자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Charter보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Charter Communications Inc., 월별 수익률
| Charter Communications Inc. (CHTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CHTR,t1 | 피제수CHTR,t1 | RCHTR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $517.46 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $493.17 | -4.69% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $436.31 | -11.53% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $495.23 | 13.50% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $396.97 | 21.17% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $342.77 | -13.65% | 5,881.63 | -2.50% | |
| 평균의 (R): | -0.12% | 1.16% | ||||
| 표준 편차: | 10.77% | 5.28% | ||||
| Charter Communications Inc. (CHTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CHTR,t1 | 피제수CHTR,t1 | RCHTR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $517.46 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $493.17 | -4.69% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $436.31 | -11.53% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $495.23 | 13.50% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $544.00 | 9.85% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $510.04 | -6.24% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $580.00 | 13.72% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $615.61 | 6.14% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $624.34 | 1.42% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $603.82 | -3.29% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $651.99 | 7.98% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $661.55 | 1.47% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $607.56 | -8.16% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $613.42 | 0.96% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $617.02 | 0.59% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $673.45 | 9.15% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $694.53 | 3.13% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $721.45 | 3.88% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $744.05 | 3.13% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $816.66 | 9.76% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $727.56 | -10.91% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $674.89 | -7.24% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $646.28 | -4.24% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $651.97 | 0.88% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $593.34 | -8.99% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $601.78 | 1.42% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $545.52 | -9.35% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $428.49 | -21.45% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $506.93 | 18.31% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $468.53 | -7.58% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $432.10 | -7.78% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $412.63 | -4.51% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $303.35 | -26.48% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $367.62 | 21.19% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $391.29 | 6.44% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $339.10 | -13.34% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $384.31 | 13.33% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $367.61 | -4.35% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $357.61 | -2.72% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $368.70 | 3.10% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $326.15 | -11.54% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $367.37 | 12.64% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $405.19 | 10.29% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $438.12 | 8.13% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $439.82 | 0.39% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $402.80 | -8.42% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $400.13 | -0.66% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $388.68 | -2.86% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $370.71 | -4.62% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $293.93 | -20.71% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $290.63 | -1.12% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $255.94 | -11.94% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $287.12 | 12.18% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $298.96 | 4.12% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $379.72 | 27.01% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $347.54 | -8.47% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $324.08 | -6.75% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $327.61 | 1.09% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $396.97 | 21.17% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $342.77 | -13.65% | 5,881.63 | -2.50% | |
| 평균의 (R): | -0.12% | 1.16% | ||||
| 표준 편차: | 10.77% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CHTR의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Charter Communications Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCHTR,t | RS&P 500,t | (RCHTR,t–RCHTR)2 | (RS&P 500,t–RS&P 500)2 | (RCHTR,t–RCHTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -4.69% | -8.41% | 20.90 | 91.63 | 43.76 |
| 2. | 2020. 3. 31. | -11.53% | -12.51% | 130.12 | 186.96 | 155.97 |
| 3. | 2020. 4. 30. | 13.50% | 12.68% | 185.69 | 132.78 | 157.02 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 21.17% | 5.73% | 453.44 | 20.87 | 97.29 |
| 59. | 2024. 12. 31. | -13.65% | -2.50% | 183.08 | 13.40 | 49.53 |
| 합계 (Σ): | 6,722.49 | 1,618.62 | 1,802.15 | |||
| t | 날짜 | RCHTR,t | RS&P 500,t | (RCHTR,t–RCHTR)2 | (RS&P 500,t–RS&P 500)2 | (RCHTR,t–RCHTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -4.69% | -8.41% | 20.90 | 91.63 | 43.76 |
| 2. | 2020. 3. 31. | -11.53% | -12.51% | 130.12 | 186.96 | 155.97 |
| 3. | 2020. 4. 30. | 13.50% | 12.68% | 185.69 | 132.78 | 157.02 |
| 4. | 2020. 5. 31. | 9.85% | 4.53% | 99.41 | 11.34 | 33.57 |
| 5. | 2020. 6. 30. | -6.24% | 1.84% | 37.45 | 0.46 | -4.15 |
| 6. | 2020. 7. 31. | 13.72% | 5.51% | 191.52 | 18.91 | 60.18 |
| 7. | 2020. 8. 31. | 6.14% | 7.01% | 39.22 | 34.17 | 36.60 |
| 8. | 2020. 9. 30. | 1.42% | -3.92% | 2.37 | 25.85 | -7.83 |
| 9. | 2020. 10. 31. | -3.29% | -2.77% | 10.01 | 15.43 | 12.43 |
| 10. | 2020. 11. 30. | 7.98% | 10.75% | 65.61 | 92.03 | 77.71 |
| 11. | 2020. 12. 31. | 1.47% | 3.71% | 2.52 | 6.51 | 4.05 |
| 12. | 2021. 1. 31. | -8.16% | -1.11% | 64.62 | 5.18 | 18.29 |
| 13. | 2021. 2. 28. | 0.96% | 2.61% | 1.18 | 2.10 | 1.57 |
| 14. | 2021. 3. 31. | 0.59% | 4.24% | 0.50 | 9.50 | 2.19 |
| 15. | 2021. 4. 30. | 9.15% | 5.24% | 85.90 | 16.66 | 37.83 |
| 16. | 2021. 5. 31. | 3.13% | 0.55% | 10.58 | 0.38 | -1.99 |
| 17. | 2021. 6. 30. | 3.88% | 2.22% | 15.99 | 1.12 | 4.24 |
| 18. | 2021. 7. 31. | 3.13% | 2.27% | 10.60 | 1.24 | 3.62 |
| 19. | 2021. 8. 31. | 9.76% | 2.90% | 97.64 | 3.02 | 17.17 |
