자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 GlaxoSmithKline보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
GlaxoSmithKline PLC, 월별 수익률
| GlaxoSmithKline PLC (GSK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GSK,t1 | 피제수GSK,t1 | RGSK,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2010. 1. 31. | $39.01 | 1,073.87 | ||||
| 1. | 2010. 2. 28. | $37.14 | $0.5737 | -3.32% | 1,104.49 | 2.85% |
| 2. | 2010. 3. 31. | $38.52 | 3.72% | 1,169.43 | 5.88% | |
| 3. | 2010. 4. 30. | $37.29 | -3.19% | 1,186.69 | 1.48% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2014. 11. 30. | $46.45 | $0.613 | 3.46% | 2,067.56 | 2.45% |
| 59. | 2014. 12. 31. | $42.74 | -7.99% | 2,058.90 | -0.42% | |
| 평균의 (R): | 0.71% | 1.18% | ||||
| 표준 편차: | 4.66% | 3.73% | ||||
| GlaxoSmithKline PLC (GSK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GSK,t1 | 피제수GSK,t1 | RGSK,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2010. 1. 31. | $39.01 | 1,073.87 | ||||
| 1. | 2010. 2. 28. | $37.14 | $0.5737 | -3.32% | 1,104.49 | 2.85% |
| 2. | 2010. 3. 31. | $38.52 | 3.72% | 1,169.43 | 5.88% | |
| 3. | 2010. 4. 30. | $37.29 | -3.19% | 1,186.69 | 1.48% | |
| 4. | 2010. 5. 31. | $33.46 | $0.4603 | -9.04% | 1,089.41 | -8.20% |
| 5. | 2010. 6. 30. | $34.01 | 1.64% | 1,030.71 | -5.39% | |
| 6. | 2010. 7. 31. | $35.17 | $0.4573 | 4.76% | 1,101.60 | 6.88% |
| 7. | 2010. 8. 31. | $37.40 | 6.34% | 1,049.33 | -4.74% | |
| 8. | 2010. 9. 30. | $39.52 | 5.67% | 1,141.20 | 8.76% | |
| 9. | 2010. 10. 31. | $39.04 | $0.5074 | 0.07% | 1,183.26 | 3.69% |
| 10. | 2010. 11. 30. | $38.28 | -1.95% | 1,180.55 | -0.23% | |
| 11. | 2010. 12. 31. | $39.22 | 2.46% | 1,257.64 | 6.53% | |
| 12. | 2011. 1. 31. | $36.33 | -7.37% | 1,286.12 | 2.26% | |
| 13. | 2011. 2. 28. | $38.61 | $0.6153 | 7.97% | 1,327.22 | 3.20% |
| 14. | 2011. 3. 31. | $38.41 | -0.52% | 1,325.83 | -0.10% | |
| 15. | 2011. 4. 30. | $43.66 | 13.67% | 1,363.61 | 2.85% | |
| 16. | 2011. 5. 31. | $43.46 | $0.5263 | 0.75% | 1,345.20 | -1.35% |
| 17. | 2011. 6. 30. | $42.90 | -1.29% | 1,320.64 | -1.83% | |
| 18. | 2011. 7. 31. | $44.42 | 3.54% | 1,292.28 | -2.15% | |
| 19. | 2011. 8. 31. | $42.83 | $0.5211 | -2.41% | 1,218.89 | -5.68% |
| 20. | 2011. 9. 30. | $41.29 | -3.60% | 1,131.42 | -7.18% | |
| 21. | 2011. 10. 31. | $44.79 | 8.48% | 1,253.30 | 10.77% | |
| 22. | 2011. 11. 30. | $44.48 | $0.543 | 0.52% | 1,246.96 | -0.51% |
| 23. | 2011. 12. 31. | $45.63 | 2.59% | 1,257.60 | 0.85% | |
| 24. | 2012. 1. 31. | $44.54 | -2.39% | 1,312.41 | 4.36% | |
| 25. | 2012. 2. 29. | $44.31 | $0.8213 | 1.33% | 1,365.68 | 4.06% |
