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 AutoZone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
AutoZone Inc.、月間収益率
| AutoZone Inc. (AZO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格AZO,t1 | 配当AZO,t1 | RAZO,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2017/09/30 | $595.11 | 2,519.36 | ||||
| 1. | 2017/10/31 | $589.50 | -0.94% | 2,575.26 | 2.22% | |
| 2. | 2017/11/30 | $686.76 | 16.50% | 2,647.58 | 2.81% | |
| 3. | 2017/12/31 | $711.37 | 3.58% | 2,673.61 | 0.98% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023/07/31 | $2,481.72 | -0.47% | 4,588.96 | 4.85% | |
| 71. | 2023/08/31 | $2,531.33 | 2.00% | 4,507.66 | -1.77% | |
| 平均 (R): | 2.31% | 0.95% | ||||
| 標準偏差： | 7.25% | 5.08% | ||||
| AutoZone Inc. (AZO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 日付 | 価格AZO,t1 | 配当AZO,t1 | RAZO,t2 | 価格S&P 500,t | RS&P 500,t3 |
| 2017/09/30 | $595.11 | 2,519.36 | ||||
| 1. | 2017/10/31 | $589.50 | -0.94% | 2,575.26 | 2.22% | |
| 2. | 2017/11/30 | $686.76 | 16.50% | 2,647.58 | 2.81% | |
| 3. | 2017/12/31 | $711.37 | 3.58% | 2,673.61 | 0.98% | |
| 4. | 2018/01/31 | $765.44 | 7.60% | 2,823.81 | 5.62% | |
| 5. | 2018/02/28 | $664.72 | -13.16% | 2,713.83 | -3.89% | |
| 6. | 2018/03/31 | $648.69 | -2.41% | 2,640.87 | -2.69% | |
| 7. | 2018/04/30 | $624.52 | -3.73% | 2,648.05 | 0.27% | |
| 8. | 2018/05/31 | $649.32 | 3.97% | 2,705.27 | 2.16% | |
| 9. | 2018/06/30 | $670.93 | 3.33% | 2,718.37 | 0.48% | |
| 10. | 2018/07/31 | $705.53 | 5.16% | 2,816.29 | 3.60% | |
| 11. | 2018/08/31 | $766.88 | 8.70% | 2,901.52 | 3.03% | |
| 12. | 2018/09/30 | $775.70 | 1.15% | 2,913.98 | 0.43% | |
| 13. | 2018/10/31 | $733.47 | -5.44% | 2,711.74 | -6.94% | |
| 14. | 2018/11/30 | $809.07 | 10.31% | 2,760.17 | 1.79% | |
| 15. | 2018/12/31 | $838.34 | 3.62% | 2,506.85 | -9.18% | |
| 16. | 2019/01/31 | $847.34 | 1.07% | 2,704.10 | 7.87% | |
| 17. | 2019/02/28 | $938.97 | 10.81% | 2,784.49 | 2.97% | |
| 18. | 2019/03/31 | $1,024.12 | 9.07% | 2,834.40 | 1.79% | |
| 19. | 2019/04/30 | $1,028.31 | 0.41% | 2,945.83 | 3.93% | |
| 20. | 2019/05/31 | $1,027.11 | -0.12% | 2,752.06 | -6.58% | |
| 21. | 2019/06/30 | $1,099.47 | 7.05% | 2,941.76 | 6.89% | |
| 22. | 2019/07/31 | $1,123.04 | 2.14% | 2,980.38 | 1.31% | |
| 23. | 2019/08/31 | $1,101.69 | -1.90% | 2,926.46 | -1.81% | |
