자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 eBay보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
eBay Inc., 월별 수익률
| eBay Inc. (EBAY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값EBAY,t1 | 피제수EBAY,t1 | REBAY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2014. 1. 31. | $53.20 | 1,782.59 | ||||
| 1. | 2014. 2. 28. | $58.77 | 10.47% | 1,859.45 | 4.31% | |
| 2. | 2014. 3. 31. | $55.24 | -6.01% | 1,872.34 | 0.69% | |
| 3. | 2014. 4. 30. | $51.83 | -6.17% | 1,883.95 | 0.62% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2018. 11. 30. | $29.85 | 2.82% | 2,760.17 | 1.79% | |
| 59. | 2018. 12. 31. | $28.07 | -5.96% | 2,506.85 | -9.18% | |
| 평균의 (R): | 0.60% | 0.63% | ||||
| 표준 편차: | 7.49% | 3.13% | ||||
| eBay Inc. (EBAY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값EBAY,t1 | 피제수EBAY,t1 | REBAY,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2014. 1. 31. | $53.20 | 1,782.59 | ||||
| 1. | 2014. 2. 28. | $58.77 | 10.47% | 1,859.45 | 4.31% | |
| 2. | 2014. 3. 31. | $55.24 | -6.01% | 1,872.34 | 0.69% | |
| 3. | 2014. 4. 30. | $51.83 | -6.17% | 1,883.95 | 0.62% | |
| 4. | 2014. 5. 31. | $50.73 | -2.12% | 1,923.57 | 2.10% | |
| 5. | 2014. 6. 30. | $50.06 | -1.32% | 1,960.23 | 1.91% | |
| 6. | 2014. 7. 31. | $52.83 | 5.53% | 1,930.67 | -1.51% | |
| 7. | 2014. 8. 31. | $55.50 | 5.05% | 2,003.37 | 3.77% | |
| 8. | 2014. 9. 30. | $56.63 | 2.04% | 1,972.29 | -1.55% | |
| 9. | 2014. 10. 31. | $52.50 | -7.29% | 2,018.05 | 2.32% | |
| 10. | 2014. 11. 30. | $54.88 | 4.53% | 2,067.56 | 2.45% | |
| 11. | 2014. 12. 31. | $56.12 | 2.26% | 2,058.90 | -0.42% | |
| 12. | 2015. 1. 31. | $53.00 | -5.56% | 1,994.99 | -3.10% | |
| 13. | 2015. 2. 28. | $57.91 | 9.26% | 2,104.50 | 5.49% | |
| 14. | 2015. 3. 31. | $57.68 | -0.40% | 2,067.89 | -1.74% | |
| 15. | 2015. 4. 30. | $58.26 | 1.01% | 2,085.51 | 0.85% | |
| 16. | 2015. 5. 31. | $61.36 | 5.32% | 2,107.39 | 1.05% | |
| 17. | 2015. 6. 30. | $60.24 | -1.83% | 2,063.11 | -2.10% | |
| 18. | 2015. 7. 31. | $28.12 | $36.71 | 7.62% | 2,103.84 | 1.97% |
| 19. | 2015. 8. 31. | $27.11 | -3.59% | 1,972.18 | -6.26% | |
| 20. | 2015. 9. 30. | $24.44 | -9.85% | 1,920.03 | -2.64% | |
| 21. | 2015. 10. 31. | $27.90 | 14.16% | 2,079.36 | 8.30% | |
| 22. | 2015. 11. 30. | $29.59 | 6.06% | 2,080.41 | 0.05% | |
| 23. | 2015. 12. 31. | $27.48 | -7.13% | 2,043.94 | -1.75% | |
| 24. | 2016. 1. 31. | $23.46 | -14.63% | 1,940.24 | -5.07% | |
| 25. | 2016. 2. 29. | $23.80 | 1.45% | 1,932.23 | -0.41% | |
| 26. | 2016. 3. 31. | $23.86 | 0.25% | 2,059.74 | 6.60% | |
