資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、普通株式 FICOのようなリスク資産の予想または必要な収益率を示します。
収益率
Fair Isaac Corp.、月間収益率
| Fair Isaac Corp. (FICO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格FICO,t1 | 配当FICO,t1 | RFICO,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/10/31 | $192.71 | 2,711.74 | ||||
| 1. | 2018/11/30 | $198.63 | 3.07% | 2,760.17 | 1.79% | |
| 2. | 2018/12/31 | $187.00 | -5.86% | 2,506.85 | -9.18% | |
| 3. | 2019/01/31 | $225.20 | 20.43% | 2,704.10 | 7.87% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024/08/31 | $1,730.27 | 8.14% | 5,648.40 | 2.28% | |
| 71. | 2024/09/30 | $1,943.52 | 12.32% | 5,762.48 | 2.02% | |
| 平均 (R): | 3.81% | 1.20% | ||||
| 標準偏差： | 10.25% | 5.15% | ||||
| Fair Isaac Corp. (FICO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格FICO,t1 | 配当FICO,t1 | RFICO,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/10/31 | $192.71 | 2,711.74 | ||||
| 1. | 2018/11/30 | $198.63 | 3.07% | 2,760.17 | 1.79% | |
| 2. | 2018/12/31 | $187.00 | -5.86% | 2,506.85 | -9.18% | |
| 3. | 2019/01/31 | $225.20 | 20.43% | 2,704.10 | 7.87% | |
| 4. | 2019/02/28 | $247.82 | 10.04% | 2,784.49 | 2.97% | |
| 5. | 2019/03/31 | $271.63 | 9.61% | 2,834.40 | 1.79% | |
| 6. | 2019/04/30 | $279.75 | 2.99% | 2,945.83 | 3.93% | |
| 7. | 2019/05/31 | $295.90 | 5.77% | 2,752.06 | -6.58% | |
| 8. | 2019/06/30 | $314.02 | 6.12% | 2,941.76 | 6.89% | |
| 9. | 2019/07/31 | $347.42 | 10.64% | 2,980.38 | 1.31% | |
| 10. | 2019/08/31 | $352.72 | 1.53% | 2,926.46 | -1.81% | |
| 11. | 2019/09/30 | $303.52 | -13.95% | 2,976.74 | 1.72% | |
| 12. | 2019/10/31 | $304.04 | 0.17% | 3,037.56 | 2.04% | |
| 13. | 2019/11/30 | $367.75 | 20.95% | 3,140.98 | 3.40% | |
| 14. | 2019/12/31 | $374.68 | 1.88% | 3,230.78 | 2.86% | |
| 15. | 2020/01/31 | $402.38 | 7.39% | 3,225.52 | -0.16% | |
| 16. | 2020/02/29 | $376.03 | -6.55% | 2,954.22 | -8.41% | |
| 17. | 2020/03/31 | $307.69 | -18.17% | 2,584.59 | -12.51% | |
| 18. | 2020/04/30 | $352.94 | 14.71% | 2,912.43 | 12.68% | |
| 19. | 2020/05/31 | $402.65 | 14.08% | 3,044.31 | 4.53% | |
| 20. | 2020/06/30 | $418.04 | 3.82% | 3,100.29 | 1.84% | |
| 21. | 2020/07/31 | $439.19 | 5.06% | 3,271.12 | 5.51% | |
| 22. | 2020/08/31 | $420.79 | -4.19% | 3,500.31 | 7.01% | |
| 23. | 2020/09/30 | $425.38 | 1.09% | 3,363.00 | -3.92% | |
