자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Cigna의 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Cigna Group, 월별 수익률
| Cigna Group (CI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CI,t1 | 피제수CI,t1 | RCI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $192.38 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $182.94 | -4.91% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $177.18 | $0.04 | -3.13% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $195.78 | 10.50% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $337.80 | 7.30% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $276.14 | $1.40 | -17.84% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.06% | 1.16% | ||||
| 표준 편차: | 8.31% | 5.28% | ||||
| Cigna Group (CI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CI,t1 | 피제수CI,t1 | RCI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $192.38 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $182.94 | -4.91% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $177.18 | $0.04 | -3.13% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $195.78 | 10.50% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $197.32 | 0.79% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $187.65 | -4.90% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $172.69 | -7.97% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $177.37 | 2.71% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $169.41 | -4.49% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $166.97 | -1.44% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $209.14 | 25.26% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $208.18 | -0.46% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $217.05 | 4.26% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $209.90 | -3.29% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $241.74 | $1.00 | 15.65% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $249.01 | 3.01% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $258.85 | 3.95% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $237.07 | $1.00 | -8.03% | 4,297.50 | 2.22% |
| 18. | 2021. 7. 31. | $229.49 | -3.20% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $211.65 | -7.77% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $200.16 | $1.00 | -4.96% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $213.61 | 6.72% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $191.90 | -10.16% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $229.63 | $1.00 | 20.18% | 4,766.18 | 4.36% |
| 24. | 2022. 1. 31. | $230.46 | 0.36% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $237.78 | 3.18% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $239.61 | $1.12 | 1.24% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $246.78 | 2.99% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $268.29 | 8.72% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $263.52 | $1.12 | -1.36% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $275.36 | 4.49% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $283.45 | 2.94% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $277.47 | $1.12 | -1.71% | 3,585.62 | -9.34% |
