자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 HCA보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
HCA Healthcare Inc., 월별 수익률
| HCA Healthcare Inc. (HCA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HCA,t1 | 피제수HCA,t1 | RHCA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $80.28 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $87.24 | 8.67% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $88.99 | 2.01% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $84.21 | -5.37% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $225.59 | -9.93% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $256.92 | $0.48 | 14.10% | 4,766.18 | 4.36% |
| 평균의 (R): | 2.54% | 1.36% | ||||
| 표준 편차: | 10.04% | 4.48% | ||||
| HCA Healthcare Inc. (HCA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HCA,t1 | 피제수HCA,t1 | RHCA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $80.28 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $87.24 | 8.67% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $88.99 | 2.01% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $84.21 | -5.37% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $81.91 | -2.73% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $87.20 | 6.46% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $80.34 | -7.87% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $78.66 | -2.09% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $79.59 | 1.18% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $75.65 | -4.95% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $85.00 | 12.36% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $87.84 | 3.34% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $101.16 | 15.16% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $99.25 | $0.35 | -1.54% | 2,713.83 | -3.89% |
| 14. | 2018. 3. 31. | $97.00 | -2.27% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $95.74 | -1.30% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $103.14 | $0.35 | 8.09% | 2,705.27 | 2.16% |
| 17. | 2018. 6. 30. | $102.60 | -0.52% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $124.23 | 21.08% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $134.11 | $0.35 | 8.23% | 2,901.52 | 3.03% |
| 20. | 2018. 9. 30. | $139.12 | 3.74% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $133.53 | -4.02% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $143.99 | $0.35 | 8.10% | 2,760.17 | 1.79% |
| 23. | 2018. 12. 31. | $124.45 | -13.57% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $139.43 | 12.04% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $139.04 | $0.40 | 0.01% | 2,784.49 | 2.97% |
| 26. | 2019. 3. 31. | $130.38 | -6.23% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $127.23 | -2.42% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $120.96 | $0.40 | -4.61% | 2,752.06 | -6.58% |
| 29. | 2019. 6. 30. | $135.17 | 11.75% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $133.51 | -1.23% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $120.20 | $0.40 | -9.67% | 2,926.46 | -1.81% |
| 32. | 2019. 9. 30. | $120.42 | 0.18% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $133.54 | 10.90% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $138.66 | $0.40 | 4.13% | 3,140.98 | 3.40% |
| 35. | 2019. 12. 31. | $147.81 | 6.60% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $138.80 | -6.10% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $127.01 | $0.43 | -8.18% | 2,954.22 | -8.41% |
