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 TPL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
Texas Pacific Land Corp.、月間収益率
| Texas Pacific Land Corp. (TPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格TPL,t1 | 配当TPL,t1 | RTPL,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $231.80 | 2,704.10 | ||||
| 1. | 2019/02/28 | $247.87 | 6.93% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $257.88 | $2.00 | 4.85% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $267.45 | 3.71% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | $557.32 | $1.0833 | -9.25% | 4,567.80 | 8.92% |
| 59. | 2023/12/31 | $524.15 | -5.95% | 4,769.83 | 4.42% | |
| 平均 (R): | 2.78% | 1.11% | ||||
| 標準偏差： | 16.07% | 5.31% | ||||
| Texas Pacific Land Corp. (TPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格TPL,t1 | 配当TPL,t1 | RTPL,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $231.80 | 2,704.10 | ||||
| 1. | 2019/02/28 | $247.87 | 6.93% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $257.88 | $2.00 | 4.85% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $267.45 | 3.71% | 2,945.83 | 3.93% | |
| 4. | 2019/05/31 | $245.67 | -8.14% | 2,752.06 | -6.58% | |
| 5. | 2019/06/30 | $262.33 | 6.78% | 2,941.76 | 6.89% | |
| 6. | 2019/07/31 | $265.73 | 1.30% | 2,980.38 | 1.31% | |
| 7. | 2019/08/31 | $218.40 | -17.81% | 2,926.46 | -1.81% | |
| 8. | 2019/09/30 | $216.52 | -0.86% | 2,976.74 | 1.72% | |
| 9. | 2019/10/31 | $189.68 | -12.40% | 3,037.56 | 2.04% | |
| 10. | 2019/11/30 | $224.99 | 18.62% | 3,140.98 | 3.40% | |
| 11. | 2019/12/31 | $260.41 | 15.74% | 3,230.78 | 2.86% | |
| 12. | 2020/01/31 | $251.90 | -3.27% | 3,225.52 | -0.16% | |
| 13. | 2020/02/29 | $231.93 | -7.93% | 2,954.22 | -8.41% | |
| 14. | 2020/03/31 | $126.67 | $5.3333 | -43.08% | 2,584.59 | -12.51% |
| 15. | 2020/04/30 | $189.88 | 49.90% | 2,912.43 | 12.68% | |
| 16. | 2020/05/31 | $195.46 | 2.94% | 3,044.31 | 4.53% | |
| 17. | 2020/06/30 | $198.23 | 1.42% | 3,100.29 | 1.84% | |
| 18. | 2020/07/31 | $177.66 | -10.38% | 3,271.12 | 5.51% | |
| 19. | 2020/08/31 | $175.57 | -1.18% | 3,500.31 | 7.01% | |
| 20. | 2020/09/30 | $150.52 | -14.27% | 3,363.00 | -3.92% | |
| 21. | 2020/10/31 | $150.14 | -0.25% | 3,269.96 | -2.77% | |
| 22. | 2020/11/30 | $203.31 | 35.41% | 3,621.63 | 10.75% | |
| 23. | 2020/12/31 | $242.33 | $3.3333 | 20.83% | 3,756.07 | 3.71% |
| 24. | 2021/01/31 | $277.41 | 14.48% | 3,714.24 | -1.11% | |
| 25. | 2021/02/28 | $368.01 | 32.66% | 3,811.15 | 2.61% | |
| 26. | 2021/03/31 | $529.81 | $0.9167 | 44.22% | 3,972.89 | 4.24% |
