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 NXP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
NXP Semiconductors N.V.、月間収益率
| NXP Semiconductors N.V. (NXPI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格NXPI,t1 | 配当NXPI,t1 | RNXPI,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2017/01/31 | $97.85 | 2,278.87 | ||||
| 1. | 2017/02/28 | $102.81 | 5.07% | 2,363.64 | 3.72% | |
| 2. | 2017/03/31 | $103.50 | 0.67% | 2,362.72 | -0.04% | |
| 3. | 2017/04/30 | $105.75 | 2.17% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021/11/30 | $223.36 | 11.20% | 4,567.00 | -0.83% | |
| 59. | 2021/12/31 | $227.78 | $0.5625 | 2.23% | 4,766.18 | 4.36% |
| 平均 (R): | 1.93% | 1.36% | ||||
| 標準偏差： | 9.12% | 4.48% | ||||
| NXP Semiconductors N.V. (NXPI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格NXPI,t1 | 配当NXPI,t1 | RNXPI,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2017/01/31 | $97.85 | 2,278.87 | ||||
| 1. | 2017/02/28 | $102.81 | 5.07% | 2,363.64 | 3.72% | |
| 2. | 2017/03/31 | $103.50 | 0.67% | 2,362.72 | -0.04% | |
| 3. | 2017/04/30 | $105.75 | 2.17% | 2,384.20 | 0.91% | |
| 4. | 2017/05/31 | $109.90 | 3.92% | 2,411.80 | 1.16% | |
| 5. | 2017/06/30 | $109.45 | -0.41% | 2,423.41 | 0.48% | |
| 6. | 2017/07/31 | $110.33 | 0.80% | 2,470.30 | 1.93% | |
| 7. | 2017/08/31 | $112.96 | 2.38% | 2,471.65 | 0.05% | |
| 8. | 2017/09/30 | $113.09 | 0.12% | 2,519.36 | 1.93% | |
| 9. | 2017/10/31 | $117.05 | 3.50% | 2,575.26 | 2.22% | |
| 10. | 2017/11/30 | $113.39 | -3.13% | 2,647.58 | 2.81% | |
| 11. | 2017/12/31 | $117.09 | 3.26% | 2,673.61 | 0.98% | |
| 12. | 2018/01/31 | $120.32 | 2.76% | 2,823.81 | 5.62% | |
| 13. | 2018/02/28 | $124.66 | 3.61% | 2,713.83 | -3.89% | |
| 14. | 2018/03/31 | $117.00 | -6.14% | 2,640.87 | -2.69% | |
| 15. | 2018/04/30 | $104.90 | -10.34% | 2,648.05 | 0.27% | |
| 16. | 2018/05/31 | $114.00 | 8.67% | 2,705.27 | 2.16% | |
| 17. | 2018/06/30 | $109.27 | -4.15% | 2,718.37 | 0.48% | |
| 18. | 2018/07/31 | $95.34 | -12.75% | 2,816.29 | 3.60% | |
| 19. | 2018/08/31 | $93.14 | -2.31% | 2,901.52 | 3.03% | |
| 20. | 2018/09/30 | $85.50 | $0.25 | -7.93% | 2,913.98 | 0.43% |
| 21. | 2018/10/31 | $74.99 | -12.29% | 2,711.74 | -6.94% | |
| 22. | 2018/11/30 | $83.37 | 11.17% | 2,760.17 | 1.79% | |
| 23. | 2018/12/31 | $73.28 | $0.25 | -11.80% | 2,506.85 | -9.18% |
| 24. | 2019/01/31 | $87.03 | 18.76% | 2,704.10 | 7.87% | |
| 25. | 2019/02/28 | $91.32 | 4.93% | 2,784.49 | 2.97% | |
| 26. | 2019/03/31 | $88.39 | $0.25 | -2.93% | 2,834.40 | 1.79% |
