자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Halliburton보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Halliburton Co., 월별 수익률
| Halliburton Co. (HAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HAL,t1 | 피제수HAL,t1 | RHAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2014. 1. 31. | $49.01 | 1,782.59 | ||||
| 1. | 2014. 2. 28. | $57.00 | 16.30% | 1,859.45 | 4.31% | |
| 2. | 2014. 3. 31. | $58.89 | $0.15 | 3.58% | 1,872.34 | 0.69% |
| 3. | 2014. 4. 30. | $63.07 | 7.10% | 1,883.95 | 0.62% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2018. 11. 30. | $31.43 | -9.37% | 2,760.17 | 1.79% | |
| 59. | 2018. 12. 31. | $26.58 | $0.18 | -14.86% | 2,506.85 | -9.18% |
| 평균의 (R): | -0.48% | 0.63% | ||||
| 표준 편차: | 9.13% | 3.13% | ||||
| Halliburton Co. (HAL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값HAL,t1 | 피제수HAL,t1 | RHAL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2014. 1. 31. | $49.01 | 1,782.59 | ||||
| 1. | 2014. 2. 28. | $57.00 | 16.30% | 1,859.45 | 4.31% | |
| 2. | 2014. 3. 31. | $58.89 | $0.15 | 3.58% | 1,872.34 | 0.69% |
| 3. | 2014. 4. 30. | $63.07 | 7.10% | 1,883.95 | 0.62% | |
| 4. | 2014. 5. 31. | $64.64 | 2.49% | 1,923.57 | 2.10% | |
| 5. | 2014. 6. 30. | $71.01 | $0.15 | 10.09% | 1,960.23 | 1.91% |
| 6. | 2014. 7. 31. | $68.99 | -2.84% | 1,930.67 | -1.51% | |
| 7. | 2014. 8. 31. | $67.61 | $0.15 | -1.78% | 2,003.37 | 3.77% |
| 8. | 2014. 9. 30. | $64.51 | -4.59% | 1,972.29 | -1.55% | |
| 9. | 2014. 10. 31. | $55.14 | -14.52% | 2,018.05 | 2.32% | |
| 10. | 2014. 11. 30. | $42.20 | -23.47% | 2,067.56 | 2.45% | |
| 11. | 2014. 12. 31. | $39.33 | $0.18 | -6.37% | 2,058.90 | -0.42% |
| 12. | 2015. 1. 31. | $39.99 | 1.68% | 1,994.99 | -3.10% | |
| 13. | 2015. 2. 28. | $42.94 | 7.38% | 2,104.50 | 5.49% | |
| 14. | 2015. 3. 31. | $43.88 | $0.18 | 2.61% | 2,067.89 | -1.74% |
| 15. | 2015. 4. 30. | $48.95 | 11.55% | 2,085.51 | 0.85% | |
| 16. | 2015. 5. 31. | $45.40 | -7.25% | 2,107.39 | 1.05% | |
| 17. | 2015. 6. 30. | $43.07 | $0.18 | -4.74% | 2,063.11 | -2.10% |
| 18. | 2015. 7. 31. | $41.79 | -2.97% | 2,103.84 | 1.97% | |
| 19. | 2015. 8. 31. | $39.35 | $0.18 | -5.41% | 1,972.18 | -6.26% |
| 20. | 2015. 9. 30. | $35.35 | -10.17% | 1,920.03 | -2.64% | |
| 21. | 2015. 10. 31. | $38.38 | 8.57% | 2,079.36 | 8.30% | |
| 22. | 2015. 11. 30. | $39.85 | 3.83% | 2,080.41 | 0.05% | |
| 23. | 2015. 12. 31. | $34.04 | $0.18 | -14.13% | 2,043.94 | -1.75% |
| 24. | 2016. 1. 31. | $31.79 | -6.61% | 1,940.24 | -5.07% | |
| 25. | 2016. 2. 29. | $32.28 | $0.18 | 2.11% | 1,932.23 | -0.41% |
| 26. | 2016. 3. 31. | $35.72 | 10.66% | 2,059.74 | 6.60% | |
