資本資産価格モデル (CAPM)
資本資産価格モデル(CAPM)は、 CSX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
CSX Corp.、月間収益率
| CSX Corp. (CSX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格CSX,t1 | 配当CSX,t1 | RCSX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $18.92 | 2,823.81 | ||||
| 1. | 2018/02/28 | $17.91 | $0.073 | -4.95% | 2,713.83 | -3.89% |
| 2. | 2018/03/31 | $18.57 | 3.69% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $19.80 | 6.62% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | $32.69 | $0.10 | 12.84% | 4,080.11 | 5.38% |
| 59. | 2022/12/31 | $30.98 | -5.23% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.27% | 0.67% | ||||
| 標準偏差： | 8.02% | 5.40% | ||||
| CSX Corp. (CSX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格CSX,t1 | 配当CSX,t1 | RCSX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $18.92 | 2,823.81 | ||||
| 1. | 2018/02/28 | $17.91 | $0.073 | -4.95% | 2,713.83 | -3.89% |
| 2. | 2018/03/31 | $18.57 | 3.69% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $19.80 | 6.62% | 2,648.05 | 0.27% | |
| 4. | 2018/05/31 | $21.55 | $0.073 | 9.21% | 2,705.27 | 2.16% |
| 5. | 2018/06/30 | $21.26 | -1.35% | 2,718.37 | 0.48% | |
| 6. | 2018/07/31 | $23.56 | 10.82% | 2,816.29 | 3.60% | |
| 7. | 2018/08/31 | $24.72 | $0.073 | 5.23% | 2,901.52 | 3.03% |
| 8. | 2018/09/30 | $24.68 | -0.16% | 2,913.98 | 0.43% | |
| 9. | 2018/10/31 | $22.95 | -7.01% | 2,711.74 | -6.94% | |
| 10. | 2018/11/30 | $24.21 | $0.073 | 5.81% | 2,760.17 | 1.79% |
| 11. | 2018/12/31 | $20.71 | -14.46% | 2,506.85 | -9.18% | |
| 12. | 2019/01/31 | $21.90 | 5.75% | 2,704.10 | 7.87% | |
| 13. | 2019/02/28 | $24.22 | $0.08 | 10.96% | 2,784.49 | 2.97% |
| 14. | 2019/03/31 | $24.94 | 2.97% | 2,834.40 | 1.79% | |
| 15. | 2019/04/30 | $26.54 | 6.42% | 2,945.83 | 3.93% | |
| 16. | 2019/05/31 | $24.82 | $0.08 | -6.18% | 2,752.06 | -6.58% |
| 17. | 2019/06/30 | $25.79 | 3.91% | 2,941.76 | 6.89% | |
| 18. | 2019/07/31 | $23.47 | -9.00% | 2,980.38 | 1.31% | |
| 19. | 2019/08/31 | $22.34 | $0.08 | -4.47% | 2,926.46 | -1.81% |
| 20. | 2019/09/30 | $23.09 | 3.36% | 2,976.74 | 1.72% | |
| 21. | 2019/10/31 | $23.42 | 1.43% | 3,037.56 | 2.04% | |
| 22. | 2019/11/30 | $23.85 | $0.08 | 2.18% | 3,140.98 | 3.40% |
| 23. | 2019/12/31 | $24.12 | 1.13% | 3,230.78 | 2.86% | |
| 24. | 2020/01/31 | $25.45 | 5.51% | 3,225.52 | -0.16% | |
| 25. | 2020/02/29 | $23.48 | $0.087 | -7.40% | 2,954.22 | -8.41% |
| 26. | 2020/03/31 | $19.10 | -18.65% | 2,584.59 | -12.51% | |
