資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 T-Mobile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
T-Mobile US Inc.、月間収益率
| T-Mobile US Inc. (TMUS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格TMUS,t1 | 配当TMUS,t1 | RTMUS,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2020/01/31 | $79.19 | 3,225.52 | ||||
| 1. | 2020/02/29 | $90.16 | 13.85% | 2,954.22 | -8.41% | |
| 2. | 2020/03/31 | $83.90 | -6.94% | 2,584.59 | -12.51% | |
| 3. | 2020/04/30 | $87.80 | 4.65% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024/11/30 | $246.94 | $0.88 | 11.05% | 6,032.38 | 5.73% |
| 59. | 2024/12/31 | $220.73 | -10.61% | 5,881.63 | -2.50% | |
| 平均 (R): | 1.99% | 1.16% | ||||
| 標準偏差： | 6.59% | 5.28% | ||||
| T-Mobile US Inc. (TMUS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格TMUS,t1 | 配当TMUS,t1 | RTMUS,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2020/01/31 | $79.19 | 3,225.52 | ||||
| 1. | 2020/02/29 | $90.16 | 13.85% | 2,954.22 | -8.41% | |
| 2. | 2020/03/31 | $83.90 | -6.94% | 2,584.59 | -12.51% | |
| 3. | 2020/04/30 | $87.80 | 4.65% | 2,912.43 | 12.68% | |
| 4. | 2020/05/31 | $100.04 | 13.94% | 3,044.31 | 4.53% | |
| 5. | 2020/06/30 | $104.15 | 4.11% | 3,100.29 | 1.84% | |
| 6. | 2020/07/31 | $107.38 | 3.10% | 3,271.12 | 5.51% | |
| 7. | 2020/08/31 | $116.68 | 8.66% | 3,500.31 | 7.01% | |
| 8. | 2020/09/30 | $114.36 | -1.99% | 3,363.00 | -3.92% | |
| 9. | 2020/10/31 | $109.57 | -4.19% | 3,269.96 | -2.77% | |
| 10. | 2020/11/30 | $132.94 | 21.33% | 3,621.63 | 10.75% | |
| 11. | 2020/12/31 | $134.85 | 1.44% | 3,756.07 | 3.71% | |
| 12. | 2021/01/31 | $126.08 | -6.50% | 3,714.24 | -1.11% | |
| 13. | 2021/02/28 | $119.97 | -4.85% | 3,811.15 | 2.61% | |
| 14. | 2021/03/31 | $125.29 | 4.43% | 3,972.89 | 4.24% | |
| 15. | 2021/04/30 | $132.13 | 5.46% | 4,181.17 | 5.24% | |
| 16. | 2021/05/31 | $141.45 | 7.05% | 4,204.11 | 0.55% | |
| 17. | 2021/06/30 | $144.83 | 2.39% | 4,297.50 | 2.22% | |
| 18. | 2021/07/31 | $144.02 | -0.56% | 4,395.26 | 2.27% | |
| 19. | 2021/08/31 | $137.02 | -4.86% | 4,522.68 | 2.90% | |
| 20. | 2021/09/30 | $127.76 | -6.76% | 4,307.54 | -4.76% | |
| 21. | 2021/10/31 | $115.03 | -9.96% | 4,605.38 | 6.91% | |
| 22. | 2021/11/30 | $108.81 | -5.41% | 4,567.00 | -0.83% | |
| 23. | 2021/12/31 | $115.98 | 6.59% | 4,766.18 | 4.36% | |
| 24. | 2022/01/31 | $108.17 | -6.73% | 4,515.55 | -5.26% | |
| 25. | 2022/02/28 | $123.21 | 13.90% | 4,373.94 | -3.14% | |
| 26. | 2022/03/31 | $128.35 | 4.17% | 4,530.41 | 3.58% | |
