資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Linde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
Linde plc、月間収益率
| Linde plc (LIN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格LIN,t1 | 配当LIN,t1 | RLIN,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $245.40 | 3,714.24 | ||||
| 1. | 2021/02/28 | $244.27 | -0.46% | 3,811.15 | 2.61% | |
| 2. | 2021/03/31 | $280.14 | $1.06 | 15.12% | 3,972.89 | 4.24% |
| 3. | 2021/04/30 | $285.84 | 2.03% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | $410.32 | -1.91% | 6,849.09 | 0.13% | |
| 59. | 2025/12/31 | $426.39 | $1.50 | 4.28% | 6,845.50 | -0.05% |
| 平均 (R): | 1.22% | 1.14% | ||||
| 標準偏差： | 5.81% | 4.37% | ||||
| Linde plc (LIN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格LIN,t1 | 配当LIN,t1 | RLIN,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $245.40 | 3,714.24 | ||||
| 1. | 2021/02/28 | $244.27 | -0.46% | 3,811.15 | 2.61% | |
| 2. | 2021/03/31 | $280.14 | $1.06 | 15.12% | 3,972.89 | 4.24% |
| 3. | 2021/04/30 | $285.84 | 2.03% | 4,181.17 | 5.24% | |
| 4. | 2021/05/31 | $300.60 | 5.16% | 4,204.11 | 0.55% | |
| 5. | 2021/06/30 | $289.10 | $1.06 | -3.47% | 4,297.50 | 2.22% |
| 6. | 2021/07/31 | $307.39 | 6.33% | 4,395.26 | 2.27% | |
| 7. | 2021/08/31 | $314.59 | 2.34% | 4,522.68 | 2.90% | |
| 8. | 2021/09/30 | $293.38 | $1.06 | -6.41% | 4,307.54 | -4.76% |
| 9. | 2021/10/31 | $319.20 | 8.80% | 4,605.38 | 6.91% | |
| 10. | 2021/11/30 | $318.14 | -0.33% | 4,567.00 | -0.83% | |
| 11. | 2021/12/31 | $346.43 | $1.06 | 9.23% | 4,766.18 | 4.36% |
| 12. | 2022/01/31 | $318.68 | -8.01% | 4,515.55 | -5.26% | |
| 13. | 2022/02/28 | $293.24 | -7.98% | 4,373.94 | -3.14% | |
| 14. | 2022/03/31 | $319.43 | $1.17 | 9.33% | 4,530.41 | 3.58% |
| 15. | 2022/04/30 | $311.96 | -2.34% | 4,131.93 | -8.80% | |
| 16. | 2022/05/31 | $324.68 | 4.08% | 4,132.15 | 0.01% | |
| 17. | 2022/06/30 | $287.53 | $1.17 | -11.08% | 3,785.38 | -8.39% |
| 18. | 2022/07/31 | $302.00 | 5.03% | 4,130.29 | 9.11% | |
| 19. | 2022/08/31 | $282.86 | -6.34% | 3,955.00 | -4.24% | |
| 20. | 2022/09/30 | $269.59 | $1.17 | -4.28% | 3,585.62 | -9.34% |
| 21. | 2022/10/31 | $297.35 | 10.30% | 3,871.98 | 7.99% | |
| 22. | 2022/11/30 | $336.48 | 13.16% | 4,080.11 | 5.38% | |
| 23. | 2022/12/31 | $326.18 | $1.17 | -2.71% | 3,839.50 | -5.90% |
| 24. | 2023/01/31 | $330.94 | 1.46% | 4,076.60 | 6.18% | |
| 25. | 2023/02/28 | $348.37 | 5.27% | 3,970.15 | -2.61% | |
| 26. | 2023/03/31 | $355.44 | $1.275 | 2.40% | 4,109.31 | 3.51% |