| 27. | 2019/04/30 | $105.62 | 19.49% | 2,945.83 | 3.93% | |
| 28. | 2019/05/31 | $88.16 | -16.53% | 2,752.06 | -6.58% | |
| 29. | 2019/06/30 | $97.61 | $0.25 | 11.00% | 2,941.76 | 6.89% |
| 30. | 2019/07/31 | $103.39 | 5.92% | 2,980.38 | 1.31% | |
| 31. | 2019/08/31 | $102.14 | -1.21% | 2,926.46 | -1.81% | |
| 32. | 2019/09/30 | $109.12 | $0.375 | 7.20% | 2,976.74 | 1.72% |
| 33. | 2019/10/31 | $113.68 | 4.18% | 3,037.56 | 2.04% | |
| 34. | 2019/11/30 | $115.58 | 1.67% | 3,140.98 | 3.40% | |
| 35. | 2019/12/31 | $127.26 | $0.375 | 10.43% | 3,230.78 | 2.86% |
| 36. | 2020/01/31 | $126.86 | -0.31% | 3,225.52 | -0.16% | |
| 37. | 2020/02/29 | $113.69 | -10.38% | 2,954.22 | -8.41% | |
| 38. | 2020/03/31 | $82.93 | $0.375 | -26.73% | 2,584.59 | -12.51% |
| 39. | 2020/04/30 | $99.57 | 20.07% | 2,912.43 | 12.68% | |
| 40. | 2020/05/31 | $96.10 | -3.48% | 3,044.31 | 4.53% | |
| 41. | 2020/06/30 | $114.04 | $0.375 | 19.06% | 3,100.29 | 1.84% |
| 42. | 2020/07/31 | $117.53 | 3.06% | 3,271.12 | 5.51% | |
| 43. | 2020/08/31 | $125.76 | 7.00% | 3,500.31 | 7.01% | |
| 44. | 2020/09/30 | $124.81 | $0.375 | -0.46% | 3,363.00 | -3.92% |
| 45. | 2020/10/31 | $135.12 | 8.26% | 3,269.96 | -2.77% | |
| 46. | 2020/11/30 | $158.42 | 17.24% | 3,621.63 | 10.75% | |
| 47. | 2020/12/31 | $159.01 | $0.375 | 0.61% | 3,756.07 | 3.71% |
| 48. | 2021/01/31 | $160.47 | 0.92% | 3,714.24 | -1.11% | |
| 49. | 2021/02/28 | $182.55 | 13.76% | 3,811.15 | 2.61% | |
| 50. | 2021/03/31 | $201.34 | $0.5625 | 10.60% | 3,972.89 | 4.24% |
| 51. | 2021/04/30 | $192.51 | -4.39% | 4,181.17 | 5.24% | |
| 52. | 2021/05/31 | $211.42 | 9.82% | 4,204.11 | 0.55% | |
| 53. | 2021/06/30 | $205.72 | $0.5625 | -2.43% | 4,297.50 | 2.22% |
| 54. | 2021/07/31 | $206.39 | 0.33% | 4,395.26 | 2.27% | |
| 55. | 2021/08/31 | $215.13 | 4.23% | 4,522.68 | 2.90% | |
| 56. | 2021/09/30 | $195.87 | $0.5625 | -8.69% | 4,307.54 | -4.76% |
| 57. | 2021/10/31 | $200.86 | 2.55% | 4,605.38 | 6.91% | |
| 58. | 2021/11/30 | $223.36 | 11.20% | 4,567.00 | -0.83% | |
| 59. | 2021/12/31 | $227.78 | $0.5625 | 2.23% | 4,766.18 | 4.36% |
| 平均 (R): | 1.93% | 1.36% | ||||
| 標準偏差： | 9.12% | 4.48% | ||||
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NXPI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
NXP Semiconductors N.V.、分散の計算、および戻り値の共分散
| t | 日付 | RNXPI,t | RS&P 500,t | (RNXPI,t–RNXPI)2 | (RS&P 500,t–RS&P 500)2 | (RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017/02/28 | 5.07% | 3.72% | 9.86 | 5.58 | 7.41 |
