자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Raytheon보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Raytheon Co., 월별 수익률
| Raytheon Co. (RTN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값RTN,t1 | 피제수RTN,t1 | RRTN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $100.05 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $108.77 | 8.72% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $109.25 | $0.67 | 1.06% | 2,067.89 | -1.74% |
| 3. | 2015. 4. 30. | $104.00 | -4.81% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | $217.42 | 2.46% | 3,140.98 | 3.40% | |
| 59. | 2019. 12. 31. | $219.74 | $0.9425 | 1.50% | 3,230.78 | 2.86% |
| 평균의 (R): | 1.67% | 0.88% | ||||
| 표준 편차: | 5.56% | 3.45% | ||||
| Raytheon Co. (RTN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값RTN,t1 | 피제수RTN,t1 | RRTN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $100.05 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $108.77 | 8.72% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $109.25 | $0.67 | 1.06% | 2,067.89 | -1.74% |
| 3. | 2015. 4. 30. | $104.00 | -4.81% | 2,085.51 | 0.85% | |
| 4. | 2015. 5. 31. | $103.26 | -0.71% | 2,107.39 | 1.05% | |
| 5. | 2015. 6. 30. | $95.68 | $0.67 | -6.69% | 2,063.11 | -2.10% |
| 6. | 2015. 7. 31. | $109.09 | 14.02% | 2,103.84 | 1.97% | |
| 7. | 2015. 8. 31. | $102.56 | -5.99% | 1,972.18 | -6.26% | |
| 8. | 2015. 9. 30. | $109.26 | 6.53% | 1,920.03 | -2.64% | |
| 9. | 2015. 10. 31. | $117.40 | $0.67 | 8.06% | 2,079.36 | 8.30% |
| 10. | 2015. 11. 30. | $124.03 | 5.65% | 2,080.41 | 0.05% | |
| 11. | 2015. 12. 31. | $124.53 | 0.40% | 2,043.94 | -1.75% | |
| 12. | 2016. 1. 31. | $128.24 | $0.67 | 3.52% | 1,940.24 | -5.07% |
| 13. | 2016. 2. 29. | $123.85 | -3.42% | 1,932.23 | -0.41% | |
| 14. | 2016. 3. 31. | $122.63 | -0.99% | 2,059.74 | 6.60% | |
| 15. | 2016. 4. 30. | $126.35 | $0.7325 | 3.63% | 2,065.30 | 0.27% |
| 16. | 2016. 5. 31. | $129.67 | 2.63% | 2,096.95 | 1.53% | |
| 17. | 2016. 6. 30. | $135.95 | 4.84% | 2,098.86 | 0.09% | |
| 18. | 2016. 7. 31. | $139.53 | $0.7325 | 3.17% | 2,173.60 | 3.56% |
| 19. | 2016. 8. 31. | $140.13 | 0.43% | 2,170.95 | -0.12% | |
| 20. | 2016. 9. 30. | $136.13 | -2.85% | 2,168.27 | -0.12% | |
| 21. | 2016. 10. 31. | $136.61 | $0.7325 | 0.89% | 2,126.15 | -1.94% |
| 22. | 2016. 11. 30. | $149.54 | 9.46% | 2,198.81 | 3.42% | |
| 23. | 2016. 12. 31. | $142.00 | $0.7325 | -4.55% | 2,238.83 | 1.82% |
| 24. | 2017. 1. 31. | $144.16 | 1.52% | 2,278.87 | 1.79% | |
| 25. | 2017. 2. 28. | $154.15 | 6.93% | 2,363.64 | 3.72% | |
