資本資産価格モデル (CAPM)
資本資産価格モデル(CAPM)は、 UALの普通株式などのリスク資産の期待収益率または必要収益率を示します。
収益率
United Airlines Holdings Inc.、月間収益率
| United Airlines Holdings Inc. (UAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格UAL,t1 | 配当UAL,t1 | RUAL,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $67.82 | 2,823.81 | ||||
| 1. | 2018/02/28 | $67.79 | -0.04% | 2,713.83 | -3.89% | |
| 2. | 2018/03/31 | $69.47 | 2.48% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $67.54 | -2.78% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | $44.17 | 2.53% | 4,080.11 | 5.38% | |
| 59. | 2022/12/31 | $37.70 | -14.65% | 3,839.50 | -5.90% | |
| 平均 (R): | -0.07% | 0.67% | ||||
| 標準偏差： | 13.19% | 5.40% | ||||
| United Airlines Holdings Inc. (UAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格UAL,t1 | 配当UAL,t1 | RUAL,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $67.82 | 2,823.81 | ||||
| 1. | 2018/02/28 | $67.79 | -0.04% | 2,713.83 | -3.89% | |
| 2. | 2018/03/31 | $69.47 | 2.48% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $67.54 | -2.78% | 2,648.05 | 0.27% | |
| 4. | 2018/05/31 | $69.59 | 3.04% | 2,705.27 | 2.16% | |
| 5. | 2018/06/30 | $69.73 | 0.20% | 2,718.37 | 0.48% | |
| 6. | 2018/07/31 | $80.40 | 15.30% | 2,816.29 | 3.60% | |
| 7. | 2018/08/31 | $87.42 | 8.73% | 2,901.52 | 3.03% | |
| 8. | 2018/09/30 | $89.06 | 1.88% | 2,913.98 | 0.43% | |
| 9. | 2018/10/31 | $85.51 | -3.99% | 2,711.74 | -6.94% | |
| 10. | 2018/11/30 | $96.70 | 13.09% | 2,760.17 | 1.79% | |
| 11. | 2018/12/31 | $83.73 | -13.41% | 2,506.85 | -9.18% | |
| 12. | 2019/01/31 | $87.27 | 4.23% | 2,704.10 | 7.87% | |
| 13. | 2019/02/28 | $87.81 | 0.62% | 2,784.49 | 2.97% | |
| 14. | 2019/03/31 | $79.78 | -9.14% | 2,834.40 | 1.79% | |
| 15. | 2019/04/30 | $88.86 | 11.38% | 2,945.83 | 3.93% | |
| 16. | 2019/05/31 | $77.65 | -12.62% | 2,752.06 | -6.58% | |
| 17. | 2019/06/30 | $87.55 | 12.75% | 2,941.76 | 6.89% | |
| 18. | 2019/07/31 | $91.91 | 4.98% | 2,980.38 | 1.31% | |
| 19. | 2019/08/31 | $84.31 | -8.27% | 2,926.46 | -1.81% | |
| 20. | 2019/09/30 | $88.41 | 4.86% | 2,976.74 | 1.72% | |
| 21. | 2019/10/31 | $90.84 | 2.75% | 3,037.56 | 2.04% | |
| 22. | 2019/11/30 | $92.80 | 2.16% | 3,140.98 | 3.40% | |
| 23. | 2019/12/31 | $88.09 | -5.08% | 3,230.78 | 2.86% | |
| 24. | 2020/01/31 | $74.80 | -15.09% | 3,225.52 | -0.16% | |
| 25. | 2020/02/29 | $61.59 | -17.66% | 2,954.22 | -8.41% | |
| 26. | 2020/03/31 | $31.55 | -48.77% | 2,584.59 | -12.51% | |
| 27. | 2020/04/30 | $29.58 | -6.24% | 2,912.43 | 12.68% | |
