資本資産価格モデル (CAPM)
資本資産価格モデル(CAPM)は、 Cignaの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
Cigna Group、月間収益率
| Cigna Group (CI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格CI,t1 | 配当CI,t1 | RCI,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $199.81 | 2,704.10 | ||||
| 1. | 2019/02/28 | $174.44 | -12.70% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $160.82 | $0.04 | -7.78% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $158.84 | -1.23% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | $262.88 | -14.98% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $299.45 | $1.23 | 14.38% | 4,769.83 | 4.42% |
| 平均 (R): | 1.12% | 1.11% | ||||
| 標準偏差： | 8.52% | 5.31% | ||||
| Cigna Group (CI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格CI,t1 | 配当CI,t1 | RCI,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $199.81 | 2,704.10 | ||||
| 1. | 2019/02/28 | $174.44 | -12.70% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $160.82 | $0.04 | -7.78% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $158.84 | -1.23% | 2,945.83 | 3.93% | |
| 4. | 2019/05/31 | $148.02 | -6.81% | 2,752.06 | -6.58% | |
| 5. | 2019/06/30 | $157.55 | 6.44% | 2,941.76 | 6.89% | |
| 6. | 2019/07/31 | $169.92 | 7.85% | 2,980.38 | 1.31% | |
| 7. | 2019/08/31 | $153.97 | -9.39% | 2,926.46 | -1.81% | |
| 8. | 2019/09/30 | $151.79 | -1.42% | 2,976.74 | 1.72% | |
| 9. | 2019/10/31 | $178.46 | 17.57% | 3,037.56 | 2.04% | |
| 10. | 2019/11/30 | $199.92 | 12.03% | 3,140.98 | 3.40% | |
| 11. | 2019/12/31 | $204.49 | 2.29% | 3,230.78 | 2.86% | |
| 12. | 2020/01/31 | $192.38 | -5.92% | 3,225.52 | -0.16% | |
| 13. | 2020/02/29 | $182.94 | -4.91% | 2,954.22 | -8.41% | |
| 14. | 2020/03/31 | $177.18 | $0.04 | -3.13% | 2,584.59 | -12.51% |
| 15. | 2020/04/30 | $195.78 | 10.50% | 2,912.43 | 12.68% | |
| 16. | 2020/05/31 | $197.32 | 0.79% | 3,044.31 | 4.53% | |
| 17. | 2020/06/30 | $187.65 | -4.90% | 3,100.29 | 1.84% | |
| 18. | 2020/07/31 | $172.69 | -7.97% | 3,271.12 | 5.51% | |
| 19. | 2020/08/31 | $177.37 | 2.71% | 3,500.31 | 7.01% | |
| 20. | 2020/09/30 | $169.41 | -4.49% | 3,363.00 | -3.92% | |
| 21. | 2020/10/31 | $166.97 | -1.44% | 3,269.96 | -2.77% | |
| 22. | 2020/11/30 | $209.14 | 25.26% | 3,621.63 | 10.75% | |
| 23. | 2020/12/31 | $208.18 | -0.46% | 3,756.07 | 3.71% | |
| 24. | 2021/01/31 | $217.05 | 4.26% | 3,714.24 | -1.11% | |
| 25. | 2021/02/28 | $209.90 | -3.29% | 3,811.15 | 2.61% | |
| 26. | 2021/03/31 | $241.74 | $1.00 | 15.65% | 3,972.89 | 4.24% |
