資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 FCX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
Freeport-McMoRan Inc.、月間収益率
| Freeport-McMoRan Inc. (FCX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格FCX,t1 | 配当FCX,t1 | RFCX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $26.91 | 3,714.24 | ||||
| 1. | 2021/02/28 | $33.91 | 26.01% | 3,811.15 | 2.61% | |
| 2. | 2021/03/31 | $32.93 | -2.89% | 3,972.89 | 4.24% | |
| 3. | 2021/04/30 | $37.71 | $0.075 | 14.74% | 4,181.17 | 5.24% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | $42.98 | 3.07% | 6,849.09 | 0.13% | |
| 59. | 2025/12/31 | $50.79 | 18.17% | 6,845.50 | -0.05% | |
| 平均 (R): | 1.88% | 1.14% | ||||
| 標準偏差： | 11.92% | 4.37% | ||||
| Freeport-McMoRan Inc. (FCX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格FCX,t1 | 配当FCX,t1 | RFCX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $26.91 | 3,714.24 | ||||
| 1. | 2021/02/28 | $33.91 | 26.01% | 3,811.15 | 2.61% | |
| 2. | 2021/03/31 | $32.93 | -2.89% | 3,972.89 | 4.24% | |
| 3. | 2021/04/30 | $37.71 | $0.075 | 14.74% | 4,181.17 | 5.24% |
| 4. | 2021/05/31 | $42.72 | 13.29% | 4,204.11 | 0.55% | |
| 5. | 2021/06/30 | $37.11 | -13.13% | 4,297.50 | 2.22% | |
| 6. | 2021/07/31 | $38.10 | $0.075 | 2.87% | 4,395.26 | 2.27% |
| 7. | 2021/08/31 | $36.39 | -4.49% | 4,522.68 | 2.90% | |
| 8. | 2021/09/30 | $32.53 | -10.61% | 4,307.54 | -4.76% | |
| 9. | 2021/10/31 | $37.72 | $0.075 | 16.19% | 4,605.38 | 6.91% |
| 10. | 2021/11/30 | $37.08 | -1.70% | 4,567.00 | -0.83% | |
| 11. | 2021/12/31 | $41.73 | 12.54% | 4,766.18 | 4.36% | |
| 12. | 2022/01/31 | $37.22 | $0.15 | -10.45% | 4,515.55 | -5.26% |
| 13. | 2022/02/28 | $46.95 | 26.14% | 4,373.94 | -3.14% | |
| 14. | 2022/03/31 | $49.74 | 5.94% | 4,530.41 | 3.58% | |
| 15. | 2022/04/30 | $40.55 | $0.15 | -18.17% | 4,131.93 | -8.80% |
| 16. | 2022/05/31 | $39.08 | -3.63% | 4,132.15 | 0.01% | |
| 17. | 2022/06/30 | $29.26 | -25.13% | 3,785.38 | -8.39% | |
| 18. | 2022/07/31 | $31.55 | $0.15 | 8.34% | 4,130.29 | 9.11% |
| 19. | 2022/08/31 | $29.60 | -6.18% | 3,955.00 | -4.24% | |
| 20. | 2022/09/30 | $27.33 | -7.67% | 3,585.62 | -9.34% | |
| 21. | 2022/10/31 | $31.69 | $0.15 | 16.50% | 3,871.98 | 7.99% |
| 22. | 2022/11/30 | $39.80 | 25.59% | 4,080.11 | 5.38% | |
| 23. | 2022/12/31 | $38.00 | -4.52% | 3,839.50 | -5.90% | |
| 24. | 2023/01/31 | $44.62 | $0.15 | 17.82% | 4,076.60 | 6.18% |
| 25. | 2023/02/28 | $40.97 | -8.18% | 3,970.15 | -2.61% | |
| 26. | 2023/03/31 | $40.91 | -0.15% | 4,109.31 | 3.51% | |