| 24. | 2020/10/31 | $391.45 | -7.98% | 3,269.96 | -2.77% | |
| 25. | 2020/11/30 | $472.78 | 20.78% | 3,621.63 | 10.75% | |
| 26. | 2020/12/31 | $511.04 | 8.09% | 3,756.07 | 3.71% | |
| 27. | 2021/01/31 | $450.11 | -11.92% | 3,714.24 | -1.11% | |
| 28. | 2021/02/28 | $457.55 | 1.65% | 3,811.15 | 2.61% | |
| 29. | 2021/03/31 | $486.05 | 6.23% | 3,972.89 | 4.24% | |
| 30. | 2021/04/30 | $521.41 | 7.27% | 4,181.17 | 5.24% | |
| 31. | 2021/05/31 | $506.06 | -2.94% | 4,204.11 | 0.55% | |
| 32. | 2021/06/30 | $502.68 | -0.67% | 4,297.50 | 2.22% | |
| 33. | 2021/07/31 | $523.91 | 4.22% | 4,395.26 | 2.27% | |
| 34. | 2021/08/31 | $459.74 | -12.25% | 4,522.68 | 2.90% | |
| 35. | 2021/09/30 | $397.93 | -13.44% | 4,307.54 | -4.76% | |
| 36. | 2021/10/31 | $398.20 | 0.07% | 4,605.38 | 6.91% | |
| 37. | 2021/11/30 | $353.13 | -11.32% | 4,567.00 | -0.83% | |
| 38. | 2021/12/31 | $433.67 | 22.81% | 4,766.18 | 4.36% | |
| 39. | 2022/01/31 | $494.99 | 14.14% | 4,515.55 | -5.26% | |
| 40. | 2022/02/28 | $471.19 | -4.81% | 4,373.94 | -3.14% | |
| 41. | 2022/03/31 | $466.46 | -1.00% | 4,530.41 | 3.58% | |
| 42. | 2022/04/30 | $373.51 | -19.93% | 4,131.93 | -8.80% | |
| 43. | 2022/05/31 | $409.55 | 9.65% | 4,132.15 | 0.01% | |
| 44. | 2022/06/30 | $400.90 | -2.11% | 3,785.38 | -8.39% | |
| 45. | 2022/07/31 | $462.03 | 15.25% | 4,130.29 | 9.11% | |
| 46. | 2022/08/31 | $449.40 | -2.73% | 3,955.00 | -4.24% | |
| 47. | 2022/09/30 | $412.01 | -8.32% | 3,585.62 | -9.34% | |
| 48. | 2022/10/31 | $478.84 | 16.22% | 3,871.98 | 7.99% | |
| 49. | 2022/11/30 | $619.72 | 29.42% | 4,080.11 | 5.38% | |
| 50. | 2022/12/31 | $598.58 | -3.41% | 3,839.50 | -5.90% | |
| 51. | 2023/01/31 | $665.95 | 11.25% | 4,076.60 | 6.18% | |
| 52. | 2023/02/28 | $677.39 | 1.72% | 3,970.15 | -2.61% | |
| 53. | 2023/03/31 | $702.69 | 3.73% | 4,109.31 | 3.51% | |
| 54. | 2023/04/30 | $727.95 | 3.59% | 4,169.48 | 1.46% | |
| 55. | 2023/05/31 | $787.67 | 8.20% | 4,179.83 | 0.25% | |
| 56. | 2023/06/30 | $809.21 | 2.73% | 4,376.86 | 4.71% | |
| 57. | 2023/07/31 | $837.97 | 3.55% | 4,588.96 | 4.85% | |
| 58. | 2023/08/31 | $904.59 | 7.95% | 4,507.66 | -1.77% | |
| 59. | 2023/09/30 | $868.53 | -3.99% | 4,288.05 | -4.87% | |
| 60. | 2023/10/31 | $845.87 | -2.61% | 4,193.80 | -2.20% | |
| 61. | 2023/11/30 | $1,087.60 | 28.58% | 4,567.80 | 8.92% | |
