資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 UnitedHealth Group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
UnitedHealth Group Inc.、月間収益率
| UnitedHealth Group Inc. (UNH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格UNH,t1 | 配当UNH,t1 | RUNH,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $333.58 | 3,714.24 | ||||
| 1. | 2021/02/28 | $332.22 | -0.41% | 3,811.15 | 2.61% | |
| 2. | 2021/03/31 | $372.07 | $1.25 | 12.37% | 3,972.89 | 4.24% |
| 3. | 2021/04/30 | $398.80 | 7.18% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | $329.77 | -3.45% | 6,849.09 | 0.13% | |
| 59. | 2025/12/31 | $330.11 | $2.21 | 0.77% | 6,845.50 | -0.05% |
| 平均 (R): | 0.52% | 1.14% | ||||
| 標準偏差： | 8.82% | 4.37% | ||||
| UnitedHealth Group Inc. (UNH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格UNH,t1 | 配当UNH,t1 | RUNH,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2021/01/31 | $333.58 | 3,714.24 | ||||
| 1. | 2021/02/28 | $332.22 | -0.41% | 3,811.15 | 2.61% | |
| 2. | 2021/03/31 | $372.07 | $1.25 | 12.37% | 3,972.89 | 4.24% |
| 3. | 2021/04/30 | $398.80 | 7.18% | 4,181.17 | 5.24% | |
| 4. | 2021/05/31 | $411.92 | 3.29% | 4,204.11 | 0.55% | |
| 5. | 2021/06/30 | $400.44 | $1.45 | -2.43% | 4,297.50 | 2.22% |
| 6. | 2021/07/31 | $412.22 | 2.94% | 4,395.26 | 2.27% | |
| 7. | 2021/08/31 | $416.27 | 0.98% | 4,522.68 | 2.90% | |
| 8. | 2021/09/30 | $390.74 | $1.45 | -5.78% | 4,307.54 | -4.76% |
| 9. | 2021/10/31 | $460.47 | 17.85% | 4,605.38 | 6.91% | |
| 10. | 2021/11/30 | $444.22 | -3.53% | 4,567.00 | -0.83% | |
| 11. | 2021/12/31 | $502.14 | $1.45 | 13.36% | 4,766.18 | 4.36% |
| 12. | 2022/01/31 | $472.57 | -5.89% | 4,515.55 | -5.26% | |
| 13. | 2022/02/28 | $475.87 | 0.70% | 4,373.94 | -3.14% | |
| 14. | 2022/03/31 | $509.97 | $1.45 | 7.47% | 4,530.41 | 3.58% |
| 15. | 2022/04/30 | $508.55 | -0.28% | 4,131.93 | -8.80% | |
| 16. | 2022/05/31 | $496.78 | -2.31% | 4,132.15 | 0.01% | |
| 17. | 2022/06/30 | $513.63 | $1.65 | 3.72% | 3,785.38 | -8.39% |
| 18. | 2022/07/31 | $542.34 | 5.59% | 4,130.29 | 9.11% | |
| 19. | 2022/08/31 | $519.33 | -4.24% | 3,955.00 | -4.24% | |
| 20. | 2022/09/30 | $505.04 | $1.65 | -2.43% | 3,585.62 | -9.34% |
| 21. | 2022/10/31 | $555.15 | 9.92% | 3,871.98 | 7.99% | |
| 22. | 2022/11/30 | $547.76 | -1.33% | 4,080.11 | 5.38% | |
| 23. | 2022/12/31 | $530.18 | $1.65 | -2.91% | 3,839.50 | -5.90% |
| 24. | 2023/01/31 | $499.19 | -5.85% | 4,076.60 | 6.18% | |
| 25. | 2023/02/28 | $475.94 | -4.66% | 3,970.15 | -2.61% | |
| 26. | 2023/03/31 | $472.59 | $1.65 | -0.36% | 4,109.31 | 3.51% |