| 26. | 2017. 3. 31. | $152.50 | -1.07% | 2,362.72 | -0.04% | |
| 27. | 2017. 4. 30. | $155.21 | $0.7975 | 2.30% | 2,384.20 | 0.91% |
| 28. | 2017. 5. 31. | $164.01 | 5.67% | 2,411.80 | 1.16% | |
| 29. | 2017. 6. 30. | $161.48 | $0.7975 | -1.06% | 2,423.41 | 0.48% |
| 30. | 2017. 7. 31. | $171.77 | 6.37% | 2,470.30 | 1.93% | |
| 31. | 2017. 8. 31. | $182.01 | 5.96% | 2,471.65 | 0.05% | |
| 32. | 2017. 9. 30. | $186.58 | 2.51% | 2,519.36 | 1.93% | |
| 33. | 2017. 10. 31. | $180.20 | $0.7975 | -2.99% | 2,575.26 | 2.22% |
| 34. | 2017. 11. 30. | $191.15 | 6.08% | 2,647.58 | 2.81% | |
| 35. | 2017. 12. 31. | $187.85 | -1.73% | 2,673.61 | 0.98% | |
| 36. | 2018. 1. 31. | $208.94 | $0.7975 | 11.65% | 2,823.81 | 5.62% |
| 37. | 2018. 2. 28. | $217.51 | 4.10% | 2,713.83 | -3.89% | |
| 38. | 2018. 3. 31. | $215.82 | -0.78% | 2,640.87 | -2.69% | |
| 39. | 2018. 4. 30. | $204.94 | $0.8675 | -4.64% | 2,648.05 | 0.27% |
| 40. | 2018. 5. 31. | $209.50 | 2.23% | 2,705.27 | 2.16% | |
| 41. | 2018. 6. 30. | $193.18 | -7.79% | 2,718.37 | 0.48% | |
| 42. | 2018. 7. 31. | $198.03 | $0.8675 | 2.96% | 2,816.29 | 3.60% |
| 43. | 2018. 8. 31. | $199.44 | 0.71% | 2,901.52 | 3.03% | |
| 44. | 2018. 9. 30. | $206.66 | 3.62% | 2,913.98 | 0.43% | |
| 45. | 2018. 10. 31. | $175.04 | $0.8675 | -14.88% | 2,711.74 | -6.94% |
| 46. | 2018. 11. 30. | $175.34 | 0.17% | 2,760.17 | 1.79% | |
| 47. | 2018. 12. 31. | $153.35 | $0.8675 | -12.05% | 2,506.85 | -9.18% |
| 48. | 2019. 1. 31. | $164.76 | 7.44% | 2,704.10 | 7.87% | |
| 49. | 2019. 2. 28. | $186.50 | 13.19% | 2,784.49 | 2.97% | |
| 50. | 2019. 3. 31. | $182.08 | -2.37% | 2,834.40 | 1.79% | |
| 51. | 2019. 4. 30. | $177.59 | $0.9425 | -1.95% | 2,945.83 | 3.93% |
| 52. | 2019. 5. 31. | $174.50 | -1.74% | 2,752.06 | -6.58% | |
| 53. | 2019. 6. 30. | $173.88 | -0.36% | 2,941.76 | 6.89% | |
| 54. | 2019. 7. 31. | $182.29 | $0.9425 | 5.38% | 2,980.38 | 1.31% |
| 55. | 2019. 8. 31. | $185.32 | 1.66% | 2,926.46 | -1.81% | |
| 56. | 2019. 9. 30. | $196.19 | 5.87% | 2,976.74 | 1.72% | |
| 57. | 2019. 10. 31. | $212.21 | $0.9425 | 8.65% | 3,037.56 | 2.04% |
| 58. | 2019. 11. 30. | $217.42 | 2.46% | 3,140.98 | 3.40% | |
| 59. | 2019. 12. 31. | $219.74 | $0.9425 | 1.50% | 3,230.78 | 2.86% |
| 평균의 (R): | 1.67% | 0.88% | ||||
| 표준 편차: | 5.56% | 3.45% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 RTN의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Raytheon Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RRTN,t | RS&P 500,t | (RRTN,t–RRTN)2 | (RS&P 500,t–RS&P 500)2 | (RRTN,t–RRTN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 8.72% | 5.49% | 49.64 | 21.25 | 32.48 |