| 27. | 2023/04/30 | $37.91 | $0.15 | -6.97% | 4,169.48 | 1.46% |
| 28. | 2023/05/31 | $34.34 | -9.42% | 4,179.83 | 0.25% | |
| 29. | 2023/06/30 | $40.00 | 16.48% | 4,376.86 | 4.71% | |
| 30. | 2023/07/31 | $44.65 | $0.15 | 12.00% | 4,588.96 | 4.85% |
| 31. | 2023/08/31 | $39.91 | -10.62% | 4,507.66 | -1.77% | |
| 32. | 2023/09/30 | $37.29 | -6.56% | 4,288.05 | -4.87% | |
| 33. | 2023/10/31 | $33.78 | $0.15 | -9.01% | 4,193.80 | -2.20% |
| 34. | 2023/11/30 | $37.32 | 10.48% | 4,567.80 | 8.92% | |
| 35. | 2023/12/31 | $42.57 | 14.07% | 4,769.83 | 4.42% | |
| 36. | 2024/01/31 | $39.69 | $0.15 | -6.41% | 4,845.65 | 1.59% |
| 37. | 2024/02/29 | $37.81 | -4.74% | 5,096.27 | 5.17% | |
| 38. | 2024/03/31 | $47.02 | 24.36% | 5,254.35 | 3.10% | |
| 39. | 2024/04/30 | $49.94 | $0.15 | 6.53% | 5,035.69 | -4.16% |
| 40. | 2024/05/31 | $52.73 | 5.59% | 5,277.51 | 4.80% | |
| 41. | 2024/06/30 | $48.60 | -7.83% | 5,460.48 | 3.47% | |
| 42. | 2024/07/31 | $45.41 | $0.15 | -6.26% | 5,522.30 | 1.13% |
| 43. | 2024/08/31 | $44.28 | -2.49% | 5,648.40 | 2.28% | |
| 44. | 2024/09/30 | $49.92 | 12.74% | 5,762.48 | 2.02% | |
| 45. | 2024/10/31 | $45.02 | $0.15 | -9.52% | 5,705.45 | -0.99% |
| 46. | 2024/11/30 | $44.20 | -1.82% | 6,032.38 | 5.73% | |
| 47. | 2024/12/31 | $38.08 | -13.85% | 5,881.63 | -2.50% | |
| 48. | 2025/01/31 | $35.85 | $0.15 | -5.46% | 6,040.53 | 2.70% |
| 49. | 2025/02/28 | $36.91 | 2.96% | 5,954.50 | -1.42% | |
| 50. | 2025/03/31 | $37.86 | 2.57% | 5,611.85 | -5.75% | |
| 51. | 2025/04/30 | $36.03 | $0.15 | -4.44% | 5,569.06 | -0.76% |
| 52. | 2025/05/31 | $38.48 | 6.80% | 5,911.69 | 6.15% | |
| 53. | 2025/06/30 | $43.35 | 12.66% | 6,204.95 | 4.96% | |
| 54. | 2025/07/31 | $40.24 | $0.15 | -6.83% | 6,339.39 | 2.17% |
| 55. | 2025/08/31 | $44.40 | 10.34% | 6,460.26 | 1.91% | |
| 56. | 2025/09/30 | $39.22 | -11.67% | 6,688.46 | 3.53% | |
| 57. | 2025/10/31 | $41.70 | $0.15 | 6.71% | 6,840.20 | 2.27% |
| 58. | 2025/11/30 | $42.98 | 3.07% | 6,849.09 | 0.13% | |
| 59. | 2025/12/31 | $50.79 | 18.17% | 6,845.50 | -0.05% | |
| 平均 (R): | 1.88% | 1.14% | ||||
| 標準偏差： | 11.92% | 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FCX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
Freeport-McMoRan Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RFCX,t | RS&P 500,t | (RFCX,t–RFCX)2 | (RS&P 500,t–RS&P 500)2 | (RFCX,t–RFCX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | 26.01% | 2.61% | 582.55 | 2.17 | 35.55 |
| 2. | 2021/03/31 | -2.89% | 4.24% | 22.72 | 9.66 | -14.81 |