| 2. | 2017/03/31 | 0.67% | -0.04% | 1.58 | 1.95 | 1.76 |
| 3. | 2017/04/30 | 2.17% | 0.91% | 0.06 | 0.20 | -0.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021/11/30 | 11.20% | -0.83% | 85.97 | 4.80 | -20.32 |
| 59. | 2021/12/31 | 2.23% | 4.36% | 0.09 | 9.02 | 0.90 |
| トータル (Σ): | 4,825.79 | 1,164.17 | 1,605.82 | |||
| t | 日付 | RNXPI,t | RS&P 500,t | (RNXPI,t–RNXPI)2 | (RS&P 500,t–RS&P 500)2 | (RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017/02/28 | 5.07% | 3.72% | 9.86 | 5.58 | 7.41 |
| 2. | 2017/03/31 | 0.67% | -0.04% | 1.58 | 1.95 | 1.76 |
| 3. | 2017/04/30 | 2.17% | 0.91% | 0.06 | 0.20 | -0.11 |
| 4. | 2017/05/31 | 3.92% | 1.16% | 3.98 | 0.04 | -0.40 |
| 5. | 2017/06/30 | -0.41% | 0.48% | 5.47 | 0.77 | 2.05 |
| 6. | 2017/07/31 | 0.80% | 1.93% | 1.27 | 0.33 | -0.65 |
| 7. | 2017/08/31 | 2.38% | 0.05% | 0.21 | 1.70 | -0.59 |
| 8. | 2017/09/30 | 0.12% | 1.93% | 3.29 | 0.33 | -1.04 |
| 9. | 2017/10/31 | 3.50% | 2.22% | 2.47 | 0.74 | 1.35 |
| 10. | 2017/11/30 | -3.13% | 2.81% | 25.57 | 2.10 | -7.33 |
| 11. | 2017/12/31 | 3.26% | 0.98% | 1.78 | 0.14 | -0.50 |
| 12. | 2018/01/31 | 2.76% | 5.62% | 0.69 | 18.15 | 3.53 |
| 13. | 2018/02/28 | 3.61% | -3.89% | 2.81 | 27.59 | -8.81 |
| 14. | 2018/03/31 | -6.14% | -2.69% | 65.20 | 16.37 | 32.67 |
| 15. | 2018/04/30 | -10.34% | 0.27% | 150.59 | 1.18 | 13.33 |
| 16. | 2018/05/31 | 8.67% | 2.16% | 45.50 | 0.64 | 5.42 |
| 17. | 2018/06/30 | -4.15% | 0.48% | 36.95 | 0.76 | 5.31 |
| 18. | 2018/07/31 | -12.75% | 3.60% | 215.44 | 5.04 | -32.94 |
| 19. | 2018/08/31 | -2.31% | 3.03% | 17.95 | 2.78 | -7.07 |
| 20. | 2018/09/30 | -7.93% | 0.43% | 97.30 | 0.86 | 9.16 |
| 21. | 2018/10/31 | -12.29% | -6.94% | 202.27 | 68.86 | 118.02 |
| 22. | 2018/11/30 | 11.17% | 1.79% | 85.47 | 0.18 | 3.96 |
| 23. | 2018/12/31 | -11.80% | -9.18% | 188.58 | 111.00 | 144.68 |
| 24. | 2019/01/31 | 18.76% | 7.87% | 283.38 | 42.39 | 109.60 |
| 25. | 2019/02/28 | 4.93% | 2.97% | 9.00 | 2.61 | 4.84 |
| 26. | 2019/03/31 | -2.93% | 1.79% | 23.66 | 0.19 | -2.11 |
| 27. | 2019/04/30 | 19.49% | 3.93% | 308.48 | 6.62 | 45.20 |
| 28. | 2019/05/31 | -16.53% | -6.58% | 340.80 | 62.97 | 146.50 |
| 29. | 2019/06/30 | 11.00% | 6.89% | 82.32 | 30.64 | 50.22 |
| 30. | 2019/07/31 | 5.92% | 1.31% | 15.93 | 0.00 | -0.18 |
| 31. | 2019/08/31 | -1.21% | -1.81% | 9.85 | 10.03 | 9.94 |
| 32. | 2019/09/30 | 7.20% | 1.72% | 27.79 | 0.13 | 1.90 |
| 33. | 2019/10/31 | 4.18% | 2.04% | 5.06 | 0.47 | 1.54 |
| 34. | 2019/11/30 | 1.67% | 3.40% | 0.07 | 4.19 | -0.53 |
