資本資産価格モデル (CAPM)
資本資産価格モデル(CAPM)は、 Merck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
Merck & Co. Inc.、月間収益率
| Merck & Co. Inc. (MRK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格MRK,t1 | 配当MRK,t1 | RMRK,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $74.43 | 2,704.10 | ||||
| 1. | 2019/02/28 | $81.29 | 9.22% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $83.17 | $0.55 | 2.99% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $78.71 | -5.36% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | $102.48 | -0.21% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $109.02 | $0.77 | 7.13% | 4,769.83 | 4.42% |
| 平均 (R): | 1.15% | 1.11% | ||||
| 標準偏差： | 6.07% | 5.31% | ||||
| Merck & Co. Inc. (MRK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格MRK,t1 | 配当MRK,t1 | RMRK,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $74.43 | 2,704.10 | ||||
| 1. | 2019/02/28 | $81.29 | 9.22% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $83.17 | $0.55 | 2.99% | 2,834.40 | 1.79% |
| 3. | 2019/04/30 | $78.71 | -5.36% | 2,945.83 | 3.93% | |
| 4. | 2019/05/31 | $79.21 | 0.64% | 2,752.06 | -6.58% | |
| 5. | 2019/06/30 | $83.85 | $0.55 | 6.55% | 2,941.76 | 6.89% |
| 6. | 2019/07/31 | $82.99 | -1.03% | 2,980.38 | 1.31% | |
| 7. | 2019/08/31 | $86.47 | 4.19% | 2,926.46 | -1.81% | |
| 8. | 2019/09/30 | $84.18 | $0.55 | -2.01% | 2,976.74 | 1.72% |
| 9. | 2019/10/31 | $86.66 | 2.95% | 3,037.56 | 2.04% | |
| 10. | 2019/11/30 | $87.18 | 0.60% | 3,140.98 | 3.40% | |
| 11. | 2019/12/31 | $90.95 | $0.61 | 5.02% | 3,230.78 | 2.86% |
| 12. | 2020/01/31 | $85.44 | -6.06% | 3,225.52 | -0.16% | |
| 13. | 2020/02/29 | $76.56 | -10.39% | 2,954.22 | -8.41% | |
| 14. | 2020/03/31 | $76.94 | $0.61 | 1.29% | 2,584.59 | -12.51% |
| 15. | 2020/04/30 | $79.34 | 3.12% | 2,912.43 | 12.68% | |
| 16. | 2020/05/31 | $80.72 | 1.74% | 3,044.31 | 4.53% | |
| 17. | 2020/06/30 | $77.33 | $0.61 | -3.44% | 3,100.29 | 1.84% |
| 18. | 2020/07/31 | $80.24 | 3.76% | 3,271.12 | 5.51% | |
| 19. | 2020/08/31 | $85.27 | 6.27% | 3,500.31 | 7.01% | |
| 20. | 2020/09/30 | $82.95 | $0.61 | -2.01% | 3,363.00 | -3.92% |
| 21. | 2020/10/31 | $75.21 | -9.33% | 3,269.96 | -2.77% | |
| 22. | 2020/11/30 | $80.39 | 6.89% | 3,621.63 | 10.75% | |
| 23. | 2020/12/31 | $81.80 | $0.65 | 2.56% | 3,756.07 | 3.71% |
| 24. | 2021/01/31 | $77.07 | -5.78% | 3,714.24 | -1.11% | |
| 25. | 2021/02/28 | $72.62 | -5.77% | 3,811.15 | 2.61% | |
| 26. | 2021/03/31 | $77.09 | $0.65 | 7.05% | 3,972.89 | 4.24% |
