자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Time Warner보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Time Warner Inc., 월별 수익률
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TWX,t1 | 피제수TWX,t1 | RTWX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2013. 1. 31. | $50.52 | 1,498.11 | ||||
| 1. | 2013. 2. 28. | $53.17 | $0.2875 | 5.81% | 1,514.68 | 1.11% |
| 2. | 2013. 3. 31. | $57.62 | 8.37% | 1,569.19 | 3.60% | |
| 3. | 2013. 4. 30. | $59.78 | 3.75% | 1,597.57 | 1.81% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2017. 11. 30. | $91.51 | -6.90% | 2,647.58 | 2.81% | |
| 59. | 2017. 12. 31. | $91.47 | -0.04% | 2,673.61 | 0.98% | |
| 평균의 (R): | 1.35% | 1.02% | ||||
| 표준 편차: | 6.00% | 2.71% | ||||
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TWX,t1 | 피제수TWX,t1 | RTWX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2013. 1. 31. | $50.52 | 1,498.11 | ||||
| 1. | 2013. 2. 28. | $53.17 | $0.2875 | 5.81% | 1,514.68 | 1.11% |
| 2. | 2013. 3. 31. | $57.62 | 8.37% | 1,569.19 | 3.60% | |
| 3. | 2013. 4. 30. | $59.78 | 3.75% | 1,597.57 | 1.81% | |
| 4. | 2013. 5. 31. | $58.37 | $0.2875 | -1.88% | 1,630.74 | 2.08% |
| 5. | 2013. 6. 30. | $57.82 | -0.94% | 1,606.28 | -1.50% | |
| 6. | 2013. 7. 31. | $62.26 | 7.68% | 1,685.73 | 4.95% | |
| 7. | 2013. 8. 31. | $60.53 | $0.2875 | -2.32% | 1,632.97 | -3.13% |
| 8. | 2013. 9. 30. | $65.81 | 8.72% | 1,681.55 | 2.97% | |
| 9. | 2013. 10. 31. | $68.74 | 4.45% | 1,756.54 | 4.46% | |
| 10. | 2013. 11. 30. | $65.71 | $0.2875 | -3.99% | 1,805.81 | 2.80% |
| 11. | 2013. 12. 31. | $69.72 | 6.10% | 1,848.36 | 2.36% | |
| 12. | 2014. 1. 31. | $62.83 | -9.88% | 1,782.59 | -3.56% | |
| 13. | 2014. 2. 28. | $67.13 | $0.3175 | 7.35% | 1,859.45 | 4.31% |
| 14. | 2014. 3. 31. | $65.33 | -2.68% | 1,872.34 | 0.69% | |
| 15. | 2014. 4. 30. | $66.46 | 1.73% | 1,883.95 | 0.62% | |
| 16. | 2014. 5. 31. | $69.83 | $0.3175 | 5.55% | 1,923.57 | 2.10% |
| 17. | 2014. 6. 30. | $70.25 | 0.60% | 1,960.23 | 1.91% | |
| 18. | 2014. 7. 31. | $83.02 | 18.18% | 1,930.67 | -1.51% | |
| 19. | 2014. 8. 31. | $77.03 | $0.3175 | -6.83% | 2,003.37 | 3.77% |
| 20. | 2014. 9. 30. | $75.21 | -2.36% | 1,972.29 | -1.55% | |
| 21. | 2014. 10. 31. | $79.47 | 5.66% | 2,018.05 | 2.32% | |
| 22. | 2014. 11. 30. | $85.12 | $0.3175 | 7.51% | 2,067.56 | 2.45% |
| 23. | 2014. 12. 31. | $85.42 | 0.35% | 2,058.90 | -0.42% | |
| 24. | 2015. 1. 31. | $77.93 | -8.77% | 1,994.99 | -3.10% | |
| 25. | 2015. 2. 28. | $81.86 | $0.35 | 5.49% | 2,104.50 | 5.49% |
