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 |
| 2020. 1. 31. | $216.05 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $199.73 | $1.60 | -6.81% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $202.73 | 1.50% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $239.22 | 18.00% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $282.87 | $2.25 | -10.94% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $260.64 | -7.86% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.83% | 1.16% | ||||
| 표준 편차: | 7.07% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $216.05 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $199.73 | $1.60 | -6.81% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $202.73 | 1.50% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $239.22 | 18.00% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $229.70 | $1.60 | -3.31% | 3,044.31 | 4.53% |
| 5. | 2020. 6. 30. | $235.86 | 2.68% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $244.67 | 3.74% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $253.32 | $1.60 | 4.19% | 3,500.31 | 7.01% |
| 8. | 2020. 9. 30. | $254.16 | 0.33% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $216.94 | -14.64% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $222.04 | $1.60 | 3.09% | 3,621.63 | 10.75% |
| 11. | 2020. 12. 31. | $229.92 | 3.55% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $241.43 | 5.01% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $224.92 | $1.76 | -6.11% | 3,811.15 | 2.61% |
| 14. | 2021. 3. 31. | $248.81 | 10.62% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $239.64 | -3.69% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $237.94 | $1.76 | 0.03% | 4,204.11 | 0.55% |
| 17. | 2021. 6. 30. | $243.75 | 2.44% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $241.54 | -0.91% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $225.53 | $1.76 | -5.90% | 4,522.68 | 2.90% |
| 20. | 2021. 9. 30. | $212.65 | -5.71% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $206.97 | -2.67% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $198.88 | $1.76 | -3.06% | 4,567.00 | -0.83% |
| 23. | 2021. 12. 31. | $224.97 | 13.12% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $227.14 | 0.96% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $226.48 | $1.94 | 0.56% | 4,373.94 | -3.14% |
| 26. | 2022. 3. 31. | $241.82 | 6.77% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $233.19 | -3.57% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $256.74 | $1.94 | 10.93% | 4,132.15 | 0.01% |
| 29. | 2022. 6. 30. | $243.30 | -5.23% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $247.47 | 1.71% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $240.30 | $1.94 | -2.11% | 3,955.00 | -4.24% |
| 32. | 2022. 9. 30. | $225.40 | -6.20% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $270.35 | 19.94% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $286.40 | $1.94 | 6.65% | 4,080.11 | 5.38% |
| 35. | 2022. 12. 31. | $262.64 | -8.30% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $252.40 | -3.90% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $231.66 | $2.13 | -7.37% | 3,970.15 | -2.61% |
| 38. | 2023. 3. 31. | $241.75 | 4.36% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $239.74 | -0.83% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $220.65 | $2.13 | -7.07% | 4,179.83 | 0.25% |
