資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 SLB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
Schlumberger Ltd.、月間収益率
| Schlumberger Ltd. (SLB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格SLB,t1 | 配当SLB,t1 | RSLB,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2020/01/31 | $33.51 | 3,225.52 | ||||
| 1. | 2020/02/29 | $27.09 | $0.50 | -17.67% | 2,954.22 | -8.41% |
| 2. | 2020/03/31 | $13.49 | -50.20% | 2,584.59 | -12.51% | |
| 3. | 2020/04/30 | $16.82 | 24.68% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024/11/30 | $43.94 | 9.66% | 6,032.38 | 5.73% | |
| 59. | 2024/12/31 | $38.34 | $0.275 | -12.12% | 5,881.63 | -2.50% |
| 平均 (R): | 1.51% | 1.16% | ||||
| 標準偏差： | 14.54% | 5.28% | ||||
| Schlumberger Ltd. (SLB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格SLB,t1 | 配当SLB,t1 | RSLB,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2020/01/31 | $33.51 | 3,225.52 | ||||
| 1. | 2020/02/29 | $27.09 | $0.50 | -17.67% | 2,954.22 | -8.41% |
| 2. | 2020/03/31 | $13.49 | -50.20% | 2,584.59 | -12.51% | |
| 3. | 2020/04/30 | $16.82 | 24.68% | 2,912.43 | 12.68% | |
| 4. | 2020/05/31 | $18.47 | 9.81% | 3,044.31 | 4.53% | |
| 5. | 2020/06/30 | $18.39 | $0.125 | 0.24% | 3,100.29 | 1.84% |
| 6. | 2020/07/31 | $18.14 | -1.36% | 3,271.12 | 5.51% | |
| 7. | 2020/08/31 | $19.01 | 4.80% | 3,500.31 | 7.01% | |
| 8. | 2020/09/30 | $15.56 | $0.125 | -17.49% | 3,363.00 | -3.92% |
| 9. | 2020/10/31 | $14.94 | -3.98% | 3,269.96 | -2.77% | |
| 10. | 2020/11/30 | $20.79 | 39.16% | 3,621.63 | 10.75% | |
| 11. | 2020/12/31 | $21.83 | $0.125 | 5.60% | 3,756.07 | 3.71% |
| 12. | 2021/01/31 | $22.21 | 1.74% | 3,714.24 | -1.11% | |
| 13. | 2021/02/28 | $27.91 | $0.125 | 26.23% | 3,811.15 | 2.61% |
| 14. | 2021/03/31 | $27.19 | -2.58% | 3,972.89 | 4.24% | |
| 15. | 2021/04/30 | $27.05 | -0.51% | 4,181.17 | 5.24% | |
| 16. | 2021/05/31 | $31.33 | 15.82% | 4,204.11 | 0.55% | |
| 17. | 2021/06/30 | $32.01 | $0.125 | 2.57% | 4,297.50 | 2.22% |
| 18. | 2021/07/31 | $28.83 | -9.93% | 4,395.26 | 2.27% | |
| 19. | 2021/08/31 | $28.04 | $0.125 | -2.31% | 4,522.68 | 2.90% |
| 20. | 2021/09/30 | $29.64 | 5.71% | 4,307.54 | -4.76% | |
| 21. | 2021/10/31 | $32.26 | 8.84% | 4,605.38 | 6.91% | |
| 22. | 2021/11/30 | $28.68 | $0.125 | -10.71% | 4,567.00 | -0.83% |
| 23. | 2021/12/31 | $29.95 | 4.43% | 4,766.18 | 4.36% | |
| 24. | 2022/01/31 | $39.07 | 30.45% | 4,515.55 | -5.26% | |
| 25. | 2022/02/28 | $39.24 | $0.125 | 0.76% | 4,373.94 | -3.14% |
| 26. | 2022/03/31 | $41.31 | 5.28% | 4,530.41 | 3.58% | |
