資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Time Warner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
Time Warner Inc.、月間収益率
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格TWX,t1 | 配当TWX,t1 | RTWX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2013/01/31 | $50.52 | 1,498.11 | ||||
| 1. | 2013/02/28 | $53.17 | $0.2875 | 5.81% | 1,514.68 | 1.11% |
| 2. | 2013/03/31 | $57.62 | 8.37% | 1,569.19 | 3.60% | |
| 3. | 2013/04/30 | $59.78 | 3.75% | 1,597.57 | 1.81% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2017/11/30 | $91.51 | -6.90% | 2,647.58 | 2.81% | |
| 59. | 2017/12/31 | $91.47 | -0.04% | 2,673.61 | 0.98% | |
| 平均 (R): | 1.35% | 1.02% | ||||
| 標準偏差： | 6.00% | 2.71% | ||||
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格TWX,t1 | 配当TWX,t1 | RTWX,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2013/01/31 | $50.52 | 1,498.11 | ||||
| 1. | 2013/02/28 | $53.17 | $0.2875 | 5.81% | 1,514.68 | 1.11% |
| 2. | 2013/03/31 | $57.62 | 8.37% | 1,569.19 | 3.60% | |
| 3. | 2013/04/30 | $59.78 | 3.75% | 1,597.57 | 1.81% | |
| 4. | 2013/05/31 | $58.37 | $0.2875 | -1.88% | 1,630.74 | 2.08% |
| 5. | 2013/06/30 | $57.82 | -0.94% | 1,606.28 | -1.50% | |
| 6. | 2013/07/31 | $62.26 | 7.68% | 1,685.73 | 4.95% | |
| 7. | 2013/08/31 | $60.53 | $0.2875 | -2.32% | 1,632.97 | -3.13% |
| 8. | 2013/09/30 | $65.81 | 8.72% | 1,681.55 | 2.97% | |
| 9. | 2013/10/31 | $68.74 | 4.45% | 1,756.54 | 4.46% | |
| 10. | 2013/11/30 | $65.71 | $0.2875 | -3.99% | 1,805.81 | 2.80% |
| 11. | 2013/12/31 | $69.72 | 6.10% | 1,848.36 | 2.36% | |
| 12. | 2014/01/31 | $62.83 | -9.88% | 1,782.59 | -3.56% | |
| 13. | 2014/02/28 | $67.13 | $0.3175 | 7.35% | 1,859.45 | 4.31% |
| 14. | 2014/03/31 | $65.33 | -2.68% | 1,872.34 | 0.69% | |
| 15. | 2014/04/30 | $66.46 | 1.73% | 1,883.95 | 0.62% | |
| 16. | 2014/05/31 | $69.83 | $0.3175 | 5.55% | 1,923.57 | 2.10% |
| 17. | 2014/06/30 | $70.25 | 0.60% | 1,960.23 | 1.91% | |
| 18. | 2014/07/31 | $83.02 | 18.18% | 1,930.67 | -1.51% | |
| 19. | 2014/08/31 | $77.03 | $0.3175 | -6.83% | 2,003.37 | 3.77% |
| 20. | 2014/09/30 | $75.21 | -2.36% | 1,972.29 | -1.55% | |
| 21. | 2014/10/31 | $79.47 | 5.66% | 2,018.05 | 2.32% | |
| 22. | 2014/11/30 | $85.12 | $0.3175 | 7.51% | 2,067.56 | 2.45% |
| 23. | 2014/12/31 | $85.42 | 0.35% | 2,058.90 | -0.42% | |
| 24. | 2015/01/31 | $77.93 | -8.77% | 1,994.99 | -3.10% | |
| 25. | 2015/02/28 | $81.86 | $0.35 | 5.49% | 2,104.50 | 5.49% |
