자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Norfolk Southern보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Norfolk Southern Corp., 월별 수익률
| Norfolk Southern Corp. (NSC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NSC,t1 | 피제수NSC,t1 | RNSC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $117.46 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $121.03 | $0.61 | 3.56% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $111.97 | -7.49% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $117.49 | 4.93% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $265.27 | $1.09 | -9.11% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $297.71 | 12.23% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.03% | 1.36% | ||||
| 표준 편차: | 7.64% | 4.48% | ||||
| Norfolk Southern Corp. (NSC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NSC,t1 | 피제수NSC,t1 | RNSC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $117.46 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $121.03 | $0.61 | 3.56% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $111.97 | -7.49% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $117.49 | 4.93% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $124.03 | $0.61 | 6.09% | 2,411.80 | 1.16% |
| 5. | 2017. 6. 30. | $121.70 | -1.88% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $112.58 | -7.49% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $120.52 | $0.61 | 7.59% | 2,471.65 | 0.05% |
| 8. | 2017. 9. 30. | $132.24 | 9.72% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $131.42 | -0.62% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $138.63 | $0.61 | 5.95% | 2,647.58 | 2.81% |
| 11. | 2017. 12. 31. | $144.90 | 4.52% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $150.88 | 4.13% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $139.08 | $0.72 | -7.34% | 2,713.83 | -3.89% |
| 14. | 2018. 3. 31. | $135.78 | -2.37% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $143.47 | 5.66% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $151.65 | $0.72 | 6.20% | 2,705.27 | 2.16% |
| 17. | 2018. 6. 30. | $150.87 | -0.51% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $169.00 | 12.02% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $173.84 | $0.80 | 3.34% | 2,901.52 | 3.03% |
| 20. | 2018. 9. 30. | $180.50 | 3.83% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $167.83 | -7.02% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $170.74 | $0.80 | 2.21% | 2,760.17 | 1.79% |
| 23. | 2018. 12. 31. | $149.54 | -12.42% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $167.74 | 12.17% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $179.30 | $0.86 | 7.40% | 2,784.49 | 2.97% |
| 26. | 2019. 3. 31. | $186.89 | 4.23% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $204.02 | 9.17% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $195.14 | $0.86 | -3.93% | 2,752.06 | -6.58% |
| 29. | 2019. 6. 30. | $199.33 | 2.15% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $191.12 | -4.12% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $174.05 | $0.94 | -8.44% | 2,926.46 | -1.81% |
| 32. | 2019. 9. 30. | $179.66 | 3.22% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $182.00 | $0.94 | 1.83% | 3,037.56 | 2.04% |
| 34. | 2019. 11. 30. | $193.50 | 6.32% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $194.13 | 0.33% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $208.21 | 7.25% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $182.35 | $0.94 | -11.97% | 2,954.22 | -8.41% |
