資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Phillips 66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
Phillips 66、月間収益率
| Phillips 66 (PSX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格PSX,t1 | 配当PSX,t1 | RPSX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2015/01/31 | $70.32 | 1,994.99 | ||||
| 1. | 2015/02/28 | $78.46 | $0.50 | 12.29% | 2,104.50 | 5.49% |
| 2. | 2015/03/31 | $78.60 | 0.18% | 2,067.89 | -1.74% | |
| 3. | 2015/04/30 | $79.31 | 0.90% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019/11/30 | $114.72 | $0.90 | -1.03% | 3,140.98 | 3.40% |
| 59. | 2019/12/31 | $111.41 | -2.89% | 3,230.78 | 2.86% | |
| 平均 (R): | 1.26% | 0.88% | ||||
| 標準偏差： | 6.69% | 3.45% | ||||
| Phillips 66 (PSX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格PSX,t1 | 配当PSX,t1 | RPSX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2015/01/31 | $70.32 | 1,994.99 | ||||
| 1. | 2015/02/28 | $78.46 | $0.50 | 12.29% | 2,104.50 | 5.49% |
| 2. | 2015/03/31 | $78.60 | 0.18% | 2,067.89 | -1.74% | |
| 3. | 2015/04/30 | $79.31 | 0.90% | 2,085.51 | 0.85% | |
| 4. | 2015/05/31 | $79.12 | $0.56 | 0.47% | 2,107.39 | 1.05% |
| 5. | 2015/06/30 | $80.56 | 1.82% | 2,063.11 | -2.10% | |
| 6. | 2015/07/31 | $79.50 | -1.32% | 2,103.84 | 1.97% | |
| 7. | 2015/08/31 | $79.07 | $0.56 | 0.16% | 1,972.18 | -6.26% |
| 8. | 2015/09/30 | $76.84 | -2.82% | 1,920.03 | -2.64% | |
| 9. | 2015/10/31 | $89.05 | 15.89% | 2,079.36 | 8.30% | |
| 10. | 2015/11/30 | $91.53 | $0.56 | 3.41% | 2,080.41 | 0.05% |
| 11. | 2015/12/31 | $81.80 | -10.63% | 2,043.94 | -1.75% | |
| 12. | 2016/01/31 | $80.15 | -2.02% | 1,940.24 | -5.07% | |
| 13. | 2016/02/29 | $79.39 | $0.56 | -0.25% | 1,932.23 | -0.41% |
| 14. | 2016/03/31 | $86.59 | 9.07% | 2,059.74 | 6.60% | |
| 15. | 2016/04/30 | $82.11 | -5.17% | 2,065.30 | 0.27% | |
| 16. | 2016/05/31 | $80.36 | $0.63 | -1.36% | 2,096.95 | 1.53% |
| 17. | 2016/06/30 | $79.34 | -1.27% | 2,098.86 | 0.09% | |
| 18. | 2016/07/31 | $76.06 | -4.13% | 2,173.60 | 3.56% | |
| 19. | 2016/08/31 | $78.45 | $0.63 | 3.97% | 2,170.95 | -0.12% |
| 20. | 2016/09/30 | $80.55 | 2.68% | 2,168.27 | -0.12% | |
| 21. | 2016/10/31 | $81.15 | 0.74% | 2,126.15 | -1.94% | |
| 22. | 2016/11/30 | $83.08 | $0.63 | 3.15% | 2,198.81 | 3.42% |
| 23. | 2016/12/31 | $86.41 | 4.01% | 2,238.83 | 1.82% | |
| 24. | 2017/01/31 | $81.62 | -5.54% | 2,278.87 | 1.79% | |
| 25. | 2017/02/28 | $78.19 | $0.63 | -3.43% | 2,363.64 | 3.72% |
| 26. | 2017/03/31 | $79.22 | 1.32% | 2,362.72 | -0.04% | |