| 26. | 2015/03/31 | $84.44 | 3.15% | 2,067.89 | -1.74% | |
| 27. | 2015/04/30 | $84.41 | -0.04% | 2,085.51 | 0.85% | |
| 28. | 2015/05/31 | $84.48 | $0.35 | 0.50% | 2,107.39 | 1.05% |
| 29. | 2015/06/30 | $87.41 | 3.47% | 2,063.11 | -2.10% | |
| 30. | 2015/07/31 | $88.04 | 0.72% | 2,103.84 | 1.97% | |
| 31. | 2015/08/31 | $71.10 | $0.35 | -18.84% | 1,972.18 | -6.26% |
| 32. | 2015/09/30 | $68.75 | -3.31% | 1,920.03 | -2.64% | |
| 33. | 2015/10/31 | $75.34 | 9.59% | 2,079.36 | 8.30% | |
| 34. | 2015/11/30 | $69.98 | $0.35 | -6.65% | 2,080.41 | 0.05% |
| 35. | 2015/12/31 | $64.67 | -7.59% | 2,043.94 | -1.75% | |
| 36. | 2016/01/31 | $70.44 | 8.92% | 1,940.24 | -5.07% | |
| 37. | 2016/02/29 | $66.20 | $0.4025 | -5.45% | 1,932.23 | -0.41% |
| 38. | 2016/03/31 | $72.55 | 9.59% | 2,059.74 | 6.60% | |
| 39. | 2016/04/30 | $75.14 | 3.57% | 2,065.30 | 0.27% | |
| 40. | 2016/05/31 | $75.66 | $0.4025 | 1.23% | 2,096.95 | 1.53% |
| 41. | 2016/06/30 | $73.54 | -2.80% | 2,098.86 | 0.09% | |
| 42. | 2016/07/31 | $76.65 | 4.23% | 2,173.60 | 3.56% | |
| 43. | 2016/08/31 | $78.41 | $0.4025 | 2.82% | 2,170.95 | -0.12% |
| 44. | 2016/09/30 | $79.61 | 1.53% | 2,168.27 | -0.12% | |
| 45. | 2016/10/31 | $88.99 | 11.78% | 2,126.15 | -1.94% | |
| 46. | 2016/11/30 | $91.82 | $0.4025 | 3.63% | 2,198.81 | 3.42% |
| 47. | 2016/12/31 | $96.53 | 5.13% | 2,238.83 | 1.82% | |
| 48. | 2017/01/31 | $96.85 | 0.33% | 2,278.87 | 1.79% | |
| 49. | 2017/02/28 | $98.21 | $0.4025 | 1.82% | 2,363.64 | 3.72% |
| 50. | 2017/03/31 | $97.71 | -0.51% | 2,362.72 | -0.04% | |
| 51. | 2017/04/30 | $99.27 | 1.60% | 2,384.20 | 0.91% | |
| 52. | 2017/05/31 | $99.49 | $0.4025 | 0.63% | 2,411.80 | 1.16% |
| 53. | 2017/06/30 | $100.41 | 0.92% | 2,423.41 | 0.48% | |
| 54. | 2017/07/31 | $102.42 | $0.4025 | 2.40% | 2,470.30 | 1.93% |
| 55. | 2017/08/31 | $101.10 | -1.29% | 2,471.65 | 0.05% | |
| 56. | 2017/09/30 | $102.45 | 1.34% | 2,519.36 | 1.93% | |
| 57. | 2017/10/31 | $98.29 | $0.4025 | -3.67% | 2,575.26 | 2.22% |
| 58. | 2017/11/30 | $91.51 | -6.90% | 2,647.58 | 2.81% | |
| 59. | 2017/12/31 | $91.47 | -0.04% | 2,673.61 | 0.98% | |
| 平均 (R): | 1.35% | 1.02% | ||||
| 標準偏差： | 6.00% | 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TWX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
Time Warner Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013/02/28 | 5.81% | 1.11% | 19.96 | 0.01 | 0.37 |
