자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Moderna보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Moderna Inc., 월별 수익률
| Moderna Inc. (MRNA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MRNA,t1 | 피제수MRNA,t1 | RMRNA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $16.60 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $22.60 | 36.14% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $20.35 | -9.96% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $26.03 | 27.91% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $77.70 | 2.29% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $99.45 | 27.99% | 4,769.83 | 4.42% | |
| 평균의 (R): | 5.88% | 1.11% | ||||
| 표준 편차: | 26.64% | 5.31% | ||||
| Moderna Inc. (MRNA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MRNA,t1 | 피제수MRNA,t1 | RMRNA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $16.60 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $22.60 | 36.14% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $20.35 | -9.96% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $26.03 | 27.91% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $20.78 | -20.17% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $14.64 | -29.55% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $13.10 | -10.52% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $15.73 | 20.08% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $15.92 | 1.21% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $16.75 | 5.21% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $20.36 | 21.55% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $19.56 | -3.93% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $20.51 | 4.86% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $25.93 | 26.43% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $29.95 | 15.50% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $45.99 | 53.56% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $61.50 | 33.72% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $64.21 | 4.41% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $74.10 | 15.40% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $64.89 | -12.43% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $70.75 | 9.03% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $67.47 | -4.64% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $152.74 | 126.38% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $104.47 | -31.60% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $173.16 | 65.75% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $154.81 | -10.60% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $130.95 | -15.41% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $178.82 | 36.56% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $185.01 | 3.46% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $234.98 | 27.01% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $353.60 | 50.48% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $376.69 | 6.53% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $384.86 | 2.17% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $345.21 | -10.30% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $352.43 | 2.09% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $253.98 | -27.93% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $169.33 | -33.33% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $153.60 | -9.29% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $172.26 | 12.15% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $134.41 | -21.97% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $145.33 | 8.12% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $142.85 | -1.71% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $164.09 | 14.87% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $132.27 | -19.39% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $118.25 | -10.60% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $150.33 | 27.13% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $175.91 | 17.02% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $179.62 | 2.11% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $176.06 | -1.98% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $138.81 | -21.16% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $153.58 | 10.64% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $132.89 | -13.47% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $127.71 | -3.90% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $121.50 | -4.86% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $117.66 | -3.16% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $113.07 | -3.90% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $103.29 | -8.65% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $75.96 | -26.46% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $77.70 | 2.29% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $99.45 | 27.99% | 4,769.83 | 4.42% | |
| 평균의 (R): | 5.88% | 1.11% | ||||
| 표준 편차: | 26.64% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MRNA의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Moderna Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMRNA,t | RS&P 500,t | (RMRNA,t–RMRNA)2 | (RS&P 500,t–RS&P 500)2 | (RMRNA,t–RMRNA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 36.14% | 2.97% | 915.97 | 3.49 | 56.51 |
| 2. | 2019. 3. 31. | -9.96% | 1.79% | 250.76 | 0.47 | -10.87 |
| 3. | 2019. 4. 30. | 27.91% | 3.93% | 485.41 | 7.98 | 62.25 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 2.29% | 8.92% | 12.88 | 61.03 | -28.04 |
| 59. | 2023. 12. 31. | 27.99% | 4.42% | 488.97 | 11.00 | 73.35 |
| 합계 (Σ): | 41,147.69 | 1,634.30 | 2,766.28 | |||
| t | 날짜 | RMRNA,t | RS&P 500,t | (RMRNA,t–RMRNA)2 | (RS&P 500,t–RS&P 500)2 | (RMRNA,t–RMRNA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 36.14% | 2.97% | 915.97 | 3.49 | 56.51 |
| 2. | 2019. 3. 31. | -9.96% | 1.79% | 250.76 | 0.47 | -10.87 |
| 3. | 2019. 4. 30. | 27.91% | 3.93% | 485.41 | 7.98 | 62.25 |
| 4. | 2019. 5. 31. | -20.17% | -6.58% | 678.53 | 59.04 | 200.15 |
| 5. | 2019. 6. 30. | -29.55% | 6.89% | 1,255.09 | 33.49 | -205.02 |
| 6. | 2019. 7. 31. | -10.52% | 1.31% | 268.92 | 0.04 | -3.39 |
| 7. | 2019. 8. 31. | 20.08% | -1.81% | 201.55 | 8.50 | -41.38 |
| 8. | 2019. 9. 30. | 1.21% | 1.72% | 21.82 | 0.37 | -2.86 |
| 9. | 2019. 10. 31. | 5.21% | 2.04% | 0.44 | 0.88 | -0.62 |
| 10. | 2019. 11. 30. | 21.55% | 3.40% | 245.63 | 5.28 | 36.03 |
| 11. | 2019. 12. 31. | -3.93% | 2.86% | 96.21 | 3.07 | -17.20 |
| 12. | 2020. 1. 31. | 4.86% | -0.16% | 1.05 | 1.61 | 1.30 |
| 13. | 2020. 2. 29. | 26.43% | -8.41% | 422.16 | 90.57 | -195.54 |
| 14. | 2020. 3. 31. | 15.50% | -12.51% | 92.62 | 185.44 | -131.05 |
| 15. | 2020. 4. 30. | 53.56% | 12.68% | 2,273.03 | 134.06 | 552.02 |
| 16. | 2020. 5. 31. | 33.72% | 4.53% | 775.35 | 11.71 | 95.30 |
| 17. | 2020. 6. 30. | 4.41% | 1.84% | 2.17 | 0.54 | -1.08 |
| 18. | 2020. 7. 31. | 15.40% | 5.51% | 90.69 | 19.40 | 41.94 |
| 19. | 2020. 8. 31. | -12.43% | 7.01% | 335.21 | 34.82 | -108.03 |
