자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Ecolab보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Ecolab Inc., 월별 수익률
| Ecolab Inc. (ECL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ECL,t1 | 피제수ECL,t1 | RECL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $120.13 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $123.97 | 3.20% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $125.34 | $0.37 | 1.40% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $129.09 | 2.99% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $221.47 | -0.34% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $234.59 | $0.51 | 6.15% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.42% | 1.36% | ||||
| 표준 편차: | 6.28% | 4.48% | ||||
| Ecolab Inc. (ECL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ECL,t1 | 피제수ECL,t1 | RECL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $120.13 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $123.97 | 3.20% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $125.34 | $0.37 | 1.40% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $129.09 | 2.99% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $132.84 | 2.90% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $132.75 | $0.37 | 0.21% | 2,423.41 | 0.48% |
| 6. | 2017. 7. 31. | $131.67 | -0.81% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $133.30 | 1.24% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $128.61 | $0.37 | -3.24% | 2,519.36 | 1.93% |
| 9. | 2017. 10. 31. | $130.66 | 1.59% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $135.92 | 4.03% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $134.18 | $0.41 | -0.98% | 2,673.61 | 0.98% |
| 12. | 2018. 1. 31. | $137.68 | 2.61% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $130.45 | -5.25% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $137.07 | $0.41 | 5.39% | 2,640.87 | -2.69% |
| 15. | 2018. 4. 30. | $144.77 | 5.62% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $142.61 | -1.49% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $140.33 | $0.41 | -1.31% | 2,718.37 | 0.48% |
| 18. | 2018. 7. 31. | $140.70 | 0.26% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $150.48 | 6.95% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $156.78 | $0.41 | 4.46% | 2,913.98 | 0.43% |
| 21. | 2018. 10. 31. | $153.15 | -2.32% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $160.49 | 4.79% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $147.35 | $0.46 | -7.90% | 2,506.85 | -9.18% |
| 24. | 2019. 1. 31. | $158.17 | 7.34% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $168.91 | 6.79% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $176.54 | $0.46 | 4.79% | 2,834.40 | 1.79% |
| 27. | 2019. 4. 30. | $184.08 | 4.27% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $184.09 | 0.01% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $197.44 | $0.46 | 7.50% | 2,941.76 | 6.89% |
| 30. | 2019. 7. 31. | $201.73 | 2.17% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $206.31 | 2.27% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $198.04 | $0.46 | -3.79% | 2,976.74 | 1.72% |
| 33. | 2019. 10. 31. | $192.07 | -3.01% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $186.67 | -2.81% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $192.99 | $0.47 | 3.64% | 3,230.78 | 2.86% |
| 36. | 2020. 1. 31. | $196.11 | 1.62% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $180.45 | -7.99% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $155.83 | $0.47 | -13.38% | 2,584.59 | -12.51% |