| 27. | 2021/04/30 | $74.50 | -3.36% | 4,181.17 | 5.24% | |
| 28. | 2021/05/31 | $75.89 | 1.87% | 4,204.11 | 0.55% | |
| 29. | 2021/06/30 | $77.77 | $3.75 | 7.42% | 4,297.50 | 2.22% |
| 30. | 2021/07/31 | $76.87 | -1.16% | 4,395.26 | 2.27% | |
| 31. | 2021/08/31 | $76.29 | -0.75% | 4,522.68 | 2.90% | |
| 32. | 2021/09/30 | $75.11 | $0.65 | -0.69% | 4,307.54 | -4.76% |
| 33. | 2021/10/31 | $88.05 | 17.23% | 4,605.38 | 6.91% | |
| 34. | 2021/11/30 | $74.91 | -14.92% | 4,567.00 | -0.83% | |
| 35. | 2021/12/31 | $76.64 | $0.69 | 3.23% | 4,766.18 | 4.36% |
| 36. | 2022/01/31 | $81.48 | 6.32% | 4,515.55 | -5.26% | |
| 37. | 2022/02/28 | $76.58 | -6.01% | 4,373.94 | -3.14% | |
| 38. | 2022/03/31 | $82.05 | $0.69 | 8.04% | 4,530.41 | 3.58% |
| 39. | 2022/04/30 | $88.69 | 8.09% | 4,131.93 | -8.80% | |
| 40. | 2022/05/31 | $92.03 | 3.77% | 4,132.15 | 0.01% | |
| 41. | 2022/06/30 | $91.17 | $0.69 | -0.18% | 3,785.38 | -8.39% |
| 42. | 2022/07/31 | $89.34 | -2.01% | 4,130.29 | 9.11% | |
| 43. | 2022/08/31 | $85.36 | -4.45% | 3,955.00 | -4.24% | |
| 44. | 2022/09/30 | $86.12 | $0.69 | 1.70% | 3,585.62 | -9.34% |
| 45. | 2022/10/31 | $101.20 | 17.51% | 3,871.98 | 7.99% | |
| 46. | 2022/11/30 | $110.12 | 8.81% | 4,080.11 | 5.38% | |
| 47. | 2022/12/31 | $110.95 | $0.73 | 1.42% | 3,839.50 | -5.90% |
| 48. | 2023/01/31 | $107.41 | -3.19% | 4,076.60 | 6.18% | |
| 49. | 2023/02/28 | $106.24 | -1.09% | 3,970.15 | -2.61% | |
| 50. | 2023/03/31 | $106.39 | $0.73 | 0.83% | 4,109.31 | 3.51% |
| 51. | 2023/04/30 | $115.47 | 8.53% | 4,169.48 | 1.46% | |
| 52. | 2023/05/31 | $110.41 | -4.38% | 4,179.83 | 0.25% | |
| 53. | 2023/06/30 | $115.39 | $0.73 | 5.17% | 4,376.86 | 4.71% |
| 54. | 2023/07/31 | $106.65 | -7.57% | 4,588.96 | 4.85% | |
| 55. | 2023/08/31 | $108.98 | 2.18% | 4,507.66 | -1.77% | |
| 56. | 2023/09/30 | $102.95 | $0.73 | -4.86% | 4,288.05 | -4.87% |
| 57. | 2023/10/31 | $102.70 | -0.24% | 4,193.80 | -2.20% | |
| 58. | 2023/11/30 | $102.48 | -0.21% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $109.02 | $0.77 | 7.13% | 4,769.83 | 4.42% |
| 平均 (R): | 1.15% | 1.11% | ||||
| 標準偏差： | 6.07% | 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MRK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
Merck & Co. Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RMRK,t | RS&P 500,t | (RMRK,t–RMRK)2 | (RS&P 500,t–RS&P 500)2 | (RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 9.22% | 2.97% | 65.09 | 3.49 | 15.06 |
