자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 TJX보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
TJX Cos. Inc., 월별 수익률
| TJX Cos. Inc. (TJX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TJX,t1 | 피제수TJX,t1 | RTJX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 2. 28. | $51.29 | 2,784.49 | ||||
| 1. | 2019. 3. 31. | $53.21 | 3.74% | 2,834.40 | 1.79% | |
| 2. | 2019. 4. 30. | $54.88 | 3.14% | 2,945.83 | 3.93% | |
| 3. | 2019. 5. 31. | $50.29 | $0.23 | -7.94% | 2,752.06 | -6.58% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 12. 31. | $120.81 | -3.88% | 5,881.63 | -2.50% | |
| 71. | 2025. 1. 31. | $124.79 | 3.29% | 6,040.53 | 2.70% | |
| 평균의 (R): | 1.59% | 1.22% | ||||
| 표준 편차: | 6.75% | 4.99% | ||||
| TJX Cos. Inc. (TJX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TJX,t1 | 피제수TJX,t1 | RTJX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 2. 28. | $51.29 | 2,784.49 | ||||
| 1. | 2019. 3. 31. | $53.21 | 3.74% | 2,834.40 | 1.79% | |
| 2. | 2019. 4. 30. | $54.88 | 3.14% | 2,945.83 | 3.93% | |
| 3. | 2019. 5. 31. | $50.29 | $0.23 | -7.94% | 2,752.06 | -6.58% |
| 4. | 2019. 6. 30. | $52.88 | 5.15% | 2,941.76 | 6.89% | |
| 5. | 2019. 7. 31. | $54.56 | 3.18% | 2,980.38 | 1.31% | |
| 6. | 2019. 8. 31. | $54.97 | $0.23 | 1.17% | 2,926.46 | -1.81% |
| 7. | 2019. 9. 30. | $55.74 | 1.40% | 2,976.74 | 1.72% | |
| 8. | 2019. 10. 31. | $57.65 | 3.43% | 3,037.56 | 2.04% | |
| 9. | 2019. 11. 30. | $61.13 | $0.23 | 6.44% | 3,140.98 | 3.40% |
| 10. | 2019. 12. 31. | $61.06 | -0.11% | 3,230.78 | 2.86% | |
| 11. | 2020. 1. 31. | $59.04 | -3.31% | 3,225.52 | -0.16% | |
| 12. | 2020. 2. 29. | $59.80 | $0.23 | 1.68% | 2,954.22 | -8.41% |
| 13. | 2020. 3. 31. | $47.81 | -20.05% | 2,584.59 | -12.51% | |
| 14. | 2020. 4. 30. | $49.05 | 2.59% | 2,912.43 | 12.68% | |
| 15. | 2020. 5. 31. | $52.76 | 7.56% | 3,044.31 | 4.53% | |
| 16. | 2020. 6. 30. | $50.56 | -4.17% | 3,100.29 | 1.84% | |
| 17. | 2020. 7. 31. | $51.99 | 2.83% | 3,271.12 | 5.51% | |
| 18. | 2020. 8. 31. | $54.79 | 5.39% | 3,500.31 | 7.01% | |
| 19. | 2020. 9. 30. | $55.65 | 1.57% | 3,363.00 | -3.92% | |
| 20. | 2020. 10. 31. | $50.80 | -8.72% | 3,269.96 | -2.77% | |
| 21. | 2020. 11. 30. | $63.51 | 25.02% | 3,621.63 | 10.75% | |
| 22. | 2020. 12. 31. | $68.29 | 7.53% | 3,756.07 | 3.71% | |
| 23. | 2021. 1. 31. | $64.04 | -6.22% | 3,714.24 | -1.11% | |
