資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Monsanto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
Monsanto Co.、月間収益率
| Monsanto Co. (MON) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格MON,t1 | 配当MON,t1 | RMON,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2011/09/30 | $60.04 | 1,131.42 | ||||
| 1. | 2011/10/31 | $72.75 | $0.30 | 21.67% | 1,253.30 | 10.77% |
| 2. | 2011/11/30 | $73.45 | 0.96% | 1,246.96 | -0.51% | |
| 3. | 2011/12/31 | $70.07 | -4.60% | 1,257.60 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2017/07/31 | $116.82 | $0.54 | -0.84% | 2,470.30 | 1.93% |
| 71. | 2017/08/31 | $117.20 | 0.33% | 2,471.65 | 0.05% | |
| 平均 (R): | 1.27% | 1.15% | ||||
| 標準偏差： | 6.07% | 3.01% | ||||
| Monsanto Co. (MON) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格MON,t1 | 配当MON,t1 | RMON,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2011/09/30 | $60.04 | 1,131.42 | ||||
| 1. | 2011/10/31 | $72.75 | $0.30 | 21.67% | 1,253.30 | 10.77% |
| 2. | 2011/11/30 | $73.45 | 0.96% | 1,246.96 | -0.51% | |
| 3. | 2011/12/31 | $70.07 | -4.60% | 1,257.60 | 0.85% | |
| 4. | 2012/01/31 | $82.05 | $0.30 | 17.53% | 1,312.41 | 4.36% |
| 5. | 2012/02/29 | $77.38 | -5.69% | 1,365.68 | 4.06% | |
| 6. | 2012/03/31 | $79.76 | 3.08% | 1,408.47 | 3.13% | |
| 7. | 2012/04/30 | $76.18 | $0.30 | -4.11% | 1,397.91 | -0.75% |
| 8. | 2012/05/31 | $77.20 | 1.34% | 1,310.33 | -6.27% | |
| 9. | 2012/06/30 | $82.78 | 7.23% | 1,362.16 | 3.96% | |
| 10. | 2012/07/31 | $85.62 | $0.30 | 3.79% | 1,379.32 | 1.26% |
| 11. | 2012/08/31 | $87.11 | 1.74% | 1,406.58 | 1.98% | |
| 12. | 2012/09/30 | $91.02 | 4.49% | 1,440.67 | 2.42% | |
| 13. | 2012/10/31 | $86.07 | $0.375 | -5.03% | 1,412.16 | -1.98% |
| 14. | 2012/11/30 | $91.59 | 6.41% | 1,416.18 | 0.28% | |
| 15. | 2012/12/31 | $94.65 | 3.34% | 1,426.19 | 0.71% | |
| 16. | 2013/01/31 | $101.35 | $0.375 | 7.47% | 1,498.11 | 5.04% |
| 17. | 2013/02/28 | $101.03 | -0.32% | 1,514.68 | 1.11% | |
| 18. | 2013/03/31 | $105.63 | 4.55% | 1,569.19 | 3.60% | |
| 19. | 2013/04/30 | $106.82 | $0.375 | 1.48% | 1,597.57 | 1.81% |
| 20. | 2013/05/31 | $100.64 | -5.79% | 1,630.74 | 2.08% | |
| 21. | 2013/06/30 | $98.80 | -1.83% | 1,606.28 | -1.50% | |
| 22. | 2013/07/31 | $98.78 | $0.375 | 0.36% | 1,685.73 | 4.95% |
