자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 UnitedHealth Group보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
UnitedHealth Group Inc., 월별 수익률
| UnitedHealth Group Inc. (UNH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UNH,t1 | 피제수UNH,t1 | RUNH,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $272.45 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $254.96 | -6.42% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $249.38 | $1.08 | -1.76% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $292.47 | 17.28% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $610.20 | 8.10% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $505.86 | $2.10 | -16.76% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.37% | 1.16% | ||||
| 표준 편차: | 6.30% | 5.28% | ||||
| UnitedHealth Group Inc. (UNH) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값UNH,t1 | 피제수UNH,t1 | RUNH,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $272.45 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $254.96 | -6.42% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $249.38 | $1.08 | -1.76% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $292.47 | 17.28% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $304.85 | 4.23% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $294.95 | $1.25 | -2.84% | 3,100.29 | 1.84% |
| 6. | 2020. 7. 31. | $302.78 | 2.65% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $312.55 | 3.23% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $311.77 | $1.25 | 0.15% | 3,363.00 | -3.92% |
| 9. | 2020. 10. 31. | $305.14 | -2.13% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $336.34 | 10.22% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $350.68 | $1.25 | 4.64% | 3,756.07 | 3.71% |
| 12. | 2021. 1. 31. | $333.58 | -4.88% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $332.22 | -0.41% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $372.07 | $1.25 | 12.37% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $398.80 | 7.18% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $411.92 | 3.29% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $400.44 | $1.45 | -2.43% | 4,297.50 | 2.22% |
| 18. | 2021. 7. 31. | $412.22 | 2.94% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $416.27 | 0.98% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $390.74 | $1.45 | -5.78% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $460.47 | 17.85% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $444.22 | -3.53% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $502.14 | $1.45 | 13.36% | 4,766.18 | 4.36% |
| 24. | 2022. 1. 31. | $472.57 | -5.89% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $475.87 | 0.70% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $509.97 | $1.45 | 7.47% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $508.55 | -0.28% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $496.78 | -2.31% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $513.63 | $1.65 | 3.72% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $542.34 | 5.59% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $519.33 | -4.24% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $505.04 | $1.65 | -2.43% | 3,585.62 | -9.34% |