| 24. | 2019/09/30 | $1,084.62 | -1.55% | 2,976.74 | 1.72% | |
| 25. | 2019/10/31 | $1,144.38 | 5.51% | 3,037.56 | 2.04% | |
| 26. | 2019/11/30 | $1,177.92 | 2.93% | 3,140.98 | 3.40% | |
| 27. | 2019/12/31 | $1,191.31 | 1.14% | 3,230.78 | 2.86% | |
| 28. | 2020/01/31 | $1,057.96 | -11.19% | 3,225.52 | -0.16% | |
| 29. | 2020/02/29 | $1,032.51 | -2.41% | 2,954.22 | -8.41% | |
| 30. | 2020/03/31 | $846.00 | -18.06% | 2,584.59 | -12.51% | |
| 31. | 2020/04/30 | $1,020.32 | 20.61% | 2,912.43 | 12.68% | |
| 32. | 2020/05/31 | $1,147.86 | 12.50% | 3,044.31 | 4.53% | |
| 33. | 2020/06/30 | $1,128.12 | -1.72% | 3,100.29 | 1.84% | |
| 34. | 2020/07/31 | $1,207.42 | 7.03% | 3,271.12 | 5.51% | |
| 35. | 2020/08/31 | $1,196.31 | -0.92% | 3,500.31 | 7.01% | |
| 36. | 2020/09/30 | $1,177.64 | -1.56% | 3,363.00 | -3.92% | |
| 37. | 2020/10/31 | $1,128.98 | -4.13% | 3,269.96 | -2.77% | |
| 38. | 2020/11/30 | $1,137.65 | 0.77% | 3,621.63 | 10.75% | |
| 39. | 2020/12/31 | $1,185.44 | 4.20% | 3,756.07 | 3.71% | |
| 40. | 2021/01/31 | $1,118.37 | -5.66% | 3,714.24 | -1.11% | |
| 41. | 2021/02/28 | $1,159.92 | 3.72% | 3,811.15 | 2.61% | |
| 42. | 2021/03/31 | $1,404.30 | 21.07% | 3,972.89 | 4.24% | |
| 43. | 2021/04/30 | $1,464.12 | 4.26% | 4,181.17 | 5.24% | |
| 44. | 2021/05/31 | $1,406.60 | -3.93% | 4,204.11 | 0.55% | |
| 45. | 2021/06/30 | $1,492.22 | 6.09% | 4,297.50 | 2.22% | |
| 46. | 2021/07/31 | $1,623.57 | 8.80% | 4,395.26 | 2.27% | |
| 47. | 2021/08/31 | $1,549.15 | -4.58% | 4,522.68 | 2.90% | |
| 48. | 2021/09/30 | $1,697.99 | 9.61% | 4,307.54 | -4.76% | |
| 49. | 2021/10/31 | $1,784.84 | 5.11% | 4,605.38 | 6.91% | |
| 50. | 2021/11/30 | $1,817.07 | 1.81% | 4,567.00 | -0.83% | |
| 51. | 2021/12/31 | $2,096.39 | 15.37% | 4,766.18 | 4.36% | |
| 52. | 2022/01/31 | $1,986.35 | -5.25% | 4,515.55 | -5.26% | |
| 53. | 2022/02/28 | $1,863.39 | -6.19% | 4,373.94 | -3.14% | |
| 54. | 2022/03/31 | $2,044.58 | 9.72% | 4,530.41 | 3.58% | |
| 55. | 2022/04/30 | $1,955.47 | -4.36% | 4,131.93 | -8.80% | |
| 56. | 2022/05/31 | $2,059.65 | 5.33% | 4,132.15 | 0.01% | |
| 57. | 2022/06/30 | $2,149.12 | 4.34% | 3,785.38 | -8.39% | |
| 58. | 2022/07/31 | $2,137.39 | -0.55% | 4,130.29 | 9.11% | |
| 59. | 2022/08/31 | $2,119.21 | -0.85% | 3,955.00 | -4.24% | |
