資本資産価格設定モデル (CAPM)
資本資産価格モデル(CAPM)は、 Zoetis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
Zoetis Inc.、月間収益率
| Zoetis Inc. (ZTS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格ZTS,t1 | 配当ZTS,t1 | RZTS,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $86.16 | 2,704.10 | ||||
| 1. | 2019/02/28 | $94.23 | 9.37% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $100.67 | 6.83% | 2,834.40 | 1.79% | |
| 3. | 2019/04/30 | $101.84 | $0.164 | 1.33% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | $176.67 | 12.53% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $197.37 | 11.72% | 4,769.83 | 4.42% | |
| 平均 (R): | 1.72% | 1.11% | ||||
| 標準偏差： | 7.08% | 5.31% | ||||
| Zoetis Inc. (ZTS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格ZTS,t1 | 配当ZTS,t1 | RZTS,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2019/01/31 | $86.16 | 2,704.10 | ||||
| 1. | 2019/02/28 | $94.23 | 9.37% | 2,784.49 | 2.97% | |
| 2. | 2019/03/31 | $100.67 | 6.83% | 2,834.40 | 1.79% | |
| 3. | 2019/04/30 | $101.84 | $0.164 | 1.33% | 2,945.83 | 3.93% |
| 4. | 2019/05/31 | $101.05 | -0.78% | 2,752.06 | -6.58% | |
| 5. | 2019/06/30 | $113.49 | 12.31% | 2,941.76 | 6.89% | |
| 6. | 2019/07/31 | $114.89 | $0.164 | 1.38% | 2,980.38 | 1.31% |
| 7. | 2019/08/31 | $126.42 | 10.04% | 2,926.46 | -1.81% | |
| 8. | 2019/09/30 | $124.59 | -1.45% | 2,976.74 | 1.72% | |
| 9. | 2019/10/31 | $127.92 | $0.164 | 2.80% | 3,037.56 | 2.04% |
| 10. | 2019/11/30 | $120.52 | -5.78% | 3,140.98 | 3.40% | |
| 11. | 2019/12/31 | $132.35 | 9.82% | 3,230.78 | 2.86% | |
| 12. | 2020/01/31 | $134.21 | $0.20 | 1.56% | 3,225.52 | -0.16% |
| 13. | 2020/02/29 | $133.23 | -0.73% | 2,954.22 | -8.41% | |
| 14. | 2020/03/31 | $117.69 | -11.66% | 2,584.59 | -12.51% | |
| 15. | 2020/04/30 | $129.31 | $0.20 | 10.04% | 2,912.43 | 12.68% |
| 16. | 2020/05/31 | $139.39 | 7.80% | 3,044.31 | 4.53% | |
| 17. | 2020/06/30 | $137.04 | -1.69% | 3,100.29 | 1.84% | |
| 18. | 2020/07/31 | $151.68 | $0.20 | 10.83% | 3,271.12 | 5.51% |
| 19. | 2020/08/31 | $160.10 | 5.55% | 3,500.31 | 7.01% | |
| 20. | 2020/09/30 | $165.37 | 3.29% | 3,363.00 | -3.92% | |
| 21. | 2020/10/31 | $158.55 | $0.20 | -4.00% | 3,269.96 | -2.77% |
| 22. | 2020/11/30 | $160.38 | 1.15% | 3,621.63 | 10.75% | |
| 23. | 2020/12/31 | $165.50 | 3.19% | 3,756.07 | 3.71% | |
| 24. | 2021/01/31 | $154.25 | $0.25 | -6.65% | 3,714.24 | -1.11% |
| 25. | 2021/02/28 | $155.24 | 0.64% | 3,811.15 | 2.61% | |
| 26. | 2021/03/31 | $157.48 | 1.44% | 3,972.89 | 4.24% | |