| 27. | 2016. 4. 30. | $41.31 | 15.65% | 2,065.30 | 0.27% | |
| 28. | 2016. 5. 31. | $42.18 | $0.18 | 2.54% | 2,096.95 | 1.53% |
| 29. | 2016. 6. 30. | $45.29 | 7.37% | 2,098.86 | 0.09% | |
| 30. | 2016. 7. 31. | $43.66 | -3.60% | 2,173.60 | 3.56% | |
| 31. | 2016. 8. 31. | $43.01 | -1.49% | 2,170.95 | -0.12% | |
| 32. | 2016. 9. 30. | $44.88 | $0.18 | 4.77% | 2,168.27 | -0.12% |
| 33. | 2016. 10. 31. | $46.00 | 2.50% | 2,126.15 | -1.94% | |
| 34. | 2016. 11. 30. | $53.09 | 15.41% | 2,198.81 | 3.42% | |
| 35. | 2016. 12. 31. | $54.09 | $0.18 | 2.22% | 2,238.83 | 1.82% |
| 36. | 2017. 1. 31. | $56.57 | 4.58% | 2,278.87 | 1.79% | |
| 37. | 2017. 2. 28. | $53.46 | $0.18 | -5.18% | 2,363.64 | 3.72% |
| 38. | 2017. 3. 31. | $49.21 | -7.95% | 2,362.72 | -0.04% | |
| 39. | 2017. 4. 30. | $45.88 | -6.77% | 2,384.20 | 0.91% | |
| 40. | 2017. 5. 31. | $45.19 | -1.50% | 2,411.80 | 1.16% | |
| 41. | 2017. 6. 30. | $42.71 | $0.18 | -5.09% | 2,423.41 | 0.48% |
| 42. | 2017. 7. 31. | $42.44 | -0.63% | 2,470.30 | 1.93% | |
| 43. | 2017. 8. 31. | $38.97 | -8.18% | 2,471.65 | 0.05% | |
| 44. | 2017. 9. 30. | $46.03 | $0.18 | 18.58% | 2,519.36 | 1.93% |
| 45. | 2017. 10. 31. | $42.74 | -7.15% | 2,575.26 | 2.22% | |
| 46. | 2017. 11. 30. | $41.78 | -2.25% | 2,647.58 | 2.81% | |
| 47. | 2017. 12. 31. | $48.87 | $0.18 | 17.40% | 2,673.61 | 0.98% |
| 48. | 2018. 1. 31. | $53.70 | 9.88% | 2,823.81 | 5.62% | |
| 49. | 2018. 2. 28. | $46.42 | -13.56% | 2,713.83 | -3.89% | |
| 50. | 2018. 3. 31. | $46.94 | $0.18 | 1.51% | 2,640.87 | -2.69% |
| 51. | 2018. 4. 30. | $52.99 | 12.89% | 2,648.05 | 0.27% | |
| 52. | 2018. 5. 31. | $49.74 | -6.13% | 2,705.27 | 2.16% | |
| 53. | 2018. 6. 30. | $45.06 | $0.18 | -9.05% | 2,718.37 | 0.48% |
| 54. | 2018. 7. 31. | $42.42 | -5.86% | 2,816.29 | 3.60% | |
| 55. | 2018. 8. 31. | $39.89 | -5.96% | 2,901.52 | 3.03% | |
| 56. | 2018. 9. 30. | $40.53 | $0.18 | 2.06% | 2,913.98 | 0.43% |
| 57. | 2018. 10. 31. | $34.68 | -14.43% | 2,711.74 | -6.94% | |
| 58. | 2018. 11. 30. | $31.43 | -9.37% | 2,760.17 | 1.79% | |
| 59. | 2018. 12. 31. | $26.58 | $0.18 | -14.86% | 2,506.85 | -9.18% |
| 평균의 (R): | -0.48% | 0.63% | ||||
| 표준 편차: | 9.13% | 3.13% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 HAL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Halliburton Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RHAL,t | RS&P 500,t | (RHAL,t–RHAL)2 | (RS&P 500,t–RS&P 500)2 | (RHAL,t–RHAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2014. 2. 28. | 16.30% | 4.31% | 281.79 | 13.57 | 61.84 |
| 2. | 2014. 3. 31. | 3.58% | 0.69% | 16.51 | 0.00 | 0.27 |