| 33. | 2022. 10. 31. | $555.15 | 9.92% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $547.76 | -1.33% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $530.18 | $1.65 | -2.91% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $499.19 | -5.85% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $475.94 | -4.66% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $472.59 | $1.65 | -0.36% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $492.09 | 4.13% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $487.24 | -0.99% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $480.64 | $1.88 | -0.97% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $506.37 | 5.35% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $476.58 | -5.88% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $504.19 | $1.88 | 6.19% | 4,288.05 | -4.87% |
| 45. | 2023. 10. 31. | $535.56 | 6.22% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $552.97 | 3.25% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $526.47 | $1.88 | -4.45% | 4,769.83 | 4.42% |
| 48. | 2024. 1. 31. | $511.74 | -2.80% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $493.60 | -3.54% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $494.70 | $1.88 | 0.60% | 5,254.35 | 3.10% |
| 51. | 2024. 4. 30. | $483.70 | -2.22% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $495.37 | 2.41% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $509.26 | $2.10 | 3.23% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $576.16 | 13.14% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $590.20 | 2.44% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $584.68 | $2.10 | -0.58% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $564.50 | -3.45% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $610.20 | 8.10% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $505.86 | $2.10 | -16.76% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.37% | 1.16% | ||||
| 표준 편차: | 6.30% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 UNH의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
UnitedHealth Group Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RUNH,t | RS&P 500,t | (RUNH,t–RUNH)2 | (RS&P 500,t–RS&P 500)2 | (RUNH,t–RUNH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.42% | -8.41% | 60.66 | 91.63 | 74.55 |
| 2. | 2020. 3. 31. | -1.76% | -12.51% | 9.82 | 186.96 | 42.85 |
| 3. | 2020. 4. 30. | 17.28% | 12.68% | 253.13 | 132.78 | 183.33 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 8.10% | 5.73% | 45.25 | 20.87 | 30.73 |
| 59. | 2024. 12. 31. | -16.76% | -2.50% | 328.48 | 13.40 | 66.34 |
| 합계 (Σ): | 2,303.00 | 1,618.62 | 1,005.26 | |||
| t | 날짜 | RUNH,t | RS&P 500,t | (RUNH,t–RUNH)2 | (RS&P 500,t–RS&P 500)2 | (RUNH,t–RUNH)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.42% | -8.41% | 60.66 | 91.63 | 74.55 |
| 2. | 2020. 3. 31. | -1.76% | -12.51% | 9.82 | 186.96 | 42.85 |
| 3. | 2020. 4. 30. | 17.28% | 12.68% | 253.13 | 132.78 | 183.33 |
| 4. | 2020. 5. 31. | 4.23% | 4.53% | 8.20 | 11.34 | 9.64 |
| 5. | 2020. 6. 30. | -2.84% | 1.84% | 17.69 | 0.46 | -2.85 |
| 6. | 2020. 7. 31. | 2.65% | 5.51% | 1.65 | 18.91 | 5.59 |
| 7. | 2020. 8. 31. | 3.23% | 7.01% | 3.45 | 34.17 | 10.86 |
| 8. | 2020. 9. 30. | 0.15% | -3.92% | 1.48 | 25.85 | 6.19 |
| 9. | 2020. 10. 31. | -2.13% | -2.77% | 12.22 | 15.43 | 13.73 |
| 10. | 2020. 11. 30. | 10.22% | 10.75% | 78.43 | 92.03 | 84.96 |
| 11. | 2020. 12. 31. | 4.64% | 3.71% | 10.67 | 6.51 | 8.33 |
| 12. | 2021. 1. 31. | -4.88% | -1.11% | 39.00 | 5.18 | 14.21 |
| 13. | 2021. 2. 28. | -0.41% | 2.61% | 3.16 | 2.10 | -2.57 |
| 14. | 2021. 3. 31. | 12.37% | 4.24% | 121.05 | 9.50 | 33.92 |
| 15. | 2021. 4. 30. | 7.18% | 5.24% | 33.82 | 16.66 | 23.73 |
| 16. | 2021. 5. 31. | 3.29% | 0.55% | 3.69 | 0.38 | -1.18 |
| 17. | 2021. 6. 30. | -2.43% | 2.22% | 14.47 | 1.12 | -4.03 |
| 18. | 2021. 7. 31. | 2.94% | 2.27% | 2.47 | 1.24 | 1.75 |
