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 |
| 2020. 1. 31. | $58.40 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $53.49 | -8.41% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $44.25 | $0.41 | -16.51% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $45.89 | 3.71% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $64.08 | $0.485 | -1.14% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $62.26 | -2.84% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.52% | 1.16% | ||||
| 표준 편차: | 5.42% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $58.40 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $53.49 | -8.41% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $44.25 | $0.41 | -16.51% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $45.89 | 3.71% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $46.68 | 1.72% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $44.68 | $0.41 | -3.41% | 3,100.29 | 1.84% |
| 6. | 2020. 7. 31. | $47.24 | 5.73% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $49.53 | 4.85% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $49.37 | $0.41 | 0.50% | 3,363.00 | -3.92% |
| 9. | 2020. 10. 31. | $48.06 | -2.65% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $51.60 | $0.41 | 8.22% | 3,621.63 | 10.75% |
| 11. | 2020. 12. 31. | $54.84 | 6.28% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $48.15 | -12.20% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $48.99 | 1.74% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $52.71 | $0.42 | 8.45% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $53.98 | 2.41% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $55.29 | 2.43% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $54.11 | $0.42 | -1.37% | 4,297.50 | 2.22% |
| 18. | 2021. 7. 31. | $57.03 | 5.40% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $56.31 | -1.26% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $52.47 | $0.42 | -6.07% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $56.37 | 7.43% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $52.45 | $0.42 | -6.21% | 4,567.00 | -0.83% |
| 23. | 2021. 12. 31. | $59.21 | 12.89% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $61.01 | 3.04% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $62.24 | 2.02% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $62.00 | $0.44 | 0.32% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $64.61 | 4.21% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $63.38 | -1.90% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $62.91 | $0.44 | -0.05% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $64.17 | 2.00% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $61.71 | -3.83% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $56.02 | $0.44 | -8.51% | 3,585.62 | -9.34% |
| 33. | 2022. 10. 31. | $59.85 | 6.84% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $63.61 | $0.44 | 7.02% | 4,080.11 | 5.38% |
