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 |
| 2020. 1. 31. | $227.05 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $224.03 | -1.33% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $237.95 | 6.21% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $251.20 | 5.57% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $468.13 | -1.65% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $402.70 | -13.98% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.26% | 1.16% | ||||
| 표준 편차: | 7.50% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $227.05 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $224.03 | -1.33% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $237.95 | 6.21% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $251.20 | 5.57% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $287.96 | 14.63% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $290.31 | 0.82% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $272.00 | -6.31% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $279.12 | 2.62% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $272.12 | -2.51% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $208.36 | -23.43% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $227.75 | 9.31% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $236.34 | 3.77% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $229.08 | -3.07% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $212.55 | -7.22% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $214.89 | 1.10% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $218.20 | 1.54% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $208.63 | -4.39% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $201.63 | -3.36% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $201.58 | -0.02% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $200.29 | -0.64% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $181.39 | -9.44% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $184.93 | 1.95% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $186.94 | 1.09% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $219.60 | 17.47% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $243.05 | 10.68% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $230.02 | -5.36% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $260.97 | 13.46% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $273.22 | 4.69% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $268.65 | -1.67% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $281.79 | 4.89% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $280.41 | -0.49% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $281.76 | 0.48% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $289.54 | 2.76% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $312.00 | 7.76% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $316.40 | 1.41% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $288.78 | -8.73% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $323.10 | 11.88% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $290.29 | -10.15% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $315.07 | 8.54% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $340.73 | 8.14% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $323.57 | -5.04% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $351.91 | 8.76% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $352.34 | 0.12% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $348.34 | -1.14% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $347.74 | -0.17% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $362.11 | 4.13% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $354.81 | -2.02% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $406.89 | 14.68% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $433.38 | 6.51% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $420.74 | -2.92% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $418.01 | -0.65% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $392.81 | -6.03% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $455.34 | 15.92% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $468.72 | 2.94% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $495.72 | 5.76% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $495.89 | 0.03% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $465.08 | -6.21% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $475.98 | 2.34% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $468.13 | -1.65% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $402.70 | -13.98% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.26% | 1.16% | ||||
| 표준 편차: | 7.50% | 5.28% | ||||
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. | 2020. 2. 29. | -1.33% | -8.41% | 6.68 | 91.63 | 24.75 |
| 2. | 2020. 3. 31. | 6.21% | -12.51% | 24.58 | 186.96 | -67.79 |
