자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Humana의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
Humana Inc., 월별 수익률
| Humana Inc. (HUM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HUM,t1 | 피제수HUM,t1 | RHUM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $308.99 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $285.04 | -7.75% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $266.00 | $0.55 | -6.49% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $255.41 | -3.98% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $484.86 | -7.41% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $457.81 | $0.885 | -5.40% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.02% | 1.11% | ||||
| 표준 편차: | 7.81% | 5.31% | ||||
| Humana Inc. (HUM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HUM,t1 | 피제수HUM,t1 | RHUM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $308.99 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $285.04 | -7.75% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $266.00 | $0.55 | -6.49% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $255.41 | -3.98% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $244.86 | -4.13% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $265.30 | $0.55 | 8.57% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $296.75 | 11.85% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $283.21 | -4.56% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $255.67 | $0.55 | -9.53% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $294.20 | 15.07% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $341.23 | 15.99% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $366.52 | $0.55 | 7.57% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $336.24 | -8.26% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $319.68 | -4.93% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $314.02 | $0.625 | -1.58% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $381.82 | 21.59% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $410.65 | 7.55% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $387.75 | $0.625 | -5.42% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $392.45 | 1.21% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $415.17 | 5.79% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $413.89 | $0.625 | -0.16% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $399.28 | -3.53% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $400.52 | 0.31% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $410.27 | $0.625 | 2.59% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $383.11 | -6.62% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $379.65 | -0.90% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $419.25 | $0.70 | 10.62% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $445.24 | 6.20% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $437.70 | -1.69% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $442.72 | $0.70 | 1.31% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $425.86 | -3.81% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $405.42 | -4.80% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $389.15 | $0.70 | -3.84% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $463.16 | 19.02% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $419.71 | -9.38% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $463.86 | $0.70 | 10.69% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $392.50 | -15.38% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $434.32 | 