자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Boeing보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Boeing Co., 월별 수익률
| Boeing Co. (BA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BA,t1 | 피제수BA,t1 | RBA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $318.27 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $275.11 | $2.055 | -12.92% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $149.14 | -45.79% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $141.02 | -5.44% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $155.44 | 4.11% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $177.00 | 13.87% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.02% | 1.16% | ||||
| 표준 편차: | 13.97% | 5.28% | ||||
| Boeing Co. (BA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BA,t1 | 피제수BA,t1 | RBA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $318.27 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $275.11 | $2.055 | -12.92% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $149.14 | -45.79% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $141.02 | -5.44% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $145.85 | 3.43% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $183.30 | 25.68% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $158.00 | -13.80% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $171.82 | 8.75% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $165.26 | -3.82% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $144.39 | -12.63% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $210.71 | 45.93% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $214.06 | 1.59% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $194.19 | -9.28% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $212.01 | 9.18% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $254.72 | 20.15% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $234.31 | -8.01% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $247.02 | 5.42% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $239.56 | -3.02% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $226.48 | -5.46% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $219.50 | -3.08% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $219.94 | 0.20% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $207.03 | -5.87% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $197.85 | -4.43% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $201.32 | 1.75% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $200.24 | -0.54% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $205.34 | 2.55% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $191.50 | -6.74% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $148.84 | -22.28% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $131.40 | -11.72% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $136.72 | 4.05% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $159.31 | 16.52% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $160.25 | 0.59% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $121.08 | -24.44% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $142.51 | 17.70% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $178.88 | 25.52% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $190.49 | 6.49% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $213.00 | 11.82% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $201.55 | -5.38% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $212.43 | 5.40% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $206.78 | -2.66% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $205.70 | -0.52% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $211.16 | 2.65% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $238.85 | 13.11% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $224.03 | -6.20% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $191.68 | -14.44% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $186.82 | -2.54% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $231.63 | 23.99% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $260.66 | 12.53% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $211.04 | -19.04% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $203.72 | -3.47% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $192.99 | -5.27% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $167.84 | -13.03% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $177.61 | 5.82% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $182.01 | 2.48% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $190.60 | 4.72% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $173.74 | -8.85% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $152.04 | -12.49% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $149.31 | -1.80% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $155.44 | 4.11% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $177.00 | 13.87% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.02% | 1.16% | ||||
| 표준 편차: | 13.97% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 BA의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Boeing Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RBA,t | RS&P 500,t | (RBA,t–RBA)2 | (RS&P 500,t–RS&P 500)2 | (RBA,t–RBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -12.92% | -8.41% | 167.26 | 91.63 | 123.80 |
| 2. | 2020. 3. 31. | -45.79% | -12.51% | 2,098.24 | 186.96 | 626.32 |
| 3. | 2020. 4. 30. | -5.44% | 12.68% | 29.84 | 132.78 | -62.94 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 4.11% | 5.73% | 16.71 | 20.87 | 18.68 |
| 59. | 2024. 12. 31. | 13.87% | -2.50% | 191.90 | 13.40 | -50.70 |
| 합계 (Σ): | 11,323.37 | 1,618.62 | 2,491.72 | |||
| t | 날짜 | RBA,t | RS&P 500,t | (RBA,t–RBA)2 | (RS&P 500,t–RS&P 500)2 | (RBA,t–RBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -12.92% | -8.41% | 167.26 | 91.63 | 123.80 |
| 2. | 2020. 3. 31. | -45.79% | -12.51% | 2,098.24 | 186.96 | 626.32 |
| 3. | 2020. 4. 30. | -5.44% | 12.68% | 29.84 | 132.78 | -62.94 |
| 4. | 2020. 5. 31. | 3.43% | 4.53% | 11.61 | 11.34 | 11.47 |
| 5. | 2020. 6. 30. | 25.68% | 1.84% | 658.41 | 0.46 | 17.39 |
| 6. | 2020. 7. 31. | -13.80% | 5.51% | 191.00 | 18.91 | -60.10 |
| 7. | 2020. 8. 31. | 8.75% | 7.01% | 76.20 | 34.17 | 51.02 |
| 8. | 2020. 9. 30. | -3.82% | -3.92% | 14.71 | 25.85 | 19.50 |
| 9. | 2020. 10. 31. | -12.63% | -2.77% | 159.93 | 15.43 | 49.67 |
| 10. | 2020. 11. 30. | 45.93% | 10.75% | 2,108.05 | 92.03 | 440.46 |
| 11. | 2020. 12. 31. | 1.59% | 3.71% | 2.47 | 6.51 | 4.01 |
| 12. | 2021. 1. 31. | -9.28% | -1.11% | 86.49 | 5.18 | 21.16 |
| 13. | 2021. 2. 28. | 9.18% | 2.61% | 83.89 | 2.10 | 13.26 |
| 14. | 2021. 3. 31. | 20.15% | 4.24% | 405.12 | 9.50 | 62.05 |
| 15. | 2021. 4. 30. | -8.01% | 5.24% | 64.49 | 16.66 | -32.77 |
| 16. | 2021. 5. 31. | 5.42% | 0.55% | 29.23 | 0.38 | -3.31 |
| 17. | 2021. 6. 30. | -3.02% | 2.22% | 9.23 | 1.12 | -3.22 |
| 18. | 2021. 7. 31. | -5.46% | 2.27% | 30.00 | 1.24 | -6.10 |
