자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Johnson Controls보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Johnson Controls International plc, 월별 수익률
| Johnson Controls International plc (JCI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값JCI,t1 | 피제수JCI,t1 | RJCI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 10. 31. | $41.39 | 2,575.26 | ||||
| 1. | 2017. 11. 30. | $37.64 | -9.06% | 2,647.58 | 2.81% | |
| 2. | 2017. 12. 31. | $38.11 | $0.26 | 1.94% | 2,673.61 | 0.98% |
| 3. | 2018. 1. 31. | $39.13 | 2.68% | 2,823.81 | 5.62% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 8. 31. | $59.06 | -15.08% | 4,507.66 | -1.77% | |
| 71. | 2023. 9. 30. | $53.21 | $0.37 | -9.28% | 4,288.05 | -4.87% |
| 평균의 (R): | 0.92% | 0.85% | ||||
| 표준 편차: | 8.29% | 5.13% | ||||
| Johnson Controls International plc (JCI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값JCI,t1 | 피제수JCI,t1 | RJCI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 10. 31. | $41.39 | 2,575.26 | ||||
| 1. | 2017. 11. 30. | $37.64 | -9.06% | 2,647.58 | 2.81% | |
| 2. | 2017. 12. 31. | $38.11 | $0.26 | 1.94% | 2,673.61 | 0.98% |
| 3. | 2018. 1. 31. | $39.13 | 2.68% | 2,823.81 | 5.62% | |
| 4. | 2018. 2. 28. | $36.87 | -5.78% | 2,713.83 | -3.89% | |
| 5. | 2018. 3. 31. | $35.24 | $0.26 | -3.72% | 2,640.87 | -2.69% |
| 6. | 2018. 4. 30. | $33.87 | -3.89% | 2,648.05 | 0.27% | |
| 7. | 2018. 5. 31. | $33.56 | -0.92% | 2,705.27 | 2.16% | |
| 8. | 2018. 6. 30. | $33.45 | $0.26 | 0.45% | 2,718.37 | 0.48% |
| 9. | 2018. 7. 31. | $37.51 | 12.14% | 2,816.29 | 3.60% | |
| 10. | 2018. 8. 31. | $37.77 | 0.69% | 2,901.52 | 3.03% | |
| 11. | 2018. 9. 30. | $35.00 | $0.26 | -6.65% | 2,913.98 | 0.43% |
| 12. | 2018. 10. 31. | $31.97 | -8.66% | 2,711.74 | -6.94% | |
| 13. | 2018. 11. 30. | $34.78 | 8.79% | 2,760.17 | 1.79% | |
| 14. | 2018. 12. 31. | $29.65 | $0.26 | -14.00% | 2,506.85 | -9.18% |
| 15. | 2019. 1. 31. | $33.77 | 13.90% | 2,704.10 | 7.87% | |
| 16. | 2019. 2. 28. | $35.27 | 4.44% | 2,784.49 | 2.97% | |
| 17. | 2019. 3. 31. | $36.94 | $0.26 | 5.47% | 2,834.40 | 1.79% |
| 18. | 2019. 4. 30. | $37.50 | 1.52% | 2,945.83 | 3.93% | |
| 19. | 2019. 5. 31. | $38.52 | 2.72% | 2,752.06 | -6.58% | |
| 20. | 2019. 6. 30. | $41.31 | $0.26 | 7.92% | 2,941.76 | 6.89% |
| 21. | 2019. 7. 31. | $42.44 | 2.74% | 2,980.38 | 1.31% | |
| 22. | 2019. 8. 31. | $42.69 | 0.59% | 2,926.46 | -1.81% | |
