자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다 CoStar Group.
수익률
CoStar Group Inc., 월별 수익률
| CoStar Group Inc. (CSGP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CSGP,t1 | 피제수CSGP,t1 | RCSGP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $34.61 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $34.21 | -1.16% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $36.27 | 6.02% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $36.67 | 1.10% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $81.04 | -2.03% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $77.28 | -4.64% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.68% | 0.67% | ||||
| 표준 편차: | 8.00% | 5.40% | ||||
| CoStar Group Inc. (CSGP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CSGP,t1 | 피제수CSGP,t1 | RCSGP,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $34.61 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $34.21 | -1.16% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $36.27 | 6.02% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $36.67 | 1.10% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $38.12 | 3.95% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $41.26 | 8.24% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $41.58 | 0.78% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $44.22 | 6.35% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $42.08 | -4.84% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $36.14 | -14.12% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $36.94 | 2.21% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $33.73 | -8.69% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $39.07 | 15.83% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $45.75 | 17.10% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $46.64 | 1.95% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $49.63 | 6.41% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $50.96 | 2.68% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $55.41 | 8.73% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $61.54 | 11.06% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $61.49 | -0.08% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $59.32 | -3.53% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $54.95 | -7.37% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $61.29 | 11.54% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $59.83 | -2.38% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $65.30 | 9.14% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $66.76 | 2.24% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $58.72 | -12.04% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $64.83 | 10.41% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $65.68 | 1.31% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $71.07 | 8.21% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $84.98 | 19.57% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $84.86 | -0.14% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $84.85 | -0.01% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $82.36 | -2.93% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $91.06 | 10.56% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $92.43 | 1.50% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $89.97 | -2.66% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $82.38 | -8.44% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $82.19 | -0.23% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $85.44 | 