자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 NOV보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
National Oilwell Varco Inc., 월별 수익률
| National Oilwell Varco Inc. (NOV) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NOV,t1 | 피제수NOV,t1 | RNOV,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $73.90 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $79.57 | 7.67% | 1,327.22 | 3.20% | |
| 2. | 2011. 3. 31. | $79.27 | $0.11 | -0.24% | 1,325.83 | -0.10% |
| 3. | 2011. 4. 30. | $76.69 | -3.25% | 1,363.61 | 2.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | $37.34 | -0.80% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $33.49 | $0.46 | -9.08% | 2,043.94 | -1.75% |
| 평균의 (R): | -0.78% | 0.84% | ||||
| 표준 편차: | 9.11% | 3.40% | ||||
| National Oilwell Varco Inc. (NOV) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NOV,t1 | 피제수NOV,t1 | RNOV,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2011. 1. 31. | $73.90 | 1,286.12 | ||||
| 1. | 2011. 2. 28. | $79.57 | 7.67% | 1,327.22 | 3.20% | |
| 2. | 2011. 3. 31. | $79.27 | $0.11 | -0.24% | 1,325.83 | -0.10% |
| 3. | 2011. 4. 30. | $76.69 | -3.25% | 1,363.61 | 2.85% | |
| 4. | 2011. 5. 31. | $72.58 | -5.36% | 1,345.20 | -1.35% | |
| 5. | 2011. 6. 30. | $78.21 | $0.11 | 7.91% | 1,320.64 | -1.83% |
| 6. | 2011. 7. 31. | $80.57 | 3.02% | 1,292.28 | -2.15% | |
| 7. | 2011. 8. 31. | $66.12 | -17.93% | 1,218.89 | -5.68% | |
| 8. | 2011. 9. 30. | $51.22 | $0.11 | -22.37% | 1,131.42 | -7.18% |
| 9. | 2011. 10. 31. | $71.33 | 39.26% | 1,253.30 | 10.77% | |
| 10. | 2011. 11. 30. | $71.70 | $0.12 | 0.69% | 1,246.96 | -0.51% |
| 11. | 2011. 12. 31. | $67.99 | -5.17% | 1,257.60 | 0.85% | |
| 12. | 2012. 1. 31. | $73.98 | 8.81% | 1,312.41 | 4.36% | |
| 13. | 2012. 2. 29. | $82.53 | 11.56% | 1,365.68 | 4.06% | |
| 14. | 2012. 3. 31. | $79.47 | $0.12 | -3.56% | 1,408.47 | 3.13% |
| 15. | 2012. 4. 30. | $75.76 | -4.67% | 1,397.91 | -0.75% | |
| 16. | 2012. 5. 31. | $66.75 | -11.89% | 1,310.33 | -6.27% | |
| 17. | 2012. 6. 30. | $64.44 | $0.12 | -3.28% | 1,362.16 | 3.96% |
| 18. | 2012. 7. 31. | $72.30 | 12.20% | 1,379.32 | 1.26% | |
| 19. | 2012. 8. 31. | $78.80 | 8.99% | 1,406.58 | 1.98% | |
| 20. | 2012. 9. 30. | $80.11 | $0.12 | 1.81% | 1,440.67 | 2.42% |
| 21. | 2012. 10. 31. | $73.70 | -8.00% | 1,412.16 | -1.98% | |
| 22. | 2012. 11. 30. | $68.30 | -7.33% | 1,416.18 | 0.28% | |
| 23. | 2012. 12. 31. | $68.35 | $0.13 | 0.26% | 1,426.19 | 0.71% |
| 24. | 2013. 1. 31. | $74.14 | 8.47% | 1,498.11 | 5.04% | |
| 25. | 2013. 2. 28. | $68.13 | -8.11% | 1,514.68 | 1.11% | |
