자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 DuPont보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
DuPont de Nemours Inc., 월별 수익률
| DuPont de Nemours Inc. (DD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DD,t1 | 피제수DD,t1 | RDD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $45.16 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $49.24 | 9.03% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $47.98 | $0.42 | -1.71% | 2,067.89 | -1.74% |
| 3. | 2015. 4. 30. | $51.00 | 6.29% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | $64.81 | $0.30 | -1.21% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $64.20 | -0.94% | 3,230.78 | 2.86% | |
| 평균의 (R): | 2.10% | 0.88% | ||||
| 표준 편차: | 20.60% | 3.45% | ||||
| DuPont de Nemours Inc. (DD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DD,t1 | 피제수DD,t1 | RDD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $45.16 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $49.24 | 9.03% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $47.98 | $0.42 | -1.71% | 2,067.89 | -1.74% |
| 3. | 2015. 4. 30. | $51.00 | 6.29% | 2,085.51 | 0.85% | |
| 4. | 2015. 5. 31. | $52.07 | 2.10% | 2,107.39 | 1.05% | |
| 5. | 2015. 6. 30. | $51.17 | $0.42 | -0.92% | 2,063.11 | -2.10% |
| 6. | 2015. 7. 31. | $47.06 | -8.03% | 2,103.84 | 1.97% | |
| 7. | 2015. 8. 31. | $43.76 | -7.01% | 1,972.18 | -6.26% | |
| 8. | 2015. 9. 30. | $42.40 | $0.42 | -2.15% | 1,920.03 | -2.64% |
| 9. | 2015. 10. 31. | $51.67 | 21.86% | 2,079.36 | 8.30% | |
| 10. | 2015. 11. 30. | $52.13 | 0.89% | 2,080.41 | 0.05% | |
| 11. | 2015. 12. 31. | $51.48 | $0.46 | -0.36% | 2,043.94 | -1.75% |
| 12. | 2016. 1. 31. | $42.00 | -18.41% | 1,940.24 | -5.07% | |
| 13. | 2016. 2. 29. | $48.61 | 15.74% | 1,932.23 | -0.41% | |
| 14. | 2016. 3. 31. | $50.86 | $0.46 | 5.57% | 2,059.74 | 6.60% |
| 15. | 2016. 4. 30. | $52.61 | 3.44% | 2,065.30 | 0.27% | |
| 16. | 2016. 5. 31. | $51.36 | -2.38% | 2,096.95 | 1.53% | |
| 17. | 2016. 6. 30. | $49.71 | $0.46 | -2.32% | 2,098.86 | 0.09% |
| 18. | 2016. 7. 31. | $53.67 | 7.97% | 2,173.60 | 3.56% | |
| 19. | 2016. 8. 31. | $53.64 | -0.06% | 2,170.95 | -0.12% | |
| 20. | 2016. 9. 30. | $51.83 | $0.46 | -2.52% | 2,168.27 | -0.12% |
| 21. | 2016. 10. 31. | $53.81 | 3.82% | 2,126.15 | -1.94% | |
| 22. | 2016. 11. 30. | $55.72 | 3.55% | 2,198.81 | 3.42% | |
| 23. | 2016. 12. 31. | $57.22 | $0.46 | 3.52% | 2,238.83 | 1.82% |
| 24. | 2017. 1. 31. | $59.63 | 4.21% | 2,278.87 | 1.79% | |
| 25. | 2017. 2. 28. | $62.26 | 4.41% | 2,363.64 | 3.72% | |
