자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 TWC보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Time Warner Cable Inc., 월별 수익률
| Time Warner Cable Inc. (TWC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TWC,t1 | 피제수TWC,t1 | RTWC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $67.83 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $72.18 | $0.48 | 7.12% | 1,327.22 | 3.20% |
| 2. | 2011. 3. 31. | $71.34 | -1.16% | 1,325.83 | -0.10% | |
| 3. | 2011. 4. 30. | $78.13 | 9.52% | 1,363.61 | 2.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | $184.77 | -2.44% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $185.59 | $0.75 | 0.85% | 2,043.94 | -1.75% |
| 평균의 (R): | 2.12% | 0.84% | ||||
| 표준 편차: | 6.31% | 3.40% | ||||
| Time Warner Cable Inc. (TWC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TWC,t1 | 피제수TWC,t1 | RTWC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $67.83 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $72.18 | $0.48 | 7.12% | 1,327.22 | 3.20% |
| 2. | 2011. 3. 31. | $71.34 | -1.16% | 1,325.83 | -0.10% | |
| 3. | 2011. 4. 30. | $78.13 | 9.52% | 1,363.61 | 2.85% | |
| 4. | 2011. 5. 31. | $77.22 | $0.48 | -0.55% | 1,345.20 | -1.35% |
| 5. | 2011. 6. 30. | $78.04 | 1.06% | 1,320.64 | -1.83% | |
| 6. | 2011. 7. 31. | $73.31 | -6.06% | 1,292.28 | -2.15% | |
| 7. | 2011. 8. 31. | $65.50 | $0.48 | -10.00% | 1,218.89 | -5.68% |
| 8. | 2011. 9. 30. | $62.67 | -4.32% | 1,131.42 | -7.18% | |
| 9. | 2011. 10. 31. | $63.69 | 1.63% | 1,253.30 | 10.77% | |
| 10. | 2011. 11. 30. | $60.48 | $0.48 | -4.29% | 1,246.96 | -0.51% |
| 11. | 2011. 12. 31. | $63.57 | 5.11% | 1,257.60 | 0.85% | |
| 12. | 2012. 1. 31. | $73.72 | 15.97% | 1,312.41 | 4.36% | |
| 13. | 2012. 2. 29. | $79.34 | $0.56 | 8.38% | 1,365.68 | 4.06% |
| 14. | 2012. 3. 31. | $81.50 | 2.72% | 1,408.47 | 3.13% | |
| 15. | 2012. 4. 30. | $80.45 | -1.29% | 1,397.91 | -0.75% | |
| 16. | 2012. 5. 31. | $75.40 | $0.56 | -5.58% | 1,310.33 | -6.27% |
| 17. | 2012. 6. 30. | $82.10 | 8.89% | 1,362.16 | 3.96% | |
| 18. | 2012. 7. 31. | $84.93 | 3.45% | 1,379.32 | 1.26% | |
| 19. | 2012. 8. 31. | $88.82 | $0.56 | 5.24% | 1,406.58 | 1.98% |
| 20. | 2012. 9. 30. | $95.06 | 7.03% | 1,440.67 | 2.42% | |
| 21. | 2012. 10. 31. | $99.15 | 4.30% | 1,412.16 | -1.98% | |
| 22. | 2012. 11. 30. | $94.89 | $0.56 | -3.73% | 1,416.18 | 0.28% |
| 23. | 2012. 12. 31. | $97.19 | 2.42% | 1,426.19 | 0.71% | |
| 24. | 2013. 1. 31. | $89.34 | -8.08% | 1,498.11 | 5.04% | |
| 25. | 2013. 2. 28. | $86.39 | $0.65 | -2.57% | 1,514.68 | 1.11% |
