資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、普通株式 U. S. Steelのようなリスク資産の予想または必要な収益率を示します。
収益率
United States Steel Corp.、月間収益率
| United States Steel Corp. (X) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格X,t1 | 配当X,t1 | RX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $37.41 | 2,823.81 | ||||
| 1. | 2018/02/28 | $43.51 | $0.05 | 16.44% | 2,713.83 | -3.89% |
| 2. | 2018/03/31 | $35.19 | -19.12% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $33.83 | -3.86% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | $26.29 | $0.05 | 29.37% | 4,080.11 | 5.38% |
| 59. | 2022/12/31 | $25.05 | -4.72% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.16% | 0.67% | ||||
| 標準偏差： | 19.70% | 5.40% | ||||
| United States Steel Corp. (X) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格X,t1 | 配当X,t1 | RX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $37.41 | 2,823.81 | ||||
| 1. | 2018/02/28 | $43.51 | $0.05 | 16.44% | 2,713.83 | -3.89% |
| 2. | 2018/03/31 | $35.19 | -19.12% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $33.83 | -3.86% | 2,648.05 | 0.27% | |
| 4. | 2018/05/31 | $36.87 | $0.05 | 9.13% | 2,705.27 | 2.16% |
| 5. | 2018/06/30 | $34.75 | -5.75% | 2,718.37 | 0.48% | |
| 6. | 2018/07/31 | $36.43 | 4.83% | 2,816.29 | 3.60% | |
| 7. | 2018/08/31 | $29.68 | $0.05 | -18.39% | 2,901.52 | 3.03% |
| 8. | 2018/09/30 | $30.48 | 2.70% | 2,913.98 | 0.43% | |
| 9. | 2018/10/31 | $26.53 | -12.96% | 2,711.74 | -6.94% | |
| 10. | 2018/11/30 | $23.06 | $0.05 | -12.89% | 2,760.17 | 1.79% |
| 11. | 2018/12/31 | $18.24 | -20.90% | 2,506.85 | -9.18% | |
| 12. | 2019/01/31 | $22.54 | 23.57% | 2,704.10 | 7.87% | |
| 13. | 2019/02/28 | $22.41 | $0.05 | -0.35% | 2,784.49 | 2.97% |
| 14. | 2019/03/31 | $19.49 | -13.03% | 2,834.40 | 1.79% | |
| 15. | 2019/04/30 | $15.60 | -19.96% | 2,945.83 | 3.93% | |
| 16. | 2019/05/31 | $11.82 | $0.05 | -23.91% | 2,752.06 | -6.58% |
| 17. | 2019/06/30 | $15.31 | 29.53% | 2,941.76 | 6.89% | |
| 18. | 2019/07/31 | $15.03 | -1.83% | 2,980.38 | 1.31% | |
| 19. | 2019/08/31 | $11.07 | $0.05 | -26.01% | 2,926.46 | -1.81% |
| 20. | 2019/09/30 | $11.55 | 4.34% | 2,976.74 | 1.72% | |
| 21. | 2019/10/31 | $11.51 | -0.35% | 3,037.56 | 2.04% | |
| 22. | 2019/11/30 | $13.12 | $0.05 | 14.42% | 3,140.98 | 3.40% |
| 23. | 2019/12/31 | $11.41 | -13.03% | 3,230.78 | 2.86% | |
| 24. | 2020/01/31 | $9.07 | -20.51% | 3,225.52 | -0.16% | |
| 25. | 2020/02/29 | $8.02 | $0.01 | -11.47% | 2,954.22 | -8.41% |
| 26. | 2020/03/31 | $6.31 | -21.32% | 2,584.59 | -12.51% | |
