자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Eaton보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Eaton Corp. plc, 월별 수익률
| Eaton Corp. plc (ETN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ETN,t1 | 피제수ETN,t1 | RETN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $76.25 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $79.77 | 4.62% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $80.56 | $0.71 | 1.88% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $82.82 | 2.81% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $227.69 | $0.86 | 9.93% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $240.82 | 5.77% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.42% | 1.11% | ||||
| 표준 편차: | 6.94% | 5.31% | ||||
| Eaton Corp. plc (ETN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ETN,t1 | 피제수ETN,t1 | RETN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $76.25 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $79.77 | 4.62% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $80.56 | $0.71 | 1.88% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $82.82 | 2.81% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $74.49 | $0.71 | -9.20% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $83.28 | 11.80% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $82.19 | -1.31% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $80.72 | $0.71 | -0.92% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $83.15 | 3.01% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $87.11 | $0.71 | 5.62% | 3,037.56 | 2.04% |
| 10. | 2019. 11. 30. | $92.50 | 6.19% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $94.72 | 2.40% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $94.47 | -0.26% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $90.72 | -3.97% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $77.69 | $0.73 | -13.56% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $83.50 | 7.48% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $84.90 | $0.73 | 2.55% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $87.48 | 3.04% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $93.13 | 6.46% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $102.10 | $0.73 | 10.42% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $102.03 | -0.07% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $103.79 | 1.72% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $121.11 | $0.73 | 17.39% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $120.14 | -0.80% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $117.70 | -2.03% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $130.19 | 10.61% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $138.28 | $0.76 | 6.80% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $142.93 | 3.36% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $145.25 | $0.76 | 2.15% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $148.18 | 2.02% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $158.05 | 6.66% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $168.36 | $0.76 | 7.00% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $149.31 | -11.32% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $164.76 | 10.35% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $162.06 | $0.76 | -1.18% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $172.82 | 6.64% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $158.43 | -8.33% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $154.29 | -2.61% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $151.76 | $0.81 | -1.11% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $145.02 | -4.44% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $138.60 | $0.81 | -3.87% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $125.99 | -9.10% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $148.39 | 17.78% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $136.64 | $0.81 | -7.37% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $133.36 | -2.40% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $150.07 | 12.53% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $163.45 | $0.81 | 9.46% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $156.95 | -3.98% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $162.21 | 3.35% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $174.93 | 7.84% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $171.34 | $0.86 | -1.56% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $167.12 | -2.46% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $175.90 | $0.86 | 5.77% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $201.10 | 14.33% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $205.32 | 2.10% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $230.37 | $0.86 | 12.62% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $213.28 | -7.42% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $207.91 | -2.52% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $227.69 | $0.86 | 9.93% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $240.82 | 5.77% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.42% | 1.11% | ||||
| 표준 편차: | 6.94% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 ETN의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Eaton Corp. plc, 수익률의 분산 및 공분산 계산
| t | 날짜 | RETN,t | RS&P 500,t | (RETN,t–RETN)2 | (RS&P 500,t–RS&P 500)2 | (RETN,t–RETN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 4.62% | 2.97% | 4.83 | 3.49 | 4.11 |
| 2. | 2019. 3. 31. | 1.88% | 1.79% | 0.29 | 0.47 | -0.37 |
| 3. | 2019. 4. 30. | 2.81% | 3.93% | 0.15 | 7.98 | 1.10 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 9.93% | 8.92% | 56.40 | 61.03 | 58.67 |
| 59. | 2023. 12. 31. | 5.77% | 4.42% | 11.22 | 11.00 | 11.11 |
| 합계 (Σ): | 2,793.38 | 1,634.30 | 1,689.89 | |||
| t | 날짜 | RETN,t | RS&P 500,t | (RETN,t–RETN)2 | (RS&P 500,t–RS&P 500)2 | (RETN,t–RETN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 4.62% | 2.97% | 4.83 | 3.49 | 4.11 |
| 2. | 2019. 3. 31. | 1.88% | 1.79% | 0.29 | 0.47 | -0.37 |
| 3. | 2019. 4. 30. | 2.81% | 3.93% | 0.15 | 7.98 | 1.10 |
| 4. | 2019. 5. 31. | -9.20% | -6.58% | 134.99 | 59.04 | 89.27 |
| 5. | 2019. 6. 30. | 11.80% | 6.89% | 88.03 | 33.49 | 54.30 |
| 6. | 2019. 7. 31. | -1.31% | 1.31% | 13.89 | 0.04 | -0.77 |
| 7. | 2019. 8. 31. | -0.92% | -1.81% | 11.17 | 8.50 | 9.74 |
| 8. | 2019. 9. 30. | 3.01% | 1.72% | 0.35 | 0.37 | 0.36 |
| 9. | 2019. 10. 31. | 5.62% | 2.04% | 10.23 | 0.88 | 3.00 |
| 10. | 2019. 11. 30. | 6.19% | 3.40% | 14.21 | 5.28 | 8.67 |
| 11. | 2019. 12. 31. | 2.40% | 2.86% | 0.00 | 3.07 | -0.03 |
| 12. | 2020. 1. 31. | -0.26% | -0.16% | 7.19 | 1.61 | 3.40 |
| 13. | 2020. 2. 29. | -3.97% | -8.41% | 40.80 | 90.57 | 60.79 |
| 14. | 2020. 3. 31. | -13.56% | -12.51% | 255.23 | 185.44 | 217.56 |
| 15. | 2020. 4. 30. | 7.48% | 12.68% | 25.61 | 134.06 | 58.60 |
| 16. | 2020. 5. 31. | 2.55% | 4.53% | 0.02 | 11.71 | 0.46 |
| 17. | 2020. 6. 30. | 3.04% | 1.84% | 0.39 | 0.54 | 0.46 |
| 18. | 2020. 7. 31. | 6.46% | 5.51% | 16.33 | 19.40 | 17.80 |