| 33. | 2022. 10. 31. | $323.06 | 16.43% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $328.89 | 1.80% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $331.34 | $1.12 | 1.09% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $316.67 | -4.43% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $292.10 | -7.76% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $255.53 | $1.23 | -12.10% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $253.29 | -0.88% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $247.41 | -2.32% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $280.60 | $1.23 | 13.91% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $295.10 | 5.17% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $276.26 | -6.38% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $286.07 | $1.23 | 4.00% | 4,288.05 | -4.87% |
| 45. | 2023. 10. 31. | $309.20 | 8.09% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $262.88 | -14.98% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $299.45 | $1.23 | 14.38% | 4,769.83 | 4.42% |
| 48. | 2024. 1. 31. | $300.95 | 0.50% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $336.14 | 11.69% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $363.19 | $1.40 | 8.46% | 5,254.35 | 3.10% |
| 51. | 2024. 4. 30. | $357.04 | -1.69% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $344.62 | -3.48% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $330.57 | $1.40 | -3.67% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $348.67 | 5.48% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $361.81 | 3.77% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $346.44 | $1.40 | -3.86% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $314.81 | -9.13% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $337.80 | 7.30% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $276.14 | $1.40 | -17.84% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.06% | 1.16% | ||||
| 표준 편차: | 8.31% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CI의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Cigna Group, 수익률의 분산 및 공분산 계산
| t | 날짜 | RCI,t | RS&P 500,t | (RCI,t–RCI)2 | (RS&P 500,t–RS&P 500)2 | (RCI,t–RCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -4.91% | -8.41% | 35.64 | 91.63 | 57.14 |
| 2. | 2020. 3. 31. | -3.13% | -12.51% | 17.55 | 186.96 | 57.28 |
| 3. | 2020. 4. 30. | 10.50% | 12.68% | 89.02 | 132.78 | 108.72 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 7.30% | 5.73% | 38.94 | 20.87 | 28.51 |
| 59. | 2024. 12. 31. | -17.84% | -2.50% | 357.27 | 13.40 | 69.19 |
| 합계 (Σ): | 4,008.77 | 1,618.62 | 859.41 | |||
| t | 날짜 | RCI,t | RS&P 500,t | (RCI,t–RCI)2 | (RS&P 500,t–RS&P 500)2 | (RCI,t–RCI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -4.91% | -8.41% | 35.64 | 91.63 | 57.14 |
| 2. | 2020. 3. 31. | -3.13% | -12.51% | 17.55 | 186.96 | 57.28 |
| 3. | 2020. 4. 30. | 10.50% | 12.68% | 89.02 | 132.78 | 108.72 |
| 4. | 2020. 5. 31. | 0.79% | 4.53% | 0.08 | 11.34 | -0.93 |
| 5. | 2020. 6. 30. | -4.90% | 1.84% | 35.56 | 0.46 | -4.04 |
| 6. | 2020. 7. 31. | -7.97% | 5.51% | 81.63 | 18.91 | -39.29 |
| 7. | 2020. 8. 31. | 2.71% | 7.01% | 2.71 | 34.17 | 9.63 |
| 8. | 2020. 9. 30. | -4.49% | -3.92% | 30.81 | 25.85 | 28.22 |
| 9. | 2020. 10. 31. | -1.44% | -2.77% | 6.26 | 15.43 | 9.83 |
| 10. | 2020. 11. 30. | 25.26% | 10.75% | 585.32 | 92.03 | 232.09 |
| 11. | 2020. 12. 31. | -0.46% | 3.71% | 2.32 | 6.51 | -3.88 |
| 12. | 2021. 1. 31. | 4.26% | -1.11% | 10.23 | 5.18 | -7.28 |
| 13. | 2021. 2. 28. | -3.29% | 2.61% | 18.98 | 2.10 | -6.31 |
| 14. | 2021. 3. 31. | 15.65% | 4.24% | 212.66 | 9.50 | 44.95 |
| 15. | 2021. 4. 30. | 3.01% | 5.24% | 3.78 | 16.66 | 7.94 |
| 16. | 2021. 5. 31. | 3.95% | 0.55% | 8.35 | 0.38 | -1.77 |
| 17. | 2021. 6. 30. | -8.03% | 2.22% | 82.64 | 1.12 | -9.64 |
| 18. | 2021. 7. 31. | -3.20% | 2.27% | 18.15 | 1.24 | -4.74 |
| 19. | 2021. 8. 31. | -7.77% | 2.90% | 78.08 | 3.02 | -15.36 |
