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 |
| 2019. 1. 31. | $187.11 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $190.08 | $1.45 | 2.36% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $189.98 | -0.05% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $179.32 | -5.61% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $269.64 | $2.13 | 6.28% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $288.02 | 6.82% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.24% | 1.11% | ||||
| 표준 편차: | 7.10% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $187.11 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $190.08 | $1.45 | 2.36% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $189.98 | -0.05% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $179.32 | -5.61% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $166.70 | $1.45 | -6.23% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $184.28 | 10.55% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $186.58 | 1.25% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $208.62 | $1.45 | 12.59% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $193.51 | -7.24% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $213.25 | 10.20% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $234.72 | $1.45 | 10.75% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $241.07 | 2.71% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $216.05 | -10.38% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $199.73 | $1.60 | -6.81% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $202.73 | 1.50% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $239.22 | 18.00% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $229.70 | $1.60 | -3.31% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $235.86 | 2.68% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $244.67 | 3.74% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $253.32 | $1.60 | 4.19% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $254.16 | 0.33% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $216.94 | -14.64% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $222.04 | $1.60 | 3.09% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $229.92 | 3.55% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $241.43 | 5.01% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $224.92 | $1.76 | -6.11% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $248.81 | 10.62% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $239.64 | -3.69% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $237.94 | $1.76 | 0.03% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $243.75 | 2.44% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $241.54 | -0.91% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $225.53 | $1.76 | -5.90% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $212.65 | -5.71% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $206.97 | -2.67% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $198.88 | $1.76 | -3.06% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $224.97 | 13.12% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $227.14 | 0.96% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $226.48 | $1.94 | 0.56% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $241.82 | 6.77% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $233.19 | -3.57% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $256.74 | $1.94 | 10.93% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $243.30 | -5.23% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $247.47 | 1.71% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $240.30 | $1.94 | -2.11% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $225.40 | -6.20% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $270.35 | 19.94% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $286.40 | $1.94 | 6.65% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $262.64 | -8.30% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $252.40 | -3.90% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $231.66 | $2.13 | -7.37% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $241.75 | 4.36% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $239.74 | -0.83% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $220.65 | $2.13 | -7.07% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $222.02 | 0.62% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $234.15 | 5.46% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $256.34 | $2.13 | 10.39% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $268.76 | 4.85% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $255.70 | -4.86% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $269.64 | $2.13 | 6.28% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $288.02 | 6.82% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.24% | 1.11% | ||||
| 표준 편차: | 7.10% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 AMGN의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 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. | 2019. 2. 28. | 2.36% | 2.97% | 1.26 | 3.49 | 2.09 |
| 2. | 2019. 3. 31. | -0.05% | 1.79% | 1.67 | 0.47 | -0.89 |
| 3. | 2019. 4. 30. | -5.61% | 3.93% | 46.95 | 7.98 | -19.36 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 6.28% | 8.92% | 25.44 | 61.03 | 39.40 |
| 59. | 2023. 12. 31. | 6.82% | 4.42% | 31.08 | 11.00 | 18.49 |
| 합계 (Σ): | 2,927.75 | 1,634.30 | 1,013.07 | |||
| 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. | 2019. 2. 28. | 2.36% | 2.97% | 1.26 | 3.49 | 2.09 |
| 2. | 2019. 3. 31. | -0.05% | 1.79% | 1.67 | 0.47 | -0.89 |
| 3. | 2019. 4. 30. | -5.61% | 3.93% | 46.95 | 7.98 | -19.36 |
| 4. | 2019. 5. 31. | -6.23% | -6.58% | 55.81 | 59.04 | 57.40 |
| 5. | 2019. 6. 30. | 10.55% | 6.89% | 86.58 | 33.49 | 53.85 |
| 6. | 2019. 7. 31. | 1.25% | 1.31% | 0.00 | 0.04 | 0.00 |
| 7. | 2019. 8. 31. | 12.59% | -1.81% | 128.79 | 8.50 | -33.08 |
| 8. | 2019. 9. 30. | -7.24% | 1.72% | 71.98 | 0.37 | -5.19 |
| 9. | 2019. 10. 31. | 10.20% | 2.04% | 80.28 | 0.88 | 8.40 |
| 10. | 2019. 11. 30. | 10.75% | 3.40% | 90.38 | 5.28 | 21.85 |
| 11. | 2019. 12. 31. | 2.71% | 2.86% | 2.14 | 3.07 | 2.57 |
| 12. | 2020. 1. 31. | -10.38% | -0.16% | 135.02 | 1.61 | 14.74 |
| 13. | 2020. 2. 29. | -6.81% | -8.41% | 64.87 | 90.57 | 76.65 |
| 14. | 2020. 3. 31. | 1.50% | -12.51% | 0.07 | 185.44 | -3.55 |
| 15. | 2020. 4. 30. | 18.00% | 12.68% | 280.83 | 134.06 | 194.03 |
| 16. | 2020. 5. 31. | -3.31% | 4.53% | 20.72 | 11.71 | -15.58 |
| 17. | 2020. 6. 30. | 2.68% | 1.84% | 2.08 | 0.54 | 1.06 |
| 18. | 2020. 7. 31. | 3.74% | 5.51% | 6.22 | 19.40 | 10.98 |
| 19. | 2020. 8. 31. | 4.19% | 7.01% | 8.69 | 34.82 | 17.40 |
| 20. | 2020. 9. 30. | 0.33% | -3.92% | 0.83 | 25.29 | 4.57 |
