자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Danaher보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Danaher Corp., 월별 수익률
| Danaher Corp. (DHR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DHR,t1 | 피제수DHR,t1 | RDHR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $110.92 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $127.02 | 14.51% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $132.02 | $0.17 | 4.07% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $132.44 | 0.32% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $223.31 | 16.30% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $231.34 | $0.24 | 3.70% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.59% | 1.11% | ||||
| 표준 편차: | 7.74% | 5.31% | ||||
| Danaher Corp. (DHR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DHR,t1 | 피제수DHR,t1 | RDHR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $110.92 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $127.02 | 14.51% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $132.02 | $0.17 | 4.07% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $132.44 | 0.32% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $132.01 | -0.32% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $142.92 | $0.17 | 8.39% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $140.50 | -1.69% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $142.09 | 1.13% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $144.43 | $0.17 | 1.77% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $137.82 | -4.58% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $145.98 | 5.92% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $153.48 | $0.17 | 5.25% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $160.87 | 4.81% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $144.58 | -10.13% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $138.41 | $0.18 | -4.14% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $163.46 | 18.10% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $166.61 | 1.93% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $176.83 | $0.18 | 6.24% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $203.80 | 15.25% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $206.47 | 1.31% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $215.33 | $0.18 | 4.38% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $229.54 | 6.60% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $224.63 | -2.14% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $222.14 | $0.18 | -1.03% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $237.84 | 7.07% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $219.67 | -7.64% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $225.08 | $0.21 | 2.56% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $253.94 | 12.82% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $256.14 | 0.87% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $268.36 | $0.21 | 4.85% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $297.49 | 10.85% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $324.16 | 8.97% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $304.44 | $0.21 | -6.02% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $311.77 | 2.41% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $321.64 | 3.17% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $329.01 | $0.21 | 2.36% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $285.79 | -13.14% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $274.41 | -3.98% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $293.33 | $0.25 | 6.99% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $251.13 | -14.39% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $263.82 | 5.05% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $253.52 | $0.25 | -3.81% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $291.47 | 14.97% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $269.91 | -7.40% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $258.29 | $0.25 | -4.21% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $251.67 | -2.56% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $273.41 | 8.64% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $265.42 | $0.25 | -2.83% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $264.38 | -0.39% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $247.53 | -6.37% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $252.04 | $0.27 | 1.93% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $236.91 | -6.00% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $229.62 | -3.08% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $240.00 | $0.27 | 4.64% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $255.06 | 6.28% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $265.00 | 3.90% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $248.10 | -6.38% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $192.02 | $0.27 | -22.49% | 4,193.80 | -2.20% |
| 58. | 2023. 11. 30. | $223.31 | 16.30% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $231.34 | $0.24 | 3.70% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.59% | 1.11% | ||||
| 표준 편차: | 7.74% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 DHR의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Danaher Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RDHR,t | RS&P 500,t | (RDHR,t–RDHR)2 | (RS&P 500,t–RS&P 500)2 | (RDHR,t–RDHR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 14.51% | 2.97% | 167.16 | 3.49 | 24.14 |
| 2. | 2019. 3. 31. | 4.07% | 1.79% | 6.17 | 0.47 | 1.71 |
| 3. | 2019. 4. 30. | 0.32% | 3.93% | 1.61 | 7.98 | -3.58 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 16.30% | 8.92% | 216.36 | 61.03 | 114.91 |
| 59. | 2023. 12. 31. | 3.70% | 4.42% | 4.48 | 11.00 | 7.02 |
| 합계 (Σ): | 3,477.56 | 1,634.30 | 1,428.80 | |||
| t | 날짜 | RDHR,t | RS&P 500,t | (RDHR,t–RDHR)2 | (RS&P 500,t–RS&P 500)2 | (RDHR,t–RDHR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 14.51% | 2.97% | 167.16 | 3.49 | 24.14 |
| 2. | 2019. 3. 31. | 4.07% | 1.79% | 6.17 | 0.47 | 1.71 |
| 3. | 2019. 4. 30. | 0.32% | 3.93% | 1.61 | 7.98 | -3.58 |
| 4. | 2019. 5. 31. | -0.32% | -6.58% | 3.65 | 59.04 | 14.68 |
| 5. | 2019. 6. 30. | 8.39% | 6.89% | 46.34 | 33.49 | 39.40 |
| 6. | 2019. 7. 31. | -1.69% | 1.31% | 10.75 | 0.04 | -0.68 |
| 7. | 2019. 8. 31. | 1.13% | -1.81% | 0.21 | 8.50 | 1.32 |
| 8. | 2019. 9. 30. | 1.77% | 1.72% | 0.03 | 0.37 | 0.11 |
| 9. | 2019. 10. 31. | -4.58% | 2.04% | 37.98 | 0.88 | -5.78 |
| 10. | 2019. 11. 30. | 5.92% | 3.40% | 18.79 | 5.28 | 9.97 |
| 11. | 2019. 12. 31. | 5.25% | 2.86% | 13.46 | 3.07 | 6.43 |
| 12. | 2020. 1. 31. | 4.81% | -0.16% | 10.43 | 1.61 | -4.10 |
| 13. | 2020. 2. 29. | -10.13% | -8.41% | 137.17 | 90.57 | 111.46 |
| 14. | 2020. 3. 31. | -4.14% | -12.51% | 32.82 | 185.44 | 78.02 |
| 15. | 2020. 4. 30. | 18.10% | 12.68% | 272.66 | 134.06 | 191.19 |
| 16. | 2020. 5. 31. | 1.93% | 4.53% | 0.12 | 11.71 | 1.17 |
| 17. | 2020. 6. 30. | 6.24% | 1.84% | 21.68 | 0.54 | 3.41 |
| 18. | 2020. 7. 31. | 15.25% | 5.51% | 186.76 | 19.40 | 60.19 |