| 20. | 2021. 9. 30. | -4.96% | -4.76% | 36.23 | 35.02 | 35.62 |
| 21. | 2021. 10. 31. | 6.72% | 6.91% | 32.00 | 33.10 | 32.54 |
| 22. | 2021. 11. 30. | -10.16% | -0.83% | 126.02 | 3.98 | 22.39 |
| 23. | 2021. 12. 31. | 20.18% | 4.36% | 365.56 | 10.24 | 61.18 |
| 24. | 2022. 1. 31. | 0.36% | -5.26% | 0.49 | 41.21 | 4.50 |
| 25. | 2022. 2. 28. | 3.18% | -3.14% | 4.47 | 18.47 | -9.08 |
| 26. | 2022. 3. 31. | 1.24% | 3.58% | 0.03 | 5.84 | 0.43 |
| 27. | 2022. 4. 30. | 2.99% | -8.80% | 3.72 | 99.14 | -19.21 |
| 28. | 2022. 5. 31. | 8.72% | 0.01% | 58.58 | 1.34 | -8.85 |
| 29. | 2022. 6. 30. | -1.36% | -8.39% | 5.87 | 91.26 | 23.15 |
| 30. | 2022. 7. 31. | 4.49% | 9.11% | 11.77 | 63.21 | 27.27 |
| 31. | 2022. 8. 31. | 2.94% | -4.24% | 3.52 | 29.22 | -10.14 |
| 32. | 2022. 9. 30. | -1.71% | -9.34% | 7.71 | 110.27 | 29.16 |
| 33. | 2022. 10. 31. | 16.43% | 7.99% | 236.17 | 46.58 | 104.89 |
| 34. | 2022. 11. 30. | 1.80% | 5.38% | 0.55 | 17.76 | 3.13 |
| 35. | 2022. 12. 31. | 1.09% | -5.90% | 0.00 | 49.82 | -0.16 |
| 36. | 2023. 1. 31. | -4.43% | 6.18% | 30.14 | 25.14 | -27.53 |
| 37. | 2023. 2. 28. | -7.76% | -2.61% | 77.82 | 14.23 | 33.28 |
| 38. | 2023. 3. 31. | -12.10% | 3.51% | 173.22 | 5.49 | -30.85 |
| 39. | 2023. 4. 30. | -0.88% | 1.46% | 3.76 | 0.09 | -0.59 |
| 40. | 2023. 5. 31. | -2.32% | 0.25% | 11.45 | 0.83 | 3.09 |
| 41. | 2023. 6. 30. | 13.91% | 4.71% | 165.11 | 12.62 | 45.65 |
| 42. | 2023. 7. 31. | 5.17% | 4.85% | 16.85 | 13.58 | 15.12 |
| 43. | 2023. 8. 31. | -6.38% | -1.77% | 55.46 | 8.60 | 21.84 |
| 44. | 2023. 9. 30. | 4.00% | -4.87% | 8.61 | 36.40 | -17.70 |
| 45. | 2023. 10. 31. | 8.09% | -2.20% | 49.32 | 11.28 | -23.59 |
| 46. | 2023. 11. 30. | -14.98% | 8.92% | 257.39 | 60.17 | -124.44 |
| 47. | 2023. 12. 31. | 14.38% | 4.42% | 177.33 | 10.64 | 43.43 |
| 48. | 2024. 1. 31. | 0.50% | 1.59% | 0.32 | 0.18 | -0.24 |
| 49. | 2024. 2. 29. | 11.69% | 5.17% | 113.00 | 16.09 | 42.64 |
| 50. | 2024. 3. 31. | 8.46% | 3.10% | 54.78 | 3.77 | 14.36 |
| 51. | 2024. 4. 30. | -1.69% | -4.16% | 7.60 | 28.33 | 14.67 |
| 52. | 2024. 5. 31. | -3.48% | 4.80% | 20.62 | 13.26 | -16.53 |
| 53. | 2024. 6. 30. | -3.67% | 3.47% | 22.41 | 5.32 | -10.91 |
| 54. | 2024. 7. 31. | 5.48% | 1.13% | 19.47 | 0.00 | -0.13 |
| 55. | 2024. 8. 31. | 3.77% | 2.28% | 7.32 | 1.26 | 3.04 |
| 56. | 2024. 9. 30. | -3.86% | 2.02% | 24.24 | 0.74 | -4.23 |
| 57. | 2024. 10. 31. | -9.13% | -0.99% | 103.89 | 4.63 | 21.92 |
| 58. | 2024. 11. 30. | 7.30% | 5.73% | 38.94 | 20.87 | 28.51 |
| 59. | 2024. 12. 31. | -17.84% | -2.50% | 357.27 | 13.40 | 69.19 |
| 합계 (Σ): | 4,008.77 | 1,618.62 | 859.41 | |||
모두 보기
분산CI = Σ(RCI,t–RCI)2 ÷ (59 – 1)
= 4,008.77 ÷ (59 – 1)
= 69.12
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산CI, S&P 500 = Σ(RCI,t–RCI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 859.41 ÷ (59 – 1)
= 14.82
체계적인 위험 추정 (β)
| 분산CI | 69.12 |
| 분산S&P 500 | 27.91 |
| 공분산CI, S&P 500 | 14.82 |
| 상관 계수CI, S&P 5001 | 0.34 |
| βCI2 | 0.53 |
| αCI3 | 0.45% |
계산
1 상관 계수CI, S&P 500
= 공분산CI, S&P 500 ÷ (표준 편차CI × 표준 편차S&P 500)
= 14.82 ÷ (8.31% × 5.28%)
= 0.34
2 βCI
= 공분산CI, S&P 500 ÷ 분산S&P 500
= 14.82 ÷ 27.91
= 0.53
3 αCI
= 평균의CI – βCI × 평균의S&P 500
= 1.06% – 0.53 × 1.16%
= 0.45%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.88% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.90% |
| 보통주의 체계적 위험Cigna | βCI | 0.53 |
| Cigna 보통주에 대한 예상 수익률3 | E(RCI) | 10.20% |
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(RCI) = RF + βCI [E(RM) – RF]
= 4.88% + 0.53 [14.90% – 4.88%]
= 10.20%