자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Vertex보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Vertex Pharmaceuticals Inc., 월별 수익률
| Vertex Pharmaceuticals Inc. (VRTX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값VRTX,t1 | 피제수VRTX,t1 | RVRTX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $229.08 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $212.55 | -7.22% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $214.89 | 1.10% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $218.20 | 1.54% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $433.61 | 1.89% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $453.36 | 4.55% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.41% | 1.14% | ||||
| 표준 편차: | 7.17% | 4.37% | ||||
| Vertex Pharmaceuticals Inc. (VRTX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값VRTX,t1 | 피제수VRTX,t1 | RVRTX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $229.08 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $212.55 | -7.22% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $214.89 | 1.10% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $218.20 | 1.54% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $208.63 | -4.39% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $201.63 | -3.36% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $201.58 | -0.02% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $200.29 | -0.64% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $181.39 | -9.44% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $184.93 | 1.95% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $186.94 | 1.09% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $219.60 | 17.47% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $243.05 | 10.68% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $230.02 | -5.36% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $260.97 | 13.46% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $273.22 | 4.69% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $268.65 | -1.67% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $281.79 | 4.89% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $280.41 | -0.49% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $281.76 | 0.48% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $289.54 | 2.76% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $312.00 | 7.76% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $316.40 | 1.41% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $288.78 | -8.73% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $323.10 | 11.88% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $290.29 | -10.15% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $315.07 | 8.54% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $340.73 | 8.14% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $323.57 | -5.04% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $351.91 | 8.76% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $352.34 | 0.12% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $348.34 | -1.14% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $347.74 | -0.17% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $362.11 | 4.13% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $354.81 | -2.02% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $406.89 | 14.68% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $433.38 | 6.51% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $420.74 | -2.92% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $418.01 | -0.65% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $392.81 | -6.03% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $455.34 | 15.92% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $468.72 | 2.94% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $495.72 | 5.76% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $495.89 | 0.03% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $465.08 | -6.21% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $475.98 | 2.34% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $468.13 | -1.65% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $402.70 | -13.98% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $461.68 | 14.65% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $479.79 | 3.92% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $484.82 | 1.05% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $509.50 | 5.09% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $442.05 | -13.24% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $445.20 | 0.71% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $456.87 | 2.62% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $391.02 | -14.41% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $391.64 | 0.16% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $425.57 | 8.66% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $433.61 | 1.89% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $453.36 | 4.55% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.41% | 1.14% | ||||
| 표준 편차: | 7.17% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 VRTX의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Vertex Pharmaceuticals Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RVRTX,t | RS&P 500,t | (RVRTX,t–RVRTX)2 | (RS&P 500,t–RS&P 500)2 | (RVRTX,t–RVRTX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -7.22% | 2.61% | 74.48 | 2.17 | -12.71 |
| 2. | 2021. 3. 31. | 1.10% | 4.24% | 0.10 | 9.66 | -0.97 |
| 3. | 2021. 4. 30. | 1.54% | 5.24% | 0.02 | 16.86 | 0.52 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 1.89% | 0.13% | 0.23 | 1.01 | -0.48 |
| 59. | 2025. 12. 31. | 4.55% | -0.05% | 9.86 | 1.41 | -3.73 |
| 합계 (Σ): | 2,982.14 | 1,108.23 | 326.04 | |||
| t | 날짜 | RVRTX,t | RS&P 500,t | (RVRTX,t–RVRTX)2 | (RS&P 500,t–RS&P 500)2 | (RVRTX,t–RVRTX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -7.22% | 2.61% | 74.48 | 2.17 | -12.71 |
| 2. | 2021. 3. 31. | 1.10% | 4.24% | 0.10 | 9.66 | -0.97 |
| 3. | 2021. 4. 30. | 1.54% | 5.24% | 0.02 | 16.86 | 0.52 |
| 4. | 2021. 5. 31. | -4.39% | 0.55% | 33.64 | 0.35 | 3.41 |
| 5. | 2021. 6. 30. | -3.36% | 2.22% | 22.75 | 1.18 | -5.18 |
| 6. | 2021. 7. 31. | -0.02% | 2.27% | 2.07 | 1.30 | -1.64 |
| 7. | 2021. 8. 31. | -0.64% | 2.90% | 4.22 | 3.11 | -3.62 |
| 8. | 2021. 9. 30. | -9.44% | -4.76% | 117.73 | 34.73 | 63.94 |
| 9. | 2021. 10. 31. | 1.95% | 6.91% | 0.29 | 33.39 | 3.11 |
| 10. | 2021. 11. 30. | 1.09% | -0.83% | 0.11 | 3.88 | 0.64 |
| 11. | 2021. 12. 31. | 17.47% | 4.36% | 257.82 | 10.40 | 51.79 |
| 12. | 2022. 1. 31. | 10.68% | -5.26% | 85.83 | 40.89 | -59.24 |
| 13. | 2022. 2. 28. | -5.36% | -3.14% | 45.90 | 18.25 | 28.95 |
| 14. | 2022. 3. 31. | 13.46% | 3.58% | 144.99 | 5.96 | 29.39 |
| 15. | 2022. 4. 30. | 4.69% | -8.80% | 10.76 | 98.64 | -32.57 |
| 16. | 2022. 5. 31. | -1.67% | 0.01% | 9.53 | 1.28 | 3.49 |
| 17. | 2022. 6. 30. | 4.89% | -8.39% | 12.09 | 90.79 | -33.13 |
| 18. | 2022. 7. 31. | -0.49% | 9.11% | 3.63 | 63.61 | -15.18 |
| 19. | 2022. 8. 31. | 0.48% | -4.24% | 0.87 | 28.95 | 5.02 |
