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 |
| 2020. 1. 31. | $179.42 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $159.81 | $0.97 | -10.39% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $141.04 | -11.75% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $159.79 | 13.29% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $244.66 | 5.43% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $228.04 | $1.34 | -6.25% | 5,881.63 | -2.50% |
| 평균의 (R): | 0.86% | 1.16% | ||||
| 표준 편차: | 7.43% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $179.42 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $159.81 | $0.97 | -10.39% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $141.04 | -11.75% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $159.79 | 13.29% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $169.86 | $0.97 | 6.91% | 3,044.31 | 4.53% |
| 5. | 2020. 6. 30. | $169.07 | -0.47% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $173.35 | 2.53% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $192.44 | $0.97 | 11.57% | 3,500.31 | 7.01% |
| 8. | 2020. 9. 30. | $196.87 | 2.30% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $177.19 | -10.00% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $204.08 | $0.97 | 15.72% | 3,621.63 | 10.75% |
| 11. | 2020. 12. 31. | $208.22 | 2.03% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $197.47 | -5.16% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $205.96 | $0.97 | 4.79% | 3,811.15 | 2.61% |
| 14. | 2021. 3. 31. | $220.41 | 7.02% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $222.09 | 0.76% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $224.73 | $1.07 | 1.67% | 4,204.11 | 0.55% |
| 17. | 2021. 6. 30. | $219.93 | -2.14% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $218.76 | -0.53% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $216.84 | $1.07 | -0.39% | 4,522.68 | 2.90% |
| 20. | 2021. 9. 30. | $196.01 | -9.61% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $241.40 | 23.16% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $235.64 | -2.39% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $251.93 | $1.18 | 7.41% | 4,766.18 | 4.36% |
| 24. | 2022. 1. 31. | $244.55 | -2.93% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $245.95 | $1.18 | 1.05% | 4,373.94 | -3.14% |
| 26. | 2022. 3. 31. | $273.21 | 11.08% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $234.29 | -14.25% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $219.78 | $1.30 | -5.64% | 4,132.15 | 0.01% |
| 29. | 2022. 6. 30. | $213.28 | -2.96% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $227.30 | 6.57% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $224.51 | $1.30 | -0.66% | 3,955.00 | -4.24% |
| 32. | 2022. 9. 30. | $194.82 | -13.22% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $197.14 | 1.19% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $217.43 | 10.29% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $207.07 | $1.30 | -4.17% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $204.19 | -1.39% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $207.28 | $1.30 | 2.15% | 3,970.15 | -2.61% |
| 38. | 2023. 3. 31. | $201.26 | -2.90% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $195.70 | -2.76% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $192.52 | $1.30 | -0.96% | 4,179.83 | 0.25% |