| 27. | 2022/04/30 | $123.14 | -4.06% | 4,131.93 | -8.80% | |
| 28. | 2022/05/31 | $133.29 | 8.24% | 4,132.15 | 0.01% | |
| 29. | 2022/06/30 | $134.54 | 0.94% | 3,785.38 | -8.39% | |
| 30. | 2022/07/31 | $143.06 | 6.33% | 4,130.29 | 9.11% | |
| 31. | 2022/08/31 | $143.96 | 0.63% | 3,955.00 | -4.24% | |
| 32. | 2022/09/30 | $134.17 | -6.80% | 3,585.62 | -9.34% | |
| 33. | 2022/10/31 | $151.56 | 12.96% | 3,871.98 | 7.99% | |
| 34. | 2022/11/30 | $151.46 | -0.07% | 4,080.11 | 5.38% | |
| 35. | 2022/12/31 | $140.00 | -7.57% | 3,839.50 | -5.90% | |
| 36. | 2023/01/31 | $149.31 | 6.65% | 4,076.60 | 6.18% | |
| 37. | 2023/02/28 | $142.18 | -4.78% | 3,970.15 | -2.61% | |
| 38. | 2023/03/31 | $144.84 | 1.87% | 4,109.31 | 3.51% | |
| 39. | 2023/04/30 | $143.90 | -0.65% | 4,169.48 | 1.46% | |
| 40. | 2023/05/31 | $137.25 | -4.62% | 4,179.83 | 0.25% | |
| 41. | 2023/06/30 | $138.90 | 1.20% | 4,376.86 | 4.71% | |
| 42. | 2023/07/31 | $137.77 | -0.81% | 4,588.96 | 4.85% | |
| 43. | 2023/08/31 | $136.25 | -1.10% | 4,507.66 | -1.77% | |
| 44. | 2023/09/30 | $140.05 | 2.79% | 4,288.05 | -4.87% | |
| 45. | 2023/10/31 | $143.86 | 2.72% | 4,193.80 | -2.20% | |
| 46. | 2023/11/30 | $150.45 | $0.65 | 5.03% | 4,567.80 | 8.92% |
| 47. | 2023/12/31 | $160.33 | 6.57% | 4,769.83 | 4.42% | |
| 48. | 2024/01/31 | $161.23 | 0.56% | 4,845.65 | 1.59% | |
| 49. | 2024/02/29 | $163.30 | $0.65 | 1.69% | 5,096.27 | 5.17% |
| 50. | 2024/03/31 | $163.22 | -0.05% | 5,254.35 | 3.10% | |
| 51. | 2024/04/30 | $164.17 | 0.58% | 5,035.69 | -4.16% | |
| 52. | 2024/05/31 | $174.96 | $0.65 | 6.97% | 5,277.51 | 4.80% |
| 53. | 2024/06/30 | $176.18 | 0.70% | 5,460.48 | 3.47% | |
| 54. | 2024/07/31 | $182.28 | 3.46% | 5,522.30 | 1.13% | |
| 55. | 2024/08/31 | $198.72 | $0.65 | 9.38% | 5,648.40 | 2.28% |
| 56. | 2024/09/30 | $206.36 | 3.84% | 5,762.48 | 2.02% | |
| 57. | 2024/10/31 | $223.16 | 8.14% | 5,705.45 | -0.99% | |
| 58. | 2024/11/30 | $246.94 | $0.88 | 11.05% | 6,032.38 | 5.73% |
| 59. | 2024/12/31 | $220.73 | -10.61% | 5,881.63 | -2.50% | |
| 平均 (R): | 1.99% | 1.16% | ||||
| 標準偏差： | 6.59% | 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TMUS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
T-Mobile US Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RTMUS,t | RS&P 500,t | (RTMUS,t–RTMUS)2 | (RS&P 500,t–RS&P 500)2 | (RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020/02/29 | 13.85% | -8.41% | 140.68 | 91.63 | -113.54 |
| 2. | 2020/03/31 | -6.94% | -12.51% | 79.83 | 186.96 | 122.17 |