| 27. | 2021/04/30 | $513.38 | -3.10% | 4,181.17 | 5.24% | |
| 28. | 2021/05/31 | $484.37 | -5.65% | 4,204.11 | 0.55% | |
| 29. | 2021/06/30 | $533.25 | $0.9167 | 10.28% | 4,297.50 | 2.22% |
| 30. | 2021/07/31 | $497.52 | -6.70% | 4,395.26 | 2.27% | |
| 31. | 2021/08/31 | $453.25 | -8.90% | 4,522.68 | 2.90% | |
| 32. | 2021/09/30 | $403.12 | $0.9167 | -10.86% | 4,307.54 | -4.76% |
| 33. | 2021/10/31 | $424.56 | 5.32% | 4,605.38 | 6.91% | |
| 34. | 2021/11/30 | $402.92 | -5.10% | 4,567.00 | -0.83% | |
| 35. | 2021/12/31 | $416.29 | $0.9167 | 3.55% | 4,766.18 | 4.36% |
| 36. | 2022/01/31 | $358.33 | -13.92% | 4,515.55 | -5.26% | |
| 37. | 2022/02/28 | $396.24 | 10.58% | 4,373.94 | -3.14% | |
| 38. | 2022/03/31 | $450.70 | $1.00 | 14.00% | 4,530.41 | 3.58% |
| 39. | 2022/04/30 | $455.53 | 1.07% | 4,131.93 | -8.80% | |
| 40. | 2022/05/31 | $522.00 | 14.59% | 4,132.15 | 0.01% | |
| 41. | 2022/06/30 | $496.01 | $7.6667 | -3.51% | 3,785.38 | -8.39% |
| 42. | 2022/07/31 | $611.28 | 23.24% | 4,130.29 | 9.11% | |
| 43. | 2022/08/31 | $613.49 | 0.36% | 3,955.00 | -4.24% | |
| 44. | 2022/09/30 | $592.41 | $1.00 | -3.27% | 3,585.62 | -9.34% |
| 45. | 2022/10/31 | $767.96 | 29.63% | 3,871.98 | 7.99% | |
| 46. | 2022/11/30 | $864.18 | 12.53% | 4,080.11 | 5.38% | |
| 47. | 2022/12/31 | $781.41 | $1.00 | -9.46% | 3,839.50 | -5.90% |
| 48. | 2023/01/31 | $665.28 | -14.86% | 4,076.60 | 6.18% | |
| 49. | 2023/02/28 | $593.40 | -10.80% | 3,970.15 | -2.61% | |
| 50. | 2023/03/31 | $567.01 | $1.0833 | -4.26% | 4,109.31 | 3.51% |
| 51. | 2023/04/30 | $492.55 | -13.13% | 4,169.48 | 1.46% | |
| 52. | 2023/05/31 | $434.57 | -11.77% | 4,179.83 | 0.25% | |
| 53. | 2023/06/30 | $438.83 | $1.0833 | 1.23% | 4,376.86 | 4.71% |
| 54. | 2023/07/31 | $502.10 | 14.42% | 4,588.96 | 4.85% | |
| 55. | 2023/08/31 | $628.25 | $1.0833 | 25.34% | 4,507.66 | -1.77% |
| 56. | 2023/09/30 | $607.85 | -3.25% | 4,288.05 | -4.87% | |
| 57. | 2023/10/31 | $615.32 | 1.23% | 4,193.80 | -2.20% | |
| 58. | 2023/11/30 | $557.32 | $1.0833 | -9.25% | 4,567.80 | 8.92% |
| 59. | 2023/12/31 | $524.15 | -5.95% | 4,769.83 | 4.42% | |
| 平均 (R): | 2.78% | 1.11% | ||||
| 標準偏差： | 16.07% | 5.31% | ||||
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TPL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
Texas Pacific Land Corp.、分散の計算、および戻り値の共分散
| t | 日付 | RTPL,t | RS&P 500,t | (RTPL,t–RTPL)2 | (RS&P 500,t–RS&P 500)2 | (RTPL,t–RTPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 6.93% | 2.97% | 17.27 | 3.49 | 7.76 |