| 27. | 2020/04/30 | $22.08 | 15.60% | 2,912.43 | 12.68% | |
| 28. | 2020/05/31 | $23.86 | $0.087 | 8.46% | 3,044.31 | 4.53% |
| 29. | 2020/06/30 | $23.25 | -2.56% | 3,100.29 | 1.84% | |
| 30. | 2020/07/31 | $23.78 | 2.28% | 3,271.12 | 5.51% | |
| 31. | 2020/08/31 | $25.49 | $0.087 | 7.56% | 3,500.31 | 7.01% |
| 32. | 2020/09/30 | $25.89 | 1.57% | 3,363.00 | -3.92% | |
| 33. | 2020/10/31 | $26.31 | 1.62% | 3,269.96 | -2.77% | |
| 34. | 2020/11/30 | $30.02 | $0.087 | 14.43% | 3,621.63 | 10.75% |
| 35. | 2020/12/31 | $30.25 | 0.77% | 3,756.07 | 3.71% | |
| 36. | 2021/01/31 | $28.59 | -5.49% | 3,714.24 | -1.11% | |
| 37. | 2021/02/28 | $30.52 | $0.093 | 7.08% | 3,811.15 | 2.61% |
| 38. | 2021/03/31 | $32.14 | 5.31% | 3,972.89 | 4.24% | |
| 39. | 2021/04/30 | $33.58 | 4.48% | 4,181.17 | 5.24% | |
| 40. | 2021/05/31 | $33.37 | $0.093 | -0.35% | 4,204.11 | 0.55% |
| 41. | 2021/06/30 | $32.08 | -3.87% | 4,297.50 | 2.22% | |
| 42. | 2021/07/31 | $32.32 | 0.75% | 4,395.26 | 2.27% | |
| 43. | 2021/08/31 | $32.53 | $0.093 | 0.94% | 4,522.68 | 2.90% |
| 44. | 2021/09/30 | $29.74 | -8.58% | 4,307.54 | -4.76% | |
| 45. | 2021/10/31 | $36.17 | 21.62% | 4,605.38 | 6.91% | |
| 46. | 2021/11/30 | $34.66 | $0.093 | -3.92% | 4,567.00 | -0.83% |
| 47. | 2021/12/31 | $37.60 | 8.48% | 4,766.18 | 4.36% | |
| 48. | 2022/01/31 | $34.22 | -8.99% | 4,515.55 | -5.26% | |
| 49. | 2022/02/28 | $33.91 | $0.10 | -0.61% | 4,373.94 | -3.14% |
| 50. | 2022/03/31 | $37.45 | 10.44% | 4,530.41 | 3.58% | |
| 51. | 2022/04/30 | $34.34 | -8.30% | 4,131.93 | -8.80% | |
| 52. | 2022/05/31 | $31.79 | $0.10 | -7.13% | 4,132.15 | 0.01% |
| 53. | 2022/06/30 | $29.06 | -8.59% | 3,785.38 | -8.39% | |
| 54. | 2022/07/31 | $32.33 | 11.25% | 4,130.29 | 9.11% | |
| 55. | 2022/08/31 | $31.65 | $0.10 | -1.79% | 3,955.00 | -4.24% |
| 56. | 2022/09/30 | $26.64 | -15.83% | 3,585.62 | -9.34% | |
| 57. | 2022/10/31 | $29.06 | 9.08% | 3,871.98 | 7.99% | |
| 58. | 2022/11/30 | $32.69 | $0.10 | 12.84% | 4,080.11 | 5.38% |
| 59. | 2022/12/31 | $30.98 | -5.23% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.27% | 0.67% | ||||
| 標準偏差： | 8.02% | 5.40% | ||||
すべて表示
1 普通株式1株当たり米ドルで、分割および株式配当を調整したデータ。
2 期間 t中のCSX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プロキシ)の収益率。
分散と共分散
CSX Corp.、分散の計算、および戻り値の共分散
| t | 日付 | RCSX,t | RS&P 500,t | (RCSX,t–RCSX)2 | (RS&P 500,t–RS&P 500)2 | (RCSX,t–RCSX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | -4.95% | -3.89% | 38.66 | 20.81 | 28.36 |
| 2. | 2018/03/31 | 3.69% | -2.69% | 5.85 | 11.26 | -8.12 |