| 27. | 2021/04/30 | $249.01 | 3.01% | 4,181.17 | 5.24% | |
| 28. | 2021/05/31 | $258.85 | 3.95% | 4,204.11 | 0.55% | |
| 29. | 2021/06/30 | $237.07 | $1.00 | -8.03% | 4,297.50 | 2.22% |
| 30. | 2021/07/31 | $229.49 | -3.20% | 4,395.26 | 2.27% | |
| 31. | 2021/08/31 | $211.65 | -7.77% | 4,522.68 | 2.90% | |
| 32. | 2021/09/30 | $200.16 | $1.00 | -4.96% | 4,307.54 | -4.76% |
| 33. | 2021/10/31 | $213.61 | 6.72% | 4,605.38 | 6.91% | |
| 34. | 2021/11/30 | $191.90 | -10.16% | 4,567.00 | -0.83% | |
| 35. | 2021/12/31 | $229.63 | $1.00 | 20.18% | 4,766.18 | 4.36% |
| 36. | 2022/01/31 | $230.46 | 0.36% | 4,515.55 | -5.26% | |
| 37. | 2022/02/28 | $237.78 | 3.18% | 4,373.94 | -3.14% | |
| 38. | 2022/03/31 | $239.61 | $1.12 | 1.24% | 4,530.41 | 3.58% |
| 39. | 2022/04/30 | $246.78 | 2.99% | 4,131.93 | -8.80% | |
| 40. | 2022/05/31 | $268.29 | 8.72% | 4,132.15 | 0.01% | |
| 41. | 2022/06/30 | $263.52 | $1.12 | -1.36% | 3,785.38 | -8.39% |
| 42. | 2022/07/31 | $275.36 | 4.49% | 4,130.29 | 9.11% | |
| 43. | 2022/08/31 | $283.45 | 2.94% | 3,955.00 | -4.24% | |
| 44. | 2022/09/30 | $277.47 | $1.12 | -1.71% | 3,585.62 | -9.34% |
| 45. | 2022/10/31 | $323.06 | 16.43% | 3,871.98 | 7.99% | |
| 46. | 2022/11/30 | $328.89 | 1.80% | 4,080.11 | 5.38% | |
| 47. | 2022/12/31 | $331.34 | $1.12 | 1.09% | 3,839.50 | -5.90% |
| 48. | 2023/01/31 | $316.67 | -4.43% | 4,076.60 | 6.18% | |
| 49. | 2023/02/28 | $292.10 | -7.76% | 3,970.15 | -2.61% | |
| 50. | 2023/03/31 | $255.53 | $1.23 | -12.10% | 4,109.31 | 3.51% |
| 51. | 2023/04/30 | $253.29 | -0.88% | 4,169.48 | 1.46% | |
| 52. | 2023/05/31 | $247.41 | -2.32% | 4,179.83 | 0.25% | |
| 53. | 2023/06/30 | $280.60 | $1.23 | 13.91% | 4,376.86 | 4.71% |
| 54. | 2023/07/31 | $295.10 | 5.17% | 4,588.96 | 4.85% | |
| 55. | 2023/08/31 | $276.26 | -6.38% | 4,507.66 | -1.77% | |
| 56. | 2023/09/30 | $286.07 | $1.23 | 4.00% | 4,288.05 | -4.87% |
| 57. | 2023/10/31 | $309.20 | 8.09% | 4,193.80 | -2.20% | |
| 58. | 2023/11/30 | $262.88 | -14.98% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $299.45 | $1.23 | 14.38% | 4,769.83 | 4.42% |
| 平均 (R): | 1.12% | 1.11% | ||||
| 標準偏差： | 8.52% | 5.31% | ||||
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CI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
Cigna Group、分散の計算、および戻り値の共分散
| t | 日付 | RCI,t | RS&P 500,t | (RCI,t–RCI)2 | (RS&P 500,t–RS&P 500)2 | (RCI,t–RCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | -12.70% | 2.97% | 190.92 | 3.49 | -25.80 |
