자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Coca-Cola보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Coca-Cola Co., 월별 수익률
| Coca-Cola Co. (KO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값KO,t1 | 피제수KO,t1 | RKO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $48.15 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $48.99 | 1.74% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $52.71 | $0.42 | 8.45% | 3,972.89 | 4.24% |
| 3. | 2021. 4. 30. | $53.98 | 2.41% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $73.12 | 6.12% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $69.91 | $0.51 | -3.69% | 6,845.50 | -0.05% |
| 평균의 (R): | 0.99% | 1.14% | ||||
| 표준 편차: | 4.59% | 4.37% | ||||
| Coca-Cola Co. (KO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값KO,t1 | 피제수KO,t1 | RKO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $48.15 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $48.99 | 1.74% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $52.71 | $0.42 | 8.45% | 3,972.89 | 4.24% |
| 3. | 2021. 4. 30. | $53.98 | 2.41% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $55.29 | 2.43% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $54.11 | $0.42 | -1.37% | 4,297.50 | 2.22% |
| 6. | 2021. 7. 31. | $57.03 | 5.40% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $56.31 | -1.26% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $52.47 | $0.42 | -6.07% | 4,307.54 | -4.76% |
| 9. | 2021. 10. 31. | $56.37 | 7.43% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $52.45 | $0.42 | -6.21% | 4,567.00 | -0.83% |
| 11. | 2021. 12. 31. | $59.21 | 12.89% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $61.01 | 3.04% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $62.24 | 2.02% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $62.00 | $0.44 | 0.32% | 4,530.41 | 3.58% |
| 15. | 2022. 4. 30. | $64.61 | 4.21% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $63.38 | -1.90% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $62.91 | $0.44 | -0.05% | 3,785.38 | -8.39% |
| 18. | 2022. 7. 31. | $64.17 | 2.00% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $61.71 | -3.83% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $56.02 | $0.44 | -8.51% | 3,585.62 | -9.34% |
| 21. | 2022. 10. 31. | $59.85 | 6.84% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $63.61 | $0.44 | 7.02% | 4,080.11 | 5.38% |
| 23. | 2022. 12. 31. | $63.61 | 0.00% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $61.32 | -3.60% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $59.51 | -2.95% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $62.03 | $0.46 | 5.01% | 4,109.31 | 3.51% |
| 27. | 2023. 4. 30. | $64.15 | 3.42% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $59.66 | -7.00% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $60.22 | $0.46 | 1.71% | 4,376.86 | 4.71% |
| 30. | 2023. 7. 31. | $61.93 | 2.84% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $59.83 | -3.39% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $55.98 | $0.46 | -5.67% | 4,288.05 | -4.87% |
| 33. | 2023. 10. 31. | $56.49 | 0.91% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $58.44 | $0.46 | 4.27% | 4,567.80 | 8.92% |
| 35. | 2023. 12. 31. | $58.93 | 0.84% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $59.49 | 0.95% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $60.02 | 0.89% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $61.18 | $0.485 | 2.74% | 5,254.35 | 3.10% |