| 38. | 2020. 3. 31. | $89.85 | -29.26% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $109.88 | 22.29% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $106.90 | -2.71% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $97.06 | -9.20% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $126.64 | 30.48% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $135.72 | 7.17% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $124.68 | -8.13% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $123.94 | -0.59% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $150.11 | 21.12% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $164.46 | 9.56% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $162.48 | -1.20% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $172.03 | 5.88% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $188.34 | $0.48 | 9.76% | 3,972.89 | 4.24% |
| 51. | 2021. 4. 30. | $201.06 | 6.75% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $214.79 | 6.83% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $206.74 | $0.48 | -3.52% | 4,297.50 | 2.22% |
| 54. | 2021. 7. 31. | $248.20 | 20.05% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $252.98 | 1.93% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $242.72 | $0.48 | -3.87% | 4,307.54 | -4.76% |
| 57. | 2021. 10. 31. | $250.46 | 3.19% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $225.59 | -9.93% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $256.92 | $0.48 | 14.10% | 4,766.18 | 4.36% |
| 평균의 (R): | 2.54% | 1.36% | ||||
| 표준 편차: | 10.04% | 4.48% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 HCA의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
HCA Healthcare Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RHCA,t | RS&P 500,t | (RHCA,t–RHCA)2 | (RS&P 500,t–RS&P 500)2 | (RHCA,t–RHCA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 8.67% | 3.72% | 37.54 | 5.58 | 14.47 |
| 2. | 2017. 3. 31. | 2.01% | -0.04% | 0.29 | 1.95 | 0.75 |
| 3. | 2017. 4. 30. | -5.37% | 0.91% | 62.64 | 0.20 | 3.55 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -9.93% | -0.83% | 155.57 | 4.80 | 27.33 |
| 59. | 2021. 12. 31. | 14.10% | 4.36% | 133.58 | 9.02 | 34.71 |
| 합계 (Σ): | 5,849.44 | 1,164.17 | 1,932.36 | |||
| t | 날짜 | RHCA,t | RS&P 500,t | (RHCA,t–RHCA)2 | (RS&P 500,t–RS&P 500)2 | (RHCA,t–RHCA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 8.67% | 3.72% | 37.54 | 5.58 | 14.47 |
| 2. | 2017. 3. 31. | 2.01% | -0.04% | 0.29 | 1.95 | 0.75 |
| 3. | 2017. 4. 30. | -5.37% | 0.91% | 62.64 | 0.20 | 3.55 |
| 4. | 2017. 5. 31. | -2.73% | 1.16% | 27.82 | 0.04 | 1.06 |
| 5. | 2017. 6. 30. | 6.46% | 0.48% | 15.33 | 0.77 | -3.43 |
| 6. | 2017. 7. 31. | -7.87% | 1.93% | 108.37 | 0.33 | -6.01 |
| 7. | 2017. 8. 31. | -2.09% | 0.05% | 21.47 | 1.70 | 6.04 |
| 8. | 2017. 9. 30. | 1.18% | 1.93% | 1.85 | 0.33 | -0.78 |
| 9. | 2017. 10. 31. | -4.95% | 2.22% | 56.15 | 0.74 | -6.45 |
| 10. | 2017. 11. 30. | 12.36% | 2.81% | 96.37 | 2.10 | 14.24 |
| 11. | 2017. 12. 31. | 3.34% | 0.98% | 0.64 | 0.14 | -0.30 |
| 12. | 2018. 1. 31. | 15.16% | 5.62% | 159.29 | 18.15 | 53.76 |
| 13. | 2018. 2. 28. | -1.54% | -3.89% | 16.69 | 27.59 | 21.46 |
| 14. | 2018. 3. 31. | -2.27% | -2.69% | 23.14 | 16.37 | 19.46 |
| 15. | 2018. 4. 30. | -1.30% | 0.27% | 14.76 | 1.18 | 4.17 |
| 16. | 2018. 5. 31. | 8.09% | 2.16% | 30.82 | 0.64 | 4.46 |
| 17. | 2018. 6. 30. | -0.52% | 0.48% | 9.40 | 0.76 | 2.68 |
| 18. | 2018. 7. 31. | 21.08% | 3.60% | 343.69 | 5.04 | 41.61 |
| 19. | 2018. 8. 31. | 8.23% | 3.03% | 32.40 | 2.78 | 9.50 |