| 3. | 2020/04/30 | 4.65% | 12.68% | 7.06 | 132.78 | 30.61 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024/11/30 | 11.05% | 5.73% | 82.06 | 20.87 | 41.39 |
| 59. | 2024/12/31 | -10.61% | -2.50% | 158.90 | 13.40 | 46.14 |
| トータル (Σ): | 2,515.13 | 1,618.62 | 902.53 | |||
| t | 日付 | RTMUS,t | RS&P 500,t | (RTMUS,t–RTMUS)2 | (RS&P 500,t–RS&P 500)2 | (RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020/02/29 | 13.85% | -8.41% | 140.68 | 91.63 | -113.54 |
| 2. | 2020/03/31 | -6.94% | -12.51% | 79.83 | 186.96 | 122.17 |
| 3. | 2020/04/30 | 4.65% | 12.68% | 7.06 | 132.78 | 30.61 |
| 4. | 2020/05/31 | 13.94% | 4.53% | 142.78 | 11.34 | 40.23 |
| 5. | 2020/06/30 | 4.11% | 1.84% | 4.48 | 0.46 | 1.43 |
| 6. | 2020/07/31 | 3.10% | 5.51% | 1.23 | 18.91 | 4.83 |
| 7. | 2020/08/31 | 8.66% | 7.01% | 44.48 | 34.17 | 38.98 |
| 8. | 2020/09/30 | -1.99% | -3.92% | 15.84 | 25.85 | 20.24 |
| 9. | 2020/10/31 | -4.19% | -2.77% | 38.20 | 15.43 | 24.28 |
| 10. | 2020/11/30 | 21.33% | 10.75% | 373.92 | 92.03 | 185.51 |
| 11. | 2020/12/31 | 1.44% | 3.71% | 0.31 | 6.51 | -1.42 |
| 12. | 2021/01/31 | -6.50% | -1.11% | 72.17 | 5.18 | 19.33 |
| 13. | 2021/02/28 | -4.85% | 2.61% | 46.76 | 2.10 | -9.90 |
| 14. | 2021/03/31 | 4.43% | 4.24% | 5.97 | 9.50 | 7.53 |
| 15. | 2021/04/30 | 5.46% | 5.24% | 12.02 | 16.66 | 14.15 |
| 16. | 2021/05/31 | 7.05% | 0.55% | 25.62 | 0.38 | -3.10 |
| 17. | 2021/06/30 | 2.39% | 2.22% | 0.16 | 1.12 | 0.42 |
| 18. | 2021/07/31 | -0.56% | 2.27% | 6.51 | 1.24 | -2.84 |
| 19. | 2021/08/31 | -4.86% | 2.90% | 46.95 | 3.02 | -11.91 |
| 20. | 2021/09/30 | -6.76% | -4.76% | 76.56 | 35.02 | 51.78 |
| 21. | 2021/10/31 | -9.96% | 6.91% | 142.94 | 33.10 | -68.78 |
| 22. | 2021/11/30 | -5.41% | -0.83% | 54.75 | 3.98 | 14.76 |
| 23. | 2021/12/31 | 6.59% | 4.36% | 21.14 | 10.24 | 14.71 |
| 24. | 2022/01/31 | -6.73% | -5.26% | 76.14 | 41.21 | 56.02 |
| 25. | 2022/02/28 | 13.90% | -3.14% | 141.90 | 18.47 | -51.19 |
| 26. | 2022/03/31 | 4.17% | 3.58% | 4.75 | 5.84 | 5.27 |
| 27. | 2022/04/30 | -4.06% | -8.80% | 36.61 | 99.14 | 60.25 |
| 28. | 2022/05/31 | 8.24% | 0.01% | 39.07 | 1.34 | -7.23 |
| 29. | 2022/06/30 | 0.94% | -8.39% | 1.11 | 91.26 | 10.07 |
| 30. | 2022/07/31 | 6.33% | 9.11% | 18.84 | 63.21 | 34.51 |
| 31. | 2022/08/31 | 0.63% | -4.24% | 1.86 | 29.22 | 7.37 |
| 32. | 2022/09/30 | -6.80% | -9.34% | 77.30 | 110.27 | 92.33 |
| 33. | 2022/10/31 | 12.96% | 7.99% | 120.33 | 46.58 | 74.87 |
| 34. | 2022/11/30 | -0.07% | 5.38% | 4.23 | 17.76 | -8.67 |