| 23. | 2013/08/31 | $97.89 | -0.90% | 1,632.97 | -3.13% | |
| 24. | 2013/09/30 | $104.37 | 6.62% | 1,681.55 | 2.97% | |
| 25. | 2013/10/31 | $104.88 | $0.43 | 0.90% | 1,756.54 | 4.46% |
| 26. | 2013/11/30 | $113.33 | 8.06% | 1,805.81 | 2.80% | |
| 27. | 2013/12/31 | $116.55 | 2.84% | 1,848.36 | 2.36% | |
| 28. | 2014/01/31 | $106.55 | $0.43 | -8.21% | 1,782.59 | -3.56% |
| 29. | 2014/02/28 | $110.02 | 3.26% | 1,859.45 | 4.31% | |
| 30. | 2014/03/31 | $113.77 | 3.41% | 1,872.34 | 0.69% | |
| 31. | 2014/04/30 | $110.70 | $0.43 | -2.32% | 1,883.95 | 0.62% |
| 32. | 2014/05/31 | $121.85 | 10.07% | 1,923.57 | 2.10% | |
| 33. | 2014/06/30 | $124.74 | 2.37% | 1,960.23 | 1.91% | |
| 34. | 2014/07/31 | $113.09 | $0.43 | -8.99% | 1,930.67 | -1.51% |
| 35. | 2014/08/31 | $115.65 | 2.26% | 2,003.37 | 3.77% | |
| 36. | 2014/09/30 | $112.51 | -2.72% | 1,972.29 | -1.55% | |
| 37. | 2014/10/31 | $115.04 | $0.49 | 2.68% | 2,018.05 | 2.32% |
| 38. | 2014/11/30 | $119.91 | 4.23% | 2,067.56 | 2.45% | |
| 39. | 2014/12/31 | $119.47 | -0.37% | 2,058.90 | -0.42% | |
| 40. | 2015/01/31 | $117.98 | $0.49 | -0.84% | 1,994.99 | -3.10% |
| 41. | 2015/02/28 | $120.43 | 2.08% | 2,104.50 | 5.49% | |
| 42. | 2015/03/31 | $112.54 | $0.49 | -6.14% | 2,067.89 | -1.74% |
| 43. | 2015/04/30 | $113.96 | 1.26% | 2,085.51 | 0.85% | |
| 44. | 2015/05/31 | $116.98 | 2.65% | 2,107.39 | 1.05% | |
| 45. | 2015/06/30 | $106.59 | $0.49 | -8.46% | 2,063.11 | -2.10% |
| 46. | 2015/07/31 | $101.89 | -4.41% | 2,103.84 | 1.97% | |
| 47. | 2015/08/31 | $97.65 | -4.16% | 1,972.18 | -6.26% | |
| 48. | 2015/09/30 | $85.34 | -12.61% | 1,920.03 | -2.64% | |
| 49. | 2015/10/31 | $93.22 | $0.54 | 9.87% | 2,079.36 | 8.30% |
| 50. | 2015/11/30 | $95.16 | 2.08% | 2,080.41 | 0.05% | |
| 51. | 2015/12/31 | $98.52 | 3.53% | 2,043.94 | -1.75% | |
| 52. | 2016/01/31 | $90.60 | $0.54 | -7.49% | 1,940.24 | -5.07% |
| 53. | 2016/02/29 | $89.99 | -0.67% | 1,932.23 | -0.41% | |
| 54. | 2016/03/31 | $87.74 | -2.50% | 2,059.74 | 6.60% | |
| 55. | 2016/04/30 | $93.68 | $0.54 | 7.39% | 2,065.30 | 0.27% |
| 56. | 2016/05/31 | $112.47 | 20.06% | 2,096.95 | 1.53% | |
| 57. | 2016/06/30 | $103.41 | -8.06% | 2,098.86 | 0.09% | |
| 58. | 2016/07/31 | $106.77 | $0.54 | 3.77% | 2,173.60 | 3.56% |
| 59. | 2016/08/31 | $106.50 | -0.25% | 2,170.95 | -0.12% | |