| 2. | 2019/03/31 | -7.78% | 1.79% | 79.30 | 0.47 | -6.11 |
| 3. | 2019/04/30 | -1.23% | 3.93% | 5.53 | 7.98 | -6.64 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | -14.98% | 8.92% | 259.23 | 61.03 | -125.78 |
| 59. | 2023/12/31 | 14.38% | 4.42% | 175.80 | 11.00 | 43.98 |
| トータル (Σ): | 4,206.88 | 1,634.30 | 833.37 | |||
| t | 日付 | RCI,t | RS&P 500,t | (RCI,t–RCI)2 | (RS&P 500,t–RS&P 500)2 | (RCI,t–RCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | -12.70% | 2.97% | 190.92 | 3.49 | -25.80 |
| 2. | 2019/03/31 | -7.78% | 1.79% | 79.30 | 0.47 | -6.11 |
| 3. | 2019/04/30 | -1.23% | 3.93% | 5.53 | 7.98 | -6.64 |
| 4. | 2019/05/31 | -6.81% | -6.58% | 62.92 | 59.04 | 60.95 |
| 5. | 2019/06/30 | 6.44% | 6.89% | 28.28 | 33.49 | 30.78 |
| 6. | 2019/07/31 | 7.85% | 1.31% | 45.31 | 0.04 | 1.39 |
| 7. | 2019/08/31 | -9.39% | -1.81% | 110.40 | 8.50 | 30.63 |
| 8. | 2019/09/30 | -1.42% | 1.72% | 6.43 | 0.37 | -1.55 |
| 9. | 2019/10/31 | 17.57% | 2.04% | 270.61 | 0.88 | 15.42 |
| 10. | 2019/11/30 | 12.03% | 3.40% | 118.92 | 5.28 | 25.07 |
| 11. | 2019/12/31 | 2.29% | 2.86% | 1.36 | 3.07 | 2.04 |
| 12. | 2020/01/31 | -5.92% | -0.16% | 49.59 | 1.61 | 8.93 |
| 13. | 2020/02/29 | -4.91% | -8.41% | 36.33 | 90.57 | 57.36 |
| 14. | 2020/03/31 | -3.13% | -12.51% | 18.04 | 185.44 | 57.83 |
| 15. | 2020/04/30 | 10.50% | 12.68% | 87.94 | 134.06 | 108.58 |
| 16. | 2020/05/31 | 0.79% | 4.53% | 0.11 | 11.71 | -1.14 |
| 17. | 2020/06/30 | -4.90% | 1.84% | 36.25 | 0.54 | -4.41 |
| 18. | 2020/07/31 | -7.97% | 5.51% | 82.67 | 19.40 | -40.05 |
| 19. | 2020/08/31 | 2.71% | 7.01% | 2.53 | 34.82 | 9.38 |
| 20. | 2020/09/30 | -4.49% | -3.92% | 31.45 | 25.29 | 28.20 |
| 21. | 2020/10/31 | -1.44% | -2.77% | 6.56 | 15.00 | 9.92 |
| 22. | 2020/11/30 | 25.26% | 10.75% | 582.54 | 93.10 | 232.88 |
| 23. | 2020/12/31 | -0.46% | 3.71% | 2.49 | 6.79 | -4.12 |
| 24. | 2021/01/31 | 4.26% | -1.11% | 9.86 | 4.93 | -6.97 |
| 25. | 2021/02/28 | -3.29% | 2.61% | 19.49 | 2.26 | -6.64 |
| 26. | 2021/03/31 | 15.65% | 4.24% | 210.99 | 9.85 | 45.58 |
| 27. | 2021/04/30 | 3.01% | 5.24% | 3.56 | 17.11 | 7.81 |
| 28. | 2021/05/31 | 3.95% | 0.55% | 8.02 | 0.31 | -1.58 |
| 29. | 2021/06/30 | -8.03% | 2.22% | 83.69 | 1.24 | -10.21 |
| 30. | 2021/07/31 | -3.20% | 2.27% | 18.64 | 1.37 | -5.05 |
| 31. | 2021/08/31 | -7.77% | 2.90% | 79.10 | 3.22 | -15.95 |
| 32. | 2021/09/30 | -4.96% | -4.76% | 36.92 | 34.37 | 35.62 |
| 33. | 2021/10/31 | 6.72% | 6.91% | 31.35 | 33.74 | 32.52 |
| 34. | 2021/11/30 | -10.16% | -0.83% | 127.32 | 3.76 | 21.88 |
