자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 BMS보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Bristol-Myers Squibb Co., 월별 수익률
| Bristol-Myers Squibb Co. (BMY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BMY,t1 | 피제수BMY,t1 | RBMY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $62.95 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $59.06 | -6.18% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $55.74 | -5.62% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $60.81 | $0.45 | 9.90% | 2,912.43 | 12.68% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $59.22 | 6.19% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $56.56 | -4.49% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.30% | 1.16% | ||||
| 표준 편차: | 6.33% | 5.28% | ||||
| Bristol-Myers Squibb Co. (BMY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BMY,t1 | 피제수BMY,t1 | RBMY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $62.95 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $59.06 | -6.18% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $55.74 | -5.62% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $60.81 | $0.45 | 9.90% | 2,912.43 | 12.68% |
| 4. | 2020. 5. 31. | $59.72 | -1.79% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $58.80 | -1.54% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $58.66 | $0.45 | 0.53% | 3,271.12 | 5.51% |
| 7. | 2020. 8. 31. | $62.20 | 6.03% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $60.29 | -3.07% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $58.45 | $0.45 | -2.31% | 3,269.96 | -2.77% |
| 10. | 2020. 11. 30. | $62.40 | 6.76% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $62.03 | $0.49 | 0.19% | 3,756.07 | 3.71% |
| 12. | 2021. 1. 31. | $61.43 | -0.97% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $61.33 | -0.16% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $63.13 | $0.49 | 3.73% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $62.42 | -1.12% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $65.72 | 5.29% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $66.82 | 1.67% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $67.87 | $0.49 | 2.30% | 4,395.26 | 2.27% |
| 19. | 2021. 8. 31. | $66.86 | -1.49% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $59.17 | $0.49 | -10.77% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $58.40 | -1.30% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $53.63 | -8.17% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $62.35 | 16.26% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $64.89 | $0.54 | 4.94% | 4,515.55 | -5.26% |
| 25. | 2022. 2. 28. | $68.67 | 5.83% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $73.03 | $0.54 | 7.14% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $75.27 | 3.07% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $75.45 | 0.24% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $77.00 | $0.54 | 2.77% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $73.78 | -4.18% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $67.41 | -8.63% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $71.09 | 5.46% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $77.47 | $0.54 | 9.73% | 3,871.98 | 7.99% |
| 34. | 2022. 11. 30. | $80.28 | 3.63% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $71.95 | -10.38% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $72.65 | $0.57 | 1.77% | 4,076.60 | 6.18% |