| 27. | 2016. 4. 30. | $24.43 | 2.39% | 2,065.30 | 0.27% | |
| 28. | 2016. 5. 31. | $24.46 | 0.12% | 2,096.95 | 1.53% | |
| 29. | 2016. 6. 30. | $23.41 | -4.29% | 2,098.86 | 0.09% | |
| 30. | 2016. 7. 31. | $31.16 | 33.11% | 2,173.60 | 3.56% | |
| 31. | 2016. 8. 31. | $32.16 | 3.21% | 2,170.95 | -0.12% | |
| 32. | 2016. 9. 30. | $32.90 | 2.30% | 2,168.27 | -0.12% | |
| 33. | 2016. 10. 31. | $28.51 | -13.34% | 2,126.15 | -1.94% | |
| 34. | 2016. 11. 30. | $27.81 | -2.46% | 2,198.81 | 3.42% | |
| 35. | 2016. 12. 31. | $29.69 | 6.76% | 2,238.83 | 1.82% | |
| 36. | 2017. 1. 31. | $31.83 | 7.21% | 2,278.87 | 1.79% | |
| 37. | 2017. 2. 28. | $33.90 | 6.50% | 2,363.64 | 3.72% | |
| 38. | 2017. 3. 31. | $33.57 | -0.97% | 2,362.72 | -0.04% | |
| 39. | 2017. 4. 30. | $33.41 | -0.48% | 2,384.20 | 0.91% | |
| 40. | 2017. 5. 31. | $34.30 | 2.66% | 2,411.80 | 1.16% | |
| 41. | 2017. 6. 30. | $34.92 | 1.81% | 2,423.41 | 0.48% | |
| 42. | 2017. 7. 31. | $35.73 | 2.32% | 2,470.30 | 1.93% | |
| 43. | 2017. 8. 31. | $36.13 | 1.12% | 2,471.65 | 0.05% | |
| 44. | 2017. 9. 30. | $38.46 | 6.45% | 2,519.36 | 1.93% | |
| 45. | 2017. 10. 31. | $37.64 | -2.13% | 2,575.26 | 2.22% | |
| 46. | 2017. 11. 30. | $34.67 | -7.89% | 2,647.58 | 2.81% | |
| 47. | 2017. 12. 31. | $37.74 | 8.85% | 2,673.61 | 0.98% | |
| 48. | 2018. 1. 31. | $40.58 | 7.53% | 2,823.81 | 5.62% | |
| 49. | 2018. 2. 28. | $42.86 | 5.62% | 2,713.83 | -3.89% | |
| 50. | 2018. 3. 31. | $40.24 | -6.11% | 2,640.87 | -2.69% | |
| 51. | 2018. 4. 30. | $37.88 | -5.86% | 2,648.05 | 0.27% | |
| 52. | 2018. 5. 31. | $37.72 | -0.42% | 2,705.27 | 2.16% | |
| 53. | 2018. 6. 30. | $36.26 | -3.87% | 2,718.37 | 0.48% | |
| 54. | 2018. 7. 31. | $33.45 | -7.75% | 2,816.29 | 3.60% | |
| 55. | 2018. 8. 31. | $34.61 | 3.47% | 2,901.52 | 3.03% | |
| 56. | 2018. 9. 30. | $33.02 | -4.59% | 2,913.98 | 0.43% | |
| 57. | 2018. 10. 31. | $29.03 | -12.08% | 2,711.74 | -6.94% | |
| 58. | 2018. 11. 30. | $29.85 | 2.82% | 2,760.17 | 1.79% | |
| 59. | 2018. 12. 31. | $28.07 | -5.96% | 2,506.85 | -9.18% | |
| 평균의 (R): | 0.60% | 0.63% | ||||
| 표준 편차: | 7.49% | 3.13% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 EBAY의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
eBay Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | REBAY,t | RS&P 500,t | (REBAY,t–REBAY)2 | (RS&P 500,t–RS&P 500)2 | (REBAY,t–REBAY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2014. 2. 28. | 10.47% | 4.31% | 97.50 | 13.57 | 36.37 |
| 2. | 2014. 3. 31. | -6.01% | 0.69% | 43.59 | 0.00 | -0.43 |