| 38. | 2020. 3. 31. | $146.00 | -19.93% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $171.10 | 17.19% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $178.29 | $0.94 | 4.75% | 3,044.31 | 4.53% |
| 41. | 2020. 6. 30. | $175.57 | -1.53% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $192.21 | 9.48% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $212.53 | $0.94 | 11.06% | 3,500.31 | 7.01% |
| 44. | 2020. 9. 30. | $213.99 | 0.69% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $209.12 | -2.28% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $237.02 | $0.94 | 13.79% | 3,621.63 | 10.75% |
| 47. | 2020. 12. 31. | $237.61 | 0.25% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $236.62 | -0.42% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $252.06 | $0.99 | 6.94% | 3,811.15 | 2.61% |
| 50. | 2021. 3. 31. | $268.52 | 6.53% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $279.24 | 3.99% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $280.90 | $0.99 | 0.95% | 4,204.11 | 0.55% |
| 53. | 2021. 6. 30. | $265.41 | -5.51% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $257.83 | -2.86% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $253.54 | $1.09 | -1.24% | 4,522.68 | 2.90% |
| 56. | 2021. 9. 30. | $239.25 | -5.64% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $293.05 | 22.49% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $265.27 | $1.09 | -9.11% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $297.71 | 12.23% | 4,766.18 | 4.36% | |
| 평균의 (R): | 2.03% | 1.36% | ||||
| 표준 편차: | 7.64% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 NSC의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Norfolk Southern Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RNSC,t | RS&P 500,t | (RNSC,t–RNSC)2 | (RS&P 500,t–RS&P 500)2 | (RNSC,t–RNSC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 3.56% | 3.72% | 2.32 | 5.58 | 3.60 |
| 2. | 2017. 3. 31. | -7.49% | -0.04% | 90.64 | 1.95 | 13.30 |
| 3. | 2017. 4. 30. | 4.93% | 0.91% | 8.38 | 0.20 | -1.30 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -9.11% | -0.83% | 124.15 | 4.80 | 24.42 |
| 59. | 2021. 12. 31. | 12.23% | 4.36% | 103.92 | 9.02 | 30.62 |
| 합계 (Σ): | 3,386.46 | 1,164.17 | 1,580.60 | |||
| t | 날짜 | RNSC,t | RS&P 500,t | (RNSC,t–RNSC)2 | (RS&P 500,t–RS&P 500)2 | (RNSC,t–RNSC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 3.56% | 3.72% | 2.32 | 5.58 | 3.60 |
| 2. | 2017. 3. 31. | -7.49% | -0.04% | 90.64 | 1.95 | 13.30 |
| 3. | 2017. 4. 30. | 4.93% | 0.91% | 8.38 | 0.20 | -1.30 |
| 4. | 2017. 5. 31. | 6.09% | 1.16% | 16.41 | 0.04 | -0.81 |
| 5. | 2017. 6. 30. | -1.88% | 0.48% | 15.31 | 0.77 | 3.43 |
| 6. | 2017. 7. 31. | -7.49% | 1.93% | 90.79 | 0.33 | -5.50 |
| 7. | 2017. 8. 31. | 7.59% | 0.05% | 30.91 | 1.70 | -7.25 |
| 8. | 2017. 9. 30. | 9.72% | 1.93% | 59.13 | 0.33 | 4.40 |
| 9. | 2017. 10. 31. | -0.62% | 2.22% | 7.05 | 0.74 | -2.29 |
| 10. | 2017. 11. 30. | 5.95% | 2.81% | 15.33 | 2.10 | 5.68 |
| 11. | 2017. 12. 31. | 4.52% | 0.98% | 6.19 | 0.14 | -0.93 |
| 12. | 2018. 1. 31. | 4.13% | 5.62% | 4.38 | 18.15 | 8.91 |
| 13. | 2018. 2. 28. | -7.34% | -3.89% | 87.95 | 27.59 | 49.26 |
| 14. | 2018. 3. 31. | -2.37% | -2.69% | 19.43 | 16.37 | 17.83 |
| 15. | 2018. 4. 30. | 5.66% | 0.27% | 13.17 | 1.18 | -3.94 |
| 16. | 2018. 5. 31. | 6.20% | 2.16% | 17.38 | 0.64 | 3.35 |
| 17. | 2018. 6. 30. | -0.51% | 0.48% | 6.50 | 0.76 | 2.23 |
| 18. | 2018. 7. 31. | 12.02% | 3.60% | 99.64 | 5.04 | 22.40 |
| 19. | 2018. 8. 31. | 3.34% | 3.03% | 1.70 | 2.78 | 2.17 |
