자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Abbott보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Abbott Laboratories, 월별 수익률
| Abbott Laboratories (ABT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ABT,t1 | 피제수ABT,t1 | RABT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $123.59 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $119.78 | -3.08% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $119.84 | 0.05% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $120.08 | $0.45 | 0.58% | 4,181.17 | 5.24% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $128.90 | 4.27% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $125.29 | -2.80% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.32% | 1.14% | ||||
| 표준 편차: | 5.60% | 4.37% | ||||
| Abbott Laboratories (ABT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ABT,t1 | 피제수ABT,t1 | RABT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $123.59 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $119.78 | -3.08% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $119.84 | 0.05% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $120.08 | $0.45 | 0.58% | 4,181.17 | 5.24% |
| 4. | 2021. 5. 31. | $116.65 | -2.86% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $115.93 | -0.62% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $120.98 | $0.45 | 4.74% | 4,395.26 | 2.27% |
| 7. | 2021. 8. 31. | $126.37 | 4.46% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $118.13 | -6.52% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $128.89 | $0.45 | 9.49% | 4,605.38 | 6.91% |
| 10. | 2021. 11. 30. | $125.77 | -2.42% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $140.74 | 11.90% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $127.46 | $0.47 | -9.10% | 4,515.55 | -5.26% |
| 13. | 2022. 2. 28. | $120.62 | -5.37% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $118.36 | -1.87% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $113.50 | $0.47 | -3.71% | 4,131.93 | -8.80% |
| 16. | 2022. 5. 31. | $117.46 | 3.49% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $108.65 | -7.50% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $108.84 | $0.47 | 0.61% | 4,130.29 | 9.11% |
| 19. | 2022. 8. 31. | $102.65 | -5.69% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $96.76 | -5.74% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $98.94 | $0.47 | 2.74% | 3,871.98 | 7.99% |
| 22. | 2022. 11. 30. | $107.58 | 8.73% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $109.79 | 2.05% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $110.55 | $0.51 | 1.16% | 4,076.60 | 6.18% |
| 25. | 2023. 2. 28. | $101.72 | -7.99% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $101.26 | -0.45% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $110.47 | $0.51 | 9.60% | 4,169.48 | 1.46% |
| 28. | 2023. 5. 31. | $102.00 | -7.67% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $109.02 | 6.88% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $111.33 | $0.51 | 2.59% | 4,588.96 | 4.85% |
| 31. | 2023. 8. 31. | $102.90 | -7.57% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $96.85 | -5.88% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $94.55 | $0.51 | -1.85% | 4,193.80 | -2.20% |
| 34. | 2023. 11. 30. | $104.29 | 10.30% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $110.07 | 5.54% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $113.15 | $0.55 | 3.30% | 4,845.65 | 1.59% |
