資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Mastercard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
Mastercard Inc.、月間収益率
| Mastercard Inc. (MA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格MA,t1 | 配当MA,t1 | RMA,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $169.00 | 2,823.81 | ||||
| 1. | 2018/02/28 | $175.76 | 4.00% | 2,713.83 | -3.89% | |
| 2. | 2018/03/31 | $175.16 | -0.34% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $178.27 | $0.25 | 1.92% | 2,648.05 | 0.27% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | $356.40 | 8.60% | 4,080.11 | 5.38% | |
| 59. | 2022/12/31 | $347.73 | -2.43% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.59% | 0.67% | ||||
| 標準偏差： | 8.04% | 5.40% | ||||
| Mastercard Inc. (MA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格MA,t1 | 配当MA,t1 | RMA,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2018/01/31 | $169.00 | 2,823.81 | ||||
| 1. | 2018/02/28 | $175.76 | 4.00% | 2,713.83 | -3.89% | |
| 2. | 2018/03/31 | $175.16 | -0.34% | 2,640.87 | -2.69% | |
| 3. | 2018/04/30 | $178.27 | $0.25 | 1.92% | 2,648.05 | 0.27% |
| 4. | 2018/05/31 | $190.12 | 6.65% | 2,705.27 | 2.16% | |
| 5. | 2018/06/30 | $196.52 | 3.37% | 2,718.37 | 0.48% | |
| 6. | 2018/07/31 | $198.00 | $0.25 | 0.88% | 2,816.29 | 3.60% |
| 7. | 2018/08/31 | $215.56 | 8.87% | 2,901.52 | 3.03% | |
| 8. | 2018/09/30 | $222.61 | 3.27% | 2,913.98 | 0.43% | |
| 9. | 2018/10/31 | $197.67 | $0.25 | -11.09% | 2,711.74 | -6.94% |
| 10. | 2018/11/30 | $201.07 | 1.72% | 2,760.17 | 1.79% | |
| 11. | 2018/12/31 | $188.65 | -6.18% | 2,506.85 | -9.18% | |
| 12. | 2019/01/31 | $211.13 | $0.33 | 12.09% | 2,704.10 | 7.87% |
| 13. | 2019/02/28 | $224.77 | 6.46% | 2,784.49 | 2.97% | |
| 14. | 2019/03/31 | $235.45 | 4.75% | 2,834.40 | 1.79% | |
| 15. | 2019/04/30 | $254.24 | $0.33 | 8.12% | 2,945.83 | 3.93% |
| 16. | 2019/05/31 | $251.49 | -1.08% | 2,752.06 | -6.58% | |
| 17. | 2019/06/30 | $264.53 | 5.19% | 2,941.76 | 6.89% | |
| 18. | 2019/07/31 | $272.27 | $0.33 | 3.05% | 2,980.38 | 1.31% |
| 19. | 2019/08/31 | $281.37 | 3.34% | 2,926.46 | -1.81% | |
| 20. | 2019/09/30 | $271.57 | -3.48% | 2,976.74 | 1.72% | |
| 21. | 2019/10/31 | $276.81 | $0.33 | 2.05% | 3,037.56 | 2.04% |
| 22. | 2019/11/30 | $292.23 | 5.57% | 3,140.98 | 3.40% | |
| 23. | 2019/12/31 | $298.59 | 2.18% | 3,230.78 | 2.86% | |
| 24. | 2020/01/31 | $315.94 | $0.40 | 5.94% | 3,225.52 | -0.16% |
| 25. | 2020/02/29 | $290.25 | -8.13% | 2,954.22 | -8.41% | |
| 26. | 2020/03/31 | $241.56 | -16.78% | 2,584.59 | -12.51% | |