| 3. | 2021/04/30 | 14.74% | 5.24% | 165.56 | 16.86 | 52.84 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | 3.07% | 0.13% | 1.42 | 1.01 | -1.20 |
| 59. | 2025/12/31 | 18.17% | -0.05% | 265.52 | 1.41 | -19.37 |
| トータル (Σ): | 8,236.19 | 1,108.23 | 1,624.95 | |||
| t | 日付 | RFCX,t | RS&P 500,t | (RFCX,t–RFCX)2 | (RS&P 500,t–RS&P 500)2 | (RFCX,t–RFCX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | 26.01% | 2.61% | 582.55 | 2.17 | 35.55 |
| 2. | 2021/03/31 | -2.89% | 4.24% | 22.72 | 9.66 | -14.81 |
| 3. | 2021/04/30 | 14.74% | 5.24% | 165.56 | 16.86 | 52.84 |
| 4. | 2021/05/31 | 13.29% | 0.55% | 130.17 | 0.35 | -6.70 |
| 5. | 2021/06/30 | -13.13% | 2.22% | 225.26 | 1.18 | -16.29 |
| 6. | 2021/07/31 | 2.87% | 2.27% | 0.99 | 1.30 | 1.13 |
| 7. | 2021/08/31 | -4.49% | 2.90% | 40.51 | 3.11 | -11.22 |
| 8. | 2021/09/30 | -10.61% | -4.76% | 155.85 | 34.73 | 73.57 |
| 9. | 2021/10/31 | 16.19% | 6.91% | 204.73 | 33.39 | 82.68 |
| 10. | 2021/11/30 | -1.70% | -0.83% | 12.77 | 3.88 | 7.04 |
| 11. | 2021/12/31 | 12.54% | 4.36% | 113.72 | 10.40 | 34.39 |
| 12. | 2022/01/31 | -10.45% | -5.26% | 151.90 | 40.89 | 78.81 |
| 13. | 2022/02/28 | 26.14% | -3.14% | 588.81 | 18.25 | -103.67 |
| 14. | 2022/03/31 | 5.94% | 3.58% | 16.53 | 5.96 | 9.93 |
| 15. | 2022/04/30 | -18.17% | -8.80% | 402.04 | 98.64 | 199.14 |
| 16. | 2022/05/31 | -3.63% | 0.01% | 30.27 | 1.28 | 6.22 |
| 17. | 2022/06/30 | -25.13% | -8.39% | 729.24 | 90.79 | 257.30 |
| 18. | 2022/07/31 | 8.34% | 9.11% | 41.76 | 63.61 | 51.54 |
| 19. | 2022/08/31 | -6.18% | -4.24% | 64.92 | 28.95 | 43.35 |
| 20. | 2022/09/30 | -7.67% | -9.34% | 91.12 | 109.74 | 100.00 |
| 21. | 2022/10/31 | 16.50% | 7.99% | 213.90 | 46.93 | 100.19 |
| 22. | 2022/11/30 | 25.59% | 5.38% | 562.41 | 17.97 | 100.53 |
| 23. | 2022/12/31 | -4.52% | -5.90% | 40.95 | 49.47 | 45.01 |
| 24. | 2023/01/31 | 17.82% | 6.18% | 254.06 | 25.39 | 80.32 |
| 25. | 2023/02/28 | -8.18% | -2.61% | 101.14 | 14.04 | 37.69 |
| 26. | 2023/03/31 | -0.15% | 3.51% | 4.09 | 5.61 | -4.79 |
| 27. | 2023/04/30 | -6.97% | 1.46% | 78.20 | 0.11 | -2.90 |
| 28. | 2023/05/31 | -9.42% | 0.25% | 127.54 | 0.79 | 10.03 |
| 29. | 2023/06/30 | 16.48% | 4.71% | 213.33 | 12.80 | 52.25 |
| 30. | 2023/07/31 | 12.00% | 4.85% | 102.48 | 13.76 | 37.56 |
| 31. | 2023/08/31 | -10.62% | -1.77% | 156.06 | 8.46 | 36.33 |
| 32. | 2023/09/30 | -6.56% | -4.87% | 71.26 | 36.10 | 50.72 |
| 33. | 2023/10/31 | -9.01% | -2.20% | 118.53 | 11.12 | 36.30 |
| 34. | 2023/11/30 | 10.48% | 8.92% | 74.01 | 60.56 | 66.95 |