| 20. | 2020. 9. 30. | 9.03% | -3.92% | 9.93 | 25.29 | -15.85 |
| 21. | 2020. 10. 31. | -4.64% | -2.77% | 110.58 | 15.00 | 40.72 |
| 22. | 2020. 11. 30. | 126.38% | 10.75% | 14,520.85 | 93.10 | 1,162.69 |
| 23. | 2020. 12. 31. | -31.60% | 3.71% | 1,404.92 | 6.79 | -97.69 |
| 24. | 2021. 1. 31. | 65.75% | -1.11% | 3,584.58 | 4.93 | -132.89 |
| 25. | 2021. 2. 28. | -10.60% | 2.61% | 271.48 | 2.26 | -24.77 |
| 26. | 2021. 3. 31. | -15.41% | 4.24% | 453.35 | 9.85 | -66.81 |
| 27. | 2021. 4. 30. | 36.56% | 5.24% | 941.04 | 17.11 | 126.90 |
| 28. | 2021. 5. 31. | 3.46% | 0.55% | 5.85 | 0.31 | 1.35 |
| 29. | 2021. 6. 30. | 27.01% | 2.22% | 446.47 | 1.24 | 23.57 |
| 30. | 2021. 7. 31. | 50.48% | 2.27% | 1,989.28 | 1.37 | 52.14 |
| 31. | 2021. 8. 31. | 6.53% | 2.90% | 0.42 | 3.22 | 1.17 |
| 32. | 2021. 9. 30. | 2.17% | -4.76% | 13.77 | 34.37 | 21.75 |
| 33. | 2021. 10. 31. | -10.30% | 6.91% | 261.86 | 33.74 | -93.99 |
| 34. | 2021. 11. 30. | 2.09% | -0.83% | 14.35 | 3.76 | 7.35 |
| 35. | 2021. 12. 31. | -27.93% | 4.36% | 1,143.40 | 10.60 | -110.08 |
| 36. | 2022. 1. 31. | -33.33% | -5.26% | 1,537.34 | 40.51 | 249.54 |
| 37. | 2022. 2. 28. | -9.29% | -3.14% | 230.10 | 17.99 | 64.35 |
| 38. | 2022. 3. 31. | 12.15% | 3.58% | 39.30 | 6.11 | 15.49 |
| 39. | 2022. 4. 30. | -21.97% | -8.80% | 775.74 | 98.04 | 275.78 |
| 40. | 2022. 5. 31. | 8.12% | 0.01% | 5.04 | 1.21 | -2.47 |
| 41. | 2022. 6. 30. | -1.71% | -8.39% | 57.55 | 90.21 | 72.05 |
| 42. | 2022. 7. 31. | 14.87% | 9.11% | 80.80 | 64.09 | 71.97 |
| 43. | 2022. 8. 31. | -19.39% | -4.24% | 638.64 | 28.62 | 135.20 |
| 44. | 2022. 9. 30. | -10.60% | -9.34% | 271.56 | 109.11 | 172.13 |
| 45. | 2022. 10. 31. | 27.13% | 7.99% | 451.54 | 47.34 | 146.21 |
| 46. | 2022. 11. 30. | 17.02% | 5.38% | 124.02 | 18.23 | 47.55 |
| 47. | 2022. 12. 31. | 2.11% | -5.90% | 14.22 | 49.04 | 26.41 |
| 48. | 2023. 1. 31. | -1.98% | 6.18% | 61.80 | 25.70 | -39.85 |
| 49. | 2023. 2. 28. | -21.16% | -2.61% | 731.01 | 13.82 | 100.50 |
| 50. | 2023. 3. 31. | 10.64% | 3.51% | 22.67 | 5.76 | 11.42 |
| 51. | 2023. 4. 30. | -13.47% | 1.46% | 374.48 | 0.13 | -6.94 |
| 52. | 2023. 5. 31. | -3.90% | 0.25% | 95.60 | 0.74 | 8.39 |
| 53. | 2023. 6. 30. | -4.86% | 4.71% | 115.39 | 13.02 | -38.76 |
| 54. | 2023. 7. 31. | -3.16% | 4.85% | 81.72 | 13.99 | -33.81 |
| 55. | 2023. 8. 31. | -3.90% | -1.77% | 95.66 | 8.28 | 28.14 |
| 56. | 2023. 9. 30. | -8.65% | -4.87% | 211.09 | 35.73 | 86.85 |
| 57. | 2023. 10. 31. | -26.46% | -2.20% | 1,045.82 | 10.92 | 106.84 |
| 58. | 2023. 11. 30. | 2.29% | 8.92% | 12.88 | 61.03 | -28.04 |
| 59. | 2023. 12. 31. | 27.99% | 4.42% | 488.97 | 11.00 | 73.35 |
| 합계 (Σ): | 41,147.69 | 1,634.30 | 2,766.28 | |||
모두 보기
분산MRNA = Σ(RMRNA,t–RMRNA)2 ÷ (59 – 1)
= 41,147.69 ÷ (59 – 1)
= 709.44
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산MRNA, S&P 500 = Σ(RMRNA,t–RMRNA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,766.28 ÷ (59 – 1)
= 47.69
체계적인 위험 추정 (β)
| 분산MRNA | 709.44 |
| 분산S&P 500 | 28.18 |
| 공분산MRNA, S&P 500 | 47.69 |
| 상관 계수MRNA, S&P 5001 | 0.34 |
| βMRNA2 | 1.69 |
| αMRNA3 | 4.01% |
계산
1 상관 계수MRNA, S&P 500
= 공분산MRNA, S&P 500 ÷ (표준 편차MRNA × 표준 편차S&P 500)
= 47.69 ÷ (26.64% × 5.31%)
= 0.34
2 βMRNA
= 공분산MRNA, S&P 500 ÷ 분산S&P 500
= 47.69 ÷ 28.18
= 1.69
3 αMRNA
= 평균의MRNA – βMRNA × 평균의S&P 500
= 5.88% – 1.69 × 1.11%
= 4.01%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Moderna | βMRNA | 1.69 |
| Moderna 보통주 예상 수익률3 | E(RMRNA) | 22.01% |
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(RMRNA) = RF + βMRNA [E(RM) – RF]
= 4.60% + 1.69 [14.89% – 4.60%]
= 22.01%