| 60. | 2022/09/30 | $2,141.93 | 1.07% | 3,585.62 | -9.34% | |
| 61. | 2022/10/31 | $2,532.88 | 18.25% | 3,871.98 | 7.99% | |
| 62. | 2022/11/30 | $2,579.00 | 1.82% | 4,080.11 | 5.38% | |
| 63. | 2022/12/31 | $2,466.18 | -4.37% | 3,839.50 | -5.90% | |
| 64. | 2023/01/31 | $2,438.85 | -1.11% | 4,076.60 | 6.18% | |
| 65. | 2023/02/28 | $2,486.54 | 1.96% | 3,970.15 | -2.61% | |
| 66. | 2023/03/31 | $2,458.15 | -1.14% | 4,109.31 | 3.51% | |
| 67. | 2023/04/30 | $2,663.31 | 8.35% | 4,169.48 | 1.46% | |
| 68. | 2023/05/31 | $2,386.84 | -10.38% | 4,179.83 | 0.25% | |
| 69. | 2023/06/30 | $2,493.36 | 4.46% | 4,376.86 | 4.71% | |
| 70. | 2023/07/31 | $2,481.72 | -0.47% | 4,588.96 | 4.85% | |
| 71. | 2023/08/31 | $2,531.33 | 2.00% | 4,507.66 | -1.77% | |
| 平均 (R): | 2.31% | 0.95% | ||||
| 標準偏差： | 7.25% | 5.08% | ||||
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AZO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
AutoZone Inc.、分散の計算、および戻り値の共分散
| t | 日付 | RAZO,t | RS&P 500,t | (RAZO,t–RAZO)2 | (RS&P 500,t–RS&P 500)2 | (RAZO,t–RAZO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017/10/31 | -0.94% | 2.22% | 10.60 | 1.61 | -4.13 |
| 2. | 2017/11/30 | 16.50% | 2.81% | 201.24 | 3.45 | 26.35 |
| 3. | 2017/12/31 | 3.58% | 0.98% | 1.61 | 0.00 | 0.04 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023/07/31 | -0.47% | 4.85% | 7.73 | 15.17 | -10.83 |
| 71. | 2023/08/31 | 2.00% | -1.77% | 0.10 | 7.41 | 0.85 |
| トータル (Σ): | 3,675.51 | 1,807.09 | 1,305.66 | |||
| t | 日付 | RAZO,t | RS&P 500,t | (RAZO,t–RAZO)2 | (RS&P 500,t–RS&P 500)2 | (RAZO,t–RAZO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017/10/31 | -0.94% | 2.22% | 10.60 | 1.61 | -4.13 |
| 2. | 2017/11/30 | 16.50% | 2.81% | 201.24 | 3.45 | 26.35 |
| 3. | 2017/12/31 | 3.58% | 0.98% | 1.61 | 0.00 | 0.04 |
| 4. | 2018/01/31 | 7.60% | 5.62% | 27.96 | 21.78 | 24.68 |
| 5. | 2018/02/28 | -13.16% | -3.89% | 239.36 | 23.48 | 74.97 |
| 6. | 2018/03/31 | -2.41% | -2.69% | 22.32 | 13.25 | 17.19 |
| 7. | 2018/04/30 | -3.73% | 0.27% | 36.47 | 0.46 | 4.10 |
| 8. | 2018/05/31 | 3.97% | 2.16% | 2.75 | 1.46 | 2.01 |
| 9. | 2018/06/30 | 3.33% | 0.48% | 1.03 | 0.22 | -0.47 |
| 10. | 2018/07/31 | 5.16% | 3.60% | 8.09 | 7.03 | 7.54 |
| 11. | 2018/08/31 | 8.70% | 3.03% | 40.74 | 4.31 | 13.25 |
| 12. | 2018/09/30 | 1.15% | 0.43% | 1.35 | 0.27 | 0.61 |