| 28. | 2020/05/31 | $28.04 | -5.21% | 3,044.31 | 4.53% | |
| 29. | 2020/06/30 | $34.61 | 23.43% | 3,100.29 | 1.84% | |
| 30. | 2020/07/31 | $31.38 | -9.33% | 3,271.12 | 5.51% | |
| 31. | 2020/08/31 | $36.00 | 14.72% | 3,500.31 | 7.01% | |
| 32. | 2020/09/30 | $34.75 | -3.47% | 3,363.00 | -3.92% | |
| 33. | 2020/10/31 | $33.86 | -2.56% | 3,269.96 | -2.77% | |
| 34. | 2020/11/30 | $45.05 | 33.05% | 3,621.63 | 10.75% | |
| 35. | 2020/12/31 | $43.25 | -4.00% | 3,756.07 | 3.71% | |
| 36. | 2021/01/31 | $39.99 | -7.54% | 3,714.24 | -1.11% | |
| 37. | 2021/02/28 | $52.68 | 31.73% | 3,811.15 | 2.61% | |
| 38. | 2021/03/31 | $57.54 | 9.23% | 3,972.89 | 4.24% | |
| 39. | 2021/04/30 | $54.40 | -5.46% | 4,181.17 | 5.24% | |
| 40. | 2021/05/31 | $58.35 | 7.26% | 4,204.11 | 0.55% | |
| 41. | 2021/06/30 | $52.29 | -10.39% | 4,297.50 | 2.22% | |
| 42. | 2021/07/31 | $46.72 | -10.65% | 4,395.26 | 2.27% | |
| 43. | 2021/08/31 | $46.51 | -0.45% | 4,522.68 | 2.90% | |
| 44. | 2021/09/30 | $47.57 | 2.28% | 4,307.54 | -4.76% | |
| 45. | 2021/10/31 | $46.14 | -3.01% | 4,605.38 | 6.91% | |
| 46. | 2021/11/30 | $42.26 | -8.41% | 4,567.00 | -0.83% | |
| 47. | 2021/12/31 | $43.78 | 3.60% | 4,766.18 | 4.36% | |
| 48. | 2022/01/31 | $42.88 | -2.06% | 4,515.55 | -5.26% | |
| 49. | 2022/02/28 | $44.40 | 3.54% | 4,373.94 | -3.14% | |
| 50. | 2022/03/31 | $46.36 | 4.41% | 4,530.41 | 3.58% | |
| 51. | 2022/04/30 | $50.50 | 8.93% | 4,131.93 | -8.80% | |
| 52. | 2022/05/31 | $47.63 | -5.68% | 4,132.15 | 0.01% | |
| 53. | 2022/06/30 | $35.42 | -25.64% | 3,785.38 | -8.39% | |
| 54. | 2022/07/31 | $36.75 | 3.75% | 4,130.29 | 9.11% | |
| 55. | 2022/08/31 | $35.01 | -4.73% | 3,955.00 | -4.24% | |
| 56. | 2022/09/30 | $32.53 | -7.08% | 3,585.62 | -9.34% | |
| 57. | 2022/10/31 | $43.08 | 32.43% | 3,871.98 | 7.99% | |
| 58. | 2022/11/30 | $44.17 | 2.53% | 4,080.11 | 5.38% | |
| 59. | 2022/12/31 | $37.70 | -14.65% | 3,839.50 | -5.90% | |
| 平均 (R): | -0.07% | 0.67% | ||||
| 標準偏差： | 13.19% | 5.40% | ||||
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におけるUAL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
United Airlines Holdings Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RUAL,t | RS&P 500,t | (RUAL,t–RUAL)2 | (RS&P 500,t–RS&P 500)2 | (RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | -0.04% | -3.89% | 0.00 | 20.81 | -0.11 |
| 2. | 2018/03/31 | 2.48% | -2.69% | 6.49 | 11.26 | -8.55 |