| 41. | 2023. 6. 30. | $222.02 | 0.62% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $234.15 | 5.46% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $256.34 | $2.13 | 10.39% | 4,507.66 | -1.77% |
| 44. | 2023. 9. 30. | $268.76 | 4.85% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $255.70 | -4.86% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $269.64 | $2.13 | 6.28% | 4,567.80 | 8.92% |
| 47. | 2023. 12. 31. | $288.02 | 6.82% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $314.26 | 9.11% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $273.83 | $2.25 | -12.15% | 5,096.27 | 5.17% |
| 50. | 2024. 3. 31. | $284.32 | 3.83% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $273.94 | -3.65% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $305.85 | $2.25 | 12.47% | 5,277.51 | 4.80% |
| 53. | 2024. 6. 30. | $312.45 | 2.16% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $332.47 | 6.41% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $333.83 | $2.25 | 1.09% | 5,648.40 | 2.28% |
| 56. | 2024. 9. 30. | $322.21 | -3.48% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $320.16 | -0.64% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $282.87 | $2.25 | -10.94% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $260.64 | -7.86% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.83% | 1.16% | ||||
| 표준 편차: | 7.07% | 5.28% | ||||
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. | 2020. 2. 29. | -6.81% | -8.41% | 58.35 | 91.63 | 73.12 |
| 2. | 2020. 3. 31. | 1.50% | -12.51% | 0.46 | 186.96 | -9.25 |
| 3. | 2020. 4. 30. | 18.00% | 12.68% | 294.95 | 132.78 | 197.90 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | -10.94% | 5.73% | 138.53 | 20.87 | -53.77 |
| 59. | 2024. 12. 31. | -7.86% | -2.50% | 75.41 | 13.40 | 31.79 |
| 합계 (Σ): | 2,899.31 | 1,618.62 | 912.04 | |||
| 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. | 2020. 2. 29. | -6.81% | -8.41% | 58.35 | 91.63 | 73.12 |
| 2. | 2020. 3. 31. | 1.50% | -12.51% | 0.46 | 186.96 | -9.25 |
| 3. | 2020. 4. 30. | 18.00% | 12.68% | 294.95 | 132.78 | 197.90 |
| 4. | 2020. 5. 31. | -3.31% | 4.53% | 17.11 | 11.34 | -13.93 |
| 5. | 2020. 6. 30. | 2.68% | 1.84% | 3.45 | 0.46 | 1.26 |
| 6. | 2020. 7. 31. | 3.74% | 5.51% | 8.47 | 18.91 | 12.66 |
| 7. | 2020. 8. 31. | 4.19% | 7.01% | 11.32 | 34.17 | 19.66 |
| 8. | 2020. 9. 30. | 0.33% | -3.92% | 0.24 | 25.85 | 2.51 |
| 9. | 2020. 10. 31. | -14.64% | -2.77% | 239.31 | 15.43 | 60.76 |
| 10. | 2020. 11. 30. | 3.09% | 10.75% | 5.12 | 92.03 | 21.71 |
| 11. | 2020. 12. 31. | 3.55% | 3.71% | 7.42 | 6.51 | 6.95 |
| 12. | 2021. 1. 31. | 5.01% | -1.11% | 17.48 | 5.18 | -9.51 |
| 13. | 2021. 2. 28. | -6.11% | 2.61% | 48.09 | 2.10 | -10.04 |
| 14. | 2021. 3. 31. | 10.62% | 4.24% | 95.97 | 9.50 | 30.20 |
| 15. | 2021. 4. 30. | -3.69% | 5.24% | 20.35 | 16.66 | -18.41 |
| 16. | 2021. 5. 31. | 0.03% | 0.55% | 0.64 | 0.38 | 0.49 |
| 17. | 2021. 6. 30. | 2.44% | 2.22% | 2.61 | 1.12 | 1.71 |
| 18. | 2021. 7. 31. | -0.91% | 2.27% | 3.00 | 1.24 | -1.93 |
| 19. | 2021. 8. 31. | -5.90% | 2.90% | 45.22 | 3.02 | -11.69 |
| 20. | 2021. 9. 30. | -5.71% | -4.76% | 42.72 | 35.02 | 38.68 |
| 21. | 2021. 10. 31. | -2.67% | 6.91% | 12.22 | 33.10 | -20.11 |
