資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 IBM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
International Business Machines Corp.、月間収益率
| International Business Machines Corp. (IBM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格IBM,t1 | 配当IBM,t1 | RIBM,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $119.11 | 3,714.24 | ||||
| 1. | 2021/02/28 | $118.93 | $1.63 | 1.22% | 3,811.15 | 2.61% |
| 2. | 2021/03/31 | $133.26 | 12.05% | 3,972.89 | 4.24% | |
| 3. | 2021/04/30 | $141.88 | 6.47% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | $308.58 | $1.68 | 0.93% | 6,849.09 | 0.13% |
| 59. | 2025/12/31 | $296.21 | -4.01% | 6,845.50 | -0.05% | |
| 平均 (R): | 2.26% | 1.14% | ||||
| 標準偏差： | 7.10% | 4.37% | ||||
| International Business Machines Corp. (IBM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格IBM,t1 | 配当IBM,t1 | RIBM,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $119.11 | 3,714.24 | ||||
| 1. | 2021/02/28 | $118.93 | $1.63 | 1.22% | 3,811.15 | 2.61% |
| 2. | 2021/03/31 | $133.26 | 12.05% | 3,972.89 | 4.24% | |
| 3. | 2021/04/30 | $141.88 | 6.47% | 4,181.17 | 5.24% | |
| 4. | 2021/05/31 | $143.74 | $1.64 | 2.47% | 4,204.11 | 0.55% |
| 5. | 2021/06/30 | $146.59 | 1.98% | 4,297.50 | 2.22% | |
| 6. | 2021/07/31 | $140.96 | -3.84% | 4,395.26 | 2.27% | |
| 7. | 2021/08/31 | $140.34 | $1.64 | 0.72% | 4,522.68 | 2.90% |
| 8. | 2021/09/30 | $138.93 | -1.00% | 4,307.54 | -4.76% | |
| 9. | 2021/10/31 | $125.10 | $8.00 | -4.20% | 4,605.38 | 6.91% |
| 10. | 2021/11/30 | $117.10 | $1.64 | -5.08% | 4,567.00 | -0.83% |
| 11. | 2021/12/31 | $133.66 | 14.14% | 4,766.18 | 4.36% | |
| 12. | 2022/01/31 | $133.57 | -0.07% | 4,515.55 | -5.26% | |
| 13. | 2022/02/28 | $122.51 | $1.64 | -7.05% | 4,373.94 | -3.14% |
| 14. | 2022/03/31 | $130.02 | 6.13% | 4,530.41 | 3.58% | |
| 15. | 2022/04/30 | $132.21 | 1.68% | 4,131.93 | -8.80% | |
| 16. | 2022/05/31 | $138.84 | $1.65 | 6.26% | 4,132.15 | 0.01% |
| 17. | 2022/06/30 | $141.19 | 1.69% | 3,785.38 | -8.39% | |
| 18. | 2022/07/31 | $130.79 | -7.37% | 4,130.29 | 9.11% | |
| 19. | 2022/08/31 | $128.45 | $1.65 | -0.53% | 3,955.00 | -4.24% |
| 20. | 2022/09/30 | $118.81 | -7.50% | 3,585.62 | -9.34% | |
| 21. | 2022/10/31 | $138.29 | 16.40% | 3,871.98 | 7.99% | |
| 22. | 2022/11/30 | $148.90 | $1.65 | 8.87% | 4,080.11 | 5.38% |
| 23. | 2022/12/31 | $140.89 | -5.38% | 3,839.50 | -5.90% | |
| 24. | 2023/01/31 | $134.73 | -4.37% | 4,076.60 | 6.18% | |
| 25. | 2023/02/28 | $129.30 | $1.65 | -2.81% | 3,970.15 | -2.61% |
