자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Northrop Grumman보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Northrop Grumman Corp., 월별 수익률
| Northrop Grumman Corp. (NOC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NOC,t1 | 피제수NOC,t1 | RNOC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $340.53 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $350.04 | 2.79% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $349.12 | $1.10 | 0.05% | 2,640.87 | -2.69% |
| 3. | 2018. 4. 30. | $322.04 | -7.76% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $533.29 | $1.73 | -2.55% | 4,080.11 | 5.38% |
| 59. | 2022. 12. 31. | $545.61 | 2.31% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.17% | 0.67% | ||||
| 표준 편차: | 6.86% | 5.40% | ||||
| Northrop Grumman Corp. (NOC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NOC,t1 | 피제수NOC,t1 | RNOC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $340.53 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $350.04 | 2.79% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $349.12 | $1.10 | 0.05% | 2,640.87 | -2.69% |
| 3. | 2018. 4. 30. | $322.04 | -7.76% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $327.25 | 1.62% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $307.70 | $1.20 | -5.61% | 2,718.37 | 0.48% |
| 6. | 2018. 7. 31. | $300.49 | -2.34% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $298.49 | $1.20 | -0.27% | 2,901.52 | 3.03% |
| 8. | 2018. 9. 30. | $317.37 | 6.33% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $261.95 | -17.46% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $259.88 | $1.20 | -0.33% | 2,760.17 | 1.79% |
| 11. | 2018. 12. 31. | $244.90 | -5.76% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $275.55 | 12.52% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $289.96 | $1.20 | 5.67% | 2,784.49 | 2.97% |
| 14. | 2019. 3. 31. | $269.60 | -7.02% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $289.91 | 7.53% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $303.25 | $1.32 | 5.06% | 2,752.06 | -6.58% |
| 17. | 2019. 6. 30. | $323.11 | 6.55% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $345.57 | 6.95% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $367.87 | 6.45% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $374.79 | $1.32 | 2.24% | 2,976.74 | 1.72% |
| 21. | 2019. 10. 31. | $352.48 | -5.95% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $351.77 | $1.32 | 0.17% | 3,140.98 | 3.40% |
| 23. | 2019. 12. 31. | $343.97 | -2.22% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $374.57 | 8.90% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $328.84 | $1.32 | -11.86% | 2,954.22 | -8.41% |
| 26. | 2020. 3. 31. | $302.55 | -7.99% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $330.67 | 9.29% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $335.20 | $1.45 | 1.81% | 3,044.31 | 4.53% |
| 29. | 2020. 6. 30. | $307.44 | -8.28% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $325.01 | 5.71% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $342.61 | $1.45 | 5.86% | 3,500.31 | 7.01% |
| 32. | 2020. 9. 30. | $315.49 | -7.92% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $289.82 | -8.14% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $302.26 | $1.45 | 4.79% | 3,621.63 | 10.75% |
| 35. | 2020. 12. 31. | $304.72 | 0.81% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $286.61 | -5.94% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $291.66 | $1.45 | 2.27% | 3,811.15 | 2.61% |