| 26. | 2012. 3. 31. | $44.91 | 1.35% | 1,408.47 | 3.13% | |
| 27. | 2012. 4. 30. | $46.23 | 2.94% | 1,397.91 | -0.75% | |
| 28. | 2012. 5. 31. | $44.11 | $0.5491 | -3.40% | 1,310.33 | -6.27% |
| 29. | 2012. 6. 30. | $45.57 | 3.31% | 1,362.16 | 3.96% | |
| 30. | 2012. 7. 31. | $46.00 | 0.94% | 1,379.32 | 1.26% | |
| 31. | 2012. 8. 31. | $45.49 | $0.5279 | 0.04% | 1,406.58 | 1.98% |
| 32. | 2012. 9. 30. | $46.24 | 1.65% | 1,440.67 | 2.42% | |
| 33. | 2012. 10. 31. | $44.90 | -2.90% | 1,412.16 | -1.98% | |
| 34. | 2012. 11. 30. | $43.01 | $0.579 | -2.92% | 1,416.18 | 0.28% |
| 35. | 2012. 12. 31. | $43.47 | 1.07% | 1,426.19 | 0.71% | |
| 36. | 2013. 1. 31. | $45.61 | 4.92% | 1,498.11 | 5.04% | |
| 37. | 2013. 2. 28. | $44.03 | $0.6895 | -1.95% | 1,514.68 | 1.11% |
| 38. | 2013. 3. 31. | $46.91 | 6.54% | 1,569.19 | 3.60% | |
| 39. | 2013. 4. 30. | $51.64 | 10.08% | 1,597.57 | 1.81% | |
| 40. | 2013. 5. 31. | $51.77 | $0.5502 | 1.32% | 1,630.74 | 2.08% |
| 41. | 2013. 6. 30. | $49.97 | -3.48% | 1,606.28 | -1.50% | |
| 42. | 2013. 7. 31. | $50.96 | 1.98% | 1,685.73 | 4.95% | |
| 43. | 2013. 8. 31. | $50.89 | $0.5532 | 0.95% | 1,632.97 | -3.13% |
| 44. | 2013. 9. 30. | $50.17 | -1.41% | 1,681.55 | 2.97% | |
| 45. | 2013. 10. 31. | $52.63 | 4.90% | 1,756.54 | 4.46% | |
| 46. | 2013. 11. 30. | $52.92 | $0.6161 | 1.72% | 1,805.81 | 2.80% |
| 47. | 2013. 12. 31. | $53.39 | 0.89% | 1,848.36 | 2.36% | |
| 48. | 2014. 1. 31. | $51.54 | -3.47% | 1,782.59 | -3.56% | |
| 49. | 2014. 2. 28. | $55.94 | $0.7496 | 9.99% | 1,859.45 | 4.31% |
| 50. | 2014. 3. 31. | $53.43 | -4.49% | 1,872.34 | 0.69% | |
| 51. | 2014. 4. 30. | $55.37 | 3.63% | 1,883.95 | 0.62% | |
| 52. | 2014. 5. 31. | $53.94 | $0.64 | -1.43% | 1,923.57 | 2.10% |
| 53. | 2014. 6. 30. | $53.48 | -0.85% | 1,960.23 | 1.91% | |
| 54. | 2014. 7. 31. | $48.37 | -9.55% | 1,930.67 | -1.51% | |
| 55. | 2014. 8. 31. | $49.10 | $0.6482 | 2.85% | 2,003.37 | 3.77% |
| 56. | 2014. 9. 30. | $45.97 | -6.37% | 1,972.29 | -1.55% | |
| 57. | 2014. 10. 31. | $45.49 | -1.04% | 2,018.05 | 2.32% | |
| 58. | 2014. 11. 30. | $46.45 | $0.613 | 3.46% | 2,067.56 | 2.45% |
| 59. | 2014. 12. 31. | $42.74 | -7.99% | 2,058.90 | -0.42% | |
| 평균의 (R): | 0.71% | 1.18% | ||||
| 표준 편차: | 4.66% | 3.73% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 GSK의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
GlaxoSmithKline PLC, 수익률의 분산 및 공분산 계산
| t | 날짜 | RGSK,t | RS&P 500,t | (RGSK,t–RGSK)2 | (RS&P 500,t–RS&P 500)2 | (RGSK,t–RGSK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2010. 2. 28. | -3.32% | 2.85% | 16.24 | 2.80 | -6.74 |
