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 |
| 2019. 1. 31. | $331.05 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $344.91 | 4.19% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $346.91 | 0.58% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $371.19 | 7.00% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $400.13 | -0.66% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $388.68 | -2.86% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.69% | 1.11% | ||||
| 표준 편차: | 9.13% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $331.05 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $344.91 | 4.19% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $346.91 | 0.58% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $371.19 | 7.00% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $376.80 | 1.51% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $395.18 | 4.88% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $385.38 | -2.48% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $409.59 | 6.28% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $412.12 | 0.62% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $467.86 | 13.53% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $470.01 | 0.46% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $485.08 | 3.21% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $517.46 | 6.68% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $493.17 | -4.69% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $436.31 | -11.53% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $495.23 | 13.50% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $544.00 | 9.85% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $510.04 | -6.24% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $580.00 | 13.72% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $615.61 | 6.14% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $624.34 | 1.42% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $603.82 | -3.29% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $651.99 | 7.98% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $661.55 | 1.47% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $607.56 | -8.16% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $613.42 | 0.96% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $617.02 | 0.59% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $673.45 | 9.15% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $694.53 | 3.13% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $721.45 | 3.88% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $744.05 | 3.13% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $816.66 | 9.76% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $727.56 | -10.91% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $674.89 | -7.24% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $646.28 | -4.24% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $651.97 | 0.88% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $593.34 | -8.99% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $601.78 | 1.42% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $545.52 | -9.35% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $428.49 | -21.45% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $506.93 | 18.31% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $468.53 | -7.58% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $432.10 | -7.78% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $412.63 | -4.51% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $303.35 | -26.48% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $367.62 | 21.19% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $391.29 | 6.44% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $339.10 | -13.34% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $384.31 | 13.33% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $367.61 | -4.35% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $357.61 | -2.72% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $368.70 | 3.10% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $326.15 | -11.54% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $367.37 | 12.64% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $405.19 | 10.29% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $438.12 | 8.13% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $439.82 | 0.39% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $402.80 | -8.42% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $400.13 | -0.66% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $388.68 | -2.86% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.69% | 1.11% | ||||
| 표준 편차: | 9.13% | 5.31% | ||||
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. | 2019. 2. 28. | 4.19% | 2.97% | 12.20 | 3.49 | 6.52 |
| 2. | 2019. 3. 31. | 0.58% | 1.79% | 0.01 | 0.47 | -0.08 |
| 3. | 2019. 4. 30. | 7.00% | 3.93% | 39.76 | 7.98 | 17.82 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -0.66% | 8.92% | 1.84 | 61.03 | -10.59 |