| 2. | 2019/03/31 | 4.85% | 1.79% | 4.28 | 0.47 | 1.42 |
| 3. | 2019/04/30 | 3.71% | 3.93% | 0.87 | 7.98 | 2.64 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | -9.25% | 8.92% | 144.64 | 61.03 | -93.95 |
| 59. | 2023/12/31 | -5.95% | 4.42% | 76.18 | 11.00 | -28.95 |
| トータル (Σ): | 14,984.07 | 1,634.30 | 2,655.68 | |||
| t | 日付 | RTPL,t | RS&P 500,t | (RTPL,t–RTPL)2 | (RS&P 500,t–RS&P 500)2 | (RTPL,t–RTPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 6.93% | 2.97% | 17.27 | 3.49 | 7.76 |
| 2. | 2019/03/31 | 4.85% | 1.79% | 4.28 | 0.47 | 1.42 |
| 3. | 2019/04/30 | 3.71% | 3.93% | 0.87 | 7.98 | 2.64 |
| 4. | 2019/05/31 | -8.14% | -6.58% | 119.25 | 59.04 | 83.91 |
| 5. | 2019/06/30 | 6.78% | 6.89% | 16.04 | 33.49 | 23.18 |
| 6. | 2019/07/31 | 1.30% | 1.31% | 2.19 | 0.04 | -0.31 |
| 7. | 2019/08/31 | -17.81% | -1.81% | 423.86 | 8.50 | 60.01 |
| 8. | 2019/09/30 | -0.86% | 1.72% | 13.23 | 0.37 | -2.23 |
| 9. | 2019/10/31 | -12.40% | 2.04% | 230.21 | 0.88 | -14.22 |
| 10. | 2019/11/30 | 18.62% | 3.40% | 250.87 | 5.28 | 36.41 |
| 11. | 2019/12/31 | 15.74% | 2.86% | 168.12 | 3.07 | 22.73 |
| 12. | 2020/01/31 | -3.27% | -0.16% | 36.54 | 1.61 | 7.67 |
| 13. | 2020/02/29 | -7.93% | -8.41% | 114.58 | 90.57 | 101.87 |
| 14. | 2020/03/31 | -43.08% | -12.51% | 2,103.27 | 185.44 | 624.53 |
| 15. | 2020/04/30 | 49.90% | 12.68% | 2,220.74 | 134.06 | 545.64 |
| 16. | 2020/05/31 | 2.94% | 4.53% | 0.03 | 11.71 | 0.55 |
| 17. | 2020/06/30 | 1.42% | 1.84% | 1.85 | 0.54 | -1.00 |
| 18. | 2020/07/31 | -10.38% | 5.51% | 173.01 | 19.40 | -57.93 |
| 19. | 2020/08/31 | -1.18% | 7.01% | 15.63 | 34.82 | -23.33 |
| 20. | 2020/09/30 | -14.27% | -3.92% | 290.51 | 25.29 | 85.71 |
| 21. | 2020/10/31 | -0.25% | -2.77% | 9.18 | 15.00 | 11.73 |
| 22. | 2020/11/30 | 35.41% | 10.75% | 1,065.17 | 93.10 | 314.91 |
| 23. | 2020/12/31 | 20.83% | 3.71% | 325.99 | 6.79 | 47.06 |
| 24. | 2021/01/31 | 14.48% | -1.11% | 136.88 | 4.93 | -25.97 |
| 25. | 2021/02/28 | 32.66% | 2.61% | 892.97 | 2.26 | 44.92 |
| 26. | 2021/03/31 | 44.22% | 4.24% | 1,717.16 | 9.85 | 130.04 |
| 27. | 2021/04/30 | -3.10% | 5.24% | 34.55 | 17.11 | -24.31 |
| 28. | 2021/05/31 | -5.65% | 0.55% | 71.02 | 0.31 | 4.70 |
| 29. | 2021/06/30 | 10.28% | 2.22% | 56.31 | 1.24 | 8.37 |
| 30. | 2021/07/31 | -6.70% | 2.27% | 89.81 | 1.37 | -11.08 |
| 31. | 2021/08/31 | -8.90% | 2.90% | 136.30 | 3.22 | -20.93 |
| 32. | 2021/09/30 | -10.86% | -4.76% | 185.90 | 34.37 | 79.94 |
| 33. | 2021/10/31 | 5.32% | 6.91% | 6.46 | 33.74 | 14.76 |
| 34. | 2021/11/30 | -5.10% | -0.83% | 61.99 | 3.76 | 15.27 |