| 27. | 2023/04/30 | $369.45 | 3.94% | 4,169.48 | 1.46% | |
| 28. | 2023/05/31 | $353.66 | -4.27% | 4,179.83 | 0.25% | |
| 29. | 2023/06/30 | $381.08 | $1.275 | 8.11% | 4,376.86 | 4.71% |
| 30. | 2023/07/31 | $390.67 | 2.52% | 4,588.96 | 4.85% | |
| 31. | 2023/08/31 | $387.04 | -0.93% | 4,507.66 | -1.77% | |
| 32. | 2023/09/30 | $372.35 | $1.275 | -3.47% | 4,288.05 | -4.87% |
| 33. | 2023/10/31 | $382.16 | 2.63% | 4,193.80 | -2.20% | |
| 34. | 2023/11/30 | $413.77 | 8.27% | 4,567.80 | 8.92% | |
| 35. | 2023/12/31 | $410.71 | $1.275 | -0.43% | 4,769.83 | 4.42% |
| 36. | 2024/01/31 | $404.83 | -1.43% | 4,845.65 | 1.59% | |
| 37. | 2024/02/29 | $448.82 | 10.87% | 5,096.27 | 5.17% | |
| 38. | 2024/03/31 | $464.32 | $1.39 | 3.76% | 5,254.35 | 3.10% |
| 39. | 2024/04/30 | $440.96 | -5.03% | 5,035.69 | -4.16% | |
| 40. | 2024/05/31 | $435.52 | -1.23% | 5,277.51 | 4.80% | |
| 41. | 2024/06/30 | $438.81 | $1.39 | 1.07% | 5,460.48 | 3.47% |
| 42. | 2024/07/31 | $453.50 | 3.35% | 5,522.30 | 1.13% | |
| 43. | 2024/08/31 | $478.25 | 5.46% | 5,648.40 | 2.28% | |
| 44. | 2024/09/30 | $476.86 | $1.39 | 0.00% | 5,762.48 | 2.02% |
| 45. | 2024/10/31 | $456.15 | -4.34% | 5,705.45 | -0.99% | |
| 46. | 2024/11/30 | $460.99 | 1.06% | 6,032.38 | 5.73% | |
| 47. | 2024/12/31 | $418.67 | $1.39 | -8.88% | 5,881.63 | -2.50% |
| 48. | 2025/01/31 | $446.12 | 6.56% | 6,040.53 | 2.70% | |
| 49. | 2025/02/28 | $467.05 | 4.69% | 5,954.50 | -1.42% | |
| 50. | 2025/03/31 | $465.64 | $1.50 | 0.02% | 5,611.85 | -5.75% |
| 51. | 2025/04/30 | $453.23 | -2.67% | 5,569.06 | -0.76% | |
| 52. | 2025/05/31 | $467.58 | 3.17% | 5,911.69 | 6.15% | |
| 53. | 2025/06/30 | $469.18 | $1.50 | 0.66% | 6,204.95 | 4.96% |
| 54. | 2025/07/31 | $460.26 | -1.90% | 6,339.39 | 2.17% | |
| 55. | 2025/08/31 | $478.29 | 3.92% | 6,460.26 | 1.91% | |
| 56. | 2025/09/30 | $475.00 | $1.50 | -0.37% | 6,688.46 | 3.53% |
| 57. | 2025/10/31 | $418.30 | -11.94% | 6,840.20 | 2.27% | |
| 58. | 2025/11/30 | $410.32 | -1.91% | 6,849.09 | 0.13% | |
| 59. | 2025/12/31 | $426.39 | $1.50 | 4.28% | 6,845.50 | -0.05% |
| 平均 (R): | 1.22% | 1.14% | ||||
| 標準偏差： | 5.81% | 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LIN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
Linde plc、分散の計算、および戻り値の共分散
| t | 日付 | RLIN,t | RS&P 500,t | (RLIN,t–RLIN)2 | (RS&P 500,t–RS&P 500)2 | (RLIN,t–RLIN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | -0.46% | 2.61% | 2.83 | 2.17 | -2.48 |