| 26. | 2013. 3. 31. | $96.06 | 11.19% | 1,569.19 | 3.60% | |
| 27. | 2013. 4. 30. | $93.89 | -2.26% | 1,597.57 | 1.81% | |
| 28. | 2013. 5. 31. | $95.51 | $0.65 | 2.42% | 1,630.74 | 2.08% |
| 29. | 2013. 6. 30. | $112.48 | 17.77% | 1,606.28 | -1.50% | |
| 30. | 2013. 7. 31. | $114.07 | 1.41% | 1,685.73 | 4.95% | |
| 31. | 2013. 8. 31. | $107.35 | $0.65 | -5.32% | 1,632.97 | -3.13% |
| 32. | 2013. 9. 30. | $111.60 | 3.96% | 1,681.55 | 2.97% | |
| 33. | 2013. 10. 31. | $120.15 | 7.66% | 1,756.54 | 4.46% | |
| 34. | 2013. 11. 30. | $138.22 | $0.65 | 15.58% | 1,805.81 | 2.80% |
| 35. | 2013. 12. 31. | $135.50 | -1.97% | 1,848.36 | 2.36% | |
| 36. | 2014. 1. 31. | $133.27 | -1.65% | 1,782.59 | -3.56% | |
| 37. | 2014. 2. 28. | $140.35 | $0.75 | 5.88% | 1,859.45 | 4.31% |
| 38. | 2014. 3. 31. | $137.18 | -2.26% | 1,872.34 | 0.69% | |
| 39. | 2014. 4. 30. | $141.46 | 3.12% | 1,883.95 | 0.62% | |
| 40. | 2014. 5. 31. | $141.16 | $0.75 | 0.32% | 1,923.57 | 2.10% |
| 41. | 2014. 6. 30. | $147.30 | 4.35% | 1,960.23 | 1.91% | |
| 42. | 2014. 7. 31. | $145.10 | -1.49% | 1,930.67 | -1.51% | |
| 43. | 2014. 8. 31. | $147.93 | $0.75 | 2.47% | 2,003.37 | 3.77% |
| 44. | 2014. 9. 30. | $143.49 | -3.00% | 1,972.29 | -1.55% | |
| 45. | 2014. 10. 31. | $147.21 | 2.59% | 2,018.05 | 2.32% | |
| 46. | 2014. 11. 30. | $149.28 | $0.75 | 1.92% | 2,067.56 | 2.45% |
| 47. | 2014. 12. 31. | $152.06 | 1.86% | 2,058.90 | -0.42% | |
| 48. | 2015. 1. 31. | $136.13 | -10.48% | 1,994.99 | -3.10% | |
| 49. | 2015. 2. 28. | $154.05 | $0.75 | 13.71% | 2,104.50 | 5.49% |
| 50. | 2015. 3. 31. | $149.88 | $0.75 | -2.22% | 2,067.89 | -1.74% |
| 51. | 2015. 4. 30. | $155.52 | 3.76% | 2,085.51 | 0.85% | |
| 52. | 2015. 5. 31. | $180.89 | 16.31% | 2,107.39 | 1.05% | |
| 53. | 2015. 6. 30. | $178.17 | $0.75 | -1.09% | 2,063.11 | -2.10% |
| 54. | 2015. 7. 31. | $190.01 | 6.65% | 2,103.84 | 1.97% | |
| 55. | 2015. 8. 31. | $186.02 | -2.10% | 1,972.18 | -6.26% | |
| 56. | 2015. 9. 30. | $179.37 | $0.75 | -3.17% | 1,920.03 | -2.64% |
| 57. | 2015. 10. 31. | $189.40 | 5.59% | 2,079.36 | 8.30% | |
| 58. | 2015. 11. 30. | $184.77 | -2.44% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $185.59 | $0.75 | 0.85% | 2,043.94 | -1.75% |
| 평균의 (R): | 2.12% | 0.84% | ||||
| 표준 편차: | 6.31% | 3.40% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 TWC의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Time Warner Cable Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RTWC,t | RS&P 500,t | (RTWC,t–RTWC)2 | (RS&P 500,t–RS&P 500)2 | (RTWC,t–RTWC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 7.12% | 3.20% | 25.00 | 5.53 | 11.75 |