| 2. | 2015. 3. 31. | 1.06% | -1.74% | 0.38 | 6.86 | 1.60 |
| 3. | 2015. 4. 30. | -4.81% | 0.85% | 41.93 | 0.00 | 0.18 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | 2.46% | 3.40% | 0.62 | 6.38 | 1.98 |
| 59. | 2019. 12. 31. | 1.50% | 2.86% | 0.03 | 3.92 | -0.34 |
| 합계 (Σ): | 1,792.81 | 688.77 | 581.47 | |||
| t | 날짜 | RRTN,t | RS&P 500,t | (RRTN,t–RRTN)2 | (RS&P 500,t–RS&P 500)2 | (RRTN,t–RRTN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 8.72% | 5.49% | 49.64 | 21.25 | 32.48 |
| 2. | 2015. 3. 31. | 1.06% | -1.74% | 0.38 | 6.86 | 1.60 |
| 3. | 2015. 4. 30. | -4.81% | 0.85% | 41.93 | 0.00 | 0.18 |
| 4. | 2015. 5. 31. | -0.71% | 1.05% | 5.67 | 0.03 | -0.40 |
| 5. | 2015. 6. 30. | -6.69% | -2.10% | 69.92 | 8.88 | 24.92 |
| 6. | 2015. 7. 31. | 14.02% | 1.97% | 152.41 | 1.20 | 13.52 |
| 7. | 2015. 8. 31. | -5.99% | -6.26% | 58.61 | 50.94 | 54.64 |
| 8. | 2015. 9. 30. | 6.53% | -2.64% | 23.65 | 12.41 | -17.13 |
| 9. | 2015. 10. 31. | 8.06% | 8.30% | 40.87 | 55.04 | 47.43 |
| 10. | 2015. 11. 30. | 5.65% | 0.05% | 15.82 | 0.69 | -3.30 |
| 11. | 2015. 12. 31. | 0.40% | -1.75% | 1.61 | 6.93 | 3.33 |
| 12. | 2016. 1. 31. | 3.52% | -5.07% | 3.41 | 35.43 | -11.00 |
| 13. | 2016. 2. 29. | -3.42% | -0.41% | 25.94 | 1.67 | 6.58 |
| 14. | 2016. 3. 31. | -0.99% | 6.60% | 7.05 | 32.72 | -15.19 |
| 15. | 2016. 4. 30. | 3.63% | 0.27% | 3.84 | 0.37 | -1.19 |
| 16. | 2016. 5. 31. | 2.63% | 1.53% | 0.92 | 0.43 | 0.63 |
| 17. | 2016. 6. 30. | 4.84% | 0.09% | 10.07 | 0.62 | -2.50 |
| 18. | 2016. 7. 31. | 3.17% | 3.56% | 2.26 | 7.19 | 4.03 |
| 19. | 2016. 8. 31. | 0.43% | -0.12% | 1.54 | 1.00 | 1.24 |
| 20. | 2016. 9. 30. | -2.85% | -0.12% | 20.47 | 1.01 | 4.54 |
| 21. | 2016. 10. 31. | 0.89% | -1.94% | 0.61 | 7.96 | 2.20 |
| 22. | 2016. 11. 30. | 9.46% | 3.42% | 60.76 | 6.44 | 19.79 |
| 23. | 2016. 12. 31. | -4.55% | 1.82% | 38.72 | 0.89 | -5.86 |
| 24. | 2017. 1. 31. | 1.52% | 1.79% | 0.02 | 0.83 | -0.14 |
| 25. | 2017. 2. 28. | 6.93% | 3.72% | 27.66 | 8.07 | 14.94 |
| 26. | 2017. 3. 31. | -1.07% | -0.04% | 7.51 | 0.84 | 2.52 |
| 27. | 2017. 4. 30. | 2.30% | 0.91% | 0.40 | 0.00 | 0.02 |
| 28. | 2017. 5. 31. | 5.67% | 1.16% | 16.00 | 0.08 | 1.11 |
| 29. | 2017. 6. 30. | -1.06% | 0.48% | 7.43 | 0.16 | 1.08 |
| 30. | 2017. 7. 31. | 6.37% | 1.93% | 22.11 | 1.11 | 4.96 |
| 31. | 2017. 8. 31. | 5.96% | 0.05% | 18.42 | 0.68 | -3.54 |
| 32. | 2017. 9. 30. | 2.51% | 1.93% | 0.71 | 1.10 | 0.88 |
| 33. | 2017. 10. 31. | -2.99% | 2.22% | 21.74 | 1.79 | -6.25 |
| 34. | 2017. 11. 30. | 6.08% | 2.81% | 19.42 | 3.72 | 8.50 |