| 3. | 2014. 4. 30. | -6.17% | 0.62% | 45.81 | 0.00 | 0.05 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2018. 11. 30. | 2.82% | 1.79% | 4.97 | 1.34 | 2.58 |
| 59. | 2018. 12. 31. | -5.96% | -9.18% | 43.02 | 96.15 | 64.31 |
| 합계 (Σ): | 3,252.48 | 566.60 | 700.73 | |||
| t | 날짜 | REBAY,t | RS&P 500,t | (REBAY,t–REBAY)2 | (RS&P 500,t–RS&P 500)2 | (REBAY,t–REBAY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2014. 2. 28. | 10.47% | 4.31% | 97.50 | 13.57 | 36.37 |
| 2. | 2014. 3. 31. | -6.01% | 0.69% | 43.59 | 0.00 | -0.43 |
| 3. | 2014. 4. 30. | -6.17% | 0.62% | 45.81 | 0.00 | 0.05 |
| 4. | 2014. 5. 31. | -2.12% | 2.10% | 7.39 | 2.18 | -4.01 |
| 5. | 2014. 6. 30. | -1.32% | 1.91% | 3.67 | 1.63 | -2.45 |
| 6. | 2014. 7. 31. | 5.53% | -1.51% | 24.38 | 4.56 | -10.55 |
| 7. | 2014. 8. 31. | 5.05% | 3.77% | 19.88 | 9.84 | 13.99 |
| 8. | 2014. 9. 30. | 2.04% | -1.55% | 2.07 | 4.75 | -3.14 |
| 9. | 2014. 10. 31. | -7.29% | 2.32% | 62.23 | 2.86 | -13.35 |
| 10. | 2014. 11. 30. | 4.53% | 2.45% | 15.51 | 3.33 | 7.19 |
| 11. | 2014. 12. 31. | 2.26% | -0.42% | 2.77 | 1.10 | -1.74 |
| 12. | 2015. 1. 31. | -5.56% | -3.10% | 37.89 | 13.93 | 22.97 |
| 13. | 2015. 2. 28. | 9.26% | 5.49% | 75.14 | 23.63 | 42.14 |
| 14. | 2015. 3. 31. | -0.40% | -1.74% | 0.99 | 5.61 | 2.35 |
| 15. | 2015. 4. 30. | 1.01% | 0.85% | 0.17 | 0.05 | 0.09 |
| 16. | 2015. 5. 31. | 5.32% | 1.05% | 22.33 | 0.18 | 1.99 |
| 17. | 2015. 6. 30. | -1.83% | -2.10% | 5.86 | 7.45 | 6.61 |
| 18. | 2015. 7. 31. | 7.62% | 1.97% | 49.34 | 1.81 | 9.46 |
| 19. | 2015. 8. 31. | -3.59% | -6.26% | 17.53 | 47.42 | 28.83 |
| 20. | 2015. 9. 30. | -9.85% | -2.64% | 109.08 | 10.71 | 34.18 |
| 21. | 2015. 10. 31. | 14.16% | 8.30% | 183.92 | 58.83 | 104.02 |
| 22. | 2015. 11. 30. | 6.06% | 0.05% | 29.83 | 0.33 | -3.15 |
| 23. | 2015. 12. 31. | -7.13% | -1.75% | 59.70 | 5.67 | 18.40 |
| 24. | 2016. 1. 31. | -14.63% | -5.07% | 231.78 | 32.51 | 86.80 |
| 25. | 2016. 2. 29. | 1.45% | -0.41% | 0.73 | 1.08 | -0.89 |
| 26. | 2016. 3. 31. | 0.25% | 6.60% | 0.12 | 35.65 | -2.05 |
| 27. | 2016. 4. 30. | 2.39% | 0.27% | 3.22 | 0.13 | -0.64 |
| 28. | 2016. 5. 31. | 0.12% | 1.53% | 0.22 | 0.82 | -0.43 |
| 29. | 2016. 6. 30. | -4.29% | 0.09% | 23.90 | 0.29 | 2.62 |
| 30. | 2016. 7. 31. | 33.11% | 3.56% | 1,056.90 | 8.60 | 95.35 |
| 31. | 2016. 8. 31. | 3.21% | -0.12% | 6.83 | 0.56 | -1.96 |
| 32. | 2016. 9. 30. | 2.30% | -0.12% | 2.91 | 0.56 | -1.28 |
| 33. | 2016. 10. 31. | -13.34% | -1.94% | 194.30 | 6.61 | 35.83 |
| 34. | 2016. 11. 30. | -2.46% | 3.42% | 9.31 | 7.78 | -8.51 |