| 38. | 2021. 3. 31. | $323.64 | 10.96% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $354.44 | 9.52% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $365.87 | $1.57 | 3.67% | 4,204.11 | 0.55% |
| 41. | 2021. 6. 30. | $363.43 | -0.67% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $363.02 | -0.11% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $367.70 | $1.57 | 1.72% | 4,522.68 | 2.90% |
| 44. | 2021. 9. 30. | $360.15 | -2.05% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $357.22 | -0.81% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $348.80 | $1.57 | -1.92% | 4,567.00 | -0.83% |
| 47. | 2021. 12. 31. | $387.07 | 10.97% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $369.90 | -4.44% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $442.14 | $1.57 | 19.95% | 4,373.94 | -3.14% |
| 50. | 2022. 3. 31. | $447.22 | 1.15% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $439.40 | -1.75% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $467.97 | $1.73 | 6.90% | 4,132.15 | 0.01% |
| 53. | 2022. 6. 30. | $478.57 | 2.27% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $478.90 | 0.07% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $477.99 | $1.73 | 0.17% | 3,955.00 | -4.24% |
| 56. | 2022. 9. 30. | $470.32 | -1.60% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $549.01 | 16.73% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $533.29 | $1.73 | -2.55% | 4,080.11 | 5.38% |
| 59. | 2022. 12. 31. | $545.61 | 2.31% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.17% | 0.67% | ||||
| 표준 편차: | 6.86% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 NOC의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Northrop Grumman Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RNOC,t | RS&P 500,t | (RNOC,t–RNOC)2 | (RS&P 500,t–RS&P 500)2 | (RNOC,t–RNOC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 2.79% | -3.89% | 2.63 | 20.81 | -7.40 |
| 2. | 2018. 3. 31. | 0.05% | -2.69% | 1.25 | 11.26 | 3.75 |
| 3. | 2018. 4. 30. | -7.76% | 0.27% | 79.68 | 0.16 | 3.52 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | -2.55% | 5.38% | 13.82 | 22.17 | -17.51 |
| 59. | 2022. 12. 31. | 2.31% | -5.90% | 1.30 | 43.08 | -7.49 |
| 합계 (Σ): | 2,731.47 | 1,691.48 | 976.36 | |||
| t | 날짜 | RNOC,t | RS&P 500,t | (RNOC,t–RNOC)2 | (RS&P 500,t–RS&P 500)2 | (RNOC,t–RNOC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 2.79% | -3.89% | 2.63 | 20.81 | -7.40 |
| 2. | 2018. 3. 31. | 0.05% | -2.69% | 1.25 | 11.26 | 3.75 |
| 3. | 2018. 4. 30. | -7.76% | 0.27% | 79.68 | 0.16 | 3.52 |
| 4. | 2018. 5. 31. | 1.62% | 2.16% | 0.20 | 2.23 | 0.67 |
| 5. | 2018. 6. 30. | -5.61% | 0.48% | 45.93 | 0.03 | 1.24 |
| 6. | 2018. 7. 31. | -2.34% | 3.60% | 12.34 | 8.62 | -10.31 |
| 7. | 2018. 8. 31. | -0.27% | 3.03% | 2.06 | 5.57 | -3.39 |
| 8. | 2018. 9. 30. | 6.33% | 0.43% | 26.58 | 0.06 | -1.22 |
| 9. | 2018. 10. 31. | -17.46% | -6.94% | 347.15 | 57.87 | 141.73 |
| 10. | 2018. 11. 30. | -0.33% | 1.79% | 2.26 | 1.25 | -1.68 |
| 11. | 2018. 12. 31. | -5.76% | -9.18% | 48.08 | 96.91 | 68.26 |
| 12. | 2019. 1. 31. | 12.52% | 7.87% | 128.72 | 51.87 | 81.71 |
| 13. | 2019. 2. 28. | 5.67% | 2.97% | 20.21 | 5.32 | 10.37 |
| 14. | 2019. 3. 31. | -7.02% | 1.79% | 67.10 | 1.27 | -9.22 |
| 15. | 2019. 4. 30. | 7.53% | 3.93% | 40.50 | 10.66 | 20.78 |
| 16. | 2019. 5. 31. | 5.06% | -6.58% | 15.11 | 52.48 | -28.16 |
| 17. | 2019. 6. 30. | 6.55% | 6.89% | 28.94 | 38.77 | 33.49 |
| 18. | 2019. 7. 31. | 6.95% | 1.31% | 33.43 | 0.42 | 3.74 |
| 19. | 2019. 8. 31. | 6.45% | -1.81% | 27.92 | 6.13 | -13.08 |
