자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Comcast보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Comcast Corp., 월별 수익률
| Comcast Corp. (CMCSA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CMCSA,t1 | 피제수CMCSA,t1 | RCMCSA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $36.57 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $38.67 | 5.74% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $39.98 | 3.39% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $43.53 | $0.21 | 9.40% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $41.89 | 1.45% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $43.85 | 4.68% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.76% | 1.11% | ||||
| 표준 편차: | 7.38% | 5.31% | ||||
| Comcast Corp. (CMCSA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CMCSA,t1 | 피제수CMCSA,t1 | RCMCSA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $36.57 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $38.67 | 5.74% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $39.98 | 3.39% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $43.53 | $0.21 | 9.40% | 2,945.83 | 3.93% |
| 4. | 2019. 5. 31. | $41.00 | -5.81% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $42.28 | 3.12% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $43.17 | $0.21 | 2.60% | 2,980.38 | 1.31% |
| 7. | 2019. 8. 31. | $44.26 | 2.52% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $45.08 | 1.85% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $44.82 | $0.21 | -0.11% | 3,037.56 | 2.04% |
| 10. | 2019. 11. 30. | $44.15 | -1.49% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $44.97 | 1.86% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $43.19 | $0.21 | -3.49% | 3,225.52 | -0.16% |
| 13. | 2020. 2. 29. | $40.43 | -6.39% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $34.38 | $0.23 | -14.40% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $37.63 | 9.45% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $39.60 | 5.24% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $38.98 | $0.23 | -0.98% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $42.80 | 9.80% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $44.81 | 4.70% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $46.26 | 3.24% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $42.24 | $0.23 | -8.19% | 3,269.96 | -2.77% |
| 22. | 2020. 11. 30. | $50.24 | 18.94% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $52.40 | 4.30% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $49.57 | $0.23 | -4.96% | 3,714.24 | -1.11% |
| 25. | 2021. 2. 28. | $52.72 | 6.35% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $54.11 | 2.64% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $56.15 | $0.25 | 4.23% | 4,181.17 | 5.24% |
| 28. | 2021. 5. 31. | $57.34 | 2.12% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $57.02 | -0.56% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $58.83 | $0.25 | 3.61% | 4,395.26 | 2.27% |
| 31. | 2021. 8. 31. | $60.68 | 3.14% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $55.93 | -7.83% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $51.43 | $0.25 | -7.60% | 4,605.38 | 6.91% |
| 34. | 2021. 11. 30. | $49.98 | -2.82% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $50.33 | 0.70% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $49.99 | $0.25 | -0.18% | 4,515.55 | -5.26% |
| 37. | 2022. 2. 28. | $46.76 | -6.46% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $46.82 | 0.13% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $39.76 | $0.27 | -14.50% | 4,131.93 | -8.80% |