| 35. | 2016. 12. 31. | 6.76% | 1.82% | 38.00 | 1.42 | 7.35 |
| 36. | 2017. 1. 31. | 7.21% | 1.79% | 43.72 | 1.35 | 7.67 |
| 37. | 2017. 2. 28. | 6.50% | 3.72% | 34.90 | 9.56 | 18.27 |
| 38. | 2017. 3. 31. | -0.97% | -0.04% | 2.46 | 0.44 | 1.05 |
| 39. | 2017. 4. 30. | -0.48% | 0.91% | 1.15 | 0.08 | -0.30 |
| 40. | 2017. 5. 31. | 2.66% | 1.16% | 4.28 | 0.28 | 1.10 |
| 41. | 2017. 6. 30. | 1.81% | 0.48% | 1.47 | 0.02 | -0.18 |
| 42. | 2017. 7. 31. | 2.32% | 1.93% | 2.97 | 1.71 | 2.25 |
| 43. | 2017. 8. 31. | 1.12% | 0.05% | 0.27 | 0.33 | -0.30 |
| 44. | 2017. 9. 30. | 6.45% | 1.93% | 34.26 | 1.70 | 7.62 |
| 45. | 2017. 10. 31. | -2.13% | 2.22% | 7.44 | 2.53 | -4.34 |
| 46. | 2017. 11. 30. | -7.89% | 2.81% | 72.01 | 4.75 | -18.50 |
| 47. | 2017. 12. 31. | 8.85% | 0.98% | 68.22 | 0.13 | 2.93 |
| 48. | 2018. 1. 31. | 7.53% | 5.62% | 48.02 | 24.90 | 34.58 |
| 49. | 2018. 2. 28. | 5.62% | -3.89% | 25.23 | 20.45 | -22.72 |
| 50. | 2018. 3. 31. | -6.11% | -2.69% | 45.00 | 11.00 | 22.25 |
| 51. | 2018. 4. 30. | -5.86% | 0.27% | 41.74 | 0.13 | 2.30 |
| 52. | 2018. 5. 31. | -0.42% | 2.16% | 1.04 | 2.35 | -1.56 |
| 53. | 2018. 6. 30. | -3.87% | 0.48% | 19.95 | 0.02 | 0.64 |
| 54. | 2018. 7. 31. | -7.75% | 3.60% | 69.64 | 8.85 | -24.82 |
| 55. | 2018. 8. 31. | 3.47% | 3.03% | 8.25 | 5.75 | 6.89 |
| 56. | 2018. 9. 30. | -4.59% | 0.43% | 26.93 | 0.04 | 1.03 |
| 57. | 2018. 10. 31. | -12.08% | -6.94% | 160.76 | 57.28 | 95.96 |
| 58. | 2018. 11. 30. | 2.82% | 1.79% | 4.97 | 1.34 | 2.58 |
| 59. | 2018. 12. 31. | -5.96% | -9.18% | 43.02 | 96.15 | 64.31 |
| 합계 (Σ): | 3,252.48 | 566.60 | 700.73 | |||
모두 보기
분산EBAY = Σ(REBAY,t–REBAY)2 ÷ (59 – 1)
= 3,252.48 ÷ (59 – 1)
= 56.08
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 566.60 ÷ (59 – 1)
= 9.77
공분산EBAY, S&P 500 = Σ(REBAY,t–REBAY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 700.73 ÷ (59 – 1)
= 12.08
체계적인 위험 추정 (β)
| 분산EBAY | 56.08 |
| 분산S&P 500 | 9.77 |
| 공분산EBAY, S&P 500 | 12.08 |
| 상관 계수EBAY, S&P 5001 | 0.52 |
| βEBAY2 | 1.24 |
| αEBAY3 | -0.18% |
계산
1 상관 계수EBAY, S&P 500
= 공분산EBAY, S&P 500 ÷ (표준 편차EBAY × 표준 편차S&P 500)
= 12.08 ÷ (7.49% × 3.13%)
= 0.52
2 βEBAY
= 공분산EBAY, S&P 500 ÷ 분산S&P 500
= 12.08 ÷ 9.77
= 1.24
3 αEBAY
= 평균의EBAY – βEBAY × 평균의S&P 500
= 0.60% – 1.24 × 0.63%
= -0.18%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험eBay | βEBAY | 1.24 |
| eBay 보통주에 대한 예상 수익률3 | E(REBAY) | 17.19% |
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(REBAY) = RF + βEBAY [E(RM) – RF]
= 4.91% + 1.24 [14.84% – 4.91%]
= 17.19%