資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Pioneer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
Pioneer Natural Resources Co.、月間収益率
| Pioneer Natural Resources Co. (PXD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格PXD,t1 | 配当PXD,t1 | RPXD,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $142.32 | 2,704.10 | ||||
| 1. | 2019/02/28 | $140.95 | -0.96% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $152.28 | $0.32 | 8.27% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $166.46 | 9.31% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | $231.64 | $3.20 | -1.74% | 4,567.80 | 8.92% |
| 59. | 2023/12/31 | $224.88 | -2.92% | 4,769.83 | 4.42% | |
| 平均 (R): | 1.96% | 1.11% | ||||
| 標準偏差： | 12.15% | 5.31% | ||||
| Pioneer Natural Resources Co. (PXD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格PXD,t1 | 配当PXD,t1 | RPXD,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $142.32 | 2,704.10 | ||||
| 1. | 2019/02/28 | $140.95 | -0.96% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $152.28 | $0.32 | 8.27% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $166.46 | 9.31% | 2,945.83 | 3.93% | |
| 4. | 2019/05/31 | $141.96 | -14.72% | 2,752.06 | -6.58% | |
| 5. | 2019/06/30 | $153.86 | 8.38% | 2,941.76 | 6.89% | |
| 6. | 2019/07/31 | $138.04 | -10.28% | 2,980.38 | 1.31% | |
| 7. | 2019/08/31 | $123.42 | -10.59% | 2,926.46 | -1.81% | |
| 8. | 2019/09/30 | $125.77 | $0.44 | 2.26% | 2,976.74 | 1.72% |
| 9. | 2019/10/31 | $123.02 | -2.19% | 3,037.56 | 2.04% | |
| 10. | 2019/11/30 | $127.84 | 3.92% | 3,140.98 | 3.40% | |
| 11. | 2019/12/31 | $151.37 | $0.44 | 18.75% | 3,230.78 | 2.86% |
| 12. | 2020/01/31 | $135.00 | -10.81% | 3,225.52 | -0.16% | |
| 13. | 2020/02/29 | $122.78 | -9.05% | 2,954.22 | -8.41% | |
| 14. | 2020/03/31 | $70.15 | $0.55 | -42.42% | 2,584.59 | -12.51% |
| 15. | 2020/04/30 | $89.31 | 27.31% | 2,912.43 | 12.68% | |
| 16. | 2020/05/31 | $91.60 | 2.56% | 3,044.31 | 4.53% | |
| 17. | 2020/06/30 | $97.70 | $0.55 | 7.26% | 3,100.29 | 1.84% |
| 18. | 2020/07/31 | $96.92 | -0.80% | 3,271.12 | 5.51% | |
| 19. | 2020/08/31 | $103.93 | 7.23% | 3,500.31 | 7.01% | |
| 20. | 2020/09/30 | $85.99 | $0.55 | -16.73% | 3,363.00 | -3.92% |
| 21. | 2020/10/31 | $79.56 | -7.48% | 3,269.96 | -2.77% | |
| 22. | 2020/11/30 | $100.58 | 26.42% | 3,621.63 | 10.75% | |
| 23. | 2020/12/31 | $113.89 | $0.55 | 13.78% | 3,756.07 | 3.71% |
| 24. | 2021/01/31 | $120.90 | 6.16% | 3,714.24 | -1.11% | |
| 25. | 2021/02/28 | $148.57 | 22.89% | 3,811.15 | 2.61% | |