| 26. | 2015. 3. 31. | $84.44 | 3.15% | 2,067.89 | -1.74% | |
| 27. | 2015. 4. 30. | $84.41 | -0.04% | 2,085.51 | 0.85% | |
| 28. | 2015. 5. 31. | $84.48 | $0.35 | 0.50% | 2,107.39 | 1.05% |
| 29. | 2015. 6. 30. | $87.41 | 3.47% | 2,063.11 | -2.10% | |
| 30. | 2015. 7. 31. | $88.04 | 0.72% | 2,103.84 | 1.97% | |
| 31. | 2015. 8. 31. | $71.10 | $0.35 | -18.84% | 1,972.18 | -6.26% |
| 32. | 2015. 9. 30. | $68.75 | -3.31% | 1,920.03 | -2.64% | |
| 33. | 2015. 10. 31. | $75.34 | 9.59% | 2,079.36 | 8.30% | |
| 34. | 2015. 11. 30. | $69.98 | $0.35 | -6.65% | 2,080.41 | 0.05% |
| 35. | 2015. 12. 31. | $64.67 | -7.59% | 2,043.94 | -1.75% | |
| 36. | 2016. 1. 31. | $70.44 | 8.92% | 1,940.24 | -5.07% | |
| 37. | 2016. 2. 29. | $66.20 | $0.4025 | -5.45% | 1,932.23 | -0.41% |
| 38. | 2016. 3. 31. | $72.55 | 9.59% | 2,059.74 | 6.60% | |
| 39. | 2016. 4. 30. | $75.14 | 3.57% | 2,065.30 | 0.27% | |
| 40. | 2016. 5. 31. | $75.66 | $0.4025 | 1.23% | 2,096.95 | 1.53% |
| 41. | 2016. 6. 30. | $73.54 | -2.80% | 2,098.86 | 0.09% | |
| 42. | 2016. 7. 31. | $76.65 | 4.23% | 2,173.60 | 3.56% | |
| 43. | 2016. 8. 31. | $78.41 | $0.4025 | 2.82% | 2,170.95 | -0.12% |
| 44. | 2016. 9. 30. | $79.61 | 1.53% | 2,168.27 | -0.12% | |
| 45. | 2016. 10. 31. | $88.99 | 11.78% | 2,126.15 | -1.94% | |
| 46. | 2016. 11. 30. | $91.82 | $0.4025 | 3.63% | 2,198.81 | 3.42% |
| 47. | 2016. 12. 31. | $96.53 | 5.13% | 2,238.83 | 1.82% | |
| 48. | 2017. 1. 31. | $96.85 | 0.33% | 2,278.87 | 1.79% | |
| 49. | 2017. 2. 28. | $98.21 | $0.4025 | 1.82% | 2,363.64 | 3.72% |
| 50. | 2017. 3. 31. | $97.71 | -0.51% | 2,362.72 | -0.04% | |
| 51. | 2017. 4. 30. | $99.27 | 1.60% | 2,384.20 | 0.91% | |
| 52. | 2017. 5. 31. | $99.49 | $0.4025 | 0.63% | 2,411.80 | 1.16% |
| 53. | 2017. 6. 30. | $100.41 | 0.92% | 2,423.41 | 0.48% | |
| 54. | 2017. 7. 31. | $102.42 | $0.4025 | 2.40% | 2,470.30 | 1.93% |
| 55. | 2017. 8. 31. | $101.10 | -1.29% | 2,471.65 | 0.05% | |
| 56. | 2017. 9. 30. | $102.45 | 1.34% | 2,519.36 | 1.93% | |
| 57. | 2017. 10. 31. | $98.29 | $0.4025 | -3.67% | 2,575.26 | 2.22% |
| 58. | 2017. 11. 30. | $91.51 | -6.90% | 2,647.58 | 2.81% | |
| 59. | 2017. 12. 31. | $91.47 | -0.04% | 2,673.61 | 0.98% | |
| 평균의 (R): | 1.35% | 1.02% | ||||
| 표준 편차: | 6.00% | 2.71% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 TWX의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Time Warner Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013. 2. 28. | 5.81% | 1.11% | 19.96 | 0.01 | 0.37 |