| 2. | 2010. 3. 31. | 3.72% | 5.88% | 9.05 | 22.11 | 14.15 |
| 3. | 2010. 4. 30. | -3.19% | 1.48% | 15.21 | 0.09 | -1.16 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2014. 11. 30. | 3.46% | 2.45% | 7.57 | 1.63 | 3.51 |
| 59. | 2014. 12. 31. | -7.99% | -0.42% | 75.59 | 2.55 | 13.88 |
| 합계 (Σ): | 1,259.77 | 809.11 | 507.46 | |||
| t | 날짜 | RGSK,t | RS&P 500,t | (RGSK,t–RGSK)2 | (RS&P 500,t–RS&P 500)2 | (RGSK,t–RGSK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2010. 2. 28. | -3.32% | 2.85% | 16.24 | 2.80 | -6.74 |
| 2. | 2010. 3. 31. | 3.72% | 5.88% | 9.05 | 22.11 | 14.15 |
| 3. | 2010. 4. 30. | -3.19% | 1.48% | 15.21 | 0.09 | -1.16 |
| 4. | 2010. 5. 31. | -9.04% | -8.20% | 94.93 | 87.90 | 91.35 |
| 5. | 2010. 6. 30. | 1.64% | -5.39% | 0.88 | 43.11 | -6.15 |
| 6. | 2010. 7. 31. | 4.76% | 6.88% | 16.39 | 32.49 | 23.08 |
| 7. | 2010. 8. 31. | 6.34% | -4.74% | 31.74 | 35.08 | -33.37 |
| 8. | 2010. 9. 30. | 5.67% | 8.76% | 24.62 | 57.42 | 37.60 |
| 9. | 2010. 10. 31. | 0.07% | 3.69% | 0.41 | 6.29 | -1.60 |
| 10. | 2010. 11. 30. | -1.95% | -0.23% | 7.04 | 1.98 | 3.73 |
| 11. | 2010. 12. 31. | 2.46% | 6.53% | 3.06 | 28.65 | 9.36 |
| 12. | 2011. 1. 31. | -7.37% | 2.26% | 65.22 | 1.18 | -8.78 |
| 13. | 2011. 2. 28. | 7.97% | 3.20% | 52.74 | 4.07 | 14.66 |
| 14. | 2011. 3. 31. | -0.52% | -0.10% | 1.50 | 1.64 | 1.57 |
| 15. | 2011. 4. 30. | 13.67% | 2.85% | 168.00 | 2.79 | 21.67 |
| 16. | 2011. 5. 31. | 0.75% | -1.35% | 0.00 | 6.39 | -0.10 |
| 17. | 2011. 6. 30. | -1.29% | -1.83% | 3.98 | 9.02 | 5.99 |
| 18. | 2011. 7. 31. | 3.54% | -2.15% | 8.04 | 11.06 | -9.43 |
| 19. | 2011. 8. 31. | -2.41% | -5.68% | 9.69 | 47.02 | 21.35 |
| 20. | 2011. 9. 30. | -3.60% | -7.18% | 18.51 | 69.79 | 35.94 |
| 21. | 2011. 10. 31. | 8.48% | 10.77% | 60.37 | 92.06 | 74.55 |
| 22. | 2011. 11. 30. | 0.52% | -0.51% | 0.03 | 2.83 | 0.31 |
| 23. | 2011. 12. 31. | 2.59% | 0.85% | 3.53 | 0.11 | -0.61 |
| 24. | 2012. 1. 31. | -2.39% | 4.36% | 9.58 | 10.12 | -9.85 |
| 25. | 2012. 2. 29. | 1.33% | 4.06% | 0.39 | 8.30 | 1.79 |
| 26. | 2012. 3. 31. | 1.35% | 3.13% | 0.42 | 3.82 | 1.27 |
| 27. | 2012. 4. 30. | 2.94% | -0.75% | 4.98 | 3.72 | -4.30 |
| 28. | 2012. 5. 31. | -3.40% | -6.27% | 16.85 | 55.40 | 30.55 |
| 29. | 2012. 6. 30. | 3.31% | 3.96% | 6.78 | 7.72 | 7.23 |
| 30. | 2012. 7. 31. | 0.94% | 1.26% | 0.06 | 0.01 | 0.02 |
| 31. | 2012. 8. 31. | 0.04% | 1.98% | 0.45 | 0.64 | -0.53 |
| 32. | 2012. 9. 30. | 1.65% | 2.42% | 0.89 | 1.55 | 1.17 |
| 33. | 2012. 10. 31. | -2.90% | -1.98% | 13.00 | 9.96 | 11.38 |
| 34. | 2012. 11. 30. | -2.92% | 0.28% | 13.15 | 0.80 | 3.24 |