| 2. | 2021/03/31 | 15.12% | 4.24% | 193.08 | 9.66 | 43.18 |
| 3. | 2021/04/30 | 2.03% | 5.24% | 0.66 | 16.86 | 3.33 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | -1.91% | 0.13% | 9.80 | 1.01 | 3.15 |
| 59. | 2025/12/31 | 4.28% | -0.05% | 9.36 | 1.41 | -3.64 |
| トータル (Σ): | 1,961.02 | 1,108.23 | 922.33 | |||
| t | 日付 | RLIN,t | RS&P 500,t | (RLIN,t–RLIN)2 | (RS&P 500,t–RS&P 500)2 | (RLIN,t–RLIN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | -0.46% | 2.61% | 2.83 | 2.17 | -2.48 |
| 2. | 2021/03/31 | 15.12% | 4.24% | 193.08 | 9.66 | 43.18 |
| 3. | 2021/04/30 | 2.03% | 5.24% | 0.66 | 16.86 | 3.33 |
| 4. | 2021/05/31 | 5.16% | 0.55% | 15.53 | 0.35 | -2.32 |
| 5. | 2021/06/30 | -3.47% | 2.22% | 22.05 | 1.18 | -5.10 |
| 6. | 2021/07/31 | 6.33% | 2.27% | 26.05 | 1.30 | 5.81 |
| 7. | 2021/08/31 | 2.34% | 2.90% | 1.25 | 3.11 | 1.97 |
| 8. | 2021/09/30 | -6.41% | -4.76% | 58.19 | 34.73 | 44.95 |
| 9. | 2021/10/31 | 8.80% | 6.91% | 57.42 | 33.39 | 43.79 |
| 10. | 2021/11/30 | -0.33% | -0.83% | 2.42 | 3.88 | 3.06 |
| 11. | 2021/12/31 | 9.23% | 4.36% | 64.04 | 10.40 | 25.81 |
| 12. | 2022/01/31 | -8.01% | -5.26% | 85.25 | 40.89 | 59.04 |
| 13. | 2022/02/28 | -7.98% | -3.14% | 84.75 | 18.25 | 39.33 |
| 14. | 2022/03/31 | 9.33% | 3.58% | 65.73 | 5.96 | 19.79 |
| 15. | 2022/04/30 | -2.34% | -8.80% | 12.68 | 98.64 | 35.37 |
| 16. | 2022/05/31 | 4.08% | 0.01% | 8.15 | 1.28 | -3.23 |
| 17. | 2022/06/30 | -11.08% | -8.39% | 151.41 | 90.79 | 117.24 |
| 18. | 2022/07/31 | 5.03% | 9.11% | 14.51 | 63.61 | 30.38 |
| 19. | 2022/08/31 | -6.34% | -4.24% | 57.17 | 28.95 | 40.68 |
| 20. | 2022/09/30 | -4.28% | -9.34% | 30.26 | 109.74 | 57.62 |
| 21. | 2022/10/31 | 10.30% | 7.99% | 82.34 | 46.93 | 62.16 |
| 22. | 2022/11/30 | 13.16% | 5.38% | 142.48 | 17.97 | 50.60 |
| 23. | 2022/12/31 | -2.71% | -5.90% | 15.50 | 49.47 | 27.69 |
| 24. | 2023/01/31 | 1.46% | 6.18% | 0.06 | 25.39 | 1.19 |
| 25. | 2023/02/28 | 5.27% | -2.61% | 16.35 | 14.04 | -15.15 |
| 26. | 2023/03/31 | 2.40% | 3.51% | 1.37 | 5.61 | 2.78 |
| 27. | 2023/04/30 | 3.94% | 1.46% | 7.39 | 0.11 | 0.89 |
| 28. | 2023/05/31 | -4.27% | 0.25% | 30.22 | 0.79 | 4.88 |
| 29. | 2023/06/30 | 8.11% | 4.71% | 47.48 | 12.80 | 24.65 |
| 30. | 2023/07/31 | 2.52% | 4.85% | 1.67 | 13.76 | 4.80 |
| 31. | 2023/08/31 | -0.93% | -1.77% | 4.63 | 8.46 | 6.26 |
| 32. | 2023/09/30 | -3.47% | -4.87% | 21.99 | 36.10 | 28.17 |
| 33. | 2023/10/31 | 2.63% | -2.20% | 1.99 | 11.12 | -4.71 |
