자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Yahoo보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Yahoo! Inc., 월별 수익률
| Yahoo! Inc. (YHOO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값YHOO,t1 | 피제수YHOO,t1 | RYHOO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2012. 1. 31. | $15.47 | 1,312.41 | ||||
| 1. | 2012. 2. 29. | $14.83 | -4.14% | 1,365.68 | 4.06% | |
| 2. | 2012. 3. 31. | $15.22 | 2.63% | 1,408.47 | 3.13% | |
| 3. | 2012. 4. 30. | $15.54 | 2.10% | 1,397.91 | -0.75% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2016. 11. 30. | $41.02 | -1.28% | 2,198.81 | 3.42% | |
| 59. | 2016. 12. 31. | $38.67 | -5.73% | 2,238.83 | 1.82% | |
| 평균의 (R): | 1.87% | 0.95% | ||||
| 표준 편차: | 8.05% | 2.98% | ||||
| Yahoo! Inc. (YHOO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값YHOO,t1 | 피제수YHOO,t1 | RYHOO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2012. 1. 31. | $15.47 | 1,312.41 | ||||
| 1. | 2012. 2. 29. | $14.83 | -4.14% | 1,365.68 | 4.06% | |
| 2. | 2012. 3. 31. | $15.22 | 2.63% | 1,408.47 | 3.13% | |
| 3. | 2012. 4. 30. | $15.54 | 2.10% | 1,397.91 | -0.75% | |
| 4. | 2012. 5. 31. | $15.24 | -1.93% | 1,310.33 | -6.27% | |
| 5. | 2012. 6. 30. | $15.83 | 3.87% | 1,362.16 | 3.96% | |
| 6. | 2012. 7. 31. | $15.84 | 0.06% | 1,379.32 | 1.26% | |
| 7. | 2012. 8. 31. | $14.65 | -7.51% | 1,406.58 | 1.98% | |
| 8. | 2012. 9. 30. | $15.98 | 9.08% | 1,440.67 | 2.42% | |
| 9. | 2012. 10. 31. | $16.84 | 5.38% | 1,412.16 | -1.98% | |
| 10. | 2012. 11. 30. | $18.77 | 11.46% | 1,416.18 | 0.28% | |
| 11. | 2012. 12. 31. | $19.90 | 6.02% | 1,426.19 | 0.71% | |
| 12. | 2013. 1. 31. | $19.63 | -1.36% | 1,498.11 | 5.04% | |
| 13. | 2013. 2. 28. | $21.31 | 8.56% | 1,514.68 | 1.11% | |
| 14. | 2013. 3. 31. | $23.53 | 10.42% | 1,569.19 | 3.60% | |
| 15. | 2013. 4. 30. | $24.73 | 5.10% | 1,597.57 | 1.81% | |
| 16. | 2013. 5. 31. | $26.30 | 6.35% | 1,630.74 | 2.08% | |
| 17. | 2013. 6. 30. | $25.13 | -4.45% | 1,606.28 | -1.50% | |
| 18. | 2013. 7. 31. | $28.09 | 11.78% | 1,685.73 | 4.95% | |
| 19. | 2013. 8. 31. | $27.12 | -3.45% | 1,632.97 | -3.13% | |
| 20. | 2013. 9. 30. | $33.17 | 22.31% | 1,681.55 | 2.97% | |
| 21. | 2013. 10. 31. | $32.94 | -0.69% | 1,756.54 | 4.46% | |
| 22. | 2013. 11. 30. | $36.98 | 12.26% | 1,805.81 | 2.80% | |
| 23. | 2013. 12. 31. | $40.44 | 9.36% | 1,848.36 | 2.36% | |
| 24. | 2014. 1. 31. | $36.01 | -10.95% | 1,782.59 | -3.56% | |
| 25. | 2014. 2. 28. | $38.67 | 7.39% | 1,859.45 | 4.31% | |
| 26. | 2014. 3. 31. | $35.90 | -7.16% | 1,872.34 | 0.69% | |
