資本資産価格モデル (CAPM)
資本資産価格モデル(CAPM)は、 YUM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
YUM! Brands Inc.、月間収益率
| YUM! Brands Inc. (YUM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格YUM,t1 | 配当YUM,t1 | RYUM,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2011/01/31 | $46.76 | 1,286.12 | ||||
| 1. | 2011/02/28 | $50.33 | 7.63% | 1,327.22 | 3.20% | |
| 2. | 2011/03/31 | $51.38 | 2.09% | 1,325.83 | -0.10% | |
| 3. | 2011/04/30 | $53.64 | $0.25 | 4.89% | 1,363.61 | 2.85% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015/11/30 | $72.51 | 2.26% | 2,080.41 | 0.05% | |
| 59. | 2015/12/31 | $73.05 | 0.74% | 2,043.94 | -1.75% | |
| 平均 (R): | 1.10% | 0.84% | ||||
| 標準偏差： | 5.95% | 3.40% | ||||
| YUM! Brands Inc. (YUM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格YUM,t1 | 配当YUM,t1 | RYUM,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2011/01/31 | $46.76 | 1,286.12 | ||||
| 1. | 2011/02/28 | $50.33 | 7.63% | 1,327.22 | 3.20% | |
| 2. | 2011/03/31 | $51.38 | 2.09% | 1,325.83 | -0.10% | |
| 3. | 2011/04/30 | $53.64 | $0.25 | 4.89% | 1,363.61 | 2.85% |
| 4. | 2011/05/31 | $55.32 | 3.13% | 1,345.20 | -1.35% | |
| 5. | 2011/06/30 | $55.24 | -0.14% | 1,320.64 | -1.83% | |
| 6. | 2011/07/31 | $52.82 | $0.25 | -3.93% | 1,292.28 | -2.15% |
| 7. | 2011/08/31 | $54.37 | 2.93% | 1,218.89 | -5.68% | |
| 8. | 2011/09/30 | $49.39 | -9.16% | 1,131.42 | -7.18% | |
| 9. | 2011/10/31 | $53.57 | $0.285 | 9.04% | 1,253.30 | 10.77% |
| 10. | 2011/11/30 | $56.04 | 4.61% | 1,246.96 | -0.51% | |
| 11. | 2011/12/31 | $59.01 | 5.30% | 1,257.60 | 0.85% | |
| 12. | 2012/01/31 | $63.33 | $0.285 | 7.80% | 1,312.41 | 4.36% |
| 13. | 2012/02/29 | $66.24 | 4.59% | 1,365.68 | 4.06% | |
| 14. | 2012/03/31 | $71.18 | 7.46% | 1,408.47 | 3.13% | |
| 15. | 2012/04/30 | $72.73 | $0.285 | 2.58% | 1,397.91 | -0.75% |
| 16. | 2012/05/31 | $70.36 | -3.26% | 1,310.33 | -6.27% | |
| 17. | 2012/06/30 | $64.42 | -8.44% | 1,362.16 | 3.96% | |
| 18. | 2012/07/31 | $64.84 | $0.285 | 1.09% | 1,379.32 | 1.26% |
| 19. | 2012/08/31 | $63.72 | -1.73% | 1,406.58 | 1.98% | |
| 20. | 2012/09/30 | $66.34 | 4.11% | 1,440.67 | 2.42% | |
| 21. | 2012/10/31 | $70.11 | $0.335 | 6.19% | 1,412.16 | -1.98% |
| 22. | 2012/11/30 | $67.08 | -4.32% | 1,416.18 | 0.28% | |
| 23. | 2012/12/31 | $66.40 | -1.01% | 1,426.19 | 0.71% | |
| 24. | 2013/01/31 | $64.94 | $0.335 | -1.69% | 1,498.11 | 5.04% |
| 25. | 2013/02/28 | $65.48 | 0.83% | 1,514.68 | 1.11% | |
| 26. | 2013/03/31 | $71.94 | 9.87% | 1,569.19 | 3.60% | |