| 26. | 2013. 3. 31. | $70.75 | $0.13 | 4.04% | 1,569.19 | 3.60% |
| 27. | 2013. 4. 30. | $65.22 | -7.82% | 1,597.57 | 1.81% | |
| 28. | 2013. 5. 31. | $70.30 | 7.79% | 1,630.74 | 2.08% | |
| 29. | 2013. 6. 30. | $68.90 | $0.26 | -1.62% | 1,606.28 | -1.50% |
| 30. | 2013. 7. 31. | $70.17 | 1.84% | 1,685.73 | 4.95% | |
| 31. | 2013. 8. 31. | $74.30 | 5.89% | 1,632.97 | -3.13% | |
| 32. | 2013. 9. 30. | $78.11 | $0.26 | 5.48% | 1,681.55 | 2.97% |
| 33. | 2013. 10. 31. | $81.18 | 3.93% | 1,756.54 | 4.46% | |
| 34. | 2013. 11. 30. | $81.50 | 0.39% | 1,805.81 | 2.80% | |
| 35. | 2013. 12. 31. | $79.53 | $0.26 | -2.10% | 1,848.36 | 2.36% |
| 36. | 2014. 1. 31. | $75.01 | -5.68% | 1,782.59 | -3.56% | |
| 37. | 2014. 2. 28. | $77.04 | 2.71% | 1,859.45 | 4.31% | |
| 38. | 2014. 3. 31. | $77.87 | $0.26 | 1.41% | 1,872.34 | 0.69% |
| 39. | 2014. 4. 30. | $78.53 | 0.85% | 1,883.95 | 0.62% | |
| 40. | 2014. 5. 31. | $81.87 | 4.25% | 1,923.57 | 2.10% | |
| 41. | 2014. 6. 30. | $82.35 | $0.46 | 1.15% | 1,960.23 | 1.91% |
| 42. | 2014. 7. 31. | $81.04 | -1.59% | 1,930.67 | -1.51% | |
| 43. | 2014. 8. 31. | $86.43 | 6.65% | 2,003.37 | 3.77% | |
| 44. | 2014. 9. 30. | $76.10 | $0.46 | -11.42% | 1,972.29 | -1.55% |
| 45. | 2014. 10. 31. | $72.64 | -4.55% | 2,018.05 | 2.32% | |
| 46. | 2014. 11. 30. | $67.04 | -7.71% | 2,067.56 | 2.45% | |
| 47. | 2014. 12. 31. | $65.53 | $0.46 | -1.57% | 2,058.90 | -0.42% |
| 48. | 2015. 1. 31. | $54.43 | -16.94% | 1,994.99 | -3.10% | |
| 49. | 2015. 2. 28. | $54.35 | -0.15% | 2,104.50 | 5.49% | |
| 50. | 2015. 3. 31. | $49.99 | $0.46 | -7.18% | 2,067.89 | -1.74% |
| 51. | 2015. 4. 30. | $54.41 | 8.84% | 2,085.51 | 0.85% | |
| 52. | 2015. 5. 31. | $49.19 | -9.59% | 2,107.39 | 1.05% | |
| 53. | 2015. 6. 30. | $48.28 | $0.46 | -0.91% | 2,063.11 | -2.10% |
| 54. | 2015. 7. 31. | $42.13 | -12.74% | 2,103.84 | 1.97% | |
| 55. | 2015. 8. 31. | $42.33 | 0.47% | 1,972.18 | -6.26% | |
| 56. | 2015. 9. 30. | $37.65 | $0.46 | -9.97% | 1,920.03 | -2.64% |
| 57. | 2015. 10. 31. | $37.64 | -0.03% | 2,079.36 | 8.30% | |
| 58. | 2015. 11. 30. | $37.34 | -0.80% | 2,080.41 | 0.05% | |
| 59. | 2015. 12. 31. | $33.49 | $0.46 | -9.08% | 2,043.94 | -1.75% |
| 평균의 (R): | -0.78% | 0.84% | ||||
| 표준 편차: | 9.11% | 3.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 NOV의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
National Oilwell Varco Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RNOV,t | RS&P 500,t | (RNOV,t–RNOV)2 | (RS&P 500,t–RS&P 500)2 | (RNOV,t–RNOV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 7.67% | 3.20% | 71.51 | 5.53 | 19.88 |