| 27. | 2017/04/30 | $79.56 | 0.43% | 2,384.20 | 0.91% | |
| 28. | 2017/05/31 | $76.11 | $0.70 | -3.46% | 2,411.80 | 1.16% |
| 29. | 2017/06/30 | $82.69 | 8.65% | 2,423.41 | 0.48% | |
| 30. | 2017/07/31 | $83.75 | 1.28% | 2,470.30 | 1.93% | |
| 31. | 2017/08/31 | $83.81 | $0.70 | 0.91% | 2,471.65 | 0.05% |
| 32. | 2017/09/30 | $91.61 | 9.31% | 2,519.36 | 1.93% | |
| 33. | 2017/10/31 | $91.08 | -0.58% | 2,575.26 | 2.22% | |
| 34. | 2017/11/30 | $97.56 | $0.70 | 7.88% | 2,647.58 | 2.81% |
| 35. | 2017/12/31 | $101.15 | 3.68% | 2,673.61 | 0.98% | |
| 36. | 2018/01/31 | $102.40 | 1.24% | 2,823.81 | 5.62% | |
| 37. | 2018/02/28 | $90.37 | $0.70 | -11.06% | 2,713.83 | -3.89% |
| 38. | 2018/03/31 | $95.92 | 6.14% | 2,640.87 | -2.69% | |
| 39. | 2018/04/30 | $111.31 | 16.04% | 2,648.05 | 0.27% | |
| 40. | 2018/05/31 | $116.49 | $0.80 | 5.37% | 2,705.27 | 2.16% |
| 41. | 2018/06/30 | $112.31 | -3.59% | 2,718.37 | 0.48% | |
| 42. | 2018/07/31 | $123.34 | 9.82% | 2,816.29 | 3.60% | |
| 43. | 2018/08/31 | $118.51 | $0.80 | -3.27% | 2,901.52 | 3.03% |
| 44. | 2018/09/30 | $112.72 | -4.89% | 2,913.98 | 0.43% | |
| 45. | 2018/10/31 | $102.82 | -8.78% | 2,711.74 | -6.94% | |
| 46. | 2018/11/30 | $93.52 | $0.80 | -8.27% | 2,760.17 | 1.79% |
| 47. | 2018/12/31 | $86.15 | -7.88% | 2,506.85 | -9.18% | |
| 48. | 2019/01/31 | $95.41 | 10.75% | 2,704.10 | 7.87% | |
| 49. | 2019/02/28 | $96.36 | $0.80 | 1.83% | 2,784.49 | 2.97% |
| 50. | 2019/03/31 | $95.17 | -1.23% | 2,834.40 | 1.79% | |
| 51. | 2019/04/30 | $94.27 | -0.95% | 2,945.83 | 3.93% | |
| 52. | 2019/05/31 | $80.80 | $0.90 | -13.33% | 2,752.06 | -6.58% |
| 53. | 2019/06/30 | $93.54 | 15.77% | 2,941.76 | 6.89% | |
| 54. | 2019/07/31 | $102.56 | 9.64% | 2,980.38 | 1.31% | |
| 55. | 2019/08/31 | $98.63 | $0.90 | -2.95% | 2,926.46 | -1.81% |
| 56. | 2019/09/30 | $102.40 | 3.82% | 2,976.74 | 1.72% | |
| 57. | 2019/10/31 | $116.82 | 14.08% | 3,037.56 | 2.04% | |
| 58. | 2019/11/30 | $114.72 | $0.90 | -1.03% | 3,140.98 | 3.40% |
| 59. | 2019/12/31 | $111.41 | -2.89% | 3,230.78 | 2.86% | |
| 平均 (R): | 1.26% | 0.88% | ||||
| 標準偏差： | 6.69% | 3.45% | ||||
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中のPSX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
Phillips 66、分散の計算、および戻り値の共分散
| t | 日付 | RPSX,t | RS&P 500,t | (RPSX,t–RPSX)2 | (RS&P 500,t–RS&P 500)2 | (RPSX,t–RPSX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015/02/28 | 12.29% | 5.49% | 121.49 | 21.25 | 50.81 |
