자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 UPC보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Union Pacific Corp., 월별 수익률
| Union Pacific Corp. (UNP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UNP,t1 | 피제수UNP,t1 | RUNP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $197.47 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $205.96 | $0.97 | 4.79% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $220.41 | 7.02% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $222.09 | 0.76% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $230.47 | 6.53% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $231.17 | $1.38 | 0.90% | 6,845.50 | -0.05% |
| 평균의 (R): | 0.67% | 1.14% | ||||
| 표준 편차: | 6.70% | 4.37% | ||||
| Union Pacific Corp. (UNP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UNP,t1 | 피제수UNP,t1 | RUNP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $197.47 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $205.96 | $0.97 | 4.79% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $220.41 | 7.02% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $222.09 | 0.76% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $224.73 | $1.07 | 1.67% | 4,204.11 | 0.55% |
| 5. | 2021. 6. 30. | $219.93 | -2.14% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $218.76 | -0.53% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $216.84 | $1.07 | -0.39% | 4,522.68 | 2.90% |
| 8. | 2021. 9. 30. | $196.01 | -9.61% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $241.40 | 23.16% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $235.64 | -2.39% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $251.93 | $1.18 | 7.41% | 4,766.18 | 4.36% |
| 12. | 2022. 1. 31. | $244.55 | -2.93% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $245.95 | $1.18 | 1.05% | 4,373.94 | -3.14% |
| 14. | 2022. 3. 31. | $273.21 | 11.08% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $234.29 | -14.25% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $219.78 | $1.30 | -5.64% | 4,132.15 | 0.01% |
| 17. | 2022. 6. 30. | $213.28 | -2.96% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $227.30 | 6.57% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $224.51 | $1.30 | -0.66% | 3,955.00 | -4.24% |
| 20. | 2022. 9. 30. | $194.82 | -13.22% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $197.14 | 1.19% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $217.43 | 10.29% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $207.07 | $1.30 | -4.17% | 3,839.50 | -5.90% |
| 24. | 2023. 1. 31. | $204.19 | -1.39% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $207.28 | $1.30 | 2.15% | 3,970.15 | -2.61% |
| 26. | 2023. 3. 31. | $201.26 | -2.90% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $195.70 | -2.76% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $192.52 | $1.30 | -0.96% | 4,179.83 | 0.25% |
| 29. | 2023. 6. 30. | $204.62 | 6.29% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $232.02 | 13.39% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $220.57 | $1.30 | -4.37% | 4,507.66 | -1.77% |
| 32. | 2023. 9. 30. | $203.63 | -7.68% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $207.61 | 1.95% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $225.27 | 8.51% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $245.62 | $1.30 | 9.61% | 4,769.83 | 4.42% |