| 27. | 2023/04/30 | $492.09 | 4.13% | 4,169.48 | 1.46% | |
| 28. | 2023/05/31 | $487.24 | -0.99% | 4,179.83 | 0.25% | |
| 29. | 2023/06/30 | $480.64 | $1.88 | -0.97% | 4,376.86 | 4.71% |
| 30. | 2023/07/31 | $506.37 | 5.35% | 4,588.96 | 4.85% | |
| 31. | 2023/08/31 | $476.58 | -5.88% | 4,507.66 | -1.77% | |
| 32. | 2023/09/30 | $504.19 | $1.88 | 6.19% | 4,288.05 | -4.87% |
| 33. | 2023/10/31 | $535.56 | 6.22% | 4,193.80 | -2.20% | |
| 34. | 2023/11/30 | $552.97 | 3.25% | 4,567.80 | 8.92% | |
| 35. | 2023/12/31 | $526.47 | $1.88 | -4.45% | 4,769.83 | 4.42% |
| 36. | 2024/01/31 | $511.74 | -2.80% | 4,845.65 | 1.59% | |
| 37. | 2024/02/29 | $493.60 | -3.54% | 5,096.27 | 5.17% | |
| 38. | 2024/03/31 | $494.70 | $1.88 | 0.60% | 5,254.35 | 3.10% |
| 39. | 2024/04/30 | $483.70 | -2.22% | 5,035.69 | -4.16% | |
| 40. | 2024/05/31 | $495.37 | 2.41% | 5,277.51 | 4.80% | |
| 41. | 2024/06/30 | $509.26 | $2.10 | 3.23% | 5,460.48 | 3.47% |
| 42. | 2024/07/31 | $576.16 | 13.14% | 5,522.30 | 1.13% | |
| 43. | 2024/08/31 | $590.20 | 2.44% | 5,648.40 | 2.28% | |
| 44. | 2024/09/30 | $584.68 | $2.10 | -0.58% | 5,762.48 | 2.02% |
| 45. | 2024/10/31 | $564.50 | -3.45% | 5,705.45 | -0.99% | |
| 46. | 2024/11/30 | $610.20 | 8.10% | 6,032.38 | 5.73% | |
| 47. | 2024/12/31 | $505.86 | $2.10 | -16.76% | 5,881.63 | -2.50% |
| 48. | 2025/01/31 | $542.49 | 7.24% | 6,040.53 | 2.70% | |
| 49. | 2025/02/28 | $474.96 | -12.45% | 5,954.50 | -1.42% | |
| 50. | 2025/03/31 | $523.75 | $2.10 | 10.71% | 5,611.85 | -5.75% |
| 51. | 2025/04/30 | $411.44 | -21.44% | 5,569.06 | -0.76% | |
| 52. | 2025/05/31 | $301.91 | -26.62% | 5,911.69 | 6.15% | |
| 53. | 2025/06/30 | $311.97 | $2.21 | 4.06% | 6,204.95 | 4.96% |
| 54. | 2025/07/31 | $249.56 | -20.01% | 6,339.39 | 2.17% | |
| 55. | 2025/08/31 | $309.87 | 24.17% | 6,460.26 | 1.91% | |
| 56. | 2025/09/30 | $345.30 | $2.21 | 12.15% | 6,688.46 | 3.53% |
| 57. | 2025/10/31 | $341.56 | -1.08% | 6,840.20 | 2.27% | |
| 58. | 2025/11/30 | $329.77 | -3.45% | 6,849.09 | 0.13% | |
| 59. | 2025/12/31 | $330.11 | $2.21 | 0.77% | 6,845.50 | -0.05% |
| 平均 (R): | 0.52% | 1.14% | ||||
| 標準偏差： | 8.82% | 4.37% | ||||
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UNH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
UnitedHealth Group Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RUNH,t | RS&P 500,t | (RUNH,t–RUNH)2 | (RS&P 500,t–RS&P 500)2 | (RUNH,t–RUNH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | -0.41% | 2.61% | 0.85 | 2.17 | -1.36 |
