자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Baxter보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Baxter International Inc., 월별 수익률
| Baxter International Inc. (BAX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BAX,t1 | 피제수BAX,t1 | RBAX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $48.49 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $53.15 | 9.61% | 1,327.22 | 3.20% | |
| 2. | 2011. 3. 31. | $53.77 | $0.31 | 1.75% | 1,325.83 | -0.10% |
| 3. | 2011. 4. 30. | $56.90 | 5.82% | 1,363.61 | 2.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | $37.65 | 0.70% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $38.15 | $0.115 | 1.63% | 2,043.94 | -1.75% |
| 평균의 (R): | 0.15% | 0.84% | ||||
| 표준 편차: | 7.55% | 3.40% | ||||
| Baxter International Inc. (BAX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값BAX,t1 | 피제수BAX,t1 | RBAX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $48.49 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $53.15 | 9.61% | 1,327.22 | 3.20% | |
| 2. | 2011. 3. 31. | $53.77 | $0.31 | 1.75% | 1,325.83 | -0.10% |
| 3. | 2011. 4. 30. | $56.90 | 5.82% | 1,363.61 | 2.85% | |
| 4. | 2011. 5. 31. | $59.52 | 4.60% | 1,345.20 | -1.35% | |
| 5. | 2011. 6. 30. | $59.69 | $0.31 | 0.81% | 1,320.64 | -1.83% |
| 6. | 2011. 7. 31. | $58.17 | -2.55% | 1,292.28 | -2.15% | |
| 7. | 2011. 8. 31. | $55.98 | -3.76% | 1,218.89 | -5.68% | |
| 8. | 2011. 9. 30. | $56.14 | $0.31 | 0.84% | 1,131.42 | -7.18% |
| 9. | 2011. 10. 31. | $54.98 | -2.07% | 1,253.30 | 10.77% | |
| 10. | 2011. 11. 30. | $51.66 | -6.04% | 1,246.96 | -0.51% | |
| 11. | 2011. 12. 31. | $49.48 | $0.335 | -3.57% | 1,257.60 | 0.85% |
| 12. | 2012. 1. 31. | $55.48 | 12.13% | 1,312.41 | 4.36% | |
| 13. | 2012. 2. 29. | $58.13 | 4.78% | 1,365.68 | 4.06% | |
| 14. | 2012. 3. 31. | $59.78 | $0.335 | 3.41% | 1,408.47 | 3.13% |
| 15. | 2012. 4. 30. | $55.41 | -7.31% | 1,397.91 | -0.75% | |
| 16. | 2012. 5. 31. | $50.62 | -8.64% | 1,310.33 | -6.27% | |
| 17. | 2012. 6. 30. | $53.15 | $0.335 | 5.66% | 1,362.16 | 3.96% |
| 18. | 2012. 7. 31. | $58.51 | 10.08% | 1,379.32 | 1.26% | |
| 19. | 2012. 8. 31. | $58.68 | 0.29% | 1,406.58 | 1.98% | |
| 20. | 2012. 9. 30. | $60.27 | $0.45 | 3.48% | 1,440.67 | 2.42% |
| 21. | 2012. 10. 31. | $62.63 | 3.92% | 1,412.16 | -1.98% | |
| 22. | 2012. 11. 30. | $66.27 | 5.81% | 1,416.18 | 0.28% | |
| 23. | 2012. 12. 31. | $66.66 | $0.45 | 1.27% | 1,426.19 | 0.71% |
| 24. | 2013. 1. 31. | $67.84 | 1.77% | 1,498.11 | 5.04% | |
| 25. | 2013. 2. 28. | $67.60 | -0.35% | 1,514.68 | 1.11% | |