| 2. | 2011. 3. 31. | -0.24% | -0.10% | 0.30 | 0.90 | -0.52 |
| 3. | 2011. 4. 30. | -3.25% | 2.85% | 6.10 | 4.02 | -4.95 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2015. 11. 30. | -0.80% | 0.05% | 0.00 | 0.63 | 0.01 |
| 59. | 2015. 12. 31. | -9.08% | -1.75% | 68.80 | 6.75 | 21.55 |
| 합계 (Σ): | 4,815.04 | 670.89 | 1,123.71 | |||
| t | 날짜 | RNOV,t | RS&P 500,t | (RNOV,t–RNOV)2 | (RS&P 500,t–RS&P 500)2 | (RNOV,t–RNOV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2011. 2. 28. | 7.67% | 3.20% | 71.51 | 5.53 | 19.88 |
| 2. | 2011. 3. 31. | -0.24% | -0.10% | 0.30 | 0.90 | -0.52 |
| 3. | 2011. 4. 30. | -3.25% | 2.85% | 6.10 | 4.02 | -4.95 |
| 4. | 2011. 5. 31. | -5.36% | -1.35% | 20.93 | 4.82 | 10.04 |
| 5. | 2011. 6. 30. | 7.91% | -1.83% | 75.56 | 7.13 | -23.21 |
| 6. | 2011. 7. 31. | 3.02% | -2.15% | 14.45 | 8.95 | -11.37 |
| 7. | 2011. 8. 31. | -17.93% | -5.68% | 294.15 | 42.56 | 111.89 |
| 8. | 2011. 9. 30. | -22.37% | -7.18% | 465.89 | 64.34 | 173.13 |
| 9. | 2011. 10. 31. | 39.26% | 10.77% | 1,603.68 | 98.56 | 397.56 |
| 10. | 2011. 11. 30. | 0.69% | -0.51% | 2.16 | 1.82 | -1.99 |
| 11. | 2011. 12. 31. | -5.17% | 0.85% | 19.28 | 0.00 | -0.04 |
| 12. | 2012. 1. 31. | 8.81% | 4.36% | 92.05 | 12.35 | 33.71 |
| 13. | 2012. 2. 29. | 11.56% | 4.06% | 152.30 | 10.33 | 39.67 |
| 14. | 2012. 3. 31. | -3.56% | 3.13% | 7.72 | 5.24 | -6.36 |
| 15. | 2012. 4. 30. | -4.67% | -0.75% | 15.09 | 2.54 | 6.19 |
| 16. | 2012. 5. 31. | -11.89% | -6.27% | 123.41 | 50.55 | 78.98 |
| 17. | 2012. 6. 30. | -3.28% | 3.96% | 6.23 | 9.68 | -7.77 |
| 18. | 2012. 7. 31. | 12.20% | 1.26% | 168.52 | 0.17 | 5.39 |
| 19. | 2012. 8. 31. | 8.99% | 1.98% | 95.54 | 1.28 | 11.06 |
| 20. | 2012. 9. 30. | 1.81% | 2.42% | 6.75 | 2.49 | 4.10 |
| 21. | 2012. 10. 31. | -8.00% | -1.98% | 52.09 | 7.97 | 20.38 |
| 22. | 2012. 11. 30. | -7.33% | 0.28% | 42.81 | 0.31 | 3.66 |
| 23. | 2012. 12. 31. | 0.26% | 0.71% | 1.10 | 0.02 | -0.14 |
| 24. | 2013. 1. 31. | 8.47% | 5.04% | 85.66 | 17.62 | 38.85 |
| 25. | 2013. 2. 28. | -8.11% | 1.11% | 53.62 | 0.07 | -1.91 |
| 26. | 2013. 3. 31. | 4.04% | 3.60% | 23.24 | 7.58 | 13.28 |
| 27. | 2013. 4. 30. | -7.82% | 1.81% | 49.45 | 0.93 | -6.78 |
| 28. | 2013. 5. 31. | 7.79% | 2.08% | 73.50 | 1.52 | 10.56 |
| 29. | 2013. 6. 30. | -1.62% | -1.50% | 0.70 | 5.50 | 1.96 |
| 30. | 2013. 7. 31. | 1.84% | 4.95% | 6.90 | 16.82 | 10.78 |
| 31. | 2013. 8. 31. | 5.89% | -3.13% | 44.48 | 15.80 | -26.51 |
| 32. | 2013. 9. 30. | 5.48% | 2.97% | 39.21 | 4.54 | 13.34 |
| 33. | 2013. 10. 31. | 3.93% | 4.46% | 22.23 | 13.07 | 17.04 |