| 26. | 2023/03/31 | $131.09 | 1.38% | 4,109.31 | 3.51% | |
| 27. | 2023/04/30 | $126.41 | -3.57% | 4,169.48 | 1.46% | |
| 28. | 2023/05/31 | $128.59 | $1.66 | 3.04% | 4,179.83 | 0.25% |
| 29. | 2023/06/30 | $133.81 | 4.06% | 4,376.86 | 4.71% | |
| 30. | 2023/07/31 | $144.18 | 7.75% | 4,588.96 | 4.85% | |
| 31. | 2023/08/31 | $146.83 | $1.66 | 2.99% | 4,507.66 | -1.77% |
| 32. | 2023/09/30 | $140.30 | -4.45% | 4,288.05 | -4.87% | |
| 33. | 2023/10/31 | $144.64 | 3.09% | 4,193.80 | -2.20% | |
| 34. | 2023/11/30 | $158.56 | $1.66 | 10.77% | 4,567.80 | 8.92% |
| 35. | 2023/12/31 | $163.55 | 3.15% | 4,769.83 | 4.42% | |
| 36. | 2024/01/31 | $183.66 | 12.30% | 4,845.65 | 1.59% | |
| 37. | 2024/02/29 | $185.03 | $1.66 | 1.65% | 5,096.27 | 5.17% |
| 38. | 2024/03/31 | $190.96 | 3.20% | 5,254.35 | 3.10% | |
| 39. | 2024/04/30 | $166.20 | -12.97% | 5,035.69 | -4.16% | |
| 40. | 2024/05/31 | $166.85 | $1.67 | 1.40% | 5,277.51 | 4.80% |
| 41. | 2024/06/30 | $172.95 | 3.66% | 5,460.48 | 3.47% | |
| 42. | 2024/07/31 | $192.14 | 11.10% | 5,522.30 | 1.13% | |
| 43. | 2024/08/31 | $202.13 | $1.67 | 6.07% | 5,648.40 | 2.28% |
| 44. | 2024/09/30 | $221.08 | 9.38% | 5,762.48 | 2.02% | |
| 45. | 2024/10/31 | $206.72 | -6.50% | 5,705.45 | -0.99% | |
| 46. | 2024/11/30 | $227.41 | $1.67 | 10.82% | 6,032.38 | 5.73% |
| 47. | 2024/12/31 | $219.83 | -3.33% | 5,881.63 | -2.50% | |
| 48. | 2025/01/31 | $255.70 | 16.32% | 6,040.53 | 2.70% | |
| 49. | 2025/02/28 | $252.44 | $1.67 | -0.62% | 5,954.50 | -1.42% |
| 50. | 2025/03/31 | $248.66 | -1.50% | 5,611.85 | -5.75% | |
| 51. | 2025/04/30 | $241.82 | -2.75% | 5,569.06 | -0.76% | |
| 52. | 2025/05/31 | $259.06 | $1.68 | 7.82% | 5,911.69 | 6.15% |
| 53. | 2025/06/30 | $294.78 | 13.79% | 6,204.95 | 4.96% | |
| 54. | 2025/07/31 | $253.15 | -14.12% | 6,339.39 | 2.17% | |
| 55. | 2025/08/31 | $243.49 | $1.68 | -3.15% | 6,460.26 | 1.91% |
| 56. | 2025/09/30 | $282.16 | 15.88% | 6,688.46 | 3.53% | |
| 57. | 2025/10/31 | $307.41 | 8.95% | 6,840.20 | 2.27% | |
| 58. | 2025/11/30 | $308.58 | $1.68 | 0.93% | 6,849.09 | 0.13% |
| 59. | 2025/12/31 | $296.21 | -4.01% | 6,845.50 | -0.05% | |
| 平均 (R): | 2.26% | 1.14% | ||||
| 標準偏差： | 7.10% | 4.37% | ||||
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IBM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
International Business Machines Corp.、分散の計算、および戻り値の共分散
| t | 日付 | RIBM,t | RS&P 500,t | (RIBM,t–RIBM)2 | (RS&P 500,t–RS&P 500)2 | (RIBM,t–RIBM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | 1.22% | 2.61% | 1.09 | 2.17 | -1.54 |