| 24. | 2021. 2. 28. | $65.99 | $0.26 | 3.45% | 3,811.15 | 2.61% |
| 25. | 2021. 3. 31. | $66.15 | 0.24% | 3,972.89 | 4.24% | |
| 26. | 2021. 4. 30. | $71.00 | 7.33% | 4,181.17 | 5.24% | |
| 27. | 2021. 5. 31. | $67.54 | $0.26 | -4.51% | 4,204.11 | 0.55% |
| 28. | 2021. 6. 30. | $67.42 | -0.18% | 4,297.50 | 2.22% | |
| 29. | 2021. 7. 31. | $68.81 | 2.06% | 4,395.26 | 2.27% | |
| 30. | 2021. 8. 31. | $72.72 | $0.26 | 6.06% | 4,522.68 | 2.90% |
| 31. | 2021. 9. 30. | $65.98 | -9.27% | 4,307.54 | -4.76% | |
| 32. | 2021. 10. 31. | $65.49 | -0.74% | 4,605.38 | 6.91% | |
| 33. | 2021. 11. 30. | $69.40 | $0.26 | 6.37% | 4,567.00 | -0.83% |
| 34. | 2021. 12. 31. | $75.92 | 9.39% | 4,766.18 | 4.36% | |
| 35. | 2022. 1. 31. | $71.97 | -5.20% | 4,515.55 | -5.26% | |
| 36. | 2022. 2. 28. | $66.10 | $0.26 | -7.79% | 4,373.94 | -3.14% |
| 37. | 2022. 3. 31. | $60.58 | -8.35% | 4,530.41 | 3.58% | |
| 38. | 2022. 4. 30. | $61.28 | 1.16% | 4,131.93 | -8.80% | |
| 39. | 2022. 5. 31. | $63.57 | $0.295 | 4.22% | 4,132.15 | 0.01% |
| 40. | 2022. 6. 30. | $55.85 | -12.14% | 3,785.38 | -8.39% | |
| 41. | 2022. 7. 31. | $61.16 | 9.51% | 4,130.29 | 9.11% | |
| 42. | 2022. 8. 31. | $62.35 | $0.295 | 2.43% | 3,955.00 | -4.24% |
| 43. | 2022. 9. 30. | $62.12 | -0.37% | 3,585.62 | -9.34% | |
| 44. | 2022. 10. 31. | $72.10 | 16.07% | 3,871.98 | 7.99% | |
| 45. | 2022. 11. 30. | $80.05 | $0.295 | 11.44% | 4,080.11 | 5.38% |
| 46. | 2022. 12. 31. | $79.60 | -0.56% | 3,839.50 | -5.90% | |
| 47. | 2023. 1. 31. | $81.86 | 2.84% | 4,076.60 | 6.18% | |
| 48. | 2023. 2. 28. | $76.60 | $0.295 | -6.07% | 3,970.15 | -2.61% |
| 49. | 2023. 3. 31. | $78.36 | 2.30% | 4,109.31 | 3.51% | |
| 50. | 2023. 4. 30. | $78.82 | 0.59% | 4,169.48 | 1.46% | |
| 51. | 2023. 5. 31. | $76.79 | $0.3325 | -2.15% | 4,179.83 | 0.25% |
| 52. | 2023. 6. 30. | $84.79 | 10.42% | 4,376.86 | 4.71% | |
| 53. | 2023. 7. 31. | $86.53 | 2.05% | 4,588.96 | 4.85% | |
| 54. | 2023. 8. 31. | $92.48 | $0.3325 | 7.26% | 4,507.66 | -1.77% |
| 55. | 2023. 9. 30. | $88.88 | -3.89% | 4,288.05 | -4.87% | |
| 56. | 2023. 10. 31. | $88.07 | -0.91% | 4,193.80 | -2.20% | |
| 57. | 2023. 11. 30. | $88.11 | $0.3325 | 0.42% | 4,567.80 | 8.92% |
| 58. | 2023. 12. 31. | $93.81 | 6.47% | 4,769.83 | 4.42% | |
| 59. | 2024. 1. 31. | $94.91 | 1.17% | 4,845.65 | 1.59% | |