| 26. | 2021/03/31 | $158.82 | $0.56 | 7.28% | 3,972.89 | 4.24% |
| 27. | 2021/04/30 | $153.83 | -3.14% | 4,181.17 | 5.24% | |
| 28. | 2021/05/31 | $152.19 | -1.07% | 4,204.11 | 0.55% | |
| 29. | 2021/06/30 | $162.52 | $0.56 | 7.16% | 4,297.50 | 2.22% |
| 30. | 2021/07/31 | $145.37 | -10.55% | 4,395.26 | 2.27% | |
| 31. | 2021/08/31 | $149.67 | 2.96% | 4,522.68 | 2.90% | |
| 32. | 2021/09/30 | $166.51 | $2.07 | 12.63% | 4,307.54 | -4.76% |
| 33. | 2021/10/31 | $186.98 | 12.29% | 4,605.38 | 6.91% | |
| 34. | 2021/11/30 | $178.32 | $3.02 | -3.02% | 4,567.00 | -0.83% |
| 35. | 2021/12/31 | $181.88 | $0.62 | 2.34% | 4,766.18 | 4.36% |
| 36. | 2022/01/31 | $218.89 | 20.35% | 4,515.55 | -5.26% | |
| 37. | 2022/02/28 | $239.60 | $3.78 | 11.19% | 4,373.94 | -3.14% |
| 38. | 2022/03/31 | $250.03 | 4.35% | 4,530.41 | 3.58% | |
| 39. | 2022/04/30 | $232.47 | -7.02% | 4,131.93 | -8.80% | |
| 40. | 2022/05/31 | $277.94 | $7.38 | 22.73% | 4,132.15 | 0.01% |
| 41. | 2022/06/30 | $223.08 | -19.74% | 3,785.38 | -8.39% | |
| 42. | 2022/07/31 | $236.95 | 6.22% | 4,130.29 | 9.11% | |
| 43. | 2022/08/31 | $253.22 | 6.87% | 3,955.00 | -4.24% | |
| 44. | 2022/09/30 | $216.53 | $8.57 | -11.10% | 3,585.62 | -9.34% |
| 45. | 2022/10/31 | $256.41 | 18.42% | 3,871.98 | 7.99% | |
| 46. | 2022/11/30 | $235.99 | $5.71 | -5.74% | 4,080.11 | 5.38% |
| 47. | 2022/12/31 | $228.39 | -3.22% | 3,839.50 | -5.90% | |
| 48. | 2023/01/31 | $230.35 | 0.86% | 4,076.60 | 6.18% | |
| 49. | 2023/02/28 | $200.41 | -13.00% | 3,970.15 | -2.61% | |
| 50. | 2023/03/31 | $204.24 | $5.58 | 4.70% | 4,109.31 | 3.51% |
| 51. | 2023/04/30 | $217.55 | 6.52% | 4,169.48 | 1.46% | |
| 52. | 2023/05/31 | $199.44 | $3.34 | -6.79% | 4,179.83 | 0.25% |
| 53. | 2023/06/30 | $207.18 | 3.88% | 4,376.86 | 4.71% | |
| 54. | 2023/07/31 | $225.67 | 8.92% | 4,588.96 | 4.85% | |
| 55. | 2023/08/31 | $237.93 | 5.43% | 4,507.66 | -1.77% | |
| 56. | 2023/09/30 | $229.55 | $1.84 | -2.75% | 4,288.05 | -4.87% |
| 57. | 2023/10/31 | $239.00 | 4.12% | 4,193.80 | -2.20% | |
| 58. | 2023/11/30 | $231.64 | $3.20 | -1.74% | 4,567.80 | 8.92% |
| 59. | 2023/12/31 | $224.88 | -2.92% | 4,769.83 | 4.42% | |
| 平均 (R): | 1.96% | 1.11% | ||||
| 標準偏差： | 12.15% | 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PXD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
Pioneer Natural Resources Co.、分散の計算、および戻り値の共分散
| t | 日付 | RPXD,t | RS&P 500,t | (RPXD,t–RPXD)2 | (RS&P 500,t–RS&P 500)2 | (RPXD,t–RPXD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | -0.96% | 2.97% | 8.57 | 3.49 | -5.46 |