| 62. | 2023/12/31 | $1,164.01 | 7.03% | 4,769.83 | 4.42% | |
| 63. | 2024/01/31 | $1,198.83 | 2.99% | 4,845.65 | 1.59% | |
| 64. | 2024/02/29 | $1,269.91 | 5.93% | 5,096.27 | 5.17% | |
| 65. | 2024/03/31 | $1,249.61 | -1.60% | 5,254.35 | 3.10% | |
| 66. | 2024/04/30 | $1,133.33 | -9.31% | 5,035.69 | -4.16% | |
| 67. | 2024/05/31 | $1,289.93 | 13.82% | 5,277.51 | 4.80% | |
| 68. | 2024/06/30 | $1,488.66 | 15.41% | 5,460.48 | 3.47% | |
| 69. | 2024/07/31 | $1,600.00 | 7.48% | 5,522.30 | 1.13% | |
| 70. | 2024/08/31 | $1,730.27 | 8.14% | 5,648.40 | 2.28% | |
| 71. | 2024/09/30 | $1,943.52 | 12.32% | 5,762.48 | 2.02% | |
| 平均 (R): | 3.81% | 1.20% | ||||
| 標準偏差： | 10.25% | 5.15% | ||||
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FICO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
Fair Isaac Corp.、分散の計算、および戻り値の共分散
| t | 日付 | RFICO,t | RS&P 500,t | (RFICO,t–RFICO)2 | (RS&P 500,t–RS&P 500)2 | (RFICO,t–RFICO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/11/30 | 3.07% | 1.79% | 0.55 | 0.34 | -0.43 |
| 2. | 2018/12/31 | -5.86% | -9.18% | 93.43 | 107.68 | 100.30 |
| 3. | 2019/01/31 | 20.43% | 7.87% | 276.13 | 44.48 | 110.83 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024/08/31 | 8.14% | 2.28% | 18.76 | 1.18 | 4.70 |
| 71. | 2024/09/30 | 12.32% | 2.02% | 72.49 | 0.67 | 6.99 |
| トータル (Σ): | 7,360.28 | 1,855.59 | 2,377.51 | |||
| t | 日付 | RFICO,t | RS&P 500,t | (RFICO,t–RFICO)2 | (RS&P 500,t–RS&P 500)2 | (RFICO,t–RFICO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/11/30 | 3.07% | 1.79% | 0.55 | 0.34 | -0.43 |
| 2. | 2018/12/31 | -5.86% | -9.18% | 93.43 | 107.68 | 100.30 |
| 3. | 2019/01/31 | 20.43% | 7.87% | 276.13 | 44.48 | 110.83 |
| 4. | 2019/02/28 | 10.04% | 2.97% | 38.86 | 3.15 | 11.06 |
| 5. | 2019/03/31 | 9.61% | 1.79% | 33.61 | 0.35 | 3.44 |
| 6. | 2019/04/30 | 2.99% | 3.93% | 0.67 | 7.47 | -2.24 |
| 7. | 2019/05/31 | 5.77% | -6.58% | 3.85 | 60.48 | -15.26 |
| 8. | 2019/06/30 | 6.12% | 6.89% | 5.35 | 32.42 | 13.17 |
| 9. | 2019/07/31 | 10.64% | 1.31% | 46.59 | 0.01 | 0.78 |
| 10. | 2019/08/31 | 1.53% | -1.81% | 5.22 | 9.05 | 6.87 |
| 11. | 2019/09/30 | -13.95% | 1.72% | 315.40 | 0.27 | -9.22 |
| 12. | 2019/10/31 | 0.17% | 2.04% | 13.24 | 0.71 | -3.07 |
| 13. | 2019/11/30 | 20.95% | 3.40% | 293.91 | 4.87 | 37.81 |