| 20. | 2019. 9. 30. | 2.24% | 1.72% | 1.15 | 1.11 | 1.13 |
| 21. | 2019. 10. 31. | -5.95% | 2.04% | 50.73 | 1.89 | -9.80 |
| 22. | 2019. 11. 30. | 0.17% | 3.40% | 0.99 | 7.50 | -2.73 |
| 23. | 2019. 12. 31. | -2.22% | 2.86% | 11.47 | 4.81 | -7.43 |
| 24. | 2020. 1. 31. | 8.90% | -0.16% | 59.70 | 0.69 | -6.41 |
| 25. | 2020. 2. 29. | -11.86% | -8.41% | 169.67 | 82.40 | 118.25 |
| 26. | 2020. 3. 31. | -7.99% | -12.51% | 83.99 | 173.67 | 120.77 |
| 27. | 2020. 4. 30. | 9.29% | 12.68% | 66.01 | 144.43 | 97.64 |
| 28. | 2020. 5. 31. | 1.81% | 4.53% | 0.41 | 14.91 | 2.47 |
| 29. | 2020. 6. 30. | -8.28% | 1.84% | 89.33 | 1.37 | -11.08 |
| 30. | 2020. 7. 31. | 5.71% | 5.51% | 20.66 | 23.46 | 22.02 |
| 31. | 2020. 8. 31. | 5.86% | 7.01% | 22.01 | 40.19 | 29.74 |
| 32. | 2020. 9. 30. | -7.92% | -3.92% | 82.54 | 21.06 | 41.70 |
| 33. | 2020. 10. 31. | -8.14% | -2.77% | 86.61 | 11.79 | 31.95 |
| 34. | 2020. 11. 30. | 4.79% | 10.75% | 13.13 | 101.77 | 36.55 |
| 35. | 2020. 12. 31. | 0.81% | 3.71% | 0.13 | 9.28 | -1.08 |
| 36. | 2021. 1. 31. | -5.94% | -1.11% | 50.59 | 3.17 | 12.66 |
| 37. | 2021. 2. 28. | 2.27% | 2.61% | 1.21 | 3.77 | 2.13 |
| 38. | 2021. 3. 31. | 10.96% | 4.24% | 95.95 | 12.80 | 35.04 |
| 39. | 2021. 4. 30. | 9.52% | 5.24% | 69.67 | 20.94 | 38.20 |
| 40. | 2021. 5. 31. | 3.67% | 0.55% | 6.24 | 0.01 | -0.29 |
| 41. | 2021. 6. 30. | -0.67% | 2.22% | 3.37 | 2.42 | -2.86 |
| 42. | 2021. 7. 31. | -0.11% | 2.27% | 1.64 | 2.59 | -2.06 |
| 43. | 2021. 8. 31. | 1.72% | 2.90% | 0.30 | 4.98 | 1.23 |
| 44. | 2021. 9. 30. | -2.05% | -4.76% | 10.39 | 29.42 | 17.48 |
| 45. | 2021. 10. 31. | -0.81% | 6.91% | 3.93 | 39.03 | -12.39 |
| 46. | 2021. 11. 30. | -1.92% | -0.83% | 9.53 | 2.25 | 4.63 |
| 47. | 2021. 12. 31. | 10.97% | 4.36% | 96.08 | 13.65 | 36.22 |
| 48. | 2022. 1. 31. | -4.44% | -5.26% | 31.42 | 35.11 | 33.21 |
| 49. | 2022. 2. 28. | 19.95% | -3.14% | 352.85 | 14.46 | -71.43 |
| 50. | 2022. 3. 31. | 1.15% | 3.58% | 0.00 | 8.47 | -0.06 |
| 51. | 2022. 4. 30. | -1.75% | -8.80% | 8.52 | 89.54 | 27.61 |
| 52. | 2022. 5. 31. | 6.90% | 0.01% | 32.79 | 0.44 | -3.79 |
| 53. | 2022. 6. 30. | 2.27% | -8.39% | 1.20 | 82.06 | -9.92 |
| 54. | 2022. 7. 31. | 0.07% | 9.11% | 1.21 | 71.32 | -9.30 |
| 55. | 2022. 8. 31. | 0.17% | -4.24% | 1.00 | 24.11 | 4.90 |
| 56. | 2022. 9. 30. | -1.60% | -9.34% | 7.70 | 100.12 | 27.76 |
| 57. | 2022. 10. 31. | 16.73% | 7.99% | 242.16 | 53.58 | 113.91 |
| 58. | 2022. 11. 30. | -2.55% | 5.38% | 13.82 | 22.17 | -17.51 |
| 59. | 2022. 12. 31. | 2.31% | -5.90% | 1.30 | 43.08 | -7.49 |
| 합계 (Σ): | 2,731.47 | 1,691.48 | 976.36 | |||
모두 보기
분산NOC = Σ(RNOC,t–RNOC)2 ÷ (59 – 1)
= 2,731.47 ÷ (59 – 1)
= 47.09
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산NOC, S&P 500 = Σ(RNOC,t–RNOC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 976.36 ÷ (59 – 1)
= 16.83
체계적인 위험 추정 (β)
| 분산NOC | 47.09 |
| 분산S&P 500 | 29.16 |
| 공분산NOC, S&P 500 | 16.83 |
| 상관 계수NOC, S&P 5001 | 0.45 |
| βNOC2 | 0.58 |
| αNOC3 | 0.78% |
계산
1 상관 계수NOC, S&P 500
= 공분산NOC, S&P 500 ÷ (표준 편차NOC × 표준 편차S&P 500)
= 16.83 ÷ (6.86% × 5.40%)
= 0.45
2 βNOC
= 공분산NOC, S&P 500 ÷ 분산S&P 500
= 16.83 ÷ 29.16
= 0.58
3 αNOC
= 평균의NOC – βNOC × 평균의S&P 500
= 1.17% – 0.58 × 0.67%
= 0.78%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.49% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.87% |
| 보통주의 체계적 위험Northrop Grumman | βNOC | 0.58 |
| Northrop Grumman 보통주의 예상 수익률3 | E(RNOC) | 10.48% |
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(RNOC) = RF + βNOC [E(RM) – RF]
= 4.49% + 0.58 [14.87% – 4.49%]
= 10.48%