자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Amgen보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Amgen Inc., 월별 수익률
| Amgen Inc. (AMGN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AMGN,t1 | 피제수AMGN,t1 | RAMGN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $241.43 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $224.92 | $1.76 | -6.11% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $248.81 | 10.62% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $239.64 | -3.69% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $345.46 | $2.38 | 16.56% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $327.31 | -5.25% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.02% | 1.14% | ||||
| 표준 편차: | 6.94% | 4.37% | ||||
| Amgen Inc. (AMGN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AMGN,t1 | 피제수AMGN,t1 | RAMGN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $241.43 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $224.92 | $1.76 | -6.11% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $248.81 | 10.62% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $239.64 | -3.69% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $237.94 | $1.76 | 0.03% | 4,204.11 | 0.55% |
| 5. | 2021. 6. 30. | $243.75 | 2.44% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $241.54 | -0.91% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $225.53 | $1.76 | -5.90% | 4,522.68 | 2.90% |
| 8. | 2021. 9. 30. | $212.65 | -5.71% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $206.97 | -2.67% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $198.88 | $1.76 | -3.06% | 4,567.00 | -0.83% |
| 11. | 2021. 12. 31. | $224.97 | 13.12% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $227.14 | 0.96% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $226.48 | $1.94 | 0.56% | 4,373.94 | -3.14% |
| 14. | 2022. 3. 31. | $241.82 | 6.77% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $233.19 | -3.57% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $256.74 | $1.94 | 10.93% | 4,132.15 | 0.01% |
| 17. | 2022. 6. 30. | $243.30 | -5.23% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $247.47 | 1.71% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $240.30 | $1.94 | -2.11% | 3,955.00 | -4.24% |
| 20. | 2022. 9. 30. | $225.40 | -6.20% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $270.35 | 19.94% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $286.40 | $1.94 | 6.65% | 4,080.11 | 5.38% |
| 23. | 2022. 12. 31. | $262.64 | -8.30% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $252.40 | -3.90% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $231.66 | $2.13 | -7.37% | 3,970.15 | -2.61% |
| 26. | 2023. 3. 31. | $241.75 | 4.36% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $239.74 | -0.83% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $220.65 | $2.13 | -7.07% | 4,179.83 | 0.25% |
| 29. | 2023. 6. 30. | $222.02 | 0.62% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $234.15 | 5.46% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $256.34 | $2.13 | 10.39% | 4,507.66 | -1.77% |
| 32. | 2023. 9. 30. | $268.76 | 4.85% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $255.70 | -4.86% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $269.64 | $2.13 | 6.28% | 4,567.80 | 8.92% |