| 3. | 2018/04/30 | 6.62% | 0.27% | 28.71 | 0.16 | -2.12 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | 12.84% | 5.38% | 133.86 | 22.17 | 54.48 |
| 59. | 2022/12/31 | -5.23% | -5.90% | 42.21 | 43.08 | 42.64 |
| トータル (Σ): | 3,730.14 | 1,691.48 | 2,116.54 | |||
| t | 日付 | RCSX,t | RS&P 500,t | (RCSX,t–RCSX)2 | (RS&P 500,t–RS&P 500)2 | (RCSX,t–RCSX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | -4.95% | -3.89% | 38.66 | 20.81 | 28.36 |
| 2. | 2018/03/31 | 3.69% | -2.69% | 5.85 | 11.26 | -8.12 |
| 3. | 2018/04/30 | 6.62% | 0.27% | 28.71 | 0.16 | -2.12 |
| 4. | 2018/05/31 | 9.21% | 2.16% | 63.07 | 2.23 | 11.87 |
| 5. | 2018/06/30 | -1.35% | 0.48% | 6.82 | 0.03 | 0.48 |
| 6. | 2018/07/31 | 10.82% | 3.60% | 91.26 | 8.62 | 28.04 |
| 7. | 2018/08/31 | 5.23% | 3.03% | 15.74 | 5.57 | 9.36 |
| 8. | 2018/09/30 | -0.16% | 0.43% | 2.04 | 0.06 | 0.34 |
| 9. | 2018/10/31 | -7.01% | -6.94% | 68.48 | 57.87 | 62.95 |
| 10. | 2018/11/30 | 5.81% | 1.79% | 20.64 | 1.25 | 5.08 |
| 11. | 2018/12/31 | -14.46% | -9.18% | 247.20 | 96.91 | 154.78 |
| 12. | 2019/01/31 | 5.75% | 7.87% | 20.07 | 51.87 | 32.27 |
| 13. | 2019/02/28 | 10.96% | 2.97% | 93.96 | 5.32 | 22.36 |
| 14. | 2019/03/31 | 2.97% | 1.79% | 2.91 | 1.27 | 1.92 |
| 15. | 2019/04/30 | 6.42% | 3.93% | 26.52 | 10.66 | 16.81 |
| 16. | 2019/05/31 | -6.18% | -6.58% | 55.43 | 52.48 | 53.93 |
| 17. | 2019/06/30 | 3.91% | 6.89% | 6.98 | 38.77 | 16.45 |
| 18. | 2019/07/31 | -9.00% | 1.31% | 105.29 | 0.42 | -6.63 |
| 19. | 2019/08/31 | -4.47% | -1.81% | 32.94 | 6.13 | 14.21 |
| 20. | 2019/09/30 | 3.36% | 1.72% | 4.37 | 1.11 | 2.20 |
| 21. | 2019/10/31 | 1.43% | 2.04% | 0.03 | 1.89 | 0.23 |
| 22. | 2019/11/30 | 2.18% | 3.40% | 0.83 | 7.50 | 2.50 |
| 23. | 2019/12/31 | 1.13% | 2.86% | 0.02 | 4.81 | -0.29 |
| 24. | 2020/01/31 | 5.51% | -0.16% | 18.05 | 0.69 | -3.52 |
| 25. | 2020/02/29 | -7.40% | -8.41% | 75.07 | 82.40 | 78.65 |
| 26. | 2020/03/31 | -18.65% | -12.51% | 396.80 | 173.67 | 262.51 |
| 27. | 2020/04/30 | 15.60% | 12.68% | 205.54 | 144.43 | 172.29 |
| 28. | 2020/05/31 | 8.46% | 4.53% | 51.70 | 14.91 | 27.76 |
| 29. | 2020/06/30 | -2.56% | 1.84% | 14.61 | 1.37 | -4.48 |
| 30. | 2020/07/31 | 2.28% | 5.51% | 1.03 | 23.46 | 4.91 |
| 31. | 2020/08/31 | 7.56% | 7.01% | 39.58 | 40.19 | 39.88 |
| 32. | 2020/09/30 | 1.57% | -3.92% | 0.09 | 21.06 | -1.39 |
| 33. | 2020/10/31 | 1.62% | -2.77% | 0.13 | 11.79 | -1.22 |
| 34. | 2020/11/30 | 14.43% | 10.75% | 173.35 | 101.77 | 132.82 |
| 35. | 2020/12/31 | 0.77% | 3.71% | 0.25 | 9.28 | -1.52 |