| 2. | 2011. 3. 31. | -1.16% | -0.10% | 10.79 | 0.90 | 3.12 |
| 3. | 2011. 4. 30. | 9.52% | 2.85% | 54.72 | 4.02 | 14.83 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | -2.44% | 0.05% | 20.84 | 0.63 | 3.63 |
| 59. | 2015. 12. 31. | 0.85% | -1.75% | 1.62 | 6.75 | 3.30 |
| 합계 (Σ): | 2,310.83 | 670.89 | 635.06 | |||
| t | 날짜 | RTWC,t | RS&P 500,t | (RTWC,t–RTWC)2 | (RS&P 500,t–RS&P 500)2 | (RTWC,t–RTWC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 7.12% | 3.20% | 25.00 | 5.53 | 11.75 |
| 2. | 2011. 3. 31. | -1.16% | -0.10% | 10.79 | 0.90 | 3.12 |
| 3. | 2011. 4. 30. | 9.52% | 2.85% | 54.72 | 4.02 | 14.83 |
| 4. | 2011. 5. 31. | -0.55% | -1.35% | 7.13 | 4.82 | 5.86 |
| 5. | 2011. 6. 30. | 1.06% | -1.83% | 1.12 | 7.13 | 2.83 |
| 6. | 2011. 7. 31. | -6.06% | -2.15% | 66.94 | 8.95 | 24.48 |
| 7. | 2011. 8. 31. | -10.00% | -5.68% | 146.88 | 42.56 | 79.06 |
| 8. | 2011. 9. 30. | -4.32% | -7.18% | 41.49 | 64.34 | 51.67 |
| 9. | 2011. 10. 31. | 1.63% | 10.77% | 0.24 | 98.56 | -4.90 |
| 10. | 2011. 11. 30. | -4.29% | -0.51% | 41.05 | 1.82 | 8.65 |
| 11. | 2011. 12. 31. | 5.11% | 0.85% | 8.93 | 0.00 | 0.03 |
| 12. | 2012. 1. 31. | 15.97% | 4.36% | 191.71 | 12.35 | 48.65 |
| 13. | 2012. 2. 29. | 8.38% | 4.06% | 39.22 | 10.33 | 20.13 |
| 14. | 2012. 3. 31. | 2.72% | 3.13% | 0.36 | 5.24 | 1.38 |
| 15. | 2012. 4. 30. | -1.29% | -0.75% | 11.62 | 2.54 | 5.44 |
| 16. | 2012. 5. 31. | -5.58% | -6.27% | 59.32 | 50.55 | 54.76 |
| 17. | 2012. 6. 30. | 8.89% | 3.96% | 45.77 | 9.68 | 21.04 |
| 18. | 2012. 7. 31. | 3.45% | 1.26% | 1.76 | 0.17 | 0.55 |
| 19. | 2012. 8. 31. | 5.24% | 1.98% | 9.73 | 1.28 | 3.53 |
| 20. | 2012. 9. 30. | 7.03% | 2.42% | 24.06 | 2.49 | 7.74 |
| 21. | 2012. 10. 31. | 4.30% | -1.98% | 4.76 | 7.97 | -6.16 |
| 22. | 2012. 11. 30. | -3.73% | 0.28% | 34.25 | 0.31 | 3.28 |
| 23. | 2012. 12. 31. | 2.42% | 0.71% | 0.09 | 0.02 | -0.04 |
| 24. | 2013. 1. 31. | -8.08% | 5.04% | 103.99 | 17.62 | -42.81 |
| 25. | 2013. 2. 28. | -2.57% | 1.11% | 22.04 | 0.07 | -1.23 |
| 26. | 2013. 3. 31. | 11.19% | 3.60% | 82.31 | 7.58 | 24.99 |
| 27. | 2013. 4. 30. | -2.26% | 1.81% | 19.18 | 0.93 | -4.22 |
| 28. | 2013. 5. 31. | 2.42% | 2.08% | 0.09 | 1.52 | 0.37 |
| 29. | 2013. 6. 30. | 17.77% | -1.50% | 244.83 | 5.50 | -36.69 |
| 30. | 2013. 7. 31. | 1.41% | 4.95% | 0.50 | 16.82 | -2.90 |
| 31. | 2013. 8. 31. | -5.32% | -3.13% | 55.38 | 15.80 | 29.58 |
| 32. | 2013. 9. 30. | 3.96% | 2.97% | 3.38 | 4.54 | 3.92 |
| 33. | 2013. 10. 31. | 7.66% | 4.46% | 30.70 | 13.07 | 20.03 |
