資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Express Scripts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
Express Scripts Holding Co.、月間収益率
| Express Scripts Holding Co. (ESRX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格ESRX,t1 | 配当ESRX,t1 | RESRX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2013/01/31 | $53.42 | 1,498.11 | ||||
| 1. | 2013/02/28 | $56.93 | 6.57% | 1,514.68 | 1.11% | |
| 2. | 2013/03/31 | $57.62 | 1.21% | 1,569.19 | 3.60% | |
| 3. | 2013/04/30 | $59.37 | 3.04% | 1,597.57 | 1.81% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2017/11/30 | $65.18 | 6.35% | 2,647.58 | 2.81% | |
| 59. | 2017/12/31 | $74.64 | 14.51% | 2,673.61 | 0.98% | |
| 平均 (R): | 0.73% | 1.02% | ||||
| 標準偏差： | 5.71% | 2.71% | ||||
| Express Scripts Holding Co. (ESRX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格ESRX,t1 | 配当ESRX,t1 | RESRX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2013/01/31 | $53.42 | 1,498.11 | ||||
| 1. | 2013/02/28 | $56.93 | 6.57% | 1,514.68 | 1.11% | |
| 2. | 2013/03/31 | $57.62 | 1.21% | 1,569.19 | 3.60% | |
| 3. | 2013/04/30 | $59.37 | 3.04% | 1,597.57 | 1.81% | |
| 4. | 2013/05/31 | $62.12 | 4.63% | 1,630.74 | 2.08% | |
| 5. | 2013/06/30 | $61.74 | -0.61% | 1,606.28 | -1.50% | |
| 6. | 2013/07/31 | $65.55 | 6.17% | 1,685.73 | 4.95% | |
| 7. | 2013/08/31 | $63.88 | -2.55% | 1,632.97 | -3.13% | |
| 8. | 2013/09/30 | $61.80 | -3.26% | 1,681.55 | 2.97% | |
| 9. | 2013/10/31 | $62.52 | 1.17% | 1,756.54 | 4.46% | |
| 10. | 2013/11/30 | $67.35 | 7.73% | 1,805.81 | 2.80% | |
| 11. | 2013/12/31 | $70.24 | 4.29% | 1,848.36 | 2.36% | |
| 12. | 2014/01/31 | $74.69 | 6.34% | 1,782.59 | -3.56% | |
| 13. | 2014/02/28 | $75.31 | 0.83% | 1,859.45 | 4.31% | |
| 14. | 2014/03/31 | $75.09 | -0.29% | 1,872.34 | 0.69% | |
| 15. | 2014/04/30 | $66.58 | -11.33% | 1,883.95 | 0.62% | |
| 16. | 2014/05/31 | $71.47 | 7.34% | 1,923.57 | 2.10% | |
| 17. | 2014/06/30 | $69.33 | -2.99% | 1,960.23 | 1.91% | |
| 18. | 2014/07/31 | $69.65 | 0.46% | 1,930.67 | -1.51% | |
| 19. | 2014/08/31 | $73.93 | 6.15% | 2,003.37 | 3.77% | |
| 20. | 2014/09/30 | $70.63 | -4.46% | 1,972.29 | -1.55% | |
| 21. | 2014/10/31 | $76.82 | 8.76% | 2,018.05 | 2.32% | |
| 22. | 2014/11/30 | $83.15 | 8.24% | 2,067.56 | 2.45% | |
| 23. | 2014/12/31 | $84.67 | 1.83% | 2,058.90 | -0.42% | |
| 24. | 2015/01/31 | $80.71 | -4.68% | 1,994.99 | -3.10% | |
| 25. | 2015/02/28 | $84.79 | 5.06% | 2,104.50 | 5.49% | |