| 2. | 2019/03/31 | 8.27% | 1.79% | 39.70 | 0.47 | 4.33 |
| 3. | 2019/04/30 | 9.31% | 3.93% | 53.99 | 7.98 | 20.76 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | -1.74% | 8.92% | 13.73 | 61.03 | -28.94 |
| 59. | 2023/12/31 | -2.92% | 4.42% | 23.84 | 11.00 | -16.20 |
| トータル (Σ): | 8,558.51 | 1,634.30 | 2,158.61 | |||
| t | 日付 | RPXD,t | RS&P 500,t | (RPXD,t–RPXD)2 | (RS&P 500,t–RS&P 500)2 | (RPXD,t–RPXD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | -0.96% | 2.97% | 8.57 | 3.49 | -5.46 |
| 2. | 2019/03/31 | 8.27% | 1.79% | 39.70 | 0.47 | 4.33 |
| 3. | 2019/04/30 | 9.31% | 3.93% | 53.99 | 7.98 | 20.76 |
| 4. | 2019/05/31 | -14.72% | -6.58% | 278.30 | 59.04 | 128.18 |
| 5. | 2019/06/30 | 8.38% | 6.89% | 41.20 | 33.49 | 37.14 |
| 6. | 2019/07/31 | -10.28% | 1.31% | 149.97 | 0.04 | -2.53 |
| 7. | 2019/08/31 | -10.59% | -1.81% | 157.64 | 8.50 | 36.60 |
| 8. | 2019/09/30 | 2.26% | 1.72% | 0.09 | 0.37 | 0.18 |
| 9. | 2019/10/31 | -2.19% | 2.04% | 17.23 | 0.88 | -3.89 |
| 10. | 2019/11/30 | 3.92% | 3.40% | 3.82 | 5.28 | 4.49 |
| 11. | 2019/12/31 | 18.75% | 2.86% | 281.76 | 3.07 | 29.43 |
| 12. | 2020/01/31 | -10.81% | -0.16% | 163.30 | 1.61 | 16.21 |
| 13. | 2020/02/29 | -9.05% | -8.41% | 121.35 | 90.57 | 104.84 |
| 14. | 2020/03/31 | -42.42% | -12.51% | 1,969.72 | 185.44 | 604.38 |
| 15. | 2020/04/30 | 27.31% | 12.68% | 642.56 | 134.06 | 293.50 |
| 16. | 2020/05/31 | 2.56% | 4.53% | 0.36 | 11.71 | 2.05 |
| 17. | 2020/06/30 | 7.26% | 1.84% | 28.04 | 0.54 | 3.88 |
| 18. | 2020/07/31 | -0.80% | 5.51% | 7.63 | 19.40 | -12.17 |
| 19. | 2020/08/31 | 7.23% | 7.01% | 27.76 | 34.82 | 31.09 |
| 20. | 2020/09/30 | -16.73% | -3.92% | 349.56 | 25.29 | 94.02 |
| 21. | 2020/10/31 | -7.48% | -2.77% | 89.15 | 15.00 | 36.56 |
| 22. | 2020/11/30 | 26.42% | 10.75% | 598.10 | 93.10 | 235.97 |
| 23. | 2020/12/31 | 13.78% | 3.71% | 139.62 | 6.79 | 30.80 |
| 24. | 2021/01/31 | 6.16% | -1.11% | 17.56 | 4.93 | -9.30 |
| 25. | 2021/02/28 | 22.89% | 2.61% | 437.75 | 2.26 | 31.45 |
| 26. | 2021/03/31 | 7.28% | 4.24% | 28.22 | 9.85 | 16.67 |
| 27. | 2021/04/30 | -3.14% | 5.24% | 26.07 | 17.11 | -21.12 |
| 28. | 2021/05/31 | -1.07% | 0.55% | 9.18 | 0.31 | 1.69 |
| 29. | 2021/06/30 | 7.16% | 2.22% | 26.95 | 1.24 | 5.79 |
| 30. | 2021/07/31 | -10.55% | 2.27% | 156.67 | 1.37 | -14.63 |
| 31. | 2021/08/31 | 2.96% | 2.90% | 0.99 | 3.22 | 1.78 |
| 32. | 2021/09/30 | 12.63% | -4.76% | 113.86 | 34.37 | -62.56 |
| 33. | 2021/10/31 | 12.29% | 6.91% | 106.70 | 33.74 | 60.00 |
| 34. | 2021/11/30 | -3.02% | -0.83% | 24.81 | 3.76 | 9.66 |
