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 Dollar Tree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
Dollar Tree Inc.、月間収益率
| Dollar Tree Inc. (DLTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格DLTR,t1 | 配当DLTR,t1 | RDLTR,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2016/02/29 | $80.25 | 1,932.23 | ||||
| 1. | 2016/03/31 | $82.46 | 2.75% | 2,059.74 | 6.60% | |
| 2. | 2016/04/30 | $79.71 | -3.33% | 2,065.30 | 0.27% | |
| 3. | 2016/05/31 | $90.54 | 13.59% | 2,096.95 | 1.53% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2021/12/31 | $140.52 | 5.00% | 4,766.18 | 4.36% | |
| 71. | 2022/01/31 | $131.22 | -6.62% | 4,515.55 | -5.26% | |
| 平均 (R): | 1.08% | 1.29% | ||||
| 標準偏差： | 8.96% | 4.25% | ||||
| Dollar Tree Inc. (DLTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格DLTR,t1 | 配当DLTR,t1 | RDLTR,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2016/02/29 | $80.25 | 1,932.23 | ||||
| 1. | 2016/03/31 | $82.46 | 2.75% | 2,059.74 | 6.60% | |
| 2. | 2016/04/30 | $79.71 | -3.33% | 2,065.30 | 0.27% | |
| 3. | 2016/05/31 | $90.54 | 13.59% | 2,096.95 | 1.53% | |
| 4. | 2016/06/30 | $94.24 | 4.09% | 2,098.86 | 0.09% | |
| 5. | 2016/07/31 | $96.29 | 2.18% | 2,173.60 | 3.56% | |
| 6. | 2016/08/31 | $82.70 | -14.11% | 2,170.95 | -0.12% | |
| 7. | 2016/09/30 | $78.93 | -4.56% | 2,168.27 | -0.12% | |
| 8. | 2016/10/31 | $75.55 | -4.28% | 2,126.15 | -1.94% | |
| 9. | 2016/11/30 | $88.16 | 16.69% | 2,198.81 | 3.42% | |
| 10. | 2016/12/31 | $77.18 | -12.45% | 2,238.83 | 1.82% | |
| 11. | 2017/01/31 | $77.19 | 0.01% | 2,278.87 | 1.79% | |
| 12. | 2017/02/28 | $76.68 | -0.66% | 2,363.64 | 3.72% | |
| 13. | 2017/03/31 | $78.46 | 2.32% | 2,362.72 | -0.04% | |
| 14. | 2017/04/30 | $82.77 | 5.49% | 2,384.20 | 0.91% | |
| 15. | 2017/05/31 | $77.70 | -6.13% | 2,411.80 | 1.16% | |
| 16. | 2017/06/30 | $69.92 | -10.01% | 2,423.41 | 0.48% | |
| 17. | 2017/07/31 | $72.08 | 3.09% | 2,470.30 | 1.93% | |
| 18. | 2017/08/31 | $79.64 | 10.49% | 2,471.65 | 0.05% | |
| 19. | 2017/09/30 | $86.82 | 9.02% | 2,519.36 | 1.93% | |
| 20. | 2017/10/31 | $91.25 | 5.10% | 2,575.26 | 2.22% | |
| 21. | 2017/11/30 | $102.76 | 12.61% | 2,647.58 | 2.81% | |
| 22. | 2017/12/31 | $107.31 | 4.43% | 2,673.61 | 0.98% | |
| 23. | 2018/01/31 | $115.00 | 7.17% | 2,823.81 | 5.62% | |