| 20. | 2018. 9. 30. | 3.83% | 0.43% | 3.23 | 0.86 | -1.67 |
| 21. | 2018. 10. 31. | -7.02% | -6.94% | 81.98 | 68.86 | 75.13 |
| 22. | 2018. 11. 30. | 2.21% | 1.79% | 0.03 | 0.18 | 0.08 |
| 23. | 2018. 12. 31. | -12.42% | -9.18% | 208.84 | 111.00 | 152.25 |
| 24. | 2019. 1. 31. | 12.17% | 7.87% | 102.74 | 42.39 | 65.99 |
| 25. | 2019. 2. 28. | 7.40% | 2.97% | 28.83 | 2.61 | 8.67 |
| 26. | 2019. 3. 31. | 4.23% | 1.79% | 4.83 | 0.19 | 0.96 |
| 27. | 2019. 4. 30. | 9.17% | 3.93% | 50.85 | 6.62 | 18.35 |
| 28. | 2019. 5. 31. | -3.93% | -6.58% | 35.59 | 62.97 | 47.34 |
| 29. | 2019. 6. 30. | 2.15% | 6.89% | 0.01 | 30.64 | 0.62 |
| 30. | 2019. 7. 31. | -4.12% | 1.31% | 37.87 | 0.00 | 0.28 |
| 31. | 2019. 8. 31. | -8.44% | -1.81% | 109.72 | 10.03 | 33.17 |
| 32. | 2019. 9. 30. | 3.22% | 1.72% | 1.41 | 0.13 | 0.43 |
| 33. | 2019. 10. 31. | 1.83% | 2.04% | 0.04 | 0.47 | -0.14 |
| 34. | 2019. 11. 30. | 6.32% | 3.40% | 18.35 | 4.19 | 8.77 |
| 35. | 2019. 12. 31. | 0.33% | 2.86% | 2.92 | 2.25 | -2.57 |
| 36. | 2020. 1. 31. | 7.25% | -0.16% | 27.23 | 2.31 | -7.94 |
| 37. | 2020. 2. 29. | -11.97% | -8.41% | 196.10 | 95.43 | 136.80 |
| 38. | 2020. 3. 31. | -19.93% | -12.51% | 482.64 | 192.37 | 304.71 |
| 39. | 2020. 4. 30. | 17.19% | 12.68% | 229.73 | 128.29 | 171.68 |
| 40. | 2020. 5. 31. | 4.75% | 4.53% | 7.38 | 10.05 | 8.61 |
| 41. | 2020. 6. 30. | -1.53% | 1.84% | 12.68 | 0.23 | -1.71 |
| 42. | 2020. 7. 31. | 9.48% | 5.51% | 55.40 | 17.24 | 30.90 |
| 43. | 2020. 8. 31. | 11.06% | 7.01% | 81.47 | 31.91 | 50.98 |
| 44. | 2020. 9. 30. | 0.69% | -3.92% | 1.82 | 27.89 | 7.12 |
| 45. | 2020. 10. 31. | -2.28% | -2.77% | 18.58 | 17.01 | 17.78 |
| 46. | 2020. 11. 30. | 13.79% | 10.75% | 138.21 | 88.30 | 110.47 |
| 47. | 2020. 12. 31. | 0.25% | 3.71% | 3.19 | 5.54 | -4.20 |
| 48. | 2021. 1. 31. | -0.42% | -1.11% | 6.01 | 6.11 | 6.06 |
| 49. | 2021. 2. 28. | 6.94% | 2.61% | 24.10 | 1.57 | 6.14 |
| 50. | 2021. 3. 31. | 6.53% | 4.24% | 20.21 | 8.33 | 12.97 |
| 51. | 2021. 4. 30. | 3.99% | 5.24% | 3.83 | 15.09 | 7.60 |
| 52. | 2021. 5. 31. | 0.95% | 0.55% | 1.18 | 0.65 | 0.88 |
| 53. | 2021. 6. 30. | -5.51% | 2.22% | 56.99 | 0.75 | -6.52 |
| 54. | 2021. 7. 31. | -2.86% | 2.27% | 23.92 | 0.84 | -4.48 |
| 55. | 2021. 8. 31. | -1.24% | 2.90% | 10.73 | 2.38 | -5.05 |
| 56. | 2021. 9. 30. | -5.64% | -4.76% | 58.84 | 37.39 | 46.91 |
| 57. | 2021. 10. 31. | 22.49% | 6.91% | 418.29 | 30.87 | 113.64 |
| 58. | 2021. 11. 30. | -9.11% | -0.83% | 124.15 | 4.80 | 24.42 |
| 59. | 2021. 12. 31. | 12.23% | 4.36% | 103.92 | 9.02 | 30.62 |
| 합계 (Σ): | 3,386.46 | 1,164.17 | 1,580.60 | |||
모두 보기
분산NSC = Σ(RNSC,t–RNSC)2 ÷ (59 – 1)
= 3,386.46 ÷ (59 – 1)
= 58.39
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산NSC, S&P 500 = Σ(RNSC,t–RNSC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,580.60 ÷ (59 – 1)
= 27.25
체계적인 위험 추정 (β)
| 분산NSC | 58.39 |
| 분산S&P 500 | 20.07 |
| 공분산NSC, S&P 500 | 27.25 |
| 상관 계수NSC, S&P 5001 | 0.80 |
| βNSC2 | 1.36 |
| αNSC3 | 0.19% |
계산
1 상관 계수NSC, S&P 500
= 공분산NSC, S&P 500 ÷ (표준 편차NSC × 표준 편차S&P 500)
= 27.25 ÷ (7.64% × 4.48%)
= 0.80
2 βNSC
= 공분산NSC, S&P 500 ÷ 분산S&P 500
= 27.25 ÷ 20.07
= 1.36
3 αNSC
= 평균의NSC – βNSC × 평균의S&P 500
= 2.03% – 1.36 × 1.36%
= 0.19%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.76% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 15.13% |
| 보통주의 체계적 위험Norfolk Southern | βNSC | 1.36 |
| Norfolk Southern 보통주의 예상 수익률3 | E(RNSC) | 18.84% |
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(RNSC) = RF + βNSC [E(RM) – RF]
= 4.76% + 1.36 [15.13% – 4.76%]
= 18.84%