| 35. | 2021/12/31 | 3.55% | 4.36% | 0.59 | 10.60 | 2.50 |
| 36. | 2022/01/31 | -13.92% | -5.26% | 278.88 | 40.51 | 106.28 |
| 37. | 2022/02/28 | 10.58% | -3.14% | 60.89 | 17.99 | -33.10 |
| 38. | 2022/03/31 | 14.00% | 3.58% | 125.89 | 6.11 | 27.73 |
| 39. | 2022/04/30 | 1.07% | -8.80% | 2.91 | 98.04 | 16.88 |
| 40. | 2022/05/31 | 14.59% | 0.01% | 139.60 | 1.21 | -13.00 |
| 41. | 2022/06/30 | -3.51% | -8.39% | 39.52 | 90.21 | 59.71 |
| 42. | 2022/07/31 | 23.24% | 9.11% | 418.73 | 64.09 | 163.82 |
| 43. | 2022/08/31 | 0.36% | -4.24% | 5.83 | 28.62 | 12.92 |
| 44. | 2022/09/30 | -3.27% | -9.34% | 36.60 | 109.11 | 63.19 |
| 45. | 2022/10/31 | 29.63% | 7.99% | 721.28 | 47.34 | 184.79 |
| 46. | 2022/11/30 | 12.53% | 5.38% | 95.11 | 18.23 | 41.64 |
| 47. | 2022/12/31 | -9.46% | -5.90% | 149.79 | 49.04 | 85.71 |
| 48. | 2023/01/31 | -14.86% | 6.18% | 311.11 | 25.70 | -89.42 |
| 49. | 2023/02/28 | -10.80% | -2.61% | 184.45 | 13.82 | 50.48 |
| 50. | 2023/03/31 | -4.26% | 3.51% | 49.58 | 5.76 | -16.89 |
| 51. | 2023/04/30 | -13.13% | 1.46% | 253.09 | 0.13 | -5.70 |
| 52. | 2023/05/31 | -11.77% | 0.25% | 211.64 | 0.74 | 12.48 |
| 53. | 2023/06/30 | 1.23% | 4.71% | 2.39 | 13.02 | -5.58 |
| 54. | 2023/07/31 | 14.42% | 4.85% | 135.52 | 13.99 | 43.54 |
| 55. | 2023/08/31 | 25.34% | -1.77% | 509.12 | 8.28 | -64.93 |
| 56. | 2023/09/30 | -3.25% | -4.87% | 36.29 | 35.73 | 36.01 |
| 57. | 2023/10/31 | 1.23% | -2.20% | 2.40 | 10.92 | 5.11 |
| 58. | 2023/11/30 | -9.25% | 8.92% | 144.64 | 61.03 | -93.95 |
| 59. | 2023/12/31 | -5.95% | 4.42% | 76.18 | 11.00 | -28.95 |
| トータル (Σ): | 14,984.07 | 1,634.30 | 2,655.68 | |||
すべて表示
分散TPL = Σ(RTPL,t–RTPL)2 ÷ (59 – 1)
= 14,984.07 ÷ (59 – 1)
= 258.35
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
共 分散TPL, S&P 500 = Σ(RTPL,t–RTPL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,655.68 ÷ (59 – 1)
= 45.79
システマティックなリスク推定 (β)
| 分散TPL | 258.35 |
| 分散S&P 500 | 28.18 |
| 共 分散TPL, S&P 500 | 45.79 |
| 相関係数TPL, S&P 5001 | 0.54 |
| βTPL2 | 1.62 |
| αTPL3 | 0.98% |
計算
1 相関係数TPL, S&P 500
= 共 分散TPL, S&P 500 ÷ (標準偏差TPL × 標準偏差S&P 500)
= 45.79 ÷ (16.07% × 5.31%)
= 0.54
2 βTPL
= 共 分散TPL, S&P 500 ÷ 分散S&P 500
= 45.79 ÷ 28.18
= 1.62
3 αTPL
= 平均TPL – βTPL × 平均S&P 500
= 2.78% – 1.62 × 1.11%
= 0.98%
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) | 13.77% |
| 普通株式のシステマティックリスクTPL | βTPL | 1.62 |
| TPL普通株式の予想収益率3 | E(RTPL) | 19.46% |
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(RTPL) = RF + βTPL [E(RM) – RF]
= 4.67% + 1.62 [13.77% – 4.67%]
= 19.46%