자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 UAL보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
United Airlines Holdings Inc., 월별 수익률
| United Airlines Holdings Inc. (UAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UAL,t1 | 피제수UAL,t1 | RUAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $39.99 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $52.68 | 31.73% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $57.54 | 9.23% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $54.40 | -5.46% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $101.96 | 8.42% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $111.82 | 9.67% | 6,845.50 | -0.05% | |
| 평균의 (R): | 2.61% | 1.14% | ||||
| 표준 편차: | 13.44% | 4.37% | ||||
| United Airlines Holdings Inc. (UAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UAL,t1 | 피제수UAL,t1 | RUAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $39.99 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $52.68 | 31.73% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $57.54 | 9.23% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $54.40 | -5.46% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $58.35 | 7.26% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $52.29 | -10.39% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $46.72 | -10.65% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $46.51 | -0.45% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $47.57 | 2.28% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $46.14 | -3.01% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $42.26 | -8.41% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $43.78 | 3.60% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $42.88 | -2.06% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $44.40 | 3.54% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $46.36 | 4.41% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $50.50 | 8.93% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $47.63 | -5.68% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $35.42 | -25.64% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $36.75 | 3.75% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $35.01 | -4.73% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $32.53 | -7.08% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $43.08 | 32.43% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $44.17 | 2.53% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $37.70 | -14.65% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $48.96 | 29.87% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $51.96 | 6.13% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $44.25 | -14.84% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $43.80 | -1.02% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $47.47 | 8.38% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $54.87 | 15.59% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $54.31 | -1.02% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $49.81 | -8.29% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $42.30 | -15.08% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $35.01 | -17.23% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $39.40 | 12.54% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $41.26 | 4.72% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $41.38 | 0.29% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $45.49 | 9.93% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $47.88 | 5.25% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $51.46 | 7.48% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $52.99 | 2.97% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $48.66 | -8.17% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $45.42 | -6.66% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $44.04 | -3.04% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $57.06 | 29.56% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $78.26 | 37.15% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $96.83 | 23.73% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $97.10 | 0.28% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $105.84 | 9.00% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $93.81 | -11.37% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $69.05 | -26.39% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $68.82 | -0.33% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $79.45 | 15.45% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $79.63 | 0.23% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $88.31 | 10.90% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $105.00 | 18.90% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $96.50 | -8.10% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $94.04 | -2.55% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $101.96 | 8.42% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $111.82 | 9.67% | 6,845.50 | -0.05% | |
| 평균의 (R): | 2.61% | 1.14% | ||||
| 표준 편차: | 13.44% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 UAL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
United Airlines Holdings Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RUAL,t | RS&P 500,t | (RUAL,t–RUAL)2 | (RS&P 500,t–RS&P 500)2 | (RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 31.73% | 2.61% | 848.27 | 2.17 | 42.90 |
| 2. | 2021. 3. 31. | 9.23% | 4.24% | 43.79 | 9.66 | 20.57 |
| 3. | 2021. 4. 30. | -5.46% | 5.24% | 65.04 | 16.86 | -33.12 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 8.42% | 0.13% | 33.80 | 1.01 | -5.85 |
| 59. | 2025. 12. 31. | 9.67% | -0.05% | 49.88 | 1.41 | -8.39 |
| 합계 (Σ): | 10,482.34 | 1,108.23 | 1,422.10 | |||
| t | 날짜 | RUAL,t | RS&P 500,t | (RUAL,t–RUAL)2 | (RS&P 500,t–RS&P 500)2 | (RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 31.73% | 2.61% | 848.27 | 2.17 | 42.90 |
| 2. | 2021. 3. 31. | 9.23% | 4.24% | 43.79 | 9.66 | 20.57 |
| 3. | 2021. 4. 30. | -5.46% | 5.24% | 65.04 | 16.86 | -33.12 |
| 4. | 2021. 5. 31. | 7.26% | 0.55% | 21.65 | 0.35 | -2.73 |
| 5. | 2021. 6. 30. | -10.39% | 2.22% | 168.83 | 1.18 | -14.10 |
| 6. | 2021. 7. 31. | -10.65% | 2.27% | 175.83 | 1.30 | -15.10 |
| 7. | 2021. 8. 31. | -0.45% | 2.90% | 9.35 | 3.11 | -5.39 |
| 8. | 2021. 9. 30. | 2.28% | -4.76% | 0.11 | 34.73 | 1.94 |
| 9. | 2021. 10. 31. | -3.01% | 6.91% | 31.52 | 33.39 | -32.44 |
| 10. | 2021. 11. 30. | -8.41% | -0.83% | 121.38 | 3.88 | 21.70 |
| 11. | 2021. 12. 31. | 3.60% | 4.36% | 0.98 | 10.40 | 3.19 |
| 12. | 2022. 1. 31. | -2.06% | -5.26% | 21.75 | 40.89 | 29.82 |
| 13. | 2022. 2. 28. | 3.54% | -3.14% | 0.88 | 18.25 | -4.00 |
| 14. | 2022. 3. 31. | 4.41% | 3.58% | 3.26 | 5.96 | 4.41 |
| 15. | 2022. 4. 30. | 8.93% | -8.80% | 39.97 | 98.64 | -62.79 |
| 16. | 2022. 5. 31. | -5.68% | 0.01% | 68.74 | 1.28 | 9.38 |
| 17. | 2022. 6. 30. | -25.64% | -8.39% | 797.67 | 90.79 | 269.10 |
| 18. | 2022. 7. 31. | 3.75% | 9.11% | 1.32 | 63.61 | 9.15 |
| 19. | 2022. 8. 31. | -4.73% | -4.24% | 53.91 | 28.95 | 39.50 |
