資本資産価格モデル (CAPM)
資本資産価格モデル(CAPM)は、 Pioneerの普通株式のようなリスク資産に対する期待または必要な収益率を示す。
収益率
Pioneer Natural Resources Co.、月次収益率
| 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 |
| 2018/01/31 | $182.91 | 2,823.81 | ||||
| 1. | 2018/02/28 | $170.23 | -6.93% | 2,713.83 | -3.89% | |
| 2. | 2018/03/31 | $171.78 | $0.16 | 1.00% | 2,640.87 | -2.69% |
| 3. | 2018/04/30 | $201.55 | 17.33% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | $235.99 | $5.71 | -5.74% | 4,080.11 | 5.38% |
| 59. | 2022/12/31 | $228.39 | -3.22% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.49% | 0.67% | ||||
| 標準偏差： | 12.51% | 5.40% | ||||
| 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 |
| 2018/01/31 | $182.91 | 2,823.81 | ||||
| 1. | 2018/02/28 | $170.23 | -6.93% | 2,713.83 | -3.89% | |
| 2. | 2018/03/31 | $171.78 | $0.16 | 1.00% | 2,640.87 | -2.69% |
| 3. | 2018/04/30 | $201.55 | 17.33% | 2,648.05 | 0.27% | |
| 4. | 2018/05/31 | $193.10 | -4.19% | 2,705.27 | 2.16% | |
| 5. | 2018/06/30 | $189.24 | -2.00% | 2,718.37 | 0.48% | |
| 6. | 2018/07/31 | $189.27 | 0.02% | 2,816.29 | 3.60% | |
| 7. | 2018/08/31 | $174.70 | -7.70% | 2,901.52 | 3.03% | |
| 8. | 2018/09/30 | $174.19 | $0.16 | -0.20% | 2,913.98 | 0.43% |
| 9. | 2018/10/31 | $147.27 | -15.45% | 2,711.74 | -6.94% | |
| 10. | 2018/11/30 | $147.75 | 0.33% | 2,760.17 | 1.79% | |
| 11. | 2018/12/31 | $131.52 | -10.98% | 2,506.85 | -9.18% | |
| 12. | 2019/01/31 | $142.32 | 8.21% | 2,704.10 | 7.87% | |
| 13. | 2019/02/28 | $140.95 | -0.96% | 2,784.49 | 2.97% | |
| 14. | 2019/03/31 | $152.28 | $0.32 | 8.27% | 2,834.40 | 1.79% |
| 15. | 2019/04/30 | $166.46 | 9.31% | 2,945.83 | 3.93% | |
| 16. | 2019/05/31 | $141.96 | -14.72% | 2,752.06 | -6.58% | |
| 17. | 2019/06/30 | $153.86 | 8.38% | 2,941.76 | 6.89% | |
| 18. | 2019/07/31 | $138.04 | -10.28% | 2,980.38 | 1.31% | |
| 19. | 2019/08/31 | $123.42 | -10.59% | 2,926.46 | -1.81% | |
| 20. | 2019/09/30 | $125.77 | $0.44 | 2.26% | 2,976.74 | 1.72% |
| 21. | 2019/10/31 | $123.02 | -2.19% | 3,037.56 | 2.04% | |
| 22. | 2019/11/30 | $127.84 | 3.92% | 3,140.98 | 3.40% | |
| 23. | 2019/12/31 | $151.37 | $0.44 | 18.75% | 3,230.78 | 2.86% |
| 24. | 2020/01/31 | $135.00 | -10.81% | 3,225.52 | -0.16% | |
| 25. | 2020/02/29 | $122.78 | -9.05% | 2,954.22 | -8.41% | |
| 26. | 2020/03/31 | $70.15 | $0.55 | -42.42% | 2,584.59 | -12.51% |
| 27. | 2020/04/30 | $89.31 | 27.31% | 2,912.43 | 12.68% | |
| 28. | 2020/05/31 | $91.60 | 2.56% | 3,044.31 | 4.53% | |