| 60. | 2016/09/30 | $102.20 | -4.04% | 2,168.27 | -0.12% | |
| 61. | 2016/10/31 | $100.77 | $0.54 | -0.87% | 2,126.15 | -1.94% |
| 62. | 2016/11/30 | $102.71 | 1.93% | 2,198.81 | 3.42% | |
| 63. | 2016/12/31 | $105.21 | 2.43% | 2,238.83 | 1.82% | |
| 64. | 2017/01/31 | $108.31 | $0.54 | 3.46% | 2,278.87 | 1.79% |
| 65. | 2017/02/28 | $113.83 | 5.10% | 2,363.64 | 3.72% | |
| 66. | 2017/03/31 | $113.20 | -0.55% | 2,362.72 | -0.04% | |
| 67. | 2017/04/30 | $116.61 | $0.54 | 3.49% | 2,384.20 | 0.91% |
| 68. | 2017/05/31 | $117.42 | 0.69% | 2,411.80 | 1.16% | |
| 69. | 2017/06/30 | $118.36 | 0.80% | 2,423.41 | 0.48% | |
| 70. | 2017/07/31 | $116.82 | $0.54 | -0.84% | 2,470.30 | 1.93% |
| 71. | 2017/08/31 | $117.20 | 0.33% | 2,471.65 | 0.05% | |
| 平均 (R): | 1.27% | 1.15% | ||||
| 標準偏差： | 6.07% | 3.01% | ||||
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MON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
Monsanto Co.、分散の計算、および戻り値の共分散
| t | 日付 | RMON,t | RS&P 500,t | (RMON,t–RMON)2 | (RS&P 500,t–RS&P 500)2 | (RMON,t–RMON)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011/10/31 | 21.67% | 10.77% | 416.05 | 92.57 | 196.25 |
| 2. | 2011/11/30 | 0.96% | -0.51% | 0.10 | 2.74 | 0.51 |
| 3. | 2011/12/31 | -4.60% | 0.85% | 34.50 | 0.09 | 1.75 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2017/07/31 | -0.84% | 1.93% | 4.48 | 0.61 | -1.66 |
| 71. | 2017/08/31 | 0.33% | 0.05% | 0.90 | 1.20 | 1.04 |
| トータル (Σ): | 2,577.67 | 633.66 | 743.38 | |||
| t | 日付 | RMON,t | RS&P 500,t | (RMON,t–RMON)2 | (RS&P 500,t–RS&P 500)2 | (RMON,t–RMON)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011/10/31 | 21.67% | 10.77% | 416.05 | 92.57 | 196.25 |
| 2. | 2011/11/30 | 0.96% | -0.51% | 0.10 | 2.74 | 0.51 |
| 3. | 2011/12/31 | -4.60% | 0.85% | 34.50 | 0.09 | 1.75 |
| 4. | 2012/01/31 | 17.53% | 4.36% | 264.18 | 10.29 | 52.13 |
| 5. | 2012/02/29 | -5.69% | 4.06% | 48.49 | 8.46 | -20.25 |
| 6. | 2012/03/31 | 3.08% | 3.13% | 3.25 | 3.93 | 3.58 |
| 7. | 2012/04/30 | -4.11% | -0.75% | 28.99 | 3.61 | 10.23 |
| 8. | 2012/05/31 | 1.34% | -6.27% | 0.00 | 54.99 | -0.50 |
| 9. | 2012/06/30 | 7.23% | 3.96% | 35.48 | 7.87 | 16.71 |
| 10. | 2012/07/31 | 3.79% | 1.26% | 6.36 | 0.01 | 0.27 |
| 11. | 2012/08/31 | 1.74% | 1.98% | 0.22 | 0.68 | 0.39 |
