자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다 AAG.
수익률
American Airlines Group Inc., 월별 수익률
| American Airlines Group Inc. (AAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AAL,t1 | 피제수AAL,t1 | RAAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $35.77 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $35.63 | $0.10 | -0.11% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $31.76 | -10.86% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $34.18 | 7.62% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $12.43 | 11.48% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $13.74 | 10.54% | 4,769.83 | 4.42% | |
| 평균의 (R): | -0.64% | 1.11% | ||||
| 표준 편차: | 13.55% | 5.31% | ||||
| American Airlines Group Inc. (AAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AAL,t1 | 피제수AAL,t1 | RAAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $35.77 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $35.63 | $0.10 | -0.11% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $31.76 | -10.86% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $34.18 | 7.62% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $27.23 | $0.10 | -20.04% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $32.61 | 19.76% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $30.51 | -6.44% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $26.31 | $0.10 | -13.44% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $26.97 | 2.51% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $30.06 | 11.46% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $28.74 | $0.10 | -4.06% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $28.68 | -0.21% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $26.84 | -6.42% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $19.05 | $0.10 | -28.65% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $12.19 | -36.01% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $12.01 | -1.48% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $10.50 | -12.57% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $13.07 | 24.48% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $11.12 | -14.92% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $13.05 | 17.36% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $12.29 | -5.82% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $11.28 | -8.22% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $14.13 | 25.27% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $15.77 | 11.61% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $17.17 | 8.88% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $20.94 | 21.96% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $23.90 | 14.14% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $21.72 | -9.12% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $24.24 | 11.60% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $21.21 | -12.50% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $20.38 | -3.91% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $19.94 | -2.16% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $20.52 | 2.91% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $19.20 | -6.43% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $17.69 | -7.86% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $17.96 | 1.53% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $16.47 | -8.30% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $17.25 | 4.74% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $18.25 | 5.80% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $18.77 | 2.85% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $17.87 | -4.79% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $12.68 | -29.04% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $13.71 | 8.12% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $12.99 | -5.25% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $12.04 | -7.31% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $14.18 | 17.77% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $14.43 | 1.76% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $12.72 | -11.85% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $16.14 | 26.89% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $15.98 | -0.99% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $14.75 | -7.70% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $13.64 | -7.53% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $14.78 | 8.36% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $17.94 | 21.38% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $16.75 | -6.63% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $14.73 | -12.06% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $12.81 | -13.03% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $11.15 | -12.96% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $12.43 | 11.48% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $13.74 | 10.54% | 4,769.83 | 4.42% | |
| 평균의 (R): | -0.64% | 1.11% | ||||
| 표준 편차: | 13.55% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 AAL의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
American Airlines Group Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RAAL,t | RS&P 500,t | (RAAL,t–RAAL)2 | (RS&P 500,t–RS&P 500)2 | (RAAL,t–RAAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -0.11% | 2.97% | 0.28 | 3.49 | 0.99 |
| 2. | 2019. 3. 31. | -10.86% | 1.79% | 104.42 | 0.47 | -7.02 |
| 3. | 2019. 4. 30. | 7.62% | 3.93% | 68.27 | 7.98 | 23.35 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 11.48% | 8.92% | 146.97 | 61.03 | 94.71 |
| 59. | 2023. 12. 31. | 10.54% | 4.42% | 125.04 | 11.00 | 37.09 |
| 합계 (Σ): | 10,647.91 | 1,634.30 | 2,506.67 | |||
| t | 날짜 | RAAL,t | RS&P 500,t | (RAAL,t–RAAL)2 | (RS&P 500,t–RS&P 500)2 | (RAAL,t–RAAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -0.11% | 2.97% | 0.28 | 3.49 | 0.99 |
| 2. | 2019. 3. 31. | -10.86% | 1.79% | 104.42 | 0.47 | -7.02 |
| 3. | 2019. 4. 30. | 7.62% | 3.93% | 68.27 | 7.98 | 23.35 |
| 4. | 2019. 5. 31. | -20.04% | -6.58% | 376.27 | 59.04 | 149.05 |
| 5. | 2019. 6. 30. | 19.76% | 6.89% | 416.19 | 33.49 | 118.06 |
| 6. | 2019. 7. 31. | -6.44% | 1.31% | 33.60 | 0.04 | -1.20 |
| 7. | 2019. 8. 31. | -13.44% | -1.81% | 163.71 | 8.50 | 37.30 |
| 8. | 2019. 9. 30. | 2.51% | 1.72% | 9.93 | 0.37 | 1.93 |
| 9. | 2019. 10. 31. | 11.46% | 2.04% | 146.42 | 0.88 | 11.34 |
| 10. | 2019. 11. 30. | -4.06% | 3.40% | 11.66 | 5.28 | -7.85 |
| 11. | 2019. 12. 31. | -0.21% | 2.86% | 0.19 | 3.07 | 0.76 |
| 12. | 2020. 1. 31. | -6.42% | -0.16% | 33.32 | 1.61 | 7.32 |
| 13. | 2020. 2. 29. | -28.65% | -8.41% | 784.45 | 90.57 | 266.55 |
| 14. | 2020. 3. 31. | -36.01% | -12.51% | 1,250.85 | 185.44 | 481.62 |
| 15. | 2020. 4. 30. | -1.48% | 12.68% | 0.69 | 134.06 | -9.65 |
| 16. | 2020. 5. 31. | -12.57% | 4.53% | 142.32 | 11.71 | -40.83 |
| 17. | 2020. 6. 30. | 24.48% | 1.84% | 630.98 | 0.54 | 18.41 |
| 18. | 2020. 7. 31. | -14.92% | 5.51% | 203.82 | 19.40 | -62.88 |
| 19. | 2020. 8. 31. | 17.36% | 7.01% | 323.97 | 34.82 | 106.21 |
| 20. | 2020. 9. 30. | -5.82% | -3.92% | 26.84 | 25.29 | 26.05 |