| 27. | 2022/04/30 | $39.01 | -5.57% | 4,131.93 | -8.80% | |
| 28. | 2022/05/31 | $45.96 | $0.175 | 18.26% | 4,132.15 | 0.01% |
| 29. | 2022/06/30 | $35.76 | -22.19% | 3,785.38 | -8.39% | |
| 30. | 2022/07/31 | $37.03 | 3.55% | 4,130.29 | 9.11% | |
| 31. | 2022/08/31 | $38.15 | 3.02% | 3,955.00 | -4.24% | |
| 32. | 2022/09/30 | $35.90 | $0.175 | -5.44% | 3,585.62 | -9.34% |
| 33. | 2022/10/31 | $52.03 | 44.93% | 3,871.98 | 7.99% | |
| 34. | 2022/11/30 | $51.55 | -0.92% | 4,080.11 | 5.38% | |
| 35. | 2022/12/31 | $53.46 | $0.175 | 4.04% | 3,839.50 | -5.90% |
| 36. | 2023/01/31 | $56.98 | 6.58% | 4,076.60 | 6.18% | |
| 37. | 2023/02/28 | $53.21 | $0.25 | -6.18% | 3,970.15 | -2.61% |
| 38. | 2023/03/31 | $49.10 | -7.72% | 4,109.31 | 3.51% | |
| 39. | 2023/04/30 | $49.35 | 0.51% | 4,169.48 | 1.46% | |
| 40. | 2023/05/31 | $42.83 | -13.21% | 4,179.83 | 0.25% | |
| 41. | 2023/06/30 | $49.12 | $0.25 | 15.27% | 4,376.86 | 4.71% |
| 42. | 2023/07/31 | $58.34 | 18.77% | 4,588.96 | 4.85% | |
| 43. | 2023/08/31 | $58.96 | 1.06% | 4,507.66 | -1.77% | |
| 44. | 2023/09/30 | $58.30 | $0.25 | -0.70% | 4,288.05 | -4.87% |
| 45. | 2023/10/31 | $55.66 | -4.53% | 4,193.80 | -2.20% | |
| 46. | 2023/11/30 | $52.04 | -6.50% | 4,567.80 | 8.92% | |
| 47. | 2023/12/31 | $52.04 | $0.25 | 0.48% | 4,769.83 | 4.42% |
| 48. | 2024/01/31 | $48.70 | -6.42% | 4,845.65 | 1.59% | |
| 49. | 2024/02/29 | $48.33 | $0.275 | -0.20% | 5,096.27 | 5.17% |
| 50. | 2024/03/31 | $54.81 | 13.41% | 5,254.35 | 3.10% | |
| 51. | 2024/04/30 | $47.48 | -13.37% | 5,035.69 | -4.16% | |
| 52. | 2024/05/31 | $45.89 | -3.35% | 5,277.51 | 4.80% | |
| 53. | 2024/06/30 | $47.18 | $0.275 | 3.41% | 5,460.48 | 3.47% |
| 54. | 2024/07/31 | $48.29 | 2.35% | 5,522.30 | 1.13% | |
| 55. | 2024/08/31 | $43.99 | -8.90% | 5,648.40 | 2.28% | |
| 56. | 2024/09/30 | $41.95 | $0.275 | -4.01% | 5,762.48 | 2.02% |
| 57. | 2024/10/31 | $40.07 | -4.48% | 5,705.45 | -0.99% | |
| 58. | 2024/11/30 | $43.94 | 9.66% | 6,032.38 | 5.73% | |
| 59. | 2024/12/31 | $38.34 | $0.275 | -12.12% | 5,881.63 | -2.50% |
| 平均 (R): | 1.51% | 1.16% | ||||
| 標準偏差： | 14.54% | 5.28% | ||||
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SLB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
Schlumberger Ltd.、分散の計算、および戻り値の共分散
| t | 日付 | RSLB,t | RS&P 500,t | (RSLB,t–RSLB)2 | (RS&P 500,t–RS&P 500)2 | (RSLB,t–RSLB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020/02/29 | -17.67% | -8.41% | 367.59 | 91.63 | 183.53 |
| 2. | 2020/03/31 | -50.20% | -12.51% | 2,673.84 | 186.96 | 707.03 |
