자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 SDI보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Steel Dynamics Inc., 월별 수익률
| Steel Dynamics Inc. (STLD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값STLD,t1 | 피제수STLD,t1 | RSTLD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $33.81 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $36.60 | 8.25% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $34.76 | $0.155 | -4.60% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $36.14 | 3.97% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $59.80 | -9.50% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $62.07 | $0.26 | 4.23% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.72% | 1.36% | ||||
| 표준 편차: | 9.98% | 4.48% | ||||
| Steel Dynamics Inc. (STLD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값STLD,t1 | 피제수STLD,t1 | RSTLD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $33.81 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $36.60 | 8.25% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $34.76 | $0.155 | -4.60% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $36.14 | 3.97% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $33.99 | -5.95% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $35.81 | $0.155 | 5.81% | 2,423.41 | 0.48% |
| 6. | 2017. 7. 31. | $35.41 | -1.12% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $34.45 | -2.71% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $34.47 | $0.155 | 0.51% | 2,519.36 | 1.93% |
| 9. | 2017. 10. 31. | $37.21 | 7.95% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $38.50 | 3.47% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $43.13 | $0.155 | 12.43% | 2,673.61 | 0.98% |
| 12. | 2018. 1. 31. | $45.40 | 5.26% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $46.25 | 1.87% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $44.22 | $0.1875 | -3.98% | 2,640.87 | -2.69% |
| 15. | 2018. 4. 30. | $44.81 | 1.33% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $49.43 | 10.31% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $45.95 | $0.1875 | -6.66% | 2,718.37 | 0.48% |
| 18. | 2018. 7. 31. | $47.09 | 2.48% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $45.73 | -2.89% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $45.19 | $0.1875 | -0.77% | 2,913.98 | 0.43% |
| 21. | 2018. 10. 31. | $39.60 | -12.37% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $35.20 | -11.11% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $30.04 | $0.1875 | -14.13% | 2,506.85 | -9.18% |
| 24. | 2019. 1. 31. | $36.59 | 21.80% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $37.32 | 2.00% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $35.27 | $0.24 | -4.85% | 2,834.40 | 1.79% |
| 27. | 2019. 4. 30. | $31.68 | -10.18% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $25.15 | -20.61% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $30.20 | $0.24 | 21.03% | 2,941.76 | 6.89% |
| 30. | 2019. 7. 31. | $31.51 | 4.34% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $27.00 | -14.31% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $29.80 | $0.24 | 11.26% | 2,976.74 | 1.72% |
| 33. | 2019. 10. 31. | $30.36 | 1.88% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $33.73 | 11.10% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $34.04 | $0.24 | 1.63% | 3,230.78 | 2.86% |
| 36. | 2020. 1. 31. | $29.88 | -12.22% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $26.63 | -10.88% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $22.54 | $0.25 | -14.42% | 2,584.59 | -12.51% |