| 2. | 2019/03/31 | 2.99% | 1.79% | 3.39 | 0.47 | 1.26 |
| 3. | 2019/04/30 | -5.36% | 3.93% | 42.40 | 7.98 | -18.40 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | -0.21% | 8.92% | 1.86 | 61.03 | -10.65 |
| 59. | 2023/12/31 | 7.13% | 4.42% | 35.81 | 11.00 | 19.85 |
| トータル (Σ): | 2,134.37 | 1,634.30 | 591.86 | |||
| t | 日付 | RMRK,t | RS&P 500,t | (RMRK,t–RMRK)2 | (RS&P 500,t–RS&P 500)2 | (RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 9.22% | 2.97% | 65.09 | 3.49 | 15.06 |
| 2. | 2019/03/31 | 2.99% | 1.79% | 3.39 | 0.47 | 1.26 |
| 3. | 2019/04/30 | -5.36% | 3.93% | 42.40 | 7.98 | -18.40 |
| 4. | 2019/05/31 | 0.64% | -6.58% | 0.26 | 59.04 | 3.95 |
| 5. | 2019/06/30 | 6.55% | 6.89% | 29.19 | 33.49 | 31.27 |
| 6. | 2019/07/31 | -1.03% | 1.31% | 4.73 | 0.04 | -0.45 |
| 7. | 2019/08/31 | 4.19% | -1.81% | 9.27 | 8.50 | -8.87 |
| 8. | 2019/09/30 | -2.01% | 1.72% | 9.99 | 0.37 | -1.94 |
| 9. | 2019/10/31 | 2.95% | 2.04% | 3.23 | 0.88 | 1.68 |
| 10. | 2019/11/30 | 0.60% | 3.40% | 0.30 | 5.28 | -1.26 |
| 11. | 2019/12/31 | 5.02% | 2.86% | 15.02 | 3.07 | 6.79 |
| 12. | 2020/01/31 | -6.06% | -0.16% | 51.95 | 1.61 | 9.14 |
| 13. | 2020/02/29 | -10.39% | -8.41% | 133.23 | 90.57 | 109.85 |
| 14. | 2020/03/31 | 1.29% | -12.51% | 0.02 | 185.44 | -1.96 |
| 15. | 2020/04/30 | 3.12% | 12.68% | 3.88 | 134.06 | 22.81 |
| 16. | 2020/05/31 | 1.74% | 4.53% | 0.35 | 11.71 | 2.02 |
| 17. | 2020/06/30 | -3.44% | 1.84% | 21.10 | 0.54 | -3.37 |
| 18. | 2020/07/31 | 3.76% | 5.51% | 6.83 | 19.40 | 11.51 |
| 19. | 2020/08/31 | 6.27% | 7.01% | 26.21 | 34.82 | 30.21 |
| 20. | 2020/09/30 | -2.01% | -3.92% | 9.95 | 25.29 | 15.86 |
| 21. | 2020/10/31 | -9.33% | -2.77% | 109.83 | 15.00 | 40.58 |
| 22. | 2020/11/30 | 6.89% | 10.75% | 32.93 | 93.10 | 55.37 |
| 23. | 2020/12/31 | 2.56% | 3.71% | 2.00 | 6.79 | 3.68 |
| 24. | 2021/01/31 | -5.78% | -1.11% | 48.05 | 4.93 | 15.38 |
| 25. | 2021/02/28 | -5.77% | 2.61% | 47.93 | 2.26 | -10.41 |
| 26. | 2021/03/31 | 7.05% | 4.24% | 34.83 | 9.85 | 18.52 |
| 27. | 2021/04/30 | -3.36% | 5.24% | 20.33 | 17.11 | -18.65 |
| 28. | 2021/05/31 | 1.87% | 0.55% | 0.51 | 0.31 | -0.40 |
| 29. | 2021/06/30 | 7.42% | 2.22% | 39.31 | 1.24 | 6.99 |
| 30. | 2021/07/31 | -1.16% | 2.27% | 5.32 | 1.37 | -2.70 |
| 31. | 2021/08/31 | -0.75% | 2.90% | 3.62 | 3.22 | -3.41 |
| 32. | 2021/09/30 | -0.69% | -4.76% | 3.40 | 34.37 | 10.81 |
| 33. | 2021/10/31 | 17.23% | 6.91% | 258.53 | 33.74 | 93.40 |
| 34. | 2021/11/30 | -14.92% | -0.83% | 258.32 | 3.76 | 31.17 |