| 37. | 2023. 2. 28. | $68.96 | -5.08% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $69.31 | 0.51% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $66.77 | $0.57 | -2.84% | 4,169.48 | 1.46% |
| 40. | 2023. 5. 31. | $64.44 | -3.49% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $63.95 | -0.76% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $62.19 | $0.57 | -1.86% | 4,588.96 | 4.85% |
| 43. | 2023. 8. 31. | $61.65 | -0.87% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $58.04 | -5.86% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $51.53 | $0.57 | -10.23% | 4,193.80 | -2.20% |
| 46. | 2023. 11. 30. | $49.38 | -4.17% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $51.31 | 3.91% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $48.87 | $0.60 | -3.59% | 4,845.65 | 1.59% |
| 49. | 2024. 2. 29. | $50.75 | 3.85% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $54.23 | 6.86% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $43.94 | $0.60 | -17.87% | 5,035.69 | -4.16% |
| 52. | 2024. 5. 31. | $41.09 | -6.49% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $41.53 | 1.07% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $47.56 | $0.60 | 15.96% | 5,522.30 | 1.13% |
| 55. | 2024. 8. 31. | $49.95 | 5.03% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $51.74 | 3.58% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $55.77 | $0.60 | 8.95% | 5,705.45 | -0.99% |
| 58. | 2024. 11. 30. | $59.22 | 6.19% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $56.56 | -4.49% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.30% | 1.16% | ||||
| 표준 편차: | 6.33% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 BMY의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Bristol-Myers Squibb Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RBMY,t | RS&P 500,t | (RBMY,t–RBMY)2 | (RS&P 500,t–RS&P 500)2 | (RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.18% | -8.41% | 42.02 | 91.63 | 62.05 |
| 2. | 2020. 3. 31. | -5.62% | -12.51% | 35.09 | 186.96 | 81.00 |
| 3. | 2020. 4. 30. | 9.90% | 12.68% | 92.17 | 132.78 | 110.63 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 6.19% | 5.73% | 34.61 | 20.87 | 26.88 |
| 59. | 2024. 12. 31. | -4.49% | -2.50% | 22.99 | 13.40 | 17.55 |
| 합계 (Σ): | 2,326.76 | 1,618.62 | 726.32 | |||
| t | 날짜 | RBMY,t | RS&P 500,t | (RBMY,t–RBMY)2 | (RS&P 500,t–RS&P 500)2 | (RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.18% | -8.41% | 42.02 | 91.63 | 62.05 |
| 2. | 2020. 3. 31. | -5.62% | -12.51% | 35.09 | 186.96 | 81.00 |
| 3. | 2020. 4. 30. | 9.90% | 12.68% | 92.17 | 132.78 | 110.63 |
| 4. | 2020. 5. 31. | -1.79% | 4.53% | 4.39 | 11.34 | -7.05 |
| 5. | 2020. 6. 30. | -1.54% | 1.84% | 3.40 | 0.46 | -1.25 |
| 6. | 2020. 7. 31. | 0.53% | 5.51% | 0.05 | 18.91 | 0.98 |
| 7. | 2020. 8. 31. | 6.03% | 7.01% | 32.86 | 34.17 | 33.51 |
| 8. | 2020. 9. 30. | -3.07% | -3.92% | 11.38 | 25.85 | 17.15 |
| 9. | 2020. 10. 31. | -2.31% | -2.77% | 6.80 | 15.43 | 10.24 |
| 10. | 2020. 11. 30. | 6.76% | 10.75% | 41.67 | 92.03 | 61.93 |
| 11. | 2020. 12. 31. | 0.19% | 3.71% | 0.01 | 6.51 | -0.28 |
| 12. | 2021. 1. 31. | -0.97% | -1.11% | 1.61 | 5.18 | 2.89 |
| 13. | 2021. 2. 28. | -0.16% | 2.61% | 0.22 | 2.10 | -0.67 |
| 14. | 2021. 3. 31. | 3.73% | 4.24% | 11.77 | 9.50 | 10.58 |
| 15. | 2021. 4. 30. | -1.12% | 5.24% | 2.04 | 16.66 | -5.83 |
| 16. | 2021. 5. 31. | 5.29% | 0.55% | 24.84 | 0.38 | -3.05 |
| 17. | 2021. 6. 30. | 1.67% | 2.22% | 1.88 | 1.12 | 1.45 |
| 18. | 2021. 7. 31. | 2.30% | 2.27% | 4.01 | 1.24 | 2.23 |
| 19. | 2021. 8. 31. | -1.49% | 2.90% | 3.21 | 3.02 | -3.11 |
