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 |
| 2020. 1. 31. | $74.80 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $61.59 | -17.66% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $31.55 | -48.77% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $29.58 | -6.24% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $96.83 | 23.73% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $97.10 | 0.28% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.63% | 1.16% | ||||
| 표준 편차: | 15.35% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $74.80 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $61.59 | -17.66% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $31.55 | -48.77% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $29.58 | -6.24% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $28.04 | -5.21% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $34.61 | 23.43% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $31.38 | -9.33% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $36.00 | 14.72% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $34.75 | -3.47% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $33.86 | -2.56% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $45.05 | 33.05% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $43.25 | -4.00% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $39.99 | -7.54% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $52.68 | 31.73% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $57.54 | 9.23% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $54.40 | -5.46% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $58.35 | 7.26% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $52.29 | -10.39% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $46.72 | -10.65% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $46.51 | -0.45% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $47.57 | 2.28% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $46.14 | -3.01% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $42.26 | -8.41% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $43.78 | 3.60% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $42.88 | -2.06% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $44.40 | 3.54% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $46.36 | 4.41% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $50.50 | 8.93% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $47.63 | -5.68% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $35.42 | -25.64% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $36.75 | 3.75% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $35.01 | -4.73% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $32.53 | -7.08% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $43.08 | 32.43% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $44.17 | 2.53% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $37.70 | -14.65% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $48.96 | 29.87% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $51.96 | 6.13% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $44.25 | -14.84% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $43.80 | -1.02% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $47.47 | 8.38% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $54.87 | 15.59% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $54.31 | -1.02% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $49.81 | -8.29% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $42.30 | -15.08% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $35.01 | -17.23% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $39.40 | 12.54% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $41.26 | 4.72% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $41.38 | 0.29% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $45.49 | 9.93% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $47.88 | 5.25% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $51.46 | 7.48% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $52.99 | 2.97% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $48.66 | -8.17% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $45.42 | -6.66% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $44.04 | -3.04% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $57.06 | 29.56% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $78.26 | 37.15% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $96.83 | 23.73% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $97.10 | 0.28% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.63% | 1.16% | ||||
| 표준 편차: | 15.35% | 5.28% | ||||
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. | 2020. 2. 29. | -17.66% | -8.41% | 372.31 | 91.63 | 184.70 |
| 2. | 2020. 3. 31. | -48.77% | -12.51% | 2,541.06 | 186.96 | 689.25 |
| 3. | 2020. 4. 30. | -6.24% | 12.68% | 62.08 | 132.78 | -90.79 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 23.73% | 5.73% | 488.14 | 20.87 | 100.94 |
