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 |
| 2019. 1. 31. | $159.07 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $167.70 | $0.88 | 5.98% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $167.20 | -0.30% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $177.04 | 5.89% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $225.27 | 8.51% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $245.62 | $1.30 | 9.61% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.19% | 1.11% | ||||
| 표준 편차: | 7.41% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $159.07 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $167.70 | $0.88 | 5.98% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $167.20 | -0.30% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $177.04 | 5.89% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $166.78 | $0.88 | -5.30% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $169.11 | 1.40% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $179.95 | 6.41% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $161.96 | $0.97 | -9.46% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $161.98 | 0.01% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $165.46 | 2.15% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $175.99 | $0.97 | 6.95% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $180.79 | 2.73% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $179.42 | -0.76% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $159.81 | $0.97 | -10.39% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $141.04 | -11.75% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $159.79 | 13.29% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $169.86 | $0.97 | 6.91% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $169.07 | -0.47% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $173.35 | 2.53% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $192.44 | $0.97 | 11.57% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $196.87 | 2.30% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $177.19 | -10.00% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $204.08 | $0.97 | 15.72% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $208.22 | 2.03% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $197.47 | -5.16% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $205.96 | $0.97 | 4.79% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $220.41 | 7.02% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $222.09 | 0.76% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $224.73 | $1.07 | 1.67% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $219.93 | -2.14% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $218.76 | -0.53% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $216.84 | $1.07 | -0.39% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $196.01 | -9.61% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $241.40 | 23.16% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $235.64 | -2.39% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $251.93 | $1.18 | 7.41% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $244.55 | -2.93% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $245.95 | $1.18 | 1.05% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $273.21 | 11.08% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $234.29 | -14.25% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $219.78 | $1.30 | -5.64% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $213.28 | -2.96% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $227.30 | 6.57% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $224.51 | $1.30 | -0.66% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $194.82 | -13.22% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $197.14 | 1.19% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $217.43 | 10.29% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $207.07 | $1.30 | -4.17% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $204.19 | -1.39% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $207.28 | $1.30 | 2.15% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $201.26 | -2.90% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $195.70 | -2.76% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $192.52 | $1.30 | -0.96% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $204.62 | 6.29% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $232.02 | 13.39% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $220.57 | $1.30 | -4.37% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $203.63 | -7.68% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $207.61 | 1.95% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $225.27 | 8.51% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $245.62 | $1.30 | 9.61% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.19% | 1.11% | ||||
| 표준 편차: | 7.41% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 UNP의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 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. | 2019. 2. 28. | 5.98% | 2.97% | 22.92 | 3.49 | 8.94 |
| 2. | 2019. 3. 31. | -0.30% | 1.79% | 2.22 | 0.47 | -1.02 |
| 3. | 2019. 4. 30. | 5.89% | 3.93% | 22.04 | 7.98 | 13.26 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 8.51% | 8.92% | 53.52 | 61.03 | 57.15 |
| 59. | 2023. 12. 31. | 9.61% | 4.42% | 70.89 | 11.00 | 27.93 |
| 합계 (Σ): | 3,180.39 | 1,634.30 | 1,780.86 | |||
| 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. | 2019. 2. 28. | 5.98% | 2.97% | 22.92 | 3.49 | 8.94 |
| 2. | 2019. 3. 31. | -0.30% | 1.79% | 2.22 | 0.47 | -1.02 |
| 3. | 2019. 4. 30. | 5.89% | 3.93% | 22.04 | 7.98 | 13.26 |
| 4. | 2019. 5. 31. | -5.30% | -6.58% | 42.11 | 59.04 | 49.86 |
| 5. | 2019. 6. 30. | 1.40% | 6.89% | 0.04 | 33.49 | 1.19 |
| 6. | 2019. 7. 31. | 6.41% | 1.31% | 27.24 | 0.04 | 1.08 |
| 7. | 2019. 8. 31. | -9.46% | -1.81% | 113.40 | 8.50 | 31.04 |
| 8. | 2019. 9. 30. | 0.01% | 1.72% | 1.39 | 0.37 | -0.72 |
| 9. | 2019. 10. 31. | 2.15% | 2.04% | 0.92 | 0.88 | 0.90 |
| 10. | 2019. 11. 30. | 6.95% | 3.40% | 33.17 | 5.28 | 13.24 |
| 11. | 2019. 12. 31. | 2.73% | 2.86% | 2.36 | 3.07 | 2.69 |
| 12. | 2020. 1. 31. | -0.76% | -0.16% | 3.80 | 1.61 | 2.47 |
| 13. | 2020. 2. 29. | -10.39% | -8.41% | 134.09 | 90.57 | 110.20 |
| 14. | 2020. 3. 31. | -11.75% | -12.51% | 167.34 | 185.44 | 176.16 |
| 15. | 2020. 4. 30. | 13.29% | 12.68% | 146.49 | 134.06 | 140.14 |
| 16. | 2020. 5. 31. | 6.91% | 4.53% | 32.70 | 11.71 | 19.57 |
| 17. | 2020. 6. 30. | -0.47% | 1.84% | 2.74 | 0.54 | -1.21 |
| 18. | 2020. 7. 31. | 2.53% | 5.51% | 1.80 | 19.40 | 5.90 |
| 19. | 2020. 8. 31. | 11.57% | 7.01% | 107.77 | 34.82 | 61.25 |
| 20. | 2020. 9. 30. | 2.30% | -3.92% | 1.23 | 25.29 | -5.59 |
| 21. | 2020. 10. 31. | -10.00% | -2.77% | 125.16 | 15.00 | 43.32 |