| 39. | 2020. 4. 30. | $193.50 | 24.17% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $212.58 | 9.86% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $198.95 | $0.47 | -6.19% | 3,100.29 | 1.84% |
| 42. | 2020. 7. 31. | $187.08 | -5.97% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $197.08 | 5.35% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $199.84 | $0.47 | 1.64% | 3,363.00 | -3.92% |
| 45. | 2020. 10. 31. | $183.59 | -8.13% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $222.15 | 21.00% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $216.36 | $0.48 | -2.39% | 3,756.07 | 3.71% |
| 48. | 2021. 1. 31. | $204.51 | -5.48% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $209.36 | 2.37% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $214.07 | $0.48 | 2.48% | 3,972.89 | 4.24% |
| 51. | 2021. 4. 30. | $224.12 | 4.69% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $215.08 | -4.03% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $205.97 | $0.48 | -4.01% | 4,297.50 | 2.22% |
| 54. | 2021. 7. 31. | $220.83 | 7.21% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $225.36 | 2.05% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $208.62 | $0.48 | -7.22% | 4,307.54 | -4.76% |
| 57. | 2021. 10. 31. | $222.22 | 6.52% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $221.47 | -0.34% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $234.59 | $0.51 | 6.15% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.42% | 1.36% | ||||
| 표준 편차: | 6.28% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 ECL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Ecolab Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RECL,t | RS&P 500,t | (RECL,t–RECL)2 | (RS&P 500,t–RS&P 500)2 | (RECL,t–RECL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 3.20% | 3.72% | 3.17 | 5.58 | 4.21 |
| 2. | 2017. 3. 31. | 1.40% | -0.04% | 0.00 | 1.95 | 0.02 |
| 3. | 2017. 4. 30. | 2.99% | 0.91% | 2.48 | 0.20 | -0.71 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -0.34% | -0.83% | 3.07 | 4.80 | 3.84 |
| 59. | 2021. 12. 31. | 6.15% | 4.36% | 22.46 | 9.02 | 14.23 |
| 합계 (Σ): | 2,283.90 | 1,164.17 | 1,169.06 | |||
| t | 날짜 | RECL,t | RS&P 500,t | (RECL,t–RECL)2 | (RS&P 500,t–RS&P 500)2 | (RECL,t–RECL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 3.20% | 3.72% | 3.17 | 5.58 | 4.21 |
| 2. | 2017. 3. 31. | 1.40% | -0.04% | 0.00 | 1.95 | 0.02 |
| 3. | 2017. 4. 30. | 2.99% | 0.91% | 2.48 | 0.20 | -0.71 |
| 4. | 2017. 5. 31. | 2.90% | 1.16% | 2.22 | 0.04 | -0.30 |
| 5. | 2017. 6. 30. | 0.21% | 0.48% | 1.45 | 0.77 | 1.06 |
| 6. | 2017. 7. 31. | -0.81% | 1.93% | 4.97 | 0.33 | -1.29 |
| 7. | 2017. 8. 31. | 1.24% | 0.05% | 0.03 | 1.70 | 0.23 |
| 8. | 2017. 9. 30. | -3.24% | 1.93% | 21.68 | 0.33 | -2.67 |
| 9. | 2017. 10. 31. | 1.59% | 2.22% | 0.03 | 0.74 | 0.15 |
| 10. | 2017. 11. 30. | 4.03% | 2.81% | 6.81 | 2.10 | 3.79 |
| 11. | 2017. 12. 31. | -0.98% | 0.98% | 5.73 | 0.14 | 0.90 |
| 12. | 2018. 1. 31. | 2.61% | 5.62% | 1.42 | 18.15 | 5.08 |
| 13. | 2018. 2. 28. | -5.25% | -3.89% | 44.45 | 27.59 | 35.02 |
| 14. | 2018. 3. 31. | 5.39% | -2.69% | 15.79 | 16.37 | -16.08 |
| 15. | 2018. 4. 30. | 5.62% | 0.27% | 17.66 | 1.18 | -4.56 |
| 16. | 2018. 5. 31. | -1.49% | 2.16% | 8.45 | 0.64 | -2.33 |
| 17. | 2018. 6. 30. | -1.31% | 0.48% | 7.44 | 0.76 | 2.38 |
| 18. | 2018. 7. 31. | 0.26% | 3.60% | 1.33 | 5.04 | -2.58 |