| 27. | 2021/04/30 | $173.03 | $0.25 | 10.03% | 4,181.17 | 5.24% |
| 28. | 2021/05/31 | $176.68 | 2.11% | 4,204.11 | 0.55% | |
| 29. | 2021/06/30 | $186.36 | 5.48% | 4,297.50 | 2.22% | |
| 30. | 2021/07/31 | $202.70 | $0.25 | 8.90% | 4,395.26 | 2.27% |
| 31. | 2021/08/31 | $204.56 | 0.92% | 4,522.68 | 2.90% | |
| 32. | 2021/09/30 | $194.14 | -5.09% | 4,307.54 | -4.76% | |
| 33. | 2021/10/31 | $216.20 | $0.25 | 11.49% | 4,605.38 | 6.91% |
| 34. | 2021/11/30 | $222.04 | 2.70% | 4,567.00 | -0.83% | |
| 35. | 2021/12/31 | $244.03 | 9.90% | 4,766.18 | 4.36% | |
| 36. | 2022/01/31 | $199.79 | $0.33 | -17.99% | 4,515.55 | -5.26% |
| 37. | 2022/02/28 | $193.65 | -3.07% | 4,373.94 | -3.14% | |
| 38. | 2022/03/31 | $188.59 | -2.61% | 4,530.41 | 3.58% | |
| 39. | 2022/04/30 | $177.25 | $0.33 | -5.84% | 4,131.93 | -8.80% |
| 40. | 2022/05/31 | $170.93 | -3.57% | 4,132.15 | 0.01% | |
| 41. | 2022/06/30 | $171.89 | 0.56% | 3,785.38 | -8.39% | |
| 42. | 2022/07/31 | $182.55 | $0.33 | 6.39% | 4,130.29 | 9.11% |
| 43. | 2022/08/31 | $156.53 | -14.25% | 3,955.00 | -4.24% | |
| 44. | 2022/09/30 | $148.29 | -5.26% | 3,585.62 | -9.34% | |
| 45. | 2022/10/31 | $150.78 | $0.33 | 1.90% | 3,871.98 | 7.99% |
| 46. | 2022/11/30 | $154.14 | 2.23% | 4,080.11 | 5.38% | |
| 47. | 2022/12/31 | $146.55 | -4.92% | 3,839.50 | -5.90% | |
| 48. | 2023/01/31 | $165.49 | $0.38 | 13.18% | 4,076.60 | 6.18% |
| 49. | 2023/02/28 | $167.00 | 0.91% | 3,970.15 | -2.61% | |
| 50. | 2023/03/31 | $166.44 | -0.34% | 4,109.31 | 3.51% | |
| 51. | 2023/04/30 | $175.78 | $0.38 | 5.84% | 4,169.48 | 1.46% |
| 52. | 2023/05/31 | $163.01 | -7.26% | 4,179.83 | 0.25% | |
| 53. | 2023/06/30 | $172.21 | 5.64% | 4,376.86 | 4.71% | |
| 54. | 2023/07/31 | $188.09 | $0.38 | 9.44% | 4,588.96 | 4.85% |
| 55. | 2023/08/31 | $190.51 | 1.29% | 4,507.66 | -1.77% | |
| 56. | 2023/09/30 | $173.98 | -8.68% | 4,288.05 | -4.87% | |
| 57. | 2023/10/31 | $157.00 | $0.38 | -9.54% | 4,193.80 | -2.20% |
| 58. | 2023/11/30 | $176.67 | 12.53% | 4,567.80 | 8.92% | |
| 59. | 2023/12/31 | $197.37 | 11.72% | 4,769.83 | 4.42% | |
| 平均 (R): | 1.72% | 1.11% | ||||
| 標準偏差： | 7.08% | 5.31% | ||||
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ZTS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
Zoetis Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RZTS,t | RS&P 500,t | (RZTS,t–RZTS)2 | (RS&P 500,t–RS&P 500)2 | (RZTS,t–RZTS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 9.37% | 2.97% | 58.49 | 3.49 | 14.28 |
| 2. | 2019/03/31 | 6.83% | 1.79% | 26.18 | 0.47 | 3.51 |