| 27. | 2020/04/30 | $7.68 | 21.71% | 2,912.43 | 12.68% | |
| 28. | 2020/05/31 | $8.04 | $0.01 | 4.82% | 3,044.31 | 4.53% |
| 29. | 2020/06/30 | $7.22 | -10.20% | 3,100.29 | 1.84% | |
| 30. | 2020/07/31 | $6.66 | -7.76% | 3,271.12 | 5.51% | |
| 31. | 2020/08/31 | $7.83 | $0.01 | 17.72% | 3,500.31 | 7.01% |
| 32. | 2020/09/30 | $7.34 | -6.26% | 3,363.00 | -3.92% | |
| 33. | 2020/10/31 | $9.66 | 31.61% | 3,269.96 | -2.77% | |
| 34. | 2020/11/30 | $14.19 | $0.01 | 47.00% | 3,621.63 | 10.75% |
| 35. | 2020/12/31 | $16.77 | 18.18% | 3,756.07 | 3.71% | |
| 36. | 2021/01/31 | $17.76 | 5.90% | 3,714.24 | -1.11% | |
| 37. | 2021/02/28 | $16.61 | $0.01 | -6.42% | 3,811.15 | 2.61% |
| 38. | 2021/03/31 | $26.17 | 57.56% | 3,972.89 | 4.24% | |
| 39. | 2021/04/30 | $23.01 | -12.07% | 4,181.17 | 5.24% | |
| 40. | 2021/05/31 | $25.93 | $0.01 | 12.73% | 4,204.11 | 0.55% |
| 41. | 2021/06/30 | $24.00 | -7.44% | 4,297.50 | 2.22% | |
| 42. | 2021/07/31 | $26.48 | 10.33% | 4,395.26 | 2.27% | |
| 43. | 2021/08/31 | $26.75 | $0.01 | 1.06% | 4,522.68 | 2.90% |
| 44. | 2021/09/30 | $21.97 | -17.87% | 4,307.54 | -4.76% | |
| 45. | 2021/10/31 | $26.39 | 20.12% | 4,605.38 | 6.91% | |
| 46. | 2021/11/30 | $22.61 | $0.05 | -14.13% | 4,567.00 | -0.83% |
| 47. | 2021/12/31 | $23.81 | 5.31% | 4,766.18 | 4.36% | |
| 48. | 2022/01/31 | $20.72 | -12.98% | 4,515.55 | -5.26% | |
| 49. | 2022/02/28 | $27.21 | $0.05 | 31.56% | 4,373.94 | -3.14% |
| 50. | 2022/03/31 | $37.74 | 38.70% | 4,530.41 | 3.58% | |
| 51. | 2022/04/30 | $30.49 | -19.21% | 4,131.93 | -8.80% | |
| 52. | 2022/05/31 | $25.07 | $0.05 | -17.61% | 4,132.15 | 0.01% |
| 53. | 2022/06/30 | $17.91 | -28.56% | 3,785.38 | -8.39% | |
| 54. | 2022/07/31 | $23.65 | 32.05% | 4,130.29 | 9.11% | |
| 55. | 2022/08/31 | $22.87 | $0.05 | -3.09% | 3,955.00 | -4.24% |
| 56. | 2022/09/30 | $18.12 | -20.77% | 3,585.62 | -9.34% | |
| 57. | 2022/10/31 | $20.36 | 12.36% | 3,871.98 | 7.99% | |
| 58. | 2022/11/30 | $26.29 | $0.05 | 29.37% | 4,080.11 | 5.38% |
| 59. | 2022/12/31 | $25.05 | -4.72% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.16% | 0.67% | ||||
| 標準偏差： | 19.70% | 5.40% | ||||
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X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
United States Steel Corp.、分散の計算、および戻り値の共分散
| t | 日付 | RX,t | RS&P 500,t | (RX,t–RX)2 | (RS&P 500,t–RS&P 500)2 | (RX,t–RX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | 16.44% | -3.89% | 233.53 | 20.81 | -69.71 |
| 2. | 2018/03/31 | -19.12% | -2.69% | 411.27 | 11.26 | 68.04 |