| 36. | 2024. 1. 31. | $243.93 | -0.69% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $253.69 | $1.30 | 4.53% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $245.93 | -3.06% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $237.16 | -3.57% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $232.82 | $1.30 | -1.28% | 5,277.51 | 4.80% |
| 41. | 2024. 6. 30. | $226.26 | -2.82% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $246.73 | 9.05% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $256.09 | $1.34 | 4.34% | 5,648.40 | 2.28% |
| 44. | 2024. 9. 30. | $246.48 | -3.75% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $232.07 | -5.85% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $244.66 | 5.43% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $228.04 | $1.34 | -6.25% | 5,881.63 | -2.50% |
| 48. | 2025. 1. 31. | $247.66 | 8.60% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $242.49 | $1.34 | -1.55% | 5,954.50 | -1.42% |
| 50. | 2025. 3. 31. | $230.28 | -5.04% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $210.53 | -8.58% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $220.30 | $1.34 | 5.28% | 5,911.69 | 6.15% |
| 53. | 2025. 6. 30. | $229.81 | 4.32% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $220.80 | -3.92% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $221.20 | $1.38 | 0.81% | 6,460.26 | 1.91% |
| 56. | 2025. 9. 30. | $234.82 | 6.16% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $216.34 | -7.87% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $230.47 | 6.53% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $231.17 | $1.38 | 0.90% | 6,845.50 | -0.05% |
| 평균의 (R): | 0.67% | 1.14% | ||||
| 표준 편차: | 6.70% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 UNP의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Union Pacific Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RUNP,t | RS&P 500,t | (RUNP,t–RUNP)2 | (RS&P 500,t–RS&P 500)2 | (RUNP,t–RUNP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 4.79% | 2.61% | 16.96 | 2.17 | 6.07 |
| 2. | 2021. 3. 31. | 7.02% | 4.24% | 40.24 | 9.66 | 19.71 |
| 3. | 2021. 4. 30. | 0.76% | 5.24% | 0.01 | 16.86 | 0.37 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 6.53% | 0.13% | 34.32 | 1.01 | -5.89 |
| 59. | 2025. 12. 31. | 0.90% | -0.05% | 0.05 | 1.41 | -0.27 |
| 합계 (Σ): | 2,602.48 | 1,108.23 | 1,127.07 | |||
| t | 날짜 | RUNP,t | RS&P 500,t | (RUNP,t–RUNP)2 | (RS&P 500,t–RS&P 500)2 | (RUNP,t–RUNP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 4.79% | 2.61% | 16.96 | 2.17 | 6.07 |
| 2. | 2021. 3. 31. | 7.02% | 4.24% | 40.24 | 9.66 | 19.71 |
| 3. | 2021. 4. 30. | 0.76% | 5.24% | 0.01 | 16.86 | 0.37 |
| 4. | 2021. 5. 31. | 1.67% | 0.55% | 1.00 | 0.35 | -0.59 |
| 5. | 2021. 6. 30. | -2.14% | 2.22% | 7.89 | 1.18 | -3.05 |
| 6. | 2021. 7. 31. | -0.53% | 2.27% | 1.45 | 1.30 | -1.37 |
| 7. | 2021. 8. 31. | -0.39% | 2.90% | 1.13 | 3.11 | -1.87 |
| 8. | 2021. 9. 30. | -9.61% | -4.76% | 105.66 | 34.73 | 60.57 |
| 9. | 2021. 10. 31. | 23.16% | 6.91% | 505.54 | 33.39 | 129.92 |
| 10. | 2021. 11. 30. | -2.39% | -0.83% | 9.36 | 3.88 | 6.02 |
| 11. | 2021. 12. 31. | 7.41% | 4.36% | 45.44 | 10.40 | 21.74 |
| 12. | 2022. 1. 31. | -2.93% | -5.26% | 12.98 | 40.89 | 23.03 |
| 13. | 2022. 2. 28. | 1.05% | -3.14% | 0.15 | 18.25 | -1.63 |
| 14. | 2022. 3. 31. | 11.08% | 3.58% | 108.38 | 5.96 | 25.41 |
| 15. | 2022. 4. 30. | -14.25% | -8.80% | 222.55 | 98.64 | 148.17 |
| 16. | 2022. 5. 31. | -5.64% | 0.01% | 39.83 | 1.28 | 7.14 |
| 17. | 2022. 6. 30. | -2.96% | -8.39% | 13.18 | 90.79 | 34.59 |
| 18. | 2022. 7. 31. | 6.57% | 9.11% | 34.82 | 63.61 | 47.06 |