| 34. | 2023/11/30 | 8.27% | 8.92% | 49.68 | 60.56 | 54.85 |
| 35. | 2023/12/31 | -0.43% | 4.42% | 2.74 | 10.80 | -5.44 |
| 36. | 2024/01/31 | -1.43% | 1.59% | 7.05 | 0.21 | -1.20 |
| 37. | 2024/02/29 | 10.87% | 5.17% | 92.99 | 16.29 | 38.92 |
| 38. | 2024/03/31 | 3.76% | 3.10% | 6.45 | 3.86 | 4.99 |
| 39. | 2024/04/30 | -5.03% | -4.16% | 39.11 | 28.06 | 33.13 |
| 40. | 2024/05/31 | -1.23% | 4.80% | 6.04 | 13.44 | -9.01 |
| 41. | 2024/06/30 | 1.07% | 3.47% | 0.02 | 5.43 | -0.35 |
| 42. | 2024/07/31 | 3.35% | 1.13% | 4.51 | 0.00 | -0.01 |
| 43. | 2024/08/31 | 5.46% | 2.28% | 17.93 | 1.32 | 4.86 |
| 44. | 2024/09/30 | 0.00% | 2.02% | 1.50 | 0.78 | -1.08 |
| 45. | 2024/10/31 | -4.34% | -0.99% | 30.98 | 4.52 | 11.83 |
| 46. | 2024/11/30 | 1.06% | 5.73% | 0.03 | 21.10 | -0.74 |
| 47. | 2024/12/31 | -8.88% | -2.50% | 102.04 | 13.21 | 36.72 |
| 48. | 2025/01/31 | 6.56% | 2.70% | 28.45 | 2.45 | 8.35 |
| 49. | 2025/02/28 | 4.69% | -1.42% | 12.03 | 6.56 | -8.88 |
| 50. | 2025/03/31 | 0.02% | -5.75% | 1.45 | 47.48 | 8.29 |
| 51. | 2025/04/30 | -2.67% | -0.76% | 15.12 | 3.60 | 7.38 |
| 52. | 2025/05/31 | 3.17% | 6.15% | 3.78 | 25.16 | 9.75 |
| 53. | 2025/06/30 | 0.66% | 4.96% | 0.31 | 14.63 | -2.14 |
| 54. | 2025/07/31 | -1.90% | 2.17% | 9.76 | 1.06 | -3.22 |
| 55. | 2025/08/31 | 3.92% | 1.91% | 7.26 | 0.59 | 2.08 |
| 56. | 2025/09/30 | -0.37% | 3.53% | 2.55 | 5.74 | -3.83 |
| 57. | 2025/10/31 | -11.94% | 2.27% | 173.18 | 1.28 | -14.90 |
| 58. | 2025/11/30 | -1.91% | 0.13% | 9.80 | 1.01 | 3.15 |
| 59. | 2025/12/31 | 4.28% | -0.05% | 9.36 | 1.41 | -3.64 |
| トータル (Σ): | 1,961.02 | 1,108.23 | 922.33 | |||
すべて表示
分散LIN = Σ(RLIN,t–RLIN)2 ÷ (59 – 1)
= 1,961.02 ÷ (59 – 1)
= 33.81
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LIN, S&P 500 = Σ(RLIN,t–RLIN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 922.33 ÷ (59 – 1)
= 15.90
システマティックなリスク推定 (β)
| 分散LIN | 33.81 |
| 分散S&P 500 | 19.11 |
| 共 分散LIN, S&P 500 | 15.90 |
| 相関係数LIN, S&P 5001 | 0.63 |
| βLIN2 | 0.83 |
| αLIN3 | 0.28% |
計算
1 相関係数LIN, S&P 500
= 共 分散LIN, S&P 500 ÷ (標準偏差LIN × 標準偏差S&P 500)
= 15.90 ÷ (5.81% × 4.37%)
= 0.63
2 βLIN
= 共 分散LIN, S&P 500 ÷ 分散S&P 500
= 15.90 ÷ 19.11
= 0.83
3 αLIN
= 平均LIN – βLIN × 平均S&P 500
= 1.22% – 0.83 × 1.14%
= 0.28%
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) | 17.36% |
| 普通株式 Linde システマティックリスク | βLIN | 0.83 |
| リンデ普通株式の期待収益率3 | E(RLIN) | 15.26% |
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(RLIN) = RF + βLIN [E(RM) – RF]
= 4.84% + 0.83 [17.36% – 4.84%]
= 15.26%