자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Merck보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Merck & Co. Inc., 월별 수익률
| Merck & Co. Inc. (MRK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MRK,t1 | 피제수MRK,t1 | RMRK,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $85.44 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $76.56 | -10.39% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $76.94 | $0.61 | 1.29% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $79.34 | 3.12% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $101.64 | -0.66% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $99.48 | $0.81 | -1.33% | 5,881.63 | -2.50% |
| 평균의 (R): | 0.77% | 1.16% | ||||
| 표준 편차: | 6.30% | 5.28% | ||||
| Merck & Co. Inc. (MRK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MRK,t1 | 피제수MRK,t1 | RMRK,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $85.44 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $76.56 | -10.39% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $76.94 | $0.61 | 1.29% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $79.34 | 3.12% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $80.72 | 1.74% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $77.33 | $0.61 | -3.44% | 3,100.29 | 1.84% |
| 6. | 2020. 7. 31. | $80.24 | 3.76% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $85.27 | 6.27% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $82.95 | $0.61 | -2.01% | 3,363.00 | -3.92% |
| 9. | 2020. 10. 31. | $75.21 | -9.33% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $80.39 | 6.89% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $81.80 | $0.65 | 2.56% | 3,756.07 | 3.71% |
| 12. | 2021. 1. 31. | $77.07 | -5.78% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $72.62 | -5.77% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $77.09 | $0.65 | 7.05% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $74.50 | -3.36% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $75.89 | 1.87% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $77.77 | $3.75 | 7.42% | 4,297.50 | 2.22% |
| 18. | 2021. 7. 31. | $76.87 | -1.16% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $76.29 | -0.75% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $75.11 | $0.65 | -0.69% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $88.05 | 17.23% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $74.91 | -14.92% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $76.64 | $0.69 | 3.23% | 4,766.18 | 4.36% |
| 24. | 2022. 1. 31. | $81.48 | 6.32% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $76.58 | -6.01% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $82.05 | $0.69 | 8.04% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $88.69 | 8.09% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $92.03 | 3.77% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $91.17 | $0.69 | -0.18% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $89.34 | -2.01% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $85.36 | -4.45% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $86.12 | $0.69 | 1.70% | 3,585.62 | -9.34% |