| 27. | 2013/04/30 | $68.12 | $0.335 | -4.84% | 1,597.57 | 1.81% |
| 28. | 2013/05/31 | $67.75 | -0.54% | 1,630.74 | 2.08% | |
| 29. | 2013/06/30 | $69.34 | 2.35% | 1,606.28 | -1.50% | |
| 30. | 2013/07/31 | $72.92 | $0.335 | 5.65% | 1,685.73 | 4.95% |
| 31. | 2013/08/31 | $70.02 | -3.98% | 1,632.97 | -3.13% | |
| 32. | 2013/09/30 | $71.39 | 1.96% | 1,681.55 | 2.97% | |
| 33. | 2013/10/31 | $67.62 | $0.37 | -4.76% | 1,756.54 | 4.46% |
| 34. | 2013/11/30 | $77.68 | 14.88% | 1,805.81 | 2.80% | |
| 35. | 2013/12/31 | $75.61 | -2.66% | 1,848.36 | 2.36% | |
| 36. | 2014/01/31 | $67.15 | $0.37 | -10.70% | 1,782.59 | -3.56% |
| 37. | 2014/02/28 | $74.08 | 10.32% | 1,859.45 | 4.31% | |
| 38. | 2014/03/31 | $75.39 | 1.77% | 1,872.34 | 0.69% | |
| 39. | 2014/04/30 | $76.99 | $0.37 | 2.61% | 1,883.95 | 0.62% |
| 40. | 2014/05/31 | $77.31 | 0.42% | 1,923.57 | 2.10% | |
| 41. | 2014/06/30 | $81.20 | 5.03% | 1,960.23 | 1.91% | |
| 42. | 2014/07/31 | $69.40 | $0.37 | -14.08% | 1,930.67 | -1.51% |
| 43. | 2014/08/31 | $72.43 | 4.37% | 2,003.37 | 3.77% | |
| 44. | 2014/09/30 | $71.98 | -0.62% | 1,972.29 | -1.55% | |
| 45. | 2014/10/31 | $71.83 | $0.41 | 0.36% | 2,018.05 | 2.32% |
| 46. | 2014/11/30 | $77.25 | 7.55% | 2,067.56 | 2.45% | |
| 47. | 2014/12/31 | $72.85 | -5.70% | 2,058.90 | -0.42% | |
| 48. | 2015/01/31 | $72.28 | $0.41 | -0.22% | 1,994.99 | -3.10% |
| 49. | 2015/02/28 | $81.11 | 12.22% | 2,104.50 | 5.49% | |
| 50. | 2015/03/31 | $78.72 | -2.95% | 2,067.89 | -1.74% | |
| 51. | 2015/04/30 | $85.96 | $0.41 | 9.72% | 2,085.51 | 0.85% |
| 52. | 2015/05/31 | $90.11 | 4.83% | 2,107.39 | 1.05% | |
| 53. | 2015/06/30 | $90.08 | -0.03% | 2,063.11 | -2.10% | |
| 54. | 2015/07/31 | $87.76 | $0.41 | -2.12% | 2,103.84 | 1.97% |
| 55. | 2015/08/31 | $79.77 | -9.10% | 1,972.18 | -6.26% | |
| 56. | 2015/09/30 | $79.95 | 0.23% | 1,920.03 | -2.64% | |
| 57. | 2015/10/31 | $70.91 | $0.46 | -10.73% | 2,079.36 | 8.30% |
| 58. | 2015/11/30 | $72.51 | 2.26% | 2,080.41 | 0.05% | |
| 59. | 2015/12/31 | $73.05 | 0.74% | 2,043.94 | -1.75% | |
| 平均 (R): | 1.10% | 0.84% | ||||
| 標準偏差： | 5.95% | 3.40% | ||||
すべて表示
1 普通株式1株当たり米ドルで、分割および株式配当を調整したデータ。
2 期間 t中のYUM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プロキシ)の収益率。
分散と共分散
YUM! Brands Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RYUM,t | RS&P 500,t | (RYUM,t–RYUM)2 | (RS&P 500,t–RS&P 500)2 | (RYUM,t–RYUM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011/02/28 | 7.63% | 3.20% | 42.76 | 5.53 | 15.37 |