| 20. | 2018. 9. 30. | 3.74% | 0.43% | 1.42 | 0.86 | -1.11 |
| 21. | 2018. 10. 31. | -4.02% | -6.94% | 43.05 | 68.86 | 54.45 |
| 22. | 2018. 11. 30. | 8.10% | 1.79% | 30.83 | 0.18 | 2.38 |
| 23. | 2018. 12. 31. | -13.57% | -9.18% | 259.64 | 111.00 | 169.76 |
| 24. | 2019. 1. 31. | 12.04% | 7.87% | 90.14 | 42.39 | 61.81 |
| 25. | 2019. 2. 28. | 0.01% | 2.97% | 6.43 | 2.61 | -4.10 |
| 26. | 2019. 3. 31. | -6.23% | 1.79% | 76.94 | 0.19 | -3.81 |
| 27. | 2019. 4. 30. | -2.42% | 3.93% | 24.59 | 6.62 | -12.76 |
| 28. | 2019. 5. 31. | -4.61% | -6.58% | 51.22 | 62.97 | 56.79 |
| 29. | 2019. 6. 30. | 11.75% | 6.89% | 84.73 | 30.64 | 50.95 |
| 30. | 2019. 7. 31. | -1.23% | 1.31% | 14.22 | 0.00 | 0.17 |
| 31. | 2019. 8. 31. | -9.67% | -1.81% | 149.15 | 10.03 | 38.68 |
| 32. | 2019. 9. 30. | 0.18% | 1.72% | 5.57 | 0.13 | -0.85 |
| 33. | 2019. 10. 31. | 10.90% | 2.04% | 69.76 | 0.47 | 5.72 |
| 34. | 2019. 11. 30. | 4.13% | 3.40% | 2.53 | 4.19 | 3.26 |
| 35. | 2019. 12. 31. | 6.60% | 2.86% | 16.45 | 2.25 | 6.09 |
| 36. | 2020. 1. 31. | -6.10% | -0.16% | 74.63 | 2.31 | 13.14 |
| 37. | 2020. 2. 29. | -8.18% | -8.41% | 115.08 | 95.43 | 104.80 |
| 38. | 2020. 3. 31. | -29.26% | -12.51% | 1,011.27 | 192.37 | 441.07 |
| 39. | 2020. 4. 30. | 22.29% | 12.68% | 390.05 | 128.29 | 223.70 |
| 40. | 2020. 5. 31. | -2.71% | 4.53% | 27.62 | 10.05 | -16.66 |
| 41. | 2020. 6. 30. | -9.20% | 1.84% | 138.01 | 0.23 | -5.65 |
| 42. | 2020. 7. 31. | 30.48% | 5.51% | 780.25 | 17.24 | 115.98 |
| 43. | 2020. 8. 31. | 7.17% | 7.01% | 21.41 | 31.91 | 26.14 |
| 44. | 2020. 9. 30. | -8.13% | -3.92% | 114.01 | 27.89 | 56.38 |
| 45. | 2020. 10. 31. | -0.59% | -2.77% | 9.84 | 17.01 | 12.94 |
| 46. | 2020. 11. 30. | 21.12% | 10.75% | 344.92 | 88.30 | 174.52 |
| 47. | 2020. 12. 31. | 9.56% | 3.71% | 49.23 | 5.54 | 16.52 |
| 48. | 2021. 1. 31. | -1.20% | -1.11% | 14.04 | 6.11 | 9.26 |
| 49. | 2021. 2. 28. | 5.88% | 2.61% | 11.12 | 1.57 | 4.17 |
| 50. | 2021. 3. 31. | 9.76% | 4.24% | 52.08 | 8.33 | 20.83 |
| 51. | 2021. 4. 30. | 6.75% | 5.24% | 17.73 | 15.09 | 16.36 |
| 52. | 2021. 5. 31. | 6.83% | 0.55% | 18.37 | 0.65 | -3.47 |
| 53. | 2021. 6. 30. | -3.52% | 2.22% | 36.81 | 0.75 | -5.24 |
| 54. | 2021. 7. 31. | 20.05% | 2.27% | 306.64 | 0.84 | 16.06 |
| 55. | 2021. 8. 31. | 1.93% | 2.90% | 0.38 | 2.38 | -0.95 |
| 56. | 2021. 9. 30. | -3.87% | -4.76% | 41.07 | 37.39 | 39.19 |
| 57. | 2021. 10. 31. | 3.19% | 6.91% | 0.42 | 30.87 | 3.59 |
| 58. | 2021. 11. 30. | -9.93% | -0.83% | 155.57 | 4.80 | 27.33 |
| 59. | 2021. 12. 31. | 14.10% | 4.36% | 133.58 | 9.02 | 34.71 |
| 합계 (Σ): | 5,849.44 | 1,164.17 | 1,932.36 | |||
모두 표시
분산HCA = Σ(RHCA,t–RHCA)2 ÷ (59 – 1)
= 5,849.44 ÷ (59 – 1)
= 100.85
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산HCA, S&P 500 = Σ(RHCA,t–RHCA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,932.36 ÷ (59 – 1)
= 33.32
체계적인 위험 추정 (β)
| 분산HCA | 100.85 |
| 분산S&P 500 | 20.07 |
| 공분산HCA, S&P 500 | 33.32 |
| 상관 계수HCA, S&P 5001 | 0.74 |
| βHCA2 | 1.66 |
| αHCA3 | 0.29% |
계산
1 상관 계수HCA, S&P 500
= 공분산HCA, S&P 500 ÷ (표준 편차HCA × 표준 편차S&P 500)
= 33.32 ÷ (10.04% × 4.48%)
= 0.74
2 βHCA
= 공분산HCA, S&P 500 ÷ 분산S&P 500
= 33.32 ÷ 20.07
= 1.66
3 αHCA
= 평균의HCA – βHCA × 평균의S&P 500
= 2.54% – 1.66 × 1.36%
= 0.29%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.82% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.46% |
| 보통주의 체계적 위험HCA | βHCA | 1.66 |
| HCA 보통주에 대한 예상 수익률3 | E(RHCA) | 19.17% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RHCA) = RF + βHCA [E(RM) – RF]
= 4.82% + 1.66 [13.46% – 4.82%]
= 19.17%