| 59. | 2024. 12. 31. | 0.28% | -2.50% | 1.84 | 13.40 | 4.96 |
| 합계 (Σ): | 13,661.16 | 1,618.62 | 2,290.77 | |||
| 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. | 2020. 2. 29. | -17.66% | -8.41% | 372.31 | 91.63 | 184.70 |
| 2. | 2020. 3. 31. | -48.77% | -12.51% | 2,541.06 | 186.96 | 689.25 |
| 3. | 2020. 4. 30. | -6.24% | 12.68% | 62.08 | 132.78 | -90.79 |
| 4. | 2020. 5. 31. | -5.21% | 4.53% | 46.80 | 11.34 | -23.03 |
| 5. | 2020. 6. 30. | 23.43% | 1.84% | 475.07 | 0.46 | 14.77 |
| 6. | 2020. 7. 31. | -9.33% | 5.51% | 120.28 | 18.91 | -47.70 |
| 7. | 2020. 8. 31. | 14.72% | 7.01% | 171.29 | 34.17 | 76.50 |
| 8. | 2020. 9. 30. | -3.47% | -3.92% | 26.08 | 25.85 | 25.96 |
| 9. | 2020. 10. 31. | -2.56% | -2.77% | 17.61 | 15.43 | 16.48 |
| 10. | 2020. 11. 30. | 33.05% | 10.75% | 986.78 | 92.03 | 301.35 |
| 11. | 2020. 12. 31. | -4.00% | 3.71% | 31.70 | 6.51 | -14.36 |
| 12. | 2021. 1. 31. | -7.54% | -1.11% | 84.13 | 5.18 | 20.87 |
| 13. | 2021. 2. 28. | 31.73% | 2.61% | 905.90 | 2.10 | 43.58 |
| 14. | 2021. 3. 31. | 9.23% | 4.24% | 57.62 | 9.50 | 23.40 |
| 15. | 2021. 4. 30. | -5.46% | 5.24% | 50.29 | 16.66 | -28.94 |
| 16. | 2021. 5. 31. | 7.26% | 0.55% | 31.65 | 0.38 | -3.45 |
| 17. | 2021. 6. 30. | -10.39% | 2.22% | 144.49 | 1.12 | -12.74 |
| 18. | 2021. 7. 31. | -10.65% | 2.27% | 150.97 | 1.24 | -13.68 |
| 19. | 2021. 8. 31. | -0.45% | 2.90% | 4.34 | 3.02 | -3.62 |
| 20. | 2021. 9. 30. | 2.28% | -4.76% | 0.42 | 35.02 | -3.81 |
| 21. | 2021. 10. 31. | -3.01% | 6.91% | 21.54 | 33.10 | -26.70 |
| 22. | 2021. 11. 30. | -8.41% | -0.83% | 100.88 | 3.98 | 20.03 |
| 23. | 2021. 12. 31. | 3.60% | 4.36% | 3.85 | 10.24 | 6.28 |
| 24. | 2022. 1. 31. | -2.06% | -5.26% | 13.62 | 41.21 | 23.69 |
| 25. | 2022. 2. 28. | 3.54% | -3.14% | 3.65 | 18.47 | -8.21 |
| 26. | 2022. 3. 31. | 4.41% | 3.58% | 7.73 | 5.84 | 6.72 |
| 27. | 2022. 4. 30. | 8.93% | -8.80% | 53.22 | 99.14 | -72.64 |
| 28. | 2022. 5. 31. | -5.68% | 0.01% | 53.55 | 1.34 | 8.46 |
| 29. | 2022. 6. 30. | -25.64% | -8.39% | 743.65 | 91.26 | 260.52 |
| 30. | 2022. 7. 31. | 3.75% | 9.11% | 4.49 | 63.21 | 16.86 |
| 31. | 2022. 8. 31. | -4.73% | -4.24% | 40.57 | 29.22 | 34.43 |
| 32. | 2022. 9. 30. | -7.08% | -9.34% | 76.01 | 110.27 | 91.55 |
| 33. | 2022. 10. 31. | 32.43% | 7.99% | 948.44 | 46.58 | 210.19 |
| 34. | 2022. 11. 30. | 2.53% | 5.38% | 0.80 | 17.76 | 3.77 |
| 35. | 2022. 12. 31. | -14.65% | -5.90% | 265.13 | 49.82 | 114.93 |
| 36. | 2023. 1. 31. | 29.87% | 6.18% | 797.08 | 25.14 | 141.56 |
| 37. | 2023. 2. 28. | 6.13% | -2.61% | 20.18 | 14.23 | -16.95 |
| 38. | 2023. 3. 31. | -14.84% | 3.51% | 271.36 | 5.49 | -38.61 |
| 39. | 2023. 4. 30. | -1.02% | 1.46% | 7.03 | 0.09 | -0.80 |
| 40. | 2023. 5. 31. | 8.38% | 0.25% | 45.48 | 0.83 | -6.16 |
| 41. | 2023. 6. 30. | 15.59% | 4.71% | 194.71 | 12.62 | 49.57 |
| 42. | 2023. 7. 31. | -1.02% | 4.85% | 7.05 | 13.58 | -9.78 |
| 43. | 2023. 8. 31. | -8.29% | -1.77% | 98.42 | 8.60 | 29.10 |
| 44. | 2023. 9. 30. | -15.08% | -4.87% | 279.29 | 36.40 | 100.83 |
| 45. | 2023. 10. 31. | -17.23% | -2.20% | 356.03 | 11.28 | 63.38 |
| 46. | 2023. 11. 30. | 12.54% | 8.92% | 118.91 | 60.17 | 84.58 |
| 47. | 2023. 12. 31. | 4.72% | 4.42% | 9.52 | 10.64 | 10.07 |
| 48. | 2024. 1. 31. | 0.29% | 1.59% | 1.81 | 0.18 | -0.58 |
| 49. | 2024. 2. 29. | 9.93% | 5.17% | 68.85 | 16.09 | 33.28 |
| 50. | 2024. 3. 31. | 5.25% | 3.10% | 13.10 | 3.77 | 7.02 |
| 51. | 2024. 4. 30. | 7.48% | -4.16% | 34.13 | 28.33 | -31.10 |
| 52. | 2024. 5. 31. | 2.97% | 4.80% | 1.79 | 13.26 | 4.87 |
| 53. | 2024. 6. 30. | -8.17% | 3.47% | 96.16 | 5.32 | -22.61 |
| 54. | 2024. 7. 31. | -6.66% | 1.13% | 68.78 | 0.00 | 0.24 |
| 55. | 2024. 8. 31. | -3.04% | 2.28% | 21.84 | 1.26 | -5.24 |
| 56. | 2024. 9. 30. | 29.56% | 2.02% | 780.04 | 0.74 | 23.97 |
| 57. | 2024. 10. 31. | 37.15% | -0.99% | 1,261.60 | 4.63 | -76.40 |
| 58. | 2024. 11. 30. | 23.73% | 5.73% | 488.14 | 20.87 | 100.94 |
| 59. | 2024. 12. 31. | 0.28% | -2.50% | 1.84 | 13.40 | 4.96 |
| 합계 (Σ): | 13,661.16 | 1,618.62 | 2,290.77 | |||
모두 보기
분산UAL = Σ(RUAL,t–RUAL)2 ÷ (59 – 1)
= 13,661.16 ÷ (59 – 1)
= 235.54
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산UAL, S&P 500 = Σ(RUAL,t–RUAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,290.77 ÷ (59 – 1)
= 39.50
체계적인 위험 추정 (β)
| 분산UAL | 235.54 |
| 분산S&P 500 | 27.91 |
| 공분산UAL, S&P 500 | 39.50 |
| 상관 계수UAL, S&P 5001 | 0.49 |
| βUAL2 | 1.42 |
| αUAL3 | -0.01% |
계산
1 상관 계수UAL, S&P 500
= 공분산UAL, S&P 500 ÷ (표준 편차UAL × 표준 편차S&P 500)
= 39.50 ÷ (15.35% × 5.28%)
= 0.49
2 βUAL
= 공분산UAL, S&P 500 ÷ 분산S&P 500
= 39.50 ÷ 27.91
= 1.42
3 αUAL
= 평균의UAL – βUAL × 평균의S&P 500
= 1.63% – 1.42 × 1.16%
= -0.01%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.76% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.72% |
| 보통주의 체계적 위험UAL | βUAL | 1.42 |
| UAL 보통주에 대한 예상 수익률3 | E(RUAL) | 18.86% |
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]
= 4.76% + 1.42 [14.72% – 4.76%]
= 18.86%