| 22. | 2021. 11. 30. | -3.06% | -0.83% | 15.08 | 3.98 | 7.75 |
| 23. | 2021. 12. 31. | 13.12% | 4.36% | 151.12 | 10.24 | 39.34 |
| 24. | 2022. 1. 31. | 0.96% | -5.26% | 0.02 | 41.21 | -0.89 |
| 25. | 2022. 2. 28. | 0.56% | -3.14% | 0.07 | 18.47 | 1.12 |
| 26. | 2022. 3. 31. | 6.77% | 3.58% | 35.38 | 5.84 | 14.37 |
| 27. | 2022. 4. 30. | -3.57% | -8.80% | 19.31 | 99.14 | 43.75 |
| 28. | 2022. 5. 31. | 10.93% | 0.01% | 102.13 | 1.34 | -11.68 |
| 29. | 2022. 6. 30. | -5.23% | -8.39% | 36.72 | 91.26 | 57.89 |
| 30. | 2022. 7. 31. | 1.71% | 9.11% | 0.79 | 63.21 | 7.07 |
| 31. | 2022. 8. 31. | -2.11% | -4.24% | 8.64 | 29.22 | 15.88 |
| 32. | 2022. 9. 30. | -6.20% | -9.34% | 49.36 | 110.27 | 73.78 |
| 33. | 2022. 10. 31. | 19.94% | 7.99% | 365.46 | 46.58 | 130.48 |
| 34. | 2022. 11. 30. | 6.65% | 5.38% | 33.98 | 17.76 | 24.56 |
| 35. | 2022. 12. 31. | -8.30% | -5.90% | 83.20 | 49.82 | 64.38 |
| 36. | 2023. 1. 31. | -3.90% | 6.18% | 22.32 | 25.14 | -23.69 |
| 37. | 2023. 2. 28. | -7.37% | -2.61% | 67.21 | 14.23 | 30.93 |
| 38. | 2023. 3. 31. | 4.36% | 3.51% | 12.46 | 5.49 | 8.27 |
| 39. | 2023. 4. 30. | -0.83% | 1.46% | 2.74 | 0.09 | -0.50 |
| 40. | 2023. 5. 31. | -7.07% | 0.25% | 62.40 | 0.83 | 7.21 |
| 41. | 2023. 6. 30. | 0.62% | 4.71% | 0.04 | 12.62 | -0.73 |
| 42. | 2023. 7. 31. | 5.46% | 4.85% | 21.51 | 13.58 | 17.09 |
| 43. | 2023. 8. 31. | 10.39% | -1.77% | 91.42 | 8.60 | -28.04 |
| 44. | 2023. 9. 30. | 4.85% | -4.87% | 16.16 | 36.40 | -24.25 |
| 45. | 2023. 10. 31. | -4.86% | -2.20% | 32.31 | 11.28 | 19.10 |
| 46. | 2023. 11. 30. | 6.28% | 8.92% | 29.81 | 60.17 | 42.35 |
| 47. | 2023. 12. 31. | 6.82% | 4.42% | 35.90 | 10.64 | 19.54 |
| 48. | 2024. 1. 31. | 9.11% | 1.59% | 68.65 | 0.18 | 3.55 |
| 49. | 2024. 2. 29. | -12.15% | 5.17% | 168.33 | 16.09 | -52.04 |
| 50. | 2024. 3. 31. | 3.83% | 3.10% | 9.03 | 3.77 | 5.83 |
| 51. | 2024. 4. 30. | -3.65% | -4.16% | 20.03 | 28.33 | 23.82 |
| 52. | 2024. 5. 31. | 12.47% | 4.80% | 135.60 | 13.26 | 42.40 |
| 53. | 2024. 6. 30. | 2.16% | 3.47% | 1.78 | 5.32 | 3.07 |
| 54. | 2024. 7. 31. | 6.41% | 1.13% | 31.16 | 0.00 | -0.16 |
| 55. | 2024. 8. 31. | 1.09% | 2.28% | 0.07 | 1.26 | 0.29 |
| 56. | 2024. 9. 30. | -3.48% | 2.02% | 18.54 | 0.74 | -3.70 |
| 57. | 2024. 10. 31. | -0.64% | -0.99% | 2.14 | 4.63 | 3.14 |
| 58. | 2024. 11. 30. | -10.94% | 5.73% | 138.53 | 20.87 | -53.77 |
| 59. | 2024. 12. 31. | -7.86% | -2.50% | 75.41 | 13.40 | 31.79 |
| 합계 (Σ): | 2,899.31 | 1,618.62 | 912.04 | |||
모두 보기
분산AMGN = Σ(RAMGN,t–RAMGN)2 ÷ (59 – 1)
= 2,899.31 ÷ (59 – 1)
= 49.99
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산AMGN, S&P 500 = Σ(RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 912.04 ÷ (59 – 1)
= 15.72
체계적인 위험 추정 (β)
| 분산AMGN | 49.99 |
| 분산S&P 500 | 27.91 |
| 공분산AMGN, S&P 500 | 15.72 |
| 상관 계수AMGN, S&P 5001 | 0.42 |
| βAMGN2 | 0.56 |
| αAMGN3 | 0.17% |
계산
1 상관 계수AMGN, S&P 500
= 공분산AMGN, S&P 500 ÷ (표준 편차AMGN × 표준 편차S&P 500)
= 15.72 ÷ (7.07% × 5.28%)
= 0.42
2 βAMGN
= 공분산AMGN, S&P 500 ÷ 분산S&P 500
= 15.72 ÷ 27.91
= 0.56
3 αAMGN
= 평균의AMGN – βAMGN × 평균의S&P 500
= 0.83% – 0.56 × 1.16%
= 0.17%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.85% |
| 보통주의 체계적 위험Amgen | βAMGN | 0.56 |
| 암젠 보통주 기대수익률3 | E(RAMGN) | 10.40% |
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]
= 4.67% + 0.56 [14.85% – 4.67%]
= 10.40%