| 41. | 2023. 6. 30. | $204.62 | 6.29% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $232.02 | 13.39% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $220.57 | $1.30 | -4.37% | 4,507.66 | -1.77% |
| 44. | 2023. 9. 30. | $203.63 | -7.68% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $207.61 | 1.95% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $225.27 | 8.51% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $245.62 | $1.30 | 9.61% | 4,769.83 | 4.42% |
| 48. | 2024. 1. 31. | $243.93 | -0.69% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $253.69 | $1.30 | 4.53% | 5,096.27 | 5.17% |
| 50. | 2024. 3. 31. | $245.93 | -3.06% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $237.16 | -3.57% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $232.82 | $1.30 | -1.28% | 5,277.51 | 4.80% |
| 53. | 2024. 6. 30. | $226.26 | -2.82% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $246.73 | 9.05% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $256.09 | $1.34 | 4.34% | 5,648.40 | 2.28% |
| 56. | 2024. 9. 30. | $246.48 | -3.75% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $232.07 | -5.85% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $244.66 | 5.43% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $228.04 | $1.34 | -6.25% | 5,881.63 | -2.50% |
| 평균의 (R): | 0.86% | 1.16% | ||||
| 표준 편차: | 7.43% | 5.28% | ||||
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. | 2020. 2. 29. | -10.39% | -8.41% | 126.51 | 91.63 | 107.66 |
| 2. | 2020. 3. 31. | -11.75% | -12.51% | 158.85 | 186.96 | 172.33 |
| 3. | 2020. 4. 30. | 13.29% | 12.68% | 154.64 | 132.78 | 143.30 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 5.43% | 5.73% | 20.85 | 20.87 | 20.86 |
| 59. | 2024. 12. 31. | -6.25% | -2.50% | 50.47 | 13.40 | 26.00 |
| 합계 (Σ): | 3,198.65 | 1,618.62 | 1,730.19 | |||
| 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. | 2020. 2. 29. | -10.39% | -8.41% | 126.51 | 91.63 | 107.66 |
| 2. | 2020. 3. 31. | -11.75% | -12.51% | 158.85 | 186.96 | 172.33 |
| 3. | 2020. 4. 30. | 13.29% | 12.68% | 154.64 | 132.78 | 143.30 |
| 4. | 2020. 5. 31. | 6.91% | 4.53% | 36.61 | 11.34 | 20.37 |
| 5. | 2020. 6. 30. | -0.47% | 1.84% | 1.75 | 0.46 | -0.90 |
| 6. | 2020. 7. 31. | 2.53% | 5.51% | 2.80 | 18.91 | 7.28 |
| 7. | 2020. 8. 31. | 11.57% | 7.01% | 114.78 | 34.17 | 62.62 |
| 8. | 2020. 9. 30. | 2.30% | -3.92% | 2.08 | 25.85 | -7.34 |
| 9. | 2020. 10. 31. | -10.00% | -2.77% | 117.83 | 15.43 | 42.64 |
| 10. | 2020. 11. 30. | 15.72% | 10.75% | 220.96 | 92.03 | 142.60 |
| 11. | 2020. 12. 31. | 2.03% | 3.71% | 1.37 | 6.51 | 2.98 |
| 12. | 2021. 1. 31. | -5.16% | -1.11% | 36.26 | 5.18 | 13.70 |
| 13. | 2021. 2. 28. | 4.79% | 2.61% | 15.46 | 2.10 | 5.69 |
| 14. | 2021. 3. 31. | 7.02% | 4.24% | 37.91 | 9.50 | 18.98 |
| 15. | 2021. 4. 30. | 0.76% | 5.24% | 0.01 | 16.66 | -0.39 |
| 16. | 2021. 5. 31. | 1.67% | 0.55% | 0.66 | 0.38 | -0.50 |
| 17. | 2021. 6. 30. | -2.14% | 2.22% | 8.97 | 1.12 | -3.17 |
| 18. | 2021. 7. 31. | -0.53% | 2.27% | 1.93 | 1.24 | -1.55 |
| 19. | 2021. 8. 31. | -0.39% | 2.90% | 1.56 | 3.02 | -2.17 |
| 20. | 2021. 9. 30. | -9.61% | -4.76% | 109.51 | 35.02 | 61.93 |
| 21. | 2021. 10. 31. | 23.16% | 6.91% | 497.22 | 33.10 | 128.29 |