| 23. | 2019. 9. 30. | $43.89 | $0.26 | 3.42% | 2,976.74 | 1.72% |
| 24. | 2019. 10. 31. | $43.33 | -1.28% | 3,037.56 | 2.04% | |
| 25. | 2019. 11. 30. | $42.83 | -1.15% | 3,140.98 | 3.40% | |
| 26. | 2019. 12. 31. | $40.71 | $0.26 | -4.34% | 3,230.78 | 2.86% |
| 27. | 2020. 1. 31. | $39.45 | -3.10% | 3,225.52 | -0.16% | |
| 28. | 2020. 2. 29. | $36.57 | -7.30% | 2,954.22 | -8.41% | |
| 29. | 2020. 3. 31. | $26.96 | $0.26 | -25.57% | 2,584.59 | -12.51% |
| 30. | 2020. 4. 30. | $29.11 | 7.97% | 2,912.43 | 12.68% | |
| 31. | 2020. 5. 31. | $31.41 | 7.90% | 3,044.31 | 4.53% | |
| 32. | 2020. 6. 30. | $34.14 | $0.26 | 9.52% | 3,100.29 | 1.84% |
| 33. | 2020. 7. 31. | $38.48 | 12.71% | 3,271.12 | 5.51% | |
| 34. | 2020. 8. 31. | $40.73 | 5.85% | 3,500.31 | 7.01% | |
| 35. | 2020. 9. 30. | $40.85 | $0.26 | 0.93% | 3,363.00 | -3.92% |
| 36. | 2020. 10. 31. | $42.21 | 3.33% | 3,269.96 | -2.77% | |
| 37. | 2020. 11. 30. | $46.04 | 9.07% | 3,621.63 | 10.75% | |
| 38. | 2020. 12. 31. | $46.59 | $0.26 | 1.76% | 3,756.07 | 3.71% |
| 39. | 2021. 1. 31. | $49.82 | 6.93% | 3,714.24 | -1.11% | |
| 40. | 2021. 2. 28. | $55.79 | 11.98% | 3,811.15 | 2.61% | |
| 41. | 2021. 3. 31. | $59.67 | $0.27 | 7.44% | 3,972.89 | 4.24% |
| 42. | 2021. 4. 30. | $62.34 | 4.47% | 4,181.17 | 5.24% | |
| 43. | 2021. 5. 31. | $66.54 | 6.74% | 4,204.11 | 0.55% | |
| 44. | 2021. 6. 30. | $68.63 | $0.27 | 3.55% | 4,297.50 | 2.22% |
| 45. | 2021. 7. 31. | $71.42 | 4.07% | 4,395.26 | 2.27% | |
| 46. | 2021. 8. 31. | $74.80 | 4.73% | 4,522.68 | 2.90% | |
| 47. | 2021. 9. 30. | $68.08 | $0.27 | -8.62% | 4,307.54 | -4.76% |
| 48. | 2021. 10. 31. | $73.37 | 7.77% | 4,605.38 | 6.91% | |
| 49. | 2021. 11. 30. | $74.76 | 1.89% | 4,567.00 | -0.83% | |
| 50. | 2021. 12. 31. | $81.31 | $0.34 | 9.22% | 4,766.18 | 4.36% |
| 51. | 2022. 1. 31. | $72.67 | -10.63% | 4,515.55 | -5.26% | |
| 52. | 2022. 2. 28. | $64.96 | -10.61% | 4,373.94 | -3.14% | |
| 53. | 2022. 3. 31. | $65.57 | $0.35 | 1.48% | 4,530.41 | 3.58% |
| 54. | 2022. 4. 30. | $59.87 | -8.69% | 4,131.93 | -8.80% | |
| 55. | 2022. 5. 31. | $54.51 | -8.95% | 4,132.15 | 0.01% | |
| 56. | 2022. 6. 30. | $47.88 | $0.35 | -11.52% | 3,785.38 | -8.39% |
| 57. | 2022. 7. 31. | $53.91 | 12.59% | 4,130.29 | 9.11% | |
| 58. | 2022. 8. 31. | $54.14 | 0.43% | 3,955.00 | -4.24% | |
| 59. | 2022. 9. 30. | $49.22 | $0.35 | -8.44% | 3,585.62 | -9.34% |