| 2. | 2015/03/31 | 0.18% | -1.74% | 1.18 | 6.86 | 2.84 |
| 3. | 2015/04/30 | 0.90% | 0.85% | 0.13 | 0.00 | 0.01 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019/11/30 | -1.03% | 3.40% | 5.25 | 6.38 | -5.79 |
| 59. | 2019/12/31 | -2.89% | 2.86% | 17.22 | 3.92 | -8.22 |
| トータル (Σ): | 2,598.43 | 688.77 | 755.71 | |||
| t | 日付 | RPSX,t | RS&P 500,t | (RPSX,t–RPSX)2 | (RS&P 500,t–RS&P 500)2 | (RPSX,t–RPSX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015/02/28 | 12.29% | 5.49% | 121.49 | 21.25 | 50.81 |
| 2. | 2015/03/31 | 0.18% | -1.74% | 1.18 | 6.86 | 2.84 |
| 3. | 2015/04/30 | 0.90% | 0.85% | 0.13 | 0.00 | 0.01 |
| 4. | 2015/05/31 | 0.47% | 1.05% | 0.64 | 0.03 | -0.14 |
| 5. | 2015/06/30 | 1.82% | -2.10% | 0.31 | 8.88 | -1.66 |
| 6. | 2015/07/31 | -1.32% | 1.97% | 6.66 | 1.20 | -2.83 |
| 7. | 2015/08/31 | 0.16% | -6.26% | 1.21 | 50.94 | 7.86 |
| 8. | 2015/09/30 | -2.82% | -2.64% | 16.69 | 12.41 | 14.39 |
| 9. | 2015/10/31 | 15.89% | 8.30% | 213.91 | 55.04 | 108.51 |
| 10. | 2015/11/30 | 3.41% | 0.05% | 4.62 | 0.69 | -1.78 |
| 11. | 2015/12/31 | -10.63% | -1.75% | 141.49 | 6.93 | 31.31 |
| 12. | 2016/01/31 | -2.02% | -5.07% | 10.77 | 35.43 | 19.53 |
| 13. | 2016/02/29 | -0.25% | -0.41% | 2.29 | 1.67 | 1.96 |
| 14. | 2016/03/31 | 9.07% | 6.60% | 60.91 | 32.72 | 44.64 |
| 15. | 2016/04/30 | -5.17% | 0.27% | 41.45 | 0.37 | 3.92 |
| 16. | 2016/05/31 | -1.36% | 1.53% | 6.91 | 0.43 | -1.72 |
| 17. | 2016/06/30 | -1.27% | 0.09% | 6.42 | 0.62 | 2.00 |
| 18. | 2016/07/31 | -4.13% | 3.56% | 29.15 | 7.19 | -14.48 |
| 19. | 2016/08/31 | 3.97% | -0.12% | 7.32 | 1.00 | -2.71 |
| 20. | 2016/09/30 | 2.68% | -0.12% | 1.99 | 1.01 | -1.42 |
| 21. | 2016/10/31 | 0.74% | -1.94% | 0.27 | 7.96 | 1.47 |
| 22. | 2016/11/30 | 3.15% | 3.42% | 3.57 | 6.44 | 4.80 |
| 23. | 2016/12/31 | 4.01% | 1.82% | 7.53 | 0.89 | 2.58 |
| 24. | 2017/01/31 | -5.54% | 1.79% | 46.35 | 0.83 | -6.19 |
| 25. | 2017/02/28 | -3.43% | 3.72% | 22.04 | 8.07 | -13.34 |
| 26. | 2017/03/31 | 1.32% | -0.04% | 0.00 | 0.84 | -0.05 |
| 27. | 2017/04/30 | 0.43% | 0.91% | 0.70 | 0.00 | -0.03 |
| 28. | 2017/05/31 | -3.46% | 1.16% | 22.29 | 0.08 | -1.31 |
| 29. | 2017/06/30 | 8.65% | 0.48% | 54.48 | 0.16 | -2.94 |
| 30. | 2017/07/31 | 1.28% | 1.93% | 0.00 | 1.11 | 0.02 |
| 31. | 2017/08/31 | 0.91% | 0.05% | 0.13 | 0.68 | 0.29 |
| 32. | 2017/09/30 | 9.31% | 1.93% | 64.68 | 1.10 | 8.45 |
| 33. | 2017/10/31 | -0.58% | 2.22% | 3.40 | 1.79 | -2.47 |
| 34. | 2017/11/30 | 7.88% | 2.81% | 43.81 | 3.72 | 12.77 |