| 35. | 2022/12/31 | -7.57% | -5.90% | 91.36 | 49.82 | 67.47 |
| 36. | 2023/01/31 | 6.65% | 6.18% | 21.70 | 25.14 | 23.36 |
| 37. | 2023/02/28 | -4.78% | -2.61% | 45.79 | 14.23 | 25.53 |
| 38. | 2023/03/31 | 1.87% | 3.51% | 0.01 | 5.49 | -0.28 |
| 39. | 2023/04/30 | -0.65% | 1.46% | 6.97 | 0.09 | -0.80 |
| 40. | 2023/05/31 | -4.62% | 0.25% | 43.73 | 0.83 | 6.04 |
| 41. | 2023/06/30 | 1.20% | 4.71% | 0.62 | 12.62 | -2.81 |
| 42. | 2023/07/31 | -0.81% | 4.85% | 7.87 | 13.58 | -10.34 |
| 43. | 2023/08/31 | -1.10% | -1.77% | 9.58 | 8.60 | 9.08 |
| 44. | 2023/09/30 | 2.79% | -4.87% | 0.64 | 36.40 | -4.81 |
| 45. | 2023/10/31 | 2.72% | -2.20% | 0.53 | 11.28 | -2.45 |
| 46. | 2023/11/30 | 5.03% | 8.92% | 9.25 | 60.17 | 23.59 |
| 47. | 2023/12/31 | 6.57% | 4.42% | 20.93 | 10.64 | 14.92 |
| 48. | 2024/01/31 | 0.56% | 1.59% | 2.05 | 0.18 | -0.61 |
| 49. | 2024/02/29 | 1.69% | 5.17% | 0.09 | 16.09 | -1.22 |
| 50. | 2024/03/31 | -0.05% | 3.10% | 4.16 | 3.77 | -3.96 |
| 51. | 2024/04/30 | 0.58% | -4.16% | 1.99 | 28.33 | 7.50 |
| 52. | 2024/05/31 | 6.97% | 4.80% | 24.77 | 13.26 | 18.12 |
| 53. | 2024/06/30 | 0.70% | 3.47% | 1.68 | 5.32 | -2.98 |
| 54. | 2024/07/31 | 3.46% | 1.13% | 2.16 | 0.00 | -0.04 |
| 55. | 2024/08/31 | 9.38% | 2.28% | 54.52 | 1.26 | 8.29 |
| 56. | 2024/09/30 | 3.84% | 2.02% | 3.43 | 0.74 | 1.59 |
| 57. | 2024/10/31 | 8.14% | -0.99% | 37.81 | 4.63 | -13.23 |
| 58. | 2024/11/30 | 11.05% | 5.73% | 82.06 | 20.87 | 41.39 |
| 59. | 2024/12/31 | -10.61% | -2.50% | 158.90 | 13.40 | 46.14 |
| トータル (Σ): | 2,515.13 | 1,618.62 | 902.53 | |||
すべて表示
分散TMUS = Σ(RTMUS,t–RTMUS)2 ÷ (59 – 1)
= 2,515.13 ÷ (59 – 1)
= 43.36
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TMUS, S&P 500 = Σ(RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 902.53 ÷ (59 – 1)
= 15.56
システマティックなリスク推定 (β)
| 分散TMUS | 43.36 |
| 分散S&P 500 | 27.91 |
| 共 分散TMUS, S&P 500 | 15.56 |
| 相関係数TMUS, S&P 5001 | 0.45 |
| βTMUS2 | 0.56 |
| αTMUS3 | 1.34% |
計算
1 相関係数TMUS, S&P 500
= 共 分散TMUS, S&P 500 ÷ (標準偏差TMUS × 標準偏差S&P 500)
= 15.56 ÷ (6.59% × 5.28%)
= 0.45
2 βTMUS
= 共 分散TMUS, S&P 500 ÷ 分散S&P 500
= 15.56 ÷ 27.91
= 0.56
3 αTMUS
= 平均TMUS – βTMUS × 平均S&P 500
= 1.99% – 0.56 × 1.16%
= 1.34%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.81% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.72% |
| 普通株式 T-Mobile システマティックリスク | βTMUS | 0.56 |
| T-Mobile普通株式の期待収益率3 | E(RTMUS) | 10.33% |
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(RTMUS) = RF + βTMUS [E(RM) – RF]
= 4.81% + 0.56 [14.72% – 4.81%]
= 10.33%