| 33. | 2022. 10. 31. | $101.20 | 17.51% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $110.12 | 8.81% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $110.95 | $0.73 | 1.42% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $107.41 | -3.19% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $106.24 | -1.09% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $106.39 | $0.73 | 0.83% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $115.47 | 8.53% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $110.41 | -4.38% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $115.39 | $0.73 | 5.17% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $106.65 | -7.57% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $108.98 | 2.18% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $102.95 | $0.73 | -4.86% | 4,288.05 | -4.87% |
| 45. | 2023. 10. 31. | $102.70 | -0.24% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $102.48 | -0.21% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $109.02 | $0.77 | 7.13% | 4,769.83 | 4.42% |
| 48. | 2024. 1. 31. | $120.78 | 10.79% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $127.15 | 5.27% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $131.95 | $0.77 | 4.38% | 5,254.35 | 3.10% |
| 51. | 2024. 4. 30. | $129.22 | -2.07% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $125.54 | -2.85% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $123.80 | $0.77 | -0.77% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $113.13 | -8.62% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $118.45 | 4.70% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $113.56 | $0.77 | -3.48% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $102.32 | -9.90% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $101.64 | -0.66% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $99.48 | $0.81 | -1.33% | 5,881.63 | -2.50% |
| 평균의 (R): | 0.77% | 1.16% | ||||
| 표준 편차: | 6.30% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MRK의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Merck & Co. Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMRK,t | RS&P 500,t | (RMRK,t–RMRK)2 | (RS&P 500,t–RS&P 500)2 | (RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -10.39% | -8.41% | 124.67 | 91.63 | 106.88 |
| 2. | 2020. 3. 31. | 1.29% | -12.51% | 0.27 | 186.96 | -7.12 |
| 3. | 2020. 4. 30. | 3.12% | 12.68% | 5.51 | 132.78 | 27.04 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | -0.66% | 5.73% | 2.06 | 20.87 | -6.57 |
| 59. | 2024. 12. 31. | -1.33% | -2.50% | 4.41 | 13.40 | 7.69 |
| 합계 (Σ): | 2,302.47 | 1,618.62 | 603.76 | |||
| t | 날짜 | RMRK,t | RS&P 500,t | (RMRK,t–RMRK)2 | (RS&P 500,t–RS&P 500)2 | (RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -10.39% | -8.41% | 124.67 | 91.63 | 106.88 |
| 2. | 2020. 3. 31. | 1.29% | -12.51% | 0.27 | 186.96 | -7.12 |
| 3. | 2020. 4. 30. | 3.12% | 12.68% | 5.51 | 132.78 | 27.04 |
| 4. | 2020. 5. 31. | 1.74% | 4.53% | 0.94 | 11.34 | 3.26 |
| 5. | 2020. 6. 30. | -3.44% | 1.84% | 17.78 | 0.46 | -2.86 |
| 6. | 2020. 7. 31. | 3.76% | 5.51% | 8.94 | 18.91 | 13.01 |
| 7. | 2020. 8. 31. | 6.27% | 7.01% | 30.21 | 34.17 | 32.13 |
| 8. | 2020. 9. 30. | -2.01% | -3.92% | 7.72 | 25.85 | 14.12 |
| 9. | 2020. 10. 31. | -9.33% | -2.77% | 102.08 | 15.43 | 39.68 |
| 10. | 2020. 11. 30. | 6.89% | 10.75% | 37.39 | 92.03 | 58.66 |
| 11. | 2020. 12. 31. | 2.56% | 3.71% | 3.20 | 6.51 | 4.57 |
| 12. | 2021. 1. 31. | -5.78% | -1.11% | 42.96 | 5.18 | 14.91 |
| 13. | 2021. 2. 28. | -5.77% | 2.61% | 42.85 | 2.10 | -9.48 |
| 14. | 2021. 3. 31. | 7.05% | 4.24% | 39.41 | 9.50 | 19.35 |
| 15. | 2021. 4. 30. | -3.36% | 5.24% | 17.07 | 16.66 | -16.86 |
| 16. | 2021. 5. 31. | 1.87% | 0.55% | 1.20 | 0.38 | -0.67 |
| 17. | 2021. 6. 30. | 7.42% | 2.22% | 44.17 | 1.12 | 7.05 |
| 18. | 2021. 7. 31. | -1.16% | 2.27% | 3.72 | 1.24 | -2.15 |