| 13. | 2018/10/31 | -5.44% | -6.94% | 60.17 | 62.28 | 61.21 |
| 14. | 2018/11/30 | 10.31% | 1.79% | 63.91 | 0.70 | 6.67 |
| 15. | 2018/12/31 | 3.62% | -9.18% | 1.70 | 102.59 | -13.22 |
| 16. | 2019/01/31 | 1.07% | 7.87% | 1.54 | 47.85 | -8.57 |
| 17. | 2019/02/28 | 10.81% | 2.97% | 72.27 | 4.09 | 17.19 |
| 18. | 2019/03/31 | 9.07% | 1.79% | 45.64 | 0.71 | 5.68 |
| 19. | 2019/04/30 | 0.41% | 3.93% | 3.62 | 8.88 | -5.67 |
| 20. | 2019/05/31 | -0.12% | -6.58% | 5.90 | 56.68 | 18.29 |
| 21. | 2019/06/30 | 7.05% | 6.89% | 22.39 | 35.31 | 28.12 |
| 22. | 2019/07/31 | 2.14% | 1.31% | 0.03 | 0.13 | -0.06 |
| 23. | 2019/08/31 | -1.90% | -1.81% | 17.76 | 7.62 | 11.63 |
| 24. | 2019/09/30 | -1.55% | 1.72% | 14.92 | 0.59 | -2.96 |
| 25. | 2019/10/31 | 5.51% | 2.04% | 10.22 | 1.19 | 3.49 |
| 26. | 2019/11/30 | 2.93% | 3.40% | 0.38 | 6.02 | 1.52 |
| 27. | 2019/12/31 | 1.14% | 2.86% | 1.38 | 3.64 | -2.24 |
| 28. | 2020/01/31 | -11.19% | -0.16% | 182.42 | 1.24 | 15.05 |
| 29. | 2020/02/29 | -2.41% | -8.41% | 22.26 | 87.65 | 44.17 |
| 30. | 2020/03/31 | -18.06% | -12.51% | 415.20 | 181.25 | 274.33 |
| 31. | 2020/04/30 | 20.61% | 12.68% | 334.62 | 137.67 | 214.63 |
| 32. | 2020/05/31 | 12.50% | 4.53% | 103.78 | 12.80 | 36.44 |
| 33. | 2020/06/30 | -1.72% | 1.84% | 16.26 | 0.79 | -3.58 |
| 34. | 2020/07/31 | 7.03% | 5.51% | 22.25 | 20.78 | 21.50 |
| 35. | 2020/08/31 | -0.92% | 7.01% | 10.45 | 36.67 | -19.58 |
| 36. | 2020/09/30 | -1.56% | -3.92% | 15.00 | 23.76 | 18.88 |
| 37. | 2020/10/31 | -4.13% | -2.77% | 41.53 | 13.82 | 23.96 |
| 38. | 2020/11/30 | 0.77% | 10.75% | 2.39 | 96.11 | -15.14 |
| 39. | 2020/12/31 | 4.20% | 3.71% | 3.56 | 7.62 | 5.21 |
| 40. | 2021/01/31 | -5.66% | -1.11% | 63.53 | 4.26 | 16.46 |
| 41. | 2021/02/28 | 3.72% | 2.61% | 1.97 | 2.75 | 2.33 |
| 42. | 2021/03/31 | 21.07% | 4.24% | 351.79 | 10.84 | 61.76 |
| 43. | 2021/04/30 | 4.26% | 5.24% | 3.79 | 18.42 | 8.36 |
| 44. | 2021/05/31 | -3.93% | 0.55% | 38.95 | 0.16 | 2.51 |
| 45. | 2021/06/30 | 6.09% | 2.22% | 14.25 | 1.61 | 4.79 |
| 46. | 2021/07/31 | 8.80% | 2.27% | 42.12 | 1.75 | 8.59 |
| 47. | 2021/08/31 | -4.58% | 2.90% | 47.56 | 3.79 | -13.43 |
| 48. | 2021/09/30 | 9.61% | -4.76% | 53.22 | 32.58 | -41.64 |
| 49. | 2021/10/31 | 5.11% | 6.91% | 7.85 | 35.56 | 16.71 |
| 50. | 2021/11/30 | 1.81% | -0.83% | 0.26 | 3.18 | 0.90 |