| 27. | 2014. 4. 30. | $35.95 | 0.14% | 1,883.95 | 0.62% | |
| 28. | 2014. 5. 31. | $34.65 | -3.62% | 1,923.57 | 2.10% | |
| 29. | 2014. 6. 30. | $35.13 | 1.39% | 1,960.23 | 1.91% | |
| 30. | 2014. 7. 31. | $35.81 | 1.94% | 1,930.67 | -1.51% | |
| 31. | 2014. 8. 31. | $38.51 | 7.54% | 2,003.37 | 3.77% | |
| 32. | 2014. 9. 30. | $40.75 | 5.82% | 1,972.29 | -1.55% | |
| 33. | 2014. 10. 31. | $46.05 | 13.01% | 2,018.05 | 2.32% | |
| 34. | 2014. 11. 30. | $51.74 | 12.36% | 2,067.56 | 2.45% | |
| 35. | 2014. 12. 31. | $50.51 | -2.38% | 2,058.90 | -0.42% | |
| 36. | 2015. 1. 31. | $43.99 | -12.91% | 1,994.99 | -3.10% | |
| 37. | 2015. 2. 28. | $44.28 | 0.66% | 2,104.50 | 5.49% | |
| 38. | 2015. 3. 31. | $44.44 | 0.36% | 2,067.89 | -1.74% | |
| 39. | 2015. 4. 30. | $42.57 | -4.21% | 2,085.51 | 0.85% | |
| 40. | 2015. 5. 31. | $42.94 | 0.87% | 2,107.39 | 1.05% | |
| 41. | 2015. 6. 30. | $39.29 | -8.50% | 2,063.11 | -2.10% | |
| 42. | 2015. 7. 31. | $36.67 | -6.67% | 2,103.84 | 1.97% | |
| 43. | 2015. 8. 31. | $32.24 | -12.08% | 1,972.18 | -6.26% | |
| 44. | 2015. 9. 30. | $28.91 | -10.33% | 1,920.03 | -2.64% | |
| 45. | 2015. 10. 31. | $35.62 | 23.21% | 2,079.36 | 8.30% | |
| 46. | 2015. 11. 30. | $33.81 | -5.08% | 2,080.41 | 0.05% | |
| 47. | 2015. 12. 31. | $33.26 | -1.63% | 2,043.94 | -1.75% | |
| 48. | 2016. 1. 31. | $29.51 | -11.27% | 1,940.24 | -5.07% | |
| 49. | 2016. 2. 29. | $31.79 | 7.73% | 1,932.23 | -0.41% | |
| 50. | 2016. 3. 31. | $36.81 | 15.79% | 2,059.74 | 6.60% | |
| 51. | 2016. 4. 30. | $36.60 | -0.57% | 2,065.30 | 0.27% | |
| 52. | 2016. 5. 31. | $37.94 | 3.66% | 2,096.95 | 1.53% | |
| 53. | 2016. 6. 30. | $37.56 | -1.00% | 2,098.86 | 0.09% | |
| 54. | 2016. 7. 31. | $38.19 | 1.68% | 2,173.60 | 3.56% | |
| 55. | 2016. 8. 31. | $42.75 | 11.94% | 2,170.95 | -0.12% | |
| 56. | 2016. 9. 30. | $43.10 | 0.82% | 2,168.27 | -0.12% | |
| 57. | 2016. 10. 31. | $41.55 | -3.60% | 2,126.15 | -1.94% | |
| 58. | 2016. 11. 30. | $41.02 | -1.28% | 2,198.81 | 3.42% | |
| 59. | 2016. 12. 31. | $38.67 | -5.73% | 2,238.83 | 1.82% | |
| 평균의 (R): | 1.87% | 0.95% | ||||
| 표준 편차: | 8.05% | 2.98% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 YHOO의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Yahoo! Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RYHOO,t | RS&P 500,t | (RYHOO,t–RYHOO)2 | (RS&P 500,t–RS&P 500)2 | (RYHOO,t–RYHOO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2012. 2. 29. | -4.14% | 4.06% | 36.12 | 9.65 | -18.67 |
| 2. | 2012. 3. 31. | 2.63% | 3.13% | 0.57 | 4.75 | 1.65 |