| 2. | 2013/03/31 | 8.37% | 3.60% | 49.31 | 6.64 | 18.09 |
| 3. | 2013/04/30 | 3.75% | 1.81% | 5.77 | 0.62 | 1.89 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2017/11/30 | -6.90% | 2.81% | 67.98 | 3.19 | -14.73 |
| 59. | 2017/12/31 | -0.04% | 0.98% | 1.93 | 0.00 | 0.05 |
| トータル (Σ): | 2,090.08 | 424.45 | 406.20 | |||
| t | 日付 | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013/02/28 | 5.81% | 1.11% | 19.96 | 0.01 | 0.37 |
| 2. | 2013/03/31 | 8.37% | 3.60% | 49.31 | 6.64 | 18.09 |
| 3. | 2013/04/30 | 3.75% | 1.81% | 5.77 | 0.62 | 1.89 |
| 4. | 2013/05/31 | -1.88% | 2.08% | 10.40 | 1.11 | -3.40 |
| 5. | 2013/06/30 | -0.94% | -1.50% | 5.24 | 6.36 | 5.77 |
| 6. | 2013/07/31 | 7.68% | 4.95% | 40.09 | 15.40 | 24.85 |
| 7. | 2013/08/31 | -2.32% | -3.13% | 13.42 | 17.24 | 15.21 |
| 8. | 2013/09/30 | 8.72% | 2.97% | 54.40 | 3.81 | 14.40 |
| 9. | 2013/10/31 | 4.45% | 4.46% | 9.64 | 11.81 | 10.67 |
| 10. | 2013/11/30 | -3.99% | 2.80% | 28.48 | 3.18 | -9.51 |
| 11. | 2013/12/31 | 6.10% | 2.36% | 22.61 | 1.78 | 6.34 |
| 12. | 2014/01/31 | -9.88% | -3.56% | 126.10 | 20.98 | 51.44 |
| 13. | 2014/02/28 | 7.35% | 4.31% | 36.03 | 10.82 | 19.74 |
| 14. | 2014/03/31 | -2.68% | 0.69% | 16.23 | 0.11 | 1.33 |
| 15. | 2014/04/30 | 1.73% | 0.62% | 0.15 | 0.16 | -0.15 |
| 16. | 2014/05/31 | 5.55% | 2.10% | 17.65 | 1.17 | 4.54 |
| 17. | 2014/06/30 | 0.60% | 1.91% | 0.56 | 0.78 | -0.66 |
| 18. | 2014/07/31 | 18.18% | -1.51% | 283.28 | 6.40 | -42.59 |
| 19. | 2014/08/31 | -6.83% | 3.77% | 66.91 | 7.53 | -22.44 |
| 20. | 2014/09/30 | -2.36% | -1.55% | 13.76 | 6.62 | 9.55 |
| 21. | 2014/10/31 | 5.66% | 2.32% | 18.64 | 1.68 | 5.60 |
| 22. | 2014/11/30 | 7.51% | 2.45% | 37.97 | 2.05 | 8.82 |
| 23. | 2014/12/31 | 0.35% | -0.42% | 0.99 | 2.08 | 1.43 |
| 24. | 2015/01/31 | -8.77% | -3.10% | 102.32 | 17.03 | 41.74 |
| 25. | 2015/02/28 | 5.49% | 5.49% | 17.18 | 19.95 | 18.52 |
| 26. | 2015/03/31 | 3.15% | -1.74% | 3.26 | 7.63 | -4.98 |
| 27. | 2015/04/30 | -0.04% | 0.85% | 1.91 | 0.03 | 0.24 |
| 28. | 2015/05/31 | 0.50% | 1.05% | 0.72 | 0.00 | -0.02 |
| 29. | 2015/06/30 | 3.47% | -2.10% | 4.50 | 9.76 | -6.63 |
| 30. | 2015/07/31 | 0.72% | 1.97% | 0.39 | 0.91 | -0.60 |
| 31. | 2015/08/31 | -18.84% | -6.26% | 407.67 | 53.00 | 147.00 |
| 32. | 2015/09/30 | -3.31% | -2.64% | 21.64 | 13.44 | 17.06 |
| 33. | 2015/10/31 | 9.59% | 8.30% | 67.87 | 52.94 | 59.94 |
| 34. | 2015/11/30 | -6.65% | 0.05% | 63.95 | 0.94 | 7.77 |