| 2. | 2021/03/31 | 12.05% | 4.24% | 95.81 | 9.66 | 30.42 |
| 3. | 2021/04/30 | 6.47% | 5.24% | 17.70 | 16.86 | 17.28 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | 0.93% | 0.13% | 1.78 | 1.01 | 1.34 |
| 59. | 2025/12/31 | -4.01% | -0.05% | 39.31 | 1.41 | 7.45 |
| トータル (Σ): | 2,919.90 | 1,108.23 | 811.16 | |||
| t | 日付 | RIBM,t | RS&P 500,t | (RIBM,t–RIBM)2 | (RS&P 500,t–RS&P 500)2 | (RIBM,t–RIBM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | 1.22% | 2.61% | 1.09 | 2.17 | -1.54 |
| 2. | 2021/03/31 | 12.05% | 4.24% | 95.81 | 9.66 | 30.42 |
| 3. | 2021/04/30 | 6.47% | 5.24% | 17.70 | 16.86 | 17.28 |
| 4. | 2021/05/31 | 2.47% | 0.55% | 0.04 | 0.35 | -0.12 |
| 5. | 2021/06/30 | 1.98% | 2.22% | 0.08 | 1.18 | -0.30 |
| 6. | 2021/07/31 | -3.84% | 2.27% | 37.23 | 1.30 | -6.95 |
| 7. | 2021/08/31 | 0.72% | 2.90% | 2.36 | 3.11 | -2.71 |
| 8. | 2021/09/30 | -1.00% | -4.76% | 10.66 | 34.73 | 19.24 |
| 9. | 2021/10/31 | -4.20% | 6.91% | 41.70 | 33.39 | -37.31 |
| 10. | 2021/11/30 | -5.08% | -0.83% | 53.95 | 3.88 | 14.47 |
| 11. | 2021/12/31 | 14.14% | 4.36% | 141.15 | 10.40 | 38.32 |
| 12. | 2022/01/31 | -0.07% | -5.26% | 5.42 | 40.89 | 14.89 |
| 13. | 2022/02/28 | -7.05% | -3.14% | 86.74 | 18.25 | 39.79 |
| 14. | 2022/03/31 | 6.13% | 3.58% | 14.97 | 5.96 | 9.45 |
| 15. | 2022/04/30 | 1.68% | -8.80% | 0.33 | 98.64 | 5.73 |
| 16. | 2022/05/31 | 6.26% | 0.01% | 16.01 | 1.28 | -4.53 |
| 17. | 2022/06/30 | 1.69% | -8.39% | 0.32 | 90.79 | 5.41 |
| 18. | 2022/07/31 | -7.37% | 9.11% | 92.68 | 63.61 | -76.78 |
| 19. | 2022/08/31 | -0.53% | -4.24% | 7.78 | 28.95 | 15.00 |
| 20. | 2022/09/30 | -7.50% | -9.34% | 95.37 | 109.74 | 102.30 |
| 21. | 2022/10/31 | 16.40% | 7.99% | 199.80 | 46.93 | 96.83 |
| 22. | 2022/11/30 | 8.87% | 5.38% | 43.62 | 17.97 | 28.00 |
| 23. | 2022/12/31 | -5.38% | -5.90% | 58.37 | 49.47 | 53.74 |
| 24. | 2023/01/31 | -4.37% | 6.18% | 44.00 | 25.39 | -33.43 |
| 25. | 2023/02/28 | -2.81% | -2.61% | 25.67 | 14.04 | 18.99 |
| 26. | 2023/03/31 | 1.38% | 3.51% | 0.77 | 5.61 | -2.08 |
| 27. | 2023/04/30 | -3.57% | 1.46% | 34.00 | 0.11 | -1.91 |
| 28. | 2023/05/31 | 3.04% | 0.25% | 0.60 | 0.79 | -0.69 |
| 29. | 2023/06/30 | 4.06% | 4.71% | 3.23 | 12.80 | 6.43 |
| 30. | 2023/07/31 | 7.75% | 4.85% | 30.13 | 13.76 | 20.36 |
| 31. | 2023/08/31 | 2.99% | -1.77% | 0.53 | 8.46 | -2.12 |
| 32. | 2023/09/30 | -4.45% | -4.87% | 45.00 | 36.10 | 40.30 |
| 33. | 2023/10/31 | 3.09% | -2.20% | 0.69 | 11.12 | -2.78 |
| 34. | 2023/11/30 | 10.77% | 8.92% | 72.43 | 60.56 | 66.23 |