| 26. | 2015/03/31 | $86.77 | 2.34% | 2,067.89 | -1.74% | |
| 27. | 2015/04/30 | $86.40 | -0.43% | 2,085.51 | 0.85% | |
| 28. | 2015/05/31 | $87.14 | 0.86% | 2,107.39 | 1.05% | |
| 29. | 2015/06/30 | $88.94 | 2.07% | 2,063.11 | -2.10% | |
| 30. | 2015/07/31 | $90.07 | 1.27% | 2,103.84 | 1.97% | |
| 31. | 2015/08/31 | $83.60 | -7.18% | 1,972.18 | -6.26% | |
| 32. | 2015/09/30 | $80.96 | -3.16% | 1,920.03 | -2.64% | |
| 33. | 2015/10/31 | $86.38 | 6.69% | 2,079.36 | 8.30% | |
| 34. | 2015/11/30 | $85.48 | -1.04% | 2,080.41 | 0.05% | |
| 35. | 2015/12/31 | $87.41 | 2.26% | 2,043.94 | -1.75% | |
| 36. | 2016/01/31 | $71.87 | -17.78% | 1,940.24 | -5.07% | |
| 37. | 2016/02/29 | $70.38 | -2.07% | 1,932.23 | -0.41% | |
| 38. | 2016/03/31 | $68.69 | -2.40% | 2,059.74 | 6.60% | |
| 39. | 2016/04/30 | $73.73 | 7.34% | 2,065.30 | 0.27% | |
| 40. | 2016/05/31 | $75.55 | 2.47% | 2,096.95 | 1.53% | |
| 41. | 2016/06/30 | $75.80 | 0.33% | 2,098.86 | 0.09% | |
| 42. | 2016/07/31 | $76.07 | 0.36% | 2,173.60 | 3.56% | |
| 43. | 2016/08/31 | $72.70 | -4.43% | 2,170.95 | -0.12% | |
| 44. | 2016/09/30 | $70.53 | -2.98% | 2,168.27 | -0.12% | |
| 45. | 2016/10/31 | $67.40 | -4.44% | 2,126.15 | -1.94% | |
| 46. | 2016/11/30 | $75.88 | 12.58% | 2,198.81 | 3.42% | |
| 47. | 2016/12/31 | $68.79 | -9.34% | 2,238.83 | 1.82% | |
| 48. | 2017/01/31 | $68.88 | 0.13% | 2,278.87 | 1.79% | |
| 49. | 2017/02/28 | $70.65 | 2.57% | 2,363.64 | 3.72% | |
| 50. | 2017/03/31 | $65.91 | -6.71% | 2,362.72 | -0.04% | |
| 51. | 2017/04/30 | $61.34 | -6.93% | 2,384.20 | 0.91% | |
| 52. | 2017/05/31 | $59.75 | -2.59% | 2,411.80 | 1.16% | |
| 53. | 2017/06/30 | $63.84 | 6.85% | 2,423.41 | 0.48% | |
| 54. | 2017/07/31 | $62.64 | -1.88% | 2,470.30 | 1.93% | |
| 55. | 2017/08/31 | $62.82 | 0.29% | 2,471.65 | 0.05% | |
| 56. | 2017/09/30 | $63.32 | 0.80% | 2,519.36 | 1.93% | |
| 57. | 2017/10/31 | $61.29 | -3.21% | 2,575.26 | 2.22% | |
| 58. | 2017/11/30 | $65.18 | 6.35% | 2,647.58 | 2.81% | |
| 59. | 2017/12/31 | $74.64 | 14.51% | 2,673.61 | 0.98% | |
| 平均 (R): | 0.73% | 1.02% | ||||
| 標準偏差： | 5.71% | 2.71% | ||||
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ESRX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
Express Scripts Holding Co.、分散の計算、および戻り値の共分散
| t | 日付 | RESRX,t | RS&P 500,t | (RESRX,t–RESRX)2 | (RS&P 500,t–RS&P 500)2 | (RESRX,t–RESRX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013/02/28 | 6.57% | 1.11% | 34.11 | 0.01 | 0.49 |
| 2. | 2013/03/31 | 1.21% | 3.60% | 0.23 | 6.64 | 1.24 |
