자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 General Dynamics보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
General Dynamics Corp., 월별 수익률
| General Dynamics Corp. (GD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GD,t1 | 피제수GD,t1 | RGD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $133.21 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $138.78 | 4.18% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $135.73 | -2.20% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $137.32 | $0.69 | 1.68% | 2,085.51 | 0.85% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | $181.74 | 2.79% | 3,140.98 | 3.40% | |
| 59. | 2019. 12. 31. | $176.35 | -2.97% | 3,230.78 | 2.86% | |
| 평균의 (R): | 0.80% | 0.88% | ||||
| 표준 편차: | 5.84% | 3.45% | ||||
| General Dynamics Corp. (GD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값GD,t1 | 피제수GD,t1 | RGD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $133.21 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $138.78 | 4.18% | 2,104.50 | 5.49% | |
| 2. | 2015. 3. 31. | $135.73 | -2.20% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $137.32 | $0.69 | 1.68% | 2,085.51 | 0.85% |
| 4. | 2015. 5. 31. | $140.16 | 2.07% | 2,107.39 | 1.05% | |
| 5. | 2015. 6. 30. | $141.69 | $0.69 | 1.58% | 2,063.11 | -2.10% |
| 6. | 2015. 7. 31. | $149.11 | 5.24% | 2,103.84 | 1.97% | |
| 7. | 2015. 8. 31. | $142.03 | -4.75% | 1,972.18 | -6.26% | |
| 8. | 2015. 9. 30. | $137.95 | -2.87% | 1,920.03 | -2.64% | |
| 9. | 2015. 10. 31. | $148.58 | $0.69 | 8.21% | 2,079.36 | 8.30% |
| 10. | 2015. 11. 30. | $146.46 | -1.43% | 2,080.41 | 0.05% | |
| 11. | 2015. 12. 31. | $137.36 | -6.21% | 2,043.94 | -1.75% | |
| 12. | 2016. 1. 31. | $133.77 | $0.69 | -2.11% | 1,940.24 | -5.07% |
| 13. | 2016. 2. 29. | $136.27 | 1.87% | 1,932.23 | -0.41% | |
| 14. | 2016. 3. 31. | $131.37 | -3.60% | 2,059.74 | 6.60% | |
| 15. | 2016. 4. 30. | $140.52 | $0.76 | 7.54% | 2,065.30 | 0.27% |
| 16. | 2016. 5. 31. | $141.87 | 0.96% | 2,096.95 | 1.53% | |
| 17. | 2016. 6. 30. | $139.24 | $0.76 | -1.32% | 2,098.86 | 0.09% |
| 18. | 2016. 7. 31. | $146.89 | 5.49% | 2,173.60 | 3.56% | |
| 19. | 2016. 8. 31. | $152.22 | 3.63% | 2,170.95 | -0.12% | |
| 20. | 2016. 9. 30. | $155.16 | 1.93% | 2,168.27 | -0.12% | |
| 21. | 2016. 10. 31. | $150.74 | $0.76 | -2.36% | 2,126.15 | -1.94% |
| 22. | 2016. 11. 30. | $175.35 | 16.33% | 2,198.81 | 3.42% | |
| 23. | 2016. 12. 31. | $172.66 | -1.53% | 2,238.83 | 1.82% | |
| 24. | 2017. 1. 31. | $181.08 | $0.76 | 5.32% | 2,278.87 | 1.79% |