| 19. | 2022. 8. 31. | -0.66% | -4.24% | 1.76 | 28.95 | 7.15 |
| 20. | 2022. 9. 30. | -13.22% | -9.34% | 193.13 | 109.74 | 145.58 |
| 21. | 2022. 10. 31. | 1.19% | 7.99% | 0.27 | 46.93 | 3.55 |
| 22. | 2022. 11. 30. | 10.29% | 5.38% | 92.53 | 17.97 | 40.78 |
| 23. | 2022. 12. 31. | -4.17% | -5.90% | 23.42 | 49.47 | 34.04 |
| 24. | 2023. 1. 31. | -1.39% | 6.18% | 4.26 | 25.39 | -10.40 |
| 25. | 2023. 2. 28. | 2.15% | -2.61% | 2.18 | 14.04 | -5.54 |
| 26. | 2023. 3. 31. | -2.90% | 3.51% | 12.80 | 5.61 | -8.47 |
| 27. | 2023. 4. 30. | -2.76% | 1.46% | 11.80 | 0.11 | -1.13 |
| 28. | 2023. 5. 31. | -0.96% | 0.25% | 2.67 | 0.79 | 1.45 |
| 29. | 2023. 6. 30. | 6.29% | 4.71% | 31.50 | 12.80 | 20.08 |
| 30. | 2023. 7. 31. | 13.39% | 4.85% | 161.74 | 13.76 | 47.18 |
| 31. | 2023. 8. 31. | -4.37% | -1.77% | 25.48 | 8.46 | 14.68 |
| 32. | 2023. 9. 30. | -7.68% | -4.87% | 69.77 | 36.10 | 50.18 |
| 33. | 2023. 10. 31. | 1.95% | -2.20% | 1.64 | 11.12 | -4.27 |
| 34. | 2023. 11. 30. | 8.51% | 8.92% | 61.36 | 60.56 | 60.96 |
| 35. | 2023. 12. 31. | 9.61% | 4.42% | 79.89 | 10.80 | 29.38 |
| 36. | 2024. 1. 31. | -0.69% | 1.59% | 1.85 | 0.21 | -0.62 |
| 37. | 2024. 2. 29. | 4.53% | 5.17% | 14.91 | 16.29 | 15.58 |
| 38. | 2024. 3. 31. | -3.06% | 3.10% | 13.93 | 3.86 | -7.34 |
| 39. | 2024. 4. 30. | -3.57% | -4.16% | 17.97 | 28.06 | 22.46 |
| 40. | 2024. 5. 31. | -1.28% | 4.80% | 3.82 | 13.44 | -7.17 |
| 41. | 2024. 6. 30. | -2.82% | 3.47% | 12.18 | 5.43 | -8.14 |
| 42. | 2024. 7. 31. | 9.05% | 1.13% | 70.13 | 0.00 | -0.03 |
| 43. | 2024. 8. 31. | 4.34% | 2.28% | 13.42 | 1.32 | 4.20 |
| 44. | 2024. 9. 30. | -3.75% | 2.02% | 19.58 | 0.78 | -3.91 |
| 45. | 2024. 10. 31. | -5.85% | -0.99% | 42.50 | 4.52 | 13.86 |
| 46. | 2024. 11. 30. | 5.43% | 5.73% | 22.58 | 21.10 | 21.83 |
| 47. | 2024. 12. 31. | -6.25% | -2.50% | 47.86 | 13.21 | 25.15 |
| 48. | 2025. 1. 31. | 8.60% | 2.70% | 62.90 | 2.45 | 12.42 |
| 49. | 2025. 2. 28. | -1.55% | -1.42% | 4.93 | 6.56 | 5.68 |
| 50. | 2025. 3. 31. | -5.04% | -5.75% | 32.58 | 47.48 | 39.33 |
| 51. | 2025. 4. 30. | -8.58% | -0.76% | 85.55 | 3.60 | 17.56 |
| 52. | 2025. 5. 31. | 5.28% | 6.15% | 21.20 | 25.16 | 23.10 |
| 53. | 2025. 6. 30. | 4.32% | 4.96% | 13.28 | 14.63 | 13.94 |
| 54. | 2025. 7. 31. | -3.92% | 2.17% | 21.10 | 1.06 | -4.73 |
| 55. | 2025. 8. 31. | 0.81% | 1.91% | 0.02 | 0.59 | 0.10 |
| 56. | 2025. 9. 30. | 6.16% | 3.53% | 30.08 | 5.74 | 13.14 |
| 57. | 2025. 10. 31. | -7.87% | 2.27% | 72.98 | 1.28 | -9.68 |
| 58. | 2025. 11. 30. | 6.53% | 0.13% | 34.32 | 1.01 | -5.89 |
| 59. | 2025. 12. 31. | 0.90% | -0.05% | 0.05 | 1.41 | -0.27 |
| 합계 (Σ): | 2,602.48 | 1,108.23 | 1,127.07 | |||
모두 보기
분산UNP = Σ(RUNP,t–RUNP)2 ÷ (59 – 1)
= 2,602.48 ÷ (59 – 1)
= 44.87
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산UNP, S&P 500 = Σ(RUNP,t–RUNP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,127.07 ÷ (59 – 1)
= 19.43
체계적인 위험 추정 (β)
| 분산UNP | 44.87 |
| 분산S&P 500 | 19.11 |
| 공분산UNP, S&P 500 | 19.43 |
| 상관 계수UNP, S&P 5001 | 0.66 |
| βUNP2 | 1.02 |
| αUNP3 | -0.48% |
계산
1 상관 계수UNP, S&P 500
= 공분산UNP, S&P 500 ÷ (표준 편차UNP × 표준 편차S&P 500)
= 19.43 ÷ (6.70% × 4.37%)
= 0.66
2 βUNP
= 공분산UNP, S&P 500 ÷ 분산S&P 500
= 19.43 ÷ 19.11
= 1.02
3 αUNP
= 평균의UNP – βUNP × 평균의S&P 500
= 0.67% – 1.02 × 1.14%
= -0.48%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험UPC | βUNP | 1.02 |
| UPC 보통주에 대한 예상 수익률3 | E(RUNP) | 17.58% |
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(RUNP) = RF + βUNP [E(RM) – RF]
= 4.54% + 1.02 [17.37% – 4.54%]
= 17.58%