| 20. | 2021. 9. 30. | -10.77% | -4.76% | 122.58 | 35.02 | 65.52 |
| 21. | 2021. 10. 31. | -1.30% | 6.91% | 2.57 | 33.10 | -9.23 |
| 22. | 2021. 11. 30. | -8.17% | -0.83% | 71.75 | 3.98 | 16.90 |
| 23. | 2021. 12. 31. | 16.26% | 4.36% | 254.62 | 10.24 | 51.06 |
| 24. | 2022. 1. 31. | 4.94% | -5.26% | 21.50 | 41.21 | -29.77 |
| 25. | 2022. 2. 28. | 5.83% | -3.14% | 30.50 | 18.47 | -23.73 |
| 26. | 2022. 3. 31. | 7.14% | 3.58% | 46.69 | 5.84 | 16.51 |
| 27. | 2022. 4. 30. | 3.07% | -8.80% | 7.64 | 99.14 | -27.53 |
| 28. | 2022. 5. 31. | 0.24% | 0.01% | 0.00 | 1.34 | 0.07 |
| 29. | 2022. 6. 30. | 2.77% | -8.39% | 6.09 | 91.26 | -23.57 |
| 30. | 2022. 7. 31. | -4.18% | 9.11% | 20.11 | 63.21 | -35.65 |
| 31. | 2022. 8. 31. | -8.63% | -4.24% | 79.86 | 29.22 | 48.30 |
| 32. | 2022. 9. 30. | 5.46% | -9.34% | 26.59 | 110.27 | -54.15 |
| 33. | 2022. 10. 31. | 9.73% | 7.99% | 88.95 | 46.58 | 64.37 |
| 34. | 2022. 11. 30. | 3.63% | 5.38% | 11.05 | 17.76 | 14.01 |
| 35. | 2022. 12. 31. | -10.38% | -5.90% | 114.04 | 49.82 | 75.38 |
| 36. | 2023. 1. 31. | 1.77% | 6.18% | 2.14 | 25.14 | 7.33 |
| 37. | 2023. 2. 28. | -5.08% | -2.61% | 28.96 | 14.23 | 20.30 |
| 38. | 2023. 3. 31. | 0.51% | 3.51% | 0.04 | 5.49 | 0.48 |
| 39. | 2023. 4. 30. | -2.84% | 1.46% | 9.89 | 0.09 | -0.95 |
| 40. | 2023. 5. 31. | -3.49% | 0.25% | 14.38 | 0.83 | 3.46 |
| 41. | 2023. 6. 30. | -0.76% | 4.71% | 1.13 | 12.62 | -3.78 |
| 42. | 2023. 7. 31. | -1.86% | 4.85% | 4.68 | 13.58 | -7.97 |
| 43. | 2023. 8. 31. | -0.87% | -1.77% | 1.37 | 8.60 | 3.43 |
| 44. | 2023. 9. 30. | -5.86% | -4.87% | 37.92 | 36.40 | 37.15 |
| 45. | 2023. 10. 31. | -10.23% | -2.20% | 111.03 | 11.28 | 35.40 |
| 46. | 2023. 11. 30. | -4.17% | 8.92% | 20.03 | 60.17 | -34.71 |
| 47. | 2023. 12. 31. | 3.91% | 4.42% | 13.00 | 10.64 | 11.76 |
| 48. | 2024. 1. 31. | -3.59% | 1.59% | 15.12 | 0.18 | -1.67 |
| 49. | 2024. 2. 29. | 3.85% | 5.17% | 12.56 | 16.09 | 14.22 |
| 50. | 2024. 3. 31. | 6.86% | 3.10% | 42.96 | 3.77 | 12.72 |
| 51. | 2024. 4. 30. | -17.87% | -4.16% | 330.19 | 28.33 | 96.72 |
| 52. | 2024. 5. 31. | -6.49% | 4.80% | 46.09 | 13.26 | -24.72 |
| 53. | 2024. 6. 30. | 1.07% | 3.47% | 0.59 | 5.32 | 1.77 |
| 54. | 2024. 7. 31. | 15.96% | 1.13% | 245.29 | 0.00 | -0.46 |
| 55. | 2024. 8. 31. | 5.03% | 2.28% | 22.30 | 1.26 | 5.30 |
| 56. | 2024. 9. 30. | 3.58% | 2.02% | 10.76 | 0.74 | 2.82 |
| 57. | 2024. 10. 31. | 8.95% | -0.99% | 74.75 | 4.63 | -18.60 |
| 58. | 2024. 11. 30. | 6.19% | 5.73% | 34.61 | 20.87 | 26.88 |
| 59. | 2024. 12. 31. | -4.49% | -2.50% | 22.99 | 13.40 | 17.55 |
| 합계 (Σ): | 2,326.76 | 1,618.62 | 726.32 | |||
모두 보기
분산BMY = Σ(RBMY,t–RBMY)2 ÷ (59 – 1)
= 2,326.76 ÷ (59 – 1)
= 40.12
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산BMY, S&P 500 = Σ(RBMY,t–RBMY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 726.32 ÷ (59 – 1)
= 12.52
체계적인 위험 추정 (β)
| 분산BMY | 40.12 |
| 분산S&P 500 | 27.91 |
| 공분산BMY, S&P 500 | 12.52 |
| 상관 계수BMY, S&P 5001 | 0.37 |
| βBMY2 | 0.45 |
| αBMY3 | -0.22% |
계산
1 상관 계수BMY, S&P 500
= 공분산BMY, S&P 500 ÷ (표준 편차BMY × 표준 편차S&P 500)
= 12.52 ÷ (6.33% × 5.28%)
= 0.37
2 βBMY
= 공분산BMY, S&P 500 ÷ 분산S&P 500
= 12.52 ÷ 27.91
= 0.45
3 αBMY
= 평균의BMY – βBMY × 평균의S&P 500
= 0.30% – 0.45 × 1.16%
= -0.22%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.53% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험BMS | βBMY | 0.45 |
| BMS 보통주 예상 수익률3 | E(RBMY) | 9.17% |
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(RBMY) = RF + βBMY [E(RM) – RF]
= 4.53% + 0.45 [14.88% – 4.53%]
= 9.17%