| 24. | 2018/02/28 | $102.64 | -10.75% | 2,713.83 | -3.89% | |
| 25. | 2018/03/31 | $94.90 | -7.54% | 2,640.87 | -2.69% | |
| 26. | 2018/04/30 | $95.89 | 1.04% | 2,648.05 | 0.27% | |
| 27. | 2018/05/31 | $82.59 | -13.87% | 2,705.27 | 2.16% | |
| 28. | 2018/06/30 | $85.00 | 2.92% | 2,718.37 | 0.48% | |
| 29. | 2018/07/31 | $91.28 | 7.39% | 2,816.29 | 3.60% | |
| 30. | 2018/08/31 | $80.51 | -11.80% | 2,901.52 | 3.03% | |
| 31. | 2018/09/30 | $81.55 | 1.29% | 2,913.98 | 0.43% | |
| 32. | 2018/10/31 | $84.30 | 3.37% | 2,711.74 | -6.94% | |
| 33. | 2018/11/30 | $86.77 | 2.93% | 2,760.17 | 1.79% | |
| 34. | 2018/12/31 | $90.32 | 4.09% | 2,506.85 | -9.18% | |
| 35. | 2019/01/31 | $96.83 | 7.21% | 2,704.10 | 7.87% | |
| 36. | 2019/02/28 | $96.33 | -0.52% | 2,784.49 | 2.97% | |
| 37. | 2019/03/31 | $105.04 | 9.04% | 2,834.40 | 1.79% | |
| 38. | 2019/04/30 | $111.28 | 5.94% | 2,945.83 | 3.93% | |
| 39. | 2019/05/31 | $101.59 | -8.71% | 2,752.06 | -6.58% | |
| 40. | 2019/06/30 | $107.39 | 5.71% | 2,941.76 | 6.89% | |
| 41. | 2019/07/31 | $101.75 | -5.25% | 2,980.38 | 1.31% | |
| 42. | 2019/08/31 | $101.53 | -0.22% | 2,926.46 | -1.81% | |
| 43. | 2019/09/30 | $114.16 | 12.44% | 2,976.74 | 1.72% | |
| 44. | 2019/10/31 | $110.40 | -3.29% | 3,037.56 | 2.04% | |
| 45. | 2019/11/30 | $91.46 | -17.16% | 3,140.98 | 3.40% | |
| 46. | 2019/12/31 | $94.05 | 2.83% | 3,230.78 | 2.86% | |
| 47. | 2020/01/31 | $87.07 | -7.42% | 3,225.52 | -0.16% | |
| 48. | 2020/02/29 | $83.03 | -4.64% | 2,954.22 | -8.41% | |
| 49. | 2020/03/31 | $73.47 | -11.51% | 2,584.59 | -12.51% | |
| 50. | 2020/04/30 | $79.67 | 8.44% | 2,912.43 | 12.68% | |
| 51. | 2020/05/31 | $97.87 | 22.84% | 3,044.31 | 4.53% | |
| 52. | 2020/06/30 | $92.68 | -5.30% | 3,100.29 | 1.84% | |
| 53. | 2020/07/31 | $93.35 | 0.72% | 3,271.12 | 5.51% | |
| 54. | 2020/08/31 | $96.27 | 3.13% | 3,500.31 | 7.01% | |
| 55. | 2020/09/30 | $91.34 | -5.12% | 3,363.00 | -3.92% | |
| 56. | 2020/10/31 | $90.32 | -1.12% | 3,269.96 | -2.77% | |
| 57. | 2020/11/30 | $109.24 | 20.95% | 3,621.63 | 10.75% | |
| 58. | 2020/12/31 | $108.04 | -1.10% | 3,756.07 | 3.71% | |
| 59. | 2021/01/31 | $101.66 | -5.91% | 3,714.24 | -1.11% | |
| 60. | 2021/02/28 | $98.20 | -3.40% | 3,811.15 | 2.61% | |
| 61. | 2021/03/31 | $114.46 | 16.56% | 3,972.89 | 4.24% | |