| 40. | 2022. 5. 31. | $44.28 | 11.37% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $39.24 | -11.38% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $37.52 | $0.27 | -3.70% | 4,130.29 | 9.11% |
| 43. | 2022. 8. 31. | $36.19 | -3.54% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $29.33 | -18.96% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $31.74 | $0.27 | 9.14% | 3,871.98 | 7.99% |
| 46. | 2022. 11. 30. | $36.64 | 15.44% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $34.97 | -4.56% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $39.35 | $0.27 | 13.30% | 4,076.60 | 6.18% |
| 49. | 2023. 2. 28. | $37.17 | -5.54% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $37.91 | 1.99% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $41.37 | $0.29 | 9.89% | 4,169.48 | 1.46% |
| 52. | 2023. 5. 31. | $39.35 | -4.88% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $41.55 | 5.59% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $45.26 | $0.29 | 9.63% | 4,588.96 | 4.85% |
| 55. | 2023. 8. 31. | $46.76 | 3.31% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $44.34 | -5.18% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $41.29 | $0.29 | -6.22% | 4,193.80 | -2.20% |
| 58. | 2023. 11. 30. | $41.89 | 1.45% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $43.85 | 4.68% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.76% | 1.11% | ||||
| 표준 편차: | 7.38% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CMCSA의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Comcast Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCMCSA,t | RS&P 500,t | (RCMCSA,t–RCMCSA)2 | (RS&P 500,t–RS&P 500)2 | (RCMCSA,t–RCMCSA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.74% | 2.97% | 24.78 | 3.49 | 9.29 |
| 2. | 2019. 3. 31. | 3.39% | 1.79% | 6.88 | 0.47 | 1.80 |
| 3. | 2019. 4. 30. | 9.40% | 3.93% | 74.65 | 7.98 | 24.41 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 1.45% | 8.92% | 0.47 | 61.03 | 5.38 |
| 59. | 2023. 12. 31. | 4.68% | 4.42% | 15.32 | 11.00 | 12.98 |
| 합계 (Σ): | 3,156.75 | 1,634.30 | 1,670.14 | |||
| t | 날짜 | RCMCSA,t | RS&P 500,t | (RCMCSA,t–RCMCSA)2 | (RS&P 500,t–RS&P 500)2 | (RCMCSA,t–RCMCSA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.74% | 2.97% | 24.78 | 3.49 | 9.29 |
| 2. | 2019. 3. 31. | 3.39% | 1.79% | 6.88 | 0.47 | 1.80 |
| 3. | 2019. 4. 30. | 9.40% | 3.93% | 74.65 | 7.98 | 24.41 |
| 4. | 2019. 5. 31. | -5.81% | -6.58% | 43.26 | 59.04 | 50.54 |
| 5. | 2019. 6. 30. | 3.12% | 6.89% | 5.56 | 33.49 | 13.64 |
| 6. | 2019. 7. 31. | 2.60% | 1.31% | 3.37 | 0.04 | 0.38 |
| 7. | 2019. 8. 31. | 2.52% | -1.81% | 3.10 | 8.50 | -5.13 |
| 8. | 2019. 9. 30. | 1.85% | 1.72% | 1.18 | 0.37 | 0.67 |
| 9. | 2019. 10. 31. | -0.11% | 2.04% | 0.77 | 0.88 | -0.82 |
| 10. | 2019. 11. 30. | -1.49% | 3.40% | 5.11 | 5.28 | -5.19 |
| 11. | 2019. 12. 31. | 1.86% | 2.86% | 1.19 | 3.07 | 1.92 |
| 12. | 2020. 1. 31. | -3.49% | -0.16% | 18.11 | 1.61 | 5.40 |
| 13. | 2020. 2. 29. | -6.39% | -8.41% | 51.20 | 90.57 | 68.10 |
| 14. | 2020. 3. 31. | -14.40% | -12.51% | 229.83 | 185.44 | 206.45 |
| 15. | 2020. 4. 30. | 9.45% | 12.68% | 75.49 | 134.06 | 100.60 |
| 16. | 2020. 5. 31. | 5.24% | 4.53% | 19.98 | 11.71 | 15.30 |
| 17. | 2020. 6. 30. | -0.98% | 1.84% | 3.06 | 0.54 | -1.28 |
| 18. | 2020. 7. 31. | 9.80% | 5.51% | 81.63 | 19.40 | 39.79 |
| 19. | 2020. 8. 31. | 4.70% | 7.01% | 15.46 | 34.82 | 23.20 |
| 20. | 2020. 9. 30. | 3.24% | -3.92% | 6.11 | 25.29 | -12.43 |