| 21. | 2020. 10. 31. | -8.22% | -2.77% | 57.38 | 15.00 | 29.33 |
| 22. | 2020. 11. 30. | 25.27% | 10.75% | 671.28 | 93.10 | 249.99 |
| 23. | 2020. 12. 31. | 11.61% | 3.71% | 150.05 | 6.79 | 31.93 |
| 24. | 2021. 1. 31. | 8.88% | -1.11% | 90.65 | 4.93 | -21.13 |
| 25. | 2021. 2. 28. | 21.96% | 2.61% | 510.76 | 2.26 | 33.97 |
| 26. | 2021. 3. 31. | 14.14% | 4.24% | 218.41 | 9.85 | 46.38 |
| 27. | 2021. 4. 30. | -9.12% | 5.24% | 71.88 | 17.11 | -35.07 |
| 28. | 2021. 5. 31. | 11.60% | 0.55% | 149.95 | 0.31 | -6.82 |
| 29. | 2021. 6. 30. | -12.50% | 2.22% | 140.58 | 1.24 | -13.23 |
| 30. | 2021. 7. 31. | -3.91% | 2.27% | 10.69 | 1.37 | -3.82 |
| 31. | 2021. 8. 31. | -2.16% | 2.90% | 2.30 | 3.22 | -2.72 |
| 32. | 2021. 9. 30. | 2.91% | -4.76% | 12.62 | 34.37 | -20.82 |
| 33. | 2021. 10. 31. | -6.43% | 6.91% | 33.52 | 33.74 | -33.63 |
| 34. | 2021. 11. 30. | -7.86% | -0.83% | 52.15 | 3.76 | 14.00 |
| 35. | 2021. 12. 31. | 1.53% | 4.36% | 4.71 | 10.60 | 7.06 |
| 36. | 2022. 1. 31. | -8.30% | -5.26% | 58.57 | 40.51 | 48.71 |
| 37. | 2022. 2. 28. | 4.74% | -3.14% | 28.93 | 17.99 | -22.82 |
| 38. | 2022. 3. 31. | 5.80% | 3.58% | 41.48 | 6.11 | 15.92 |
| 39. | 2022. 4. 30. | 2.85% | -8.80% | 12.20 | 98.04 | -34.58 |
| 40. | 2022. 5. 31. | -4.79% | 0.01% | 17.24 | 1.21 | 4.57 |
| 41. | 2022. 6. 30. | -29.04% | -8.39% | 806.56 | 90.21 | 269.74 |
| 42. | 2022. 7. 31. | 8.12% | 9.11% | 76.85 | 64.09 | 70.18 |
| 43. | 2022. 8. 31. | -5.25% | -4.24% | 21.24 | 28.62 | 24.65 |
| 44. | 2022. 9. 30. | -7.31% | -9.34% | 44.49 | 109.11 | 69.67 |
| 45. | 2022. 10. 31. | 17.77% | 7.99% | 339.20 | 47.34 | 126.72 |
| 46. | 2022. 11. 30. | 1.76% | 5.38% | 5.79 | 18.23 | 10.27 |
| 47. | 2022. 12. 31. | -11.85% | -5.90% | 125.60 | 49.04 | 78.48 |
| 48. | 2023. 1. 31. | 26.89% | 6.18% | 757.90 | 25.70 | 139.56 |
| 49. | 2023. 2. 28. | -0.99% | -2.61% | 0.12 | 13.82 | 1.29 |
| 50. | 2023. 3. 31. | -7.70% | 3.51% | 49.76 | 5.76 | -16.92 |
| 51. | 2023. 4. 30. | -7.53% | 1.46% | 47.37 | 0.13 | -2.47 |
| 52. | 2023. 5. 31. | 8.36% | 0.25% | 81.02 | 0.74 | -7.72 |
| 53. | 2023. 6. 30. | 21.38% | 4.71% | 485.03 | 13.02 | 79.46 |
| 54. | 2023. 7. 31. | -6.63% | 4.85% | 35.88 | 13.99 | -22.40 |
| 55. | 2023. 8. 31. | -12.06% | -1.77% | 130.34 | 8.28 | 32.85 |
| 56. | 2023. 9. 30. | -13.03% | -4.87% | 153.55 | 35.73 | 74.07 |
| 57. | 2023. 10. 31. | -12.96% | -2.20% | 151.67 | 10.92 | 40.69 |
| 58. | 2023. 11. 30. | 11.48% | 8.92% | 146.97 | 61.03 | 94.71 |
| 59. | 2023. 12. 31. | 10.54% | 4.42% | 125.04 | 11.00 | 37.09 |
| 합계 (Σ): | 10,647.91 | 1,634.30 | 2,506.67 | |||
모두 표시
분산AAL = Σ(RAAL,t–RAAL)2 ÷ (59 – 1)
= 10,647.91 ÷ (59 – 1)
= 183.58
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산AAL, S&P 500 = Σ(RAAL,t–RAAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,506.67 ÷ (59 – 1)
= 43.22
체계적인 위험 추정 (β)
| 분산AAL | 183.58 |
| 분산S&P 500 | 28.18 |
| 공분산AAL, S&P 500 | 43.22 |
| 상관 계수AAL, S&P 5001 | 0.60 |
| βAAL2 | 1.53 |
| αAAL3 | -2.34% |
계산
1 상관 계수AAL, S&P 500
= 공분산AAL, S&P 500 ÷ (표준 편차AAL × 표준 편차S&P 500)
= 43.22 ÷ (13.55% × 5.31%)
= 0.60
2 βAAL
= 공분산AAL, S&P 500 ÷ 분산S&P 500
= 43.22 ÷ 28.18
= 1.53
3 αAAL
= 평균의AAL – βAAL × 평균의S&P 500
= -0.64% – 1.53 × 1.11%
= -2.34%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.86% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.54% |
| 보통주 AAG 의 체계적인 리스크 | βAAL | 1.53 |
| AAG 보통주에 대한 예상 수익률3 | E(RAAL) | 18.17% |
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(RAAL) = RF + βAAL [E(RM) – RF]
= 4.86% + 1.53 [13.54% – 4.86%]
= 18.17%