| 3. | 2014. 4. 30. | 7.10% | 0.62% | 57.49 | 0.00 | -0.06 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2018. 11. 30. | -9.37% | 1.79% | 78.99 | 1.34 | -10.29 |
| 59. | 2018. 12. 31. | -14.86% | -9.18% | 206.63 | 96.15 | 140.95 |
| 합계 (Σ): | 4,830.18 | 566.60 | 659.66 | |||
| t | 날짜 | RHAL,t | RS&P 500,t | (RHAL,t–RHAL)2 | (RS&P 500,t–RS&P 500)2 | (RHAL,t–RHAL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2014. 2. 28. | 16.30% | 4.31% | 281.79 | 13.57 | 61.84 |
| 2. | 2014. 3. 31. | 3.58% | 0.69% | 16.51 | 0.00 | 0.27 |
| 3. | 2014. 4. 30. | 7.10% | 0.62% | 57.49 | 0.00 | -0.06 |
| 4. | 2014. 5. 31. | 2.49% | 2.10% | 8.84 | 2.18 | 4.39 |
| 5. | 2014. 6. 30. | 10.09% | 1.91% | 111.74 | 1.63 | 13.51 |
| 6. | 2014. 7. 31. | -2.84% | -1.51% | 5.57 | 4.56 | 5.04 |
| 7. | 2014. 8. 31. | -1.78% | 3.77% | 1.69 | 9.84 | -4.08 |
| 8. | 2014. 9. 30. | -4.59% | -1.55% | 16.82 | 4.75 | 8.94 |
| 9. | 2014. 10. 31. | -14.52% | 2.32% | 197.15 | 2.86 | -23.76 |
| 10. | 2014. 11. 30. | -23.47% | 2.45% | 528.25 | 3.33 | -41.95 |
| 11. | 2014. 12. 31. | -6.37% | -0.42% | 34.70 | 1.10 | 6.17 |
| 12. | 2015. 1. 31. | 1.68% | -3.10% | 4.67 | 13.93 | -8.07 |
| 13. | 2015. 2. 28. | 7.38% | 5.49% | 61.79 | 23.63 | 38.21 |
| 14. | 2015. 3. 31. | 2.61% | -1.74% | 9.56 | 5.61 | -7.32 |
| 15. | 2015. 4. 30. | 11.55% | 0.85% | 144.92 | 0.05 | 2.70 |
| 16. | 2015. 5. 31. | -7.25% | 1.05% | 45.81 | 0.18 | -2.85 |
| 17. | 2015. 6. 30. | -4.74% | -2.10% | 18.08 | 7.45 | 11.60 |
| 18. | 2015. 7. 31. | -2.97% | 1.97% | 6.19 | 1.81 | -3.35 |
| 19. | 2015. 8. 31. | -5.41% | -6.26% | 24.25 | 47.42 | 33.91 |
| 20. | 2015. 9. 30. | -10.17% | -2.64% | 93.73 | 10.71 | 31.68 |
| 21. | 2015. 10. 31. | 8.57% | 8.30% | 82.00 | 58.83 | 69.46 |
| 22. | 2015. 11. 30. | 3.83% | 0.05% | 18.61 | 0.33 | -2.49 |
| 23. | 2015. 12. 31. | -14.13% | -1.75% | 186.16 | 5.67 | 32.49 |
| 24. | 2016. 1. 31. | -6.61% | -5.07% | 37.53 | 32.51 | 34.93 |
| 25. | 2016. 2. 29. | 2.11% | -0.41% | 6.72 | 1.08 | -2.70 |
| 26. | 2016. 3. 31. | 10.66% | 6.60% | 124.12 | 35.65 | 66.52 |
| 27. | 2016. 4. 30. | 15.65% | 0.27% | 260.29 | 0.13 | -5.78 |
| 28. | 2016. 5. 31. | 2.54% | 1.53% | 9.15 | 0.82 | 2.74 |
| 29. | 2016. 6. 30. | 7.37% | 0.09% | 61.73 | 0.29 | -4.22 |
| 30. | 2016. 7. 31. | -3.60% | 3.56% | 9.70 | 8.60 | -9.14 |
| 31. | 2016. 8. 31. | -1.49% | -0.12% | 1.01 | 0.56 | 0.75 |
| 32. | 2016. 9. 30. | 4.77% | -0.12% | 27.57 | 0.56 | -3.95 |
| 33. | 2016. 10. 31. | 2.50% | -1.94% | 8.88 | 6.61 | -7.66 |
| 34. | 2016. 11. 30. | 15.41% | 3.42% | 252.71 | 7.78 | 44.34 |