| 2. | 2021/03/31 | 12.37% | 4.24% | 140.55 | 9.66 | 36.84 |
| 3. | 2021/04/30 | 7.18% | 5.24% | 44.47 | 16.86 | 27.38 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025/11/30 | -3.45% | 0.13% | 15.74 | 1.01 | 3.99 |
| 59. | 2025/12/31 | 0.77% | -0.05% | 0.07 | 1.41 | -0.31 |
| トータル (Σ): | 4,509.86 | 1,108.23 | 471.19 | |||
| t | 日付 | RUNH,t | RS&P 500,t | (RUNH,t–RUNH)2 | (RS&P 500,t–RS&P 500)2 | (RUNH,t–RUNH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021/02/28 | -0.41% | 2.61% | 0.85 | 2.17 | -1.36 |
| 2. | 2021/03/31 | 12.37% | 4.24% | 140.55 | 9.66 | 36.84 |
| 3. | 2021/04/30 | 7.18% | 5.24% | 44.47 | 16.86 | 27.38 |
| 4. | 2021/05/31 | 3.29% | 0.55% | 7.70 | 0.35 | -1.63 |
| 5. | 2021/06/30 | -2.43% | 2.22% | 8.71 | 1.18 | -3.20 |
| 6. | 2021/07/31 | 2.94% | 2.27% | 5.88 | 1.30 | 2.76 |
| 7. | 2021/08/31 | 0.98% | 2.90% | 0.22 | 3.11 | 0.82 |
| 8. | 2021/09/30 | -5.78% | -4.76% | 39.70 | 34.73 | 37.13 |
| 9. | 2021/10/31 | 17.85% | 6.91% | 300.32 | 33.39 | 100.14 |
| 10. | 2021/11/30 | -3.53% | -0.83% | 16.36 | 3.88 | 7.97 |
| 11. | 2021/12/31 | 13.36% | 4.36% | 165.10 | 10.40 | 41.44 |
| 12. | 2022/01/31 | -5.89% | -5.26% | 41.02 | 40.89 | 40.96 |
| 13. | 2022/02/28 | 0.70% | -3.14% | 0.03 | 18.25 | -0.78 |
| 14. | 2022/03/31 | 7.47% | 3.58% | 48.37 | 5.96 | 16.98 |
| 15. | 2022/04/30 | -0.28% | -8.80% | 0.63 | 98.64 | 7.89 |
| 16. | 2022/05/31 | -2.31% | 0.01% | 8.01 | 1.28 | 3.20 |
| 17. | 2022/06/30 | 3.72% | -8.39% | 10.29 | 90.79 | -30.57 |
| 18. | 2022/07/31 | 5.59% | 9.11% | 25.74 | 63.61 | 40.47 |
| 19. | 2022/08/31 | -4.24% | -4.24% | 22.64 | 28.95 | 25.60 |
| 20. | 2022/09/30 | -2.43% | -9.34% | 8.70 | 109.74 | 30.90 |
| 21. | 2022/10/31 | 9.92% | 7.99% | 88.48 | 46.93 | 64.43 |
| 22. | 2022/11/30 | -1.33% | 5.38% | 3.41 | 17.97 | -7.83 |
| 23. | 2022/12/31 | -2.91% | -5.90% | 11.72 | 49.47 | 24.08 |
| 24. | 2023/01/31 | -5.85% | 6.18% | 40.46 | 25.39 | -32.05 |
| 25. | 2023/02/28 | -4.66% | -2.61% | 26.76 | 14.04 | 19.39 |
| 26. | 2023/03/31 | -0.36% | 3.51% | 0.76 | 5.61 | -2.07 |
| 27. | 2023/04/30 | 4.13% | 1.46% | 13.03 | 0.11 | 1.18 |
| 28. | 2023/05/31 | -0.99% | 0.25% | 2.25 | 0.79 | 1.33 |
| 29. | 2023/06/30 | -0.97% | 4.71% | 2.20 | 12.80 | -5.31 |
| 30. | 2023/07/31 | 5.35% | 4.85% | 23.40 | 13.76 | 17.95 |
| 31. | 2023/08/31 | -5.88% | -1.77% | 40.95 | 8.46 | 18.61 |
| 32. | 2023/09/30 | 6.19% | -4.87% | 32.17 | 36.10 | -34.08 |
| 33. | 2023/10/31 | 6.22% | -2.20% | 32.56 | 11.12 | -19.02 |
| 34. | 2023/11/30 | 3.25% | 8.92% | 7.48 | 60.56 | 21.28 |