| 19. | 2021. 8. 31. | -0.75% | 2.90% | 2.33 | 3.02 | -2.65 |
| 20. | 2021. 9. 30. | -0.69% | -4.76% | 2.15 | 35.02 | 8.68 |
| 21. | 2021. 10. 31. | 17.23% | 6.91% | 270.79 | 33.10 | 94.67 |
| 22. | 2021. 11. 30. | -14.92% | -0.83% | 246.35 | 3.98 | 31.31 |
| 23. | 2021. 12. 31. | 3.23% | 4.36% | 6.04 | 10.24 | 7.87 |
| 24. | 2022. 1. 31. | 6.32% | -5.26% | 30.72 | 41.21 | -35.58 |
| 25. | 2022. 2. 28. | -6.01% | -3.14% | 46.05 | 18.47 | 29.16 |
| 26. | 2022. 3. 31. | 8.04% | 3.58% | 52.88 | 5.84 | 17.57 |
| 27. | 2022. 4. 30. | 8.09% | -8.80% | 53.59 | 99.14 | -72.89 |
| 28. | 2022. 5. 31. | 3.77% | 0.01% | 8.96 | 1.34 | -3.46 |
| 29. | 2022. 6. 30. | -0.18% | -8.39% | 0.92 | 91.26 | 9.14 |
| 30. | 2022. 7. 31. | -2.01% | 9.11% | 7.73 | 63.21 | -22.10 |
| 31. | 2022. 8. 31. | -4.45% | -4.24% | 27.32 | 29.22 | 28.25 |
| 32. | 2022. 9. 30. | 1.70% | -9.34% | 0.86 | 110.27 | -9.73 |
| 33. | 2022. 10. 31. | 17.51% | 7.99% | 280.16 | 46.58 | 114.24 |
| 34. | 2022. 11. 30. | 8.81% | 5.38% | 64.67 | 17.76 | 33.89 |
| 35. | 2022. 12. 31. | 1.42% | -5.90% | 0.42 | 49.82 | -4.55 |
| 36. | 2023. 1. 31. | -3.19% | 6.18% | 15.71 | 25.14 | -19.87 |
| 37. | 2023. 2. 28. | -1.09% | -2.61% | 3.47 | 14.23 | 7.02 |
| 38. | 2023. 3. 31. | 0.83% | 3.51% | 0.00 | 5.49 | 0.13 |
| 39. | 2023. 4. 30. | 8.53% | 1.46% | 60.25 | 0.09 | 2.35 |
| 40. | 2023. 5. 31. | -4.38% | 0.25% | 26.57 | 0.83 | 4.71 |
| 41. | 2023. 6. 30. | 5.17% | 4.71% | 19.35 | 12.62 | 15.63 |
| 42. | 2023. 7. 31. | -7.57% | 4.85% | 69.67 | 13.58 | -30.75 |
| 43. | 2023. 8. 31. | 2.18% | -1.77% | 1.99 | 8.60 | -4.14 |
| 44. | 2023. 9. 30. | -4.86% | -4.87% | 31.76 | 36.40 | 34.00 |
| 45. | 2023. 10. 31. | -0.24% | -2.20% | 1.03 | 11.28 | 3.41 |
| 46. | 2023. 11. 30. | -0.21% | 8.92% | 0.97 | 60.17 | -7.65 |
| 47. | 2023. 12. 31. | 7.13% | 4.42% | 40.46 | 10.64 | 20.75 |
| 48. | 2024. 1. 31. | 10.79% | 1.59% | 100.29 | 0.18 | 4.29 |
| 49. | 2024. 2. 29. | 5.27% | 5.17% | 20.27 | 16.09 | 18.06 |
| 50. | 2024. 3. 31. | 4.38% | 3.10% | 13.02 | 3.77 | 7.00 |
| 51. | 2024. 4. 30. | -2.07% | -4.16% | 8.07 | 28.33 | 15.12 |
| 52. | 2024. 5. 31. | -2.85% | 4.80% | 13.11 | 13.26 | -13.18 |
| 53. | 2024. 6. 30. | -0.77% | 3.47% | 2.39 | 5.32 | -3.56 |
| 54. | 2024. 7. 31. | -8.62% | 1.13% | 88.19 | 0.00 | 0.27 |
| 55. | 2024. 8. 31. | 4.70% | 2.28% | 15.45 | 1.26 | 4.41 |
| 56. | 2024. 9. 30. | -3.48% | 2.02% | 18.07 | 0.74 | -3.65 |
| 57. | 2024. 10. 31. | -9.90% | -0.99% | 113.85 | 4.63 | 22.95 |
| 58. | 2024. 11. 30. | -0.66% | 5.73% | 2.06 | 20.87 | -6.57 |
| 59. | 2024. 12. 31. | -1.33% | -2.50% | 4.41 | 13.40 | 7.69 |
| 합계 (Σ): | 2,302.47 | 1,618.62 | 603.76 | |||
모두 보기
분산MRK = Σ(RMRK,t–RMRK)2 ÷ (59 – 1)
= 2,302.47 ÷ (59 – 1)
= 39.70
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산MRK, S&P 500 = Σ(RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 603.76 ÷ (59 – 1)
= 10.41
체계적인 위험 추정 (β)
| 분산MRK | 39.70 |
| 분산S&P 500 | 27.91 |
| 공분산MRK, S&P 500 | 10.41 |
| 상관 계수MRK, S&P 5001 | 0.31 |
| βMRK2 | 0.37 |
| αMRK3 | 0.34% |
계산
1 상관 계수MRK, S&P 500
= 공분산MRK, S&P 500 ÷ (표준 편차MRK × 표준 편차S&P 500)
= 10.41 ÷ (6.30% × 5.28%)
= 0.31
2 βMRK
= 공분산MRK, S&P 500 ÷ 분산S&P 500
= 10.41 ÷ 27.91
= 0.37
3 αMRK
= 평균의MRK – βMRK × 평균의S&P 500
= 0.77% – 0.37 × 1.16%
= 0.34%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Merck | βMRK | 0.37 |
| Merck 보통주에 대한 예상 수익률3 | E(RMRK) | 8.44% |
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(RMRK) = RF + βMRK [E(RM) – RF]
= 4.60% + 0.37 [14.89% – 4.60%]
= 8.44%