| 26. | 2017. 3. 31. | $63.54 | $0.46 | 2.79% | 2,362.72 | -0.04% |
| 27. | 2017. 4. 30. | $62.80 | -1.16% | 2,384.20 | 0.91% | |
| 28. | 2017. 5. 31. | $61.96 | -1.34% | 2,411.80 | 1.16% | |
| 29. | 2017. 6. 30. | $63.07 | $0.46 | 2.53% | 2,423.41 | 0.48% |
| 30. | 2017. 7. 31. | $64.24 | $0.46 | 2.58% | 2,470.30 | 1.93% |
| 31. | 2017. 8. 31. | $66.65 | 3.75% | 2,471.65 | 0.05% | |
| 32. | 2017. 9. 30. | $69.23 | 3.87% | 2,519.36 | 1.93% | |
| 33. | 2017. 10. 31. | $72.31 | 4.45% | 2,575.26 | 2.22% | |
| 34. | 2017. 11. 30. | $71.96 | $0.38 | 0.04% | 2,647.58 | 2.81% |
| 35. | 2017. 12. 31. | $71.22 | -1.03% | 2,673.61 | 0.98% | |
| 36. | 2018. 1. 31. | $75.58 | 6.12% | 2,823.81 | 5.62% | |
| 37. | 2018. 2. 28. | $70.30 | $0.38 | -6.48% | 2,713.83 | -3.89% |
| 38. | 2018. 3. 31. | $63.71 | -9.37% | 2,640.87 | -2.69% | |
| 39. | 2018. 4. 30. | $63.24 | -0.74% | 2,648.05 | 0.27% | |
| 40. | 2018. 5. 31. | $64.11 | $0.38 | 1.98% | 2,705.27 | 2.16% |
| 41. | 2018. 6. 30. | $65.92 | 2.82% | 2,718.37 | 0.48% | |
| 42. | 2018. 7. 31. | $68.77 | 4.32% | 2,816.29 | 3.60% | |
| 43. | 2018. 8. 31. | $70.13 | $0.38 | 2.53% | 2,901.52 | 3.03% |
| 44. | 2018. 9. 30. | $64.31 | -8.30% | 2,913.98 | 0.43% | |
| 45. | 2018. 10. 31. | $53.92 | -16.16% | 2,711.74 | -6.94% | |
| 46. | 2018. 11. 30. | $57.85 | $0.38 | 7.99% | 2,760.17 | 1.79% |
| 47. | 2018. 12. 31. | $53.48 | -7.55% | 2,506.85 | -9.18% | |
| 48. | 2019. 1. 31. | $53.81 | 0.62% | 2,704.10 | 7.87% | |
| 49. | 2019. 2. 28. | $53.23 | $0.38 | -0.37% | 2,784.49 | 2.97% |
| 50. | 2019. 3. 31. | $53.31 | 0.15% | 2,834.40 | 1.79% | |
| 51. | 2019. 4. 30. | $38.45 | -27.87% | 2,945.83 | 3.93% | |
| 52. | 2019. 5. 31. | $30.52 | -20.62% | 2,752.06 | -6.58% | |
| 53. | 2019. 6. 30. | $75.07 | 145.97% | 2,941.76 | 6.89% | |
| 54. | 2019. 7. 31. | $72.16 | $0.30 | -3.48% | 2,980.38 | 1.31% |
| 55. | 2019. 8. 31. | $67.93 | -5.86% | 2,926.46 | -1.81% | |
| 56. | 2019. 9. 30. | $71.31 | 4.98% | 2,976.74 | 1.72% | |
| 57. | 2019. 10. 31. | $65.91 | -7.57% | 3,037.56 | 2.04% | |
| 58. | 2019. 11. 30. | $64.81 | $0.30 | -1.21% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $64.20 | -0.94% | 3,230.78 | 2.86% | |
| 평균의 (R): | 2.10% | 0.88% | ||||
| 표준 편차: | 20.60% | 3.45% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 DD의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
DuPont de Nemours Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RDD,t | RS&P 500,t | (RDD,t–RDD)2 | (RS&P 500,t–RS&P 500)2 | (RDD,t–RDD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 9.03% | 5.49% | 48.07 | 21.25 | 31.96 |