| 34. | 2013. 11. 30. | 15.58% | 2.80% | 181.17 | 3.84 | 26.38 |
| 35. | 2013. 12. 31. | -1.97% | 2.36% | 16.72 | 2.28 | -6.18 |
| 36. | 2014. 1. 31. | -1.65% | -3.56% | 14.19 | 19.39 | 16.58 |
| 37. | 2014. 2. 28. | 5.88% | 4.31% | 14.10 | 12.02 | 13.02 |
| 38. | 2014. 3. 31. | -2.26% | 0.69% | 19.18 | 0.02 | 0.66 |
| 39. | 2014. 4. 30. | 3.12% | 0.62% | 1.00 | 0.05 | -0.22 |
| 40. | 2014. 5. 31. | 0.32% | 2.10% | 3.25 | 1.58 | -2.27 |
| 41. | 2014. 6. 30. | 4.35% | 1.91% | 4.97 | 1.13 | 2.37 |
| 42. | 2014. 7. 31. | -1.49% | -1.51% | 13.06 | 5.54 | 8.50 |
| 43. | 2014. 8. 31. | 2.47% | 3.77% | 0.12 | 8.53 | 1.01 |
| 44. | 2014. 9. 30. | -3.00% | -1.55% | 26.24 | 5.74 | 12.27 |
| 45. | 2014. 10. 31. | 2.59% | 2.32% | 0.22 | 2.18 | 0.70 |
| 46. | 2014. 11. 30. | 1.92% | 2.45% | 0.04 | 2.59 | -0.33 |
| 47. | 2014. 12. 31. | 1.86% | -0.42% | 0.07 | 1.60 | 0.33 |
| 48. | 2015. 1. 31. | -10.48% | -3.10% | 158.68 | 15.59 | 49.74 |
| 49. | 2015. 2. 28. | 13.71% | 5.49% | 134.42 | 21.57 | 53.85 |
| 50. | 2015. 3. 31. | -2.22% | -1.74% | 18.84 | 6.68 | 11.22 |
| 51. | 2015. 4. 30. | 3.76% | 0.85% | 2.70 | 0.00 | 0.01 |
| 52. | 2015. 5. 31. | 16.31% | 1.05% | 201.42 | 0.04 | 2.90 |
| 53. | 2015. 6. 30. | -1.09% | -2.10% | 10.30 | 8.68 | 9.46 |
| 54. | 2015. 7. 31. | 6.65% | 1.97% | 20.47 | 1.28 | 5.11 |
| 55. | 2015. 8. 31. | -2.10% | -6.26% | 17.81 | 50.45 | 29.98 |
| 56. | 2015. 9. 30. | -3.17% | -2.64% | 28.01 | 12.17 | 18.47 |
| 57. | 2015. 10. 31. | 5.59% | 8.30% | 12.05 | 55.56 | 25.87 |
| 58. | 2015. 11. 30. | -2.44% | 0.05% | 20.84 | 0.63 | 3.63 |
| 59. | 2015. 12. 31. | 0.85% | -1.75% | 1.62 | 6.75 | 3.30 |
| 합계 (Σ): | 2,310.83 | 670.89 | 635.06 | |||
모두 표시
분산TWC = Σ(RTWC,t–RTWC)2 ÷ (59 – 1)
= 2,310.83 ÷ (59 – 1)
= 39.84
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 670.89 ÷ (59 – 1)
= 11.57
공분산TWC, S&P 500 = Σ(RTWC,t–RTWC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 635.06 ÷ (59 – 1)
= 10.95
체계적인 위험 추정 (β)
| 분산TWC | 39.84 |
| 분산S&P 500 | 11.57 |
| 공분산TWC, S&P 500 | 10.95 |
| 상관 계수TWC, S&P 5001 | 0.51 |
| βTWC2 | 0.95 |
| αTWC3 | 1.32% |
계산
1 상관 계수TWC, S&P 500
= 공분산TWC, S&P 500 ÷ (표준 편차TWC × 표준 편차S&P 500)
= 10.95 ÷ (6.31% × 3.40%)
= 0.51
2 βTWC
= 공분산TWC, S&P 500 ÷ 분산S&P 500
= 10.95 ÷ 11.57
= 0.95
3 αTWC
= 평균의TWC – βTWC × 평균의S&P 500
= 2.12% – 0.95 × 0.84%
= 1.32%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.42% |
| 보통주의 체계적 위험TWC | βTWC | 0.95 |
| TWC 보통주의 예상 수익률3 | E(RTWC) | 12.95% |
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(RTWC) = RF + βTWC [E(RM) – RF]
= 4.67% + 0.95 [13.42% – 4.67%]
= 12.95%