| 26. | 2013. 3. 31. | $72.64 | $0.45 | 8.12% | 1,569.19 | 3.60% |
| 27. | 2013. 4. 30. | $69.87 | -3.81% | 1,597.57 | 1.81% | |
| 28. | 2013. 5. 31. | $70.33 | 0.66% | 1,630.74 | 2.08% | |
| 29. | 2013. 6. 30. | $69.27 | $0.49 | -0.81% | 1,606.28 | -1.50% |
| 30. | 2013. 7. 31. | $73.04 | 5.44% | 1,685.73 | 4.95% | |
| 31. | 2013. 8. 31. | $69.56 | -4.76% | 1,632.97 | -3.13% | |
| 32. | 2013. 9. 30. | $65.69 | $0.49 | -4.86% | 1,681.55 | 2.97% |
| 33. | 2013. 10. 31. | $65.87 | 0.27% | 1,756.54 | 4.46% | |
| 34. | 2013. 11. 30. | $68.45 | 3.92% | 1,805.81 | 2.80% | |
| 35. | 2013. 12. 31. | $69.55 | $0.49 | 2.32% | 1,848.36 | 2.36% |
| 36. | 2014. 1. 31. | $68.30 | -1.80% | 1,782.59 | -3.56% | |
| 37. | 2014. 2. 28. | $69.50 | 1.76% | 1,859.45 | 4.31% | |
| 38. | 2014. 3. 31. | $73.58 | $0.49 | 6.58% | 1,872.34 | 0.69% |
| 39. | 2014. 4. 30. | $72.79 | -1.07% | 1,883.95 | 0.62% | |
| 40. | 2014. 5. 31. | $74.41 | 2.23% | 1,923.57 | 2.10% | |
| 41. | 2014. 6. 30. | $72.30 | $0.52 | -2.14% | 1,960.23 | 1.91% |
| 42. | 2014. 7. 31. | $74.69 | 3.31% | 1,930.67 | -1.51% | |
| 43. | 2014. 8. 31. | $74.98 | 0.39% | 2,003.37 | 3.77% | |
| 44. | 2014. 9. 30. | $71.77 | $0.52 | -3.59% | 1,972.29 | -1.55% |
| 45. | 2014. 10. 31. | $70.14 | -2.27% | 2,018.05 | 2.32% | |
| 46. | 2014. 11. 30. | $73.00 | 4.08% | 2,067.56 | 2.45% | |
| 47. | 2014. 12. 31. | $73.29 | $0.52 | 1.11% | 2,058.90 | -0.42% |
| 48. | 2015. 1. 31. | $70.31 | -4.07% | 1,994.99 | -3.10% | |
| 49. | 2015. 2. 28. | $69.15 | -1.65% | 2,104.50 | 5.49% | |
| 50. | 2015. 3. 31. | $68.50 | $0.52 | -0.19% | 2,067.89 | -1.74% |
| 51. | 2015. 4. 30. | $68.74 | 0.35% | 2,085.51 | 0.85% | |
| 52. | 2015. 5. 31. | $66.61 | $0.52 | -2.34% | 2,107.39 | 1.05% |
| 53. | 2015. 6. 30. | $69.93 | 4.98% | 2,063.11 | -2.10% | |
| 54. | 2015. 7. 31. | $40.08 | -42.69% | 2,103.84 | 1.97% | |
| 55. | 2015. 8. 31. | $38.45 | -4.07% | 1,972.18 | -6.26% | |
| 56. | 2015. 9. 30. | $32.85 | $0.115 | -14.27% | 1,920.03 | -2.64% |
| 57. | 2015. 10. 31. | $37.39 | 13.82% | 2,079.36 | 8.30% | |
| 58. | 2015. 11. 30. | $37.65 | 0.70% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $38.15 | $0.115 | 1.63% | 2,043.94 | -1.75% |
| 평균의 (R): | 0.15% | 0.84% | ||||
| 표준 편차: | 7.55% | 3.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 BAX의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Baxter International Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RBAX,t | RS&P 500,t | (RBAX,t–RBAX)2 | (RS&P 500,t–RS&P 500)2 | (RBAX,t–RBAX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 9.61% | 3.20% | 89.44 | 5.53 | 22.23 |