| 3. | 2013/04/30 | 3.04% | 1.81% | 5.32 | 0.62 | 1.81 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2017/11/30 | 6.35% | 2.81% | 31.54 | 3.19 | 10.03 |
| 59. | 2017/12/31 | 14.51% | 0.98% | 189.98 | 0.00 | -0.54 |
| トータル (Σ): | 1,888.17 | 424.45 | 388.57 | |||
| t | 日付 | RESRX,t | RS&P 500,t | (RESRX,t–RESRX)2 | (RS&P 500,t–RS&P 500)2 | (RESRX,t–RESRX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013/02/28 | 6.57% | 1.11% | 34.11 | 0.01 | 0.49 |
| 2. | 2013/03/31 | 1.21% | 3.60% | 0.23 | 6.64 | 1.24 |
| 3. | 2013/04/30 | 3.04% | 1.81% | 5.32 | 0.62 | 1.81 |
| 4. | 2013/05/31 | 4.63% | 2.08% | 15.22 | 1.11 | 4.11 |
| 5. | 2013/06/30 | -0.61% | -1.50% | 1.80 | 6.36 | 3.39 |
| 6. | 2013/07/31 | 6.17% | 4.95% | 29.60 | 15.40 | 21.35 |
| 7. | 2013/08/31 | -2.55% | -3.13% | 10.75 | 17.24 | 13.61 |
| 8. | 2013/09/30 | -3.26% | 2.97% | 15.89 | 3.81 | -7.78 |
| 9. | 2013/10/31 | 1.17% | 4.46% | 0.19 | 11.81 | 1.49 |
| 10. | 2013/11/30 | 7.73% | 2.80% | 48.93 | 3.18 | 12.47 |
| 11. | 2013/12/31 | 4.29% | 2.36% | 12.68 | 1.78 | 4.75 |
| 12. | 2014/01/31 | 6.34% | -3.56% | 31.42 | 20.98 | -25.67 |
| 13. | 2014/02/28 | 0.83% | 4.31% | 0.01 | 10.82 | 0.33 |
| 14. | 2014/03/31 | -0.29% | 0.69% | 1.05 | 0.11 | 0.34 |
| 15. | 2014/04/30 | -11.33% | 0.62% | 145.53 | 0.16 | 4.85 |
| 16. | 2014/05/31 | 7.34% | 2.10% | 43.75 | 1.17 | 7.15 |
| 17. | 2014/06/30 | -2.99% | 1.91% | 13.87 | 0.78 | -3.29 |
| 18. | 2014/07/31 | 0.46% | -1.51% | 0.07 | 6.40 | 0.68 |
| 19. | 2014/08/31 | 6.15% | 3.77% | 29.32 | 7.53 | 14.85 |
| 20. | 2014/09/30 | -4.46% | -1.55% | 26.98 | 6.62 | 13.37 |
| 21. | 2014/10/31 | 8.76% | 2.32% | 64.54 | 1.68 | 10.43 |
| 22. | 2014/11/30 | 8.24% | 2.45% | 56.39 | 2.05 | 10.75 |
| 23. | 2014/12/31 | 1.83% | -0.42% | 1.20 | 2.08 | -1.58 |
| 24. | 2015/01/31 | -4.68% | -3.10% | 29.24 | 17.03 | 22.31 |
| 25. | 2015/02/28 | 5.06% | 5.49% | 18.70 | 19.95 | 19.32 |
| 26. | 2015/03/31 | 2.34% | -1.74% | 2.58 | 7.63 | -4.43 |
| 27. | 2015/04/30 | -0.43% | 0.85% | 1.34 | 0.03 | 0.20 |
| 28. | 2015/05/31 | 0.86% | 1.05% | 0.02 | 0.00 | 0.00 |
| 29. | 2015/06/30 | 2.07% | -2.10% | 1.78 | 9.76 | -4.17 |
| 30. | 2015/07/31 | 1.27% | 1.97% | 0.29 | 0.91 | 0.51 |
| 31. | 2015/08/31 | -7.18% | -6.26% | 62.63 | 53.00 | 57.62 |
| 32. | 2015/09/30 | -3.16% | -2.64% | 15.12 | 13.44 | 14.26 |
| 33. | 2015/10/31 | 6.69% | 8.30% | 35.57 | 52.94 | 43.40 |
| 34. | 2015/11/30 | -1.04% | 0.05% | 3.14 | 0.94 | 1.72 |