| 20. | 2022. 9. 30. | -7.08% | -9.34% | 93.93 | 109.74 | 101.53 |
| 21. | 2022. 10. 31. | 32.43% | 7.99% | 889.46 | 46.93 | 204.30 |
| 22. | 2022. 11. 30. | 2.53% | 5.38% | 0.01 | 17.97 | -0.33 |
| 23. | 2022. 12. 31. | -14.65% | -5.90% | 297.76 | 49.47 | 121.36 |
| 24. | 2023. 1. 31. | 29.87% | 6.18% | 743.08 | 25.39 | 137.36 |
| 25. | 2023. 2. 28. | 6.13% | -2.61% | 12.39 | 14.04 | -13.19 |
| 26. | 2023. 3. 31. | -14.84% | 3.51% | 304.37 | 5.61 | -41.33 |
| 27. | 2023. 4. 30. | -1.02% | 1.46% | 13.14 | 0.11 | -1.19 |
| 28. | 2023. 5. 31. | 8.38% | 0.25% | 33.31 | 0.79 | -5.12 |
| 29. | 2023. 6. 30. | 15.59% | 4.71% | 168.50 | 12.80 | 46.44 |
| 30. | 2023. 7. 31. | -1.02% | 4.85% | 13.17 | 13.76 | -13.46 |
| 31. | 2023. 8. 31. | -8.29% | -1.77% | 118.67 | 8.46 | 31.68 |
| 32. | 2023. 9. 30. | -15.08% | -4.87% | 312.76 | 36.10 | 106.25 |
| 33. | 2023. 10. 31. | -17.23% | -2.20% | 393.70 | 11.12 | 66.15 |
| 34. | 2023. 11. 30. | 12.54% | 8.92% | 98.63 | 60.56 | 77.28 |
| 35. | 2023. 12. 31. | 4.72% | 4.42% | 4.46 | 10.80 | 6.94 |
| 36. | 2024. 1. 31. | 0.29% | 1.59% | 5.37 | 0.21 | -1.05 |
| 37. | 2024. 2. 29. | 9.93% | 5.17% | 53.65 | 16.29 | 29.56 |
| 38. | 2024. 3. 31. | 5.25% | 3.10% | 7.00 | 3.86 | 5.20 |
| 39. | 2024. 4. 30. | 7.48% | -4.16% | 23.71 | 28.06 | -25.80 |
| 40. | 2024. 5. 31. | 2.97% | 4.80% | 0.13 | 13.44 | 1.34 |
| 41. | 2024. 6. 30. | -8.17% | 3.47% | 116.19 | 5.43 | -25.12 |
| 42. | 2024. 7. 31. | -6.66% | 1.13% | 85.86 | 0.00 | 0.04 |
| 43. | 2024. 8. 31. | -3.04% | 2.28% | 31.88 | 1.32 | -6.48 |
| 44. | 2024. 9. 30. | 29.56% | 2.02% | 726.64 | 0.78 | 23.82 |
| 45. | 2024. 10. 31. | 37.15% | -0.99% | 1,193.43 | 4.52 | -73.44 |
| 46. | 2024. 11. 30. | 23.73% | 5.73% | 446.09 | 21.10 | 97.03 |
| 47. | 2024. 12. 31. | 0.28% | -2.50% | 5.42 | 13.21 | 8.47 |
| 48. | 2025. 1. 31. | 9.00% | 2.70% | 40.87 | 2.45 | 10.01 |
| 49. | 2025. 2. 28. | -11.37% | -1.42% | 195.27 | 6.56 | 35.78 |
| 50. | 2025. 3. 31. | -26.39% | -5.75% | 841.10 | 47.48 | 199.84 |
| 51. | 2025. 4. 30. | -0.33% | -0.76% | 8.65 | 3.60 | 5.58 |
| 52. | 2025. 5. 31. | 15.45% | 6.15% | 164.82 | 25.16 | 64.40 |
| 53. | 2025. 6. 30. | 0.23% | 4.96% | 5.67 | 14.63 | -9.11 |
| 54. | 2025. 7. 31. | 10.90% | 2.17% | 68.77 | 1.06 | 8.55 |
| 55. | 2025. 8. 31. | 18.90% | 1.91% | 265.41 | 0.59 | 12.55 |
| 56. | 2025. 9. 30. | -8.10% | 3.53% | 114.56 | 5.74 | -25.65 |
| 57. | 2025. 10. 31. | -2.55% | 2.27% | 26.60 | 1.28 | -5.84 |
| 58. | 2025. 11. 30. | 8.42% | 0.13% | 33.80 | 1.01 | -5.85 |
| 59. | 2025. 12. 31. | 9.67% | -0.05% | 49.88 | 1.41 | -8.39 |
| 합계 (Σ): | 10,482.34 | 1,108.23 | 1,422.10 | |||
모두 보기
분산UAL = Σ(RUAL,t–RUAL)2 ÷ (59 – 1)
= 10,482.34 ÷ (59 – 1)
= 180.73
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산UAL, S&P 500 = Σ(RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,422.10 ÷ (59 – 1)
= 24.52
체계적인 위험 추정 (β)
| 분산UAL | 180.73 |
| 분산S&P 500 | 19.11 |
| 공분산UAL, S&P 500 | 24.52 |
| 상관 계수UAL, S&P 5001 | 0.42 |
| βUAL2 | 1.28 |
| αUAL3 | 1.15% |
계산
1 상관 계수UAL, S&P 500
= 공분산UAL, S&P 500 ÷ (표준 편차UAL × 표준 편차S&P 500)
= 24.52 ÷ (13.44% × 4.37%)
= 0.42
2 βUAL
= 공분산UAL, S&P 500 ÷ 분산S&P 500
= 24.52 ÷ 19.11
= 1.28
3 αUAL
= 평균의UAL – βUAL × 평균의S&P 500
= 2.61% – 1.28 × 1.14%
= 1.15%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험UAL | βUAL | 1.28 |
| UAL 보통주에 대한 예상 수익률3 | E(RUAL) | 21.00% |
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(RUAL) = RF + βUAL [E(RM) – RF]
= 4.54% + 1.28 [17.37% – 4.54%]
= 21.00%