 3.49 | 9.98 |
| 2. | 2019/03/31 | 2.99% | 1.79% | 3.91 | 0.47 | 1.36 |
| 3. | 2019/04/30 | -0.08% | 3.93% | 1.18 | 7.98 | -3.07 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | 10.30% | 8.92% | 86.29 | 61.03 | 72.57 |
| 59. | 2023/12/31 | 5.54% | 4.42% | 20.52 | 11.00 | 15.03 |
| トータル (Σ): | 2,184.19 | 1,634.30 | 1,226.05 | |||
| t | 日付 | RABT,t | RS&P 500,t | (RABT,t–RABT)2 | (RS&P 500,t–RS&P 500)2 | (RABT,t–RABT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 6.36% | 2.97% | 28.58 | 3.49 | 9.98 |
| 2. | 2019/03/31 | 2.99% | 1.79% | 3.91 | 0.47 | 1.36 |
| 3. | 2019/04/30 | -0.08% | 3.93% | 1.18 | 7.98 | -3.07 |
| 4. | 2019/05/31 | -4.31% | -6.58% | 28.34 | 59.04 | 40.90 |
| 5. | 2019/06/30 | 10.47% | 6.89% | 89.43 | 33.49 | 54.73 |
| 6. | 2019/07/31 | 3.95% | 1.31% | 8.62 | 0.04 | 0.61 |
| 7. | 2019/08/31 | -2.04% | -1.81% | 9.34 | 8.50 | 8.91 |
| 8. | 2019/09/30 | -1.93% | 1.72% | 8.68 | 0.37 | -1.80 |
| 9. | 2019/10/31 | 0.31% | 2.04% | 0.49 | 0.88 | -0.66 |
| 10. | 2019/11/30 | 2.20% | 3.40% | 1.41 | 5.28 | 2.73 |
| 11. | 2019/12/31 | 1.65% | 2.86% | 0.41 | 3.07 | 1.12 |
| 12. | 2020/01/31 | 0.74% | -0.16% | 0.08 | 1.61 | 0.35 |
| 13. | 2020/02/29 | -11.60% | -8.41% | 159.11 | 90.57 | 120.05 |
| 14. | 2020/03/31 | 2.44% | -12.51% | 2.04 | 185.44 | -19.45 |
| 15. | 2020/04/30 | 17.16% | 12.68% | 260.72 | 134.06 | 186.96 |
| 16. | 2020/05/31 | 3.07% | 4.53% | 4.25 | 11.71 | 7.05 |
| 17. | 2020/06/30 | -3.68% | 1.84% | 21.98 | 0.54 | -3.44 |
| 18. | 2020/07/31 | 10.47% | 5.51% | 89.40 | 19.40 | 41.64 |
| 19. | 2020/08/31 | 8.77% | 7.01% | 60.25 | 34.82 | 45.80 |
| 20. | 2020/09/30 | -0.58% | -3.92% | 2.55 | 25.29 | 8.03 |
| 21. | 2020/10/31 | -3.09% | -2.77% | 16.81 | 15.00 | 15.87 |
| 22. | 2020/11/30 | 2.96% | 10.75% | 3.79 | 93.10 | 18.78 |
| 23. | 2020/12/31 | 1.17% | 3.71% | 0.03 | 6.79 | 0.42 |
| 24. | 2021/01/31 | 13.29% | -1.11% | 150.72 | 4.93 | -27.25 |
| 25. | 2021/02/28 | -3.08% | 2.61% | 16.77 | 2.26 | -6.16 |
| 26. | 2021/03/31 | 0.05% | 4.24% | 0.93 | 9.85 | -3.02 |
| 27. | 2021/04/30 | 0.58% | 5.24% | 0.19 | 17.11 | -1.80 |
| 28. | 2021/05/31 | -2.86% | 0.55% | 14.96 | 0.31 | 2.16 |
| 29. | 2021/06/30 | -0.62% | 2.22% | 2.65 | 1.24 | -1.82 |
| 30. | 2021/07/31 | 4.74% | 2.27% | 13.93 | 1.37 | 4.36 |
| 31. | 2021/08/31 | 4.46% | 2.90% | 11.86 | 3.22 | 6.17 |
| 32. | 2021/09/30 | -6.52% | -4.76% | 56.74 | 34.37 | 44.16 |
| 33. | 2021/10/31 | 9.49% | 6.91% | 71.87 | 33.74 | 49.24 |
| 34. | 2021/11/30 | -2.42% | -0.83% | 11.78 | 3.76 | 6.66 |