| 3. | 2020/04/30 | 24.68% | 12.68% | 537.26 | 132.78 | 267.09 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024/11/30 | 9.66% | 5.73% | 66.45 | 20.87 | 37.25 |
| 59. | 2024/12/31 | -12.12% | -2.50% | 185.64 | 13.40 | 49.87 |
| トータル (Σ): | 12,269.35 | 1,618.62 | 2,463.14 | |||
| t | 日付 | RSLB,t | RS&P 500,t | (RSLB,t–RSLB)2 | (RS&P 500,t–RS&P 500)2 | (RSLB,t–RSLB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020/02/29 | -17.67% | -8.41% | 367.59 | 91.63 | 183.53 |
| 2. | 2020/03/31 | -50.20% | -12.51% | 2,673.84 | 186.96 | 707.03 |
| 3. | 2020/04/30 | 24.68% | 12.68% | 537.26 | 132.78 | 267.09 |
| 4. | 2020/05/31 | 9.81% | 4.53% | 68.95 | 11.34 | 27.96 |
| 5. | 2020/06/30 | 0.24% | 1.84% | 1.59 | 0.46 | -0.86 |
| 6. | 2020/07/31 | -1.36% | 5.51% | 8.21 | 18.91 | -12.46 |
| 7. | 2020/08/31 | 4.80% | 7.01% | 10.82 | 34.17 | 19.23 |
| 8. | 2020/09/30 | -17.49% | -3.92% | 360.88 | 25.85 | 96.58 |
| 9. | 2020/10/31 | -3.98% | -2.77% | 30.15 | 15.43 | 21.57 |
| 10. | 2020/11/30 | 39.16% | 10.75% | 1,417.56 | 92.03 | 361.19 |
| 11. | 2020/12/31 | 5.60% | 3.71% | 16.79 | 6.51 | 10.45 |
| 12. | 2021/01/31 | 1.74% | -1.11% | 0.06 | 5.18 | -0.53 |
| 13. | 2021/02/28 | 26.23% | 2.61% | 611.12 | 2.10 | 35.79 |
| 14. | 2021/03/31 | -2.58% | 4.24% | 16.69 | 9.50 | -12.60 |
| 15. | 2021/04/30 | -0.51% | 5.24% | 4.08 | 16.66 | -8.25 |
| 16. | 2021/05/31 | 15.82% | 0.55% | 204.96 | 0.38 | -8.77 |
| 17. | 2021/06/30 | 2.57% | 2.22% | 1.13 | 1.12 | 1.13 |
| 18. | 2021/07/31 | -9.93% | 2.27% | 130.89 | 1.24 | -12.74 |
| 19. | 2021/08/31 | -2.31% | 2.90% | 14.54 | 3.02 | -6.63 |
| 20. | 2021/09/30 | 5.71% | -4.76% | 17.64 | 35.02 | -24.86 |
| 21. | 2021/10/31 | 8.84% | 6.91% | 53.78 | 33.10 | 42.19 |
| 22. | 2021/11/30 | -10.71% | -0.83% | 149.23 | 3.98 | 24.37 |
| 23. | 2021/12/31 | 4.43% | 4.36% | 8.54 | 10.24 | 9.35 |
| 24. | 2022/01/31 | 30.45% | -5.26% | 837.79 | 41.21 | -185.82 |
| 25. | 2022/02/28 | 0.76% | -3.14% | 0.56 | 18.47 | 3.23 |
| 26. | 2022/03/31 | 5.28% | 3.58% | 14.21 | 5.84 | 9.11 |
| 27. | 2022/04/30 | -5.57% | -8.80% | 50.04 | 99.14 | 70.43 |
| 28. | 2022/05/31 | 18.26% | 0.01% | 280.84 | 1.34 | -19.37 |
| 29. | 2022/06/30 | -22.19% | -8.39% | 561.66 | 91.26 | 226.41 |
| 30. | 2022/07/31 | 3.55% | 9.11% | 4.18 | 63.21 | 16.26 |
| 31. | 2022/08/31 | 3.02% | -4.24% | 2.31 | 29.22 | -8.21 |
| 32. | 2022/09/30 | -5.44% | -9.34% | 48.24 | 110.27 | 72.93 |
| 33. | 2022/10/31 | 44.93% | 7.99% | 1,885.66 | 46.58 | 296.37 |
| 34. | 2022/11/30 | -0.92% | 5.38% | 5.90 | 17.76 | -10.23 |