| 37. | 2024. 2. 29. | $118.64 | 4.85% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $113.66 | -4.20% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $105.97 | $0.55 | -6.28% | 5,035.69 | -4.16% |
| 40. | 2024. 5. 31. | $102.19 | -3.57% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $103.91 | 1.68% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $105.94 | $0.55 | 2.48% | 5,522.30 | 1.13% |
| 43. | 2024. 8. 31. | $113.27 | 6.92% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $114.01 | 0.65% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $113.37 | $0.55 | -0.08% | 5,705.45 | -0.99% |
| 46. | 2024. 11. 30. | $118.77 | 4.76% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $113.11 | -4.77% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $127.93 | $0.59 | 13.62% | 6,040.53 | 2.70% |
| 49. | 2025. 2. 28. | $138.01 | 7.88% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $132.65 | -3.88% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $130.75 | $0.59 | -0.99% | 5,569.06 | -0.76% |
| 52. | 2025. 5. 31. | $133.58 | 2.16% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $136.01 | 1.82% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $126.19 | $0.59 | -6.79% | 6,339.39 | 2.17% |
| 55. | 2025. 8. 31. | $132.66 | 5.13% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $133.94 | 0.96% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $123.62 | $0.59 | -7.26% | 6,840.20 | 2.27% |
| 58. | 2025. 11. 30. | $128.90 | 4.27% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $125.29 | -2.80% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.32% | 1.14% | ||||
| 표준 편차: | 5.60% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 ABT의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Abbott Laboratories, 수익률의 분산 및 공분산 계산
| t | 날짜 | RABT,t | RS&P 500,t | (RABT,t–RABT)2 | (RS&P 500,t–RS&P 500)2 | (RABT,t–RABT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -3.08% | 2.61% | 11.58 | 2.17 | -5.01 |
| 2. | 2021. 3. 31. | 0.05% | 4.24% | 0.07 | 9.66 | -0.84 |
| 3. | 2021. 4. 30. | 0.58% | 5.24% | 0.07 | 16.86 | 1.05 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 4.27% | 0.13% | 15.61 | 1.01 | -3.97 |
| 59. | 2025. 12. 31. | -2.80% | -0.05% | 9.74 | 1.41 | 3.71 |
| 합계 (Σ): | 1,819.01 | 1,108.23 | 829.71 | |||
| t | 날짜 | RABT,t | RS&P 500,t | (RABT,t–RABT)2 | (RS&P 500,t–RS&P 500)2 | (RABT,t–RABT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -3.08% | 2.61% | 11.58 | 2.17 | -5.01 |
| 2. | 2021. 3. 31. | 0.05% | 4.24% | 0.07 | 9.66 | -0.84 |
| 3. | 2021. 4. 30. | 0.58% | 5.24% | 0.07 | 16.86 | 1.05 |
| 4. | 2021. 5. 31. | -2.86% | 0.55% | 10.09 | 0.35 | 1.87 |
| 5. | 2021. 6. 30. | -0.62% | 2.22% | 0.88 | 1.18 | -1.02 |
| 6. | 2021. 7. 31. | 4.74% | 2.27% | 19.57 | 1.30 | 5.04 |
| 7. | 2021. 8. 31. | 4.46% | 2.90% | 17.10 | 3.11 | 7.29 |
| 8. | 2021. 9. 30. | -6.52% | -4.76% | 46.80 | 34.73 | 40.32 |
| 9. | 2021. 10. 31. | 9.49% | 6.91% | 84.07 | 33.39 | 52.98 |
| 10. | 2021. 11. 30. | -2.42% | -0.83% | 7.51 | 3.88 | 5.40 |
| 11. | 2021. 12. 31. | 11.90% | 4.36% | 134.14 | 10.40 | 37.35 |
| 12. | 2022. 1. 31. | -9.10% | -5.26% | 88.78 | 40.89 | 60.25 |
| 13. | 2022. 2. 28. | -5.37% | -3.14% | 32.34 | 18.25 | 24.30 |
| 14. | 2022. 3. 31. | -1.87% | 3.58% | 4.81 | 5.96 | -5.36 |
| 15. | 2022. 4. 30. | -3.71% | -8.80% | 16.24 | 98.64 | 40.02 |
| 16. | 2022. 5. 31. | 3.49% | 0.01% | 10.04 | 1.28 | -3.58 |
| 17. | 2022. 6. 30. | -7.50% | -8.39% | 61.17 | 90.79 | 74.52 |
| 18. | 2022. 7. 31. | 0.61% | 9.11% | 0.08 | 63.61 | 2.29 |