| 35. | 2023/12/31 | 14.07% | 4.42% | 148.62 | 10.80 | 40.07 |
| 36. | 2024/01/31 | -6.41% | 1.59% | 68.72 | 0.21 | -3.76 |
| 37. | 2024/02/29 | -4.74% | 5.17% | 43.73 | 16.29 | -26.69 |
| 38. | 2024/03/31 | 24.36% | 3.10% | 505.44 | 3.86 | 44.19 |
| 39. | 2024/04/30 | 6.53% | -4.16% | 21.65 | 28.06 | -24.65 |
| 40. | 2024/05/31 | 5.59% | 4.80% | 13.77 | 13.44 | 13.60 |
| 41. | 2024/06/30 | -7.83% | 3.47% | 94.26 | 5.43 | -22.63 |
| 42. | 2024/07/31 | -6.26% | 1.13% | 66.12 | 0.00 | 0.03 |
| 43. | 2024/08/31 | -2.49% | 2.28% | 19.05 | 1.32 | -5.01 |
| 44. | 2024/09/30 | 12.74% | 2.02% | 117.95 | 0.78 | 9.60 |
| 45. | 2024/10/31 | -9.52% | -0.99% | 129.77 | 4.52 | 24.22 |
| 46. | 2024/11/30 | -1.82% | 5.73% | 13.67 | 21.10 | -16.99 |
| 47. | 2024/12/31 | -13.85% | -2.50% | 247.20 | 13.21 | 57.15 |
| 48. | 2025/01/31 | -5.46% | 2.70% | 53.86 | 2.45 | -11.49 |
| 49. | 2025/02/28 | 2.96% | -1.42% | 1.17 | 6.56 | -2.77 |
| 50. | 2025/03/31 | 2.57% | -5.75% | 0.49 | 47.48 | -4.80 |
| 51. | 2025/04/30 | -4.44% | -0.76% | 39.87 | 3.60 | 11.99 |
| 52. | 2025/05/31 | 6.80% | 6.15% | 24.24 | 25.16 | 24.70 |
| 53. | 2025/06/30 | 12.66% | 4.96% | 116.20 | 14.63 | 41.23 |
| 54. | 2025/07/31 | -6.83% | 2.17% | 75.77 | 1.06 | -8.97 |
| 55. | 2025/08/31 | 10.34% | 1.91% | 71.60 | 0.59 | 6.52 |
| 56. | 2025/09/30 | -11.67% | 3.53% | 183.42 | 5.74 | -32.45 |
| 57. | 2025/10/31 | 6.71% | 2.27% | 23.32 | 1.28 | 5.47 |
| 58. | 2025/11/30 | 3.07% | 0.13% | 1.42 | 1.01 | -1.20 |
| 59. | 2025/12/31 | 18.17% | -0.05% | 265.52 | 1.41 | -19.37 |
| トータル (Σ): | 8,236.19 | 1,108.23 | 1,624.95 | |||
すべて表示
分散FCX = Σ(RFCX,t–RFCX)2 ÷ (59 – 1)
= 8,236.19 ÷ (59 – 1)
= 142.00
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FCX, S&P 500 = Σ(RFCX,t–RFCX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,624.95 ÷ (59 – 1)
= 28.02
システマティックなリスク推定 (β)
| 分散FCX | 142.00 |
| 分散S&P 500 | 19.11 |
| 共 分散FCX, S&P 500 | 28.02 |
| 相関係数FCX, S&P 5001 | 0.54 |
| βFCX2 | 1.47 |
| αFCX3 | 0.21% |
計算
1 相関係数FCX, S&P 500
= 共 分散FCX, S&P 500 ÷ (標準偏差FCX × 標準偏差S&P 500)
= 28.02 ÷ (11.92% × 4.37%)
= 0.54
2 βFCX
= 共 分散FCX, S&P 500 ÷ 分散S&P 500
= 28.02 ÷ 19.11
= 1.47
3 αFCX
= 平均FCX – βFCX × 平均S&P 500
= 1.88% – 1.47 × 1.14%
= 0.21%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.95% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 17.36% |
| 普通株式 FCX システマティックリスク | βFCX | 1.47 |
| FCX普通株式の期待収益率3 | E(RFCX) | 23.15% |
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(RFCX) = RF + βFCX [E(RM) – RF]
= 4.95% + 1.47 [17.36% – 4.95%]
= 23.15%