| 19. | 2020. 8. 31. | 10.42% | 7.01% | 63.97 | 34.82 | 47.19 |
| 20. | 2020. 9. 30. | -0.07% | -3.92% | 6.18 | 25.29 | 12.50 |
| 21. | 2020. 10. 31. | 1.72% | -2.77% | 0.48 | 15.00 | 2.68 |
| 22. | 2020. 11. 30. | 17.39% | 10.75% | 224.20 | 93.10 | 144.47 |
| 23. | 2020. 12. 31. | -0.80% | 3.71% | 10.36 | 6.79 | -8.39 |
| 24. | 2021. 1. 31. | -2.03% | -1.11% | 19.79 | 4.93 | 9.87 |
| 25. | 2021. 2. 28. | 10.61% | 2.61% | 67.14 | 2.26 | 12.32 |
| 26. | 2021. 3. 31. | 6.80% | 4.24% | 19.18 | 9.85 | 13.74 |
| 27. | 2021. 4. 30. | 3.36% | 5.24% | 0.89 | 17.11 | 3.91 |
| 28. | 2021. 5. 31. | 2.15% | 0.55% | 0.07 | 0.31 | 0.15 |
| 29. | 2021. 6. 30. | 2.02% | 2.22% | 0.16 | 1.24 | -0.45 |
| 30. | 2021. 7. 31. | 6.66% | 2.27% | 18.00 | 1.37 | 4.96 |
| 31. | 2021. 8. 31. | 7.00% | 2.90% | 21.04 | 3.22 | 8.22 |
| 32. | 2021. 9. 30. | -11.32% | -4.76% | 188.59 | 34.37 | 80.51 |
| 33. | 2021. 10. 31. | 10.35% | 6.91% | 62.88 | 33.74 | 46.06 |
| 34. | 2021. 11. 30. | -1.18% | -0.83% | 12.93 | 3.76 | 6.97 |
| 35. | 2021. 12. 31. | 6.64% | 4.36% | 17.82 | 10.60 | 13.74 |
| 36. | 2022. 1. 31. | -8.33% | -5.26% | 115.44 | 40.51 | 68.38 |
| 37. | 2022. 2. 28. | -2.61% | -3.14% | 25.31 | 17.99 | 21.34 |
| 38. | 2022. 3. 31. | -1.11% | 3.58% | 12.48 | 6.11 | -8.73 |
| 39. | 2022. 4. 30. | -4.44% | -8.80% | 47.04 | 98.04 | 67.91 |
| 40. | 2022. 5. 31. | -3.87% | 0.01% | 39.52 | 1.21 | 6.92 |
| 41. | 2022. 6. 30. | -9.10% | -8.39% | 132.61 | 90.21 | 109.38 |
| 42. | 2022. 7. 31. | 17.78% | 9.11% | 235.97 | 64.09 | 122.98 |
| 43. | 2022. 8. 31. | -7.37% | -4.24% | 95.85 | 28.62 | 52.38 |
| 44. | 2022. 9. 30. | -2.40% | -9.34% | 23.21 | 109.11 | 50.33 |
| 45. | 2022. 10. 31. | 12.53% | 7.99% | 102.26 | 47.34 | 69.58 |
| 46. | 2022. 11. 30. | 9.46% | 5.38% | 49.53 | 18.23 | 30.05 |
| 47. | 2022. 12. 31. | -3.98% | -5.90% | 40.89 | 49.04 | 44.78 |
| 48. | 2023. 1. 31. | 3.35% | 6.18% | 0.87 | 25.70 | 4.73 |
| 49. | 2023. 2. 28. | 7.84% | -2.61% | 29.42 | 13.82 | -20.16 |
| 50. | 2023. 3. 31. | -1.56% | 3.51% | 15.83 | 5.76 | -9.55 |
| 51. | 2023. 4. 30. | -2.46% | 1.46% | 23.82 | 0.13 | -1.75 |
| 52. | 2023. 5. 31. | 5.77% | 0.25% | 11.23 | 0.74 | -2.87 |
| 53. | 2023. 6. 30. | 14.33% | 4.71% | 141.82 | 13.02 | 42.97 |
| 54. | 2023. 7. 31. | 2.10% | 4.85% | 0.10 | 13.99 | -1.19 |
| 55. | 2023. 8. 31. | 12.62% | -1.77% | 104.07 | 8.28 | -29.36 |
| 56. | 2023. 9. 30. | -7.42% | -4.87% | 96.75 | 35.73 | 58.80 |
| 57. | 2023. 10. 31. | -2.52% | -2.20% | 24.36 | 10.92 | 16.31 |
| 58. | 2023. 11. 30. | 9.93% | 8.92% | 56.40 | 61.03 | 58.67 |
| 59. | 2023. 12. 31. | 5.77% | 4.42% | 11.22 | 11.00 | 11.11 |
| 합계 (Σ): | 2,793.38 | 1,634.30 | 1,689.89 | |||
모두 보기
분산ETN = Σ(RETN,t–RETN)2 ÷ (59 – 1)
= 2,793.38 ÷ (59 – 1)
= 48.16
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산ETN, S&P 500 = Σ(RETN,t–RETN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,689.89 ÷ (59 – 1)
= 29.14
체계적인 위험 추정 (β)
| 분산ETN | 48.16 |
| 분산S&P 500 | 28.18 |
| 공분산ETN, S&P 500 | 29.14 |
| 상관 계수ETN, S&P 5001 | 0.79 |
| βETN2 | 1.03 |
| αETN3 | 1.27% |
계산
1 상관 계수ETN, S&P 500
= 공분산ETN, S&P 500 ÷ (표준 편차ETN × 표준 편차S&P 500)
= 29.14 ÷ (6.94% × 5.31%)
= 0.79
2 βETN
= 공분산ETN, S&P 500 ÷ 분산S&P 500
= 29.14 ÷ 28.18
= 1.03
3 αETN
= 평균의ETN – βETN × 평균의S&P 500
= 2.42% – 1.03 × 1.11%
= 1.27%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.65% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Eaton | βETN | 1.03 |
| Eaton 보통주에 대한 예상 수익률3 | E(RETN) | 14.10% |
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(RETN) = RF + βETN [E(RM) – RF]
= 4.65% + 1.03 [13.79% – 4.65%]
= 14.10%