자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 U. S. Steel의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
United States Steel Corp., 월별 수익률
| United States Steel Corp. (X) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값X,t1 | 피제수X,t1 | RX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $37.41 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $43.51 | $0.05 | 16.44% | 2,713.83 | -3.89% |
| 2. | 2018. 3. 31. | $35.19 | -19.12% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $33.83 | -3.86% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $26.29 | $0.05 | 29.37% | 4,080.11 | 5.38% |
| 59. | 2022. 12. 31. | $25.05 | -4.72% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.16% | 0.67% | ||||
| 표준 편차: | 19.70% | 5.40% | ||||
| United States Steel Corp. (X) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값X,t1 | 피제수X,t1 | RX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $37.41 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $43.51 | $0.05 | 16.44% | 2,713.83 | -3.89% |
| 2. | 2018. 3. 31. | $35.19 | -19.12% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $33.83 | -3.86% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $36.87 | $0.05 | 9.13% | 2,705.27 | 2.16% |
| 5. | 2018. 6. 30. | $34.75 | -5.75% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $36.43 | 4.83% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $29.68 | $0.05 | -18.39% | 2,901.52 | 3.03% |
| 8. | 2018. 9. 30. | $30.48 | 2.70% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $26.53 | -12.96% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $23.06 | $0.05 | -12.89% | 2,760.17 | 1.79% |
| 11. | 2018. 12. 31. | $18.24 | -20.90% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $22.54 | 23.57% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $22.41 | $0.05 | -0.35% | 2,784.49 | 2.97% |
| 14. | 2019. 3. 31. | $19.49 | -13.03% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $15.60 | -19.96% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $11.82 | $0.05 | -23.91% | 2,752.06 | -6.58% |
| 17. | 2019. 6. 30. | $15.31 | 29.53% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $15.03 | -1.83% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $11.07 | $0.05 | -26.01% | 2,926.46 | -1.81% |
| 20. | 2019. 9. 30. | $11.55 | 4.34% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $11.51 | -0.35% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $13.12 | $0.05 | 14.42% | 3,140.98 | 3.40% |
| 23. | 2019. 12. 31. | $11.41 | -13.03% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $9.07 | -20.51% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $8.02 | $0.01 | -11.47% | 2,954.22 | -8.41% |
| 26. | 2020. 3. 31. | $6.31 | -21.32% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $7.68 | 21.71% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $8.04 | $0.01 | 4.82% | 3,044.31 | 4.53% |
| 29. | 2020. 6. 30. | $7.22 | -10.20% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $6.66 | -7.76% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $7.83 | $0.01 | 17.72% | 3,500.31 | 7.01% |
| 32. | 2020. 9. 30. | $7.34 | -6.26% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $9.66 | 31.61% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $14.19 | $0.01 | 47.00% | 3,621.63 | 10.75% |
| 35. | 2020. 12. 31. | $16.77 | 18.18% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $17.76 | 5.90% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $16.61 | $0.01 | -6.42% | 3,811.15 | 2.61% |