| 35. | 2015/12/31 | 2.26% | -1.75% | 2.33 | 7.70 | -4.24 |
| 36. | 2016/01/31 | -17.78% | -5.07% | 342.57 | 37.16 | 112.83 |
| 37. | 2016/02/29 | -2.07% | -0.41% | 7.86 | 2.06 | 4.02 |
| 38. | 2016/03/31 | -2.40% | 6.60% | 9.81 | 31.10 | -17.46 |
| 39. | 2016/04/30 | 7.34% | 0.27% | 43.65 | 0.57 | -4.97 |
| 40. | 2016/05/31 | 2.47% | 1.53% | 3.02 | 0.26 | 0.89 |
| 41. | 2016/06/30 | 0.33% | 0.09% | 0.16 | 0.87 | 0.37 |
| 42. | 2016/07/31 | 0.36% | 3.56% | 0.14 | 6.44 | -0.95 |
| 43. | 2016/08/31 | -4.43% | -0.12% | 26.63 | 1.31 | 5.90 |
| 44. | 2016/09/30 | -2.98% | -0.12% | 13.80 | 1.31 | 4.26 |
| 45. | 2016/10/31 | -4.44% | -1.94% | 26.71 | 8.79 | 15.32 |
| 46. | 2016/11/30 | 12.58% | 3.42% | 140.45 | 5.74 | 28.39 |
| 47. | 2016/12/31 | -9.34% | 1.82% | 101.49 | 0.64 | -8.04 |
| 48. | 2017/01/31 | 0.13% | 1.79% | 0.36 | 0.59 | -0.46 |
| 49. | 2017/02/28 | 2.57% | 3.72% | 3.38 | 7.28 | 4.96 |
| 50. | 2017/03/31 | -6.71% | -0.04% | 55.35 | 1.13 | 7.90 |
| 51. | 2017/04/30 | -6.93% | 0.91% | 58.74 | 0.01 | 0.87 |
| 52. | 2017/05/31 | -2.59% | 1.16% | 11.04 | 0.02 | -0.45 |
| 53. | 2017/06/30 | 6.85% | 0.48% | 37.39 | 0.29 | -3.31 |
| 54. | 2017/07/31 | -1.88% | 1.93% | 6.81 | 0.83 | -2.38 |
| 55. | 2017/08/31 | 0.29% | 0.05% | 0.20 | 0.94 | 0.43 |
| 56. | 2017/09/30 | 0.80% | 1.93% | 0.00 | 0.82 | 0.06 |
| 57. | 2017/10/31 | -3.21% | 2.22% | 15.50 | 1.43 | -4.71 |
| 58. | 2017/11/30 | 6.35% | 2.81% | 31.54 | 3.19 | 10.03 |
| 59. | 2017/12/31 | 14.51% | 0.98% | 189.98 | 0.00 | -0.54 |
| トータル (Σ): | 1,888.17 | 424.45 | 388.57 | |||
すべて表示
分散ESRX = Σ(RESRX,t–RESRX)2 ÷ (59 – 1)
= 1,888.17 ÷ (59 – 1)
= 32.55
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 424.45 ÷ (59 – 1)
= 7.32
共 分散ESRX, S&P 500 = Σ(RESRX,t–RESRX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 388.57 ÷ (59 – 1)
= 6.70
システマティックなリスク推定 (β)
| 分散ESRX | 32.55 |
| 分散S&P 500 | 7.32 |
| 共 分散ESRX, S&P 500 | 6.70 |
| 相関係数ESRX, S&P 5001 | 0.43 |
| βESRX2 | 0.92 |
| αESRX3 | -0.21% |
計算
1 相関係数ESRX, S&P 500
= 共 分散ESRX, S&P 500 ÷ (標準偏差ESRX × 標準偏差S&P 500)
= 6.70 ÷ (5.71% × 2.71%)
= 0.43
2 βESRX
= 共 分散ESRX, S&P 500 ÷ 分散S&P 500
= 6.70 ÷ 7.32
= 0.92
3 αESRX
= 平均ESRX – βESRX × 平均S&P 500
= 0.73% – 0.92 × 1.02%
= -0.21%
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) | 13.79% |
| 普通株式 Express Scripts システマティックリスク | βESRX | 0.92 |
| Express Scripts普通株式の期待収益率3 | E(RESRX) | 13.02% |
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(RESRX) = RF + βESRX [E(RM) – RF]
= 4.67% + 0.92 [13.79% – 4.67%]
= 13.02%