| 60. | 2022. 10. 31. | $57.84 | 17.51% | 3,871.98 | 7.99% | |
| 61. | 2022. 11. 30. | $66.44 | 14.87% | 4,080.11 | 5.38% | |
| 62. | 2022. 12. 31. | $64.00 | $0.35 | -3.15% | 3,839.50 | -5.90% |
| 63. | 2023. 1. 31. | $69.57 | 8.70% | 4,076.60 | 6.18% | |
| 64. | 2023. 2. 28. | $62.72 | -9.85% | 3,970.15 | -2.61% | |
| 65. | 2023. 3. 31. | $60.22 | $0.36 | -3.41% | 4,109.31 | 3.51% |
| 66. | 2023. 4. 30. | $59.84 | -0.63% | 4,169.48 | 1.46% | |
| 67. | 2023. 5. 31. | $59.70 | -0.23% | 4,179.83 | 0.25% | |
| 68. | 2023. 6. 30. | $68.14 | $0.37 | 14.76% | 4,376.86 | 4.71% |
| 69. | 2023. 7. 31. | $69.55 | 2.07% | 4,588.96 | 4.85% | |
| 70. | 2023. 8. 31. | $59.06 | -15.08% | 4,507.66 | -1.77% | |
| 71. | 2023. 9. 30. | $53.21 | $0.37 | -9.28% | 4,288.05 | -4.87% |
| 평균의 (R): | 0.92% | 0.85% | ||||
| 표준 편차: | 8.29% | 5.13% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 JCI의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Johnson Controls International plc, 수익률의 분산 및 공분산 계산
| t | 날짜 | RJCI,t | RS&P 500,t | (RJCI,t–RJCI)2 | (RS&P 500,t–RS&P 500)2 | (RJCI,t–RJCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 11. 30. | -9.06% | 2.81% | 99.56 | 3.83 | -19.53 |
| 2. | 2017. 12. 31. | 1.94% | 0.98% | 1.04 | 0.02 | 0.13 |
| 3. | 2018. 1. 31. | 2.68% | 5.62% | 3.09 | 22.72 | 8.38 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 8. 31. | -15.08% | -1.77% | 256.01 | 6.88 | 41.97 |
| 71. | 2023. 9. 30. | -9.28% | -4.87% | 103.96 | 32.75 | 58.36 |
| 합계 (Σ): | 4,811.07 | 1,838.69 | 2,278.06 | |||
| t | 날짜 | RJCI,t | RS&P 500,t | (RJCI,t–RJCI)2 | (RS&P 500,t–RS&P 500)2 | (RJCI,t–RJCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 11. 30. | -9.06% | 2.81% | 99.56 | 3.83 | -19.53 |
| 2. | 2017. 12. 31. | 1.94% | 0.98% | 1.04 | 0.02 | 0.13 |
| 3. | 2018. 1. 31. | 2.68% | 5.62% | 3.09 | 22.72 | 8.38 |
| 4. | 2018. 2. 28. | -5.78% | -3.89% | 44.80 | 22.52 | 31.77 |
| 5. | 2018. 3. 31. | -3.72% | -2.69% | 21.47 | 12.53 | 16.40 |
| 6. | 2018. 4. 30. | -3.89% | 0.27% | 23.09 | 0.34 | 2.78 |
| 7. | 2018. 5. 31. | -0.92% | 2.16% | 3.36 | 1.71 | -2.40 |
| 8. | 2018. 6. 30. | 0.45% | 0.48% | 0.22 | 0.13 | 0.17 |
| 9. | 2018. 7. 31. | 12.14% | 3.60% | 125.89 | 7.57 | 30.86 |
| 10. | 2018. 8. 31. | 0.69% | 3.03% | 0.05 | 4.73 | -0.49 |
| 11. | 2018. 9. 30. | -6.65% | 0.43% | 57.20 | 0.18 | 3.19 |
| 12. | 2018. 10. 31. | -8.66% | -6.94% | 91.68 | 60.71 | 74.60 |