| 21. | 2020. 10. 31. | -8.19% | -2.77% | 80.24 | 15.00 | 34.69 |
| 22. | 2020. 11. 30. | 18.94% | 10.75% | 330.31 | 93.10 | 175.36 |
| 23. | 2020. 12. 31. | 4.30% | 3.71% | 12.49 | 6.79 | 9.21 |
| 24. | 2021. 1. 31. | -4.96% | -1.11% | 32.80 | 4.93 | 12.71 |
| 25. | 2021. 2. 28. | 6.35% | 2.61% | 31.25 | 2.26 | 8.40 |
| 26. | 2021. 3. 31. | 2.64% | 4.24% | 3.50 | 9.85 | 5.87 |
| 27. | 2021. 4. 30. | 4.23% | 5.24% | 12.02 | 17.11 | 14.34 |
| 28. | 2021. 5. 31. | 2.12% | 0.55% | 1.83 | 0.31 | -0.75 |
| 29. | 2021. 6. 30. | -0.56% | 2.22% | 1.75 | 1.24 | -1.48 |
| 30. | 2021. 7. 31. | 3.61% | 2.27% | 8.11 | 1.37 | 3.33 |
| 31. | 2021. 8. 31. | 3.14% | 2.90% | 5.66 | 3.22 | 4.27 |
| 32. | 2021. 9. 30. | -7.83% | -4.76% | 73.84 | 34.37 | 50.38 |
| 33. | 2021. 10. 31. | -7.60% | 6.91% | 69.95 | 33.74 | -48.58 |
| 34. | 2021. 11. 30. | -2.82% | -0.83% | 12.85 | 3.76 | 6.95 |
| 35. | 2021. 12. 31. | 0.70% | 4.36% | 0.00 | 10.60 | -0.21 |
| 36. | 2022. 1. 31. | -0.18% | -5.26% | 0.89 | 40.51 | 6.01 |
| 37. | 2022. 2. 28. | -6.46% | -3.14% | 52.22 | 17.99 | 30.65 |
| 38. | 2022. 3. 31. | 0.13% | 3.58% | 0.41 | 6.11 | -1.57 |
| 39. | 2022. 4. 30. | -14.50% | -8.80% | 233.09 | 98.04 | 151.17 |
| 40. | 2022. 5. 31. | 11.37% | 0.01% | 112.43 | 1.21 | -11.67 |
| 41. | 2022. 6. 30. | -11.38% | -8.39% | 147.55 | 90.21 | 115.37 |
| 42. | 2022. 7. 31. | -3.70% | 9.11% | 19.89 | 64.09 | -35.71 |
| 43. | 2022. 8. 31. | -3.54% | -4.24% | 18.57 | 28.62 | 23.06 |
| 44. | 2022. 9. 30. | -18.96% | -9.34% | 388.89 | 109.11 | 205.99 |
| 45. | 2022. 10. 31. | 9.14% | 7.99% | 70.10 | 47.34 | 57.61 |
| 46. | 2022. 11. 30. | 15.44% | 5.38% | 215.30 | 18.23 | 62.65 |
| 47. | 2022. 12. 31. | -4.56% | -5.90% | 28.33 | 49.04 | 37.28 |
| 48. | 2023. 1. 31. | 13.30% | 6.18% | 157.06 | 25.70 | 63.53 |
| 49. | 2023. 2. 28. | -5.54% | -2.61% | 39.75 | 13.82 | 23.44 |
| 50. | 2023. 3. 31. | 1.99% | 3.51% | 1.50 | 5.76 | 2.94 |
| 51. | 2023. 4. 30. | 9.89% | 1.46% | 83.30 | 0.13 | 3.27 |
| 52. | 2023. 5. 31. | -4.88% | 0.25% | 31.90 | 0.74 | 4.84 |
| 53. | 2023. 6. 30. | 5.59% | 4.71% | 23.29 | 13.02 | 17.41 |
| 54. | 2023. 7. 31. | 9.63% | 4.85% | 78.54 | 13.99 | 33.14 |
| 55. | 2023. 8. 31. | 3.31% | -1.77% | 6.50 | 8.28 | -7.34 |
| 56. | 2023. 9. 30. | -5.18% | -4.87% | 35.29 | 35.73 | 35.51 |
| 57. | 2023. 10. 31. | -6.22% | -2.20% | 48.85 | 10.92 | 23.09 |
| 58. | 2023. 11. 30. | 1.45% | 8.92% | 0.47 | 61.03 | 5.38 |
| 59. | 2023. 12. 31. | 4.68% | 4.42% | 15.32 | 11.00 | 12.98 |
| 합계 (Σ): | 3,156.75 | 1,634.30 | 1,670.14 | |||
모두 보기
분산CMCSA = Σ(RCMCSA,t–RCMCSA)2 ÷ (59 – 1)
= 3,156.75 ÷ (59 – 1)
= 54.43
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산CMCSA, S&P 500 = Σ(RCMCSA,t–RCMCSA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,670.14 ÷ (59 – 1)
= 28.80
체계적인 위험 추정 (β)
| 분산CMCSA | 54.43 |
| 분산S&P 500 | 28.18 |
| 공분산CMCSA, S&P 500 | 28.80 |
| 상관 계수CMCSA, S&P 5001 | 0.74 |
| βCMCSA2 | 1.02 |
| αCMCSA3 | -0.37% |
계산
1 상관 계수CMCSA, S&P 500
= 공분산CMCSA, S&P 500 ÷ (표준 편차CMCSA × 표준 편차S&P 500)
= 28.80 ÷ (7.38% × 5.31%)
= 0.74
2 βCMCSA
= 공분산CMCSA, S&P 500 ÷ 분산S&P 500
= 28.80 ÷ 28.18
= 1.02
3 αCMCSA
= 평균의CMCSA – βCMCSA × 평균의S&P 500
= 0.76% – 1.02 × 1.11%
= -0.37%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.65% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Comcast | βCMCSA | 1.02 |
| Comcast 보통주에 대한 예상 수익률3 | E(RCMCSA) | 13.99% |
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(RCMCSA) = RF + βCMCSA [E(RM) – RF]
= 4.65% + 1.02 [13.79% – 4.65%]
= 13.99%