| 2. | 2011/03/31 | 2.09% | -0.10% | 0.98 | 0.90 | -0.94 |
| 3. | 2011/04/30 | 4.89% | 2.85% | 14.36 | 4.02 | 7.60 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015/11/30 | 2.26% | 0.05% | 1.35 | 0.63 | -0.92 |
| 59. | 2015/12/31 | 0.74% | -1.75% | 0.12 | 6.75 | 0.91 |
| トータル (Σ): | 2,050.05 | 670.89 | 470.80 | |||
| t | 日付 | RYUM,t | RS&P 500,t | (RYUM,t–RYUM)2 | (RS&P 500,t–RS&P 500)2 | (RYUM,t–RYUM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011/02/28 | 7.63% | 3.20% | 42.76 | 5.53 | 15.37 |
| 2. | 2011/03/31 | 2.09% | -0.10% | 0.98 | 0.90 | -0.94 |
| 3. | 2011/04/30 | 4.89% | 2.85% | 14.36 | 4.02 | 7.60 |
| 4. | 2011/05/31 | 3.13% | -1.35% | 4.15 | 4.82 | -4.47 |
| 5. | 2011/06/30 | -0.14% | -1.83% | 1.54 | 7.13 | 3.31 |
| 6. | 2011/07/31 | -3.93% | -2.15% | 25.24 | 8.95 | 15.03 |
| 7. | 2011/08/31 | 2.93% | -5.68% | 3.38 | 42.56 | -12.00 |
| 8. | 2011/09/30 | -9.16% | -7.18% | 105.17 | 64.34 | 82.26 |
| 9. | 2011/10/31 | 9.04% | 10.77% | 63.11 | 98.56 | 78.87 |
| 10. | 2011/11/30 | 4.61% | -0.51% | 12.35 | 1.82 | -4.75 |
| 11. | 2011/12/31 | 5.30% | 0.85% | 17.67 | 0.00 | 0.04 |
| 12. | 2012/01/31 | 7.80% | 4.36% | 45.00 | 12.35 | 23.57 |
| 13. | 2012/02/29 | 4.59% | 4.06% | 12.24 | 10.33 | 11.25 |
| 14. | 2012/03/31 | 7.46% | 3.13% | 40.47 | 5.24 | 14.56 |
| 15. | 2012/04/30 | 2.58% | -0.75% | 2.20 | 2.54 | -2.36 |
| 16. | 2012/05/31 | -3.26% | -6.27% | 18.96 | 50.55 | 30.96 |
| 17. | 2012/06/30 | -8.44% | 3.96% | 90.98 | 9.68 | -29.67 |
| 18. | 2012/07/31 | 1.09% | 1.26% | 0.00 | 0.17 | 0.00 |
| 19. | 2012/08/31 | -1.73% | 1.98% | 7.97 | 1.28 | -3.19 |
| 20. | 2012/09/30 | 4.11% | 2.42% | 9.10 | 2.49 | 4.76 |
| 21. | 2012/10/31 | 6.19% | -1.98% | 25.93 | 7.97 | -14.38 |
| 22. | 2012/11/30 | -4.32% | 0.28% | 29.35 | 0.31 | 3.03 |
| 23. | 2012/12/31 | -1.01% | 0.71% | 4.45 | 0.02 | 0.29 |
| 24. | 2013/01/31 | -1.69% | 5.04% | 7.78 | 17.62 | -11.71 |
| 25. | 2013/02/28 | 0.83% | 1.11% | 0.07 | 0.07 | -0.07 |
| 26. | 2013/03/31 | 9.87% | 3.60% | 76.91 | 7.58 | 24.15 |
| 27. | 2013/04/30 | -4.84% | 1.81% | 35.29 | 0.93 | -5.73 |
| 28. | 2013/05/31 | -0.54% | 2.08% | 2.69 | 1.52 | -2.02 |
| 29. | 2013/06/30 | 2.35% | -1.50% | 1.57 | 5.50 | -2.93 |
| 30. | 2013/07/31 | 5.65% | 4.95% | 20.70 | 16.82 | 18.66 |
| 31. | 2013/08/31 | -3.98% | -3.13% | 25.73 | 15.80 | 20.16 |
| 32. | 2013/09/30 | 1.96% | 2.97% | 0.74 | 4.54 | 1.83 |
| 33. | 2013/10/31 | -4.76% | 4.46% | 34.32 | 13.07 | -21.18 |
| 34. | 2013/11/30 | 14.88% | 2.80% | 189.93 | 3.84 | 27.01 |