| 62. | 2021/04/30 | $114.90 | 0.38% | 4,181.17 | 5.24% | |
| 63. | 2021/05/31 | $97.50 | -15.14% | 4,204.11 | 0.55% | |
| 64. | 2021/06/30 | $99.50 | 2.05% | 4,297.50 | 2.22% | |
| 65. | 2021/07/31 | $99.79 | 0.29% | 4,395.26 | 2.27% | |
| 66. | 2021/08/31 | $90.54 | -9.27% | 4,522.68 | 2.90% | |
| 67. | 2021/09/30 | $95.72 | 5.72% | 4,307.54 | -4.76% | |
| 68. | 2021/10/31 | $107.76 | 12.58% | 4,605.38 | 6.91% | |
| 69. | 2021/11/30 | $133.83 | 24.19% | 4,567.00 | -0.83% | |
| 70. | 2021/12/31 | $140.52 | 5.00% | 4,766.18 | 4.36% | |
| 71. | 2022/01/31 | $131.22 | -6.62% | 4,515.55 | -5.26% | |
| 平均 (R): | 1.08% | 1.29% | ||||
| 標準偏差： | 8.96% | 4.25% | ||||
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DLTR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
Dollar Tree Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RDLTR,t | RS&P 500,t | (RDLTR,t–RDLTR)2 | (RS&P 500,t–RS&P 500)2 | (RDLTR,t–RDLTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2016/03/31 | 2.75% | 6.60% | 2.79 | 28.16 | 8.87 |
| 2. | 2016/04/30 | -3.33% | 0.27% | 19.52 | 1.05 | 4.52 |
| 3. | 2016/05/31 | 13.59% | 1.53% | 156.34 | 0.06 | 3.00 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2021/12/31 | 5.00% | 4.36% | 15.33 | 9.42 | 12.02 |
| 71. | 2022/01/31 | -6.62% | -5.26% | 59.31 | 42.91 | 50.45 |
| トータル (Σ): | 5,617.47 | 1,262.70 | 1,008.02 | |||
| t | 日付 | RDLTR,t | RS&P 500,t | (RDLTR,t–RDLTR)2 | (RS&P 500,t–RS&P 500)2 | (RDLTR,t–RDLTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2016/03/31 | 2.75% | 6.60% | 2.79 | 28.16 | 8.87 |
| 2. | 2016/04/30 | -3.33% | 0.27% | 19.52 | 1.05 | 4.52 |
| 3. | 2016/05/31 | 13.59% | 1.53% | 156.34 | 0.06 | 3.00 |
| 4. | 2016/06/30 | 4.09% | 0.09% | 9.02 | 1.44 | -3.61 |
| 5. | 2016/07/31 | 2.18% | 3.56% | 1.19 | 5.15 | 2.48 |
| 6. | 2016/08/31 | -14.11% | -0.12% | 230.94 | 2.00 | 21.49 |
| 7. | 2016/09/30 | -4.56% | -0.12% | 31.83 | 2.00 | 7.99 |
| 8. | 2016/10/31 | -4.28% | -1.94% | 28.79 | 10.46 | 17.36 |
| 9. | 2016/11/30 | 16.69% | 3.42% | 243.61 | 4.52 | 33.17 |
| 10. | 2016/12/31 | -12.45% | 1.82% | 183.27 | 0.28 | -7.15 |
| 11. | 2017/01/31 | 0.01% | 1.79% | 1.14 | 0.25 | -0.53 |
| 12. | 2017/02/28 | -0.66% | 3.72% | 3.04 | 5.89 | -4.23 |
| 13. | 2017/03/31 | 2.32% | -0.04% | 1.53 | 1.77 | -1.65 |