| 22. | 2021. 11. 30. | -2.39% | -0.83% | 10.53 | 3.98 | 6.47 |
| 23. | 2021. 12. 31. | 7.41% | 4.36% | 42.97 | 10.24 | 20.98 |
| 24. | 2022. 1. 31. | -2.93% | -5.26% | 14.35 | 41.21 | 24.32 |
| 25. | 2022. 2. 28. | 1.05% | -3.14% | 0.04 | 18.47 | -0.84 |
| 26. | 2022. 3. 31. | 11.08% | 3.58% | 104.55 | 5.84 | 24.70 |
| 27. | 2022. 4. 30. | -14.25% | -8.80% | 228.13 | 99.14 | 150.39 |
| 28. | 2022. 5. 31. | -5.64% | 0.01% | 42.21 | 1.34 | 7.51 |
| 29. | 2022. 6. 30. | -2.96% | -8.39% | 14.56 | 91.26 | 36.46 |
| 30. | 2022. 7. 31. | 6.57% | 9.11% | 32.66 | 63.21 | 45.44 |
| 31. | 2022. 8. 31. | -0.66% | -4.24% | 2.29 | 29.22 | 8.18 |
| 32. | 2022. 9. 30. | -13.22% | -9.34% | 198.33 | 110.27 | 147.88 |
| 33. | 2022. 10. 31. | 1.19% | 7.99% | 0.11 | 46.58 | 2.27 |
| 34. | 2022. 11. 30. | 10.29% | 5.38% | 88.99 | 17.76 | 39.75 |
| 35. | 2022. 12. 31. | -4.17% | -5.90% | 25.25 | 49.82 | 35.47 |
| 36. | 2023. 1. 31. | -1.39% | 6.18% | 5.06 | 25.14 | -11.28 |
| 37. | 2023. 2. 28. | 2.15% | -2.61% | 1.67 | 14.23 | -4.87 |
| 38. | 2023. 3. 31. | -2.90% | 3.51% | 14.16 | 5.49 | -8.82 |
| 39. | 2023. 4. 30. | -2.76% | 1.46% | 13.11 | 0.09 | -1.10 |
| 40. | 2023. 5. 31. | -0.96% | 0.25% | 3.31 | 0.83 | 1.66 |
| 41. | 2023. 6. 30. | 6.29% | 4.71% | 29.45 | 12.62 | 19.28 |
| 42. | 2023. 7. 31. | 13.39% | 4.85% | 157.06 | 13.58 | 46.18 |
| 43. | 2023. 8. 31. | -4.37% | -1.77% | 27.39 | 8.60 | 15.35 |
| 44. | 2023. 9. 30. | -7.68% | -4.87% | 72.91 | 36.40 | 51.52 |
| 45. | 2023. 10. 31. | 1.95% | -2.20% | 1.20 | 11.28 | -3.68 |
| 46. | 2023. 11. 30. | 8.51% | 8.92% | 58.49 | 60.17 | 59.32 |
| 47. | 2023. 12. 31. | 9.61% | 4.42% | 76.60 | 10.64 | 28.55 |
| 48. | 2024. 1. 31. | -0.69% | 1.59% | 2.39 | 0.18 | -0.66 |
| 49. | 2024. 2. 29. | 4.53% | 5.17% | 13.51 | 16.09 | 14.74 |
| 50. | 2024. 3. 31. | -3.06% | 3.10% | 15.35 | 3.77 | -7.60 |
| 51. | 2024. 4. 30. | -3.57% | -4.16% | 19.58 | 28.33 | 23.55 |
| 52. | 2024. 5. 31. | -1.28% | 4.80% | 4.58 | 13.26 | -7.79 |
| 53. | 2024. 6. 30. | -2.82% | 3.47% | 13.51 | 5.32 | -8.48 |
| 54. | 2024. 7. 31. | 9.05% | 1.13% | 67.05 | 0.00 | -0.24 |
| 55. | 2024. 8. 31. | 4.34% | 2.28% | 12.10 | 1.26 | 3.90 |
| 56. | 2024. 9. 30. | -3.75% | 2.02% | 21.26 | 0.74 | -3.96 |
| 57. | 2024. 10. 31. | -5.85% | -0.99% | 44.95 | 4.63 | 14.42 |
| 58. | 2024. 11. 30. | 5.43% | 5.73% | 20.85 | 20.87 | 20.86 |
| 59. | 2024. 12. 31. | -6.25% | -2.50% | 50.47 | 13.40 | 26.00 |
| 합계 (Σ): | 3,198.65 | 1,618.62 | 1,730.19 | |||
모두 보기
분산UNP = Σ(RUNP,t–RUNP)2 ÷ (59 – 1)
= 3,198.65 ÷ (59 – 1)
= 55.15
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산UNP, S&P 500 = Σ(RUNP,t–RUNP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,730.19 ÷ (59 – 1)
= 29.83
체계적인 위험 추정 (β)
| 분산UNP | 55.15 |
| 분산S&P 500 | 27.91 |
| 공분산UNP, S&P 500 | 29.83 |
| 상관 계수UNP, S&P 5001 | 0.76 |
| βUNP2 | 1.07 |
| αUNP3 | -0.38% |
계산
1 상관 계수UNP, S&P 500
= 공분산UNP, S&P 500 ÷ (표준 편차UNP × 표준 편차S&P 500)
= 29.83 ÷ (7.43% × 5.28%)
= 0.76
2 βUNP
= 공분산UNP, S&P 500 ÷ 분산S&P 500
= 29.83 ÷ 27.91
= 1.07
3 αUNP
= 평균의UNP – βUNP × 평균의S&P 500
= 0.86% – 1.07 × 1.16%
= -0.38%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.87% |
| 보통주의 체계적 위험UPC | βUNP | 1.07 |
| UPC 보통주에 대한 예상 수익률3 | E(RUNP) | 15.58% |
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]
= 4.56% + 1.07 [14.87% – 4.56%]
= 15.58%