자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Delta보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Delta Air Lines Inc., 월별 수익률
| Delta Air Lines Inc. (DAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DAL,t1 | 피제수DAL,t1 | RDAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $47.24 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $49.93 | $0.2025 | 6.12% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $45.96 | -7.95% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $45.44 | -1.13% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $36.20 | -7.49% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $39.08 | 7.96% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.38% | 1.36% | ||||
| 표준 편차: | 10.57% | 4.48% | ||||
| Delta Air Lines Inc. (DAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DAL,t1 | 피제수DAL,t1 | RDAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $47.24 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $49.93 | $0.2025 | 6.12% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $45.96 | -7.95% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $45.44 | -1.13% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $49.13 | $0.2025 | 8.57% | 2,411.80 | 1.16% |
| 5. | 2017. 6. 30. | $53.74 | 9.38% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $49.36 | -8.15% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $47.19 | $0.305 | -3.78% | 2,471.65 | 0.05% |
| 8. | 2017. 9. 30. | $48.22 | 2.18% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $50.03 | 3.75% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $52.92 | $0.305 | 6.39% | 2,647.58 | 2.81% |
| 11. | 2017. 12. 31. | $56.00 | 5.82% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $56.77 | 1.38% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $53.90 | $0.305 | -4.52% | 2,713.83 | -3.89% |
| 14. | 2018. 3. 31. | $54.81 | 1.69% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $52.22 | -4.73% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $54.05 | $0.305 | 4.09% | 2,705.27 | 2.16% |
| 17. | 2018. 6. 30. | $49.54 | -8.34% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $54.42 | $0.35 | 10.56% | 2,816.29 | 3.60% |
| 19. | 2018. 8. 31. | $58.48 | 7.46% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $57.83 | -1.11% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $54.73 | -5.36% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $60.71 | $0.35 | 11.57% | 2,760.17 | 1.79% |
| 23. | 2018. 12. 31. | $49.90 | -17.81% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $49.43 | -0.94% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $49.58 | $0.35 | 1.01% | 2,784.49 | 2.97% |
| 26. | 2019. 3. 31. | $51.65 | 4.18% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $58.29 | 12.86% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $51.50 | $0.35 | -11.05% | 2,752.06 | -6.58% |
| 29. | 2019. 6. 30. | $56.75 | 10.19% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $61.04 | $0.4025 | 8.27% | 2,980.38 | 1.31% |
| 31. | 2019. 8. 31. | $57.86 | -5.21% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $57.60 | -0.45% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $55.08 | $0.4025 | -3.68% | 3,037.56 | 2.04% |
| 34. | 2019. 11. 30. | $57.31 | 4.05% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $58.48 | 2.04% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $55.74 | -4.69% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $46.13 | $0.4025 | -16.52% | 2,954.22 | -8.41% |