| 2. | 2013. 3. 31. | 8.37% | 3.60% | 49.31 | 6.64 | 18.09 |
| 3. | 2013. 4. 30. | 3.75% | 1.81% | 5.77 | 0.62 | 1.89 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2017. 11. 30. | -6.90% | 2.81% | 67.98 | 3.19 | -14.73 |
| 59. | 2017. 12. 31. | -0.04% | 0.98% | 1.93 | 0.00 | 0.05 |
| 합계 (Σ): | 2,090.08 | 424.45 | 406.20 | |||
| t | 날짜 | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2013. 2. 28. | 5.81% | 1.11% | 19.96 | 0.01 | 0.37 |
| 2. | 2013. 3. 31. | 8.37% | 3.60% | 49.31 | 6.64 | 18.09 |
| 3. | 2013. 4. 30. | 3.75% | 1.81% | 5.77 | 0.62 | 1.89 |
| 4. | 2013. 5. 31. | -1.88% | 2.08% | 10.40 | 1.11 | -3.40 |
| 5. | 2013. 6. 30. | -0.94% | -1.50% | 5.24 | 6.36 | 5.77 |
| 6. | 2013. 7. 31. | 7.68% | 4.95% | 40.09 | 15.40 | 24.85 |
| 7. | 2013. 8. 31. | -2.32% | -3.13% | 13.42 | 17.24 | 15.21 |
| 8. | 2013. 9. 30. | 8.72% | 2.97% | 54.40 | 3.81 | 14.40 |
| 9. | 2013. 10. 31. | 4.45% | 4.46% | 9.64 | 11.81 | 10.67 |
| 10. | 2013. 11. 30. | -3.99% | 2.80% | 28.48 | 3.18 | -9.51 |
| 11. | 2013. 12. 31. | 6.10% | 2.36% | 22.61 | 1.78 | 6.34 |
| 12. | 2014. 1. 31. | -9.88% | -3.56% | 126.10 | 20.98 | 51.44 |
| 13. | 2014. 2. 28. | 7.35% | 4.31% | 36.03 | 10.82 | 19.74 |
| 14. | 2014. 3. 31. | -2.68% | 0.69% | 16.23 | 0.11 | 1.33 |
| 15. | 2014. 4. 30. | 1.73% | 0.62% | 0.15 | 0.16 | -0.15 |
| 16. | 2014. 5. 31. | 5.55% | 2.10% | 17.65 | 1.17 | 4.54 |
| 17. | 2014. 6. 30. | 0.60% | 1.91% | 0.56 | 0.78 | -0.66 |
| 18. | 2014. 7. 31. | 18.18% | -1.51% | 283.28 | 6.40 | -42.59 |
| 19. | 2014. 8. 31. | -6.83% | 3.77% | 66.91 | 7.53 | -22.44 |
| 20. | 2014. 9. 30. | -2.36% | -1.55% | 13.76 | 6.62 | 9.55 |
| 21. | 2014. 10. 31. | 5.66% | 2.32% | 18.64 | 1.68 | 5.60 |
| 22. | 2014. 11. 30. | 7.51% | 2.45% | 37.97 | 2.05 | 8.82 |
| 23. | 2014. 12. 31. | 0.35% | -0.42% | 0.99 | 2.08 | 1.43 |
| 24. | 2015. 1. 31. | -8.77% | -3.10% | 102.32 | 17.03 | 41.74 |
| 25. | 2015. 2. 28. | 5.49% | 5.49% | 17.18 | 19.95 | 18.52 |
| 26. | 2015. 3. 31. | 3.15% | -1.74% | 3.26 | 7.63 | -4.98 |
| 27. | 2015. 4. 30. | -0.04% | 0.85% | 1.91 | 0.03 | 0.24 |
| 28. | 2015. 5. 31. | 0.50% | 1.05% | 0.72 | 0.00 | -0.02 |
| 29. | 2015. 6. 30. | 3.47% | -2.10% | 4.50 | 9.76 | -6.63 |
| 30. | 2015. 7. 31. | 0.72% | 1.97% | 0.39 | 0.91 | -0.60 |
| 31. | 2015. 8. 31. | -18.84% | -6.26% | 407.67 | 53.00 | 147.00 |
| 32. | 2015. 9. 30. | -3.31% | -2.64% | 21.64 | 13.44 | 17.06 |
| 33. | 2015. 10. 31. | 9.59% | 8.30% | 67.87 | 52.94 | 59.94 |
| 34. | 2015. 11. 30. | -6.65% | 0.05% | 63.95 | 0.94 | 7.77 |