| 3. | 2019/04/30 | 1.33% | 3.93% | 0.15 | 7.98 | -1.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023/11/30 | 12.53% | 8.92% | 116.87 | 61.03 | 84.45 |
| 59. | 2023/12/31 | 11.72% | 4.42% | 99.97 | 11.00 | 33.17 |
| トータル (Σ): | 2,908.39 | 1,634.30 | 1,446.63 | |||
| t | 日付 | RZTS,t | RS&P 500,t | (RZTS,t–RZTS)2 | (RS&P 500,t–RS&P 500)2 | (RZTS,t–RZTS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019/02/28 | 9.37% | 2.97% | 58.49 | 3.49 | 14.28 |
| 2. | 2019/03/31 | 6.83% | 1.79% | 26.18 | 0.47 | 3.51 |
| 3. | 2019/04/30 | 1.33% | 3.93% | 0.15 | 7.98 | -1.11 |
| 4. | 2019/05/31 | -0.78% | -6.58% | 6.22 | 59.04 | 19.16 |
| 5. | 2019/06/30 | 12.31% | 6.89% | 112.20 | 33.49 | 61.30 |
| 6. | 2019/07/31 | 1.38% | 1.31% | 0.12 | 0.04 | -0.07 |
| 7. | 2019/08/31 | 10.04% | -1.81% | 69.18 | 8.50 | -24.25 |
| 8. | 2019/09/30 | -1.45% | 1.72% | 10.02 | 0.37 | -1.94 |
| 9. | 2019/10/31 | 2.80% | 2.04% | 1.18 | 0.88 | 1.02 |
| 10. | 2019/11/30 | -5.78% | 3.40% | 56.29 | 5.28 | -17.25 |
| 11. | 2019/12/31 | 9.82% | 2.86% | 65.57 | 3.07 | 14.20 |
| 12. | 2020/01/31 | 1.56% | -0.16% | 0.03 | 1.61 | 0.21 |
| 13. | 2020/02/29 | -0.73% | -8.41% | 5.99 | 90.57 | 23.30 |
| 14. | 2020/03/31 | -11.66% | -12.51% | 179.08 | 185.44 | 182.24 |
| 15. | 2020/04/30 | 10.04% | 12.68% | 69.31 | 134.06 | 96.39 |
| 16. | 2020/05/31 | 7.80% | 4.53% | 36.93 | 11.71 | 20.80 |
| 17. | 2020/06/30 | -1.69% | 1.84% | 11.59 | 0.54 | -2.50 |
| 18. | 2020/07/31 | 10.83% | 5.51% | 83.01 | 19.40 | 40.13 |
| 19. | 2020/08/31 | 5.55% | 7.01% | 14.69 | 34.82 | 22.62 |
| 20. | 2020/09/30 | 3.29% | -3.92% | 2.48 | 25.29 | -7.91 |
| 21. | 2020/10/31 | -4.00% | -2.77% | 32.73 | 15.00 | 22.16 |
| 22. | 2020/11/30 | 1.15% | 10.75% | 0.32 | 93.10 | -5.44 |
| 23. | 2020/12/31 | 3.19% | 3.71% | 2.17 | 6.79 | 3.84 |
| 24. | 2021/01/31 | -6.65% | -1.11% | 69.97 | 4.93 | 18.57 |
| 25. | 2021/02/28 | 0.64% | 2.61% | 1.16 | 2.26 | -1.62 |
| 26. | 2021/03/31 | 1.44% | 4.24% | 0.08 | 9.85 | -0.86 |
| 27. | 2021/04/30 | 10.03% | 5.24% | 69.14 | 17.11 | 34.40 |
| 28. | 2021/05/31 | 2.11% | 0.55% | 0.15 | 0.31 | -0.22 |
| 29. | 2021/06/30 | 5.48% | 2.22% | 14.14 | 1.24 | 4.20 |
| 30. | 2021/07/31 | 8.90% | 2.27% | 51.61 | 1.37 | 8.40 |
| 31. | 2021/08/31 | 0.92% | 2.90% | 0.64 | 3.22 | -1.44 |
| 32. | 2021/09/30 | -5.09% | -4.76% | 46.40 | 34.37 | 39.94 |
| 33. | 2021/10/31 | 11.49% | 6.91% | 95.52 | 33.74 | 56.77 |
| 34. | 2021/11/30 | 2.70% | -0.83% | 0.97 | 3.76 | -1.91 |