| 60. | 2024. 2. 29. | $99.14 | $0.3325 | 4.81% | 5,096.27 | 5.17% |
| 61. | 2024. 3. 31. | $101.42 | 2.30% | 5,254.35 | 3.10% | |
| 62. | 2024. 4. 30. | $94.09 | -7.23% | 5,035.69 | -4.16% | |
| 63. | 2024. 5. 31. | $103.10 | $0.375 | 9.97% | 5,277.51 | 4.80% |
| 64. | 2024. 6. 30. | $110.10 | 6.79% | 5,460.48 | 3.47% | |
| 65. | 2024. 7. 31. | $113.02 | 2.65% | 5,522.30 | 1.13% | |
| 66. | 2024. 8. 31. | $117.27 | $0.375 | 4.09% | 5,648.40 | 2.28% |
| 67. | 2024. 9. 30. | $117.54 | 0.23% | 5,762.48 | 2.02% | |
| 68. | 2024. 10. 31. | $113.03 | -3.84% | 5,705.45 | -0.99% | |
| 69. | 2024. 11. 30. | $125.69 | $0.375 | 11.53% | 6,032.38 | 5.73% |
| 70. | 2024. 12. 31. | $120.81 | -3.88% | 5,881.63 | -2.50% | |
| 71. | 2025. 1. 31. | $124.79 | 3.29% | 6,040.53 | 2.70% | |
| 평균의 (R): | 1.59% | 1.22% | ||||
| 표준 편차: | 6.75% | 4.99% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 TJX의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
TJX Cos. Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RTJX,t | RS&P 500,t | (RTJX,t–RTJX)2 | (RS&P 500,t–RS&P 500)2 | (RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 3. 31. | 3.74% | 1.79% | 4.62 | 0.33 | 1.23 |
| 2. | 2019. 4. 30. | 3.14% | 3.93% | 2.39 | 7.35 | 4.19 |
| 3. | 2019. 5. 31. | -7.94% | -6.58% | 90.97 | 60.81 | 74.37 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 12. 31. | -3.88% | -2.50% | 29.98 | 13.83 | 20.36 |
| 71. | 2025. 1. 31. | 3.29% | 2.70% | 2.89 | 2.20 | 2.52 |
| 합계 (Σ): | 3,189.56 | 1,741.16 | 1,580.86 | |||
| t | 날짜 | RTJX,t | RS&P 500,t | (RTJX,t–RTJX)2 | (RS&P 500,t–RS&P 500)2 | (RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 3. 31. | 3.74% | 1.79% | 4.62 | 0.33 | 1.23 |
| 2. | 2019. 4. 30. | 3.14% | 3.93% | 2.39 | 7.35 | 4.19 |
| 3. | 2019. 5. 31. | -7.94% | -6.58% | 90.97 | 60.81 | 74.37 |
| 4. | 2019. 6. 30. | 5.15% | 6.89% | 12.65 | 32.18 | 20.18 |
| 5. | 2019. 7. 31. | 3.18% | 1.31% | 2.51 | 0.01 | 0.15 |
| 6. | 2019. 8. 31. | 1.17% | -1.81% | 0.18 | 9.18 | 1.27 |
| 7. | 2019. 9. 30. | 1.40% | 1.72% | 0.04 | 0.25 | -0.10 |
| 8. | 2019. 10. 31. | 3.43% | 2.04% | 3.36 | 0.68 | 1.51 |
| 9. | 2019. 11. 30. | 6.44% | 3.40% | 23.45 | 4.77 | 10.58 |
| 10. | 2019. 12. 31. | -0.11% | 2.86% | 2.92 | 2.69 | -2.80 |
| 11. | 2020. 1. 31. | -3.31% | -0.16% | 24.02 | 1.91 | 6.78 |
| 12. | 2020. 2. 29. | 1.68% | -8.41% | 0.01 | 92.76 | -0.81 |