| 19. | 2021. 8. 31. | -3.08% | 2.90% | 9.61 | 3.02 | -5.39 |
| 20. | 2021. 9. 30. | 0.20% | -4.76% | 0.03 | 35.02 | -1.08 |
| 21. | 2021. 10. 31. | -5.87% | 6.91% | 34.66 | 33.10 | -33.87 |
| 22. | 2021. 11. 30. | -4.43% | -0.83% | 19.82 | 3.98 | 8.88 |
| 23. | 2021. 12. 31. | 1.75% | 4.36% | 3.01 | 10.24 | 5.56 |
| 24. | 2022. 1. 31. | -0.54% | -5.26% | 0.31 | 41.21 | 3.56 |
| 25. | 2022. 2. 28. | 2.55% | -3.14% | 6.40 | 18.47 | -10.87 |
| 26. | 2022. 3. 31. | -6.74% | 3.58% | 45.67 | 5.84 | -16.33 |
| 27. | 2022. 4. 30. | -22.28% | -8.80% | 497.04 | 99.14 | 221.98 |
| 28. | 2022. 5. 31. | -11.72% | 0.01% | 137.71 | 1.34 | 13.56 |
| 29. | 2022. 6. 30. | 4.05% | -8.39% | 16.25 | 91.26 | -38.51 |
| 30. | 2022. 7. 31. | 16.52% | 9.11% | 272.42 | 63.21 | 131.22 |
| 31. | 2022. 8. 31. | 0.59% | -4.24% | 0.33 | 29.22 | -3.09 |
| 32. | 2022. 9. 30. | -24.44% | -9.34% | 598.32 | 110.27 | 256.86 |
| 33. | 2022. 10. 31. | 17.70% | 7.99% | 312.63 | 46.58 | 120.68 |
| 34. | 2022. 11. 30. | 25.52% | 5.38% | 650.42 | 17.76 | 107.47 |
| 35. | 2022. 12. 31. | 6.49% | -5.90% | 41.90 | 49.82 | -45.69 |
| 36. | 2023. 1. 31. | 11.82% | 6.18% | 139.22 | 25.14 | 59.16 |
| 37. | 2023. 2. 28. | -5.38% | -2.61% | 29.09 | 14.23 | 20.35 |
| 38. | 2023. 3. 31. | 5.40% | 3.51% | 28.95 | 5.49 | 12.61 |
| 39. | 2023. 4. 30. | -2.66% | 1.46% | 7.17 | 0.09 | -0.81 |
| 40. | 2023. 5. 31. | -0.52% | 0.25% | 0.29 | 0.83 | 0.49 |
| 41. | 2023. 6. 30. | 2.65% | 4.71% | 6.95 | 12.62 | 9.37 |
| 42. | 2023. 7. 31. | 13.11% | 4.85% | 171.50 | 13.58 | 48.25 |
| 43. | 2023. 8. 31. | -6.20% | -1.77% | 38.72 | 8.60 | 18.25 |
| 44. | 2023. 9. 30. | -14.44% | -4.87% | 209.02 | 36.40 | 87.23 |
| 45. | 2023. 10. 31. | -2.54% | -2.20% | 6.52 | 11.28 | 8.58 |
| 46. | 2023. 11. 30. | 23.99% | 8.92% | 574.47 | 60.17 | 185.91 |
| 47. | 2023. 12. 31. | 12.53% | 4.42% | 156.63 | 10.64 | 40.82 |
| 48. | 2024. 1. 31. | -19.04% | 1.59% | 363.05 | 0.18 | -8.16 |
| 49. | 2024. 2. 29. | -3.47% | 5.17% | 12.15 | 16.09 | -13.98 |
| 50. | 2024. 3. 31. | -5.27% | 3.10% | 27.93 | 3.77 | -10.26 |
| 51. | 2024. 4. 30. | -13.03% | -4.16% | 170.29 | 28.33 | 69.46 |
| 52. | 2024. 5. 31. | 5.82% | 4.80% | 33.68 | 13.26 | 21.13 |
| 53. | 2024. 6. 30. | 2.48% | 3.47% | 6.05 | 5.32 | 5.67 |
| 54. | 2024. 7. 31. | 4.72% | 1.13% | 22.11 | 0.00 | -0.14 |
| 55. | 2024. 8. 31. | -8.85% | 2.28% | 78.56 | 1.26 | -9.95 |
| 56. | 2024. 9. 30. | -12.49% | 2.02% | 156.44 | 0.74 | -10.74 |
| 57. | 2024. 10. 31. | -1.80% | -0.99% | 3.29 | 4.63 | 3.90 |
| 58. | 2024. 11. 30. | 4.11% | 5.73% | 16.71 | 20.87 | 18.68 |
| 59. | 2024. 12. 31. | 13.87% | -2.50% | 191.90 | 13.40 | -50.70 |
| 합계 (Σ): | 11,323.37 | 1,618.62 | 2,491.72 | |||
모두 보기
분산BA = Σ(RBA,t–RBA)2 ÷ (59 – 1)
= 11,323.37 ÷ (59 – 1)
= 195.23
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산BA, S&P 500 = Σ(RBA,t–RBA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,491.72 ÷ (59 – 1)
= 42.96
체계적인 위험 추정 (β)
| 분산BA | 195.23 |
| 분산S&P 500 | 27.91 |
| 공분산BA, S&P 500 | 42.96 |
| 상관 계수BA, S&P 5001 | 0.58 |
| βBA2 | 1.54 |
| αBA3 | -1.77% |
계산
1 상관 계수BA, S&P 500
= 공분산BA, S&P 500 ÷ (표준 편차BA × 표준 편차S&P 500)
= 42.96 ÷ (13.97% × 5.28%)
= 0.58
2 βBA
= 공분산BA, S&P 500 ÷ 분산S&P 500
= 42.96 ÷ 27.91
= 1.54
3 αBA
= 평균의BA – βBA × 평균의S&P 500
= 0.02% – 1.54 × 1.16%
= -1.77%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Boeing | βBA | 1.54 |
| Boeing 보통주에 대한 예상 수익률3 | E(RBA) | 20.44% |
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(RBA) = RF + βBA [E(RM) – RF]
= 4.60% + 1.54 [14.89% – 4.60%]
= 20.44%