10.65% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $435.17 | $0.7875 | 0.38% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $444.56 | 2.16% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $454.23 | 2.18% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $468.07 | $0.7875 | 3.22% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $482.00 | 2.98% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $481.78 | -0.05% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $485.19 | $0.7875 | 0.87% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $558.08 | 15.02% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $549.90 | -1.47% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $512.19 | $0.7875 | -6.71% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $511.70 | -0.10% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $495.02 | -3.26% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $485.46 | $0.885 | -1.75% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $530.49 | 9.28% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $501.87 | -5.40% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $447.13 | $0.885 | -10.73% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $456.83 | 2.17% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $461.63 | 1.05% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $486.52 | $0.885 | 5.58% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $523.69 | 7.64% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $484.86 | -7.41% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $457.81 | $0.885 | -5.40% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.02% | 1.11% | ||||
| 표준 편차: | 7.81% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 HUM의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Humana Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RHUM,t | RS&P 500,t | (RHUM,t–RHUM)2 | (RS&P 500,t–RS&P 500)2 | (RHUM,t–RHUM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -7.75% | 2.97% | 76.90 | 3.49 | -16.37 |
| 2. | 2019. 3. 31. | -6.49% | 1.79% | 56.33 | 0.47 | -5.15 |
| 3. | 2019. 4. 30. | -3.98% | 3.93% | 25.00 | 7.98 | -14.13 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -7.41% | 8.92% | 71.12 | 61.03 | -65.88 |
| 59. | 2023. 12. 31. | -5.40% | 4.42% | 41.15 | 11.00 | -21.28 |
| 합계 (Σ): | 3,534.00 | 1,634.30 | 792.91 | |||
| t | 날짜 | RHUM,t | RS&P 500,t | (RHUM,t–RHUM)2 | (RS&P 500,t–RS&P 500)2 | (RHUM,t–RHUM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -7.75% | 2.97% | 76.90 | 3.49 | -16.37 |
| 2. | 2019. 3. 31. | -6.49% | 1.79% | 56.33 | 0.47 | -5.15 |
| 3. | 2019. 4. 30. | -3.98% | 3.93% | 25.00 | 7.98 | -14.13 |
| 4. | 2019. 5. 31. | -4.13% | -6.58% | 26.51 | 59.04 | 39.56 |
| 5. | 2019. 6. 30. | 8.57% | 6.89% | 57.06 | 33.49 | 43.72 |
| 6. | 2019. 7. 31. | 11.85% | 1.31% | 117.42 | 0.04 | 2.24 |
| 7. | 2019. 8. 31. | -4.56% | -1.81% | 31.15 | 8.50 | 16.27 |
| 8. | 2019. 9. 30. | -9.53% | 1.72% | 111.27 | 0.37 | -6.46 |
| 9. | 2019. 10. 31. | 15.07% | 2.04% | 197.45 | 0.88 | 13.17 |
| 10. | 2019. 11. 30. | 15.99% | 3.40% | 224.02 | 5.28 | 34.41 |
| 11. | 2019. 12. 31. | 7.57% | 2.86% | 42.96 | 3.07 | 11.49 |
| 12. | 2020. 1. 31. | -8.26% | -0.16% | 86.12 | 1.61 | 11.77 |
| 13. | 2020. 2. 29. | -4.93% | -8.41% | 35.32 | 90.57 | 56.56 |
| 14. | 2020. 3. 31. | -1.58% | -12.51% | 6.73 | 185.44 | 35.32 |
| 15. | 2020. 4. 30. | 21.59% | 12.68% | 423.23 | 134.06 | 238.20 |
| 16. | 2020. 5. 31. | 7.55% | 4.53% | 42.67 | 11.71 | 22.36 |
| 17. | 2020. 6. 30. | -5.42% | 1.84% | 41.51 | 0.54 | -4.72 |