| 12. | 2012/09/30 | 4.49% | 2.42% | 10.35 | 1.62 | 4.09 |
| 13. | 2012/10/31 | -5.03% | -1.98% | 39.67 | 9.79 | 19.71 |
| 14. | 2012/11/30 | 6.41% | 0.28% | 26.44 | 0.75 | -4.45 |
| 15. | 2012/12/31 | 3.34% | 0.71% | 4.28 | 0.20 | -0.92 |
| 16. | 2013/01/31 | 7.47% | 5.04% | 38.48 | 15.15 | 24.14 |
| 17. | 2013/02/28 | -0.32% | 1.11% | 2.52 | 0.00 | 0.07 |
| 18. | 2013/03/31 | 4.55% | 3.60% | 10.77 | 5.99 | 8.03 |
| 19. | 2013/04/30 | 1.48% | 1.81% | 0.04 | 0.43 | 0.14 |
| 20. | 2013/05/31 | -5.79% | 2.08% | 49.80 | 0.86 | -6.53 |
| 21. | 2013/06/30 | -1.83% | -1.50% | 9.61 | 7.03 | 8.22 |
| 22. | 2013/07/31 | 0.36% | 4.95% | 0.83 | 14.41 | -3.46 |
| 23. | 2013/08/31 | -0.90% | -3.13% | 4.72 | 18.32 | 9.30 |
| 24. | 2013/09/30 | 6.62% | 2.97% | 28.60 | 3.33 | 9.76 |
| 25. | 2013/10/31 | 0.90% | 4.46% | 0.14 | 10.95 | -1.23 |
| 26. | 2013/11/30 | 8.06% | 2.80% | 46.04 | 2.74 | 11.22 |
| 27. | 2013/12/31 | 2.84% | 2.36% | 2.46 | 1.45 | 1.89 |
| 28. | 2014/01/31 | -8.21% | -3.56% | 89.92 | 22.17 | 44.65 |
| 29. | 2014/02/28 | 3.26% | 4.31% | 3.94 | 9.99 | 6.27 |
| 30. | 2014/03/31 | 3.41% | 0.69% | 4.57 | 0.21 | -0.98 |
| 31. | 2014/04/30 | -2.32% | 0.62% | 12.90 | 0.28 | 1.91 |
| 32. | 2014/05/31 | 10.07% | 2.10% | 77.45 | 0.91 | 8.38 |
| 33. | 2014/06/30 | 2.37% | 1.91% | 1.21 | 0.57 | 0.83 |
| 34. | 2014/07/31 | -8.99% | -1.51% | 105.40 | 7.07 | 27.30 |
| 35. | 2014/08/31 | 2.26% | 3.77% | 0.98 | 6.84 | 2.59 |
| 36. | 2014/09/30 | -2.72% | -1.55% | 15.89 | 7.30 | 10.77 |
| 37. | 2014/10/31 | 2.68% | 2.32% | 2.00 | 1.37 | 1.65 |
| 38. | 2014/11/30 | 4.23% | 2.45% | 8.77 | 1.70 | 3.86 |
| 39. | 2014/12/31 | -0.37% | -0.42% | 2.69 | 2.46 | 2.57 |
| 40. | 2015/01/31 | -0.84% | -3.10% | 4.45 | 18.10 | 8.97 |
| 41. | 2015/02/28 | 2.08% | 5.49% | 0.65 | 18.82 | 3.49 |
| 42. | 2015/03/31 | -6.14% | -1.74% | 55.00 | 8.35 | 21.44 |
| 43. | 2015/04/30 | 1.26% | 0.85% | 0.00 | 0.09 | 0.00 |
| 44. | 2015/05/31 | 2.65% | 1.05% | 1.90 | 0.01 | -0.14 |
| 45. | 2015/06/30 | -8.46% | -2.10% | 94.76 | 10.57 | 31.66 |
| 46. | 2015/07/31 | -4.41% | 1.97% | 32.27 | 0.68 | -4.68 |
| 47. | 2015/08/31 | -4.16% | -6.26% | 29.52 | 54.89 | 40.25 |
| 48. | 2015/09/30 | -12.61% | -2.64% | 192.60 | 14.40 | 52.67 |
| 49. | 2015/10/31 | 9.87% | 8.30% | 73.87 | 51.09 | 61.43 |