| 2. | 2015. 3. 31. | -1.71% | -1.74% | 14.50 | 6.86 | 9.97 |
| 3. | 2015. 4. 30. | 6.29% | 0.85% | 17.58 | 0.00 | -0.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | -1.21% | 3.40% | 10.99 | 6.38 | -8.37 |
| 59. | 2019. 12. 31. | -0.94% | 2.86% | 9.26 | 3.92 | -6.02 |
| 합계 (Σ): | 24,624.11 | 688.77 | 1,707.82 | |||
| t | 날짜 | RDD,t | RS&P 500,t | (RDD,t–RDD)2 | (RS&P 500,t–RS&P 500)2 | (RDD,t–RDD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 9.03% | 5.49% | 48.07 | 21.25 | 31.96 |
| 2. | 2015. 3. 31. | -1.71% | -1.74% | 14.50 | 6.86 | 9.97 |
| 3. | 2015. 4. 30. | 6.29% | 0.85% | 17.58 | 0.00 | -0.11 |
| 4. | 2015. 5. 31. | 2.10% | 1.05% | 0.00 | 0.03 | 0.00 |
| 5. | 2015. 6. 30. | -0.92% | -2.10% | 9.14 | 8.88 | 9.01 |
| 6. | 2015. 7. 31. | -8.03% | 1.97% | 102.69 | 1.20 | -11.10 |
| 7. | 2015. 8. 31. | -7.01% | -6.26% | 83.06 | 50.94 | 65.05 |
| 8. | 2015. 9. 30. | -2.15% | -2.64% | 18.06 | 12.41 | 14.97 |
| 9. | 2015. 10. 31. | 21.86% | 8.30% | 390.53 | 55.04 | 146.62 |
| 10. | 2015. 11. 30. | 0.89% | 0.05% | 1.47 | 0.69 | 1.00 |
| 11. | 2015. 12. 31. | -0.36% | -1.75% | 6.08 | 6.93 | 6.49 |
| 12. | 2016. 1. 31. | -18.41% | -5.07% | 420.92 | 35.43 | 122.13 |
| 13. | 2016. 2. 29. | 15.74% | -0.41% | 185.96 | 1.67 | -17.62 |
| 14. | 2016. 3. 31. | 5.57% | 6.60% | 12.07 | 32.72 | 19.87 |
| 15. | 2016. 4. 30. | 3.44% | 0.27% | 1.79 | 0.37 | -0.82 |
| 16. | 2016. 5. 31. | -2.38% | 1.53% | 20.05 | 0.43 | -2.93 |
| 17. | 2016. 6. 30. | -2.32% | 0.09% | 19.52 | 0.62 | 3.48 |
| 18. | 2016. 7. 31. | 7.97% | 3.56% | 34.40 | 7.19 | 15.73 |
| 19. | 2016. 8. 31. | -0.06% | -0.12% | 4.65 | 1.00 | 2.16 |
| 20. | 2016. 9. 30. | -2.52% | -0.12% | 21.33 | 1.01 | 4.63 |
| 21. | 2016. 10. 31. | 3.82% | -1.94% | 2.95 | 7.96 | -4.85 |
| 22. | 2016. 11. 30. | 3.55% | 3.42% | 2.10 | 6.44 | 3.68 |
| 23. | 2016. 12. 31. | 3.52% | 1.82% | 2.01 | 0.89 | 1.33 |
| 24. | 2017. 1. 31. | 4.21% | 1.79% | 4.45 | 0.83 | 1.92 |
| 25. | 2017. 2. 28. | 4.41% | 3.72% | 5.33 | 8.07 | 6.56 |
| 26. | 2017. 3. 31. | 2.79% | -0.04% | 0.48 | 0.84 | -0.64 |
| 27. | 2017. 4. 30. | -1.16% | 0.91% | 10.67 | 0.00 | -0.10 |
| 28. | 2017. 5. 31. | -1.34% | 1.16% | 11.83 | 0.08 | -0.96 |
| 29. | 2017. 6. 30. | 2.53% | 0.48% | 0.19 | 0.16 | -0.17 |
| 30. | 2017. 7. 31. | 2.58% | 1.93% | 0.23 | 1.11 | 0.51 |
| 31. | 2017. 8. 31. | 3.75% | 0.05% | 2.72 | 0.68 | -1.36 |
| 32. | 2017. 9. 30. | 3.87% | 1.93% | 3.13 | 1.10 | 1.86 |
| 33. | 2017. 10. 31. | 4.45% | 2.22% | 5.51 | 1.79 | 3.15 |
| 34. | 2017. 11. 30. | 0.04% | 2.81% | 4.24 | 3.72 | -3.97 |