| 25. | 2017. 2. 28. | $189.81 | 4.82% | 2,363.64 | 3.72% | |
| 26. | 2017. 3. 31. | $187.20 | -1.38% | 2,362.72 | -0.04% | |
| 27. | 2017. 4. 30. | $193.79 | $0.84 | 3.97% | 2,384.20 | 0.91% |
| 28. | 2017. 5. 31. | $203.25 | 4.88% | 2,411.80 | 1.16% | |
| 29. | 2017. 6. 30. | $198.10 | -2.53% | 2,423.41 | 0.48% | |
| 30. | 2017. 7. 31. | $196.33 | $0.84 | -0.47% | 2,470.30 | 1.93% |
| 31. | 2017. 8. 31. | $201.35 | 2.56% | 2,471.65 | 0.05% | |
| 32. | 2017. 9. 30. | $205.58 | 2.10% | 2,519.36 | 1.93% | |
| 33. | 2017. 10. 31. | $202.98 | $0.84 | -0.86% | 2,575.26 | 2.22% |
| 34. | 2017. 11. 30. | $207.16 | 2.06% | 2,647.58 | 2.81% | |
| 35. | 2017. 12. 31. | $203.45 | -1.79% | 2,673.61 | 0.98% | |
| 36. | 2018. 1. 31. | $222.48 | $0.84 | 9.77% | 2,823.81 | 5.62% |
| 37. | 2018. 2. 28. | $222.45 | -0.01% | 2,713.83 | -3.89% | |
| 38. | 2018. 3. 31. | $220.90 | -0.70% | 2,640.87 | -2.69% | |
| 39. | 2018. 4. 30. | $201.31 | $0.93 | -8.45% | 2,648.05 | 0.27% |
| 40. | 2018. 5. 31. | $201.71 | 0.20% | 2,705.27 | 2.16% | |
| 41. | 2018. 6. 30. | $186.41 | -7.59% | 2,718.37 | 0.48% | |
| 42. | 2018. 7. 31. | $199.76 | $0.93 | 7.66% | 2,816.29 | 3.60% |
| 43. | 2018. 8. 31. | $193.40 | -3.18% | 2,901.52 | 3.03% | |
| 44. | 2018. 9. 30. | $204.72 | 5.85% | 2,913.98 | 0.43% | |
| 45. | 2018. 10. 31. | $172.58 | $0.93 | -15.25% | 2,711.74 | -6.94% |
| 46. | 2018. 11. 30. | $184.89 | 7.13% | 2,760.17 | 1.79% | |
| 47. | 2018. 12. 31. | $157.21 | -14.97% | 2,506.85 | -9.18% | |
| 48. | 2019. 1. 31. | $171.17 | $0.93 | 9.47% | 2,704.10 | 7.87% |
| 49. | 2019. 2. 28. | $170.22 | -0.56% | 2,784.49 | 2.97% | |
| 50. | 2019. 3. 31. | $169.28 | -0.55% | 2,834.40 | 1.79% | |
| 51. | 2019. 4. 30. | $178.72 | $1.02 | 6.18% | 2,945.83 | 3.93% |
| 52. | 2019. 5. 31. | $160.82 | -10.02% | 2,752.06 | -6.58% | |
| 53. | 2019. 6. 30. | $181.82 | 13.06% | 2,941.76 | 6.89% | |
| 54. | 2019. 7. 31. | $185.94 | $1.02 | 2.83% | 2,980.38 | 1.31% |
| 55. | 2019. 8. 31. | $191.27 | 2.87% | 2,926.46 | -1.81% | |
| 56. | 2019. 9. 30. | $182.73 | -4.46% | 2,976.74 | 1.72% | |
| 57. | 2019. 10. 31. | $176.80 | $1.02 | -2.69% | 3,037.56 | 2.04% |
| 58. | 2019. 11. 30. | $181.74 | 2.79% | 3,140.98 | 3.40% | |
| 59. | 2019. 12. 31. | $176.35 | -2.97% | 3,230.78 | 2.86% | |
| 평균의 (R): | 0.80% | 0.88% | ||||
| 표준 편차: | 5.84% | 3.45% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 GD의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
General Dynamics Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RGD,t | RS&P 500,t | (RGD,t–RGD)2 | (RS&P 500,t–RS&P 500)2 | (RGD,t–RGD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 4.18% | 5.49% | 11.41 | 21.25 | 15.57 |