| 3. | 2018/04/30 | -2.78% | 0.27% | 7.34 | 0.16 | 1.07 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | 2.53% | 5.38% | 6.75 | 22.17 | 12.24 |
| 59. | 2022/12/31 | -14.65% | -5.90% | 212.55 | 43.08 | 95.69 |
| トータル (Σ): | 10,091.57 | 1,691.48 | 2,315.49 | |||
| t | 日付 | RUAL,t | RS&P 500,t | (RUAL,t–RUAL)2 | (RS&P 500,t–RS&P 500)2 | (RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | -0.04% | -3.89% | 0.00 | 20.81 | -0.11 |
| 2. | 2018/03/31 | 2.48% | -2.69% | 6.49 | 11.26 | -8.55 |
| 3. | 2018/04/30 | -2.78% | 0.27% | 7.34 | 0.16 | 1.07 |
| 4. | 2018/05/31 | 3.04% | 2.16% | 9.63 | 2.23 | 4.64 |
| 5. | 2018/06/30 | 0.20% | 0.48% | 0.07 | 0.03 | -0.05 |
| 6. | 2018/07/31 | 15.30% | 3.60% | 236.26 | 8.62 | 45.12 |
| 7. | 2018/08/31 | 8.73% | 3.03% | 77.44 | 5.57 | 20.77 |
| 8. | 2018/09/30 | 1.88% | 0.43% | 3.78 | 0.06 | -0.46 |
| 9. | 2018/10/31 | -3.99% | -6.94% | 15.35 | 57.87 | 29.80 |
| 10. | 2018/11/30 | 13.09% | 1.79% | 173.05 | 1.25 | 14.72 |
| 11. | 2018/12/31 | -13.41% | -9.18% | 178.06 | 96.91 | 131.36 |
| 12. | 2019/01/31 | 4.23% | 7.87% | 18.46 | 51.87 | 30.94 |
| 13. | 2019/02/28 | 0.62% | 2.97% | 0.47 | 5.32 | 1.59 |
| 14. | 2019/03/31 | -9.14% | 1.79% | 82.37 | 1.27 | -10.22 |
| 15. | 2019/04/30 | 11.38% | 3.93% | 131.10 | 10.66 | 37.38 |
| 16. | 2019/05/31 | -12.62% | -6.58% | 157.42 | 52.48 | 90.89 |
| 17. | 2019/06/30 | 12.75% | 6.89% | 164.31 | 38.77 | 79.81 |
| 18. | 2019/07/31 | 4.98% | 1.31% | 25.49 | 0.42 | 3.26 |
| 19. | 2019/08/31 | -8.27% | -1.81% | 67.24 | 6.13 | 20.30 |
| 20. | 2019/09/30 | 4.86% | 1.72% | 24.32 | 1.11 | 5.19 |
| 21. | 2019/10/31 | 2.75% | 2.04% | 7.94 | 1.89 | 3.88 |
| 22. | 2019/11/30 | 2.16% | 3.40% | 4.96 | 7.50 | 6.10 |
| 23. | 2019/12/31 | -5.08% | 2.86% | 25.07 | 4.81 | -10.98 |
| 24. | 2020/01/31 | -15.09% | -0.16% | 225.54 | 0.69 | 12.46 |
| 25. | 2020/02/29 | -17.66% | -8.41% | 309.47 | 82.40 | 159.69 |
| 26. | 2020/03/31 | -48.77% | -12.51% | 2,372.22 | 173.67 | 641.87 |
| 27. | 2020/04/30 | -6.24% | 12.68% | 38.13 | 144.43 | -74.21 |
| 28. | 2020/05/31 | -5.21% | 4.53% | 26.39 | 14.91 | -19.84 |
| 29. | 2020/06/30 | 23.43% | 1.84% | 552.23 | 1.37 | 27.55 |
| 30. | 2020/07/31 | -9.33% | 5.51% | 85.82 | 23.46 | -44.87 |
| 31. | 2020/08/31 | 14.72% | 7.01% | 218.79 | 40.19 | 93.78 |
| 32. | 2020/09/30 | -3.47% | -3.92% | 11.58 | 21.06 | 15.62 |
| 33. | 2020/10/31 | -2.56% | -2.77% | 6.21 | 11.79 | 8.56 |
| 34. | 2020/11/30 | 33.05% | 10.75% | 1,096.71 | 101.77 | 334.08 |
| 35. | 2020/12/31 | -4.00% | 3.71% | 15.42 | 9.28 | -11.96 |