| 13. | 2020. 3. 31. | -20.05% | -12.51% | 468.43 | 188.57 | 297.20 |
| 14. | 2020. 4. 30. | 2.59% | 12.68% | 1.00 | 131.43 | 11.47 |
| 15. | 2020. 5. 31. | 7.56% | 4.53% | 35.65 | 10.94 | 19.75 |
| 16. | 2020. 6. 30. | -4.17% | 1.84% | 33.21 | 0.38 | -3.57 |
| 17. | 2020. 7. 31. | 2.83% | 5.51% | 1.53 | 18.41 | 5.30 |
| 18. | 2020. 8. 31. | 5.39% | 7.01% | 14.38 | 33.48 | 21.95 |
| 19. | 2020. 9. 30. | 1.57% | -3.92% | 0.00 | 26.45 | 0.12 |
| 20. | 2020. 10. 31. | -8.72% | -2.77% | 106.26 | 15.89 | 41.09 |
| 21. | 2020. 11. 30. | 25.02% | 10.75% | 548.81 | 90.91 | 223.36 |
| 22. | 2020. 12. 31. | 7.53% | 3.71% | 35.20 | 6.21 | 14.79 |
| 23. | 2021. 1. 31. | -6.22% | -1.11% | 61.10 | 5.45 | 18.24 |
| 24. | 2021. 2. 28. | 3.45% | 2.61% | 3.45 | 1.93 | 2.58 |
| 25. | 2021. 3. 31. | 0.24% | 4.24% | 1.82 | 9.14 | -4.08 |
| 26. | 2021. 4. 30. | 7.33% | 5.24% | 32.93 | 16.18 | 23.08 |
| 27. | 2021. 5. 31. | -4.51% | 0.55% | 37.21 | 0.45 | 4.10 |
| 28. | 2021. 6. 30. | -0.18% | 2.22% | 3.14 | 1.00 | -1.77 |
| 29. | 2021. 7. 31. | 2.06% | 2.27% | 0.22 | 1.11 | 0.49 |
| 30. | 2021. 8. 31. | 6.06% | 2.90% | 19.96 | 2.82 | 7.50 |
| 31. | 2021. 9. 30. | -9.27% | -4.76% | 117.97 | 35.72 | 64.92 |
| 32. | 2021. 10. 31. | -0.74% | 6.91% | 5.46 | 32.43 | -13.30 |
| 33. | 2021. 11. 30. | 6.37% | -0.83% | 22.79 | 4.22 | -9.80 |
| 34. | 2021. 12. 31. | 9.39% | 4.36% | 60.87 | 9.87 | 24.51 |
| 35. | 2022. 1. 31. | -5.20% | -5.26% | 46.18 | 41.97 | 44.03 |
| 36. | 2022. 2. 28. | -7.79% | -3.14% | 88.13 | 18.98 | 40.89 |
| 37. | 2022. 3. 31. | -8.35% | 3.58% | 98.88 | 5.56 | -23.44 |
| 38. | 2022. 4. 30. | 1.16% | -8.80% | 0.19 | 100.31 | 4.38 |
| 39. | 2022. 5. 31. | 4.22% | 0.01% | 6.89 | 1.48 | -3.19 |
| 40. | 2022. 6. 30. | -12.14% | -8.39% | 188.71 | 92.39 | 132.04 |
| 41. | 2022. 7. 31. | 9.51% | 9.11% | 62.64 | 62.28 | 62.46 |
| 42. | 2022. 8. 31. | 2.43% | -4.24% | 0.70 | 29.86 | -4.56 |
| 43. | 2022. 9. 30. | -0.37% | -9.34% | 3.85 | 111.50 | 20.72 |
| 44. | 2022. 10. 31. | 16.07% | 7.99% | 209.46 | 45.78 | 97.93 |
| 45. | 2022. 11. 30. | 11.44% | 5.38% | 96.87 | 17.27 | 40.90 |
| 46. | 2022. 12. 31. | -0.56% | -5.90% | 4.64 | 50.65 | 15.34 |
| 47. | 2023. 1. 31. | 2.84% | 6.18% | 1.55 | 24.55 | 6.18 |
| 48. | 2023. 2. 28. | -6.07% | -2.61% | 58.65 | 14.68 | 29.34 |
| 49. | 2023. 3. 31. | 2.30% | 3.51% | 0.50 | 5.22 | 1.61 |