| 27. | 2020/04/30 | $274.97 | $0.40 | 14.00% | 2,912.43 | 12.68% |
| 28. | 2020/05/31 | $300.89 | 9.43% | 3,044.31 | 4.53% | |
| 29. | 2020/06/30 | $295.70 | -1.72% | 3,100.29 | 1.84% | |
| 30. | 2020/07/31 | $308.53 | $0.40 | 4.47% | 3,271.12 | 5.51% |
| 31. | 2020/08/31 | $358.19 | 16.10% | 3,500.31 | 7.01% | |
| 32. | 2020/09/30 | $338.17 | -5.59% | 3,363.00 | -3.92% | |
| 33. | 2020/10/31 | $288.64 | $0.40 | -14.53% | 3,269.96 | -2.77% |
| 34. | 2020/11/30 | $336.51 | 16.58% | 3,621.63 | 10.75% | |
| 35. | 2020/12/31 | $356.94 | 6.07% | 3,756.07 | 3.71% | |
| 36. | 2021/01/31 | $316.29 | $0.44 | -11.27% | 3,714.24 | -1.11% |
| 37. | 2021/02/28 | $353.85 | 11.88% | 3,811.15 | 2.61% | |
| 38. | 2021/03/31 | $356.05 | 0.62% | 3,972.89 | 4.24% | |
| 39. | 2021/04/30 | $382.06 | $0.44 | 7.43% | 4,181.17 | 5.24% |
| 40. | 2021/05/31 | $360.58 | -5.62% | 4,204.11 | 0.55% | |
| 41. | 2021/06/30 | $365.09 | 1.25% | 4,297.50 | 2.22% | |
| 42. | 2021/07/31 | $385.94 | $0.44 | 5.83% | 4,395.26 | 2.27% |
| 43. | 2021/08/31 | $346.23 | -10.29% | 4,522.68 | 2.90% | |
| 44. | 2021/09/30 | $347.68 | 0.42% | 4,307.54 | -4.76% | |
| 45. | 2021/10/31 | $335.52 | $0.44 | -3.37% | 4,605.38 | 6.91% |
| 46. | 2021/11/30 | $314.92 | -6.14% | 4,567.00 | -0.83% | |
| 47. | 2021/12/31 | $359.32 | 14.10% | 4,766.18 | 4.36% | |
| 48. | 2022/01/31 | $386.38 | $0.49 | 7.67% | 4,515.55 | -5.26% |
| 49. | 2022/02/28 | $360.82 | -6.62% | 4,373.94 | -3.14% | |
| 50. | 2022/03/31 | $357.38 | -0.95% | 4,530.41 | 3.58% | |
| 51. | 2022/04/30 | $363.38 | $0.49 | 1.82% | 4,131.93 | -8.80% |
| 52. | 2022/05/31 | $357.87 | -1.52% | 4,132.15 | 0.01% | |
| 53. | 2022/06/30 | $315.48 | -11.85% | 3,785.38 | -8.39% | |
| 54. | 2022/07/31 | $353.79 | $0.49 | 12.30% | 4,130.29 | 9.11% |
| 55. | 2022/08/31 | $324.37 | -8.32% | 3,955.00 | -4.24% | |
| 56. | 2022/09/30 | $284.34 | -12.34% | 3,585.62 | -9.34% | |
| 57. | 2022/10/31 | $328.18 | $0.49 | 15.59% | 3,871.98 | 7.99% |
| 58. | 2022/11/30 | $356.40 | 8.60% | 4,080.11 | 5.38% | |
| 59. | 2022/12/31 | $347.73 | -2.43% | 3,839.50 | -5.90% | |
| 平均 (R): | 1.59% | 0.67% | ||||
| 標準偏差： | 8.04% | 5.40% | ||||
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中のMA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
Mastercard Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RMA,t | RS&P 500,t | (RMA,t–RMA)2 | (RS&P 500,t–RS&P 500)2 | (RMA,t–RMA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | 4.00% | -3.89% | 5.80 | 20.81 | -10.98 |
