자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Waste Management보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Waste Management Inc., 월별 수익률
| Waste Management Inc. (WM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값WM,t1 | 피제수WM,t1 | RWM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $69.50 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $73.32 | 5.50% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $72.92 | $0.425 | 0.03% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $72.78 | -0.19% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $160.67 | 0.27% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $166.90 | $0.575 | 4.24% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.79% | 1.36% | ||||
| 표준 편차: | 4.98% | 4.48% | ||||
| Waste Management Inc. (WM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값WM,t1 | 피제수WM,t1 | RWM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $69.50 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $73.32 | 5.50% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $72.92 | $0.425 | 0.03% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $72.78 | -0.19% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $72.91 | 0.18% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $73.35 | $0.425 | 1.19% | 2,423.41 | 0.48% |
| 6. | 2017. 7. 31. | $75.15 | 2.45% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $77.11 | 2.61% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $78.27 | $0.425 | 2.06% | 2,519.36 | 1.93% |
| 9. | 2017. 10. 31. | $82.17 | 4.98% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $82.25 | $0.425 | 0.61% | 2,647.58 | 2.81% |
| 11. | 2017. 12. 31. | $86.30 | 4.92% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $88.43 | 2.47% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $86.32 | -2.39% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $84.12 | $0.465 | -2.01% | 2,640.87 | -2.69% |
| 15. | 2018. 4. 30. | $81.29 | -3.36% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $82.71 | 1.75% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $81.34 | $0.465 | -1.09% | 2,718.37 | 0.48% |
| 18. | 2018. 7. 31. | $90.00 | 10.65% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $90.90 | 1.00% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $90.36 | $0.465 | -0.08% | 2,913.98 | 0.43% |
| 21. | 2018. 10. 31. | $89.47 | -0.98% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $93.75 | $0.465 | 5.30% | 2,760.17 | 1.79% |
| 23. | 2018. 12. 31. | $88.99 | -5.08% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $95.67 | 7.51% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $101.25 | 5.83% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $103.91 | $0.5125 | 3.13% | 2,834.40 | 1.79% |
| 27. | 2019. 4. 30. | $107.34 | 3.30% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $109.35 | 1.87% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $115.37 | $0.5125 | 5.97% | 2,941.76 | 6.89% |
| 30. | 2019. 7. 31. | $117.00 | 1.41% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $119.35 | 2.01% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $115.00 | $0.5125 | -3.22% | 2,976.74 | 1.72% |
| 33. | 2019. 10. 31. | $112.21 | -2.43% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $112.91 | 0.62% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $113.96 | $0.5125 | 1.38% | 3,230.78 | 2.86% |
| 36. | 2020. 1. 31. | $121.70 | 6.79% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $110.81 | -8.95% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $92.56 | $0.545 | -15.98% | 2,584.59 | -12.51% |