| 19. | 2021. 8. 31. | 0.98% | 2.90% | 0.15 | 3.02 | -0.67 |
| 20. | 2021. 9. 30. | -5.78% | -4.76% | 51.17 | 35.02 | 42.34 |
| 21. | 2021. 10. 31. | 17.85% | 6.91% | 271.48 | 33.10 | 94.79 |
| 22. | 2021. 11. 30. | -3.53% | -0.83% | 23.99 | 3.98 | 9.77 |
| 23. | 2021. 12. 31. | 13.36% | 4.36% | 143.91 | 10.24 | 38.39 |
| 24. | 2022. 1. 31. | -5.89% | -5.26% | 52.67 | 41.21 | 46.59 |
| 25. | 2022. 2. 28. | 0.70% | -3.14% | 0.45 | 18.47 | 2.88 |
| 26. | 2022. 3. 31. | 7.47% | 3.58% | 37.23 | 5.84 | 14.74 |
| 27. | 2022. 4. 30. | -0.28% | -8.80% | 2.71 | 99.14 | 16.40 |
| 28. | 2022. 5. 31. | -2.31% | 0.01% | 13.57 | 1.34 | 4.26 |
| 29. | 2022. 6. 30. | 3.72% | -8.39% | 5.55 | 91.26 | -22.50 |
| 30. | 2022. 7. 31. | 5.59% | 9.11% | 17.82 | 63.21 | 33.56 |
| 31. | 2022. 8. 31. | -4.24% | -4.24% | 31.49 | 29.22 | 30.33 |
| 32. | 2022. 9. 30. | -2.43% | -9.34% | 14.46 | 110.27 | 39.93 |
| 33. | 2022. 10. 31. | 9.92% | 7.99% | 73.16 | 46.58 | 58.38 |
| 34. | 2022. 11. 30. | -1.33% | 5.38% | 7.29 | 17.76 | -11.38 |
| 35. | 2022. 12. 31. | -2.91% | -5.90% | 18.29 | 49.82 | 30.19 |
| 36. | 2023. 1. 31. | -5.85% | 6.18% | 52.04 | 25.14 | -36.17 |
| 37. | 2023. 2. 28. | -4.66% | -2.61% | 36.32 | 14.23 | 22.73 |
| 38. | 2023. 3. 31. | -0.36% | 3.51% | 2.98 | 5.49 | -4.05 |
| 39. | 2023. 4. 30. | 4.13% | 1.46% | 7.60 | 0.09 | 0.84 |
| 40. | 2023. 5. 31. | -0.99% | 0.25% | 5.54 | 0.83 | 2.15 |
| 41. | 2023. 6. 30. | -0.97% | 4.71% | 5.46 | 12.62 | -8.30 |
| 42. | 2023. 7. 31. | 5.35% | 4.85% | 15.88 | 13.58 | 14.68 |
| 43. | 2023. 8. 31. | -5.88% | -1.77% | 52.59 | 8.60 | 21.27 |
| 44. | 2023. 9. 30. | 6.19% | -4.87% | 23.22 | 36.40 | -29.07 |
| 45. | 2023. 10. 31. | 6.22% | -2.20% | 23.55 | 11.28 | -16.30 |
| 46. | 2023. 11. 30. | 3.25% | 8.92% | 3.54 | 60.17 | 14.60 |
| 47. | 2023. 12. 31. | -4.45% | 4.42% | 33.89 | 10.64 | -18.99 |
| 48. | 2024. 1. 31. | -2.80% | 1.59% | 17.36 | 0.18 | -1.78 |
| 49. | 2024. 2. 29. | -3.54% | 5.17% | 24.14 | 16.09 | -19.71 |
| 50. | 2024. 3. 31. | 0.60% | 3.10% | 0.59 | 3.77 | -1.48 |
| 51. | 2024. 4. 30. | -2.22% | -4.16% | 12.91 | 28.33 | 19.12 |
| 52. | 2024. 5. 31. | 2.41% | 4.80% | 1.09 | 13.26 | 3.80 |
| 53. | 2024. 6. 30. | 3.23% | 3.47% | 3.46 | 5.32 | 4.29 |
| 54. | 2024. 7. 31. | 13.14% | 1.13% | 138.48 | 0.00 | -0.34 |
| 55. | 2024. 8. 31. | 2.44% | 2.28% | 1.14 | 1.26 | 1.20 |
| 56. | 2024. 9. 30. | -0.58% | 2.02% | 3.80 | 0.74 | -1.67 |
| 57. | 2024. 10. 31. | -3.45% | -0.99% | 23.24 | 4.63 | 10.37 |
| 58. | 2024. 11. 30. | 8.10% | 5.73% | 45.25 | 20.87 | 30.73 |
| 59. | 2024. 12. 31. | -16.76% | -2.50% | 328.48 | 13.40 | 66.34 |
| 합계 (Σ): | 2,303.00 | 1,618.62 | 1,005.26 | |||
모두 보기
분산UNH = Σ(RUNH,t–RUNH)2 ÷ (59 – 1)
= 2,303.00 ÷ (59 – 1)
= 39.71
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산UNH, S&P 500 = Σ(RUNH,t–RUNH)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,005.26 ÷ (59 – 1)
= 17.33
체계적인 위험 추정 (β)
| 분산UNH | 39.71 |
| 분산S&P 500 | 27.91 |
| 공분산UNH, S&P 500 | 17.33 |
| 상관 계수UNH, S&P 5001 | 0.52 |
| βUNH2 | 0.62 |
| αUNH3 | 0.65% |
계산
1 상관 계수UNH, S&P 500
= 공분산UNH, S&P 500 ÷ (표준 편차UNH × 표준 편차S&P 500)
= 17.33 ÷ (6.30% × 5.28%)
= 0.52
2 βUNH
= 공분산UNH, S&P 500 ÷ 분산S&P 500
= 17.33 ÷ 27.91
= 0.62
3 αUNH
= 평균의UNH – βUNH × 평균의S&P 500
= 1.37% – 0.62 × 1.16%
= 0.65%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.53% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험UnitedHealth Group | βUNH | 0.62 |
| UnitedHealth Group 보통주에 대한 예상 수익률3 | E(RUNH) | 10.96% |
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(RUNH) = RF + βUNH [E(RM) – RF]
= 4.53% + 0.62 [14.88% – 4.53%]
= 10.96%