| 29. | 2020/06/30 | $97.70 | $0.55 | 7.26% | 3,100.29 | 1.84% |
| 30. | 2020/07/31 | $96.92 | -0.80% | 3,271.12 | 5.51% | |
| 31. | 2020/08/31 | $103.93 | 7.23% | 3,500.31 | 7.01% | |
| 32. | 2020/09/30 | $85.99 | $0.55 | -16.73% | 3,363.00 | -3.92% |
| 33. | 2020/10/31 | $79.56 | -7.48% | 3,269.96 | -2.77% | |
| 34. | 2020/11/30 | $100.58 | 26.42% | 3,621.63 | 10.75% | |
| 35. | 2020/12/31 | $113.89 | $0.55 | 13.78% | 3,756.07 | 3.71% |
| 36. | 2021/01/31 | $120.90 | 6.16% | 3,714.24 | -1.11% | |
| 37. | 2021/02/28 | $148.57 | 22.89% | 3,811.15 | 2.61% | |
| 38. | 2021/03/31 | $158.82 | $0.56 | 7.28% | 3,972.89 | 4.24% |
| 39. | 2021/04/30 | $153.83 | -3.14% | 4,181.17 | 5.24% | |
| 40. | 2021/05/31 | $152.19 | -1.07% | 4,204.11 | 0.55% | |
| 41. | 2021/06/30 | $162.52 | $0.56 | 7.16% | 4,297.50 | 2.22% |
| 42. | 2021/07/31 | $145.37 | -10.55% | 4,395.26 | 2.27% | |
| 43. | 2021/08/31 | $149.67 | 2.96% | 4,522.68 | 2.90% | |
| 44. | 2021/09/30 | $166.51 | $2.07 | 12.63% | 4,307.54 | -4.76% |
| 45. | 2021/10/31 | $186.98 | 12.29% | 4,605.38 | 6.91% | |
| 46. | 2021/11/30 | $178.32 | $3.02 | -3.02% | 4,567.00 | -0.83% |
| 47. | 2021/12/31 | $181.88 | $0.62 | 2.34% | 4,766.18 | 4.36% |
| 48. | 2022/01/31 | $218.89 | 20.35% | 4,515.55 | -5.26% | |
| 49. | 2022/02/28 | $239.60 | $3.78 | 11.19% | 4,373.94 | -3.14% |
| 50. | 2022/03/31 | $250.03 | 4.35% | 4,530.41 | 3.58% | |
| 51. | 2022/04/30 | $232.47 | -7.02% | 4,131.93 | -8.80% | |
| 52. | 2022/05/31 | $277.94 | $7.38 | 22.73% | 4,132.15 | 0.01% |
| 53. | 2022/06/30 | $223.08 | -19.74% | 3,785.38 | -8.39% | |
| 54. | 2022/07/31 | $236.95 | 6.22% | 4,130.29 | 9.11% | |
| 55. | 2022/08/31 | $253.22 | 6.87% | 3,955.00 | -4.24% | |
| 56. | 2022/09/30 | $216.53 | $8.57 | -11.10% | 3,585.62 | -9.34% |
| 57. | 2022/10/31 | $256.41 | 18.42% | 3,871.98 | 7.99% | |
| 58. | 2022/11/30 | $235.99 | $5.71 | -5.74% | 4,080.11 | 5.38% |
| 59. | 2022/12/31 | $228.39 | -3.22% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.49% | 0.67% | ||||
| 標準偏差： | 12.51% | 5.40% | ||||
すべて表示
1 普通株式1株当たり米ドルのデータ(分割および株式配当調整後)
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.、リターンの差異と共分散の計算
| 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. | 2018/02/28 | -6.93% | -3.89% | 70.99 | 20.81 | 38.43 |
| 2. | 2018/03/31 | 1.00% | -2.69% | 0.24 | 11.26 | 1.64 |
| 3. | 2018/04/30 | 17.33% | 0.27% | 250.82 | 0.16 | -6.25 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | -5.74% | 5.38% | 52.27 | 22.17 | -34.04 |