| 39. | 2020. 4. 30. | $100.02 | 8.06% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $106.75 | 6.73% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $105.91 | $0.545 | -0.28% | 3,100.29 | 1.84% |
| 42. | 2020. 7. 31. | $109.60 | 3.48% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $114.00 | 4.01% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $113.17 | $0.545 | -0.25% | 3,363.00 | -3.92% |
| 45. | 2020. 10. 31. | $107.91 | -4.65% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $119.13 | 10.40% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $117.93 | $0.545 | -0.55% | 3,756.07 | 3.71% |
| 48. | 2021. 1. 31. | $111.32 | -5.61% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $110.89 | -0.39% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $129.02 | $0.575 | 16.87% | 3,972.89 | 4.24% |
| 51. | 2021. 4. 30. | $137.97 | 6.94% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $140.68 | 1.96% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $140.11 | $0.575 | 0.00% | 4,297.50 | 2.22% |
| 54. | 2021. 7. 31. | $148.26 | 5.82% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $155.11 | 4.62% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $149.36 | $0.575 | -3.34% | 4,307.54 | -4.76% |
| 57. | 2021. 10. 31. | $160.23 | 7.28% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $160.67 | 0.27% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $166.90 | $0.575 | 4.24% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.79% | 1.36% | ||||
| 표준 편차: | 4.98% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 WM의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Waste Management Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RWM,t | RS&P 500,t | (RWM,t–RWM)2 | (RS&P 500,t–RS&P 500)2 | (RWM,t–RWM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 5.50% | 3.72% | 13.76 | 5.58 | 8.76 |
| 2. | 2017. 3. 31. | 0.03% | -0.04% | 3.07 | 1.95 | 2.45 |
| 3. | 2017. 4. 30. | -0.19% | 0.91% | 3.91 | 0.20 | 0.89 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | 0.27% | -0.83% | 2.29 | 4.80 | 3.31 |
| 59. | 2021. 12. 31. | 4.24% | 4.36% | 6.00 | 9.02 | 7.35 |
| 합계 (Σ): | 1,440.81 | 1,164.17 | 959.75 | |||
| t | 날짜 | RWM,t | RS&P 500,t | (RWM,t–RWM)2 | (RS&P 500,t–RS&P 500)2 | (RWM,t–RWM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 5.50% | 3.72% | 13.76 | 5.58 | 8.76 |
| 2. | 2017. 3. 31. | 0.03% | -0.04% | 3.07 | 1.95 | 2.45 |
| 3. | 2017. 4. 30. | -0.19% | 0.91% | 3.91 | 0.20 | 0.89 |
| 4. | 2017. 5. 31. | 0.18% | 1.16% | 2.59 | 0.04 | 0.32 |
| 5. | 2017. 6. 30. | 1.19% | 0.48% | 0.36 | 0.77 | 0.53 |
| 6. | 2017. 7. 31. | 2.45% | 1.93% | 0.45 | 0.33 | 0.39 |
| 7. | 2017. 8. 31. | 2.61% | 0.05% | 0.67 | 1.70 | -1.07 |
| 8. | 2017. 9. 30. | 2.06% | 1.93% | 0.07 | 0.33 | 0.15 |
| 9. | 2017. 10. 31. | 4.98% | 2.22% | 10.22 | 0.74 | 2.75 |
| 10. | 2017. 11. 30. | 0.61% | 2.81% | 1.37 | 2.10 | -1.70 |
| 11. | 2017. 12. 31. | 4.92% | 0.98% | 9.84 | 0.14 | -1.18 |
| 12. | 2018. 1. 31. | 2.47% | 5.62% | 0.46 | 18.15 | 2.90 |
| 13. | 2018. 2. 28. | -2.39% | -3.89% | 17.41 | 27.59 | 21.92 |
| 14. | 2018. 3. 31. | -2.01% | -2.69% | 14.41 | 16.37 | 15.36 |
| 15. | 2018. 4. 30. | -3.36% | 0.27% | 26.53 | 1.18 | 5.59 |
| 16. | 2018. 5. 31. | 1.75% | 2.16% | 0.00 | 0.64 | -0.03 |
| 17. | 2018. 6. 30. | -1.09% | 0.48% | 8.30 | 0.76 | 2.52 |
| 18. | 2018. 7. 31. | 10.65% | 3.60% | 78.50 | 5.04 | 19.88 |
| 19. | 2018. 8. 31. | 1.00% | 3.03% | 0.62 | 2.78 | -1.31 |