| 2. | 2018/03/31 | -0.34% | -2.69% | 3.74 | 11.26 | 6.49 |
| 3. | 2018/04/30 | 1.92% | 0.27% | 0.11 | 0.16 | -0.13 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022/11/30 | 8.60% | 5.38% | 49.10 | 22.17 | 32.99 |
| 59. | 2022/12/31 | -2.43% | -5.90% | 16.20 | 43.08 | 26.42 |
| トータル (Σ): | 3,750.56 | 1,691.48 | 1,838.87 | |||
| t | 日付 | RMA,t | RS&P 500,t | (RMA,t–RMA)2 | (RS&P 500,t–RS&P 500)2 | (RMA,t–RMA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018/02/28 | 4.00% | -3.89% | 5.80 | 20.81 | -10.98 |
| 2. | 2018/03/31 | -0.34% | -2.69% | 3.74 | 11.26 | 6.49 |
| 3. | 2018/04/30 | 1.92% | 0.27% | 0.11 | 0.16 | -0.13 |
| 4. | 2018/05/31 | 6.65% | 2.16% | 25.55 | 2.23 | 7.55 |
| 5. | 2018/06/30 | 3.37% | 0.48% | 3.15 | 0.03 | -0.32 |
| 6. | 2018/07/31 | 0.88% | 3.60% | 0.51 | 8.62 | -2.09 |
| 7. | 2018/08/31 | 8.87% | 3.03% | 52.95 | 5.57 | 17.17 |
| 8. | 2018/09/30 | 3.27% | 0.43% | 2.82 | 0.06 | -0.40 |
| 9. | 2018/10/31 | -11.09% | -6.94% | 160.86 | 57.87 | 96.48 |
| 10. | 2018/11/30 | 1.72% | 1.79% | 0.02 | 1.25 | 0.14 |
| 11. | 2018/12/31 | -6.18% | -9.18% | 60.36 | 96.91 | 76.48 |
| 12. | 2019/01/31 | 12.09% | 7.87% | 110.23 | 51.87 | 75.61 |
| 13. | 2019/02/28 | 6.46% | 2.97% | 23.70 | 5.32 | 11.23 |
| 14. | 2019/03/31 | 4.75% | 1.79% | 9.98 | 1.27 | 3.56 |
| 15. | 2019/04/30 | 8.12% | 3.93% | 42.62 | 10.66 | 21.31 |
| 16. | 2019/05/31 | -1.08% | -6.58% | 7.15 | 52.48 | 19.37 |
| 17. | 2019/06/30 | 5.19% | 6.89% | 12.91 | 38.77 | 22.37 |
| 18. | 2019/07/31 | 3.05% | 1.31% | 2.13 | 0.42 | 0.94 |
| 19. | 2019/08/31 | 3.34% | -1.81% | 3.06 | 6.13 | -4.33 |
| 20. | 2019/09/30 | -3.48% | 1.72% | 25.76 | 1.11 | -5.34 |
| 21. | 2019/10/31 | 2.05% | 2.04% | 0.21 | 1.89 | 0.63 |
| 22. | 2019/11/30 | 5.57% | 3.40% | 15.83 | 7.50 | 10.89 |
| 23. | 2019/12/31 | 2.18% | 2.86% | 0.34 | 4.81 | 1.28 |
| 24. | 2020/01/31 | 5.94% | -0.16% | 18.94 | 0.69 | -3.61 |
| 25. | 2020/02/29 | -8.13% | -8.41% | 94.54 | 82.40 | 88.27 |
| 26. | 2020/03/31 | -16.78% | -12.51% | 337.36 | 173.67 | 242.05 |
| 27. | 2020/04/30 | 14.00% | 12.68% | 153.87 | 144.43 | 149.07 |
| 28. | 2020/05/31 | 9.43% | 4.53% | 61.38 | 14.91 | 30.25 |
| 29. | 2020/06/30 | -1.72% | 1.84% | 11.00 | 1.37 | -3.89 |
| 30. | 2020/07/31 | 4.47% | 5.51% | 8.31 | 23.46 | 13.96 |
| 31. | 2020/08/31 | 16.10% | 7.01% | 210.35 | 40.19 | 91.95 |
| 32. | 2020/09/30 | -5.59% | -3.92% | 51.57 | 21.06 | 32.96 |
| 33. | 2020/10/31 | -14.53% | -2.77% | 259.86 | 11.79 | 55.34 |
| 34. | 2020/11/30 | 16.58% | 10.75% | 224.78 | 101.77 | 151.24 |