| 59. | 2023. 12. 31. | -2.86% | 4.42% | 12.64 | 11.00 | -11.79 |
| 합계 (Σ): | 4,829.48 | 1,634.30 | 1,680.45 | |||
| 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. | 2019. 2. 28. | 4.19% | 2.97% | 12.20 | 3.49 | 6.52 |
| 2. | 2019. 3. 31. | 0.58% | 1.79% | 0.01 | 0.47 | -0.08 |
| 3. | 2019. 4. 30. | 7.00% | 3.93% | 39.76 | 7.98 | 17.82 |
| 4. | 2019. 5. 31. | 1.51% | -6.58% | 0.67 | 59.04 | -6.29 |
| 5. | 2019. 6. 30. | 4.88% | 6.89% | 17.51 | 33.49 | 24.22 |
| 6. | 2019. 7. 31. | -2.48% | 1.31% | 10.07 | 0.04 | -0.66 |
| 7. | 2019. 8. 31. | 6.28% | -1.81% | 31.24 | 8.50 | -16.29 |
| 8. | 2019. 9. 30. | 0.62% | 1.72% | 0.01 | 0.37 | -0.05 |
| 9. | 2019. 10. 31. | 13.53% | 2.04% | 164.66 | 0.88 | 12.03 |
| 10. | 2019. 11. 30. | 0.46% | 3.40% | 0.05 | 5.28 | -0.54 |
| 11. | 2019. 12. 31. | 3.21% | 2.86% | 6.32 | 3.07 | 4.41 |
| 12. | 2020. 1. 31. | 6.68% | -0.16% | 35.78 | 1.61 | -7.59 |
| 13. | 2020. 2. 29. | -4.69% | -8.41% | 29.02 | 90.57 | 51.27 |
| 14. | 2020. 3. 31. | -11.53% | -12.51% | 149.39 | 185.44 | 166.45 |
| 15. | 2020. 4. 30. | 13.50% | 12.68% | 164.12 | 134.06 | 148.33 |
| 16. | 2020. 5. 31. | 9.85% | 4.53% | 83.81 | 11.71 | 31.33 |
| 17. | 2020. 6. 30. | -6.24% | 1.84% | 48.11 | 0.54 | -5.08 |
| 18. | 2020. 7. 31. | 13.72% | 5.51% | 169.61 | 19.40 | 57.36 |
| 19. | 2020. 8. 31. | 6.14% | 7.01% | 29.66 | 34.82 | 32.14 |
| 20. | 2020. 9. 30. | 1.42% | -3.92% | 0.53 | 25.29 | -3.65 |
| 21. | 2020. 10. 31. | -3.29% | -2.77% | 15.84 | 15.00 | 15.41 |
| 22. | 2020. 11. 30. | 7.98% | 10.75% | 53.06 | 93.10 | 70.28 |
| 23. | 2020. 12. 31. | 1.47% | 3.71% | 0.60 | 6.79 | 2.01 |
| 24. | 2021. 1. 31. | -8.16% | -1.11% | 78.40 | 4.93 | 19.65 |
| 25. | 2021. 2. 28. | 0.96% | 2.61% | 0.07 | 2.26 | 0.41 |
| 26. | 2021. 3. 31. | 0.59% | 4.24% | 0.01 | 9.85 | -0.33 |
| 27. | 2021. 4. 30. | 9.15% | 5.24% | 71.44 | 17.11 | 34.96 |
| 28. | 2021. 5. 31. | 3.13% | 0.55% | 5.94 | 0.31 | -1.36 |
| 29. | 2021. 6. 30. | 3.88% | 2.22% | 10.13 | 1.24 | 3.55 |
| 30. | 2021. 7. 31. | 3.13% | 2.27% | 5.95 | 1.37 | 2.85 |
| 31. | 2021. 8. 31. | 9.76% | 2.90% | 82.18 | 3.22 | 16.26 |
| 32. | 2021. 9. 30. | -10.91% | -4.76% | 134.64 | 34.37 | 68.03 |
| 33. | 2021. 10. 31. | -7.24% | 6.91% | 62.92 | 33.74 | -46.08 |
| 34. | 2021. 11. 30. | -4.24% | -0.83% | 24.33 | 3.76 | 9.57 |
| 35. | 2021. 12. 31. | 0.88% | 4.36% | 0.04 | 10.60 | 0.61 |
| 36. | 2022. 1. 31. | -8.99% | -5.26% | 93.82 | 40.51 | 61.64 |
| 37. | 2022. 2. 28. | 1.42% | -3.14% | 0.53 | 17.99 | -3.09 |
| 38. | 2022. 3. 31. | -9.35% | 3.58% | 100.84 | 6.11 | -24.82 |
| 39. | 2022. 4. 30. | -21.45% | -8.80% | 490.45 | 98.04 | 219.28 |
| 40. | 2022. 5. 31. | 18.31% | 0.01% | 310.22 | 1.21 | -19.38 |
| 41. | 2022. 6. 30. | -7.58% | -8.39% | 68.36 | 90.21 | 78.53 |
| 42. | 2022. 7. 31. | -7.78% | 9.11% | 71.72 | 64.09 | -67.80 |
| 43. | 2022. 8. 31. | -4.51% | -4.24% | 27.03 | 28.62 | 27.81 |
| 44. | 2022. 9. 30. | -26.48% | -9.34% | 738.59 | 109.11 | 283.87 |
| 45. | 2022. 10. 31. | 21.19% | 7.99% | 419.99 | 47.34 | 141.01 |
| 46. | 2022. 11. 30. | 6.44% | 5.38% | 33.01 | 18.23 | 24.53 |
| 47. | 2022. 12. 31. | -13.34% | -5.90% | 196.87 | 49.04 | 98.26 |
| 48. | 2023. 1. 31. | 13.33% | 6.18% | 159.75 | 25.70 | 64.07 |
| 49. | 2023. 2. 28. | -4.35% | -2.61% | 25.39 | 13.82 | 18.73 |
| 50. | 2023. 3. 31. | -2.72% | 3.51% | 11.65 | 5.76 | -8.19 |
| 51. | 2023. 4. 30. | 3.10% | 1.46% | 5.80 | 0.13 | 0.86 |
| 52. | 2023. 5. 31. | -11.54% | 0.25% | 149.66 | 0.74 | 10.49 |
| 53. | 2023. 6. 30. | 12.64% | 4.71% | 142.69 | 13.02 | 43.10 |
| 54. | 2023. 7. 31. | 10.29% | 4.85% | 92.19 | 13.99 | 35.91 |
| 55. | 2023. 8. 31. | 8.13% | -1.77% | 55.26 | 8.28 | -21.39 |
| 56. | 2023. 9. 30. | 0.39% | -4.87% | 0.09 | 35.73 | 1.82 |
| 57. | 2023. 10. 31. | -8.42% | -2.20% | 83.00 | 10.92 | 30.10 |
| 58. | 2023. 11. 30. | -0.66% | 8.92% | 1.84 | 61.03 | -10.59 |
| 59. | 2023. 12. 31. | -2.86% | 4.42% | 12.64 | 11.00 | -11.79 |
| 합계 (Σ): | 4,829.48 | 1,634.30 | 1,680.45 | |||
모두 보기
분산CHTR = Σ(RCHTR,t–RCHTR)2 ÷ (59 – 1)
= 4,829.48 ÷ (59 – 1)
= 83.27
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산CHTR, S&P 500 = Σ(RCHTR,t–RCHTR)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,680.45 ÷ (59 – 1)
= 28.97
체계적인 위험 추정 (β)
| 분산CHTR | 83.27 |
| 분산S&P 500 | 28.18 |
| 공분산CHTR, S&P 500 | 28.97 |
| 상관 계수CHTR, S&P 5001 | 0.60 |
| βCHTR2 | 1.03 |
| αCHTR3 | -0.44% |
계산
1 상관 계수CHTR, S&P 500
= 공분산CHTR, S&P 500 ÷ (표준 편차CHTR × 표준 편차S&P 500)
= 28.97 ÷ (9.13% × 5.31%)
= 0.60
2 βCHTR
= 공분산CHTR, S&P 500 ÷ 분산S&P 500
= 28.97 ÷ 28.18
= 1.03
3 αCHTR
= 평균의CHTR – βCHTR × 평균의S&P 500
= 0.69% – 1.03 × 1.11%
= -0.44%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.94% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험Charter | βCHTR | 1.03 |
| Charter 보통주의 예상 수익률3 | E(RCHTR) | 15.12% |
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(RCHTR) = RF + βCHTR [E(RM) – RF]
= 4.94% + 1.03 [14.84% – 4.94%]
= 15.12%