| 35. | 2019/12/31 | 10.43% | 2.86% | 72.26 | 2.25 | 12.76 |
| 36. | 2020/01/31 | -0.31% | -0.16% | 5.04 | 2.31 | 3.41 |
| 37. | 2020/02/29 | -10.38% | -8.41% | 151.57 | 95.43 | 120.27 |
| 38. | 2020/03/31 | -26.73% | -12.51% | 821.16 | 192.37 | 397.45 |
| 39. | 2020/04/30 | 20.07% | 12.68% | 328.89 | 128.29 | 205.41 |
| 40. | 2020/05/31 | -3.48% | 4.53% | 29.32 | 10.05 | -17.17 |
| 41. | 2020/06/30 | 19.06% | 1.84% | 293.39 | 0.23 | 8.24 |
| 42. | 2020/07/31 | 3.06% | 5.51% | 1.28 | 17.24 | 4.69 |
| 43. | 2020/08/31 | 7.00% | 7.01% | 25.73 | 31.91 | 28.65 |
| 44. | 2020/09/30 | -0.46% | -3.92% | 5.70 | 27.89 | 12.60 |
| 45. | 2020/10/31 | 8.26% | -2.77% | 40.08 | 17.01 | -26.11 |
| 46. | 2020/11/30 | 17.24% | 10.75% | 234.53 | 88.30 | 143.90 |
| 47. | 2020/12/31 | 0.61% | 3.71% | 1.74 | 5.54 | -3.11 |
| 48. | 2021/01/31 | 0.92% | -1.11% | 1.02 | 6.11 | 2.50 |
| 49. | 2021/02/28 | 13.76% | 2.61% | 139.95 | 1.57 | 14.80 |
| 50. | 2021/03/31 | 10.60% | 4.24% | 75.20 | 8.33 | 25.03 |
| 51. | 2021/04/30 | -4.39% | 5.24% | 39.88 | 15.09 | -24.53 |
| 52. | 2021/05/31 | 9.82% | 0.55% | 62.30 | 0.65 | -6.39 |
| 53. | 2021/06/30 | -2.43% | 2.22% | 19.01 | 0.75 | -3.76 |
| 54. | 2021/07/31 | 0.33% | 2.27% | 2.57 | 0.84 | -1.47 |
| 55. | 2021/08/31 | 4.23% | 2.90% | 5.31 | 2.38 | 3.55 |
| 56. | 2021/09/30 | -8.69% | -4.76% | 112.80 | 37.39 | 64.95 |
| 57. | 2021/10/31 | 2.55% | 6.91% | 0.38 | 30.87 | 3.43 |
| 58. | 2021/11/30 | 11.20% | -0.83% | 85.97 | 4.80 | -20.32 |
| 59. | 2021/12/31 | 2.23% | 4.36% | 0.09 | 9.02 | 0.90 |
| トータル (Σ): | 4,825.79 | 1,164.17 | 1,605.82 | |||
すべて表示
分散NXPI = Σ(RNXPI,t–RNXPI)2 ÷ (59 – 1)
= 4,825.79 ÷ (59 – 1)
= 83.20
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
共 分散NXPI, S&P 500 = Σ(RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,605.82 ÷ (59 – 1)
= 27.69
システマティックなリスク推定 (β)
| 分散NXPI | 83.20 |
| 分散S&P 500 | 20.07 |
| 共 分散NXPI, S&P 500 | 27.69 |
| 相関係数NXPI, S&P 5001 | 0.68 |
| βNXPI2 | 1.38 |
| αNXPI3 | 0.06% |
計算
1 相関係数NXPI, S&P 500
= 共 分散NXPI, S&P 500 ÷ (標準偏差NXPI × 標準偏差S&P 500)
= 27.69 ÷ (9.12% × 4.48%)
= 0.68
2 βNXPI
= 共 分散NXPI, S&P 500 ÷ 分散S&P 500
= 27.69 ÷ 20.07
= 1.38
3 αNXPI
= 平均NXPI – βNXPI × 平均S&P 500
= 1.93% – 1.38 × 1.36%
= 0.06%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.94% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 14.84% |
| 普通株式のシステマティックリスクNXP | βNXPI | 1.38 |
| NXP普通株式の予想収益率3 | E(RNXPI) | 18.59% |
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(RNXPI) = RF + βNXPI [E(RM) – RF]
= 4.94% + 1.38 [14.84% – 4.94%]
= 18.59%