| 3. | 2012. 4. 30. | 2.10% | -0.75% | 0.05 | 2.90 | -0.39 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2016. 11. 30. | -1.28% | 3.42% | 9.92 | 6.07 | -7.76 |
| 59. | 2016. 12. 31. | -5.73% | 1.82% | 57.79 | 0.75 | -6.59 |
| 합계 (Σ): | 3,761.33 | 514.91 | 816.37 | |||
| t | 날짜 | RYHOO,t | RS&P 500,t | (RYHOO,t–RYHOO)2 | (RS&P 500,t–RS&P 500)2 | (RYHOO,t–RYHOO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2012. 2. 29. | -4.14% | 4.06% | 36.12 | 9.65 | -18.67 |
| 2. | 2012. 3. 31. | 2.63% | 3.13% | 0.57 | 4.75 | 1.65 |
| 3. | 2012. 4. 30. | 2.10% | -0.75% | 0.05 | 2.90 | -0.39 |
| 4. | 2012. 5. 31. | -1.93% | -6.27% | 14.47 | 52.10 | 27.46 |
| 5. | 2012. 6. 30. | 3.87% | 3.96% | 3.99 | 9.02 | 6.00 |
| 6. | 2012. 7. 31. | 0.06% | 1.26% | 3.28 | 0.09 | -0.56 |
| 7. | 2012. 8. 31. | -7.51% | 1.98% | 88.10 | 1.05 | -9.61 |
| 8. | 2012. 9. 30. | 9.08% | 2.42% | 51.91 | 2.16 | 10.60 |
| 9. | 2012. 10. 31. | 5.38% | -1.98% | 12.31 | 8.60 | -10.29 |
| 10. | 2012. 11. 30. | 11.46% | 0.28% | 91.92 | 0.45 | -6.41 |
| 11. | 2012. 12. 31. | 6.02% | 0.71% | 17.20 | 0.06 | -1.02 |
| 12. | 2013. 1. 31. | -1.36% | 5.04% | 10.43 | 16.73 | -13.21 |
| 13. | 2013. 2. 28. | 8.56% | 1.11% | 44.69 | 0.02 | 1.02 |
| 14. | 2013. 3. 31. | 10.42% | 3.60% | 73.00 | 7.00 | 22.61 |
| 15. | 2013. 4. 30. | 5.10% | 1.81% | 10.41 | 0.73 | 2.76 |
| 16. | 2013. 5. 31. | 6.35% | 2.08% | 20.03 | 1.26 | 5.03 |
| 17. | 2013. 6. 30. | -4.45% | -1.50% | 39.97 | 6.02 | 15.51 |
| 18. | 2013. 7. 31. | 11.78% | 4.95% | 98.12 | 15.95 | 39.56 |
| 19. | 2013. 8. 31. | -3.45% | -3.13% | 28.37 | 16.67 | 21.75 |
| 20. | 2013. 9. 30. | 22.31% | 2.97% | 417.59 | 4.09 | 41.32 |
| 21. | 2013. 10. 31. | -0.69% | 4.46% | 6.59 | 12.30 | -9.00 |
| 22. | 2013. 11. 30. | 12.26% | 2.80% | 107.98 | 3.43 | 19.25 |
| 23. | 2013. 12. 31. | 9.36% | 2.36% | 56.00 | 1.97 | 10.50 |
| 24. | 2014. 1. 31. | -10.95% | -3.56% | 164.55 | 20.35 | 57.87 |
| 25. | 2014. 2. 28. | 7.39% | 4.31% | 30.40 | 11.28 | 18.52 |
| 26. | 2014. 3. 31. | -7.16% | 0.69% | 81.66 | 0.07 | 2.35 |
| 27. | 2014. 4. 30. | 0.14% | 0.62% | 3.01 | 0.11 | 0.58 |
| 28. | 2014. 5. 31. | -3.62% | 2.10% | 30.13 | 1.32 | -6.31 |
| 29. | 2014. 6. 30. | 1.39% | 1.91% | 0.24 | 0.91 | -0.47 |
| 30. | 2014. 7. 31. | 1.94% | -1.51% | 0.00 | 6.06 | -0.15 |
| 31. | 2014. 8. 31. | 7.54% | 3.77% | 32.11 | 7.91 | 15.94 |
| 32. | 2014. 9. 30. | 5.82% | -1.55% | 15.55 | 6.27 | -9.87 |
| 33. | 2014. 10. 31. | 13.01% | 2.32% | 123.94 | 1.87 | 15.22 |
| 34. | 2014. 11. 30. | 12.36% | 2.45% | 109.89 | 2.25 | 15.73 |
| 35. | 2014. 12. 31. | -2.38% | -0.42% | 18.07 | 1.88 | 5.83 |