| 13. | 2018. 11. 30. | 8.79% | 1.79% | 61.97 | 0.87 | 7.36 |
| 14. | 2018. 12. 31. | -14.00% | -9.18% | 222.60 | 100.58 | 149.63 |
| 15. | 2019. 1. 31. | 13.90% | 7.87% | 168.42 | 49.24 | 91.07 |
| 16. | 2019. 2. 28. | 4.44% | 2.97% | 12.42 | 4.50 | 7.48 |
| 17. | 2019. 3. 31. | 5.47% | 1.79% | 20.74 | 0.89 | 4.29 |
| 18. | 2019. 4. 30. | 1.52% | 3.93% | 0.36 | 9.49 | 1.84 |
| 19. | 2019. 5. 31. | 2.72% | -6.58% | 3.25 | 55.19 | -13.39 |
| 20. | 2019. 6. 30. | 7.92% | 6.89% | 49.00 | 36.50 | 42.29 |
| 21. | 2019. 7. 31. | 2.74% | 1.31% | 3.30 | 0.21 | 0.84 |
| 22. | 2019. 8. 31. | 0.59% | -1.81% | 0.11 | 7.08 | 0.87 |
| 23. | 2019. 9. 30. | 3.42% | 1.72% | 6.26 | 0.75 | 2.17 |
| 24. | 2019. 10. 31. | -1.28% | 2.04% | 4.81 | 1.42 | -2.61 |
| 25. | 2019. 11. 30. | -1.15% | 3.40% | 4.29 | 6.52 | -5.29 |
| 26. | 2019. 12. 31. | -4.34% | 2.86% | 27.67 | 4.03 | -10.56 |
| 27. | 2020. 1. 31. | -3.10% | -0.16% | 16.10 | 1.03 | 4.07 |
| 28. | 2020. 2. 29. | -7.30% | -8.41% | 67.54 | 85.79 | 76.12 |
| 29. | 2020. 3. 31. | -25.57% | -12.51% | 701.46 | 178.57 | 353.92 |
| 30. | 2020. 4. 30. | 7.97% | 12.68% | 49.80 | 140.02 | 83.51 |
| 31. | 2020. 5. 31. | 7.90% | 4.53% | 48.77 | 13.52 | 25.68 |
| 32. | 2020. 6. 30. | 9.52% | 1.84% | 73.99 | 0.98 | 8.49 |
| 33. | 2020. 7. 31. | 12.71% | 5.51% | 139.12 | 21.71 | 54.95 |
| 34. | 2020. 8. 31. | 5.85% | 7.01% | 24.30 | 37.89 | 30.34 |
| 35. | 2020. 9. 30. | 0.93% | -3.92% | 0.00 | 22.79 | -0.07 |
| 36. | 2020. 10. 31. | 3.33% | -2.77% | 5.82 | 13.09 | -8.72 |
| 37. | 2020. 11. 30. | 9.07% | 10.75% | 66.52 | 98.08 | 80.77 |
| 38. | 2020. 12. 31. | 1.76% | 3.71% | 0.71 | 8.18 | 2.41 |
| 39. | 2021. 1. 31. | 6.93% | -1.11% | 36.18 | 3.86 | -11.82 |
| 40. | 2021. 2. 28. | 11.98% | 2.61% | 122.45 | 3.09 | 19.45 |
| 41. | 2021. 3. 31. | 7.44% | 4.24% | 42.52 | 11.51 | 22.12 |
| 42. | 2021. 4. 30. | 4.47% | 5.24% | 12.65 | 19.28 | 15.62 |
| 43. | 2021. 5. 31. | 6.74% | 0.55% | 33.87 | 0.09 | -1.76 |
| 44. | 2021. 6. 30. | 3.55% | 2.22% | 6.91 | 1.88 | 3.60 |
| 45. | 2021. 7. 31. | 4.07% | 2.27% | 9.91 | 2.03 | 4.48 |
| 46. | 2021. 8. 31. | 4.73% | 2.90% | 14.55 | 4.19 | 7.81 |
| 47. | 2021. 9. 30. | -8.62% | -4.76% | 91.02 | 31.45 | 53.51 |
| 48. | 2021. 10. 31. | 7.77% | 6.91% | 46.96 | 36.76 | 41.55 |
| 49. | 2021. 11. 30. | 1.89% | -0.83% | 0.95 | 2.84 | -1.65 |
| 50. | 2021. 12. 31. | 9.22% | 4.36% | 68.87 | 12.32 | 29.13 |