| 35. | 2017. 12. 31. | -1.73% | 0.98% | 11.54 | 0.01 | -0.35 |
| 36. | 2018. 1. 31. | 11.65% | 5.62% | 99.63 | 22.46 | 47.30 |
| 37. | 2018. 2. 28. | 4.10% | -3.89% | 5.91 | 22.79 | -11.61 |
| 38. | 2018. 3. 31. | -0.78% | -2.69% | 5.99 | 12.73 | 8.73 |
| 39. | 2018. 4. 30. | -4.64% | 0.27% | 39.81 | 0.37 | 3.83 |
| 40. | 2018. 5. 31. | 2.23% | 2.16% | 0.31 | 1.64 | 0.71 |
| 41. | 2018. 6. 30. | -7.79% | 0.48% | 89.49 | 0.16 | 3.74 |
| 42. | 2018. 7. 31. | 2.96% | 3.60% | 1.66 | 7.41 | 3.51 |
| 43. | 2018. 8. 31. | 0.71% | 3.03% | 0.92 | 4.61 | -2.06 |
| 44. | 2018. 9. 30. | 3.62% | 0.43% | 3.80 | 0.20 | -0.88 |
| 45. | 2018. 10. 31. | -14.88% | -6.94% | 273.93 | 61.14 | 129.42 |
| 46. | 2018. 11. 30. | 0.17% | 1.79% | 2.25 | 0.82 | -1.36 |
| 47. | 2018. 12. 31. | -12.05% | -9.18% | 188.15 | 101.14 | 137.95 |
| 48. | 2019. 1. 31. | 7.44% | 7.87% | 33.30 | 48.85 | 40.33 |
| 49. | 2019. 2. 28. | 13.19% | 2.97% | 132.82 | 4.38 | 24.13 |
| 50. | 2019. 3. 31. | -2.37% | 1.79% | 16.32 | 0.83 | -3.69 |
| 51. | 2019. 4. 30. | -1.95% | 3.93% | 13.09 | 9.32 | -11.04 |
| 52. | 2019. 5. 31. | -1.74% | -6.58% | 11.63 | 55.61 | 25.43 |
| 53. | 2019. 6. 30. | -0.36% | 6.89% | 4.10 | 36.17 | -12.18 |
| 54. | 2019. 7. 31. | 5.38% | 1.31% | 13.75 | 0.19 | 1.61 |
| 55. | 2019. 8. 31. | 1.66% | -1.81% | 0.00 | 7.23 | 0.02 |
| 56. | 2019. 9. 30. | 5.87% | 1.72% | 17.60 | 0.70 | 3.52 |
| 57. | 2019. 10. 31. | 8.65% | 2.04% | 48.66 | 1.36 | 8.12 |
| 58. | 2019. 11. 30. | 2.46% | 3.40% | 0.62 | 6.38 | 1.98 |
| 59. | 2019. 12. 31. | 1.50% | 2.86% | 0.03 | 3.92 | -0.34 |
| 합계 (Σ): | 1,792.81 | 688.77 | 581.47 | |||
모두 보기
분산RTN = Σ(RRTN,t–RRTN)2 ÷ (59 – 1)
= 1,792.81 ÷ (59 – 1)
= 30.91
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
공분산RTN, S&P 500 = Σ(RRTN,t–RRTN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 581.47 ÷ (59 – 1)
= 10.03
체계적인 위험 추정 (β)
| 분산RTN | 30.91 |
| 분산S&P 500 | 11.88 |
| 공분산RTN, S&P 500 | 10.03 |
| 상관 계수RTN, S&P 5001 | 0.52 |
| βRTN2 | 0.84 |
| αRTN3 | 0.93% |
계산
1 상관 계수RTN, S&P 500
= 공분산RTN, S&P 500 ÷ (표준 편차RTN × 표준 편차S&P 500)
= 10.03 ÷ (5.56% × 3.45%)
= 0.52
2 βRTN
= 공분산RTN, S&P 500 ÷ 분산S&P 500
= 10.03 ÷ 11.88
= 0.84
3 αRTN
= 평균의RTN – βRTN × 평균의S&P 500
= 1.67% – 0.84 × 0.88%
= 0.93%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.44% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주의 체계적 위험Raytheon | βRTN | 0.84 |
| Raytheon 보통주에 대한 예상 수익률3 | E(RRTN) | 12.31% |
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(RRTN) = RF + βRTN [E(RM) – RF]
= 4.44% + 0.84 [13.77% – 4.44%]
= 12.31%