| 3. | 2020. 4. 30. | 5.57% | 12.68% | 18.60 | 132.78 | 49.70 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | -1.65% | 5.73% | 8.44 | 20.87 | -13.27 |
| 59. | 2024. 12. 31. | -13.98% | -2.50% | 232.02 | 13.40 | 55.75 |
| 합계 (Σ): | 3,258.87 | 1,618.62 | 637.85 | |||
| 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. | 2020. 2. 29. | -1.33% | -8.41% | 6.68 | 91.63 | 24.75 |
| 2. | 2020. 3. 31. | 6.21% | -12.51% | 24.58 | 186.96 | -67.79 |
| 3. | 2020. 4. 30. | 5.57% | 12.68% | 18.60 | 132.78 | 49.70 |
| 4. | 2020. 5. 31. | 14.63% | 4.53% | 178.98 | 11.34 | 45.04 |
| 5. | 2020. 6. 30. | 0.82% | 1.84% | 0.19 | 0.46 | -0.30 |
| 6. | 2020. 7. 31. | -6.31% | 5.51% | 57.19 | 18.91 | -32.89 |
| 7. | 2020. 8. 31. | 2.62% | 7.01% | 1.86 | 34.17 | 7.96 |
| 8. | 2020. 9. 30. | -2.51% | -3.92% | 14.16 | 25.85 | 19.13 |
| 9. | 2020. 10. 31. | -23.43% | -2.77% | 609.41 | 15.43 | 96.96 |
| 10. | 2020. 11. 30. | 9.31% | 10.75% | 64.81 | 92.03 | 77.23 |
| 11. | 2020. 12. 31. | 3.77% | 3.71% | 6.33 | 6.51 | 6.42 |
| 12. | 2021. 1. 31. | -3.07% | -1.11% | 18.72 | 5.18 | 9.84 |
| 13. | 2021. 2. 28. | -7.22% | 2.61% | 71.76 | 2.10 | -12.27 |
| 14. | 2021. 3. 31. | 1.10% | 4.24% | 0.02 | 9.50 | -0.48 |
| 15. | 2021. 4. 30. | 1.54% | 5.24% | 0.08 | 16.66 | 1.16 |
| 16. | 2021. 5. 31. | -4.39% | 0.55% | 31.82 | 0.38 | 3.46 |
| 17. | 2021. 6. 30. | -3.36% | 2.22% | 21.26 | 1.12 | -4.89 |
| 18. | 2021. 7. 31. | -0.02% | 2.27% | 1.64 | 1.24 | -1.43 |
| 19. | 2021. 8. 31. | -0.64% | 2.90% | 3.59 | 3.02 | -3.29 |
| 20. | 2021. 9. 30. | -9.44% | -4.76% | 114.31 | 35.02 | 63.27 |
| 21. | 2021. 10. 31. | 1.95% | 6.91% | 0.48 | 33.10 | 4.01 |
| 22. | 2021. 11. 30. | 1.09% | -0.83% | 0.03 | 3.98 | 0.34 |
| 23. | 2021. 12. 31. | 17.47% | 4.36% | 262.94 | 10.24 | 51.89 |
| 24. | 2022. 1. 31. | 10.68% | -5.26% | 88.80 | 41.21 | -60.49 |
| 25. | 2022. 2. 28. | -5.36% | -3.14% | 43.78 | 18.47 | 28.43 |
| 26. | 2022. 3. 31. | 13.46% | 3.58% | 148.84 | 5.84 | 29.48 |
| 27. | 2022. 4. 30. | 4.69% | -8.80% | 11.82 | 99.14 | -34.24 |
| 28. | 2022. 5. 31. | -1.67% | 0.01% | 8.57 | 1.34 | 3.38 |
| 29. | 2022. 6. 30. | 4.89% | -8.39% | 13.22 | 91.26 | -34.73 |
| 30. | 2022. 7. 31. | -0.49% | 9.11% | 3.05 | 63.21 | -13.87 |
| 31. | 2022. 8. 31. | 0.48% | -4.24% | 0.60 | 29.22 | 4.18 |
| 32. | 2022. 9. 30. | 2.76% | -9.34% | 2.27 | 110.27 | -15.81 |
| 33. | 2022. 10. 31. | 7.76% | 7.99% | 42.27 | 46.58 | 44.38 |
| 34. | 2022. 11. 30. | 1.41% | 5.38% | 0.02 | 17.76 | 0.65 |
| 35. | 2022. 12. 31. | -8.73% | -5.90% | 99.70 | 49.82 | 70.48 |
| 36. | 2023. 1. 31. | 11.88% | 6.18% | 112.98 | 25.14 | 53.29 |
| 37. | 2023. 2. 28. | -10.15% | -2.61% | 130.19 | 14.23 | 43.04 |
| 38. | 2023. 3. 31. | 8.54% | 3.51% | 53.01 | 5.49 | 17.07 |
| 39. | 2023. 4. 30. | 8.14% | 1.46% | 47.46 | 0.09 | 2.09 |
| 40. | 2023. 5. 31. | -5.04% | 0.25% | 39.58 | 0.83 | 5.74 |
| 41. | 2023. 6. 30. | 8.76% | 4.71% | 56.30 | 12.62 | 26.66 |
| 42. | 2023. 7. 31. | 0.12% | 4.85% | 1.28 | 13.58 | -4.18 |
| 43. | 2023. 8. 31. | -1.14% | -1.77% | 5.71 | 8.60 | 7.01 |
| 44. | 2023. 9. 30. | -0.17% | -4.87% | 2.04 | 36.40 | 8.61 |
| 45. | 2023. 10. 31. | 4.13% | -2.20% | 8.28 | 11.28 | -9.66 |
| 46. | 2023. 11. 30. | -2.02% | 8.92% | 10.70 | 60.17 | -25.37 |
| 47. | 2023. 12. 31. | 14.68% | 4.42% | 180.18 | 10.64 | 43.78 |
| 48. | 2024. 1. 31. | 6.51% | 1.59% | 27.62 | 0.18 | 2.25 |
| 49. | 2024. 2. 29. | -2.92% | 5.17% | 17.40 | 16.09 | -16.73 |
| 50. | 2024. 3. 31. | -0.65% | 3.10% | 3.63 | 3.77 | -3.70 |
| 51. | 2024. 4. 30. | -6.03% | -4.16% | 53.05 | 28.33 | 38.77 |
| 52. | 2024. 5. 31. | 15.92% | 4.80% | 215.01 | 13.26 | 53.39 |
| 53. | 2024. 6. 30. | 2.94% | 3.47% | 2.83 | 5.32 | 3.88 |
| 54. | 2024. 7. 31. | 5.76% | 1.13% | 20.30 | 0.00 | -0.13 |
| 55. | 2024. 8. 31. | 0.03% | 2.28% | 1.49 | 1.26 | -1.37 |
| 56. | 2024. 9. 30. | -6.21% | 2.02% | 55.78 | 0.74 | -6.41 |
| 57. | 2024. 10. 31. | 2.34% | -0.99% | 1.18 | 4.63 | -2.34 |
| 58. | 2024. 11. 30. | -1.65% | 5.73% | 8.44 | 20.87 | -13.27 |
| 59. | 2024. 12. 31. | -13.98% | -2.50% | 232.02 | 13.40 | 55.75 |
| 합계 (Σ): | 3,258.87 | 1,618.62 | 637.85 | |||
모두 보기
분산VRTX = Σ(RVRTX,t–RVRTX)2 ÷ (59 – 1)
= 3,258.87 ÷ (59 – 1)
= 56.19
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산VRTX, S&P 500 = Σ(RVRTX,t–RVRTX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 637.85 ÷ (59 – 1)
= 11.00
체계적인 위험 추정 (β)
| 분산VRTX | 56.19 |
| 분산S&P 500 | 27.91 |
| 공분산VRTX, S&P 500 | 11.00 |
| 상관 계수VRTX, S&P 5001 | 0.28 |
| βVRTX2 | 0.39 |
| αVRTX3 | 0.80% |
계산
1 상관 계수VRTX, S&P 500
= 공분산VRTX, S&P 500 ÷ (표준 편차VRTX × 표준 편차S&P 500)
= 11.00 ÷ (7.50% × 5.28%)
= 0.28
2 βVRTX
= 공분산VRTX, S&P 500 ÷ 분산S&P 500
= 11.00 ÷ 27.91
= 0.39
3 αVRTX
= 평균의VRTX – βVRTX × 평균의S&P 500
= 1.26% – 0.39 × 1.16%
= 0.80%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.78% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험Vertex | βVRTX | 0.39 |
| Vertex 보통주의 예상 수익률3 | E(RVRTX) | 8.76% |
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]
= 4.78% + 0.39 [14.88% – 4.78%]
= 8.76%