3.95% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $85.40 | -0.05% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $82.82 | -3.02% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $88.85 | 7.28% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $84.74 | -4.63% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $86.06 | 1.56% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $86.05 | -0.01% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $77.76 | -9.63% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $79.03 | 1.63% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $70.16 | -11.22% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $61.01 | -13.04% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $66.61 | 9.18% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $63.62 | -4.49% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $60.94 | -4.21% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $60.41 | -0.87% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $72.59 | 20.16% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $69.64 | -4.06% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $69.65 | 0.01% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $82.72 | 18.77% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $81.04 | -2.03% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $77.28 | -4.64% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.68% | 0.67% | ||||
| 표준 편차: | 8.00% | 5.40% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 CSGP의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
CoStar Group Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCSGP,t | RS&P 500,t | (RCSGP,t–RCSGP)2 | (RS&P 500,t–RS&P 500)2 | (RCSGP,t–RCSGP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -1.16% | -3.89% | 8.02 | 20.81 | 12.92 |
| 2. | 2018. 3. 31. | 6.02% | -2.69% | 18.88 | 11.26 | -14.58 |
| 3. | 2018. 4. 30. | 1.10% | 0.27% | 0.33 | 0.16 | 0.23 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | -2.03% | 5.38% | 13.74 | 22.17 | -17.46 |
| 59. | 2022. 12. 31. | -4.64% | -5.90% | 39.89 | 43.08 | 41.46 |
| 합계 (Σ): | 3,711.35 | 1,691.48 | 1,478.53 | |||
| t | 날짜 | RCSGP,t | RS&P 500,t | (RCSGP,t–RCSGP)2 | (RS&P 500,t–RS&P 500)2 | (RCSGP,t–RCSGP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -1.16% | -3.89% | 8.02 | 20.81 | 12.92 |
| 2. | 2018. 3. 31. | 6.02% | -2.69% | 18.88 | 11.26 | -14.58 |
| 3. | 2018. 4. 30. | 1.10% | 0.27% | 0.33 | 0.16 | 0.23 |
| 4. | 2018. 5. 31. | 3.95% | 2.16% | 5.19 | 2.23 | 3.40 |
| 5. | 2018. 6. 30. | 8.24% | 0.48% | 43.04 | 0.03 | -1.20 |
| 6. | 2018. 7. 31. | 0.78% | 3.60% | 0.81 | 8.62 | -2.64 |
| 7. | 2018. 8. 31. | 6.35% | 3.03% | 21.83 | 5.57 | 11.03 |
| 8. | 2018. 9. 30. | -4.84% | 0.43% | 42.46 | 0.06 | 1.55 |
| 9. | 2018. 10. 31. | -14.12% | -6.94% | 249.40 | 57.87 | 120.13 |
| 10. | 2018. 11. 30. | 2.21% | 1.79% | 0.29 | 1.25 | 0.60 |
| 11. | 2018. 12. 31. | -8.69% | -9.18% | 107.46 | 96.91 | 102.05 |
| 12. | 2019. 1. 31. | 15.83% | 7.87% | 200.37 | 51.87 | 101.94 |
| 13. | 2019. 2. 28. | 17.10% | 2.97% | 237.81 | 5.32 | 35.56 |
| 14. | 2019. 3. 31. | 1.95% | 1.79% | 0.07 | 1.27 | 0.30 |
| 15. | 2019. 4. 30. | 6.41% | 3.93% | 22.41 | 10.66 | 15.46 |
| 16. | 2019. 5. 31. | 2.68% | -6.58% | 1.01 | 52.48 | -7.27 |
| 17. | 2019. 6. 30. | 8.73% | 6.89% | 49.79 | 38.77 | 43.93 |
| 18. | 2019. 7. 31. | 11.06% | 1.31% | 88.11 | 0.42 | 6.07 |
| 19. | 2019. 8. 31. | -0.08% | -1.81% | 3.09 | 6.13 | 4.35 |
| 20. | 2019. 9. 30. | -3.53% | 1.72% | 27.10 | 1.11 | -5.47 |