| 2. | 2011. 3. 31. | 1.75% | -0.10% | 2.55 | 0.90 | -1.52 |
| 3. | 2011. 4. 30. | 5.82% | 2.85% | 32.13 | 4.02 | 11.36 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | 0.70% | 0.05% | 0.29 | 0.63 | -0.43 |
| 59. | 2015. 12. 31. | 1.63% | -1.75% | 2.19 | 6.75 | -3.85 |
| 합계 (Σ): | 3,305.71 | 670.89 | 397.17 | |||
| t | 날짜 | RBAX,t | RS&P 500,t | (RBAX,t–RBAX)2 | (RS&P 500,t–RS&P 500)2 | (RBAX,t–RBAX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 9.61% | 3.20% | 89.44 | 5.53 | 22.23 |
| 2. | 2011. 3. 31. | 1.75% | -0.10% | 2.55 | 0.90 | -1.52 |
| 3. | 2011. 4. 30. | 5.82% | 2.85% | 32.13 | 4.02 | 11.36 |
| 4. | 2011. 5. 31. | 4.60% | -1.35% | 19.82 | 4.82 | -9.77 |
| 5. | 2011. 6. 30. | 0.81% | -1.83% | 0.43 | 7.13 | -1.75 |
| 6. | 2011. 7. 31. | -2.55% | -2.15% | 7.29 | 8.95 | 8.08 |
| 7. | 2011. 8. 31. | -3.76% | -5.68% | 15.35 | 42.56 | 25.56 |
| 8. | 2011. 9. 30. | 0.84% | -7.18% | 0.47 | 64.34 | -5.51 |
| 9. | 2011. 10. 31. | -2.07% | 10.77% | 4.92 | 98.56 | -22.03 |
| 10. | 2011. 11. 30. | -6.04% | -0.51% | 38.33 | 1.82 | 8.36 |
| 11. | 2011. 12. 31. | -3.57% | 0.85% | 13.87 | 0.00 | -0.03 |
| 12. | 2012. 1. 31. | 12.13% | 4.36% | 143.36 | 12.35 | 42.07 |
| 13. | 2012. 2. 29. | 4.78% | 4.06% | 21.38 | 10.33 | 14.86 |
| 14. | 2012. 3. 31. | 3.41% | 3.13% | 10.64 | 5.24 | 7.47 |
| 15. | 2012. 4. 30. | -7.31% | -0.75% | 55.69 | 2.54 | 11.90 |
| 16. | 2012. 5. 31. | -8.64% | -6.27% | 77.39 | 50.55 | 62.55 |
| 17. | 2012. 6. 30. | 5.66% | 3.96% | 30.33 | 9.68 | 17.13 |
| 18. | 2012. 7. 31. | 10.08% | 1.26% | 98.64 | 0.17 | 4.12 |
| 19. | 2012. 8. 31. | 0.29% | 1.98% | 0.02 | 1.28 | 0.16 |
| 20. | 2012. 9. 30. | 3.48% | 2.42% | 11.05 | 2.49 | 5.25 |
| 21. | 2012. 10. 31. | 3.92% | -1.98% | 14.16 | 7.97 | -10.63 |
| 22. | 2012. 11. 30. | 5.81% | 0.28% | 32.03 | 0.31 | -3.17 |
| 23. | 2012. 12. 31. | 1.27% | 0.71% | 1.24 | 0.02 | -0.15 |
| 24. | 2013. 1. 31. | 1.77% | 5.04% | 2.62 | 17.62 | 6.79 |
| 25. | 2013. 2. 28. | -0.35% | 1.11% | 0.26 | 0.07 | -0.13 |
| 26. | 2013. 3. 31. | 8.12% | 3.60% | 63.50 | 7.58 | 21.95 |
| 27. | 2013. 4. 30. | -3.81% | 1.81% | 15.73 | 0.93 | -3.82 |
| 28. | 2013. 5. 31. | 0.66% | 2.08% | 0.26 | 1.52 | 0.62 |
| 29. | 2013. 6. 30. | -0.81% | -1.50% | 0.93 | 5.50 | 2.26 |
| 30. | 2013. 7. 31. | 5.44% | 4.95% | 27.98 | 16.82 | 21.70 |
| 31. | 2013. 8. 31. | -4.76% | -3.13% | 24.18 | 15.80 | 19.54 |
| 32. | 2013. 9. 30. | -4.86% | 2.97% | 25.12 | 4.54 | -10.68 |
| 33. | 2013. 10. 31. | 0.27% | 4.46% | 0.01 | 13.07 | 0.44 |