| 14. | 2019/12/31 | 1.88% | 2.86% | 3.71 | 2.76 | -3.20 |
| 15. | 2020/01/31 | 7.39% | -0.16% | 12.83 | 1.85 | -4.88 |
| 16. | 2020/02/29 | -6.55% | -8.41% | 107.31 | 92.35 | 99.55 |
| 17. | 2020/03/31 | -18.17% | -12.51% | 483.33 | 187.99 | 301.43 |
| 18. | 2020/04/30 | 14.71% | 12.68% | 118.72 | 131.91 | 125.14 |
| 19. | 2020/05/31 | 14.08% | 4.53% | 105.55 | 11.08 | 34.20 |
| 20. | 2020/06/30 | 3.82% | 1.84% | 0.00 | 0.41 | 0.01 |
| 21. | 2020/07/31 | 5.06% | 5.51% | 1.56 | 18.59 | 5.38 |
| 22. | 2020/08/31 | -4.19% | 7.01% | 64.00 | 33.73 | -46.46 |
| 23. | 2020/09/30 | 1.09% | -3.92% | 7.40 | 26.23 | 13.93 |
| 24. | 2020/10/31 | -7.98% | -2.77% | 138.93 | 15.73 | 46.74 |
| 25. | 2020/11/30 | 20.78% | 10.75% | 287.84 | 91.31 | 162.12 |
| 26. | 2020/12/31 | 8.09% | 3.71% | 18.33 | 6.32 | 10.76 |
| 27. | 2021/01/31 | -11.92% | -1.11% | 247.54 | 5.35 | 36.39 |
| 28. | 2021/02/28 | 1.65% | 2.61% | 4.66 | 1.99 | -3.04 |
| 29. | 2021/03/31 | 6.23% | 4.24% | 5.85 | 9.27 | 7.36 |
| 30. | 2021/04/30 | 7.27% | 5.24% | 12.00 | 16.35 | 14.01 |
| 31. | 2021/05/31 | -2.94% | 0.55% | 45.62 | 0.42 | 4.39 |
| 32. | 2021/06/30 | -0.67% | 2.22% | 20.06 | 1.05 | -4.58 |
| 33. | 2021/07/31 | 4.22% | 2.27% | 0.17 | 1.16 | 0.44 |
| 34. | 2021/08/31 | -12.25% | 2.90% | 257.89 | 2.89 | -27.30 |
| 35. | 2021/09/30 | -13.44% | -4.76% | 297.74 | 35.47 | 102.77 |
| 36. | 2021/10/31 | 0.07% | 6.91% | 14.01 | 32.67 | -21.39 |
| 37. | 2021/11/30 | -11.32% | -0.83% | 228.89 | 4.13 | 30.75 |
| 38. | 2021/12/31 | 22.81% | 4.36% | 360.88 | 10.00 | 60.07 |
| 39. | 2022/01/31 | 14.14% | -5.26% | 106.69 | 41.70 | -66.70 |
| 40. | 2022/02/28 | -4.81% | -3.14% | 74.28 | 18.79 | 37.36 |
| 41. | 2022/03/31 | -1.00% | 3.58% | 23.18 | 5.66 | -11.45 |
| 42. | 2022/04/30 | -19.93% | -8.80% | 563.46 | 99.89 | 237.25 |
| 43. | 2022/05/31 | 9.65% | 0.01% | 34.09 | 1.42 | -6.97 |
| 44. | 2022/06/30 | -2.11% | -8.39% | 35.08 | 91.99 | 56.80 |
| 45. | 2022/07/31 | 15.25% | 9.11% | 130.82 | 62.61 | 90.50 |
| 46. | 2022/08/31 | -2.73% | -4.24% | 42.83 | 29.63 | 35.62 |
| 47. | 2022/09/30 | -8.32% | -9.34% | 147.15 | 111.06 | 127.84 |
| 48. | 2022/10/31 | 16.22% | 7.99% | 154.00 | 46.07 | 84.23 |
| 49. | 2022/11/30 | 29.42% | 5.38% | 655.90 | 17.44 | 106.96 |
| 50. | 2022/12/31 | -3.41% | -5.90% | 52.16 | 50.36 | 51.25 |