| 35. | 2022/12/31 | 4.04% | -5.90% | 6.44 | 49.82 | -17.92 |
| 36. | 2023/01/31 | 6.58% | 6.18% | 25.79 | 25.14 | 25.46 |
| 37. | 2023/02/28 | -6.18% | -2.61% | 59.04 | 14.23 | 28.99 |
| 38. | 2023/03/31 | -7.72% | 3.51% | 85.20 | 5.49 | -21.63 |
| 39. | 2023/04/30 | 0.51% | 1.46% | 0.99 | 0.09 | -0.30 |
| 40. | 2023/05/31 | -13.21% | 0.25% | 216.62 | 0.83 | 13.44 |
| 41. | 2023/06/30 | 15.27% | 4.71% | 189.43 | 12.62 | 48.90 |
| 42. | 2023/07/31 | 18.77% | 4.85% | 298.05 | 13.58 | 63.61 |
| 43. | 2023/08/31 | 1.06% | -1.77% | 0.20 | 8.60 | 1.30 |
| 44. | 2023/09/30 | -0.70% | -4.87% | 4.85 | 36.40 | 13.28 |
| 45. | 2023/10/31 | -4.53% | -2.20% | 36.41 | 11.28 | 20.27 |
| 46. | 2023/11/30 | -6.50% | 8.92% | 64.16 | 60.17 | -62.13 |
| 47. | 2023/12/31 | 0.48% | 4.42% | 1.05 | 10.64 | -3.35 |
| 48. | 2024/01/31 | -6.42% | 1.59% | 62.79 | 0.18 | -3.39 |
| 49. | 2024/02/29 | -0.20% | 5.17% | 2.89 | 16.09 | -6.82 |
| 50. | 2024/03/31 | 13.41% | 3.10% | 141.65 | 3.77 | 23.10 |
| 51. | 2024/04/30 | -13.37% | -4.16% | 221.40 | 28.33 | 79.20 |
| 52. | 2024/05/31 | -3.35% | 4.80% | 23.57 | 13.26 | -17.68 |
| 53. | 2024/06/30 | 3.41% | 3.47% | 3.63 | 5.32 | 4.39 |
| 54. | 2024/07/31 | 2.35% | 1.13% | 0.72 | 0.00 | -0.02 |
| 55. | 2024/08/31 | -8.90% | 2.28% | 108.38 | 1.26 | -11.68 |
| 56. | 2024/09/30 | -4.01% | 2.02% | 30.45 | 0.74 | -4.74 |
| 57. | 2024/10/31 | -4.48% | -0.99% | 35.85 | 4.63 | 12.88 |
| 58. | 2024/11/30 | 9.66% | 5.73% | 66.45 | 20.87 | 37.25 |
| 59. | 2024/12/31 | -12.12% | -2.50% | 185.64 | 13.40 | 49.87 |
| トータル (Σ): | 12,269.35 | 1,618.62 | 2,463.14 | |||
すべて表示
分散SLB = Σ(RSLB,t–RSLB)2 ÷ (59 – 1)
= 12,269.35 ÷ (59 – 1)
= 211.54
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
共 分散SLB, S&P 500 = Σ(RSLB,t–RSLB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,463.14 ÷ (59 – 1)
= 42.47
システマティックなリスク推定 (β)
| 分散SLB | 211.54 |
| 分散S&P 500 | 27.91 |
| 共 分散SLB, S&P 500 | 42.47 |
| 相関係数SLB, S&P 5001 | 0.55 |
| βSLB2 | 1.52 |
| αSLB3 | -0.26% |
計算
1 相関係数SLB, S&P 500
= 共 分散SLB, S&P 500 ÷ (標準偏差SLB × 標準偏差S&P 500)
= 42.47 ÷ (14.54% × 5.28%)
= 0.55
2 βSLB
= 共 分散SLB, S&P 500 ÷ 分散S&P 500
= 42.47 ÷ 27.91
= 1.52
3 αSLB
= 平均SLB – βSLB × 平均S&P 500
= 1.51% – 1.52 × 1.16%
= -0.26%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.42% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 15.02% |
| 普通株式 SLB システマティックリスク | βSLB | 1.52 |
| SLB普通株式の期待収益率3 | E(RSLB) | 20.56% |
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(RSLB) = RF + βSLB [E(RM) – RF]
= 4.42% + 1.52 [15.02% – 4.42%]
= 20.56%