| 35. | 2023. 12. 31. | $288.02 | 6.82% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $314.26 | 9.11% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $273.83 | $2.25 | -12.15% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $284.32 | 3.83% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $273.94 | -3.65% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $305.85 | $2.25 | 12.47% | 5,277.51 | 4.80% |
| 41. | 2024. 6. 30. | $312.45 | 2.16% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $332.47 | 6.41% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $333.83 | $2.25 | 1.09% | 5,648.40 | 2.28% |
| 44. | 2024. 9. 30. | $322.21 | -3.48% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $320.16 | -0.64% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $282.87 | $2.25 | -10.94% | 6,032.38 | 5.73% |
| 47. | 2024. 12. 31. | $260.64 | -7.86% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $285.42 | 9.51% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $308.06 | $2.38 | 8.77% | 5,954.50 | -1.42% |
| 50. | 2025. 3. 31. | $311.55 | 1.13% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $290.92 | -6.62% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $288.18 | $2.38 | -0.12% | 5,911.69 | 6.15% |
| 53. | 2025. 6. 30. | $279.21 | -3.11% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $295.10 | 5.69% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $287.71 | $2.38 | -1.70% | 6,460.26 | 1.91% |
| 56. | 2025. 9. 30. | $282.20 | -1.92% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $298.43 | 5.75% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $345.46 | $2.38 | 16.56% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $327.31 | -5.25% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.02% | 1.14% | ||||
| 표준 편차: | 6.94% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 AMGN의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Amgen Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RAMGN,t | RS&P 500,t | (RAMGN,t–RAMGN)2 | (RS&P 500,t–RS&P 500)2 | (RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -6.11% | 2.61% | 50.80 | 2.17 | -10.50 |
| 2. | 2021. 3. 31. | 10.62% | 4.24% | 92.23 | 9.66 | 29.85 |
| 3. | 2021. 4. 30. | -3.69% | 5.24% | 22.12 | 16.86 | -19.31 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 16.56% | 0.13% | 241.45 | 1.01 | -15.63 |
| 59. | 2025. 12. 31. | -5.25% | -0.05% | 39.33 | 1.41 | 7.45 |
| 합계 (Σ): | 2,790.10 | 1,108.23 | 526.96 | |||
| t | 날짜 | RAMGN,t | RS&P 500,t | (RAMGN,t–RAMGN)2 | (RS&P 500,t–RS&P 500)2 | (RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -6.11% | 2.61% | 50.80 | 2.17 | -10.50 |
| 2. | 2021. 3. 31. | 10.62% | 4.24% | 92.23 | 9.66 | 29.85 |
| 3. | 2021. 4. 30. | -3.69% | 5.24% | 22.12 | 16.86 | -19.31 |
| 4. | 2021. 5. 31. | 0.03% | 0.55% | 0.99 | 0.35 | 0.58 |
| 5. | 2021. 6. 30. | 2.44% | 2.22% | 2.03 | 1.18 | 1.55 |
| 6. | 2021. 7. 31. | -0.91% | 2.27% | 3.70 | 1.30 | -2.19 |
| 7. | 2021. 8. 31. | -5.90% | 2.90% | 47.85 | 3.11 | -12.19 |
| 8. | 2021. 9. 30. | -5.71% | -4.76% | 45.28 | 34.73 | 39.65 |
| 9. | 2021. 10. 31. | -2.67% | 6.91% | 13.61 | 33.39 | -21.32 |
| 10. | 2021. 11. 30. | -3.06% | -0.83% | 16.62 | 3.88 | 8.03 |
| 11. | 2021. 12. 31. | 13.12% | 4.36% | 146.43 | 10.40 | 39.03 |
| 12. | 2022. 1. 31. | 0.96% | -5.26% | 0.00 | 40.89 | 0.34 |
| 13. | 2022. 2. 28. | 0.56% | -3.14% | 0.21 | 18.25 | 1.94 |
| 14. | 2022. 3. 31. | 6.77% | 3.58% | 33.12 | 5.96 | 14.05 |
| 15. | 2022. 4. 30. | -3.57% | -8.80% | 21.04 | 98.64 | 45.55 |
| 16. | 2022. 5. 31. | 10.93% | 0.01% | 98.27 | 1.28 | -11.21 |
| 17. | 2022. 6. 30. | -5.23% | -8.39% | 39.10 | 90.79 | 59.58 |
| 18. | 2022. 7. 31. | 1.71% | 9.11% | 0.48 | 63.61 | 5.55 |