| 39. | 2020. 4. 30. | $24.27 | 7.68% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $26.56 | 9.44% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $26.09 | $0.25 | -0.83% | 3,100.29 | 1.84% |
| 42. | 2020. 7. 31. | $27.41 | 5.06% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $29.52 | 7.70% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $28.63 | $0.25 | -2.17% | 3,363.00 | -3.92% |
| 45. | 2020. 10. 31. | $31.48 | 9.95% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $36.21 | 15.03% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $36.87 | $0.25 | 2.51% | 3,756.07 | 3.71% |
| 48. | 2021. 1. 31. | $34.27 | -7.05% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $41.58 | 21.33% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $50.76 | $0.26 | 22.70% | 3,972.89 | 4.24% |
| 51. | 2021. 4. 30. | $54.22 | 6.82% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $62.43 | 15.14% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $59.60 | $0.26 | -4.12% | 4,297.50 | 2.22% |
| 54. | 2021. 7. 31. | $64.45 | 8.14% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $67.49 | 4.72% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $58.48 | $0.26 | -12.96% | 4,307.54 | -4.76% |
| 57. | 2021. 10. 31. | $66.08 | 13.00% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $59.80 | -9.50% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $62.07 | $0.26 | 4.23% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.72% | 1.36% | ||||
| 표준 편차: | 9.98% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 STLD의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Steel Dynamics Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RSTLD,t | RS&P 500,t | (RSTLD,t–RSTLD)2 | (RS&P 500,t–RS&P 500)2 | (RSTLD,t–RSTLD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 8.25% | 3.72% | 42.61 | 5.58 | 15.42 |
| 2. | 2017. 3. 31. | -4.60% | -0.04% | 40.04 | 1.95 | 8.84 |
| 3. | 2017. 4. 30. | 3.97% | 0.91% | 5.04 | 0.20 | -1.01 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -9.50% | -0.83% | 126.06 | 4.80 | 24.60 |
| 59. | 2021. 12. 31. | 4.23% | 4.36% | 6.28 | 9.02 | 7.53 |
| 합계 (Σ): | 5,773.13 | 1,164.17 | 1,736.03 | |||
| t | 날짜 | RSTLD,t | RS&P 500,t | (RSTLD,t–RSTLD)2 | (RS&P 500,t–RS&P 500)2 | (RSTLD,t–RSTLD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 8.25% | 3.72% | 42.61 | 5.58 | 15.42 |
| 2. | 2017. 3. 31. | -4.60% | -0.04% | 40.04 | 1.95 | 8.84 |
| 3. | 2017. 4. 30. | 3.97% | 0.91% | 5.04 | 0.20 | -1.01 |
| 4. | 2017. 5. 31. | -5.95% | 1.16% | 58.88 | 0.04 | 1.54 |
| 5. | 2017. 6. 30. | 5.81% | 0.48% | 16.70 | 0.77 | -3.58 |
| 6. | 2017. 7. 31. | -1.12% | 1.93% | 8.07 | 0.33 | -1.64 |
| 7. | 2017. 8. 31. | -2.71% | 0.05% | 19.67 | 1.70 | 5.78 |
| 8. | 2017. 9. 30. | 0.51% | 1.93% | 1.48 | 0.33 | -0.70 |
| 9. | 2017. 10. 31. | 7.95% | 2.22% | 38.75 | 0.74 | 5.36 |
| 10. | 2017. 11. 30. | 3.47% | 2.81% | 3.04 | 2.10 | 2.53 |
| 11. | 2017. 12. 31. | 12.43% | 0.98% | 114.59 | 0.14 | -4.01 |
| 12. | 2018. 1. 31. | 5.26% | 5.62% | 12.52 | 18.15 | 15.08 |
| 13. | 2018. 2. 28. | 1.87% | -3.89% | 0.02 | 27.59 | -0.78 |
| 14. | 2018. 3. 31. | -3.98% | -2.69% | 32.58 | 16.37 | 23.10 |
| 15. | 2018. 4. 30. | 1.33% | 0.27% | 0.15 | 1.18 | 0.42 |
| 16. | 2018. 5. 31. | 10.31% | 2.16% | 73.72 | 0.64 | 6.89 |
| 17. | 2018. 6. 30. | -6.66% | 0.48% | 70.31 | 0.76 | 7.33 |
| 18. | 2018. 7. 31. | 2.48% | 3.60% | 0.57 | 5.04 | 1.70 |
| 19. | 2018. 8. 31. | -2.89% | 3.03% | 21.27 | 2.78 | -7.70 |
| 20. | 2018. 9. 30. | -0.77% | 0.43% | 6.22 | 0.86 | 2.32 |