| 38. | 2021. 3. 31. | $26.17 | 57.56% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $23.01 | -12.07% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $25.93 | $0.01 | 12.73% | 4,204.11 | 0.55% |
| 41. | 2021. 6. 30. | $24.00 | -7.44% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $26.48 | 10.33% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $26.75 | $0.01 | 1.06% | 4,522.68 | 2.90% |
| 44. | 2021. 9. 30. | $21.97 | -17.87% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $26.39 | 20.12% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $22.61 | $0.05 | -14.13% | 4,567.00 | -0.83% |
| 47. | 2021. 12. 31. | $23.81 | 5.31% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $20.72 | -12.98% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $27.21 | $0.05 | 31.56% | 4,373.94 | -3.14% |
| 50. | 2022. 3. 31. | $37.74 | 38.70% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $30.49 | -19.21% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $25.07 | $0.05 | -17.61% | 4,132.15 | 0.01% |
| 53. | 2022. 6. 30. | $17.91 | -28.56% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $23.65 | 32.05% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $22.87 | $0.05 | -3.09% | 3,955.00 | -4.24% |
| 56. | 2022. 9. 30. | $18.12 | -20.77% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $20.36 | 12.36% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $26.29 | $0.05 | 29.37% | 4,080.11 | 5.38% |
| 59. | 2022. 12. 31. | $25.05 | -4.72% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.16% | 0.67% | ||||
| 표준 편차: | 19.70% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 X의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
United States Steel Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RX,t | RS&P 500,t | (RX,t–RX)2 | (RS&P 500,t–RS&P 500)2 | (RX,t–RX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 16.44% | -3.89% | 233.53 | 20.81 | -69.71 |
| 2. | 2018. 3. 31. | -19.12% | -2.69% | 411.27 | 11.26 | 68.04 |
| 3. | 2018. 4. 30. | -3.86% | 0.27% | 25.23 | 0.16 | 1.98 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 29.37% | 5.38% | 796.00 | 22.17 | 132.85 |
| 59. | 2022. 12. 31. | -4.72% | -5.90% | 34.51 | 43.08 | 38.56 |
| 합계 (Σ): | 22,504.49 | 1,691.48 | 3,655.99 | |||
| t | 날짜 | RX,t | RS&P 500,t | (RX,t–RX)2 | (RS&P 500,t–RS&P 500)2 | (RX,t–RX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 16.44% | -3.89% | 233.53 | 20.81 | -69.71 |
| 2. | 2018. 3. 31. | -19.12% | -2.69% | 411.27 | 11.26 | 68.04 |
| 3. | 2018. 4. 30. | -3.86% | 0.27% | 25.23 | 0.16 | 1.98 |
| 4. | 2018. 5. 31. | 9.13% | 2.16% | 63.62 | 2.23 | 11.92 |
| 5. | 2018. 6. 30. | -5.75% | 0.48% | 47.72 | 0.03 | 1.26 |
| 6. | 2018. 7. 31. | 4.83% | 3.60% | 13.52 | 8.62 | 10.79 |
| 7. | 2018. 8. 31. | -18.39% | 3.03% | 382.17 | 5.57 | -46.13 |
| 8. | 2018. 9. 30. | 2.70% | 0.43% | 2.36 | 0.06 | -0.36 |
| 9. | 2018. 10. 31. | -12.96% | -6.94% | 199.29 | 57.87 | 107.39 |
| 10. | 2018. 11. 30. | -12.89% | 1.79% | 197.37 | 1.25 | -15.72 |
| 11. | 2018. 12. 31. | -20.90% | -9.18% | 486.63 | 96.91 | 217.16 |
| 12. | 2019. 1. 31. | 23.57% | 7.87% | 502.51 | 51.87 | 161.44 |
| 13. | 2019. 2. 28. | -0.35% | 2.97% | 2.29 | 5.32 | -3.49 |
| 14. | 2019. 3. 31. | -13.03% | 1.79% | 201.29 | 1.27 | -15.97 |
| 15. | 2019. 4. 30. | -19.96% | 3.93% | 445.92 | 10.66 | -68.94 |
| 16. | 2019. 5. 31. | -23.91% | -6.58% | 628.41 | 52.48 | 181.60 |
| 17. | 2019. 6. 30. | 29.53% | 6.89% | 804.77 | 38.77 | 176.63 |
| 18. | 2019. 7. 31. | -1.83% | 1.31% | 8.92 | 0.42 | -1.93 |
| 19. | 2019. 8. 31. | -26.01% | -1.81% | 738.34 | 6.13 | 67.27 |