| 51. | 2023/01/31 | 11.25% | 6.18% | 55.42 | 24.76 | 37.05 |
| 52. | 2023/02/28 | 1.72% | -2.61% | 4.38 | 14.52 | 7.97 |
| 53. | 2023/03/31 | 3.73% | 3.51% | 0.01 | 5.32 | -0.17 |
| 54. | 2023/04/30 | 3.59% | 1.46% | 0.05 | 0.07 | -0.06 |
| 55. | 2023/05/31 | 8.20% | 0.25% | 19.30 | 0.90 | -4.18 |
| 56. | 2023/06/30 | 2.73% | 4.71% | 1.16 | 12.35 | -3.78 |
| 57. | 2023/07/31 | 3.55% | 4.85% | 0.07 | 13.30 | -0.94 |
| 58. | 2023/08/31 | 7.95% | -1.77% | 17.14 | 8.82 | -12.30 |
| 59. | 2023/09/30 | -3.99% | -4.87% | 60.79 | 36.86 | 47.33 |
| 60. | 2023/10/31 | -2.61% | -2.20% | 41.21 | 11.54 | 21.81 |
| 61. | 2023/11/30 | 28.58% | 8.92% | 613.41 | 59.58 | 191.18 |
| 62. | 2023/12/31 | 7.03% | 4.42% | 10.34 | 10.39 | 10.36 |
| 63. | 2024/01/31 | 2.99% | 1.59% | 0.67 | 0.15 | -0.32 |
| 64. | 2024/02/29 | 5.93% | 5.17% | 4.49 | 15.79 | 8.42 |
| 65. | 2024/03/31 | -1.60% | 3.10% | 29.26 | 3.62 | -10.29 |
| 66. | 2024/04/30 | -9.31% | -4.16% | 172.03 | 28.73 | 70.31 |
| 67. | 2024/05/31 | 13.82% | 4.80% | 100.14 | 12.98 | 36.06 |
| 68. | 2024/06/30 | 15.41% | 3.47% | 134.46 | 5.14 | 26.30 |
| 69. | 2024/07/31 | 7.48% | 1.13% | 13.46 | 0.00 | -0.25 |
| 70. | 2024/08/31 | 8.14% | 2.28% | 18.76 | 1.18 | 4.70 |
| 71. | 2024/09/30 | 12.32% | 2.02% | 72.49 | 0.67 | 6.99 |
| トータル (Σ): | 7,360.28 | 1,855.59 | 2,377.51 | |||
すべて表示
分散FICO = Σ(RFICO,t–RFICO)2 ÷ (71 – 1)
= 7,360.28 ÷ (71 – 1)
= 105.15
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,855.59 ÷ (71 – 1)
= 26.51
共 分散FICO, S&P 500 = Σ(RFICO,t–RFICO)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,377.51 ÷ (71 – 1)
= 33.96
システマティックなリスク推定 (β)
| 分散FICO | 105.15 |
| 分散S&P 500 | 26.51 |
| 共 分散FICO, S&P 500 | 33.96 |
| 相関係数FICO, S&P 5001 | 0.64 |
| βFICO2 | 1.28 |
| αFICO3 | 2.27% |
計算
1 相関係数FICO, S&P 500
= 共 分散FICO, S&P 500 ÷ (標準偏差FICO × 標準偏差S&P 500)
= 33.96 ÷ (10.25% × 5.15%)
= 0.64
2 βFICO
= 共 分散FICO, S&P 500 ÷ 分散S&P 500
= 33.96 ÷ 26.51
= 1.28
3 αFICO
= 平均FICO – βFICO × 平均S&P 500
= 3.81% – 1.28 × 1.20%
= 2.27%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.71% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.85% |
| 普通株式のシステマティックリスクFICO | βFICO | 1.28 |
| FICO普通株式の予想収益率3 | E(RFICO) | 17.71% |
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(RFICO) = RF + βFICO [E(RM) – RF]
= 4.71% + 1.28 [14.85% – 4.71%]
= 17.71%