| 35. | 2023/12/31 | 3.15% | 4.42% | 0.79 | 10.80 | 2.91 |
| 36. | 2024/01/31 | 12.30% | 1.59% | 100.70 | 0.21 | 4.55 |
| 37. | 2024/02/29 | 1.65% | 5.17% | 0.37 | 16.29 | -2.47 |
| 38. | 2024/03/31 | 3.20% | 3.10% | 0.89 | 3.86 | 1.86 |
| 39. | 2024/04/30 | -12.97% | -4.16% | 231.86 | 28.06 | 80.67 |
| 40. | 2024/05/31 | 1.40% | 4.80% | 0.75 | 13.44 | -3.17 |
| 41. | 2024/06/30 | 3.66% | 3.47% | 1.95 | 5.43 | 3.25 |
| 42. | 2024/07/31 | 11.10% | 1.13% | 78.05 | 0.00 | -0.04 |
| 43. | 2024/08/31 | 6.07% | 2.28% | 14.50 | 1.32 | 4.37 |
| 44. | 2024/09/30 | 9.38% | 2.02% | 50.61 | 0.78 | 6.29 |
| 45. | 2024/10/31 | -6.50% | -0.99% | 76.67 | 4.52 | 18.61 |
| 46. | 2024/11/30 | 10.82% | 5.73% | 73.20 | 21.10 | 39.30 |
| 47. | 2024/12/31 | -3.33% | -2.50% | 31.29 | 13.21 | 20.34 |
| 48. | 2025/01/31 | 16.32% | 2.70% | 197.58 | 2.45 | 22.01 |
| 49. | 2025/02/28 | -0.62% | -1.42% | 8.31 | 6.56 | 7.38 |
| 50. | 2025/03/31 | -1.50% | -5.75% | 14.12 | 47.48 | 25.90 |
| 51. | 2025/04/30 | -2.75% | -0.76% | 25.12 | 3.60 | 9.52 |
| 52. | 2025/05/31 | 7.82% | 6.15% | 30.95 | 25.16 | 27.91 |
| 53. | 2025/06/30 | 13.79% | 4.96% | 132.88 | 14.63 | 44.09 |
| 54. | 2025/07/31 | -14.12% | 2.17% | 268.41 | 1.06 | -16.88 |
| 55. | 2025/08/31 | -3.15% | 1.91% | 29.30 | 0.59 | -4.17 |
| 56. | 2025/09/30 | 15.88% | 3.53% | 185.52 | 5.74 | 32.64 |
| 57. | 2025/10/31 | 8.95% | 2.27% | 44.73 | 1.28 | 7.57 |
| 58. | 2025/11/30 | 0.93% | 0.13% | 1.78 | 1.01 | 1.34 |
| 59. | 2025/12/31 | -4.01% | -0.05% | 39.31 | 1.41 | 7.45 |
| トータル (Σ): | 2,919.90 | 1,108.23 | 811.16 | |||
すべて表示
分散IBM = Σ(RIBM,t–RIBM)2 ÷ (59 – 1)
= 2,919.90 ÷ (59 – 1)
= 50.34
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
共 分散IBM, S&P 500 = Σ(RIBM,t–RIBM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 811.16 ÷ (59 – 1)
= 13.99
システマティックなリスク推定 (β)
| 分散IBM | 50.34 |
| 分散S&P 500 | 19.11 |
| 共 分散IBM, S&P 500 | 13.99 |
| 相関係数IBM, S&P 5001 | 0.45 |
| βIBM2 | 0.73 |
| αIBM3 | 1.43% |
計算
1 相関係数IBM, S&P 500
= 共 分散IBM, S&P 500 ÷ (標準偏差IBM × 標準偏差S&P 500)
= 13.99 ÷ (7.10% × 4.37%)
= 0.45
2 βIBM
= 共 分散IBM, S&P 500 ÷ 分散S&P 500
= 13.99 ÷ 19.11
= 0.73
3 αIBM
= 平均IBM – βIBM × 平均S&P 500
= 2.26% – 0.73 × 1.14%
= 1.43%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.84% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 17.37% |
| 普通株式 IBM システマティックリスク | βIBM | 0.73 |
| IBM普通株式の期待収益率3 | E(RIBM) | 14.01% |
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(RIBM) = RF + βIBM [E(RM) – RF]
= 4.84% + 0.73 [17.37% – 4.84%]
= 14.01%