| 59. | 2022/12/31 | -3.22% | -5.90% | 22.22 | 43.08 | 30.94 |
| トータル (Σ): | 9,071.39 | 1,691.48 | 2,405.59 | |||
| 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. | 2018/02/28 | -6.93% | -3.89% | 70.99 | 20.81 | 38.43 |
| 2. | 2018/03/31 | 1.00% | -2.69% | 0.24 | 11.26 | 1.64 |
| 3. | 2018/04/30 | 17.33% | 0.27% | 250.82 | 0.16 | -6.25 |
| 4. | 2018/05/31 | -4.19% | 2.16% | 32.32 | 2.23 | -8.50 |
| 5. | 2018/06/30 | -2.00% | 0.48% | 12.19 | 0.03 | 0.64 |
| 6. | 2018/07/31 | 0.02% | 3.60% | 2.18 | 8.62 | -4.34 |
| 7. | 2018/08/31 | -7.70% | 3.03% | 84.47 | 5.57 | -21.69 |
| 8. | 2018/09/30 | -0.20% | 0.43% | 2.87 | 0.06 | 0.40 |
| 9. | 2018/10/31 | -15.45% | -6.94% | 287.21 | 57.87 | 128.92 |
| 10. | 2018/11/30 | 0.33% | 1.79% | 1.36 | 1.25 | -1.31 |
| 11. | 2018/12/31 | -10.98% | -9.18% | 155.69 | 96.91 | 122.83 |
| 12. | 2019/01/31 | 8.21% | 7.87% | 45.14 | 51.87 | 48.39 |
| 13. | 2019/02/28 | -0.96% | 2.97% | 6.03 | 5.32 | -5.66 |
| 14. | 2019/03/31 | 8.27% | 1.79% | 45.87 | 1.27 | 7.62 |
| 15. | 2019/04/30 | 9.31% | 3.93% | 61.14 | 10.66 | 25.53 |
| 16. | 2019/05/31 | -14.72% | -6.58% | 262.80 | 52.48 | 117.44 |
| 17. | 2019/06/30 | 8.38% | 6.89% | 47.47 | 38.77 | 42.90 |
| 18. | 2019/07/31 | -10.28% | 1.31% | 138.65 | 0.42 | -7.61 |
| 19. | 2019/08/31 | -10.59% | -1.81% | 146.02 | 6.13 | 29.92 |
| 20. | 2019/09/30 | 2.26% | 1.72% | 0.59 | 1.11 | 0.81 |
| 21. | 2019/10/31 | -2.19% | 2.04% | 13.54 | 1.89 | -5.06 |
| 22. | 2019/11/30 | 3.92% | 3.40% | 5.88 | 7.50 | 6.64 |
| 23. | 2019/12/31 | 18.75% | 2.86% | 297.81 | 4.81 | 37.83 |
| 24. | 2020/01/31 | -10.81% | -0.16% | 151.47 | 0.69 | 10.21 |
| 25. | 2020/02/29 | -9.05% | -8.41% | 111.19 | 82.40 | 95.72 |
| 26. | 2020/03/31 | -42.42% | -12.51% | 1,928.11 | 173.67 | 578.67 |
| 27. | 2020/04/30 | 27.31% | 12.68% | 666.67 | 144.43 | 310.30 |
| 28. | 2020/05/31 | 2.56% | 4.53% | 1.15 | 14.91 | 4.14 |
| 29. | 2020/06/30 | 7.26% | 1.84% | 33.26 | 1.37 | 6.76 |
| 30. | 2020/07/31 | -0.80% | 5.51% | 5.25 | 23.46 | -11.10 |
| 31. | 2020/08/31 | 7.23% | 7.01% | 32.95 | 40.19 | 36.39 |
| 32. | 2020/09/30 | -16.73% | -3.92% | 332.16 | 21.06 | 83.64 |
| 33. | 2020/10/31 | -7.48% | -2.77% | 80.47 | 11.79 | 30.80 |
| 34. | 2020/11/30 | 26.42% | 10.75% | 621.38 | 101.77 | 251.47 |
| 35. | 2020/12/31 | 13.78% | 3.71% | 150.97 | 9.28 | 37.42 |
| 36. | 2021/01/31 | 6.16% | -1.11% | 21.74 | 3.17 | -8.30 |