| 21. | 2018. 10. 31. | -12.37% | -6.94% | 198.64 | 68.86 | 116.96 |
| 22. | 2018. 11. 30. | -11.11% | 1.79% | 164.74 | 0.18 | -5.49 |
| 23. | 2018. 12. 31. | -14.13% | -9.18% | 251.24 | 111.00 | 166.99 |
| 24. | 2019. 1. 31. | 21.80% | 7.87% | 403.21 | 42.39 | 130.73 |
| 25. | 2019. 2. 28. | 2.00% | 2.97% | 0.07 | 2.61 | 0.44 |
| 26. | 2019. 3. 31. | -4.85% | 1.79% | 43.22 | 0.19 | -2.86 |
| 27. | 2019. 4. 30. | -10.18% | 3.93% | 141.68 | 6.62 | -30.63 |
| 28. | 2019. 5. 31. | -20.61% | -6.58% | 498.92 | 62.97 | 177.26 |
| 29. | 2019. 6. 30. | 21.03% | 6.89% | 372.86 | 30.64 | 106.88 |
| 30. | 2019. 7. 31. | 4.34% | 1.31% | 6.83 | 0.00 | -0.12 |
| 31. | 2019. 8. 31. | -14.31% | -1.81% | 257.19 | 10.03 | 50.79 |
| 32. | 2019. 9. 30. | 11.26% | 1.72% | 90.92 | 0.13 | 3.43 |
| 33. | 2019. 10. 31. | 1.88% | 2.04% | 0.02 | 0.47 | 0.11 |
| 34. | 2019. 11. 30. | 11.10% | 3.40% | 87.91 | 4.19 | 19.19 |
| 35. | 2019. 12. 31. | 1.63% | 2.86% | 0.01 | 2.25 | -0.14 |
| 36. | 2020. 1. 31. | -12.22% | -0.16% | 194.46 | 2.31 | 21.21 |
| 37. | 2020. 2. 29. | -10.88% | -8.41% | 158.78 | 95.43 | 123.10 |
| 38. | 2020. 3. 31. | -14.42% | -12.51% | 260.63 | 192.37 | 223.91 |
| 39. | 2020. 4. 30. | 7.68% | 12.68% | 35.42 | 128.29 | 67.41 |
| 40. | 2020. 5. 31. | 9.44% | 4.53% | 59.47 | 10.05 | 24.45 |
| 41. | 2020. 6. 30. | -0.83% | 1.84% | 6.51 | 0.23 | -1.23 |
| 42. | 2020. 7. 31. | 5.06% | 5.51% | 11.12 | 17.24 | 13.85 |
| 43. | 2020. 8. 31. | 7.70% | 7.01% | 35.69 | 31.91 | 33.74 |
| 44. | 2020. 9. 30. | -2.17% | -3.92% | 15.15 | 27.89 | 20.55 |
| 45. | 2020. 10. 31. | 9.95% | -2.77% | 67.74 | 17.01 | -33.95 |
| 46. | 2020. 11. 30. | 15.03% | 10.75% | 176.92 | 88.30 | 124.99 |
| 47. | 2020. 12. 31. | 2.51% | 3.71% | 0.62 | 5.54 | 1.86 |
| 48. | 2021. 1. 31. | -7.05% | -1.11% | 77.02 | 6.11 | 21.69 |
| 49. | 2021. 2. 28. | 21.33% | 2.61% | 384.41 | 1.57 | 24.53 |
| 50. | 2021. 3. 31. | 22.70% | 4.24% | 440.12 | 8.33 | 60.54 |
| 51. | 2021. 4. 30. | 6.82% | 5.24% | 25.93 | 15.09 | 19.78 |
| 52. | 2021. 5. 31. | 15.14% | 0.55% | 180.04 | 0.65 | -10.86 |
| 53. | 2021. 6. 30. | -4.12% | 2.22% | 34.11 | 0.75 | -5.04 |
| 54. | 2021. 7. 31. | 8.14% | 2.27% | 41.13 | 0.84 | 5.88 |
| 55. | 2021. 8. 31. | 4.72% | 2.90% | 8.96 | 2.38 | 4.61 |
| 56. | 2021. 9. 30. | -12.96% | -4.76% | 215.77 | 37.39 | 89.82 |
| 57. | 2021. 10. 31. | 13.00% | 6.91% | 127.05 | 30.87 | 62.63 |
| 58. | 2021. 11. 30. | -9.50% | -0.83% | 126.06 | 4.80 | 24.60 |
| 59. | 2021. 12. 31. | 4.23% | 4.36% | 6.28 | 9.02 | 7.53 |
| 합계 (Σ): | 5,773.13 | 1,164.17 | 1,736.03 | |||
모두 보기
분산STLD = Σ(RSTLD,t–RSTLD)2 ÷ (59 – 1)
= 5,773.13 ÷ (59 – 1)
= 99.54
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산STLD, S&P 500 = Σ(RSTLD,t–RSTLD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,736.03 ÷ (59 – 1)
= 29.93
체계적인 위험 추정 (β)
| 분산STLD | 99.54 |
| 분산S&P 500 | 20.07 |
| 공분산STLD, S&P 500 | 29.93 |
| 상관 계수STLD, S&P 5001 | 0.67 |
| βSTLD2 | 1.49 |
| αSTLD3 | -0.30% |
계산
1 상관 계수STLD, S&P 500
= 공분산STLD, S&P 500 ÷ (표준 편차STLD × 표준 편차S&P 500)
= 29.93 ÷ (9.98% × 4.48%)
= 0.67
2 βSTLD
= 공분산STLD, S&P 500 ÷ 분산S&P 500
= 29.93 ÷ 20.07
= 1.49
3 αSTLD
= 평균의STLD – βSTLD × 평균의S&P 500
= 1.72% – 1.49 × 1.36%
= -0.30%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.88% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.90% |
| 보통주의 체계적 위험 SDI | βSTLD | 1.49 |
| SDI 보통주 예상 수익률3 | E(RSTLD) | 19.82% |
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(RSTLD) = RF + βSTLD [E(RM) – RF]
= 4.88% + 1.49 [14.90% – 4.88%]
= 19.82%