| 35. | 2021/12/31 | 20.18% | 4.36% | 363.37 | 10.60 | 62.06 |
| 36. | 2022/01/31 | 0.36% | -5.26% | 0.58 | 40.51 | 4.83 |
| 37. | 2022/02/28 | 3.18% | -3.14% | 4.23 | 17.99 | -8.72 |
| 38. | 2022/03/31 | 1.24% | 3.58% | 0.01 | 6.11 | 0.30 |
| 39. | 2022/04/30 | 2.99% | -8.80% | 3.51 | 98.04 | -18.54 |
| 40. | 2022/05/31 | 8.72% | 0.01% | 57.70 | 1.21 | -8.36 |
| 41. | 2022/06/30 | -1.36% | -8.39% | 6.15 | 90.21 | 23.56 |
| 42. | 2022/07/31 | 4.49% | 9.11% | 11.38 | 64.09 | 27.00 |
| 43. | 2022/08/31 | 2.94% | -4.24% | 3.30 | 28.62 | -9.73 |
| 44. | 2022/09/30 | -1.71% | -9.34% | 8.04 | 109.11 | 29.61 |
| 45. | 2022/10/31 | 16.43% | 7.99% | 234.41 | 47.34 | 105.34 |
| 46. | 2022/11/30 | 1.80% | 5.38% | 0.47 | 18.23 | 2.92 |
| 47. | 2022/12/31 | 1.09% | -5.90% | 0.00 | 49.04 | 0.24 |
| 48. | 2023/01/31 | -4.43% | 6.18% | 30.78 | 25.70 | -28.12 |
| 49. | 2023/02/28 | -7.76% | -2.61% | 78.84 | 13.82 | 33.00 |
| 50. | 2023/03/31 | -12.10% | 3.51% | 174.74 | 5.76 | -31.72 |
| 51. | 2023/04/30 | -0.88% | 1.46% | 3.99 | 0.13 | -0.72 |
| 52. | 2023/05/31 | -2.32% | 0.25% | 11.84 | 0.74 | 2.95 |
| 53. | 2023/06/30 | 13.91% | 4.71% | 163.63 | 13.02 | 46.15 |
| 54. | 2023/07/31 | 5.17% | 4.85% | 16.38 | 13.99 | 15.14 |
| 55. | 2023/08/31 | -6.38% | -1.77% | 56.32 | 8.28 | 21.59 |
| 56. | 2023/09/30 | 4.00% | -4.87% | 8.27 | 35.73 | -17.19 |
| 57. | 2023/10/31 | 8.09% | -2.20% | 48.52 | 10.92 | -23.01 |
| 58. | 2023/11/30 | -14.98% | 8.92% | 259.23 | 61.03 | -125.78 |
| 59. | 2023/12/31 | 14.38% | 4.42% | 175.80 | 11.00 | 43.98 |
| トータル (Σ): | 4,206.88 | 1,634.30 | 833.37 | |||
すべて表示
分散CI = Σ(RCI,t–RCI)2 ÷ (59 – 1)
= 4,206.88 ÷ (59 – 1)
= 72.53
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
共 分散CI, S&P 500 = Σ(RCI,t–RCI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 833.37 ÷ (59 – 1)
= 14.37
システマティックリスク推定 (β)
| 分散CI | 72.53 |
| 分散S&P 500 | 28.18 |
| 共 分散CI, S&P 500 | 14.37 |
| 相関係数CI, S&P 5001 | 0.32 |
| βCI2 | 0.51 |
| αCI3 | 0.56% |
計算
1 相関係数CI, S&P 500
= 共 分散CI, S&P 500 ÷ (標準偏差CI × 標準偏差S&P 500)
= 14.37 ÷ (8.52% × 5.31%)
= 0.32
2 βCI
= 共 分散CI, S&P 500 ÷ 分散S&P 500
= 14.37 ÷ 28.18
= 0.51
3 αCI
= 平均CI – βCI × 平均S&P 500
= 1.12% – 0.51 × 1.11%
= 0.56%
期待収益率
| 仮定 | ||
| LT財務省総合の収益率1 | RF | 4.79% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.48% |
| 普通株式 Cigna システマティックリスク | βCI | 0.51 |
| シグナ普通株式の期待収益率3 | E(RCI) | 9.22% |
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(RCI) = RF + βCI [E(RM) – RF]
= 4.79% + 0.51 [13.48% – 4.79%]
= 9.22%