| 20. | 2021. 9. 30. | -10.91% | -4.76% | 116.37 | 35.02 | 63.84 |
| 21. | 2021. 10. 31. | -7.24% | 6.91% | 50.65 | 33.10 | -40.94 |
| 22. | 2021. 11. 30. | -4.24% | -0.83% | 16.95 | 3.98 | 8.21 |
| 23. | 2021. 12. 31. | 0.88% | 4.36% | 1.01 | 10.24 | 3.21 |
| 24. | 2022. 1. 31. | -8.99% | -5.26% | 78.68 | 41.21 | 56.94 |
| 25. | 2022. 2. 28. | 1.42% | -3.14% | 2.39 | 18.47 | -6.64 |
| 26. | 2022. 3. 31. | -9.35% | 3.58% | 85.13 | 5.84 | -22.29 |
| 27. | 2022. 4. 30. | -21.45% | -8.80% | 454.98 | 99.14 | 212.38 |
| 28. | 2022. 5. 31. | 18.31% | 0.01% | 339.62 | 1.34 | -21.30 |
| 29. | 2022. 6. 30. | -7.58% | -8.39% | 55.54 | 91.26 | 71.19 |
| 30. | 2022. 7. 31. | -7.78% | 9.11% | 58.56 | 63.21 | -60.84 |
| 31. | 2022. 8. 31. | -4.51% | -4.24% | 19.21 | 29.22 | 23.69 |
| 32. | 2022. 9. 30. | -26.48% | -9.34% | 694.91 | 110.27 | 276.81 |
| 33. | 2022. 10. 31. | 21.19% | 7.99% | 454.09 | 46.58 | 145.44 |
| 34. | 2022. 11. 30. | 6.44% | 5.38% | 43.05 | 17.76 | 27.65 |
| 35. | 2022. 12. 31. | -13.34% | -5.90% | 174.64 | 49.82 | 93.28 |
| 36. | 2023. 1. 31. | 13.33% | 6.18% | 181.04 | 25.14 | 67.46 |
| 37. | 2023. 2. 28. | -4.35% | -2.61% | 17.83 | 14.23 | 15.93 |
| 38. | 2023. 3. 31. | -2.72% | 3.51% | 6.75 | 5.49 | -6.09 |
| 39. | 2023. 4. 30. | 3.10% | 1.46% | 10.39 | 0.09 | 0.98 |
| 40. | 2023. 5. 31. | -11.54% | 0.25% | 130.37 | 0.83 | 10.43 |
| 41. | 2023. 6. 30. | 12.64% | 4.71% | 162.84 | 12.62 | 45.33 |
| 42. | 2023. 7. 31. | 10.29% | 4.85% | 108.52 | 13.58 | 38.38 |
| 43. | 2023. 8. 31. | 8.13% | -1.77% | 68.06 | 8.60 | -24.20 |
| 44. | 2023. 9. 30. | 0.39% | -4.87% | 0.26 | 36.40 | -3.08 |
| 45. | 2023. 10. 31. | -8.42% | -2.20% | 68.80 | 11.28 | 27.86 |
| 46. | 2023. 11. 30. | -0.66% | 8.92% | 0.29 | 60.17 | -4.19 |
| 47. | 2023. 12. 31. | -2.86% | 4.42% | 7.50 | 10.64 | -8.93 |
| 48. | 2024. 1. 31. | -4.62% | 1.59% | 20.26 | 0.18 | -1.93 |
| 49. | 2024. 2. 29. | -20.71% | 5.17% | 423.91 | 16.09 | -82.58 |
| 50. | 2024. 3. 31. | -1.12% | 3.10% | 1.00 | 3.77 | -1.94 |
| 51. | 2024. 4. 30. | -11.94% | -4.16% | 139.56 | 28.33 | 62.88 |
| 52. | 2024. 5. 31. | 12.18% | 4.80% | 151.42 | 13.26 | 44.80 |
| 53. | 2024. 6. 30. | 4.12% | 3.47% | 18.03 | 5.32 | 9.79 |
| 54. | 2024. 7. 31. | 27.01% | 1.13% | 736.38 | 0.00 | -0.79 |
| 55. | 2024. 8. 31. | -8.47% | 2.28% | 69.76 | 1.26 | -9.37 |
| 56. | 2024. 9. 30. | -6.75% | 2.02% | 43.93 | 0.74 | -5.69 |
| 57. | 2024. 10. 31. | 1.09% | -0.99% | 1.47 | 4.63 | -2.61 |
| 58. | 2024. 11. 30. | 21.17% | 5.73% | 453.44 | 20.87 | 97.29 |
| 59. | 2024. 12. 31. | -13.65% | -2.50% | 183.08 | 13.40 | 49.53 |
| 합계 (Σ): | 6,722.49 | 1,618.62 | 1,802.15 | |||
모두 보기
분산CHTR = Σ(RCHTR,t–RCHTR)2 ÷ (59 – 1)
= 6,722.49 ÷ (59 – 1)
= 115.91
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산CHTR, S&P 500 = Σ(RCHTR,t–RCHTR)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,802.15 ÷ (59 – 1)
= 31.07
체계적인 위험 추정 (β)
| 분산CHTR | 115.91 |
| 분산S&P 500 | 27.91 |
| 공분산CHTR, S&P 500 | 31.07 |
| 상관 계수CHTR, S&P 5001 | 0.55 |
| βCHTR2 | 1.11 |
| αCHTR3 | -1.42% |
계산
1 상관 계수CHTR, S&P 500
= 공분산CHTR, S&P 500 ÷ (표준 편차CHTR × 표준 편차S&P 500)
= 31.07 ÷ (10.77% × 5.28%)
= 0.55
2 βCHTR
= 공분산CHTR, S&P 500 ÷ 분산S&P 500
= 31.07 ÷ 27.91
= 1.11
3 αCHTR
= 평균의CHTR – βCHTR × 평균의S&P 500
= -0.12% – 1.11 × 1.16%
= -1.42%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.84% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Charter | βCHTR | 1.11 |
| Charter 보통주의 예상 수익률3 | E(RCHTR) | 18.79% |
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(RCHTR) = RF + βCHTR [E(RM) – RF]
= 4.84% + 1.11 [17.37% – 4.84%]
= 18.79%