| 36. | 2021/01/31 | -7.54% | -1.11% | 55.78 | 3.17 | 13.30 |
| 37. | 2021/02/28 | 31.73% | 2.61% | 1,011.35 | 3.77 | 61.77 |
| 38. | 2021/03/31 | 9.23% | 4.24% | 86.38 | 12.80 | 33.25 |
| 39. | 2021/04/30 | -5.46% | 5.24% | 29.03 | 20.94 | -24.66 |
| 40. | 2021/05/31 | 7.26% | 0.55% | 53.73 | 0.01 | -0.86 |
| 41. | 2021/06/30 | -10.39% | 2.22% | 106.44 | 2.42 | -16.04 |
| 42. | 2021/07/31 | -10.65% | 2.27% | 112.01 | 2.59 | -17.02 |
| 43. | 2021/08/31 | -0.45% | 2.90% | 0.14 | 4.98 | -0.85 |
| 44. | 2021/09/30 | 2.28% | -4.76% | 5.51 | 29.42 | -12.73 |
| 45. | 2021/10/31 | -3.01% | 6.91% | 8.63 | 39.03 | -18.35 |
| 46. | 2021/11/30 | -8.41% | -0.83% | 69.56 | 2.25 | 12.51 |
| 47. | 2021/12/31 | 3.60% | 4.36% | 13.44 | 13.65 | 13.54 |
| 48. | 2022/01/31 | -2.06% | -5.26% | 3.95 | 35.11 | 11.77 |
| 49. | 2022/02/28 | 3.54% | -3.14% | 13.06 | 14.46 | -13.74 |
| 50. | 2022/03/31 | 4.41% | 3.58% | 20.10 | 8.47 | 13.05 |
| 51. | 2022/04/30 | 8.93% | -8.80% | 80.98 | 89.54 | -85.15 |
| 52. | 2022/05/31 | -5.68% | 0.01% | 31.52 | 0.44 | 3.71 |
| 53. | 2022/06/30 | -25.64% | -8.39% | 653.64 | 82.06 | 231.60 |
| 54. | 2022/07/31 | 3.75% | 9.11% | 14.62 | 71.32 | 32.29 |
| 55. | 2022/08/31 | -4.73% | -4.24% | 21.77 | 24.11 | 22.91 |
| 56. | 2022/09/30 | -7.08% | -9.34% | 49.21 | 100.12 | 70.19 |
| 57. | 2022/10/31 | 32.43% | 7.99% | 1,056.27 | 53.58 | 237.89 |
| 58. | 2022/11/30 | 2.53% | 5.38% | 6.75 | 22.17 | 12.24 |
| 59. | 2022/12/31 | -14.65% | -5.90% | 212.55 | 43.08 | 95.69 |
| トータル (Σ): | 10,091.57 | 1,691.48 | 2,315.49 | |||
すべて表示
分散UAL = Σ(RUAL,t–RUAL)2 ÷ (59 – 1)
= 10,091.57 ÷ (59 – 1)
= 173.99
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
共 分散UAL, S&P 500 = Σ(RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,315.49 ÷ (59 – 1)
= 39.92
システマティックリスク推定 (β)
| 分散UAL | 173.99 |
| 分散S&P 500 | 29.16 |
| 共 分散UAL, S&P 500 | 39.92 |
| 相関係数UAL, S&P 5001 | 0.56 |
| βUAL2 | 1.37 |
| αUAL3 | -0.98% |
計算
1 相関係数UAL, S&P 500
= 共 分散UAL, S&P 500 ÷ (標準偏差UAL × 標準偏差S&P 500)
= 39.92 ÷ (13.19% × 5.40%)
= 0.56
2 βUAL
= 共 分散UAL, S&P 500 ÷ 分散S&P 500
= 39.92 ÷ 29.16
= 1.37
3 αUAL
= 平均UAL – βUAL × 平均S&P 500
= -0.07% – 1.37 × 0.67%
= -0.98%
期待収益率
| 仮定 | ||
| LT財務省総合の収益率1 | RF | 4.83% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.48% |
| 普通株式 UAL システマティックリスク | βUAL | 1.37 |
| UAL普通株式の期待収益率3 | E(RUAL) | 16.67% |
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(RUAL) = RF + βUAL [E(RM) – RF]
= 4.83% + 1.37 [13.48% – 4.83%]
= 16.67%