| 38. | 2020. 3. 31. | $28.53 | -38.15% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $25.91 | -9.18% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $25.21 | -2.70% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $28.05 | 11.27% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $24.97 | -10.98% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $30.85 | 23.55% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $30.58 | -0.88% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $30.64 | 0.20% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $40.25 | 31.36% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $40.21 | -0.10% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $37.96 | -5.60% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $47.94 | 26.29% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $48.28 | 0.71% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $46.92 | -2.82% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $47.68 | 1.62% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $43.26 | -9.27% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $39.90 | -7.77% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $40.44 | 1.35% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $42.61 | 5.37% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $39.13 | -8.17% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $36.20 | -7.49% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $39.08 | 7.96% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.38% | 1.36% | ||||
| 표준 편차: | 10.57% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 DAL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Delta Air Lines Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RDAL,t | RS&P 500,t | (RDAL,t–RDAL)2 | (RS&P 500,t–RS&P 500)2 | (RDAL,t–RDAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 6.12% | 3.72% | 32.93 | 5.58 | 13.55 |
| 2. | 2017. 3. 31. | -7.95% | -0.04% | 69.49 | 1.95 | 11.64 |
| 3. | 2017. 4. 30. | -1.13% | 0.91% | 2.30 | 0.20 | 0.68 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -7.49% | -0.83% | 61.98 | 4.80 | 17.25 |
| 59. | 2021. 12. 31. | 7.96% | 4.36% | 57.32 | 9.02 | 22.74 |
| 합계 (Σ): | 6,476.17 | 1,164.17 | 1,501.70 | |||
| t | 날짜 | RDAL,t | RS&P 500,t | (RDAL,t–RDAL)2 | (RS&P 500,t–RS&P 500)2 | (RDAL,t–RDAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 6.12% | 3.72% | 32.93 | 5.58 | 13.55 |
| 2. | 2017. 3. 31. | -7.95% | -0.04% | 69.49 | 1.95 | 11.64 |
| 3. | 2017. 4. 30. | -1.13% | 0.91% | 2.30 | 0.20 | 0.68 |
| 4. | 2017. 5. 31. | 8.57% | 1.16% | 66.93 | 0.04 | -1.64 |
| 5. | 2017. 6. 30. | 9.38% | 0.48% | 80.97 | 0.77 | -7.89 |
| 6. | 2017. 7. 31. | -8.15% | 1.93% | 72.85 | 0.33 | -4.92 |
| 7. | 2017. 8. 31. | -3.78% | 0.05% | 17.33 | 1.70 | 5.43 |
| 8. | 2017. 9. 30. | 2.18% | 1.93% | 3.23 | 0.33 | 1.03 |
| 9. | 2017. 10. 31. | 3.75% | 2.22% | 11.35 | 0.74 | 2.90 |
| 10. | 2017. 11. 30. | 6.39% | 2.81% | 36.01 | 2.10 | 8.70 |
| 11. | 2017. 12. 31. | 5.82% | 0.98% | 29.54 | 0.14 | -2.04 |
| 12. | 2018. 1. 31. | 1.38% | 5.62% | 0.98 | 18.15 | 4.22 |
| 13. | 2018. 2. 28. | -4.52% | -3.89% | 24.04 | 27.59 | 25.75 |
| 14. | 2018. 3. 31. | 1.69% | -2.69% | 1.70 | 16.37 | -5.27 |
| 15. | 2018. 4. 30. | -4.73% | 0.27% | 26.12 | 1.18 | 5.55 |
| 16. | 2018. 5. 31. | 4.09% | 2.16% | 13.72 | 0.64 | 2.97 |
| 17. | 2018. 6. 30. | -8.34% | 0.48% | 76.20 | 0.76 | 7.63 |
| 18. | 2018. 7. 31. | 10.56% | 3.60% | 103.47 | 5.04 | 22.83 |
| 19. | 2018. 8. 31. | 7.46% | 3.03% | 50.06 | 2.78 | 11.81 |