| 34. | 2013. 11. 30. | 3.92% | 2.80% | 14.17 | 3.84 | 7.38 |
| 35. | 2013. 12. 31. | 2.32% | 2.36% | 4.71 | 2.28 | 3.28 |
| 36. | 2014. 1. 31. | -1.80% | -3.56% | 3.80 | 19.39 | 8.59 |
| 37. | 2014. 2. 28. | 1.76% | 4.31% | 2.57 | 12.02 | 5.56 |
| 38. | 2014. 3. 31. | 6.58% | 0.69% | 41.25 | 0.02 | -0.97 |
| 39. | 2014. 4. 30. | -1.07% | 0.62% | 1.50 | 0.05 | 0.28 |
| 40. | 2014. 5. 31. | 2.23% | 2.10% | 4.30 | 1.58 | 2.61 |
| 41. | 2014. 6. 30. | -2.14% | 1.91% | 5.24 | 1.13 | -2.43 |
| 42. | 2014. 7. 31. | 3.31% | -1.51% | 9.94 | 5.54 | -7.42 |
| 43. | 2014. 8. 31. | 0.39% | 3.77% | 0.06 | 8.53 | 0.69 |
| 44. | 2014. 9. 30. | -3.59% | -1.55% | 13.99 | 5.74 | 8.96 |
| 45. | 2014. 10. 31. | -2.27% | 2.32% | 5.88 | 2.18 | -3.58 |
| 46. | 2014. 11. 30. | 4.08% | 2.45% | 15.40 | 2.59 | 6.31 |
| 47. | 2014. 12. 31. | 1.11% | -0.42% | 0.92 | 1.60 | -1.21 |
| 48. | 2015. 1. 31. | -4.07% | -3.10% | 17.80 | 15.59 | 16.66 |
| 49. | 2015. 2. 28. | -1.65% | 5.49% | 3.25 | 21.57 | -8.37 |
| 50. | 2015. 3. 31. | -0.19% | -1.74% | 0.12 | 6.68 | 0.88 |
| 51. | 2015. 4. 30. | 0.35% | 0.85% | 0.04 | 0.00 | 0.00 |
| 52. | 2015. 5. 31. | -2.34% | 1.05% | 6.22 | 0.04 | -0.51 |
| 53. | 2015. 6. 30. | 4.98% | -2.10% | 23.34 | 8.68 | -14.23 |
| 54. | 2015. 7. 31. | -42.69% | 1.97% | 1,835.12 | 1.28 | -48.38 |
| 55. | 2015. 8. 31. | -4.07% | -6.26% | 17.80 | 50.45 | 29.97 |
| 56. | 2015. 9. 30. | -14.27% | -2.64% | 207.88 | 12.17 | 50.30 |
| 57. | 2015. 10. 31. | 13.82% | 8.30% | 186.81 | 55.56 | 101.87 |
| 58. | 2015. 11. 30. | 0.70% | 0.05% | 0.29 | 0.63 | -0.43 |
| 59. | 2015. 12. 31. | 1.63% | -1.75% | 2.19 | 6.75 | -3.85 |
| 합계 (Σ): | 3,305.71 | 670.89 | 397.17 | |||
모두 보기
분산BAX = Σ(RBAX,t–RBAX)2 ÷ (59 – 1)
= 3,305.71 ÷ (59 – 1)
= 57.00
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 670.89 ÷ (59 – 1)
= 11.57
공분산BAX, S&P 500 = Σ(RBAX,t–RBAX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 397.17 ÷ (59 – 1)
= 6.85
체계적인 위험 추정 (β)
| 분산BAX | 57.00 |
| 분산S&P 500 | 11.57 |
| 공분산BAX, S&P 500 | 6.85 |
| 상관 계수BAX, S&P 5001 | 0.27 |
| βBAX2 | 0.59 |
| αBAX3 | -0.35% |
계산
1 상관 계수BAX, S&P 500
= 공분산BAX, S&P 500 ÷ (표준 편차BAX × 표준 편차S&P 500)
= 6.85 ÷ (7.55% × 3.40%)
= 0.27
2 βBAX
= 공분산BAX, S&P 500 ÷ 분산S&P 500
= 6.85 ÷ 11.57
= 0.59
3 αBAX
= 평균의BAX – βBAX × 평균의S&P 500
= 0.15% – 0.59 × 0.84%
= -0.35%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Baxter | βBAX | 0.59 |
| 박스터 보통주에 대한 기대 수익률3 | E(RBAX) | 10.07% |
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(RBAX) = RF + βBAX [E(RM) – RF]
= 4.67% + 0.59 [13.79% – 4.67%]
= 10.07%