| 35. | 2021/12/31 | 11.90% | 4.36% | 118.61 | 10.60 | 35.45 |
| 36. | 2022/01/31 | -9.10% | -5.26% | 102.29 | 40.51 | 64.37 |
| 37. | 2022/02/28 | -5.37% | -3.14% | 40.68 | 17.99 | 27.06 |
| 38. | 2022/03/31 | -1.87% | 3.58% | 8.33 | 6.11 | -7.13 |
| 39. | 2022/04/30 | -3.71% | -8.80% | 22.29 | 98.04 | 46.75 |
| 40. | 2022/05/31 | 3.49% | 0.01% | 6.14 | 1.21 | -2.73 |
| 41. | 2022/06/30 | -7.50% | -8.39% | 72.46 | 90.21 | 80.85 |
| 42. | 2022/07/31 | 0.61% | 9.11% | 0.16 | 64.09 | -3.24 |
| 43. | 2022/08/31 | -5.69% | -4.24% | 44.88 | 28.62 | 35.84 |
| 44. | 2022/09/30 | -5.74% | -9.34% | 45.56 | 109.11 | 70.51 |
| 45. | 2022/10/31 | 2.74% | 7.99% | 2.98 | 47.34 | 11.88 |
| 46. | 2022/11/30 | 8.73% | 5.38% | 59.61 | 18.23 | 32.96 |
| 47. | 2022/12/31 | 2.05% | -5.90% | 1.09 | 49.04 | -7.30 |
| 48. | 2023/01/31 | 1.16% | 6.18% | 0.02 | 25.70 | 0.73 |
| 49. | 2023/02/28 | -7.99% | -2.61% | 80.99 | 13.82 | 33.45 |
| 50. | 2023/03/31 | -0.45% | 3.51% | 2.14 | 5.76 | -3.51 |
| 51. | 2023/04/30 | 9.60% | 1.46% | 73.74 | 0.13 | 3.08 |
| 52. | 2023/05/31 | -7.67% | 0.25% | 75.33 | 0.74 | 7.44 |
| 53. | 2023/06/30 | 6.88% | 4.71% | 34.46 | 13.02 | 21.18 |
| 54. | 2023/07/31 | 2.59% | 4.85% | 2.48 | 13.99 | 5.89 |
| 55. | 2023/08/31 | -7.57% | -1.77% | 73.69 | 8.28 | 24.70 |
| 56. | 2023/09/30 | -5.88% | -4.87% | 47.49 | 35.73 | 41.20 |
| 57. | 2023/10/31 | -1.85% | -2.20% | 8.18 | 10.92 | 9.45 |
| 58. | 2023/11/30 | 10.30% | 8.92% | 86.29 | 61.03 | 72.57 |
| 59. | 2023/12/31 | 5.54% | 4.42% | 20.52 | 11.00 | 15.03 |
| トータル (Σ): | 2,184.19 | 1,634.30 | 1,226.05 | |||
すべて表示
分散ABT = Σ(RABT,t–RABT)2 ÷ (59 – 1)
= 2,184.19 ÷ (59 – 1)
= 37.66
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
共 分散ABT, S&P 500 = Σ(RABT,t–RABT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,226.05 ÷ (59 – 1)
= 21.14
システマティックなリスク推定 (β)
| 分散ABT | 37.66 |
| 分散S&P 500 | 28.18 |
| 共 分散ABT, S&P 500 | 21.14 |
| 相関係数ABT, S&P 5001 | 0.65 |
| βABT2 | 0.75 |
| αABT3 | 0.18% |
計算
1 相関係数ABT, S&P 500
= 共 分散ABT, S&P 500 ÷ (標準偏差ABT × 標準偏差S&P 500)
= 21.14 ÷ (6.14% × 5.31%)
= 0.65
2 βABT
= 共 分散ABT, S&P 500 ÷ 分散S&P 500
= 21.14 ÷ 28.18
= 0.75
3 αABT
= 平均ABT – βABT × 平均S&P 500
= 1.01% – 0.75 × 1.11%
= 0.18%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.48% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.84% |
| 普通株式 Abbott システマティックリスク | βABT | 0.75 |
| アボット普通株式の期待収益率3 | E(RABT) | 11.50% |
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(RABT) = RF + βABT [E(RM) – RF]
= 4.48% + 0.75 [13.84% – 4.48%]
= 11.50%