| 39. | 2024. 4. 30. | $61.77 | 0.96% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $62.93 | 1.88% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $63.65 | $0.485 | 1.91% | 5,460.48 | 3.47% |
| 42. | 2024. 7. 31. | $66.74 | 4.85% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $72.47 | 8.59% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $71.86 | $0.485 | -0.17% | 5,762.48 | 2.02% |
| 45. | 2024. 10. 31. | $65.31 | -9.11% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $64.08 | $0.485 | -1.14% | 6,032.38 | 5.73% |
| 47. | 2024. 12. 31. | $62.26 | -2.84% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $63.48 | 1.96% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $71.21 | 12.18% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $71.62 | $0.51 | 1.29% | 5,611.85 | -5.75% |
| 51. | 2025. 4. 30. | $72.55 | 1.30% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $72.10 | -0.62% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $70.75 | $0.51 | -1.17% | 6,204.95 | 4.96% |
| 54. | 2025. 7. 31. | $67.89 | -4.04% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $68.99 | 1.62% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $66.32 | $0.51 | -3.13% | 6,688.46 | 3.53% |
| 57. | 2025. 10. 31. | $68.90 | 3.89% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $73.12 | 6.12% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $69.91 | $0.51 | -3.69% | 6,845.50 | -0.05% |
| 평균의 (R): | 0.99% | 1.14% | ||||
| 표준 편차: | 4.59% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 KO의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Coca-Cola Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RKO,t | RS&P 500,t | (RKO,t–RKO)2 | (RS&P 500,t–RS&P 500)2 | (RKO,t–RKO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 1.74% | 2.61% | 0.56 | 2.17 | 1.11 |
| 2. | 2021. 3. 31. | 8.45% | 4.24% | 55.62 | 9.66 | 23.18 |
| 3. | 2021. 4. 30. | 2.41% | 5.24% | 2.01 | 16.86 | 5.82 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 6.12% | 0.13% | 26.34 | 1.01 | -5.16 |
| 59. | 2025. 12. 31. | -3.69% | -0.05% | 21.95 | 1.41 | 5.57 |
| 합계 (Σ): | 1,220.31 | 1,108.23 | 408.64 | |||
| t | 날짜 | RKO,t | RS&P 500,t | (RKO,t–RKO)2 | (RS&P 500,t–RS&P 500)2 | (RKO,t–RKO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 1.74% | 2.61% | 0.56 | 2.17 | 1.11 |
| 2. | 2021. 3. 31. | 8.45% | 4.24% | 55.62 | 9.66 | 23.18 |
| 3. | 2021. 4. 30. | 2.41% | 5.24% | 2.01 | 16.86 | 5.82 |
| 4. | 2021. 5. 31. | 2.43% | 0.55% | 2.06 | 0.35 | -0.84 |
| 5. | 2021. 6. 30. | -1.37% | 2.22% | 5.61 | 1.18 | -2.57 |
| 6. | 2021. 7. 31. | 5.40% | 2.27% | 19.39 | 1.30 | 5.01 |
| 7. | 2021. 8. 31. | -1.26% | 2.90% | 5.09 | 3.11 | -3.98 |
| 8. | 2021. 9. 30. | -6.07% | -4.76% | 49.94 | 34.73 | 41.64 |
| 9. | 2021. 10. 31. | 7.43% | 6.91% | 41.47 | 33.39 | 37.21 |
| 10. | 2021. 11. 30. | -6.21% | -0.83% | 51.87 | 3.88 | 14.18 |
| 11. | 2021. 12. 31. | 12.89% | 4.36% | 141.50 | 10.40 | 38.36 |
| 12. | 2022. 1. 31. | 3.04% | -5.26% | 4.19 | 40.89 | -13.09 |
| 13. | 2022. 2. 28. | 2.02% | -3.14% | 1.05 | 18.25 | -4.37 |
| 14. | 2022. 3. 31. | 0.32% | 3.58% | 0.45 | 5.96 | -1.64 |
| 15. | 2022. 4. 30. | 4.21% | -8.80% | 10.35 | 98.64 | -31.95 |
| 16. | 2022. 5. 31. | -1.90% | 0.01% | 8.39 | 1.28 | 3.28 |
| 17. | 2022. 6. 30. | -0.05% | -8.39% | 1.08 | 90.79 | 9.91 |
| 18. | 2022. 7. 31. | 2.00% | 9.11% | 1.02 | 63.61 | 8.05 |
| 19. | 2022. 8. 31. | -3.83% | -4.24% | 23.30 | 28.95 | 25.97 |