| 21. | 2020. 10. 31. | -14.64% | -2.77% | 252.35 | 15.00 | 61.52 |
| 22. | 2020. 11. 30. | 3.09% | 10.75% | 3.41 | 93.10 | 17.82 |
| 23. | 2020. 12. 31. | 3.55% | 3.71% | 5.33 | 6.79 | 6.01 |
| 24. | 2021. 1. 31. | 5.01% | -1.11% | 14.17 | 4.93 | -8.36 |
| 25. | 2021. 2. 28. | -6.11% | 2.61% | 54.03 | 2.26 | -11.05 |
| 26. | 2021. 3. 31. | 10.62% | 4.24% | 87.99 | 9.85 | 29.44 |
| 27. | 2021. 4. 30. | -3.69% | 5.24% | 24.27 | 17.11 | -20.38 |
| 28. | 2021. 5. 31. | 0.03% | 0.55% | 1.48 | 0.31 | 0.68 |
| 29. | 2021. 6. 30. | 2.44% | 2.22% | 1.44 | 1.24 | 1.34 |
| 30. | 2021. 7. 31. | -0.91% | 2.27% | 4.61 | 1.37 | -2.51 |
| 31. | 2021. 8. 31. | -5.90% | 2.90% | 50.99 | 3.22 | -12.80 |
| 32. | 2021. 9. 30. | -5.71% | -4.76% | 48.33 | 34.37 | 40.76 |
| 33. | 2021. 10. 31. | -2.67% | 6.91% | 15.31 | 33.74 | -22.72 |
| 34. | 2021. 11. 30. | -3.06% | -0.83% | 18.49 | 3.76 | 8.34 |
| 35. | 2021. 12. 31. | 13.12% | 4.36% | 141.07 | 10.60 | 38.67 |
| 36. | 2022. 1. 31. | 0.96% | -5.26% | 0.08 | 40.51 | 1.76 |
| 37. | 2022. 2. 28. | 0.56% | -3.14% | 0.46 | 17.99 | 2.87 |
| 38. | 2022. 3. 31. | 6.77% | 3.58% | 30.60 | 6.11 | 13.67 |
| 39. | 2022. 4. 30. | -3.57% | -8.80% | 23.14 | 98.04 | 47.63 |
| 40. | 2022. 5. 31. | 10.93% | 0.01% | 93.89 | 1.21 | -10.66 |
| 41. | 2022. 6. 30. | -5.23% | -8.39% | 41.94 | 90.21 | 61.51 |
| 42. | 2022. 7. 31. | 1.71% | 9.11% | 0.22 | 64.09 | 3.78 |
| 43. | 2022. 8. 31. | -2.11% | -4.24% | 11.25 | 28.62 | 17.95 |
| 44. | 2022. 9. 30. | -6.20% | -9.34% | 55.38 | 109.11 | 77.73 |
| 45. | 2022. 10. 31. | 19.94% | 7.99% | 349.73 | 47.34 | 128.67 |
| 46. | 2022. 11. 30. | 6.65% | 5.38% | 29.30 | 18.23 | 23.11 |
| 47. | 2022. 12. 31. | -8.30% | -5.90% | 90.96 | 49.04 | 66.79 |
| 48. | 2023. 1. 31. | -3.90% | 6.18% | 26.42 | 25.70 | -26.06 |
| 49. | 2023. 2. 28. | -7.37% | -2.61% | 74.21 | 13.82 | 32.02 |
| 50. | 2023. 3. 31. | 4.36% | 3.51% | 9.70 | 5.76 | 7.47 |
| 51. | 2023. 4. 30. | -0.83% | 1.46% | 4.30 | 0.13 | -0.74 |
| 52. | 2023. 5. 31. | -7.07% | 0.25% | 69.15 | 0.74 | 7.13 |
| 53. | 2023. 6. 30. | 0.62% | 4.71% | 0.38 | 13.02 | -2.24 |
| 54. | 2023. 7. 31. | 5.46% | 4.85% | 17.83 | 13.99 | 15.79 |
| 55. | 2023. 8. 31. | 10.39% | -1.77% | 83.64 | 8.28 | -26.32 |
| 56. | 2023. 9. 30. | 4.85% | -4.87% | 12.99 | 35.73 | -21.54 |
| 57. | 2023. 10. 31. | -4.86% | -2.20% | 37.22 | 10.92 | 20.16 |
| 58. | 2023. 11. 30. | 6.28% | 8.92% | 25.44 | 61.03 | 39.40 |
| 59. | 2023. 12. 31. | 6.82% | 4.42% | 31.08 | 11.00 | 18.49 |
| 합계 (Σ): | 2,927.75 | 1,634.30 | 1,013.07 | |||
모두 표시
분산AMGN = Σ(RAMGN,t–RAMGN)2 ÷ (59 – 1)
= 2,927.75 ÷ (59 – 1)
= 50.48
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산AMGN, S&P 500 = Σ(RAMGN,t–RAMGN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,013.07 ÷ (59 – 1)
= 17.47
체계적인 위험 추정 (β)
| 분산AMGN | 50.48 |
| 분산S&P 500 | 28.18 |
| 공분산AMGN, S&P 500 | 17.47 |
| 상관 계수AMGN, S&P 5001 | 0.46 |
| βAMGN2 | 0.62 |
| αAMGN3 | 0.56% |
계산
1 상관 계수AMGN, S&P 500
= 공분산AMGN, S&P 500 ÷ (표준 편차AMGN × 표준 편차S&P 500)
= 17.47 ÷ (7.10% × 5.31%)
= 0.46
2 βAMGN
= 공분산AMGN, S&P 500 ÷ 분산S&P 500
= 17.47 ÷ 28.18
= 0.62
3 αAMGN
= 평균의AMGN – βAMGN × 평균의S&P 500
= 1.24% – 0.62 × 1.11%
= 0.56%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주의 체계적 위험Amgen | βAMGN | 0.62 |
| 암젠 보통주 기대수익률3 | E(RAMGN) | 10.27% |
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(RAMGN) = RF + βAMGN [E(RM) – RF]
= 4.56% + 0.62 [13.77% – 4.56%]
= 10.27%