| 2. | 2015. 3. 31. | -2.20% | -1.74% | 9.01 | 6.86 | 7.86 |
| 3. | 2015. 4. 30. | 1.68% | 0.85% | 0.77 | 0.00 | -0.02 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | 2.79% | 3.40% | 3.96 | 6.38 | 5.03 |
| 59. | 2019. 12. 31. | -2.97% | 2.86% | 14.21 | 3.92 | -7.46 |
| 합계 (Σ): | 1,975.33 | 688.77 | 785.06 | |||
| t | 날짜 | RGD,t | RS&P 500,t | (RGD,t–RGD)2 | (RS&P 500,t–RS&P 500)2 | (RGD,t–RGD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 4.18% | 5.49% | 11.41 | 21.25 | 15.57 |
| 2. | 2015. 3. 31. | -2.20% | -1.74% | 9.01 | 6.86 | 7.86 |
| 3. | 2015. 4. 30. | 1.68% | 0.85% | 0.77 | 0.00 | -0.02 |
| 4. | 2015. 5. 31. | 2.07% | 1.05% | 1.60 | 0.03 | 0.21 |
| 5. | 2015. 6. 30. | 1.58% | -2.10% | 0.61 | 8.88 | -2.32 |
| 6. | 2015. 7. 31. | 5.24% | 1.97% | 19.65 | 1.20 | 4.85 |
| 7. | 2015. 8. 31. | -4.75% | -6.26% | 30.83 | 50.94 | 39.63 |
| 8. | 2015. 9. 30. | -2.87% | -2.64% | 13.52 | 12.41 | 12.95 |
| 9. | 2015. 10. 31. | 8.21% | 8.30% | 54.79 | 55.04 | 54.92 |
| 10. | 2015. 11. 30. | -1.43% | 0.05% | 4.98 | 0.69 | 1.85 |
| 11. | 2015. 12. 31. | -6.21% | -1.75% | 49.24 | 6.93 | 18.47 |
| 12. | 2016. 1. 31. | -2.11% | -5.07% | 8.50 | 35.43 | 17.35 |
| 13. | 2016. 2. 29. | 1.87% | -0.41% | 1.13 | 1.67 | -1.38 |
| 14. | 2016. 3. 31. | -3.60% | 6.60% | 19.36 | 32.72 | -25.17 |
| 15. | 2016. 4. 30. | 7.54% | 0.27% | 45.42 | 0.37 | -4.11 |
| 16. | 2016. 5. 31. | 0.96% | 1.53% | 0.02 | 0.43 | 0.10 |
| 17. | 2016. 6. 30. | -1.32% | 0.09% | 4.50 | 0.62 | 1.67 |
| 18. | 2016. 7. 31. | 5.49% | 3.56% | 22.00 | 7.19 | 12.58 |
| 19. | 2016. 8. 31. | 3.63% | -0.12% | 7.98 | 1.00 | -2.83 |
| 20. | 2016. 9. 30. | 1.93% | -0.12% | 1.27 | 1.01 | -1.13 |
| 21. | 2016. 10. 31. | -2.36% | -1.94% | 10.00 | 7.96 | 8.92 |
| 22. | 2016. 11. 30. | 16.33% | 3.42% | 240.94 | 6.44 | 39.40 |
| 23. | 2016. 12. 31. | -1.53% | 1.82% | 5.47 | 0.89 | -2.20 |
| 24. | 2017. 1. 31. | 5.32% | 1.79% | 20.37 | 0.83 | 4.10 |
| 25. | 2017. 2. 28. | 4.82% | 3.72% | 16.14 | 8.07 | 11.41 |
| 26. | 2017. 3. 31. | -1.38% | -0.04% | 4.75 | 0.84 | 2.00 |
| 27. | 2017. 4. 30. | 3.97% | 0.91% | 10.02 | 0.00 | 0.09 |
| 28. | 2017. 5. 31. | 4.88% | 1.16% | 16.63 | 0.08 | 1.14 |
| 29. | 2017. 6. 30. | -2.53% | 0.48% | 11.14 | 0.16 | 1.33 |
| 30. | 2017. 7. 31. | -0.47% | 1.93% | 1.62 | 1.11 | -1.34 |
| 31. | 2017. 8. 31. | 2.56% | 0.05% | 3.07 | 0.68 | -1.45 |
| 32. | 2017. 9. 30. | 2.10% | 1.93% | 1.68 | 1.10 | 1.36 |
| 33. | 2017. 10. 31. | -0.86% | 2.22% | 2.76 | 1.79 | -2.22 |