| 35. | 2015. 12. 31. | -7.59% | -1.75% | 79.83 | 7.70 | 24.80 |
| 36. | 2016. 1. 31. | 8.92% | -5.07% | 57.38 | 37.16 | -46.18 |
| 37. | 2016. 2. 29. | -5.45% | -0.41% | 46.17 | 2.06 | 9.75 |
| 38. | 2016. 3. 31. | 9.59% | 6.60% | 67.98 | 31.10 | 45.98 |
| 39. | 2016. 4. 30. | 3.57% | 0.27% | 4.94 | 0.57 | -1.67 |
| 40. | 2016. 5. 31. | 1.23% | 1.53% | 0.01 | 0.26 | -0.06 |
| 41. | 2016. 6. 30. | -2.80% | 0.09% | 17.22 | 0.87 | 3.86 |
| 42. | 2016. 7. 31. | 4.23% | 3.56% | 8.31 | 6.44 | 7.32 |
| 43. | 2016. 8. 31. | 2.82% | -0.12% | 2.17 | 1.31 | -1.69 |
| 44. | 2016. 9. 30. | 1.53% | -0.12% | 0.03 | 1.31 | -0.21 |
| 45. | 2016. 10. 31. | 11.78% | -1.94% | 108.90 | 8.79 | -30.94 |
| 46. | 2016. 11. 30. | 3.63% | 3.42% | 5.22 | 5.74 | 5.47 |
| 47. | 2016. 12. 31. | 5.13% | 1.82% | 14.31 | 0.64 | 3.02 |
| 48. | 2017. 1. 31. | 0.33% | 1.79% | 1.03 | 0.59 | -0.78 |
| 49. | 2017. 2. 28. | 1.82% | 3.72% | 0.22 | 7.28 | 1.28 |
| 50. | 2017. 3. 31. | -0.51% | -0.04% | 3.45 | 1.13 | 1.97 |
| 51. | 2017. 4. 30. | 1.60% | 0.91% | 0.06 | 0.01 | -0.03 |
| 52. | 2017. 5. 31. | 0.63% | 1.16% | 0.52 | 0.02 | -0.10 |
| 53. | 2017. 6. 30. | 0.92% | 0.48% | 0.18 | 0.29 | 0.23 |
| 54. | 2017. 7. 31. | 2.40% | 1.93% | 1.11 | 0.83 | 0.96 |
| 55. | 2017. 8. 31. | -1.29% | 0.05% | 6.95 | 0.94 | 2.55 |
| 56. | 2017. 9. 30. | 1.34% | 1.93% | 0.00 | 0.82 | -0.01 |
| 57. | 2017. 10. 31. | -3.67% | 2.22% | 25.15 | 1.43 | -6.00 |
| 58. | 2017. 11. 30. | -6.90% | 2.81% | 67.98 | 3.19 | -14.73 |
| 59. | 2017. 12. 31. | -0.04% | 0.98% | 1.93 | 0.00 | 0.05 |
| 합계 (Σ): | 2,090.08 | 424.45 | 406.20 | |||
모두 보기
분산TWX = Σ(RTWX,t–RTWX)2 ÷ (59 – 1)
= 2,090.08 ÷ (59 – 1)
= 36.04
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 424.45 ÷ (59 – 1)
= 7.32
공분산TWX, S&P 500 = Σ(RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 406.20 ÷ (59 – 1)
= 7.00
체계적인 위험 추정 (β)
| 분산TWX | 36.04 |
| 분산S&P 500 | 7.32 |
| 공분산TWX, S&P 500 | 7.00 |
| 상관 계수TWX, S&P 5001 | 0.43 |
| βTWX2 | 0.96 |
| αTWX3 | 0.37% |
계산
1 상관 계수TWX, S&P 500
= 공분산TWX, S&P 500 ÷ (표준 편차TWX × 표준 편차S&P 500)
= 7.00 ÷ (6.00% × 2.71%)
= 0.43
2 βTWX
= 공분산TWX, S&P 500 ÷ 분산S&P 500
= 7.00 ÷ 7.32
= 0.96
3 αTWX
= 평균의TWX – βTWX × 평균의S&P 500
= 1.35% – 0.96 × 1.02%
= 0.37%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Time Warner | βTWX | 0.96 |
| Time Warner 보통주의 예상 수익률3 | E(RTWX) | 13.39% |
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(RTWX) = RF + βTWX [E(RM) – RF]
= 4.67% + 0.96 [13.79% – 4.67%]
= 13.39%