| 21. | 2019. 10. 31. | -7.37% | 2.04% | 81.78 | 1.89 | -12.45 |
| 22. | 2019. 11. 30. | 11.54% | 3.40% | 97.25 | 7.50 | 27.00 |
| 23. | 2019. 12. 31. | -2.38% | 2.86% | 16.47 | 4.81 | -8.90 |
| 24. | 2020. 1. 31. | 9.14% | -0.16% | 55.74 | 0.69 | -6.19 |
| 25. | 2020. 2. 29. | 2.24% | -8.41% | 0.31 | 82.40 | -5.08 |
| 26. | 2020. 3. 31. | -12.04% | -12.51% | 188.23 | 173.67 | 180.80 |
| 27. | 2020. 4. 30. | 10.41% | 12.68% | 76.19 | 144.43 | 104.90 |
| 28. | 2020. 5. 31. | 1.31% | 4.53% | 0.13 | 14.91 | -1.41 |
| 29. | 2020. 6. 30. | 8.21% | 1.84% | 42.64 | 1.37 | 7.65 |
| 30. | 2020. 7. 31. | 19.57% | 5.51% | 320.26 | 23.46 | 86.68 |
| 31. | 2020. 8. 31. | -0.14% | 7.01% | 3.30 | 40.19 | -11.52 |
| 32. | 2020. 9. 30. | -0.01% | -3.92% | 2.85 | 21.06 | 7.75 |
| 33. | 2020. 10. 31. | -2.93% | -2.77% | 21.26 | 11.79 | 15.83 |
| 34. | 2020. 11. 30. | 10.56% | 10.75% | 78.98 | 101.77 | 89.65 |
| 35. | 2020. 12. 31. | 1.50% | 3.71% | 0.03 | 9.28 | -0.52 |
| 36. | 2021. 1. 31. | -2.66% | -1.11% | 18.82 | 3.17 | 7.72 |
| 37. | 2021. 2. 28. | -8.44% | 2.61% | 102.26 | 3.77 | -19.64 |
| 38. | 2021. 3. 31. | -0.23% | 4.24% | 3.64 | 12.80 | -6.82 |
| 39. | 2021. 4. 30. | 3.95% | 5.24% | 5.19 | 20.94 | 10.42 |
| 40. | 2021. 5. 31. | -0.05% | 0.55% | 2.97 | 0.01 | 0.20 |
| 41. | 2021. 6. 30. | -3.02% | 2.22% | 22.07 | 2.42 | -7.30 |
| 42. | 2021. 7. 31. | 7.28% | 2.27% | 31.41 | 2.59 | 9.01 |
| 43. | 2021. 8. 31. | -4.63% | 2.90% | 39.72 | 4.98 | -14.07 |
| 44. | 2021. 9. 30. | 1.56% | -4.76% | 0.01 | 29.42 | 0.64 |
| 45. | 2021. 10. 31. | -0.01% | 6.91% | 2.85 | 39.03 | -10.55 |
| 46. | 2021. 11. 30. | -9.63% | -0.83% | 127.93 | 2.25 | 16.97 |
| 47. | 2021. 12. 31. | 1.63% | 4.36% | 0.00 | 13.65 | -0.16 |
| 48. | 2022. 1. 31. | -11.22% | -5.26% | 166.41 | 35.11 | 76.43 |
| 49. | 2022. 2. 28. | -13.04% | -3.14% | 216.62 | 14.46 | 55.97 |
| 50. | 2022. 3. 31. | 9.18% | 3.58% | 56.29 | 8.47 | 21.84 |
| 51. | 2022. 4. 30. | -4.49% | -8.80% | 38.01 | 89.54 | 58.34 |
| 52. | 2022. 5. 31. | -4.21% | 0.01% | 34.68 | 0.44 | 3.89 |
| 53. | 2022. 6. 30. | -0.87% | -8.39% | 6.48 | 82.06 | 23.06 |
| 54. | 2022. 7. 31. | 20.16% | 9.11% | 341.72 | 71.32 | 156.11 |
| 55. | 2022. 8. 31. | -4.06% | -4.24% | 32.95 | 24.11 | 28.19 |
| 56. | 2022. 9. 30. | 0.01% | -9.34% | 2.76 | 100.12 | 16.63 |
| 57. | 2022. 10. 31. | 18.77% | 7.99% | 292.03 | 53.58 | 125.08 |
| 58. | 2022. 11. 30. | -2.03% | 5.38% | 13.74 | 22.17 | -17.46 |
| 59. | 2022. 12. 31. | -4.64% | -5.90% | 39.89 | 43.08 | 41.46 |
| 합계 (Σ): | 3,711.35 | 1,691.48 | 1,478.53 | |||
모두 표시
분산CSGP = Σ(RCSGP,t–RCSGP)2 ÷ (59 – 1)
= 3,711.35 ÷ (59 – 1)
= 63.99
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산CSGP, S&P 500 = Σ(RCSGP,t–RCSGP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,478.53 ÷ (59 – 1)
= 25.49
체계적인 위험 추정 (β)
| 분산CSGP | 63.99 |
| 분산S&P 500 | 29.16 |
| 공분산CSGP, S&P 500 | 25.49 |
| 상관 계수CSGP, S&P 5001 | 0.59 |
| βCSGP2 | 0.87 |
| αCSGP3 | 1.09% |
계산
1 상관 계수CSGP, S&P 500
= 공분산CSGP, S&P 500 ÷ (표준 편차CSGP × 표준 편차S&P 500)
= 25.49 ÷ (8.00% × 5.40%)
= 0.59
2 βCSGP
= 공분산CSGP, S&P 500 ÷ 분산S&P 500
= 25.49 ÷ 29.16
= 0.87
3 αCSGP
= 평균의CSGP – βCSGP × 평균의S&P 500
= 1.68% – 0.87 × 0.67%
= 1.09%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.62% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.69% |
| 보통주 CoStar Group 의 체계적인 리스크 | βCSGP | 0.87 |
| CoStar Group 보통주에 대한 예상 수익률3 | E(RCSGP) | 12.55% |
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(RCSGP) = RF + βCSGP [E(RM) – RF]
= 4.62% + 0.87 [13.69% – 4.62%]
= 12.55%