| 35. | 2015/12/31 | -7.59% | -1.75% | 79.83 | 7.70 | 24.80 |
| 36. | 2016/01/31 | 8.92% | -5.07% | 57.38 | 37.16 | -46.18 |
| 37. | 2016/02/29 | -5.45% | -0.41% | 46.17 | 2.06 | 9.75 |
| 38. | 2016/03/31 | 9.59% | 6.60% | 67.98 | 31.10 | 45.98 |
| 39. | 2016/04/30 | 3.57% | 0.27% | 4.94 | 0.57 | -1.67 |
| 40. | 2016/05/31 | 1.23% | 1.53% | 0.01 | 0.26 | -0.06 |
| 41. | 2016/06/30 | -2.80% | 0.09% | 17.22 | 0.87 | 3.86 |
| 42. | 2016/07/31 | 4.23% | 3.56% | 8.31 | 6.44 | 7.32 |
| 43. | 2016/08/31 | 2.82% | -0.12% | 2.17 | 1.31 | -1.69 |
| 44. | 2016/09/30 | 1.53% | -0.12% | 0.03 | 1.31 | -0.21 |
| 45. | 2016/10/31 | 11.78% | -1.94% | 108.90 | 8.79 | -30.94 |
| 46. | 2016/11/30 | 3.63% | 3.42% | 5.22 | 5.74 | 5.47 |
| 47. | 2016/12/31 | 5.13% | 1.82% | 14.31 | 0.64 | 3.02 |
| 48. | 2017/01/31 | 0.33% | 1.79% | 1.03 | 0.59 | -0.78 |
| 49. | 2017/02/28 | 1.82% | 3.72% | 0.22 | 7.28 | 1.28 |
| 50. | 2017/03/31 | -0.51% | -0.04% | 3.45 | 1.13 | 1.97 |
| 51. | 2017/04/30 | 1.60% | 0.91% | 0.06 | 0.01 | -0.03 |
| 52. | 2017/05/31 | 0.63% | 1.16% | 0.52 | 0.02 | -0.10 |
| 53. | 2017/06/30 | 0.92% | 0.48% | 0.18 | 0.29 | 0.23 |
| 54. | 2017/07/31 | 2.40% | 1.93% | 1.11 | 0.83 | 0.96 |
| 55. | 2017/08/31 | -1.29% | 0.05% | 6.95 | 0.94 | 2.55 |
| 56. | 2017/09/30 | 1.34% | 1.93% | 0.00 | 0.82 | -0.01 |
| 57. | 2017/10/31 | -3.67% | 2.22% | 25.15 | 1.43 | -6.00 |
| 58. | 2017/11/30 | -6.90% | 2.81% | 67.98 | 3.19 | -14.73 |
| 59. | 2017/12/31 | -0.04% | 0.98% | 1.93 | 0.00 | 0.05 |
| トータル (Σ): | 2,090.08 | 424.45 | 406.20 | |||
すべて表示
分散TWX = Σ(RTWX,t–RTWX)2 ÷ (59 – 1)
= 2,090.08 ÷ (59 – 1)
= 36.04
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TWX, S&P 500 = Σ(RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 406.20 ÷ (59 – 1)
= 7.00
システマティックなリスク推定 (β)
| 分散TWX | 36.04 |
| 分散S&P 500 | 7.32 |
| 共 分散TWX, S&P 500 | 7.00 |
| 相関係数TWX, S&P 5001 | 0.43 |
| βTWX2 | 0.96 |
| αTWX3 | 0.37% |
計算
1 相関係数TWX, S&P 500
= 共 分散TWX, S&P 500 ÷ (標準偏差TWX × 標準偏差S&P 500)
= 7.00 ÷ (6.00% × 2.71%)
= 0.43
2 βTWX
= 共 分散TWX, S&P 500 ÷ 分散S&P 500
= 7.00 ÷ 7.32
= 0.96
3 αTWX
= 平均TWX – βTWX × 平均S&P 500
= 1.35% – 0.96 × 1.02%
= 0.37%
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 Time Warner システマティックリスク | βTWX | 0.96 |
| タイムワーナー普通株の期待収益率3 | E(RTWX) | 13.39% |
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(RTWX) = RF + βTWX [E(RM) – RF]
= 4.67% + 0.96 [13.79% – 4.67%]
= 13.39%