| 35. | 2022. 12. 31. | $63.61 | 0.00% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $61.32 | -3.60% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $59.51 | -2.95% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $62.03 | $0.46 | 5.01% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $64.15 | 3.42% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $59.66 | -7.00% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $60.22 | $0.46 | 1.71% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $61.93 | 2.84% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $59.83 | -3.39% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $55.98 | $0.46 | -5.67% | 4,288.05 | -4.87% |
| 45. | 2023. 10. 31. | $56.49 | 0.91% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $58.44 | $0.46 | 4.27% | 4,567.80 | 8.92% |
| 47. | 2023. 12. 31. | $58.93 | 0.84% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $59.49 | 0.95% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $60.02 | 0.89% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $61.18 | $0.485 | 2.74% | 5,254.35 | 3.10% |
| 51. | 2024. 4. 30. | $61.77 | 0.96% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $62.93 | 1.88% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $63.65 | $0.485 | 1.91% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $66.74 | 4.85% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $72.47 | 8.59% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $71.86 | $0.485 | -0.17% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $65.31 | -9.11% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $64.08 | $0.485 | -1.14% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $62.26 | -2.84% | 5,881.63 | -2.50% | |
| 평균의 (R): | 0.52% | 1.16% | ||||
| 표준 편차: | 5.42% | 5.28% | ||||
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. | 2020. 2. 29. | -8.41% | -8.41% | 79.71 | 91.63 | 85.46 |
| 2. | 2020. 3. 31. | -16.51% | -12.51% | 289.96 | 186.96 | 232.83 |
| 3. | 2020. 4. 30. | 3.71% | 12.68% | 10.15 | 132.78 | 36.71 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | -1.14% | 5.73% | 2.76 | 20.87 | -7.59 |
| 59. | 2024. 12. 31. | -2.84% | -2.50% | 11.29 | 13.40 | 12.30 |
| 합계 (Σ): | 1,701.15 | 1,618.62 | 998.51 | |||
| 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. | 2020. 2. 29. | -8.41% | -8.41% | 79.71 | 91.63 | 85.46 |
| 2. | 2020. 3. 31. | -16.51% | -12.51% | 289.96 | 186.96 | 232.83 |
| 3. | 2020. 4. 30. | 3.71% | 12.68% | 10.15 | 132.78 | 36.71 |
| 4. | 2020. 5. 31. | 1.72% | 4.53% | 1.44 | 11.34 | 4.04 |
| 5. | 2020. 6. 30. | -3.41% | 1.84% | 15.42 | 0.46 | -2.66 |
| 6. | 2020. 7. 31. | 5.73% | 5.51% | 27.14 | 18.91 | 22.65 |
| 7. | 2020. 8. 31. | 4.85% | 7.01% | 18.72 | 34.17 | 25.29 |
| 8. | 2020. 9. 30. | 0.50% | -3.92% | 0.00 | 25.85 | 0.08 |
| 9. | 2020. 10. 31. | -2.65% | -2.77% | 10.07 | 15.43 | 12.47 |
| 10. | 2020. 11. 30. | 8.22% | 10.75% | 59.27 | 92.03 | 73.85 |
| 11. | 2020. 12. 31. | 6.28% | 3.71% | 33.16 | 6.51 | 14.69 |
| 12. | 2021. 1. 31. | -12.20% | -1.11% | 161.79 | 5.18 | 28.94 |
| 13. | 2021. 2. 28. | 1.74% | 2.61% | 1.50 | 2.10 | 1.77 |
| 14. | 2021. 3. 31. | 8.45% | 4.24% | 62.89 | 9.50 | 24.45 |
| 15. | 2021. 4. 30. | 2.41% | 5.24% | 3.57 | 16.66 | 7.71 |
| 16. | 2021. 5. 31. | 2.43% | 0.55% | 3.63 | 0.38 | -1.17 |
| 17. | 2021. 6. 30. | -1.37% | 2.22% | 3.59 | 1.12 | -2.01 |
| 18. | 2021. 7. 31. | 5.40% | 2.27% | 23.77 | 1.24 | 5.43 |
| 19. | 2021. 8. 31. | -1.26% | 2.90% | 3.18 | 3.02 | -3.10 |
| 20. | 2021. 9. 30. | -6.07% | -4.76% | 43.48 | 35.02 | 39.02 |
| 21. | 2021. 10. 31. | 7.43% | 6.91% | 47.78 | 33.10 | 39.77 |