| 35. | 2023/12/31 | -4.45% | 4.42% | 24.68 | 10.80 | -16.33 |
| 36. | 2024/01/31 | -2.80% | 1.59% | 10.98 | 0.21 | -1.50 |
| 37. | 2024/02/29 | -3.54% | 5.17% | 16.49 | 16.29 | -16.39 |
| 38. | 2024/03/31 | 0.60% | 3.10% | 0.01 | 3.86 | 0.17 |
| 39. | 2024/04/30 | -2.22% | -4.16% | 7.50 | 28.06 | 14.51 |
| 40. | 2024/05/31 | 2.41% | 4.80% | 3.60 | 13.44 | 6.95 |
| 41. | 2024/06/30 | 3.23% | 3.47% | 7.36 | 5.43 | 6.32 |
| 42. | 2024/07/31 | 13.14% | 1.13% | 159.29 | 0.00 | -0.05 |
| 43. | 2024/08/31 | 2.44% | 2.28% | 3.69 | 1.32 | 2.20 |
| 44. | 2024/09/30 | -0.58% | 2.02% | 1.20 | 0.78 | -0.97 |
| 45. | 2024/10/31 | -3.45% | -0.99% | 15.74 | 4.52 | 8.43 |
| 46. | 2024/11/30 | 8.10% | 5.73% | 57.45 | 21.10 | 34.82 |
| 47. | 2024/12/31 | -16.76% | -2.50% | 298.29 | 13.21 | 62.78 |
| 48. | 2025/01/31 | 7.24% | 2.70% | 45.23 | 2.45 | 10.53 |
| 49. | 2025/02/28 | -12.45% | -1.42% | 168.07 | 6.56 | 33.19 |
| 50. | 2025/03/31 | 10.71% | -5.75% | 104.01 | 47.48 | -70.28 |
| 51. | 2025/04/30 | -21.44% | -0.76% | 482.21 | 3.60 | 41.69 |
| 52. | 2025/05/31 | -26.62% | 6.15% | 736.42 | 25.16 | -136.13 |
| 53. | 2025/06/30 | 4.06% | 4.96% | 12.59 | 14.63 | 13.57 |
| 54. | 2025/07/31 | -20.01% | 2.17% | 421.11 | 1.06 | -21.15 |
| 55. | 2025/08/31 | 24.17% | 1.91% | 559.35 | 0.59 | 18.22 |
| 56. | 2025/09/30 | 12.15% | 3.53% | 135.28 | 5.74 | 27.87 |
| 57. | 2025/10/31 | -1.08% | 2.27% | 2.56 | 1.28 | -1.81 |
| 58. | 2025/11/30 | -3.45% | 0.13% | 15.74 | 1.01 | 3.99 |
| 59. | 2025/12/31 | 0.77% | -0.05% | 0.07 | 1.41 | -0.31 |
| トータル (Σ): | 4,509.86 | 1,108.23 | 471.19 | |||
すべて表示
分散UNH = Σ(RUNH,t–RUNH)2 ÷ (59 – 1)
= 4,509.86 ÷ (59 – 1)
= 77.76
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
共 分散UNH, S&P 500 = Σ(RUNH,t–RUNH)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 471.19 ÷ (59 – 1)
= 8.12
システマティックなリスク推定 (β)
| 分散UNH | 77.76 |
| 分散S&P 500 | 19.11 |
| 共 分散UNH, S&P 500 | 8.12 |
| 相関係数UNH, S&P 5001 | 0.21 |
| βUNH2 | 0.43 |
| αUNH3 | 0.03% |
計算
1 相関係数UNH, S&P 500
= 共 分散UNH, S&P 500 ÷ (標準偏差UNH × 標準偏差S&P 500)
= 8.12 ÷ (8.82% × 4.37%)
= 0.21
2 βUNH
= 共 分散UNH, S&P 500 ÷ 分散S&P 500
= 8.12 ÷ 19.11
= 0.43
3 αUNH
= 平均UNH – βUNH × 平均S&P 500
= 0.52% – 0.43 × 1.14%
= 0.03%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.54% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 17.37% |
| 普通株式 UnitedHealth Group システマティックリスク | βUNH | 0.43 |
| ユナイテッドヘルス・グループ普通株式の期待収益率3 | E(RUNH) | 9.99% |
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(RUNH) = RF + βUNH [E(RM) – RF]
= 4.54% + 0.43 [17.37% – 4.54%]
= 9.99%