| 51. | 2022. 1. 31. | -10.63% | -5.26% | 133.26 | 37.33 | 70.53 |
| 52. | 2022. 2. 28. | -10.61% | -3.14% | 132.88 | 15.90 | 45.96 |
| 53. | 2022. 3. 31. | 1.48% | 3.58% | 0.31 | 7.43 | 1.53 |
| 54. | 2022. 4. 30. | -8.69% | -8.80% | 92.36 | 93.06 | 92.71 |
| 55. | 2022. 5. 31. | -8.95% | 0.01% | 97.42 | 0.72 | 8.35 |
| 56. | 2022. 6. 30. | -11.52% | -8.39% | 154.71 | 85.44 | 114.97 |
| 57. | 2022. 7. 31. | 12.59% | 9.11% | 136.34 | 68.23 | 96.45 |
| 58. | 2022. 8. 31. | 0.43% | -4.24% | 0.24 | 25.96 | 2.50 |
| 59. | 2022. 9. 30. | -8.44% | -9.34% | 87.59 | 103.85 | 95.37 |
| 60. | 2022. 10. 31. | 17.51% | 7.99% | 275.41 | 50.91 | 118.41 |
| 61. | 2022. 11. 30. | 14.87% | 5.38% | 194.63 | 20.47 | 63.11 |
| 62. | 2022. 12. 31. | -3.15% | -5.90% | 16.51 | 45.54 | 27.42 |
| 63. | 2023. 1. 31. | 8.70% | 6.18% | 60.61 | 28.35 | 41.45 |
| 64. | 2023. 2. 28. | -9.85% | -2.61% | 115.86 | 11.99 | 37.27 |
| 65. | 2023. 3. 31. | -3.41% | 3.51% | 18.75 | 7.04 | -11.49 |
| 66. | 2023. 4. 30. | -0.63% | 1.46% | 2.40 | 0.38 | -0.95 |
| 67. | 2023. 5. 31. | -0.23% | 0.25% | 1.33 | 0.36 | 0.69 |
| 68. | 2023. 6. 30. | 14.76% | 4.71% | 191.53 | 14.92 | 53.46 |
| 69. | 2023. 7. 31. | 2.07% | 4.85% | 1.33 | 15.96 | 4.60 |
| 70. | 2023. 8. 31. | -15.08% | -1.77% | 256.01 | 6.88 | 41.97 |
| 71. | 2023. 9. 30. | -9.28% | -4.87% | 103.96 | 32.75 | 58.36 |
| 합계 (Σ): | 4,811.07 | 1,838.69 | 2,278.06 | |||
모두 보기
분산JCI = Σ(RJCI,t–RJCI)2 ÷ (71 – 1)
= 4,811.07 ÷ (71 – 1)
= 68.73
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,838.69 ÷ (71 – 1)
= 26.27
공분산JCI, S&P 500 = Σ(RJCI,t–RJCI)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,278.06 ÷ (71 – 1)
= 32.54
체계적인 위험 추정 (β)
| 분산JCI | 68.73 |
| 분산S&P 500 | 26.27 |
| 공분산JCI, S&P 500 | 32.54 |
| 상관 계수JCI, S&P 5001 | 0.77 |
| βJCI2 | 1.24 |
| αJCI3 | -0.14% |
계산
1 상관 계수JCI, S&P 500
= 공분산JCI, S&P 500 ÷ (표준 편차JCI × 표준 편차S&P 500)
= 32.54 ÷ (8.29% × 5.13%)
= 0.77
2 βJCI
= 공분산JCI, S&P 500 ÷ 분산S&P 500
= 32.54 ÷ 26.27
= 1.24
3 αJCI
= 평균의JCI – βJCI × 평균의S&P 500
= 0.92% – 1.24 × 0.85%
= -0.14%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.88% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.90% |
| 보통주의 체계적 위험Johnson Controls | βJCI | 1.24 |
| Johnson Controls 보통주에 대한 예상 수익률3 | E(RJCI) | 17.29% |
1 10년 이내에 만기가 도래하거나 콜링할 수 없는 모든 미결제 고정 쿠폰 미국 국채에 대한 입찰 수익률의 비가중 평균(무위험 수익률 대리).
2 자세히 보기 »
3 E(RJCI) = RF + βJCI [E(RM) – RF]
= 4.88% + 1.24 [14.90% – 4.88%]
= 17.29%