| 19. | 2022. 8. 31. | -2.11% | -4.24% | 9.80 | 28.95 | 16.85 |
| 20. | 2022. 9. 30. | -6.20% | -9.34% | 52.11 | 109.74 | 75.62 |
| 21. | 2022. 10. 31. | 19.94% | 7.99% | 358.14 | 46.93 | 129.64 |
| 22. | 2022. 11. 30. | 6.65% | 5.38% | 31.77 | 17.97 | 23.89 |
| 23. | 2022. 12. 31. | -8.30% | -5.90% | 86.75 | 49.47 | 65.51 |
| 24. | 2023. 1. 31. | -3.90% | 6.18% | 24.17 | 25.39 | -24.78 |
| 25. | 2023. 2. 28. | -7.37% | -2.61% | 70.41 | 14.04 | 31.44 |
| 26. | 2023. 3. 31. | 4.36% | 3.51% | 11.14 | 5.61 | 7.91 |
| 27. | 2023. 4. 30. | -0.83% | 1.46% | 3.42 | 0.11 | -0.61 |
| 28. | 2023. 5. 31. | -7.07% | 0.25% | 65.48 | 0.79 | 7.19 |
| 29. | 2023. 6. 30. | 0.62% | 4.71% | 0.16 | 12.80 | -1.42 |
| 30. | 2023. 7. 31. | 5.46% | 4.85% | 19.76 | 13.76 | 16.49 |
| 31. | 2023. 8. 31. | 10.39% | -1.77% | 87.77 | 8.46 | -27.24 |
| 32. | 2023. 9. 30. | 4.85% | -4.87% | 14.65 | 36.10 | -22.99 |
| 33. | 2023. 10. 31. | -4.86% | -2.20% | 34.54 | 11.12 | 19.60 |
| 34. | 2023. 11. 30. | 6.28% | 8.92% | 27.74 | 60.56 | 40.99 |
| 35. | 2023. 12. 31. | 6.82% | 4.42% | 33.62 | 10.80 | 19.06 |
| 36. | 2024. 1. 31. | 9.11% | 1.59% | 65.49 | 0.21 | 3.67 |
| 37. | 2024. 2. 29. | -12.15% | 5.17% | 173.37 | 16.29 | -53.14 |
| 38. | 2024. 3. 31. | 3.83% | 3.10% | 7.91 | 3.86 | 5.53 |
| 39. | 2024. 4. 30. | -3.65% | -4.16% | 21.80 | 28.06 | 24.73 |
| 40. | 2024. 5. 31. | 12.47% | 4.80% | 131.15 | 13.44 | 41.98 |
| 41. | 2024. 6. 30. | 2.16% | 3.47% | 1.30 | 5.43 | 2.66 |
| 42. | 2024. 7. 31. | 6.41% | 1.13% | 29.05 | 0.00 | -0.02 |
| 43. | 2024. 8. 31. | 1.09% | 2.28% | 0.00 | 1.32 | 0.08 |
| 44. | 2024. 9. 30. | -3.48% | 2.02% | 20.24 | 0.78 | -3.97 |
| 45. | 2024. 10. 31. | -0.64% | -0.99% | 2.74 | 4.52 | 3.52 |
| 46. | 2024. 11. 30. | -10.94% | 5.73% | 143.10 | 21.10 | -54.96 |
| 47. | 2024. 12. 31. | -7.86% | -2.50% | 78.79 | 13.21 | 32.27 |
| 48. | 2025. 1. 31. | 9.51% | 2.70% | 72.07 | 2.45 | 13.29 |
| 49. | 2025. 2. 28. | 8.77% | -1.42% | 60.03 | 6.56 | -19.84 |
| 50. | 2025. 3. 31. | 1.13% | -5.75% | 0.01 | 47.48 | -0.79 |
| 51. | 2025. 4. 30. | -6.62% | -0.76% | 58.36 | 3.60 | 14.50 |
| 52. | 2025. 5. 31. | -0.12% | 6.15% | 1.30 | 25.16 | -5.73 |
| 53. | 2025. 6. 30. | -3.11% | 4.96% | 17.06 | 14.63 | -15.80 |
| 54. | 2025. 7. 31. | 5.69% | 2.17% | 21.84 | 1.06 | 4.82 |
| 55. | 2025. 8. 31. | -1.70% | 1.91% | 7.37 | 0.59 | -2.09 |
| 56. | 2025. 9. 30. | -1.92% | 3.53% | 8.60 | 5.74 | -7.03 |
| 57. | 2025. 10. 31. | 5.75% | 2.27% | 22.41 | 1.28 | 5.36 |
| 58. | 2025. 11. 30. | 16.56% | 0.13% | 241.45 | 1.01 | -15.63 |
| 59. | 2025. 12. 31. | -5.25% | -0.05% | 39.33 | 1.41 | 7.45 |
| 합계 (Σ): | 2,790.10 | 1,108.23 | 526.96 | |||
모두 보기
분산AMGN = Σ(RAMGN,t–RAMGN)2 ÷ (59 – 1)
= 2,790.10 ÷ (59 – 1)
= 48.11
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산AMGN, S&P 500 = Σ(RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 526.96 ÷ (59 – 1)
= 9.09
체계적인 위험 추정 (β)
| 분산AMGN | 48.11 |
| 분산S&P 500 | 19.11 |
| 공분산AMGN, S&P 500 | 9.09 |
| 상관 계수AMGN, S&P 5001 | 0.30 |
| βAMGN2 | 0.48 |
| αAMGN3 | 0.48% |
계산
1 상관 계수AMGN, S&P 500
= 공분산AMGN, S&P 500 ÷ (표준 편차AMGN × 표준 편차S&P 500)
= 9.09 ÷ (6.94% × 4.37%)
= 0.30
2 βAMGN
= 공분산AMGN, S&P 500 ÷ 분산S&P 500
= 9.09 ÷ 19.11
= 0.48
3 αAMGN
= 평균의AMGN – βAMGN × 평균의S&P 500
= 1.02% – 0.48 × 1.14%
= 0.48%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Amgen | βAMGN | 0.48 |
| 암젠 보통주 기대수익률3 | E(RAMGN) | 10.64% |
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(RAMGN) = RF + βAMGN [E(RM) – RF]
= 4.54% + 0.48 [17.37% – 4.54%]
= 10.64%