| 19. | 2022. 8. 31. | -5.69% | -4.24% | 36.09 | 28.95 | 32.32 |
| 20. | 2022. 9. 30. | -5.74% | -9.34% | 36.71 | 109.74 | 63.47 |
| 21. | 2022. 10. 31. | 2.74% | 7.99% | 5.85 | 46.93 | 16.56 |
| 22. | 2022. 11. 30. | 8.73% | 5.38% | 70.76 | 17.97 | 35.66 |
| 23. | 2022. 12. 31. | 2.05% | -5.90% | 3.01 | 49.47 | -12.19 |
| 24. | 2023. 1. 31. | 1.16% | 6.18% | 0.70 | 25.39 | 4.21 |
| 25. | 2023. 2. 28. | -7.99% | -2.61% | 69.02 | 14.04 | 31.13 |
| 26. | 2023. 3. 31. | -0.45% | 3.51% | 0.60 | 5.61 | -1.83 |
| 27. | 2023. 4. 30. | 9.60% | 1.46% | 86.09 | 0.11 | 3.04 |
| 28. | 2023. 5. 31. | -7.67% | 0.25% | 63.81 | 0.79 | 7.09 |
| 29. | 2023. 6. 30. | 6.88% | 4.71% | 43.06 | 12.80 | 23.48 |
| 30. | 2023. 7. 31. | 2.59% | 4.85% | 5.14 | 13.76 | 8.41 |
| 31. | 2023. 8. 31. | -7.57% | -1.77% | 62.29 | 8.46 | 22.95 |
| 32. | 2023. 9. 30. | -5.88% | -4.87% | 38.44 | 36.10 | 37.25 |
| 33. | 2023. 10. 31. | -1.85% | -2.20% | 4.70 | 11.12 | 7.23 |
| 34. | 2023. 11. 30. | 10.30% | 8.92% | 99.62 | 60.56 | 77.67 |
| 35. | 2023. 12. 31. | 5.54% | 4.42% | 27.27 | 10.80 | 17.16 |
| 36. | 2024. 1. 31. | 3.30% | 1.59% | 8.86 | 0.21 | 1.35 |
| 37. | 2024. 2. 29. | 4.85% | 5.17% | 20.53 | 16.29 | 18.29 |
| 38. | 2024. 3. 31. | -4.20% | 3.10% | 20.41 | 3.86 | -8.88 |
| 39. | 2024. 4. 30. | -6.28% | -4.16% | 43.59 | 28.06 | 34.98 |
| 40. | 2024. 5. 31. | -3.57% | 4.80% | 15.11 | 13.44 | -14.25 |
| 41. | 2024. 6. 30. | 1.68% | 3.47% | 1.86 | 5.43 | 3.18 |
| 42. | 2024. 7. 31. | 2.48% | 1.13% | 4.68 | 0.00 | -0.01 |
| 43. | 2024. 8. 31. | 6.92% | 2.28% | 43.54 | 1.32 | 7.57 |
| 44. | 2024. 9. 30. | 0.65% | 2.02% | 0.11 | 0.78 | 0.29 |
| 45. | 2024. 10. 31. | -0.08% | -0.99% | 0.16 | 4.52 | 0.85 |
| 46. | 2024. 11. 30. | 4.76% | 5.73% | 19.74 | 21.10 | 20.41 |
| 47. | 2024. 12. 31. | -4.77% | -2.50% | 25.87 | 13.21 | 18.49 |
| 48. | 2025. 1. 31. | 13.62% | 2.70% | 176.98 | 2.45 | 20.83 |
| 49. | 2025. 2. 28. | 7.88% | -1.42% | 57.13 | 6.56 | -19.35 |
| 50. | 2025. 3. 31. | -3.88% | -5.75% | 17.68 | 47.48 | 28.97 |
| 51. | 2025. 4. 30. | -0.99% | -0.76% | 1.71 | 3.60 | 2.48 |
| 52. | 2025. 5. 31. | 2.16% | 6.15% | 3.40 | 25.16 | 9.25 |
| 53. | 2025. 6. 30. | 1.82% | 4.96% | 2.25 | 14.63 | 5.73 |
| 54. | 2025. 7. 31. | -6.79% | 2.17% | 50.51 | 1.06 | -7.32 |
| 55. | 2025. 8. 31. | 5.13% | 1.91% | 23.10 | 0.59 | 3.70 |
| 56. | 2025. 9. 30. | 0.96% | 3.53% | 0.42 | 5.74 | 1.54 |
| 57. | 2025. 10. 31. | -7.26% | 2.27% | 57.53 | 1.28 | -8.59 |
| 58. | 2025. 11. 30. | 4.27% | 0.13% | 15.61 | 1.01 | -3.97 |
| 59. | 2025. 12. 31. | -2.80% | -0.05% | 9.74 | 1.41 | 3.71 |
| 합계 (Σ): | 1,819.01 | 1,108.23 | 829.71 | |||
모두 보기
분산ABT = Σ(RABT,t–RABT)2 ÷ (59 – 1)
= 1,819.01 ÷ (59 – 1)
= 31.36
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산ABT, S&P 500 = Σ(RABT,t–RABT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 829.71 ÷ (59 – 1)
= 14.31
체계적인 위험 추정 (β)
| 분산ABT | 31.36 |
| 분산S&P 500 | 19.11 |
| 공분산ABT, S&P 500 | 14.31 |
| 상관 계수ABT, S&P 5001 | 0.58 |
| βABT2 | 0.75 |
| αABT3 | -0.53% |
계산
1 상관 계수ABT, S&P 500
= 공분산ABT, S&P 500 ÷ (표준 편차ABT × 표준 편차S&P 500)
= 14.31 ÷ (5.60% × 4.37%)
= 0.58
2 βABT
= 공분산ABT, S&P 500 ÷ 분산S&P 500
= 14.31 ÷ 19.11
= 0.75
3 αABT
= 평균의ABT – βABT × 평균의S&P 500
= 0.32% – 0.75 × 1.14%
= -0.53%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Abbott | βABT | 0.75 |
| Abbott 보통주에 대한 예상 수익률3 | E(RABT) | 14.14% |
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(RABT) = RF + βABT [E(RM) – RF]
= 4.54% + 0.75 [17.37% – 4.54%]
= 14.14%