| 50. | 2015/11/30 | 2.08% | 0.05% | 0.66 | 1.21 | -0.89 |
| 51. | 2015/12/31 | 3.53% | -1.75% | 5.10 | 8.43 | -6.56 |
| 52. | 2016/01/31 | -7.49% | -5.07% | 76.78 | 38.74 | 54.54 |
| 53. | 2016/02/29 | -0.67% | -0.41% | 3.78 | 2.44 | 3.04 |
| 54. | 2016/03/31 | -2.50% | 6.60% | 14.23 | 29.68 | -20.55 |
| 55. | 2016/04/30 | 7.39% | 0.27% | 37.38 | 0.78 | -5.38 |
| 56. | 2016/05/31 | 20.06% | 1.53% | 352.91 | 0.15 | 7.17 |
| 57. | 2016/06/30 | -8.06% | 0.09% | 87.00 | 1.12 | 9.88 |
| 58. | 2016/07/31 | 3.77% | 3.56% | 6.25 | 5.81 | 6.03 |
| 59. | 2016/08/31 | -0.25% | -0.12% | 2.32 | 1.62 | 1.94 |
| 60. | 2016/09/30 | -4.04% | -0.12% | 28.19 | 1.62 | 6.76 |
| 61. | 2016/10/31 | -0.87% | -1.94% | 4.59 | 9.57 | 6.63 |
| 62. | 2016/11/30 | 1.93% | 3.42% | 0.43 | 5.14 | 1.48 |
| 63. | 2016/12/31 | 2.43% | 1.82% | 1.35 | 0.45 | 0.78 |
| 64. | 2017/01/31 | 3.46% | 1.79% | 4.79 | 0.41 | 1.40 |
| 65. | 2017/02/28 | 5.10% | 3.72% | 14.63 | 6.60 | 9.83 |
| 66. | 2017/03/31 | -0.55% | -0.04% | 3.33 | 1.42 | 2.17 |
| 67. | 2017/04/30 | 3.49% | 0.91% | 4.92 | 0.06 | -0.54 |
| 68. | 2017/05/31 | 0.69% | 1.16% | 0.33 | 0.00 | 0.00 |
| 69. | 2017/06/30 | 0.80% | 0.48% | 0.22 | 0.45 | 0.32 |
| 70. | 2017/07/31 | -0.84% | 1.93% | 4.48 | 0.61 | -1.66 |
| 71. | 2017/08/31 | 0.33% | 0.05% | 0.90 | 1.20 | 1.04 |
| トータル (Σ): | 2,577.67 | 633.66 | 743.38 | |||
すべて表示
分散MON = Σ(RMON,t–RMON)2 ÷ (71 – 1)
= 2,577.67 ÷ (71 – 1)
= 36.82
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 633.66 ÷ (71 – 1)
= 9.05
共 分散MON, S&P 500 = Σ(RMON,t–RMON)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 743.38 ÷ (71 – 1)
= 10.62
システマティックなリスク推定 (β)
| 分散MON | 36.82 |
| 分散S&P 500 | 9.05 |
| 共 分散MON, S&P 500 | 10.62 |
| 相関係数MON, S&P 5001 | 0.58 |
| βMON2 | 1.17 |
| αMON3 | -0.08% |
計算
1 相関係数MON, S&P 500
= 共 分散MON, S&P 500 ÷ (標準偏差MON × 標準偏差S&P 500)
= 10.62 ÷ (6.07% × 3.01%)
= 0.58
2 βMON
= 共 分散MON, S&P 500 ÷ 分散S&P 500
= 10.62 ÷ 9.05
= 1.17
3 αMON
= 平均MON – βMON × 平均S&P 500
= 1.27% – 1.17 × 1.15%
= -0.08%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.76% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.73% |
| 普通株式 Monsanto システマティックリスク | βMON | 1.17 |
| モンサント普通株の期待収益率3 | E(RMON) | 16.45% |
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(RMON) = RF + βMON [E(RM) – RF]
= 4.76% + 1.17 [14.73% – 4.76%]
= 16.45%