| 19. | 2020. 8. 31. | 1.31% | 7.01% | 0.08 | 34.82 | -1.63 |
| 20. | 2020. 9. 30. | 4.38% | -3.92% | 7.80 | 25.29 | -14.04 |
| 21. | 2020. 10. 31. | 6.60% | -2.77% | 25.13 | 15.00 | -19.41 |
| 22. | 2020. 11. 30. | -2.14% | 10.75% | 13.88 | 93.10 | -35.94 |
| 23. | 2020. 12. 31. | -1.03% | 3.71% | 6.83 | 6.79 | -6.81 |
| 24. | 2021. 1. 31. | 7.07% | -1.11% | 30.05 | 4.93 | -12.17 |
| 25. | 2021. 2. 28. | -7.64% | 2.61% | 85.11 | 2.26 | -13.87 |
| 26. | 2021. 3. 31. | 2.56% | 4.24% | 0.95 | 9.85 | 3.05 |
| 27. | 2021. 4. 30. | 12.82% | 5.24% | 126.25 | 17.11 | 46.48 |
| 28. | 2021. 5. 31. | 0.87% | 0.55% | 0.52 | 0.31 | 0.40 |
| 29. | 2021. 6. 30. | 4.85% | 2.22% | 10.67 | 1.24 | 3.64 |
| 30. | 2021. 7. 31. | 10.85% | 2.27% | 85.91 | 1.37 | 10.83 |
| 31. | 2021. 8. 31. | 8.97% | 2.90% | 54.45 | 3.22 | 13.23 |
| 32. | 2021. 9. 30. | -6.02% | -4.76% | 57.83 | 34.37 | 44.58 |
| 33. | 2021. 10. 31. | 2.41% | 6.91% | 0.68 | 33.74 | 4.77 |
| 34. | 2021. 11. 30. | 3.17% | -0.83% | 2.50 | 3.76 | -3.06 |
| 35. | 2021. 12. 31. | 2.36% | 4.36% | 0.59 | 10.60 | 2.51 |
| 36. | 2022. 1. 31. | -13.14% | -5.26% | 216.75 | 40.51 | 93.70 |
| 37. | 2022. 2. 28. | -3.98% | -3.14% | 31.00 | 17.99 | 23.62 |
| 38. | 2022. 3. 31. | 6.99% | 3.58% | 29.16 | 6.11 | 13.35 |
| 39. | 2022. 4. 30. | -14.39% | -8.80% | 255.12 | 98.04 | 158.15 |
| 40. | 2022. 5. 31. | 5.05% | 0.01% | 12.02 | 1.21 | -3.82 |
| 41. | 2022. 6. 30. | -3.81% | -8.39% | 29.11 | 90.21 | 51.24 |
| 42. | 2022. 7. 31. | 14.97% | 9.11% | 179.11 | 64.09 | 107.14 |
| 43. | 2022. 8. 31. | -7.40% | -4.24% | 80.69 | 28.62 | 48.06 |
| 44. | 2022. 9. 30. | -4.21% | -9.34% | 33.62 | 109.11 | 60.57 |
| 45. | 2022. 10. 31. | -2.56% | 7.99% | 17.21 | 47.34 | -28.55 |
| 46. | 2022. 11. 30. | 8.64% | 5.38% | 49.74 | 18.23 | 30.11 |
| 47. | 2022. 12. 31. | -2.83% | -5.90% | 19.51 | 49.04 | 30.93 |
| 48. | 2023. 1. 31. | -0.39% | 6.18% | 3.91 | 25.70 | -10.03 |
| 49. | 2023. 2. 28. | -6.37% | -2.61% | 63.35 | 13.82 | 29.59 |
| 50. | 2023. 3. 31. | 1.93% | 3.51% | 0.12 | 5.76 | 0.83 |
| 51. | 2023. 4. 30. | -6.00% | 1.46% | 57.59 | 0.13 | -2.72 |
| 52. | 2023. 5. 31. | -3.08% | 0.25% | 21.74 | 0.74 | 4.00 |
| 53. | 2023. 6. 30. | 4.64% | 4.71% | 9.32 | 13.02 | 11.01 |
| 54. | 2023. 7. 31. | 6.28% | 4.85% | 21.99 | 13.99 | 17.54 |
| 55. | 2023. 8. 31. | 3.90% | -1.77% | 5.34 | 8.28 | -6.65 |
| 56. | 2023. 9. 30. | -6.38% | -4.87% | 63.41 | 35.73 | 47.60 |
| 57. | 2023. 10. 31. | -22.49% | -2.20% | 579.89 | 10.92 | 79.56 |
| 58. | 2023. 11. 30. | 16.30% | 8.92% | 216.36 | 61.03 | 114.91 |
| 59. | 2023. 12. 31. | 3.70% | 4.42% | 4.48 | 11.00 | 7.02 |
| 합계 (Σ): | 3,477.56 | 1,634.30 | 1,428.80 | |||
모두 보기
분산DHR = Σ(RDHR,t–RDHR)2 ÷ (59 – 1)
= 3,477.56 ÷ (59 – 1)
= 59.96
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산DHR, S&P 500 = Σ(RDHR,t–RDHR)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,428.80 ÷ (59 – 1)
= 24.63
체계적인 위험 추정 (β)
| 분산DHR | 59.96 |
| 분산S&P 500 | 28.18 |
| 공분산DHR, S&P 500 | 24.63 |
| 상관 계수DHR, S&P 5001 | 0.60 |
| βDHR2 | 0.87 |
| αDHR3 | 0.62% |
계산
1 상관 계수DHR, S&P 500
= 공분산DHR, S&P 500 ÷ (표준 편차DHR × 표준 편차S&P 500)
= 24.63 ÷ (7.74% × 5.31%)
= 0.60
2 βDHR
= 공분산DHR, S&P 500 ÷ 분산S&P 500
= 24.63 ÷ 28.18
= 0.87
3 αDHR
= 평균의DHR – βDHR × 평균의S&P 500
= 1.59% – 0.87 × 1.11%
= 0.62%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.65% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Danaher | βDHR | 0.87 |
| Danaher 보통주에 대한 기대 수익률3 | E(RDHR) | 12.64% |
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(RDHR) = RF + βDHR [E(RM) – RF]
= 4.65% + 0.87 [13.79% – 4.65%]
= 12.64%