| 35. | 2016. 12. 31. | 2.22% | 1.82% | 7.33 | 1.42 | 3.23 |
| 36. | 2017. 1. 31. | 4.58% | 1.79% | 25.69 | 1.35 | 5.88 |
| 37. | 2017. 2. 28. | -5.18% | 3.72% | 22.05 | 9.56 | -14.52 |
| 38. | 2017. 3. 31. | -7.95% | -0.04% | 55.74 | 0.44 | 4.98 |
| 39. | 2017. 4. 30. | -6.77% | 0.91% | 39.48 | 0.08 | -1.77 |
| 40. | 2017. 5. 31. | -1.50% | 1.16% | 1.04 | 0.28 | -0.54 |
| 41. | 2017. 6. 30. | -5.09% | 0.48% | 21.21 | 0.02 | 0.68 |
| 42. | 2017. 7. 31. | -0.63% | 1.93% | 0.02 | 1.71 | -0.19 |
| 43. | 2017. 8. 31. | -8.18% | 0.05% | 59.17 | 0.33 | 4.41 |
| 44. | 2017. 9. 30. | 18.58% | 1.93% | 363.37 | 1.70 | 24.83 |
| 45. | 2017. 10. 31. | -7.15% | 2.22% | 44.40 | 2.53 | -10.60 |
| 46. | 2017. 11. 30. | -2.25% | 2.81% | 3.11 | 4.75 | -3.84 |
| 47. | 2017. 12. 31. | 17.40% | 0.98% | 319.86 | 0.13 | 6.35 |
| 48. | 2018. 1. 31. | 9.88% | 5.62% | 107.48 | 24.90 | 51.73 |
| 49. | 2018. 2. 28. | -13.56% | -3.89% | 170.90 | 20.45 | 59.12 |
| 50. | 2018. 3. 31. | 1.51% | -2.69% | 3.97 | 11.00 | -6.61 |
| 51. | 2018. 4. 30. | 12.89% | 0.27% | 178.83 | 0.13 | -4.76 |
| 52. | 2018. 5. 31. | -6.13% | 2.16% | 31.91 | 2.35 | -8.66 |
| 53. | 2018. 6. 30. | -9.05% | 0.48% | 73.33 | 0.02 | 1.23 |
| 54. | 2018. 7. 31. | -5.86% | 3.60% | 28.89 | 8.85 | -15.99 |
| 55. | 2018. 8. 31. | -5.96% | 3.03% | 30.03 | 5.75 | -13.14 |
| 56. | 2018. 9. 30. | 2.06% | 0.43% | 6.45 | 0.04 | -0.50 |
| 57. | 2018. 10. 31. | -14.43% | -6.94% | 194.60 | 57.28 | 105.58 |
| 58. | 2018. 11. 30. | -9.37% | 1.79% | 78.99 | 1.34 | -10.29 |
| 59. | 2018. 12. 31. | -14.86% | -9.18% | 206.63 | 96.15 | 140.95 |
| 합계 (Σ): | 4,830.18 | 566.60 | 659.66 | |||
모두 보기
분산HAL = Σ(RHAL,t–RHAL)2 ÷ (59 – 1)
= 4,830.18 ÷ (59 – 1)
= 83.28
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 566.60 ÷ (59 – 1)
= 9.77
공분산HAL, S&P 500 = Σ(RHAL,t–RHAL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 659.66 ÷ (59 – 1)
= 11.37
체계적인 위험 추정 (β)
| 분산HAL | 83.28 |
| 분산S&P 500 | 9.77 |
| 공분산HAL, S&P 500 | 11.37 |
| 상관 계수HAL, S&P 5001 | 0.40 |
| βHAL2 | 1.16 |
| αHAL3 | -1.22% |
계산
1 상관 계수HAL, S&P 500
= 공분산HAL, S&P 500 ÷ (표준 편차HAL × 표준 편차S&P 500)
= 11.37 ÷ (9.13% × 3.13%)
= 0.40
2 βHAL
= 공분산HAL, S&P 500 ÷ 분산S&P 500
= 11.37 ÷ 9.77
= 1.16
3 αHAL
= 평균의HAL – βHAL × 평균의S&P 500
= -0.48% – 1.16 × 0.63%
= -1.22%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.49% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.87% |
| 보통주의 체계적 위험Halliburton | βHAL | 1.16 |
| Halliburton 보통주에 대한 예상 수익률3 | E(RHAL) | 16.58% |
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(RHAL) = RF + βHAL [E(RM) – RF]
= 4.49% + 1.16 [14.87% – 4.49%]
= 16.58%