| 14. | 2017/04/30 | 5.49% | 0.91% | 19.45 | 0.15 | -1.69 |
| 15. | 2017/05/31 | -6.13% | 1.16% | 51.96 | 0.02 | 0.97 |
| 16. | 2017/06/30 | -10.01% | 0.48% | 123.12 | 0.66 | 9.00 |
| 17. | 2017/07/31 | 3.09% | 1.93% | 4.03 | 0.41 | 1.29 |
| 18. | 2017/08/31 | 10.49% | 0.05% | 88.46 | 1.53 | -11.64 |
| 19. | 2017/09/30 | 9.02% | 1.93% | 62.93 | 0.41 | 5.06 |
| 20. | 2017/10/31 | 5.10% | 2.22% | 16.16 | 0.86 | 3.72 |
| 21. | 2017/11/30 | 12.61% | 2.81% | 132.96 | 2.30 | 17.48 |
| 22. | 2017/12/31 | 4.43% | 0.98% | 11.19 | 0.10 | -1.03 |
| 23. | 2018/01/31 | 7.17% | 5.62% | 37.01 | 18.71 | 26.31 |
| 24. | 2018/02/28 | -10.75% | -3.89% | 139.97 | 26.90 | 61.37 |
| 25. | 2018/03/31 | -7.54% | -2.69% | 74.37 | 15.85 | 34.33 |
| 26. | 2018/04/30 | 1.04% | 0.27% | 0.00 | 1.04 | 0.04 |
| 27. | 2018/05/31 | -13.87% | 2.16% | 223.59 | 0.75 | -12.99 |
| 28. | 2018/06/30 | 2.92% | 0.48% | 3.37 | 0.65 | -1.48 |
| 29. | 2018/07/31 | 7.39% | 3.60% | 39.76 | 5.34 | 14.56 |
| 30. | 2018/08/31 | -11.80% | 3.03% | 165.94 | 3.01 | -22.34 |
| 31. | 2018/09/30 | 1.29% | 0.43% | 0.04 | 0.74 | -0.18 |
| 32. | 2018/10/31 | 3.37% | -6.94% | 5.24 | 67.78 | -18.85 |
| 33. | 2018/11/30 | 2.93% | 1.79% | 3.41 | 0.24 | 0.91 |
| 34. | 2018/12/31 | 4.09% | -9.18% | 9.05 | 109.62 | -31.50 |
| 35. | 2019/01/31 | 7.21% | 7.87% | 37.51 | 43.25 | 40.28 |
| 36. | 2019/02/28 | -0.52% | 2.97% | 2.56 | 2.82 | -2.69 |
| 37. | 2019/03/31 | 9.04% | 1.79% | 63.34 | 0.25 | 3.98 |
| 38. | 2019/04/30 | 5.94% | 3.93% | 23.60 | 6.96 | 12.82 |
| 39. | 2019/05/31 | -8.71% | -6.58% | 95.86 | 61.94 | 77.05 |
| 40. | 2019/06/30 | 5.71% | 6.89% | 21.40 | 31.37 | 25.91 |
| 41. | 2019/07/31 | -5.25% | 1.31% | 40.13 | 0.00 | -0.13 |
| 42. | 2019/08/31 | -0.22% | -1.81% | 1.69 | 9.62 | 4.03 |
| 43. | 2019/09/30 | 12.44% | 1.72% | 128.97 | 0.18 | 4.84 |
| 44. | 2019/10/31 | -3.29% | 2.04% | 19.15 | 0.56 | -3.29 |
| 45. | 2019/11/30 | -17.16% | 3.40% | 332.65 | 4.46 | -38.53 |
| 46. | 2019/12/31 | 2.83% | 2.86% | 3.06 | 2.45 | 2.74 |
| 47. | 2020/01/31 | -7.42% | -0.16% | 72.33 | 2.12 | 12.37 |
| 48. | 2020/02/29 | -4.64% | -8.41% | 32.75 | 94.15 | 55.53 |
| 49. | 2020/03/31 | -11.51% | -12.51% | 158.68 | 190.56 | 173.89 |
| 50. | 2020/04/30 | 8.44% | 12.68% | 54.11 | 129.78 | 83.80 |