| 34. | 2013. 11. 30. | 0.39% | 2.80% | 1.39 | 3.84 | 2.31 |
| 35. | 2013. 12. 31. | -2.10% | 2.36% | 1.73 | 2.28 | -1.99 |
| 36. | 2014. 1. 31. | -5.68% | -3.56% | 24.00 | 19.39 | 21.57 |
| 37. | 2014. 2. 28. | 2.71% | 4.31% | 12.18 | 12.02 | 12.10 |
| 38. | 2014. 3. 31. | 1.41% | 0.69% | 4.83 | 0.02 | -0.33 |
| 39. | 2014. 4. 30. | 0.85% | 0.62% | 2.66 | 0.05 | -0.37 |
| 40. | 2014. 5. 31. | 4.25% | 2.10% | 25.37 | 1.58 | 6.34 |
| 41. | 2014. 6. 30. | 1.15% | 1.91% | 3.73 | 1.13 | 2.05 |
| 42. | 2014. 7. 31. | -1.59% | -1.51% | 0.65 | 5.54 | 1.90 |
| 43. | 2014. 8. 31. | 6.65% | 3.77% | 55.28 | 8.53 | 21.72 |
| 44. | 2014. 9. 30. | -11.42% | -1.55% | 113.12 | 5.74 | 25.48 |
| 45. | 2014. 10. 31. | -4.55% | 2.32% | 14.16 | 2.18 | -5.55 |
| 46. | 2014. 11. 30. | -7.71% | 2.45% | 47.96 | 2.59 | -11.14 |
| 47. | 2014. 12. 31. | -1.57% | -0.42% | 0.61 | 1.60 | 0.99 |
| 48. | 2015. 1. 31. | -16.94% | -3.10% | 260.98 | 15.59 | 63.79 |
| 49. | 2015. 2. 28. | -0.15% | 5.49% | 0.41 | 21.57 | 2.96 |
| 50. | 2015. 3. 31. | -7.18% | -1.74% | 40.85 | 6.68 | 16.52 |
| 51. | 2015. 4. 30. | 8.84% | 0.85% | 92.66 | 0.00 | 0.07 |
| 52. | 2015. 5. 31. | -9.59% | 1.05% | 77.61 | 0.04 | -1.80 |
| 53. | 2015. 6. 30. | -0.91% | -2.10% | 0.02 | 8.68 | 0.39 |
| 54. | 2015. 7. 31. | -12.74% | 1.97% | 142.90 | 1.28 | -13.50 |
| 55. | 2015. 8. 31. | 0.47% | -6.26% | 1.58 | 50.45 | -8.94 |
| 56. | 2015. 9. 30. | -9.97% | -2.64% | 84.37 | 12.17 | 32.05 |
| 57. | 2015. 10. 31. | -0.03% | 8.30% | 0.57 | 55.56 | 5.65 |
| 58. | 2015. 11. 30. | -0.80% | 0.05% | 0.00 | 0.63 | 0.01 |
| 59. | 2015. 12. 31. | -9.08% | -1.75% | 68.80 | 6.75 | 21.55 |
| 합계 (Σ): | 4,815.04 | 670.89 | 1,123.71 | |||
모두 보기
분산NOV = Σ(RNOV,t–RNOV)2 ÷ (59 – 1)
= 4,815.04 ÷ (59 – 1)
= 83.02
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 670.89 ÷ (59 – 1)
= 11.57
공분산NOV, S&P 500 = Σ(RNOV,t–RNOV)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,123.71 ÷ (59 – 1)
= 19.37
체계적인 위험 추정 (β)
| 분산NOV | 83.02 |
| 분산S&P 500 | 11.57 |
| 공분산NOV, S&P 500 | 19.37 |
| 상관 계수NOV, S&P 5001 | 0.63 |
| βNOV2 | 1.67 |
| αNOV3 | -2.20% |
계산
1 상관 계수NOV, S&P 500
= 공분산NOV, S&P 500 ÷ (표준 편차NOV × 표준 편차S&P 500)
= 19.37 ÷ (9.11% × 3.40%)
= 0.63
2 βNOV
= 공분산NOV, S&P 500 ÷ 분산S&P 500
= 19.37 ÷ 11.57
= 1.67
3 αNOV
= 평균의NOV – βNOV × 평균의S&P 500
= -0.78% – 1.67 × 0.84%
= -2.20%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험NOV | βNOV | 1.67 |
| NOV 보통주의 예상 수익률3 | E(RNOV) | 21.83% |
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(RNOV) = RF + βNOV [E(RM) – RF]
= 4.60% + 1.67 [14.89% – 4.60%]
= 21.83%