| 35. | 2020/12/31 | 6.07% | 3.71% | 20.06 | 9.28 | 13.64 |
| 36. | 2021/01/31 | -11.27% | -1.11% | 165.31 | 3.17 | 22.89 |
| 37. | 2021/02/28 | 11.88% | 2.61% | 105.74 | 3.77 | 19.97 |
| 38. | 2021/03/31 | 0.62% | 4.24% | 0.94 | 12.80 | -3.47 |
| 39. | 2021/04/30 | 7.43% | 5.24% | 34.07 | 20.94 | 26.71 |
| 40. | 2021/05/31 | -5.62% | 0.55% | 52.05 | 0.01 | 0.85 |
| 41. | 2021/06/30 | 1.25% | 2.22% | 0.12 | 2.42 | -0.53 |
| 42. | 2021/07/31 | 5.83% | 2.27% | 17.97 | 2.59 | 6.82 |
| 43. | 2021/08/31 | -10.29% | 2.90% | 141.16 | 4.98 | -26.52 |
| 44. | 2021/09/30 | 0.42% | -4.76% | 1.38 | 29.42 | 6.36 |
| 45. | 2021/10/31 | -3.37% | 6.91% | 24.63 | 39.03 | -31.01 |
| 46. | 2021/11/30 | -6.14% | -0.83% | 59.78 | 2.25 | 11.60 |
| 47. | 2021/12/31 | 14.10% | 4.36% | 156.42 | 13.65 | 46.21 |
| 48. | 2022/01/31 | 7.67% | -5.26% | 36.91 | 35.11 | -36.00 |
| 49. | 2022/02/28 | -6.62% | -3.14% | 67.36 | 14.46 | 31.21 |
| 50. | 2022/03/31 | -0.95% | 3.58% | 6.48 | 8.47 | -7.41 |
| 51. | 2022/04/30 | 1.82% | -8.80% | 0.05 | 89.54 | -2.12 |
| 52. | 2022/05/31 | -1.52% | 0.01% | 9.66 | 0.44 | 2.06 |
| 53. | 2022/06/30 | -11.85% | -8.39% | 180.56 | 82.06 | 121.72 |
| 54. | 2022/07/31 | 12.30% | 9.11% | 114.63 | 71.32 | 90.42 |
| 55. | 2022/08/31 | -8.32% | -4.24% | 98.16 | 24.11 | 48.65 |
| 56. | 2022/09/30 | -12.34% | -9.34% | 194.13 | 100.12 | 139.42 |
| 57. | 2022/10/31 | 15.59% | 7.99% | 195.96 | 53.58 | 102.46 |
| 58. | 2022/11/30 | 8.60% | 5.38% | 49.10 | 22.17 | 32.99 |
| 59. | 2022/12/31 | -2.43% | -5.90% | 16.20 | 43.08 | 26.42 |
| トータル (Σ): | 3,750.56 | 1,691.48 | 1,838.87 | |||
すべて表示
分散MA = Σ(RMA,t–RMA)2 ÷ (59 – 1)
= 3,750.56 ÷ (59 – 1)
= 64.66
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MA, S&P 500 = Σ(RMA,t–RMA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,838.87 ÷ (59 – 1)
= 31.70
システマティックなリスク推定 (β)
| 分散MA | 64.66 |
| 分散S&P 500 | 29.16 |
| 共 分散MA, S&P 500 | 31.70 |
| 相関係数MA, S&P 5001 | 0.73 |
| βMA2 | 1.09 |
| αMA3 | 0.87% |
計算
1 相関係数MA, S&P 500
= 共 分散MA, S&P 500 ÷ (標準偏差MA × 標準偏差S&P 500)
= 31.70 ÷ (8.04% × 5.40%)
= 0.73
2 βMA
= 共 分散MA, S&P 500 ÷ 分散S&P 500
= 31.70 ÷ 29.16
= 1.09
3 αMA
= 平均MA – βMA × 平均S&P 500
= 1.59% – 1.09 × 0.67%
= 0.87%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.68% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.92% |
| 普通株式 Mastercard システマティックリスク | βMA | 1.09 |
| Mastercard普通株式の期待収益率3 | E(RMA) | 15.81% |
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(RMA) = RF + βMA [E(RM) – RF]
= 4.68% + 1.09 [14.92% – 4.68%]
= 15.81%