| 20. | 2018. 9. 30. | -1.11% | 0.43% | 2.24 | 0.86 | 1.39 |
| 21. | 2018. 10. 31. | -5.36% | -6.94% | 33.01 | 68.86 | 47.68 |
| 22. | 2018. 11. 30. | 11.57% | 1.79% | 125.01 | 0.18 | 4.79 |
| 23. | 2018. 12. 31. | -17.81% | -9.18% | 330.91 | 111.00 | 191.65 |
| 24. | 2019. 1. 31. | -0.94% | 7.87% | 1.76 | 42.39 | -8.64 |
| 25. | 2019. 2. 28. | 1.01% | 2.97% | 0.39 | 2.61 | 1.01 |
| 26. | 2019. 3. 31. | 4.18% | 1.79% | 14.37 | 0.19 | 1.65 |
| 27. | 2019. 4. 30. | 12.86% | 3.93% | 155.52 | 6.62 | 32.09 |
| 28. | 2019. 5. 31. | -11.05% | -6.58% | 130.72 | 62.97 | 90.73 |
| 29. | 2019. 6. 30. | 10.19% | 6.89% | 96.22 | 30.64 | 54.30 |
| 30. | 2019. 7. 31. | 8.27% | 1.31% | 62.15 | 0.00 | -0.36 |
| 31. | 2019. 8. 31. | -5.21% | -1.81% | 31.30 | 10.03 | 17.72 |
| 32. | 2019. 9. 30. | -0.45% | 1.72% | 0.70 | 0.13 | -0.30 |
| 33. | 2019. 10. 31. | -3.68% | 2.04% | 16.49 | 0.47 | -2.78 |
| 34. | 2019. 11. 30. | 4.05% | 3.40% | 13.42 | 4.19 | 7.50 |
| 35. | 2019. 12. 31. | 2.04% | 2.86% | 2.74 | 2.25 | 2.49 |
| 36. | 2020. 1. 31. | -4.69% | -0.16% | 25.71 | 2.31 | 7.71 |
| 37. | 2020. 2. 29. | -16.52% | -8.41% | 285.73 | 95.43 | 165.13 |
| 38. | 2020. 3. 31. | -38.15% | -12.51% | 1,485.18 | 192.37 | 534.52 |
| 39. | 2020. 4. 30. | -9.18% | 12.68% | 91.55 | 128.29 | -108.37 |
| 40. | 2020. 5. 31. | -2.70% | 4.53% | 9.53 | 10.05 | -9.79 |
| 41. | 2020. 6. 30. | 11.27% | 1.84% | 118.38 | 0.23 | 5.23 |
| 42. | 2020. 7. 31. | -10.98% | 5.51% | 129.17 | 17.24 | -47.19 |
| 43. | 2020. 8. 31. | 23.55% | 7.01% | 536.54 | 31.91 | 130.84 |
| 44. | 2020. 9. 30. | -0.88% | -3.92% | 1.59 | 27.89 | 6.65 |
| 45. | 2020. 10. 31. | 0.20% | -2.77% | 0.04 | 17.01 | 0.78 |
| 46. | 2020. 11. 30. | 31.36% | 10.75% | 959.72 | 88.30 | 291.10 |
| 47. | 2020. 12. 31. | -0.10% | 3.71% | 0.23 | 5.54 | -1.14 |
| 48. | 2021. 1. 31. | -5.60% | -1.11% | 35.77 | 6.11 | 14.78 |
| 49. | 2021. 2. 28. | 26.29% | 2.61% | 671.12 | 1.57 | 32.41 |
| 50. | 2021. 3. 31. | 0.71% | 4.24% | 0.11 | 8.33 | 0.94 |
| 51. | 2021. 4. 30. | -2.82% | 5.24% | 10.25 | 15.09 | -12.44 |
| 52. | 2021. 5. 31. | 1.62% | 0.55% | 1.52 | 0.65 | -1.00 |
| 53. | 2021. 6. 30. | -9.27% | 2.22% | 93.22 | 0.75 | -8.34 |
| 54. | 2021. 7. 31. | -7.77% | 2.27% | 66.45 | 0.84 | -7.47 |
| 55. | 2021. 8. 31. | 1.35% | 2.90% | 0.94 | 2.38 | 1.49 |
| 56. | 2021. 9. 30. | 5.37% | -4.76% | 24.81 | 37.39 | -30.46 |
| 57. | 2021. 10. 31. | -8.17% | 6.91% | 73.14 | 30.87 | -47.52 |
| 58. | 2021. 11. 30. | -7.49% | -0.83% | 61.98 | 4.80 | 17.25 |
| 59. | 2021. 12. 31. | 7.96% | 4.36% | 57.32 | 9.02 | 22.74 |
| 합계 (Σ): | 6,476.17 | 1,164.17 | 1,501.70 | |||
모두 보기
분산DAL = Σ(RDAL,t–RDAL)2 ÷ (59 – 1)
= 6,476.17 ÷ (59 – 1)
= 111.66
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산DAL, S&P 500 = Σ(RDAL,t–RDAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,501.70 ÷ (59 – 1)
= 25.89
체계적인 위험 추정 (β)
| 분산DAL | 111.66 |
| 분산S&P 500 | 20.07 |
| 공분산DAL, S&P 500 | 25.89 |
| 상관 계수DAL, S&P 5001 | 0.55 |
| βDAL2 | 1.29 |
| αDAL3 | -1.37% |
계산
1 상관 계수DAL, S&P 500
= 공분산DAL, S&P 500 ÷ (표준 편차DAL × 표준 편차S&P 500)
= 25.89 ÷ (10.57% × 4.48%)
= 0.55
2 βDAL
= 공분산DAL, S&P 500 ÷ 분산S&P 500
= 25.89 ÷ 20.07
= 1.29
3 αDAL
= 평균의DAL – βDAL × 평균의S&P 500
= 0.38% – 1.29 × 1.36%
= -1.37%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Delta | βDAL | 1.29 |
| 델타 보통주의 예상 수익률3 | E(RDAL) | 16.43% |
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(RDAL) = RF + βDAL [E(RM) – RF]
= 4.67% + 1.29 [13.79% – 4.67%]
= 16.43%