| 20. | 2019. 9. 30. | 4.34% | 1.72% | 10.10 | 1.11 | 3.34 |
| 21. | 2019. 10. 31. | -0.35% | 2.04% | 2.26 | 1.89 | -2.07 |
| 22. | 2019. 11. 30. | 14.42% | 3.40% | 175.95 | 7.50 | 36.32 |
| 23. | 2019. 12. 31. | -13.03% | 2.86% | 201.39 | 4.81 | -31.11 |
| 24. | 2020. 1. 31. | -20.51% | -0.16% | 469.42 | 0.69 | 17.97 |
| 25. | 2020. 2. 29. | -11.47% | -8.41% | 159.37 | 82.40 | 114.60 |
| 26. | 2020. 3. 31. | -21.32% | -12.51% | 505.33 | 173.67 | 296.25 |
| 27. | 2020. 4. 30. | 21.71% | 12.68% | 422.46 | 144.43 | 247.01 |
| 28. | 2020. 5. 31. | 4.82% | 4.53% | 13.39 | 14.91 | 14.13 |
| 29. | 2020. 6. 30. | -10.20% | 1.84% | 128.98 | 1.37 | -13.31 |
| 30. | 2020. 7. 31. | -7.76% | 5.51% | 79.46 | 23.46 | -43.17 |
| 31. | 2020. 8. 31. | 17.72% | 7.01% | 274.23 | 40.19 | 104.99 |
| 32. | 2020. 9. 30. | -6.26% | -3.92% | 54.99 | 21.06 | 34.03 |
| 33. | 2020. 10. 31. | 31.61% | -2.77% | 927.19 | 11.79 | -104.54 |
| 34. | 2020. 11. 30. | 47.00% | 10.75% | 2,101.32 | 101.77 | 462.43 |
| 35. | 2020. 12. 31. | 18.18% | 3.71% | 289.82 | 9.28 | 51.85 |
| 36. | 2021. 1. 31. | 5.90% | -1.11% | 22.52 | 3.17 | -8.45 |
| 37. | 2021. 2. 28. | -6.42% | 2.61% | 57.41 | 3.77 | -14.72 |
| 38. | 2021. 3. 31. | 57.56% | 4.24% | 3,180.72 | 12.80 | 201.75 |
| 39. | 2021. 4. 30. | -12.07% | 5.24% | 175.10 | 20.94 | -60.55 |
| 40. | 2021. 5. 31. | 12.73% | 0.55% | 134.00 | 0.01 | -1.37 |
| 41. | 2021. 6. 30. | -7.44% | 2.22% | 73.98 | 2.42 | -13.37 |
| 42. | 2021. 7. 31. | 10.33% | 2.27% | 84.19 | 2.59 | 14.76 |
| 43. | 2021. 8. 31. | 1.06% | 2.90% | 0.01 | 4.98 | -0.22 |
| 44. | 2021. 9. 30. | -17.87% | -4.76% | 362.03 | 29.42 | 103.19 |
| 45. | 2021. 10. 31. | 20.12% | 6.91% | 359.50 | 39.03 | 118.46 |
| 46. | 2021. 11. 30. | -14.13% | -0.83% | 233.84 | 2.25 | 22.94 |
| 47. | 2021. 12. 31. | 5.31% | 4.36% | 17.22 | 13.65 | 15.33 |
| 48. | 2022. 1. 31. | -12.98% | -5.26% | 199.81 | 35.11 | 83.76 |
| 49. | 2022. 2. 28. | 31.56% | -3.14% | 924.52 | 14.46 | -115.62 |
| 50. | 2022. 3. 31. | 38.70% | 3.58% | 1,409.34 | 8.47 | 109.27 |
| 51. | 2022. 4. 30. | -19.21% | -8.80% | 414.86 | 89.54 | 192.73 |
| 52. | 2022. 5. 31. | -17.61% | 0.01% | 352.32 | 0.44 | 12.41 |
| 53. | 2022. 6. 30. | -28.56% | -8.39% | 883.15 | 82.06 | 269.20 |
| 54. | 2022. 7. 31. | 32.05% | 9.11% | 954.27 | 71.32 | 260.88 |
| 55. | 2022. 8. 31. | -3.09% | -4.24% | 18.02 | 24.11 | 20.84 |
| 56. | 2022. 9. 30. | -20.77% | -9.34% | 480.81 | 100.12 | 219.41 |
| 57. | 2022. 10. 31. | 12.36% | 7.99% | 125.53 | 53.58 | 82.01 |
| 58. | 2022. 11. 30. | 29.37% | 5.38% | 796.00 | 22.17 | 132.85 |
| 59. | 2022. 12. 31. | -4.72% | -5.90% | 34.51 | 43.08 | 38.56 |
| 합계 (Σ): | 22,504.49 | 1,691.48 | 3,655.99 | |||
모두 보기
분산X = Σ(RX,t–RX)2 ÷ (59 – 1)
= 22,504.49 ÷ (59 – 1)
= 388.01
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산X, S&P 500 = Σ(RX,t–RX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,655.99 ÷ (59 – 1)
= 63.03
체계적인 위험 추정 (β)
| 분산X | 388.01 |
| 분산S&P 500 | 29.16 |
| 공분산X, S&P 500 | 63.03 |
| 상관 계수X, S&P 5001 | 0.59 |
| βX2 | 2.16 |
| αX3 | -0.28% |
계산
1 상관 계수X, S&P 500
= 공분산X, S&P 500 ÷ (표준 편차X × 표준 편차S&P 500)
= 63.03 ÷ (19.70% × 5.40%)
= 0.59
2 βX
= 공분산X, S&P 500 ÷ 분산S&P 500
= 63.03 ÷ 29.16
= 2.16
3 αX
= 평균의X – βX × 평균의S&P 500
= 1.16% – 2.16 × 0.67%
= -0.28%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험U. S. Steel | βX | 2.16 |
| U.S. Steel 보통주의 예상 수익률3 | E(RX) | 24.37% |
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(RX) = RF + βX [E(RM) – RF]
= 4.67% + 2.16 [13.79% – 4.67%]
= 24.37%