| 35. | 2021/12/31 | 9.90% | 4.36% | 67.00 | 10.60 | 26.65 |
| 36. | 2022/01/31 | -17.99% | -5.26% | 388.56 | 40.51 | 125.45 |
| 37. | 2022/02/28 | -3.07% | -3.14% | 22.96 | 17.99 | 20.32 |
| 38. | 2022/03/31 | -2.61% | 3.58% | 18.76 | 6.11 | -10.70 |
| 39. | 2022/04/30 | -5.84% | -8.80% | 57.10 | 98.04 | 74.82 |
| 40. | 2022/05/31 | -3.57% | 0.01% | 27.92 | 1.21 | 5.81 |
| 41. | 2022/06/30 | 0.56% | -8.39% | 1.34 | 90.21 | 10.98 |
| 42. | 2022/07/31 | 6.39% | 9.11% | 21.86 | 64.09 | 37.43 |
| 43. | 2022/08/31 | -14.25% | -4.24% | 255.10 | 28.62 | 85.45 |
| 44. | 2022/09/30 | -5.26% | -9.34% | 48.75 | 109.11 | 72.93 |
| 45. | 2022/10/31 | 1.90% | 7.99% | 0.03 | 47.34 | 1.26 |
| 46. | 2022/11/30 | 2.23% | 5.38% | 0.26 | 18.23 | 2.18 |
| 47. | 2022/12/31 | -4.92% | -5.90% | 44.12 | 49.04 | 46.52 |
| 48. | 2023/01/31 | 13.18% | 6.18% | 131.45 | 25.70 | 58.12 |
| 49. | 2023/02/28 | 0.91% | -2.61% | 0.65 | 13.82 | 2.99 |
| 50. | 2023/03/31 | -0.34% | 3.51% | 4.22 | 5.76 | -4.93 |
| 51. | 2023/04/30 | 5.84% | 1.46% | 16.99 | 0.13 | 1.48 |
| 52. | 2023/05/31 | -7.26% | 0.25% | 80.69 | 0.74 | 7.70 |
| 53. | 2023/06/30 | 5.64% | 4.71% | 15.41 | 13.02 | 14.16 |
| 54. | 2023/07/31 | 9.44% | 4.85% | 59.66 | 13.99 | 28.89 |
| 55. | 2023/08/31 | 1.29% | -1.77% | 0.19 | 8.28 | 1.24 |
| 56. | 2023/09/30 | -8.68% | -4.87% | 108.05 | 35.73 | 62.14 |
| 57. | 2023/10/31 | -9.54% | -2.20% | 126.78 | 10.92 | 37.20 |
| 58. | 2023/11/30 | 12.53% | 8.92% | 116.87 | 61.03 | 84.45 |
| 59. | 2023/12/31 | 11.72% | 4.42% | 99.97 | 11.00 | 33.17 |
| トータル (Σ): | 2,908.39 | 1,634.30 | 1,446.63 | |||
すべて表示
分散ZTS = Σ(RZTS,t–RZTS)2 ÷ (59 – 1)
= 2,908.39 ÷ (59 – 1)
= 50.14
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ZTS, S&P 500 = Σ(RZTS,t–RZTS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,446.63 ÷ (59 – 1)
= 24.94
システマティックなリスク推定 (β)
| 分散ZTS | 50.14 |
| 分散S&P 500 | 28.18 |
| 共 分散ZTS, S&P 500 | 24.94 |
| 相関係数ZTS, S&P 5001 | 0.66 |
| βZTS2 | 0.89 |
| αZTS3 | 0.74% |
計算
1 相関係数ZTS, S&P 500
= 共 分散ZTS, S&P 500 ÷ (標準偏差ZTS × 標準偏差S&P 500)
= 24.94 ÷ (7.08% × 5.31%)
= 0.66
2 βZTS
= 共 分散ZTS, S&P 500 ÷ 分散S&P 500
= 24.94 ÷ 28.18
= 0.89
3 αZTS
= 平均ZTS – βZTS × 平均S&P 500
= 1.72% – 0.89 × 1.11%
= 0.74%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.67% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 13.79% |
| 普通株式 Zoetis システマティックリスク | βZTS | 0.89 |
| ゾエティス普通株式の期待収益率3 | E(RZTS) | 12.74% |
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(RZTS) = RF + βZTS [E(RM) – RF]
= 4.67% + 0.89 [13.79% – 4.67%]
= 12.74%