| 51. | 2020/05/31 | 22.84% | 4.53% | 473.55 | 10.47 | 70.42 |
| 52. | 2020/06/30 | -5.30% | 1.84% | 40.78 | 0.30 | -3.49 |
| 53. | 2020/07/31 | 0.72% | 5.51% | 0.13 | 17.79 | -1.52 |
| 54. | 2020/08/31 | 3.13% | 7.01% | 4.18 | 32.65 | 11.69 |
| 55. | 2020/09/30 | -5.12% | -3.92% | 38.49 | 27.20 | 32.35 |
| 56. | 2020/10/31 | -1.12% | -2.77% | 4.84 | 16.47 | 8.93 |
| 57. | 2020/11/30 | 20.95% | 10.75% | 394.61 | 89.54 | 187.97 |
| 58. | 2020/12/31 | -1.10% | 3.71% | 4.76 | 5.86 | -5.28 |
| 59. | 2021/01/31 | -5.91% | -1.11% | 48.83 | 5.79 | 16.81 |
| 60. | 2021/02/28 | -3.40% | 2.61% | 20.13 | 1.73 | -5.91 |
| 61. | 2021/03/31 | 16.56% | 4.24% | 239.48 | 8.71 | 45.68 |
| 62. | 2021/04/30 | 0.38% | 5.24% | 0.49 | 15.60 | -2.76 |
| 63. | 2021/05/31 | -15.14% | 0.55% | 263.30 | 0.55 | 12.07 |
| 64. | 2021/06/30 | 2.05% | 2.22% | 0.94 | 0.86 | 0.90 |
| 65. | 2021/07/31 | 0.29% | 2.27% | 0.63 | 0.97 | -0.78 |
| 66. | 2021/08/31 | -9.27% | 2.90% | 107.17 | 2.58 | -16.63 |
| 67. | 2021/09/30 | 5.72% | -4.76% | 21.51 | 36.59 | -28.06 |
| 68. | 2021/10/31 | 12.58% | 6.91% | 132.14 | 31.61 | 64.63 |
| 69. | 2021/11/30 | 24.19% | -0.83% | 534.06 | 4.52 | -49.12 |
| 70. | 2021/12/31 | 5.00% | 4.36% | 15.33 | 9.42 | 12.02 |
| 71. | 2022/01/31 | -6.62% | -5.26% | 59.31 | 42.91 | 50.45 |
| トータル (Σ): | 5,617.47 | 1,262.70 | 1,008.02 | |||
すべて表示
分散DLTR = Σ(RDLTR,t–RDLTR)2 ÷ (71 – 1)
= 5,617.47 ÷ (71 – 1)
= 80.25
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04
共 分散DLTR, S&P 500 = Σ(RDLTR,t–RDLTR)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,008.02 ÷ (71 – 1)
= 14.40
システマティックなリスク推定 (β)
| 分散DLTR | 80.25 |
| 分散S&P 500 | 18.04 |
| 共 分散DLTR, S&P 500 | 14.40 |
| 相関係数DLTR, S&P 5001 | 0.38 |
| βDLTR2 | 0.80 |
| αDLTR3 | 0.05% |
計算
1 相関係数DLTR, S&P 500
= 共 分散DLTR, S&P 500 ÷ (標準偏差DLTR × 標準偏差S&P 500)
= 14.40 ÷ (8.96% × 4.25%)
= 0.38
2 βDLTR
= 共 分散DLTR, S&P 500 ÷ 分散S&P 500
= 14.40 ÷ 18.04
= 0.80
3 αDLTR
= 平均DLTR – βDLTR × 平均S&P 500
= 1.08% – 0.80 × 1.29%
= 0.05%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.49% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.94% |
| 普通株式のシステマティックリスクDollar Tree | βDLTR | 0.80 |
| Dollar Tree普通株式の期待収益率3 | E(RDLTR) | 12.83% |
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(RDLTR) = RF + βDLTR [E(RM) – RF]
= 4.49% + 0.80 [14.94% – 4.49%]
= 12.83%