| 20. | 2018. 9. 30. | -0.08% | 0.43% | 3.49 | 0.86 | 1.74 |
| 21. | 2018. 10. 31. | -0.98% | -6.94% | 7.68 | 68.86 | 23.00 |
| 22. | 2018. 11. 30. | 5.30% | 1.79% | 12.37 | 0.18 | 1.51 |
| 23. | 2018. 12. 31. | -5.08% | -9.18% | 47.11 | 111.00 | 72.32 |
| 24. | 2019. 1. 31. | 7.51% | 7.87% | 32.72 | 42.39 | 37.24 |
| 25. | 2019. 2. 28. | 5.83% | 2.97% | 16.37 | 2.61 | 6.53 |
| 26. | 2019. 3. 31. | 3.13% | 1.79% | 1.81 | 0.19 | 0.59 |
| 27. | 2019. 4. 30. | 3.30% | 3.93% | 2.29 | 6.62 | 3.90 |
| 28. | 2019. 5. 31. | 1.87% | -6.58% | 0.01 | 62.97 | -0.68 |
| 29. | 2019. 6. 30. | 5.97% | 6.89% | 17.53 | 30.64 | 23.18 |
| 30. | 2019. 7. 31. | 1.41% | 1.31% | 0.14 | 0.00 | 0.02 |
| 31. | 2019. 8. 31. | 2.01% | -1.81% | 0.05 | 10.03 | -0.70 |
| 32. | 2019. 9. 30. | -3.22% | 1.72% | 25.02 | 0.13 | -1.80 |
| 33. | 2019. 10. 31. | -2.43% | 2.04% | 17.75 | 0.47 | -2.89 |
| 34. | 2019. 11. 30. | 0.62% | 3.40% | 1.35 | 4.19 | -2.38 |
| 35. | 2019. 12. 31. | 1.38% | 2.86% | 0.16 | 2.25 | -0.60 |
| 36. | 2020. 1. 31. | 6.79% | -0.16% | 25.05 | 2.31 | -7.61 |
| 37. | 2020. 2. 29. | -8.95% | -8.41% | 115.24 | 95.43 | 104.87 |
| 38. | 2020. 3. 31. | -15.98% | -12.51% | 315.58 | 192.37 | 246.39 |
| 39. | 2020. 4. 30. | 8.06% | 12.68% | 39.35 | 128.29 | 71.05 |
| 40. | 2020. 5. 31. | 6.73% | 4.53% | 24.42 | 10.05 | 15.67 |
| 41. | 2020. 6. 30. | -0.28% | 1.84% | 4.26 | 0.23 | -0.99 |
| 42. | 2020. 7. 31. | 3.48% | 5.51% | 2.88 | 17.24 | 7.05 |
| 43. | 2020. 8. 31. | 4.01% | 7.01% | 4.96 | 31.91 | 12.58 |
| 44. | 2020. 9. 30. | -0.25% | -3.92% | 4.15 | 27.89 | 10.75 |
| 45. | 2020. 10. 31. | -4.65% | -2.77% | 41.40 | 17.01 | 26.54 |
| 46. | 2020. 11. 30. | 10.40% | 10.75% | 74.15 | 88.30 | 80.91 |
| 47. | 2020. 12. 31. | -0.55% | 3.71% | 5.46 | 5.54 | -5.50 |
| 48. | 2021. 1. 31. | -5.61% | -1.11% | 54.64 | 6.11 | 18.27 |
| 49. | 2021. 2. 28. | -0.39% | 2.61% | 4.72 | 1.57 | -2.72 |
| 50. | 2021. 3. 31. | 16.87% | 4.24% | 227.45 | 8.33 | 43.52 |
| 51. | 2021. 4. 30. | 6.94% | 5.24% | 26.53 | 15.09 | 20.01 |
| 52. | 2021. 5. 31. | 1.96% | 0.55% | 0.03 | 0.65 | -0.14 |
| 53. | 2021. 6. 30. | 0.00% | 2.22% | 3.18 | 0.75 | -1.54 |
| 54. | 2021. 7. 31. | 5.82% | 2.27% | 16.24 | 0.84 | 3.70 |
| 55. | 2021. 8. 31. | 4.62% | 2.90% | 8.03 | 2.38 | 4.37 |
| 56. | 2021. 9. 30. | -3.34% | -4.76% | 26.24 | 37.39 | 31.33 |
| 57. | 2021. 10. 31. | 7.28% | 6.91% | 30.15 | 30.87 | 30.51 |
| 58. | 2021. 11. 30. | 0.27% | -0.83% | 2.29 | 4.80 | 3.31 |
| 59. | 2021. 12. 31. | 4.24% | 4.36% | 6.00 | 9.02 | 7.35 |
| 합계 (Σ): | 1,440.81 | 1,164.17 | 959.75 | |||
모두 보기
분산WM = Σ(RWM,t–RWM)2 ÷ (59 – 1)
= 1,440.81 ÷ (59 – 1)
= 24.84
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산WM, S&P 500 = Σ(RWM,t–RWM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 959.75 ÷ (59 – 1)
= 16.55
체계적인 위험 추정 (β)
| 분산WM | 24.84 |
| 분산S&P 500 | 20.07 |
| 공분산WM, S&P 500 | 16.55 |
| 상관 계수WM, S&P 5001 | 0.74 |
| βWM2 | 0.82 |
| αWM3 | 0.67% |
계산
1 상관 계수WM, S&P 500
= 공분산WM, S&P 500 ÷ (표준 편차WM × 표준 편차S&P 500)
= 16.55 ÷ (4.98% × 4.48%)
= 0.74
2 βWM
= 공분산WM, S&P 500 ÷ 분산S&P 500
= 16.55 ÷ 20.07
= 0.82
3 αWM
= 평균의WM – βWM × 평균의S&P 500
= 1.79% – 0.82 × 1.36%
= 0.67%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.88% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험Waste Management | βWM | 0.82 |
| Waste Management 보통주에 대한 예상 수익률3 | E(RWM) | 13.12% |
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(RWM) = RF + βWM [E(RM) – RF]
= 4.88% + 0.82 [14.88% – 4.88%]
= 13.12%