| 20. | 2022. 9. 30. | 2.76% | -9.34% | 1.81 | 109.74 | -14.11 |
| 21. | 2022. 10. 31. | 7.76% | 7.99% | 40.23 | 46.93 | 43.45 |
| 22. | 2022. 11. 30. | 1.41% | 5.38% | 0.00 | 17.97 | -0.02 |
| 23. | 2022. 12. 31. | -8.73% | -5.90% | 102.89 | 49.47 | 71.34 |
| 24. | 2023. 1. 31. | 11.88% | 6.18% | 109.63 | 25.39 | 52.76 |
| 25. | 2023. 2. 28. | -10.15% | -2.61% | 133.84 | 14.04 | 43.35 |
| 26. | 2023. 3. 31. | 8.54% | 3.51% | 50.72 | 5.61 | 16.87 |
| 27. | 2023. 4. 30. | 8.14% | 1.46% | 45.29 | 0.11 | 2.21 |
| 28. | 2023. 5. 31. | -5.04% | 0.25% | 41.61 | 0.79 | 5.73 |
| 29. | 2023. 6. 30. | 8.76% | 4.71% | 53.94 | 12.80 | 26.28 |
| 30. | 2023. 7. 31. | 0.12% | 4.85% | 1.67 | 13.76 | -4.79 |
| 31. | 2023. 8. 31. | -1.14% | -1.77% | 6.50 | 8.46 | 7.41 |
| 32. | 2023. 9. 30. | -0.17% | -4.87% | 2.52 | 36.10 | 9.53 |
| 33. | 2023. 10. 31. | 4.13% | -2.20% | 7.39 | 11.12 | -9.06 |
| 34. | 2023. 11. 30. | -2.02% | 8.92% | 11.77 | 60.56 | -26.69 |
| 35. | 2023. 12. 31. | 14.68% | 4.42% | 175.94 | 10.80 | 43.60 |
| 36. | 2024. 1. 31. | 6.51% | 1.59% | 25.97 | 0.21 | 2.31 |
| 37. | 2024. 2. 29. | -2.92% | 5.17% | 18.76 | 16.29 | -17.48 |
| 38. | 2024. 3. 31. | -0.65% | 3.10% | 4.26 | 3.86 | -4.06 |
| 39. | 2024. 4. 30. | -6.03% | -4.16% | 55.40 | 28.06 | 39.43 |
| 40. | 2024. 5. 31. | 15.92% | 4.80% | 210.38 | 13.44 | 53.17 |
| 41. | 2024. 6. 30. | 2.94% | 3.47% | 2.32 | 5.43 | 3.55 |
| 42. | 2024. 7. 31. | 5.76% | 1.13% | 18.89 | 0.00 | -0.02 |
| 43. | 2024. 8. 31. | 0.03% | 2.28% | 1.90 | 1.32 | -1.58 |
| 44. | 2024. 9. 30. | -6.21% | 2.02% | 58.18 | 0.78 | -6.74 |
| 45. | 2024. 10. 31. | 2.34% | -0.99% | 0.86 | 4.52 | -1.98 |
| 46. | 2024. 11. 30. | -1.65% | 5.73% | 9.38 | 21.10 | -14.07 |
| 47. | 2024. 12. 31. | -13.98% | -2.50% | 236.89 | 13.21 | 55.95 |
| 48. | 2025. 1. 31. | 14.65% | 2.70% | 175.08 | 2.45 | 20.71 |
| 49. | 2025. 2. 28. | 3.92% | -1.42% | 6.29 | 6.56 | -6.42 |
| 50. | 2025. 3. 31. | 1.05% | -5.75% | 0.13 | 47.48 | 2.52 |
| 51. | 2025. 4. 30. | 5.09% | -0.76% | 13.52 | 3.60 | -6.98 |
| 52. | 2025. 5. 31. | -13.24% | 6.15% | 214.70 | 25.16 | -73.50 |
| 53. | 2025. 6. 30. | 0.71% | 4.96% | 0.49 | 14.63 | -2.68 |
| 54. | 2025. 7. 31. | 2.62% | 2.17% | 1.46 | 1.06 | 1.24 |
| 55. | 2025. 8. 31. | -14.41% | 1.91% | 250.51 | 0.59 | -12.20 |
| 56. | 2025. 9. 30. | 0.16% | 3.53% | 1.58 | 5.74 | -3.01 |
| 57. | 2025. 10. 31. | 8.66% | 2.27% | 52.55 | 1.28 | 8.21 |
| 58. | 2025. 11. 30. | 1.89% | 0.13% | 0.23 | 1.01 | -0.48 |
| 59. | 2025. 12. 31. | 4.55% | -0.05% | 9.86 | 1.41 | -3.73 |
| 합계 (Σ): | 2,982.14 | 1,108.23 | 326.04 | |||
모두 보기
분산VRTX = Σ(RVRTX,t–RVRTX)2 ÷ (59 – 1)
= 2,982.14 ÷ (59 – 1)
= 51.42
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산VRTX, S&P 500 = Σ(RVRTX,t–RVRTX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 326.04 ÷ (59 – 1)
= 5.62
체계적인 위험 추정 (β)
| 분산VRTX | 51.42 |
| 분산S&P 500 | 19.11 |
| 공분산VRTX, S&P 500 | 5.62 |
| 상관 계수VRTX, S&P 5001 | 0.18 |
| βVRTX2 | 0.29 |
| αVRTX3 | 1.08% |
계산
1 상관 계수VRTX, S&P 500
= 공분산VRTX, S&P 500 ÷ (표준 편차VRTX × 표준 편차S&P 500)
= 5.62 ÷ (7.17% × 4.37%)
= 0.18
2 βVRTX
= 공분산VRTX, S&P 500 ÷ 분산S&P 500
= 5.62 ÷ 19.11
= 0.29
3 αVRTX
= 평균의VRTX – βVRTX × 평균의S&P 500
= 1.41% – 0.29 × 1.14%
= 1.08%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.95% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.36% |
| 보통주의 체계적 위험Vertex | βVRTX | 0.29 |
| Vertex 보통주의 예상 수익률3 | E(RVRTX) | 8.60% |
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(RVRTX) = RF + βVRTX [E(RM) – RF]
= 4.95% + 0.29 [17.36% – 4.95%]
= 8.60%