| 37. | 2021/02/28 | 22.89% | 2.61% | 457.69 | 3.77 | 41.56 |
| 38. | 2021/03/31 | 7.28% | 4.24% | 33.44 | 12.80 | 20.69 |
| 39. | 2021/04/30 | -3.14% | 5.24% | 21.48 | 20.94 | -21.21 |
| 40. | 2021/05/31 | -1.07% | 0.55% | 6.55 | 0.01 | 0.30 |
| 41. | 2021/06/30 | 7.16% | 2.22% | 32.07 | 2.42 | 8.80 |
| 42. | 2021/07/31 | -10.55% | 2.27% | 145.09 | 2.59 | -19.37 |
| 43. | 2021/08/31 | 2.96% | 2.90% | 2.15 | 4.98 | 3.27 |
| 44. | 2021/09/30 | 12.63% | -4.76% | 124.13 | 29.42 | -60.43 |
| 45. | 2021/10/31 | 12.29% | 6.91% | 116.65 | 39.03 | 67.48 |
| 46. | 2021/11/30 | -3.02% | -0.83% | 20.33 | 2.25 | 6.76 |
| 47. | 2021/12/31 | 2.34% | 4.36% | 0.72 | 13.65 | 3.14 |
| 48. | 2022/01/31 | 20.35% | -5.26% | 355.54 | 35.11 | -111.72 |
| 49. | 2022/02/28 | 11.19% | -3.14% | 94.00 | 14.46 | -36.87 |
| 50. | 2022/03/31 | 4.35% | 3.58% | 8.18 | 8.47 | 8.33 |
| 51. | 2022/04/30 | -7.02% | -8.80% | 72.52 | 89.54 | 80.58 |
| 52. | 2022/05/31 | 22.73% | 0.01% | 451.19 | 0.44 | -14.05 |
| 53. | 2022/06/30 | -19.74% | -8.39% | 450.75 | 82.06 | 192.32 |
| 54. | 2022/07/31 | 6.22% | 9.11% | 22.32 | 71.32 | 39.90 |
| 55. | 2022/08/31 | 6.87% | -4.24% | 28.87 | 24.11 | -26.39 |
| 56. | 2022/09/30 | -11.10% | -9.34% | 158.71 | 100.12 | 126.06 |
| 57. | 2022/10/31 | 18.42% | 7.99% | 286.45 | 53.58 | 123.88 |
| 58. | 2022/11/30 | -5.74% | 5.38% | 52.27 | 22.17 | -34.04 |
| 59. | 2022/12/31 | -3.22% | -5.90% | 22.22 | 43.08 | 30.94 |
| トータル (Σ): | 9,071.39 | 1,691.48 | 2,405.59 | |||
すべて表示
分散PXD = Σ(RPXD,t–RPXD)2 ÷ (59 – 1)
= 9,071.39 ÷ (59 – 1)
= 156.40
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PXD, S&P 500 = Σ(RPXD,t–RPXD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,405.59 ÷ (59 – 1)
= 41.48
体系的なリスク推定 (β)
| 分散PXD | 156.40 |
| 分散S&P 500 | 29.16 |
| 共 分散PXD, S&P 500 | 41.48 |
| 相関係数PXD, S&P 5001 | 0.61 |
| βPXD2 | 1.42 |
| αPXD3 | 0.54% |
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)
= 41.48 ÷ (12.51% × 5.40%)
= 0.61
2 βPXD
= 共 分散PXD, S&P 500 ÷ 分散S&P 500
= 41.48 ÷ 29.16
= 1.42
3 αPXD
= 平均PXD – βPXD × 平均S&P 500
= 1.49% – 1.42 × 0.67%
= 0.54%
期待収益率
| 仮定 | ||
| LT財務省コンポジットの収益率1 | RF | 4.08% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.78% |
| 普通株式の Pioneer のシステマティックリスク | βPXD | 1.42 |
| パイオニア普通株式の予想収益率3 | E(RPXD) | 17.87% |
1 10年以内に期限も呼び出もできないすべての未払いの固定クーポン米国債の入札利回りの加重平均(リスクフリーの収益率プロキシ)。
2 詳細を見る »
3 E(RPXD) = RF + βPXD [E(RM) – RF]
= 4.08% + 1.42 [13.78% – 4.08%]
= 17.87%