| 22. | 2020. 11. 30. | 15.72% | 10.75% | 211.19 | 93.10 | 140.22 |
| 23. | 2020. 12. 31. | 2.03% | 3.71% | 0.70 | 6.79 | 2.18 |
| 24. | 2021. 1. 31. | -5.16% | -1.11% | 40.37 | 4.93 | 14.10 |
| 25. | 2021. 2. 28. | 4.79% | 2.61% | 12.96 | 2.26 | 5.41 |
| 26. | 2021. 3. 31. | 7.02% | 4.24% | 33.93 | 9.85 | 18.28 |
| 27. | 2021. 4. 30. | 0.76% | 5.24% | 0.18 | 17.11 | -1.77 |
| 28. | 2021. 5. 31. | 1.67% | 0.55% | 0.23 | 0.31 | -0.27 |
| 29. | 2021. 6. 30. | -2.14% | 2.22% | 11.07 | 1.24 | -3.71 |
| 30. | 2021. 7. 31. | -0.53% | 2.27% | 2.97 | 1.37 | -2.01 |
| 31. | 2021. 8. 31. | -0.39% | 2.90% | 2.49 | 3.22 | -2.83 |
| 32. | 2021. 9. 30. | -9.61% | -4.76% | 116.58 | 34.37 | 63.30 |
| 33. | 2021. 10. 31. | 23.16% | 6.91% | 482.51 | 33.74 | 127.59 |
| 34. | 2021. 11. 30. | -2.39% | -0.83% | 12.79 | 3.76 | 6.94 |
| 35. | 2021. 12. 31. | 7.41% | 4.36% | 38.73 | 10.60 | 20.26 |
| 36. | 2022. 1. 31. | -2.93% | -5.26% | 16.98 | 40.51 | 26.22 |
| 37. | 2022. 2. 28. | 1.05% | -3.14% | 0.02 | 17.99 | 0.58 |
| 38. | 2022. 3. 31. | 11.08% | 3.58% | 97.86 | 6.11 | 24.45 |
| 39. | 2022. 4. 30. | -14.25% | -8.80% | 238.28 | 98.04 | 152.84 |
| 40. | 2022. 5. 31. | -5.64% | 0.01% | 46.64 | 1.21 | 7.52 |
| 41. | 2022. 6. 30. | -2.96% | -8.39% | 17.21 | 90.21 | 39.40 |
| 42. | 2022. 7. 31. | 6.57% | 9.11% | 28.97 | 64.09 | 43.09 |
| 43. | 2022. 8. 31. | -0.66% | -4.24% | 3.41 | 28.62 | 9.88 |
| 44. | 2022. 9. 30. | -13.22% | -9.34% | 207.80 | 109.11 | 150.57 |
| 45. | 2022. 10. 31. | 1.19% | 7.99% | 0.00 | 47.34 | 0.00 |
| 46. | 2022. 11. 30. | 10.29% | 5.38% | 82.83 | 18.23 | 38.86 |
| 47. | 2022. 12. 31. | -4.17% | -5.90% | 28.71 | 49.04 | 37.52 |
| 48. | 2023. 1. 31. | -1.39% | 6.18% | 6.67 | 25.70 | -13.09 |
| 49. | 2023. 2. 28. | 2.15% | -2.61% | 0.92 | 13.82 | -3.56 |
| 50. | 2023. 3. 31. | -2.90% | 3.51% | 16.77 | 5.76 | -9.83 |
| 51. | 2023. 4. 30. | -2.76% | 1.46% | 15.63 | 0.13 | -1.42 |
| 52. | 2023. 5. 31. | -0.96% | 0.25% | 4.63 | 0.74 | 1.85 |
| 53. | 2023. 6. 30. | 6.29% | 4.71% | 25.95 | 13.02 | 18.38 |
| 54. | 2023. 7. 31. | 13.39% | 4.85% | 148.83 | 13.99 | 45.63 |
| 55. | 2023. 8. 31. | -4.37% | -1.77% | 30.97 | 8.28 | 16.01 |
| 56. | 2023. 9. 30. | -7.68% | -4.87% | 78.69 | 35.73 | 53.03 |
| 57. | 2023. 10. 31. | 1.95% | -2.20% | 0.58 | 10.92 | -2.52 |
| 58. | 2023. 11. 30. | 8.51% | 8.92% | 53.52 | 61.03 | 57.15 |
| 59. | 2023. 12. 31. | 9.61% | 4.42% | 70.89 | 11.00 | 27.93 |
| 합계 (Σ): | 3,180.39 | 1,634.30 | 1,780.86 | |||
모두 표시
분산UNP = Σ(RUNP,t–RUNP)2 ÷ (59 – 1)
= 3,180.39 ÷ (59 – 1)
= 54.83
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산UNP, S&P 500 = Σ(RUNP,t–RUNP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,780.86 ÷ (59 – 1)
= 30.70
체계적인 위험 추정 (β)
| 분산UNP | 54.83 |
| 분산S&P 500 | 28.18 |
| 공분산UNP, S&P 500 | 30.70 |
| 상관 계수UNP, S&P 5001 | 0.78 |
| βUNP2 | 1.09 |
| αUNP3 | -0.01% |
계산
1 상관 계수UNP, S&P 500
= 공분산UNP, S&P 500 ÷ (표준 편차UNP × 표준 편차S&P 500)
= 30.70 ÷ (7.41% × 5.31%)
= 0.78
2 βUNP
= 공분산UNP, S&P 500 ÷ 분산S&P 500
= 30.70 ÷ 28.18
= 1.09
3 αUNP
= 평균의UNP – βUNP × 평균의S&P 500
= 1.19% – 1.09 × 1.11%
= -0.01%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.80% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.50% |
| 보통주의 체계적 위험UPC | βUNP | 1.09 |
| UPC 보통주에 대한 예상 수익률3 | E(RUNP) | 14.28% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RUNP) = RF + βUNP [E(RM) – RF]
= 4.80% + 1.09 [13.50% – 4.80%]
= 14.28%