| 35. | 2021/12/31 | 3.23% | 4.36% | 4.33 | 10.60 | 6.78 |
| 36. | 2022/01/31 | 6.32% | -5.26% | 26.69 | 40.51 | -32.88 |
| 37. | 2022/02/28 | -6.01% | -3.14% | 51.31 | 17.99 | 30.38 |
| 38. | 2022/03/31 | 8.04% | 3.58% | 47.54 | 6.11 | 17.04 |
| 39. | 2022/04/30 | 8.09% | -8.80% | 48.21 | 98.04 | -68.75 |
| 40. | 2022/05/31 | 3.77% | 0.01% | 6.85 | 1.21 | -2.88 |
| 41. | 2022/06/30 | -0.18% | -8.39% | 1.78 | 90.21 | 12.67 |
| 42. | 2022/07/31 | -2.01% | 9.11% | 9.96 | 64.09 | -25.27 |
| 43. | 2022/08/31 | -4.45% | -4.24% | 31.41 | 28.62 | 29.98 |
| 44. | 2022/09/30 | 1.70% | -9.34% | 0.30 | 109.11 | -5.74 |
| 45. | 2022/10/31 | 17.51% | 7.99% | 267.69 | 47.34 | 112.57 |
| 46. | 2022/11/30 | 8.81% | 5.38% | 58.75 | 18.23 | 32.73 |
| 47. | 2022/12/31 | 1.42% | -5.90% | 0.07 | 49.04 | -1.87 |
| 48. | 2023/01/31 | -3.19% | 6.18% | 18.83 | 25.70 | -22.00 |
| 49. | 2023/02/28 | -1.09% | -2.61% | 5.01 | 13.82 | 8.32 |
| 50. | 2023/03/31 | 0.83% | 3.51% | 0.10 | 5.76 | -0.77 |
| 51. | 2023/04/30 | 8.53% | 1.46% | 54.55 | 0.13 | 2.65 |
| 52. | 2023/05/31 | -4.38% | 0.25% | 30.59 | 0.74 | 4.74 |
| 53. | 2023/06/30 | 5.17% | 4.71% | 16.18 | 13.02 | 14.51 |
| 54. | 2023/07/31 | -7.57% | 4.85% | 76.10 | 13.99 | -32.63 |
| 55. | 2023/08/31 | 2.18% | -1.77% | 1.07 | 8.28 | -2.98 |
| 56. | 2023/09/30 | -4.86% | -4.87% | 36.15 | 35.73 | 35.94 |
| 57. | 2023/10/31 | -0.24% | -2.20% | 1.94 | 10.92 | 4.60 |
| 58. | 2023/11/30 | -0.21% | 8.92% | 1.86 | 61.03 | -10.65 |
| 59. | 2023/12/31 | 7.13% | 4.42% | 35.81 | 11.00 | 19.85 |
| トータル (Σ): | 2,134.37 | 1,634.30 | 591.86 | |||
すべて表示
分散MRK = Σ(RMRK,t–RMRK)2 ÷ (59 – 1)
= 2,134.37 ÷ (59 – 1)
= 36.80
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MRK, S&P 500 = Σ(RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 591.86 ÷ (59 – 1)
= 10.20
システマティックリスク推定 (β)
| 分散MRK | 36.80 |
| 分散S&P 500 | 28.18 |
| 共 分散MRK, S&P 500 | 10.20 |
| 相関係数MRK, S&P 5001 | 0.32 |
| βMRK2 | 0.36 |
| αMRK3 | 0.75% |
計算
1 相関係数MRK, S&P 500
= 共 分散MRK, S&P 500 ÷ (標準偏差MRK × 標準偏差S&P 500)
= 10.20 ÷ (6.07% × 5.31%)
= 0.32
2 βMRK
= 共 分散MRK, S&P 500 ÷ 分散S&P 500
= 10.20 ÷ 28.18
= 0.36
3 αMRK
= 平均MRK – βMRK × 平均S&P 500
= 1.15% – 0.36 × 1.11%
= 0.75%
期待収益率
| 仮定 | ||
| LT財務省総合の収益率1 | RF | 4.86% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.54% |
| 普通株式 Merck システマティックリスク | βMRK | 0.36 |
| メルク普通株式の期待収益率3 | E(RMRK) | 8.00% |
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(RMRK) = RF + βMRK [E(RM) – RF]
= 4.86% + 0.36 [13.54% – 4.86%]
= 8.00%