| 3. | 2018/04/30 | -3.86% | 0.27% | 25.23 | 0.16 | 1.98 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | 29.37% | 5.38% | 796.00 | 22.17 | 132.85 |
| 59. | 2022/12/31 | -4.72% | -5.90% | 34.51 | 43.08 | 38.56 |
| トータル (Σ): | 22,504.49 | 1,691.48 | 3,655.99 | |||
| t | 日付 | RX,t | RS&P 500,t | (RX,t–RX)2 | (RS&P 500,t–RS&P 500)2 | (RX,t–RX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | 16.44% | -3.89% | 233.53 | 20.81 | -69.71 |
| 2. | 2018/03/31 | -19.12% | -2.69% | 411.27 | 11.26 | 68.04 |
| 3. | 2018/04/30 | -3.86% | 0.27% | 25.23 | 0.16 | 1.98 |
| 4. | 2018/05/31 | 9.13% | 2.16% | 63.62 | 2.23 | 11.92 |
| 5. | 2018/06/30 | -5.75% | 0.48% | 47.72 | 0.03 | 1.26 |
| 6. | 2018/07/31 | 4.83% | 3.60% | 13.52 | 8.62 | 10.79 |
| 7. | 2018/08/31 | -18.39% | 3.03% | 382.17 | 5.57 | -46.13 |
| 8. | 2018/09/30 | 2.70% | 0.43% | 2.36 | 0.06 | -0.36 |
| 9. | 2018/10/31 | -12.96% | -6.94% | 199.29 | 57.87 | 107.39 |
| 10. | 2018/11/30 | -12.89% | 1.79% | 197.37 | 1.25 | -15.72 |
| 11. | 2018/12/31 | -20.90% | -9.18% | 486.63 | 96.91 | 217.16 |
| 12. | 2019/01/31 | 23.57% | 7.87% | 502.51 | 51.87 | 161.44 |
| 13. | 2019/02/28 | -0.35% | 2.97% | 2.29 | 5.32 | -3.49 |
| 14. | 2019/03/31 | -13.03% | 1.79% | 201.29 | 1.27 | -15.97 |
| 15. | 2019/04/30 | -19.96% | 3.93% | 445.92 | 10.66 | -68.94 |
| 16. | 2019/05/31 | -23.91% | -6.58% | 628.41 | 52.48 | 181.60 |
| 17. | 2019/06/30 | 29.53% | 6.89% | 804.77 | 38.77 | 176.63 |
| 18. | 2019/07/31 | -1.83% | 1.31% | 8.92 | 0.42 | -1.93 |
| 19. | 2019/08/31 | -26.01% | -1.81% | 738.34 | 6.13 | 67.27 |
| 20. | 2019/09/30 | 4.34% | 1.72% | 10.10 | 1.11 | 3.34 |
| 21. | 2019/10/31 | -0.35% | 2.04% | 2.26 | 1.89 | -2.07 |
| 22. | 2019/11/30 | 14.42% | 3.40% | 175.95 | 7.50 | 36.32 |
| 23. | 2019/12/31 | -13.03% | 2.86% | 201.39 | 4.81 | -31.11 |
| 24. | 2020/01/31 | -20.51% | -0.16% | 469.42 | 0.69 | 17.97 |
| 25. | 2020/02/29 | -11.47% | -8.41% | 159.37 | 82.40 | 114.60 |
| 26. | 2020/03/31 | -21.32% | -12.51% | 505.33 | 173.67 | 296.25 |
| 27. | 2020/04/30 | 21.71% | 12.68% | 422.46 | 144.43 | 247.01 |
| 28. | 2020/05/31 | 4.82% | 4.53% | 13.39 | 14.91 | 14.13 |
| 29. | 2020/06/30 | -10.20% | 1.84% | 128.98 | 1.37 | -13.31 |
| 30. | 2020/07/31 | -7.76% | 5.51% | 79.46 | 23.46 | -43.17 |
| 31. | 2020/08/31 | 17.72% | 7.01% | 274.23 | 40.19 | 104.99 |
| 32. | 2020/09/30 | -6.26% | -3.92% | 54.99 | 21.06 | 34.03 |
| 33. | 2020/10/31 | 31.61% | -2.77% | 927.19 | 11.79 | -104.54 |
| 34. | 2020/11/30 | 47.00% | 10.75% | 2,101.32 | 101.77 | 462.43 |