| 35. | 2021/12/31 | 2.34% | 4.36% | 0.14 | 10.60 | 1.24 |
| 36. | 2022/01/31 | 20.35% | -5.26% | 337.99 | 40.51 | -117.01 |
| 37. | 2022/02/28 | 11.19% | -3.14% | 85.08 | 17.99 | -39.13 |
| 38. | 2022/03/31 | 4.35% | 3.58% | 5.71 | 6.11 | 5.90 |
| 39. | 2022/04/30 | -7.02% | -8.80% | 80.77 | 98.04 | 88.99 |
| 40. | 2022/05/31 | 22.73% | 0.01% | 431.39 | 1.21 | -22.86 |
| 41. | 2022/06/30 | -19.74% | -8.39% | 470.99 | 90.21 | 206.12 |
| 42. | 2022/07/31 | 6.22% | 9.11% | 18.09 | 64.09 | 34.05 |
| 43. | 2022/08/31 | 6.87% | -4.24% | 24.03 | 28.62 | -26.23 |
| 44. | 2022/09/30 | -11.10% | -9.34% | 170.80 | 109.11 | 136.51 |
| 45. | 2022/10/31 | 18.42% | 7.99% | 270.72 | 47.34 | 113.21 |
| 46. | 2022/11/30 | -5.74% | 5.38% | 59.31 | 18.23 | -32.88 |
| 47. | 2022/12/31 | -3.22% | -5.90% | 26.88 | 49.04 | 36.31 |
| 48. | 2023/01/31 | 0.86% | 6.18% | 1.22 | 25.70 | -5.61 |
| 49. | 2023/02/28 | -13.00% | -2.61% | 223.85 | 13.82 | 55.61 |
| 50. | 2023/03/31 | 4.70% | 3.51% | 7.46 | 5.76 | 6.55 |
| 51. | 2023/04/30 | 6.52% | 1.46% | 20.73 | 0.13 | 1.63 |
| 52. | 2023/05/31 | -6.79% | 0.25% | 76.62 | 0.74 | 7.51 |
| 53. | 2023/06/30 | 3.88% | 4.71% | 3.67 | 13.02 | 6.92 |
| 54. | 2023/07/31 | 8.92% | 4.85% | 48.45 | 13.99 | 26.03 |
| 55. | 2023/08/31 | 5.43% | -1.77% | 12.03 | 8.28 | -9.98 |
| 56. | 2023/09/30 | -2.75% | -4.87% | 22.21 | 35.73 | 28.17 |
| 57. | 2023/10/31 | 4.12% | -2.20% | 4.63 | 10.92 | -7.11 |
| 58. | 2023/11/30 | -1.74% | 8.92% | 13.73 | 61.03 | -28.94 |
| 59. | 2023/12/31 | -2.92% | 4.42% | 23.84 | 11.00 | -16.20 |
| トータル (Σ): | 8,558.51 | 1,634.30 | 2,158.61 | |||
すべて表示
分散PXD = Σ(RPXD,t–RPXD)2 ÷ (59 – 1)
= 8,558.51 ÷ (59 – 1)
= 147.56
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PXD, S&P 500 = Σ(RPXD,t–RPXD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,158.61 ÷ (59 – 1)
= 37.22
システマティックなリスク推定 (β)
| 分散PXD | 147.56 |
| 分散S&P 500 | 28.18 |
| 共 分散PXD, S&P 500 | 37.22 |
| 相関係数PXD, S&P 5001 | 0.58 |
| βPXD2 | 1.32 |
| αPXD3 | 0.50% |
計算
1 相関係数PXD, S&P 500
= 共 分散PXD, S&P 500 ÷ (標準偏差PXD × 標準偏差S&P 500)
= 37.22 ÷ (12.15% × 5.31%)
= 0.58
2 βPXD
= 共 分散PXD, S&P 500 ÷ 分散S&P 500
= 37.22 ÷ 28.18
= 1.32
3 αPXD
= 平均PXD – βPXD × 平均S&P 500
= 1.96% – 1.32 × 1.11%
= 0.50%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.75% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.88% |
| 普通株式 Pioneer システマティックリスク | βPXD | 1.32 |
| パイオニア普通株式の期待収益率3 | E(RPXD) | 18.13% |
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(RPXD) = RF + βPXD [E(RM) – RF]
= 4.75% + 1.32 [14.88% – 4.75%]
= 18.13%