| 35. | 2013/12/31 | -2.66% | 2.36% | 14.14 | 2.28 | -5.68 |
| 36. | 2014/01/31 | -10.70% | -3.56% | 139.13 | 19.39 | 51.94 |
| 37. | 2014/02/28 | 10.32% | 4.31% | 85.09 | 12.02 | 31.98 |
| 38. | 2014/03/31 | 1.77% | 0.69% | 0.45 | 0.02 | -0.10 |
| 39. | 2014/04/30 | 2.61% | 0.62% | 2.30 | 0.05 | -0.34 |
| 40. | 2014/05/31 | 0.42% | 2.10% | 0.46 | 1.58 | -0.86 |
| 41. | 2014/06/30 | 5.03% | 1.91% | 15.49 | 1.13 | 4.18 |
| 42. | 2014/07/31 | -14.08% | -1.51% | 230.20 | 5.54 | 35.70 |
| 43. | 2014/08/31 | 4.37% | 3.77% | 10.69 | 8.53 | 9.55 |
| 44. | 2014/09/30 | -0.62% | -1.55% | 2.95 | 5.74 | 4.11 |
| 45. | 2014/10/31 | 0.36% | 2.32% | 0.54 | 2.18 | -1.08 |
| 46. | 2014/11/30 | 7.55% | 2.45% | 41.60 | 2.59 | 10.38 |
| 47. | 2014/12/31 | -5.70% | -0.42% | 46.13 | 1.60 | 8.58 |
| 48. | 2015/01/31 | -0.22% | -3.10% | 1.73 | 15.59 | 5.19 |
| 49. | 2015/02/28 | 12.22% | 5.49% | 123.67 | 21.57 | 51.65 |
| 50. | 2015/03/31 | -2.95% | -1.74% | 16.34 | 6.68 | 10.45 |
| 51. | 2015/04/30 | 9.72% | 0.85% | 74.34 | 0.00 | 0.06 |
| 52. | 2015/05/31 | 4.83% | 1.05% | 13.93 | 0.04 | 0.76 |
| 53. | 2015/06/30 | -0.03% | -2.10% | 1.27 | 8.68 | 3.33 |
| 54. | 2015/07/31 | -2.12% | 1.97% | 10.34 | 1.28 | -3.63 |
| 55. | 2015/08/31 | -9.10% | -6.26% | 104.04 | 50.45 | 72.45 |
| 56. | 2015/09/30 | 0.23% | -2.64% | 0.76 | 12.17 | 3.04 |
| 57. | 2015/10/31 | -10.73% | 8.30% | 139.89 | 55.56 | -88.16 |
| 58. | 2015/11/30 | 2.26% | 0.05% | 1.35 | 0.63 | -0.92 |
| 59. | 2015/12/31 | 0.74% | -1.75% | 0.12 | 6.75 | 0.91 |
| トータル (Σ): | 2,050.05 | 670.89 | 470.80 | |||
すべて表示
分散YUM = Σ(RYUM,t–RYUM)2 ÷ (59 – 1)
= 2,050.05 ÷ (59 – 1)
= 35.35
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 670.89 ÷ (59 – 1)
= 11.57
共 分散YUM, S&P 500 = Σ(RYUM,t–RYUM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 470.80 ÷ (59 – 1)
= 8.12
システマティックリスク推定 (β)
| 分散YUM | 35.35 |
| 分散S&P 500 | 11.57 |
| 共 分散YUM, S&P 500 | 8.12 |
| 相関係数YUM, S&P 5001 | 0.40 |
| βYUM2 | 0.70 |
| αYUM3 | 0.50% |
計算
1 相関係数YUM, S&P 500
= 共 分散YUM, S&P 500 ÷ (標準偏差YUM × 標準偏差S&P 500)
= 8.12 ÷ (5.95% × 3.40%)
= 0.40
2 βYUM
= 共 分散YUM, S&P 500 ÷ 分散S&P 500
= 8.12 ÷ 11.57
= 0.70
3 αYUM
= 平均YUM – βYUM × 平均S&P 500
= 1.10% – 0.70 × 0.84%
= 0.50%
期待収益率
| 仮定 | ||
| LT財務省総合の収益率1 | RF | 4.70% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.42% |
| 普通株式 YUM システマティックリスク | βYUM | 0.70 |
| YUM普通株式の期待収益率3 | E(RYUM) | 10.82% |
1 10年以内に期限が到来またはコール可能でないすべての固定クーポン米国債の入札利回りの非加重平均(リスクフリー収益率プロキシ)。
2 詳細を見る »
3 E(RYUM) = RF + βYUM [E(RM) – RF]
= 4.70% + 0.70 [13.42% – 4.70%]
= 10.82%