| 35. | 2012. 12. 31. | 1.07% | 0.71% | 0.13 | 0.22 | -0.17 |
| 36. | 2013. 1. 31. | 4.92% | 5.04% | 17.77 | 14.94 | 16.30 |
| 37. | 2013. 2. 28. | -1.95% | 1.11% | 7.07 | 0.01 | 0.19 |
| 38. | 2013. 3. 31. | 6.54% | 3.60% | 34.04 | 5.86 | 14.12 |
| 39. | 2013. 4. 30. | 10.08% | 1.81% | 87.91 | 0.40 | 5.91 |
| 40. | 2013. 5. 31. | 1.32% | 2.08% | 0.37 | 0.81 | 0.55 |
| 41. | 2013. 6. 30. | -3.48% | -1.50% | 17.50 | 7.17 | 11.20 |
| 42. | 2013. 7. 31. | 1.98% | 4.95% | 1.62 | 14.20 | 4.80 |
| 43. | 2013. 8. 31. | 0.95% | -3.13% | 0.06 | 18.55 | -1.04 |
| 44. | 2013. 9. 30. | -1.41% | 2.97% | 4.50 | 3.23 | -3.81 |
| 45. | 2013. 10. 31. | 4.90% | 4.46% | 17.61 | 10.77 | 13.77 |
| 46. | 2013. 11. 30. | 1.72% | 2.80% | 1.03 | 2.65 | 1.65 |
| 47. | 2013. 12. 31. | 0.89% | 2.36% | 0.03 | 1.39 | 0.21 |
| 48. | 2014. 1. 31. | -3.47% | -3.56% | 17.41 | 22.43 | 19.76 |
| 49. | 2014. 2. 28. | 9.99% | 4.31% | 86.20 | 9.82 | 29.10 |
| 50. | 2014. 3. 31. | -4.49% | 0.69% | 26.98 | 0.23 | 2.52 |
| 51. | 2014. 4. 30. | 3.63% | 0.62% | 8.55 | 0.31 | -1.63 |
| 52. | 2014. 5. 31. | -1.43% | 2.10% | 4.55 | 0.86 | -1.97 |
| 53. | 2014. 6. 30. | -0.85% | 1.91% | 2.43 | 0.53 | -1.14 |
| 54. | 2014. 7. 31. | -9.55% | -1.51% | 105.31 | 7.21 | 27.56 |
| 55. | 2014. 8. 31. | 2.85% | 3.77% | 4.59 | 6.70 | 5.54 |
| 56. | 2014. 9. 30. | -6.37% | -1.55% | 50.15 | 7.45 | 19.33 |
| 57. | 2014. 10. 31. | -1.04% | 2.32% | 3.07 | 1.31 | -2.00 |
| 58. | 2014. 11. 30. | 3.46% | 2.45% | 7.57 | 1.63 | 3.51 |
| 59. | 2014. 12. 31. | -7.99% | -0.42% | 75.59 | 2.55 | 13.88 |
| 합계 (Σ): | 1,259.77 | 809.11 | 507.46 | |||
모두 표시
분산GSK = Σ(RGSK,t–RGSK)2 ÷ (59 – 1)
= 1,259.77 ÷ (59 – 1)
= 21.72
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 809.11 ÷ (59 – 1)
= 13.95
공분산GSK, S&P 500 = Σ(RGSK,t–RGSK)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 507.46 ÷ (59 – 1)
= 8.75
체계적인 위험 추정 (β)
| 분산GSK | 21.72 |
| 분산S&P 500 | 13.95 |
| 공분산GSK, S&P 500 | 8.75 |
| 상관 계수GSK, S&P 5001 | 0.50 |
| βGSK2 | 0.63 |
| αGSK3 | -0.03% |
계산
1 상관 계수GSK, S&P 500
= 공분산GSK, S&P 500 ÷ (표준 편차GSK × 표준 편차S&P 500)
= 8.75 ÷ (4.66% × 3.73%)
= 0.50
2 βGSK
= 공분산GSK, S&P 500 ÷ 분산S&P 500
= 8.75 ÷ 13.95
= 0.63
3 αGSK
= 평균의GSK – βGSK × 평균의S&P 500
= 0.71% – 0.63 × 1.18%
= -0.03%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.86% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.52% |
| 보통주의 체계적 위험GlaxoSmithKline | βGSK | 0.63 |
| 글락소스미스클라인(GlaxoSmithKline) 보통주 기대수익률3 | E(RGSK) | 10.29% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RGSK) = RF + βGSK [E(RM) – RF]
= 4.86% + 0.63 [13.52% – 4.86%]
= 10.29%