| 35. | 2017. 12. 31. | -1.03% | 0.98% | 9.80 | 0.01 | -0.33 |
| 36. | 2018. 1. 31. | 6.12% | 5.62% | 16.16 | 22.46 | 19.05 |
| 37. | 2018. 2. 28. | -6.48% | -3.89% | 73.69 | 22.79 | 40.98 |
| 38. | 2018. 3. 31. | -9.37% | -2.69% | 131.69 | 12.73 | 40.94 |
| 39. | 2018. 4. 30. | -0.74% | 0.27% | 8.06 | 0.37 | 1.72 |
| 40. | 2018. 5. 31. | 1.98% | 2.16% | 0.02 | 1.64 | -0.16 |
| 41. | 2018. 6. 30. | 2.82% | 0.48% | 0.52 | 0.16 | -0.29 |
| 42. | 2018. 7. 31. | 4.32% | 3.60% | 4.94 | 7.41 | 6.05 |
| 43. | 2018. 8. 31. | 2.53% | 3.03% | 0.18 | 4.61 | 0.92 |
| 44. | 2018. 9. 30. | -8.30% | 0.43% | 108.17 | 0.20 | 4.68 |
| 45. | 2018. 10. 31. | -16.16% | -6.94% | 333.34 | 61.14 | 142.76 |
| 46. | 2018. 11. 30. | 7.99% | 1.79% | 34.72 | 0.82 | 5.34 |
| 47. | 2018. 12. 31. | -7.55% | -9.18% | 93.23 | 101.14 | 97.10 |
| 48. | 2019. 1. 31. | 0.62% | 7.87% | 2.20 | 48.85 | -10.37 |
| 49. | 2019. 2. 28. | -0.37% | 2.97% | 6.12 | 4.38 | -5.18 |
| 50. | 2019. 3. 31. | 0.15% | 1.79% | 3.81 | 0.83 | -1.78 |
| 51. | 2019. 4. 30. | -27.87% | 3.93% | 898.56 | 9.32 | -91.49 |
| 52. | 2019. 5. 31. | -20.62% | -6.58% | 516.45 | 55.61 | 169.46 |
| 53. | 2019. 6. 30. | 145.97% | 6.89% | 20,698.14 | 36.17 | 865.21 |
| 54. | 2019. 7. 31. | -3.48% | 1.31% | 31.12 | 0.19 | -2.42 |
| 55. | 2019. 8. 31. | -5.86% | -1.81% | 63.41 | 7.23 | 21.41 |
| 56. | 2019. 9. 30. | 4.98% | 1.72% | 8.26 | 0.70 | 2.41 |
| 57. | 2019. 10. 31. | -7.57% | 2.04% | 93.59 | 1.36 | -11.26 |
| 58. | 2019. 11. 30. | -1.21% | 3.40% | 10.99 | 6.38 | -8.37 |
| 59. | 2019. 12. 31. | -0.94% | 2.86% | 9.26 | 3.92 | -6.02 |
| 합계 (Σ): | 24,624.11 | 688.77 | 1,707.82 | |||
모두 보기
분산DD = Σ(RDD,t–RDD)2 ÷ (59 – 1)
= 24,624.11 ÷ (59 – 1)
= 424.55
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
공분산DD, S&P 500 = Σ(RDD,t–RDD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,707.82 ÷ (59 – 1)
= 29.45
체계적인 위험 추정 (β)
| 분산DD | 424.55 |
| 분산S&P 500 | 11.88 |
| 공분산DD, S&P 500 | 29.45 |
| 상관 계수DD, S&P 5001 | 0.41 |
| βDD2 | 2.48 |
| αDD3 | -0.08% |
계산
1 상관 계수DD, S&P 500
= 공분산DD, S&P 500 ÷ (표준 편차DD × 표준 편차S&P 500)
= 29.45 ÷ (20.60% × 3.45%)
= 0.41
2 βDD
= 공분산DD, S&P 500 ÷ 분산S&P 500
= 29.45 ÷ 11.88
= 2.48
3 αDD
= 평균의DD – βDD × 평균의S&P 500
= 2.10% – 2.48 × 0.88%
= -0.08%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.68% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.78% |
| 보통주의 체계적 위험DuPont | βDD | 2.48 |
| 듀폰 보통주 예상 수익률3 | E(RDD) | 27.25% |
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(RDD) = RF + βDD [E(RM) – RF]
= 4.68% + 2.48 [13.78% – 4.68%]
= 27.25%