| 50. | 2023. 4. 30. | 0.59% | 1.46% | 1.01 | 0.06 | -0.25 |
| 51. | 2023. 5. 31. | -2.15% | 0.25% | 14.04 | 0.94 | 3.64 |
| 52. | 2023. 6. 30. | 10.42% | 4.71% | 77.88 | 12.21 | 30.83 |
| 53. | 2023. 7. 31. | 2.05% | 4.85% | 0.21 | 13.15 | 1.66 |
| 54. | 2023. 8. 31. | 7.26% | -1.77% | 32.12 | 8.95 | -16.96 |
| 55. | 2023. 9. 30. | -3.89% | -4.87% | 30.09 | 37.11 | 33.42 |
| 56. | 2023. 10. 31. | -0.91% | -2.20% | 6.27 | 11.68 | 8.56 |
| 57. | 2023. 11. 30. | 0.42% | 8.92% | 1.37 | 59.26 | -9.01 |
| 58. | 2023. 12. 31. | 6.47% | 4.42% | 23.78 | 10.26 | 15.62 |
| 59. | 2024. 1. 31. | 1.17% | 1.59% | 0.18 | 0.14 | -0.16 |
| 60. | 2024. 2. 29. | 4.81% | 5.17% | 10.33 | 15.62 | 12.70 |
| 61. | 2024. 3. 31. | 2.30% | 3.10% | 0.50 | 3.54 | 1.33 |
| 62. | 2024. 4. 30. | -7.23% | -4.16% | 77.80 | 28.96 | 47.47 |
| 63. | 2024. 5. 31. | 9.97% | 4.80% | 70.25 | 12.83 | 30.02 |
| 64. | 2024. 6. 30. | 6.79% | 3.47% | 27.00 | 5.05 | 11.68 |
| 65. | 2024. 7. 31. | 2.65% | 1.13% | 1.12 | 0.01 | -0.09 |
| 66. | 2024. 8. 31. | 4.09% | 2.28% | 6.25 | 1.13 | 2.66 |
| 67. | 2024. 9. 30. | 0.23% | 2.02% | 1.86 | 0.64 | -1.09 |
| 68. | 2024. 10. 31. | -3.84% | -0.99% | 29.49 | 4.88 | 12.00 |
| 69. | 2024. 11. 30. | 11.53% | 5.73% | 98.79 | 20.34 | 44.83 |
| 70. | 2024. 12. 31. | -3.88% | -2.50% | 29.98 | 13.83 | 20.36 |
| 71. | 2025. 1. 31. | 3.29% | 2.70% | 2.89 | 2.20 | 2.52 |
| 합계 (Σ): | 3,189.56 | 1,741.16 | 1,580.86 | |||
모두 보기
분산TJX = Σ(RTJX,t–RTJX)2 ÷ (71 – 1)
= 3,189.56 ÷ (71 – 1)
= 45.57
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,741.16 ÷ (71 – 1)
= 24.87
공분산TJX, S&P 500 = Σ(RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,580.86 ÷ (71 – 1)
= 22.58
체계적인 위험 추정 (β)
| 분산TJX | 45.57 |
| 분산S&P 500 | 24.87 |
| 공분산TJX, S&P 500 | 22.58 |
| 상관 계수TJX, S&P 5001 | 0.67 |
| βTJX2 | 0.91 |
| αTJX3 | 0.49% |
계산
1 상관 계수TJX, S&P 500
= 공분산TJX, S&P 500 ÷ (표준 편차TJX × 표준 편차S&P 500)
= 22.58 ÷ (6.75% × 4.99%)
= 0.67
2 βTJX
= 공분산TJX, S&P 500 ÷ 분산S&P 500
= 22.58 ÷ 24.87
= 0.91
3 αTJX
= 평균의TJX – βTJX × 평균의S&P 500
= 1.59% – 0.91 × 1.22%
= 0.49%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.71% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.85% |
| 보통주의 체계적 위험TJX | βTJX | 0.91 |
| TJX 보통주에 대한 예상 수익률3 | E(RTJX) | 13.92% |
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(RTJX) = RF + βTJX [E(RM) – RF]
= 4.71% + 0.91 [14.85% – 4.71%]
= 13.92%