| 20. | 2022. 9. 30. | -8.51% | -9.34% | 90.26 | 109.74 | 99.52 |
| 21. | 2022. 10. 31. | 6.84% | 7.99% | 34.15 | 46.93 | 40.03 |
| 22. | 2022. 11. 30. | 7.02% | 5.38% | 36.30 | 17.97 | 25.54 |
| 23. | 2022. 12. 31. | 0.00% | -5.90% | 0.99 | 49.47 | 6.98 |
| 24. | 2023. 1. 31. | -3.60% | 6.18% | 21.10 | 25.39 | -23.15 |
| 25. | 2023. 2. 28. | -2.95% | -2.61% | 15.56 | 14.04 | 14.78 |
| 26. | 2023. 3. 31. | 5.01% | 3.51% | 16.12 | 5.61 | 9.51 |
| 27. | 2023. 4. 30. | 3.42% | 1.46% | 5.88 | 0.11 | 0.80 |
| 28. | 2023. 5. 31. | -7.00% | 0.25% | 63.88 | 0.79 | 7.10 |
| 29. | 2023. 6. 30. | 1.71% | 4.71% | 0.51 | 12.80 | 2.56 |
| 30. | 2023. 7. 31. | 2.84% | 4.85% | 3.41 | 13.76 | 6.85 |
| 31. | 2023. 8. 31. | -3.39% | -1.77% | 19.22 | 8.46 | 12.75 |
| 32. | 2023. 9. 30. | -5.67% | -4.87% | 44.34 | 36.10 | 40.01 |
| 33. | 2023. 10. 31. | 0.91% | -2.20% | 0.01 | 11.12 | 0.27 |
| 34. | 2023. 11. 30. | 4.27% | 8.92% | 10.71 | 60.56 | 25.47 |
| 35. | 2023. 12. 31. | 0.84% | 4.42% | 0.02 | 10.80 | -0.51 |
| 36. | 2024. 1. 31. | 0.95% | 1.59% | 0.00 | 0.21 | -0.02 |
| 37. | 2024. 2. 29. | 0.89% | 5.17% | 0.01 | 16.29 | -0.41 |
| 38. | 2024. 3. 31. | 2.74% | 3.10% | 3.05 | 3.86 | 3.44 |
| 39. | 2024. 4. 30. | 0.96% | -4.16% | 0.00 | 28.06 | 0.15 |
| 40. | 2024. 5. 31. | 1.88% | 4.80% | 0.78 | 13.44 | 3.24 |
| 41. | 2024. 6. 30. | 1.91% | 3.47% | 0.85 | 5.43 | 2.15 |
| 42. | 2024. 7. 31. | 4.85% | 1.13% | 14.91 | 0.00 | -0.02 |
| 43. | 2024. 8. 31. | 8.59% | 2.28% | 57.65 | 1.32 | 8.71 |
| 44. | 2024. 9. 30. | -0.17% | 2.02% | 1.36 | 0.78 | -1.03 |
| 45. | 2024. 10. 31. | -9.11% | -0.99% | 102.17 | 4.52 | 21.49 |
| 46. | 2024. 11. 30. | -1.14% | 5.73% | 4.55 | 21.10 | -9.80 |
| 47. | 2024. 12. 31. | -2.84% | -2.50% | 14.69 | 13.21 | 13.93 |
| 48. | 2025. 1. 31. | 1.96% | 2.70% | 0.93 | 2.45 | 1.51 |
| 49. | 2025. 2. 28. | 12.18% | -1.42% | 125.08 | 6.56 | -28.64 |
| 50. | 2025. 3. 31. | 1.29% | -5.75% | 0.09 | 47.48 | -2.06 |
| 51. | 2025. 4. 30. | 1.30% | -0.76% | 0.09 | 3.60 | -0.58 |
| 52. | 2025. 5. 31. | -0.62% | 6.15% | 2.60 | 25.16 | -8.09 |
| 53. | 2025. 6. 30. | -1.17% | 4.96% | 4.66 | 14.63 | -8.25 |
| 54. | 2025. 7. 31. | -4.04% | 2.17% | 25.36 | 1.06 | -5.19 |
| 55. | 2025. 8. 31. | 1.62% | 1.91% | 0.39 | 0.59 | 0.48 |
| 56. | 2025. 9. 30. | -3.13% | 3.53% | 17.01 | 5.74 | -9.88 |
| 57. | 2025. 10. 31. | 3.89% | 2.27% | 8.39 | 1.28 | 3.28 |
| 58. | 2025. 11. 30. | 6.12% | 0.13% | 26.34 | 1.01 | -5.16 |
| 59. | 2025. 12. 31. | -3.69% | -0.05% | 21.95 | 1.41 | 5.57 |
| 합계 (Σ): | 1,220.31 | 1,108.23 | 408.64 | |||
모두 보기
분산KO = Σ(RKO,t–RKO)2 ÷ (59 – 1)
= 1,220.31 ÷ (59 – 1)
= 21.04
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산KO, S&P 500 = Σ(RKO,t–RKO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 408.64 ÷ (59 – 1)
= 7.05
체계적인 위험 추정 (β)
| 분산KO | 21.04 |
| 분산S&P 500 | 19.11 |
| 공분산KO, S&P 500 | 7.05 |
| 상관 계수KO, S&P 5001 | 0.35 |
| βKO2 | 0.37 |
| αKO3 | 0.57% |
계산
1 상관 계수KO, S&P 500
= 공분산KO, S&P 500 ÷ (표준 편차KO × 표준 편차S&P 500)
= 7.05 ÷ (4.59% × 4.37%)
= 0.35
2 βKO
= 공분산KO, S&P 500 ÷ 분산S&P 500
= 7.05 ÷ 19.11
= 0.37
3 αKO
= 평균의KO – βKO × 평균의S&P 500
= 0.99% – 0.37 × 1.14%
= 0.57%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.84% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Coca-Cola | βKO | 0.37 |
| Coca-Cola 보통주 예상 수익률3 | E(RKO) | 9.46% |
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(RKO) = RF + βKO [E(RM) – RF]
= 4.84% + 0.37 [17.37% – 4.84%]
= 9.46%