| 36. | 2015. 1. 31. | -12.91% | -3.10% | 218.50 | 16.46 | 59.97 |
| 37. | 2015. 2. 28. | 0.66% | 5.49% | 1.47 | 20.58 | -5.51 |
| 38. | 2015. 3. 31. | 0.36% | -1.74% | 2.29 | 7.25 | 4.07 |
| 39. | 2015. 4. 30. | -4.21% | 0.85% | 36.98 | 0.01 | 0.61 |
| 40. | 2015. 5. 31. | 0.87% | 1.05% | 1.01 | 0.01 | -0.10 |
| 41. | 2015. 6. 30. | -8.50% | -2.10% | 107.61 | 9.33 | 31.68 |
| 42. | 2015. 7. 31. | -6.67% | 1.97% | 72.96 | 1.04 | -8.72 |
| 43. | 2015. 8. 31. | -12.08% | -6.26% | 194.72 | 52.00 | 100.62 |
| 44. | 2015. 9. 30. | -10.33% | -2.64% | 148.89 | 12.94 | 43.89 |
| 45. | 2015. 10. 31. | 23.21% | 8.30% | 455.25 | 53.96 | 156.73 |
| 46. | 2015. 11. 30. | -5.08% | 0.05% | 48.37 | 0.81 | 6.28 |
| 47. | 2015. 12. 31. | -1.63% | -1.75% | 12.25 | 7.32 | 9.47 |
| 48. | 2016. 1. 31. | -11.27% | -5.07% | 172.87 | 36.32 | 79.24 |
| 49. | 2016. 2. 29. | 7.73% | -0.41% | 34.26 | 1.87 | -7.99 |
| 50. | 2016. 3. 31. | 15.79% | 6.60% | 193.70 | 31.88 | 78.58 |
| 51. | 2016. 4. 30. | -0.57% | 0.27% | 5.97 | 0.47 | 1.67 |
| 52. | 2016. 5. 31. | 3.66% | 1.53% | 3.20 | 0.34 | 1.04 |
| 53. | 2016. 6. 30. | -1.00% | 0.09% | 8.27 | 0.74 | 2.48 |
| 54. | 2016. 7. 31. | 1.68% | 3.56% | 0.04 | 6.80 | -0.51 |
| 55. | 2016. 8. 31. | 11.94% | -0.12% | 101.34 | 1.16 | -10.82 |
| 56. | 2016. 9. 30. | 0.82% | -0.12% | 1.11 | 1.16 | 1.14 |
| 57. | 2016. 10. 31. | -3.60% | -1.94% | 29.92 | 8.38 | 15.84 |
| 58. | 2016. 11. 30. | -1.28% | 3.42% | 9.92 | 6.07 | -7.76 |
| 59. | 2016. 12. 31. | -5.73% | 1.82% | 57.79 | 0.75 | -6.59 |
| 합계 (Σ): | 3,761.33 | 514.91 | 816.37 | |||
모두 보기
분산YHOO = Σ(RYHOO,t–RYHOO)2 ÷ (59 – 1)
= 3,761.33 ÷ (59 – 1)
= 64.85
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 514.91 ÷ (59 – 1)
= 8.88
공분산YHOO, S&P 500 = Σ(RYHOO,t–RYHOO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 816.37 ÷ (59 – 1)
= 14.08
체계적인 위험 추정 (β)
| 분산YHOO | 64.85 |
| 분산S&P 500 | 8.88 |
| 공분산YHOO, S&P 500 | 14.08 |
| 상관 계수YHOO, S&P 5001 | 0.59 |
| βYHOO2 | 1.59 |
| αYHOO3 | 0.36% |
계산
1 상관 계수YHOO, S&P 500
= 공분산YHOO, S&P 500 ÷ (표준 편차YHOO × 표준 편차S&P 500)
= 14.08 ÷ (8.05% × 2.98%)
= 0.59
2 βYHOO
= 공분산YHOO, S&P 500 ÷ 분산S&P 500
= 14.08 ÷ 8.88
= 1.59
3 αYHOO
= 평균의YHOO – βYHOO × 평균의S&P 500
= 1.87% – 1.59 × 0.95%
= 0.36%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.65% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.99% |
| 보통주의 체계적 위험Yahoo | βYHOO | 1.59 |
| Yahoo 보통주에 대한 예상 수익률3 | E(RYHOO) | 21.04% |
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(RYHOO) = RF + βYHOO [E(RM) – RF]
= 4.65% + 1.59 [14.99% – 4.65%]
= 21.04%