| 51. | 2021/12/31 | 15.37% | 4.36% | 170.55 | 11.63 | 44.53 |
| 52. | 2022/01/31 | -5.25% | -5.26% | 57.18 | 38.56 | 46.96 |
| 53. | 2022/02/28 | -6.19% | -3.14% | 72.30 | 16.71 | 34.75 |
| 54. | 2022/03/31 | 9.72% | 3.58% | 54.92 | 6.90 | 19.46 |
| 55. | 2022/04/30 | -4.36% | -8.80% | 44.50 | 95.00 | 65.02 |
| 56. | 2022/05/31 | 5.33% | 0.01% | 9.09 | 0.89 | -2.85 |
| 57. | 2022/06/30 | 4.34% | -8.39% | 4.13 | 87.29 | -18.98 |
| 58. | 2022/07/31 | -0.55% | 9.11% | 8.17 | 66.59 | -23.33 |
| 59. | 2022/08/31 | -0.85% | -4.24% | 10.01 | 26.99 | 16.43 |
| 60. | 2022/09/30 | 1.07% | -9.34% | 1.54 | 105.90 | 12.77 |
| 61. | 2022/10/31 | 18.25% | 7.99% | 254.07 | 49.49 | 112.14 |
| 62. | 2022/11/30 | 1.82% | 5.38% | 0.24 | 19.57 | -2.18 |
| 63. | 2022/12/31 | -4.37% | -5.90% | 44.72 | 46.90 | 45.80 |
| 64. | 2023/01/31 | -1.11% | 6.18% | 11.70 | 27.29 | -17.87 |
| 65. | 2023/02/28 | 1.96% | -2.61% | 0.13 | 12.69 | 1.27 |
| 66. | 2023/03/31 | -1.14% | 3.51% | 11.93 | 6.52 | -8.82 |
| 67. | 2023/04/30 | 8.35% | 1.46% | 36.40 | 0.26 | 3.10 |
| 68. | 2023/05/31 | -10.38% | 0.25% | 161.12 | 0.49 | 8.92 |
| 69. | 2023/06/30 | 4.46% | 4.71% | 4.62 | 14.16 | 8.09 |
| 70. | 2023/07/31 | -0.47% | 4.85% | 7.73 | 15.17 | -10.83 |
| 71. | 2023/08/31 | 2.00% | -1.77% | 0.10 | 7.41 | 0.85 |
| トータル (Σ): | 3,675.51 | 1,807.09 | 1,305.66 | |||
すべて表示
分散AZO = Σ(RAZO,t–RAZO)2 ÷ (71 – 1)
= 3,675.51 ÷ (71 – 1)
= 52.51
分散S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,807.09 ÷ (71 – 1)
= 25.82
共 分散AZO, S&P 500 = Σ(RAZO,t–RAZO)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,305.66 ÷ (71 – 1)
= 18.65
システマティックなリスク推定 (β)
| 分散AZO | 52.51 |
| 分散S&P 500 | 25.82 |
| 共 分散AZO, S&P 500 | 18.65 |
| 相関係数AZO, S&P 5001 | 0.51 |
| βAZO2 | 0.72 |
| αAZO3 | 1.63% |
計算
1 相関係数AZO, S&P 500
= 共 分散AZO, S&P 500 ÷ (標準偏差AZO × 標準偏差S&P 500)
= 18.65 ÷ (7.25% × 5.08%)
= 0.51
2 βAZO
= 共 分散AZO, S&P 500 ÷ 分散S&P 500
= 18.65 ÷ 25.82
= 0.72
3 αAZO
= 平均AZO – βAZO × 平均S&P 500
= 2.31% – 0.72 × 0.95%
= 1.63%
期待収益率
| 仮定 | ||
| LT国債総合の収益率1 | RF | 4.60% |
| 市場ポートフォリオの期待収益率2 | E(RM) | 15.13% |
| 普通株式のシステマティックリスクAutoZone | βAZO | 0.72 |
| AutoZone普通株式の予想収益率3 | E(RAZO) | 12.21% |
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(RAZO) = RF + βAZO [E(RM) – RF]
= 4.60% + 0.72 [15.13% – 4.60%]
= 12.21%