| 35. | 2017/12/31 | 3.68% | 0.98% | 5.83 | 0.01 | 0.25 |
| 36. | 2018/01/31 | 1.24% | 5.62% | 0.00 | 22.46 | -0.14 |
| 37. | 2018/02/28 | -11.06% | -3.89% | 152.00 | 22.79 | 58.86 |
| 38. | 2018/03/31 | 6.14% | -2.69% | 23.78 | 12.73 | -17.40 |
| 39. | 2018/04/30 | 16.04% | 0.27% | 218.45 | 0.37 | -8.98 |
| 40. | 2018/05/31 | 5.37% | 2.16% | 16.87 | 1.64 | 5.27 |
| 41. | 2018/06/30 | -3.59% | 0.48% | 23.55 | 0.16 | 1.92 |
| 42. | 2018/07/31 | 9.82% | 3.60% | 73.21 | 7.41 | 23.30 |
| 43. | 2018/08/31 | -3.27% | 3.03% | 20.54 | 4.61 | -9.73 |
| 44. | 2018/09/30 | -4.89% | 0.43% | 37.83 | 0.20 | 2.77 |
| 45. | 2018/10/31 | -8.78% | -6.94% | 100.95 | 61.14 | 78.57 |
| 46. | 2018/11/30 | -8.27% | 1.79% | 90.85 | 0.82 | -8.64 |
| 47. | 2018/12/31 | -7.88% | -9.18% | 83.64 | 101.14 | 91.97 |
| 48. | 2019/01/31 | 10.75% | 7.87% | 89.95 | 48.85 | 66.29 |
| 49. | 2019/02/28 | 1.83% | 2.97% | 0.32 | 4.38 | 1.19 |
| 50. | 2019/03/31 | -1.23% | 1.79% | 6.25 | 0.83 | -2.28 |
| 51. | 2019/04/30 | -0.95% | 3.93% | 4.89 | 9.32 | -6.75 |
| 52. | 2019/05/31 | -13.33% | -6.58% | 213.12 | 55.61 | 108.86 |
| 53. | 2019/06/30 | 15.77% | 6.89% | 210.33 | 36.17 | 87.22 |
| 54. | 2019/07/31 | 9.64% | 1.31% | 70.20 | 0.19 | 3.63 |
| 55. | 2019/08/31 | -2.95% | -1.81% | 17.80 | 7.23 | 11.34 |
| 56. | 2019/09/30 | 3.82% | 1.72% | 6.54 | 0.70 | 2.15 |
| 57. | 2019/10/31 | 14.08% | 2.04% | 164.29 | 1.36 | 14.92 |
| 58. | 2019/11/30 | -1.03% | 3.40% | 5.25 | 6.38 | -5.79 |
| 59. | 2019/12/31 | -2.89% | 2.86% | 17.22 | 3.92 | -8.22 |
| トータル (Σ): | 2,598.43 | 688.77 | 755.71 | |||
すべて表示
分散PSX = Σ(RPSX,t–RPSX)2 ÷ (59 – 1)
= 2,598.43 ÷ (59 – 1)
= 44.80
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
共 分散PSX, S&P 500 = Σ(RPSX,t–RPSX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 755.71 ÷ (59 – 1)
= 13.03
システマティックなリスク推定 (β)
| 分散PSX | 44.80 |
| 分散S&P 500 | 11.88 |
| 共 分散PSX, S&P 500 | 13.03 |
| 相関係数PSX, S&P 5001 | 0.56 |
| βPSX2 | 1.10 |
| αPSX3 | 0.30% |
計算
1 相関係数PSX, S&P 500
= 共 分散PSX, S&P 500 ÷ (標準偏差PSX × 標準偏差S&P 500)
= 13.03 ÷ (6.69% × 3.45%)
= 0.56
2 βPSX
= 共 分散PSX, S&P 500 ÷ 分散S&P 500
= 13.03 ÷ 11.88
= 1.10
3 αPSX
= 平均PSX – βPSX × 平均S&P 500
= 1.26% – 1.10 × 0.88%
= 0.30%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.56% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.87% |
| 普通株式 Phillips 66 システマティックリスク | βPSX | 1.10 |
| フィリップス66普通株式の期待収益率3 | E(RPSX) | 15.87% |
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(RPSX) = RF + βPSX [E(RM) – RF]
= 4.56% + 1.10 [14.87% – 4.56%]
= 15.87%