| 35. | 2020/12/31 | 18.18% | 3.71% | 289.82 | 9.28 | 51.85 |
| 36. | 2021/01/31 | 5.90% | -1.11% | 22.52 | 3.17 | -8.45 |
| 37. | 2021/02/28 | -6.42% | 2.61% | 57.41 | 3.77 | -14.72 |
| 38. | 2021/03/31 | 57.56% | 4.24% | 3,180.72 | 12.80 | 201.75 |
| 39. | 2021/04/30 | -12.07% | 5.24% | 175.10 | 20.94 | -60.55 |
| 40. | 2021/05/31 | 12.73% | 0.55% | 134.00 | 0.01 | -1.37 |
| 41. | 2021/06/30 | -7.44% | 2.22% | 73.98 | 2.42 | -13.37 |
| 42. | 2021/07/31 | 10.33% | 2.27% | 84.19 | 2.59 | 14.76 |
| 43. | 2021/08/31 | 1.06% | 2.90% | 0.01 | 4.98 | -0.22 |
| 44. | 2021/09/30 | -17.87% | -4.76% | 362.03 | 29.42 | 103.19 |
| 45. | 2021/10/31 | 20.12% | 6.91% | 359.50 | 39.03 | 118.46 |
| 46. | 2021/11/30 | -14.13% | -0.83% | 233.84 | 2.25 | 22.94 |
| 47. | 2021/12/31 | 5.31% | 4.36% | 17.22 | 13.65 | 15.33 |
| 48. | 2022/01/31 | -12.98% | -5.26% | 199.81 | 35.11 | 83.76 |
| 49. | 2022/02/28 | 31.56% | -3.14% | 924.52 | 14.46 | -115.62 |
| 50. | 2022/03/31 | 38.70% | 3.58% | 1,409.34 | 8.47 | 109.27 |
| 51. | 2022/04/30 | -19.21% | -8.80% | 414.86 | 89.54 | 192.73 |
| 52. | 2022/05/31 | -17.61% | 0.01% | 352.32 | 0.44 | 12.41 |
| 53. | 2022/06/30 | -28.56% | -8.39% | 883.15 | 82.06 | 269.20 |
| 54. | 2022/07/31 | 32.05% | 9.11% | 954.27 | 71.32 | 260.88 |
| 55. | 2022/08/31 | -3.09% | -4.24% | 18.02 | 24.11 | 20.84 |
| 56. | 2022/09/30 | -20.77% | -9.34% | 480.81 | 100.12 | 219.41 |
| 57. | 2022/10/31 | 12.36% | 7.99% | 125.53 | 53.58 | 82.01 |
| 58. | 2022/11/30 | 29.37% | 5.38% | 796.00 | 22.17 | 132.85 |
| 59. | 2022/12/31 | -4.72% | -5.90% | 34.51 | 43.08 | 38.56 |
| トータル (Σ): | 22,504.49 | 1,691.48 | 3,655.99 | |||
すべて表示
分散X = Σ(RX,t–RX)2 ÷ (59 – 1)
= 22,504.49 ÷ (59 – 1)
= 388.01
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
共 分散X, S&P 500 = Σ(RX,t–RX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,655.99 ÷ (59 – 1)
= 63.03
システマティックなリスク推定 (β)
| 分散X | 388.01 |
| 分散S&P 500 | 29.16 |
| 共 分散X, S&P 500 | 63.03 |
| 相関係数X, S&P 5001 | 0.59 |
| βX2 | 2.16 |
| αX3 | -0.28% |
計算
1 相関係数X, S&P 500
= 共 分散X, S&P 500 ÷ (標準偏差X × 標準偏差S&P 500)
= 63.03 ÷ (19.70% × 5.40%)
= 0.59
2 βX
= 共 分散X, S&P 500 ÷ 分散S&P 500
= 63.03 ÷ 29.16
= 2.16
3 αX
= 平均X – βX × 平均S&P 500
= 1.16% – 2.16 × 0.67%
= -0.28%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.67% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.79% |
| 普通株式のシステマティックリスクU. S. Steel | βX | 2.16 |
| USスチール普通株式の予想収益率3 | E(RX) | 24.37% |
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(RX) = RF + βX [E(RM) – RF]
= 4.67% + 2.16 [13.79% – 4.67%]
= 24.37%