| 19. | 2018. 8. 31. | 6.95% | 3.03% | 30.64 | 2.78 | 9.24 |
| 20. | 2018. 9. 30. | 4.46% | 0.43% | 9.26 | 0.86 | -2.83 |
| 21. | 2018. 10. 31. | -2.32% | -6.94% | 13.92 | 68.86 | 30.96 |
| 22. | 2018. 11. 30. | 4.79% | 1.79% | 11.41 | 0.18 | 1.45 |
| 23. | 2018. 12. 31. | -7.90% | -9.18% | 86.79 | 111.00 | 98.15 |
| 24. | 2019. 1. 31. | 7.34% | 7.87% | 35.14 | 42.39 | 38.59 |
| 25. | 2019. 2. 28. | 6.79% | 2.97% | 28.89 | 2.61 | 8.68 |
| 26. | 2019. 3. 31. | 4.79% | 1.79% | 11.38 | 0.19 | 1.47 |
| 27. | 2019. 4. 30. | 4.27% | 3.93% | 8.15 | 6.62 | 7.35 |
| 28. | 2019. 5. 31. | 0.01% | -6.58% | 1.99 | 62.97 | 11.19 |
| 29. | 2019. 6. 30. | 7.50% | 6.89% | 37.04 | 30.64 | 33.69 |
| 30. | 2019. 7. 31. | 2.17% | 1.31% | 0.57 | 0.00 | -0.03 |
| 31. | 2019. 8. 31. | 2.27% | -1.81% | 0.73 | 10.03 | -2.71 |
| 32. | 2019. 9. 30. | -3.79% | 1.72% | 27.05 | 0.13 | -1.87 |
| 33. | 2019. 10. 31. | -3.01% | 2.04% | 19.63 | 0.47 | -3.04 |
| 34. | 2019. 11. 30. | -2.81% | 3.40% | 17.87 | 4.19 | -8.65 |
| 35. | 2019. 12. 31. | 3.64% | 2.86% | 4.94 | 2.25 | 3.34 |
| 36. | 2020. 1. 31. | 1.62% | -0.16% | 0.04 | 2.31 | -0.31 |
| 37. | 2020. 2. 29. | -7.99% | -8.41% | 88.37 | 95.43 | 91.84 |
| 38. | 2020. 3. 31. | -13.38% | -12.51% | 219.00 | 192.37 | 205.26 |
| 39. | 2020. 4. 30. | 24.17% | 12.68% | 517.94 | 128.29 | 257.77 |
| 40. | 2020. 5. 31. | 9.86% | 4.53% | 71.32 | 10.05 | 26.77 |
| 41. | 2020. 6. 30. | -6.19% | 1.84% | 57.85 | 0.23 | -3.66 |
| 42. | 2020. 7. 31. | -5.97% | 5.51% | 54.49 | 17.24 | -30.65 |
| 43. | 2020. 8. 31. | 5.35% | 7.01% | 15.44 | 31.91 | 22.20 |
| 44. | 2020. 9. 30. | 1.64% | -3.92% | 0.05 | 27.89 | -1.18 |
| 45. | 2020. 10. 31. | -8.13% | -2.77% | 91.14 | 17.01 | 39.38 |
| 46. | 2020. 11. 30. | 21.00% | 10.75% | 383.68 | 88.30 | 184.06 |
| 47. | 2020. 12. 31. | -2.39% | 3.71% | 14.48 | 5.54 | -8.96 |
| 48. | 2021. 1. 31. | -5.48% | -1.11% | 47.51 | 6.11 | 17.04 |
| 49. | 2021. 2. 28. | 2.37% | 2.61% | 0.91 | 1.57 | 1.20 |
| 50. | 2021. 3. 31. | 2.48% | 4.24% | 1.13 | 8.33 | 3.07 |
| 51. | 2021. 4. 30. | 4.69% | 5.24% | 10.75 | 15.09 | 12.74 |
| 52. | 2021. 5. 31. | -4.03% | 0.55% | 29.69 | 0.65 | 4.41 |
| 53. | 2021. 6. 30. | -4.01% | 2.22% | 29.46 | 0.75 | -4.69 |
| 54. | 2021. 7. 31. | 7.21% | 2.27% | 33.63 | 0.84 | 5.32 |
| 55. | 2021. 8. 31. | 2.05% | 2.90% | 0.40 | 2.38 | 0.98 |
| 56. | 2021. 9. 30. | -7.22% | -4.76% | 74.49 | 37.39 | 52.77 |
| 57. | 2021. 10. 31. | 6.52% | 6.91% | 26.05 | 30.87 | 28.36 |
| 58. | 2021. 11. 30. | -0.34% | -0.83% | 3.07 | 4.80 | 3.84 |
| 59. | 2021. 12. 31. | 6.15% | 4.36% | 22.46 | 9.02 | 14.23 |
| 합계 (Σ): | 2,283.90 | 1,164.17 | 1,169.06 | |||
모두 보기
분산ECL = Σ(RECL,t–RECL)2 ÷ (59 – 1)
= 2,283.90 ÷ (59 – 1)
= 39.38
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산ECL, S&P 500 = Σ(RECL,t–RECL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,169.06 ÷ (59 – 1)
= 20.16
체계적인 위험 추정 (β)
| 분산ECL | 39.38 |
| 분산S&P 500 | 20.07 |
| 공분산ECL, S&P 500 | 20.16 |
| 상관 계수ECL, S&P 5001 | 0.72 |
| βECL2 | 1.00 |
| αECL3 | 0.05% |
계산
1 상관 계수ECL, S&P 500
= 공분산ECL, S&P 500 ÷ (표준 편차ECL × 표준 편차S&P 500)
= 20.16 ÷ (6.28% × 4.48%)
= 0.72
2 βECL
= 공분산ECL, S&P 500 ÷ 분산S&P 500
= 20.16 ÷ 20.07
= 1.00
3 αECL
= 평균의ECL – βECL × 평균의S&P 500
= 1.42% – 1.00 × 1.36%
= 0.05%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Ecolab | βECL | 1.00 |
| 이콜랩 보통주의 예상 수익률3 | E(RECL) | 14.93% |
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(RECL) = RF + βECL [E(RM) – RF]
= 4.60% + 1.00 [14.89% – 4.60%]
= 14.93%