| 18. | 2020. 7. 31. | 1.21% | 5.51% | 0.04 | 19.40 | 0.85 |
| 19. | 2020. 8. 31. | 5.79% | 7.01% | 22.76 | 34.82 | 28.15 |
| 20. | 2020. 9. 30. | -0.16% | -3.92% | 1.38 | 25.29 | 5.91 |
| 21. | 2020. 10. 31. | -3.53% | -2.77% | 20.69 | 15.00 | 17.61 |
| 22. | 2020. 11. 30. | 0.31% | 10.75% | 0.50 | 93.10 | -6.83 |
| 23. | 2020. 12. 31. | 2.59% | 3.71% | 2.47 | 6.79 | 4.10 |
| 24. | 2021. 1. 31. | -6.62% | -1.11% | 58.34 | 4.93 | 16.95 |
| 25. | 2021. 2. 28. | -0.90% | 2.61% | 3.69 | 2.26 | -2.89 |
| 26. | 2021. 3. 31. | 10.62% | 4.24% | 92.10 | 9.85 | 30.11 |
| 27. | 2021. 4. 30. | 6.20% | 5.24% | 26.84 | 17.11 | 21.43 |
| 28. | 2021. 5. 31. | -1.69% | 0.55% | 7.35 | 0.31 | 1.51 |
| 29. | 2021. 6. 30. | 1.31% | 2.22% | 0.08 | 1.24 | 0.32 |
| 30. | 2021. 7. 31. | -3.81% | 2.27% | 23.30 | 1.37 | -5.64 |
| 31. | 2021. 8. 31. | -4.80% | 2.90% | 33.85 | 3.22 | -10.43 |
| 32. | 2021. 9. 30. | -3.84% | -4.76% | 23.61 | 34.37 | 28.49 |
| 33. | 2021. 10. 31. | 19.02% | 6.91% | 324.00 | 33.74 | 104.55 |
| 34. | 2021. 11. 30. | -9.38% | -0.83% | 108.15 | 3.76 | 20.17 |
| 35. | 2021. 12. 31. | 10.69% | 4.36% | 93.46 | 10.60 | 31.47 |
| 36. | 2022. 1. 31. | -15.38% | -5.26% | 269.04 | 40.51 | 104.39 |
| 37. | 2022. 2. 28. | 10.65% | -3.14% | 92.86 | 17.99 | -40.88 |
| 38. | 2022. 3. 31. | 0.38% | 3.58% | 0.41 | 6.11 | -1.59 |
| 39. | 2022. 4. 30. | 2.16% | -8.80% | 1.30 | 98.04 | -11.28 |
| 40. | 2022. 5. 31. | 2.18% | 0.01% | 1.34 | 1.21 | -1.27 |
| 41. | 2022. 6. 30. | 3.22% | -8.39% | 4.85 | 90.21 | -20.91 |
| 42. | 2022. 7. 31. | 2.98% | 9.11% | 3.83 | 64.09 | 15.67 |
| 43. | 2022. 8. 31. | -0.05% | -4.24% | 1.13 | 28.62 | 5.69 |
| 44. | 2022. 9. 30. | 0.87% | -9.34% | 0.02 | 109.11 | 1.54 |
| 45. | 2022. 10. 31. | 15.02% | 7.99% | 196.13 | 47.34 | 96.36 |
| 46. | 2022. 11. 30. | -1.47% | 5.38% | 6.17 | 18.23 | -10.61 |
| 47. | 2022. 12. 31. | -6.71% | -5.90% | 59.80 | 49.04 | 54.15 |
| 48. | 2023. 1. 31. | -0.10% | 6.18% | 1.24 | 25.70 | -5.65 |
| 49. | 2023. 2. 28. | -3.26% | -2.61% | 18.30 | 13.82 | 15.90 |
| 50. | 2023. 3. 31. | -1.75% | 3.51% | 7.68 | 5.76 | -6.65 |
| 51. | 2023. 4. 30. | 9.28% | 1.46% | 68.18 | 0.13 | 2.96 |
| 52. | 2023. 5. 31. | -5.40% | 0.25% | 41.13 | 0.74 | 5.50 |
| 53. | 2023. 6. 30. | -10.73% | 4.71% | 138.04 | 13.02 | -42.39 |
| 54. | 2023. 7. 31. | 2.17% | 4.85% | 1.32 | 13.99 | 4.31 |
| 55. | 2023. 8. 31. | 1.05% | -1.77% | 0.00 | 8.28 | -0.09 |
| 56. | 2023. 9. 30. | 5.58% | -4.87% | 20.84 | 35.73 | -27.29 |
| 57. | 2023. 10. 31. | 7.64% | -2.20% | 43.85 | 10.92 | -21.88 |
| 58. | 2023. 11. 30. | -7.41% | 8.92% | 71.12 | 61.03 | -65.88 |
| 59. | 2023. 12. 31. | -5.40% | 4.42% | 41.15 | 11.00 | -21.28 |
| 합계 (Σ): | 3,534.00 | 1,634.30 | 792.91 | |||
모두 보기
분산HUM = Σ(RHUM,t–RHUM)2 ÷ (59 – 1)
= 3,534.00 ÷ (59 – 1)
= 60.93
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산HUM, S&P 500 = Σ(RHUM,t–RHUM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 792.91 ÷ (59 – 1)
= 13.67
체계적인 위험 추정 (β)
| 분산HUM | 60.93 |
| 분산S&P 500 | 28.18 |
| 공분산HUM, S&P 500 | 13.67 |
| 상관 계수HUM, S&P 5001 | 0.33 |
| βHUM2 | 0.49 |
| αHUM3 | 0.48% |
계산
1 상관 계수HUM, S&P 500
= 공분산HUM, S&P 500 ÷ (표준 편차HUM × 표준 편차S&P 500)
= 13.67 ÷ (7.81% × 5.31%)
= 0.33
2 βHUM
= 공분산HUM, S&P 500 ÷ 분산S&P 500
= 13.67 ÷ 28.18
= 0.49
3 αHUM
= 평균의HUM – βHUM × 평균의S&P 500
= 1.02% – 0.49 × 1.11%
= 0.48%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Humana | βHUM | 0.49 |
| Humana 보통주에 대한 예상 수익률3 | E(RHUM) | 9.59% |
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(RHUM) = RF + βHUM [E(RM) – RF]
= 4.60% + 0.49 [14.89% – 4.60%]
= 9.59%