| 22. | 2021. 11. 30. | -6.21% | -0.83% | 45.29 | 3.98 | 13.42 |
| 23. | 2021. 12. 31. | 12.89% | 4.36% | 152.97 | 10.24 | 39.58 |
| 24. | 2022. 1. 31. | 3.04% | -5.26% | 6.35 | 41.21 | -16.17 |
| 25. | 2022. 2. 28. | 2.02% | -3.14% | 2.24 | 18.47 | -6.43 |
| 26. | 2022. 3. 31. | 0.32% | 3.58% | 0.04 | 5.84 | -0.48 |
| 27. | 2022. 4. 30. | 4.21% | -8.80% | 13.61 | 99.14 | -36.73 |
| 28. | 2022. 5. 31. | -1.90% | 0.01% | 5.88 | 1.34 | 2.80 |
| 29. | 2022. 6. 30. | -0.05% | -8.39% | 0.32 | 91.26 | 5.42 |
| 30. | 2022. 7. 31. | 2.00% | 9.11% | 2.20 | 63.21 | 11.79 |
| 31. | 2022. 8. 31. | -3.83% | -4.24% | 18.96 | 29.22 | 23.53 |
| 32. | 2022. 9. 30. | -8.51% | -9.34% | 81.51 | 110.27 | 94.80 |
| 33. | 2022. 10. 31. | 6.84% | 7.99% | 39.90 | 46.58 | 43.11 |
| 34. | 2022. 11. 30. | 7.02% | 5.38% | 42.21 | 17.76 | 27.38 |
| 35. | 2022. 12. 31. | 0.00% | -5.90% | 0.27 | 49.82 | 3.67 |
| 36. | 2023. 1. 31. | -3.60% | 6.18% | 16.98 | 25.14 | -20.66 |
| 37. | 2023. 2. 28. | -2.95% | -2.61% | 12.06 | 14.23 | 13.10 |
| 38. | 2023. 3. 31. | 5.01% | 3.51% | 20.13 | 5.49 | 10.52 |
| 39. | 2023. 4. 30. | 3.42% | 1.46% | 8.39 | 0.09 | 0.88 |
| 40. | 2023. 5. 31. | -7.00% | 0.25% | 56.55 | 0.83 | 6.87 |
| 41. | 2023. 6. 30. | 1.71% | 4.71% | 1.41 | 12.62 | 4.22 |
| 42. | 2023. 7. 31. | 2.84% | 4.85% | 5.38 | 13.58 | 8.55 |
| 43. | 2023. 8. 31. | -3.39% | -1.77% | 15.30 | 8.60 | 11.47 |
| 44. | 2023. 9. 30. | -5.67% | -4.87% | 38.27 | 36.40 | 37.32 |
| 45. | 2023. 10. 31. | 0.91% | -2.20% | 0.15 | 11.28 | -1.31 |
| 46. | 2023. 11. 30. | 4.27% | 8.92% | 14.03 | 60.17 | 29.05 |
| 47. | 2023. 12. 31. | 0.84% | 4.42% | 0.10 | 10.64 | 1.04 |
| 48. | 2024. 1. 31. | 0.95% | 1.59% | 0.18 | 0.18 | 0.18 |
| 49. | 2024. 2. 29. | 0.89% | 5.17% | 0.14 | 16.09 | 1.49 |
| 50. | 2024. 3. 31. | 2.74% | 3.10% | 4.93 | 3.77 | 4.31 |
| 51. | 2024. 4. 30. | 0.96% | -4.16% | 0.20 | 28.33 | -2.36 |
| 52. | 2024. 5. 31. | 1.88% | 4.80% | 1.84 | 13.26 | 4.94 |
| 53. | 2024. 6. 30. | 1.91% | 3.47% | 1.94 | 5.32 | 3.21 |
| 54. | 2024. 7. 31. | 4.85% | 1.13% | 18.79 | 0.00 | -0.13 |
| 55. | 2024. 8. 31. | 8.59% | 2.28% | 65.05 | 1.26 | 9.05 |
| 56. | 2024. 9. 30. | -0.17% | 2.02% | 0.48 | 0.74 | -0.59 |
| 57. | 2024. 10. 31. | -9.11% | -0.99% | 92.84 | 4.63 | 20.73 |
| 58. | 2024. 11. 30. | -1.14% | 5.73% | 2.76 | 20.87 | -7.59 |
| 59. | 2024. 12. 31. | -2.84% | -2.50% | 11.29 | 13.40 | 12.30 |
| 합계 (Σ): | 1,701.15 | 1,618.62 | 998.51 | |||
모두 보기
분산KO = Σ(RKO,t–RKO)2 ÷ (59 – 1)
= 1,701.15 ÷ (59 – 1)
= 29.33
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산KO, S&P 500 = Σ(RKO,t–RKO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 998.51 ÷ (59 – 1)
= 17.22
체계적인 위험 추정 (β)
| 분산KO | 29.33 |
| 분산S&P 500 | 27.91 |
| 공분산KO, S&P 500 | 17.22 |
| 상관 계수KO, S&P 5001 | 0.60 |
| βKO2 | 0.62 |
| αKO3 | -0.20% |
계산
1 상관 계수KO, S&P 500
= 공분산KO, S&P 500 ÷ (표준 편차KO × 표준 편차S&P 500)
= 17.22 ÷ (5.42% × 5.28%)
= 0.60
2 βKO
= 공분산KO, S&P 500 ÷ 분산S&P 500
= 17.22 ÷ 27.91
= 0.62
3 αKO
= 평균의KO – βKO × 평균의S&P 500
= 0.52% – 0.62 × 1.16%
= -0.20%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.87% |
| 보통주의 체계적 위험Coca-Cola | βKO | 0.62 |
| Coca-Cola 보통주 예상 수익률3 | E(RKO) | 10.92% |
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]
= 4.56% + 0.62 [14.87% – 4.56%]
= 10.92%