| 34. | 2017. 11. 30. | 2.06% | 2.81% | 1.58 | 3.72 | 2.42 |
| 35. | 2017. 12. 31. | -1.79% | 0.98% | 6.73 | 0.01 | -0.27 |
| 36. | 2018. 1. 31. | 9.77% | 5.62% | 80.33 | 22.46 | 42.47 |
| 37. | 2018. 2. 28. | -0.01% | -3.89% | 0.67 | 22.79 | 3.90 |
| 38. | 2018. 3. 31. | -0.70% | -2.69% | 2.25 | 12.73 | 5.35 |
| 39. | 2018. 4. 30. | -8.45% | 0.27% | 85.59 | 0.37 | 5.62 |
| 40. | 2018. 5. 31. | 0.20% | 2.16% | 0.37 | 1.64 | -0.78 |
| 41. | 2018. 6. 30. | -7.59% | 0.48% | 70.38 | 0.16 | 3.31 |
| 42. | 2018. 7. 31. | 7.66% | 3.60% | 47.01 | 7.41 | 18.67 |
| 43. | 2018. 8. 31. | -3.18% | 3.03% | 15.90 | 4.61 | -8.56 |
| 44. | 2018. 9. 30. | 5.85% | 0.43% | 25.49 | 0.20 | -2.27 |
| 45. | 2018. 10. 31. | -15.25% | -6.94% | 257.58 | 61.14 | 125.50 |
| 46. | 2018. 11. 30. | 7.13% | 1.79% | 40.05 | 0.82 | 5.74 |
| 47. | 2018. 12. 31. | -14.97% | -9.18% | 248.85 | 101.14 | 158.65 |
| 48. | 2019. 1. 31. | 9.47% | 7.87% | 75.12 | 48.85 | 60.58 |
| 49. | 2019. 2. 28. | -0.56% | 2.97% | 1.85 | 4.38 | -2.85 |
| 50. | 2019. 3. 31. | -0.55% | 1.79% | 1.84 | 0.83 | -1.24 |
| 51. | 2019. 4. 30. | 6.18% | 3.93% | 28.89 | 9.32 | 16.41 |
| 52. | 2019. 5. 31. | -10.02% | -6.58% | 117.07 | 55.61 | 80.68 |
| 53. | 2019. 6. 30. | 13.06% | 6.89% | 150.16 | 36.17 | 73.69 |
| 54. | 2019. 7. 31. | 2.83% | 1.31% | 4.09 | 0.19 | 0.88 |
| 55. | 2019. 8. 31. | 2.87% | -1.81% | 4.25 | 7.23 | -5.54 |
| 56. | 2019. 9. 30. | -4.46% | 1.72% | 27.76 | 0.70 | -4.42 |
| 57. | 2019. 10. 31. | -2.69% | 2.04% | 12.19 | 1.36 | -4.06 |
| 58. | 2019. 11. 30. | 2.79% | 3.40% | 3.96 | 6.38 | 5.03 |
| 59. | 2019. 12. 31. | -2.97% | 2.86% | 14.21 | 3.92 | -7.46 |
| 합계 (Σ): | 1,975.33 | 688.77 | 785.06 | |||
모두 보기
분산GD = Σ(RGD,t–RGD)2 ÷ (59 – 1)
= 1,975.33 ÷ (59 – 1)
= 34.06
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
공분산GD, S&P 500 = Σ(RGD,t–RGD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 785.06 ÷ (59 – 1)
= 13.54
체계적인 위험 추정 (β)
| 분산GD | 34.06 |
| 분산S&P 500 | 11.88 |
| 공분산GD, S&P 500 | 13.54 |
| 상관 계수GD, S&P 5001 | 0.67 |
| βGD2 | 1.14 |
| αGD3 | -0.20% |
계산
1 상관 계수GD, S&P 500
= 공분산GD, S&P 500 ÷ (표준 편차GD × 표준 편차S&P 500)
= 13.54 ÷ (5.84% × 3.45%)
= 0.67
2 βGD
= 공분산GD, S&P 500 ÷ 분산S&P 500
= 13.54 ÷ 11.88
= 1.14
3 αGD
= 평균의GD – βGD × 평균의S&P 500
= 0.80% – 1.14 × 0.88%
= -0.20%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험General Dynamics | βGD | 1.14 |
| General Dynamics 보통주에 대한 예상 수익률3 | E(RGD) | 15.06% |
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(RGD) = RF + βGD [E(RM) – RF]
= 4.67% + 1.14 [13.79% – 4.67%]
= 15.06%