| 36. | 2021/01/31 | -5.49% | -1.11% | 45.61 | 3.17 | 12.02 |
| 37. | 2021/02/28 | 7.08% | 2.61% | 33.76 | 3.77 | 11.29 |
| 38. | 2021/03/31 | 5.31% | 4.24% | 16.34 | 12.80 | 14.46 |
| 39. | 2021/04/30 | 4.48% | 5.24% | 10.33 | 20.94 | 14.71 |
| 40. | 2021/05/31 | -0.35% | 0.55% | 2.61 | 0.01 | 0.19 |
| 41. | 2021/06/30 | -3.87% | 2.22% | 26.33 | 2.42 | -7.98 |
| 42. | 2021/07/31 | 0.75% | 2.27% | 0.27 | 2.59 | -0.83 |
| 43. | 2021/08/31 | 0.94% | 2.90% | 0.11 | 4.98 | -0.73 |
| 44. | 2021/09/30 | -8.58% | -4.76% | 96.87 | 29.42 | 53.38 |
| 45. | 2021/10/31 | 21.62% | 6.91% | 414.33 | 39.03 | 127.17 |
| 46. | 2021/11/30 | -3.92% | -0.83% | 26.87 | 2.25 | 7.77 |
| 47. | 2021/12/31 | 8.48% | 4.36% | 52.08 | 13.65 | 26.66 |
| 48. | 2022/01/31 | -8.99% | -5.26% | 105.16 | 35.11 | 60.76 |
| 49. | 2022/02/28 | -0.61% | -3.14% | 3.53 | 14.46 | 7.15 |
| 50. | 2022/03/31 | 10.44% | 3.58% | 84.16 | 8.47 | 26.70 |
| 51. | 2022/04/30 | -8.30% | -8.80% | 91.59 | 89.54 | 90.55 |
| 52. | 2022/05/31 | -7.13% | 0.01% | 70.56 | 0.44 | 5.56 |
| 53. | 2022/06/30 | -8.59% | -8.39% | 97.09 | 82.06 | 89.26 |
| 54. | 2022/07/31 | 11.25% | 9.11% | 99.74 | 71.32 | 84.34 |
| 55. | 2022/08/31 | -1.79% | -4.24% | 9.36 | 24.11 | 15.02 |
| 56. | 2022/09/30 | -15.83% | -9.34% | 292.24 | 100.12 | 171.06 |
| 57. | 2022/10/31 | 9.08% | 7.99% | 61.13 | 53.58 | 57.23 |
| 58. | 2022/11/30 | 12.84% | 5.38% | 133.86 | 22.17 | 54.48 |
| 59. | 2022/12/31 | -5.23% | -5.90% | 42.21 | 43.08 | 42.64 |
| トータル (Σ): | 3,730.14 | 1,691.48 | 2,116.54 | |||
すべて表示
分散CSX = Σ(RCSX,t–RCSX)2 ÷ (59 – 1)
= 3,730.14 ÷ (59 – 1)
= 64.31
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CSX, S&P 500 = Σ(RCSX,t–RCSX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,116.54 ÷ (59 – 1)
= 36.49
システマティックリスク推定 (β)
| 分散CSX | 64.31 |
| 分散S&P 500 | 29.16 |
| 共 分散CSX, S&P 500 | 36.49 |
| 相関係数CSX, S&P 5001 | 0.84 |
| βCSX2 | 1.25 |
| αCSX3 | 0.43% |
計算
1 相関係数CSX, S&P 500
= 共 分散CSX, S&P 500 ÷ (標準偏差CSX × 標準偏差S&P 500)
= 36.49 ÷ (8.02% × 5.40%)
= 0.84
2 βCSX
= 共 分散CSX, S&P 500 ÷ 分散S&P 500
= 36.49 ÷ 29.16
= 1.25
3 αCSX
= 平均CSX – βCSX × 平均S&P 500
= 1.27% – 1.25 × 0.67%
= 0.43%
期待収益率
| 仮定 | ||
| LT財務省総合の収益率1 | RF | 4.90% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.55% |
| 普通株式 CSX システマティックリスク | βCSX | 1.25 |
| CSX普通株式の期待収益率3 | E(RCSX) | 15.72% |
1 10年以内に期限が到来またはコール可能でないすべての固定クーポン米国債の入札利回りの非加重平均(リスクフリー収益率プロキシ)。
2 詳細を見る »
3 E(RCSX) = RF + βCSX [E(RM) – RF]
= 4.90% + 1.25 [13.55% – 4.90%]
= 15.72%