자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Lockheed Martin보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Lockheed Martin Corp., 월별 수익률
| Lockheed Martin Corp. (LMT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LMT,t1 | 피제수LMT,t1 | RLMT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $289.69 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $309.41 | $2.20 | 7.57% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $300.16 | -2.99% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $333.33 | 11.05% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $447.77 | $3.15 | -0.82% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $453.24 | 1.22% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.20% | 1.11% | ||||
| 표준 편차: | 6.70% | 5.31% | ||||
| Lockheed Martin Corp. (LMT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LMT,t1 | 피제수LMT,t1 | RLMT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $289.69 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $309.41 | $2.20 | 7.57% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $300.16 | -2.99% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $333.33 | 11.05% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $338.54 | $2.20 | 2.22% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $363.54 | 7.38% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $362.17 | -0.38% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $384.11 | $2.20 | 6.67% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $390.06 | 1.55% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $376.68 | -3.43% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $391.03 | $2.40 | 4.45% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $389.38 | -0.42% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $428.12 | 9.95% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $369.87 | $2.40 | -13.05% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $338.95 | -8.36% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $389.06 | 14.78% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $388.44 | $2.40 | 0.46% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $364.92 | -6.05% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $378.97 | 3.85% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $390.26 | $2.40 | 3.61% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $383.28 | -1.79% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $350.13 | -8.65% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $365.00 | $2.60 | 4.99% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $354.98 | -2.75% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $321.82 | -9.34% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $330.25 | $2.60 | 3.43% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $369.50 | 11.88% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $380.56 | 2.99% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $382.20 | $2.60 | 1.11% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $378.35 | -1.01% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $371.67 | -1.77% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $359.80 | $2.60 | -2.49% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $345.10 | -4.09% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $332.32 | -3.70% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $333.32 | $2.80 | 1.14% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $355.41 | 6.63% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $389.13 | 9.49% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $433.80 | $2.80 | 12.20% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $441.40 | 1.75% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $432.12 | -2.10% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $440.11 | $2.80 | 2.50% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $429.96 | -2.31% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $413.81 | -3.76% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $420.11 | $2.80 | 2.20% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $386.29 | -8.05% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $486.68 | 25.99% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $485.19 | $3.00 | 0.31% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $486.49 | 0.27% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $463.26 | -4.78% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $474.26 | $3.00 | 3.02% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $472.73 | -0.32% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $464.45 | -1.75% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $444.01 | $3.00 | -3.75% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $460.38 | 3.69% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $446.37 | -3.04% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $448.35 | $3.00 | 1.12% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $408.96 | -8.79% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $454.64 | 11.17% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $447.77 | $3.15 | -0.82% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $453.24 | 1.22% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.20% | 1.11% | ||||
| 표준 편차: | 6.70% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 LMT의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Lockheed Martin Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RLMT,t | RS&P 500,t | (RLMT,t–RLMT)2 | (RS&P 500,t–RS&P 500)2 | (RLMT,t–RLMT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 7.57% | 2.97% | 40.51 | 3.49 | 11.88 |
| 2. | 2019. 3. 31. | -2.99% | 1.79% | 17.57 | 0.47 | -2.88 |
| 3. | 2019. 4. 30. | 11.05% | 3.93% | 97.00 | 7.98 | 27.83 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -0.82% | 8.92% | 4.08 | 61.03 | -15.78 |
| 59. | 2023. 12. 31. | 1.22% | 4.42% | 0.00 | 11.00 | 0.07 |
| 합계 (Σ): | 2,605.09 | 1,634.30 | 792.22 | |||
| t | 날짜 | RLMT,t | RS&P 500,t | (RLMT,t–RLMT)2 | (RS&P 500,t–RS&P 500)2 | (RLMT,t–RLMT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 7.57% | 2.97% | 40.51 | 3.49 | 11.88 |
| 2. | 2019. 3. 31. | -2.99% | 1.79% | 17.57 | 0.47 | -2.88 |
| 3. | 2019. 4. 30. | 11.05% | 3.93% | 97.00 | 7.98 | 27.83 |
| 4. | 2019. 5. 31. | 2.22% | -6.58% | 1.04 | 59.04 | -7.85 |
| 5. | 2019. 6. 30. | 7.38% | 6.89% | 38.23 | 33.49 | 35.78 |
| 6. | 2019. 7. 31. | -0.38% | 1.31% | 2.49 | 0.04 | -0.33 |
| 7. | 2019. 8. 31. | 6.67% | -1.81% | 29.85 | 8.50 | -15.93 |
| 8. | 2019. 9. 30. | 1.55% | 1.72% | 0.12 | 0.37 | 0.21 |
| 9. | 2019. 10. 31. | -3.43% | 2.04% | 21.46 | 0.88 | -4.34 |
| 10. | 2019. 11. 30. | 4.45% | 3.40% | 10.53 | 5.28 | 7.46 |
| 11. | 2019. 12. 31. | -0.42% | 2.86% | 2.64 | 3.07 | -2.85 |
| 12. | 2020. 1. 31. | 9.95% | -0.16% | 76.51 | 1.61 | -11.10 |
| 13. | 2020. 2. 29. | -13.05% | -8.41% | 202.99 | 90.57 | 135.59 |
| 14. | 2020. 3. 31. | -8.36% | -12.51% | 91.42 | 185.44 | 130.21 |
| 15. | 2020. 4. 30. | 14.78% | 12.68% | 184.47 | 134.06 | 157.26 |
| 16. | 2020. 5. 31. | 0.46% | 4.53% | 0.55 | 11.71 | -2.55 |
| 17. | 2020. 6. 30. | -6.05% | 1.84% | 52.66 | 0.54 | -5.32 |
| 18. | 2020. 7. 31. | 3.85% | 5.51% | 7.01 | 19.40 | 11.66 |
| 19. | 2020. 8. 31. | 3.61% | 7.01% | 5.81 | 34.82 | 14.22 |
| 20. | 2020. 9. 30. | -1.79% | -3.92% | 8.94 | 25.29 | 15.04 |
| 21. | 2020. 10. 31. | -8.65% | -2.77% | 97.04 | 15.00 | 38.15 |
| 22. | 2020. 11. 30. | 4.99% | 10.75% | 14.35 | 93.10 | 36.55 |
| 23. | 2020. 12. 31. | -2.75% | 3.71% | 15.58 | 6.79 | -10.29 |
| 24. | 2021. 1. 31. | -9.34% | -1.11% | 111.16 | 4.93 | 23.40 |
| 25. | 2021. 2. 28. | 3.43% | 2.61% | 4.95 | 2.26 | 3.35 |
| 26. | 2021. 3. 31. | 11.88% | 4.24% | 114.13 | 9.85 | 33.52 |
| 27. | 2021. 4. 30. | 2.99% | 5.24% | 3.21 | 17.11 | 7.41 |
| 28. | 2021. 5. 31. | 1.11% | 0.55% | 0.01 | 0.31 | 0.05 |
| 29. | 2021. 6. 30. | -1.01% | 2.22% | 4.88 | 1.24 | -2.46 |
| 30. | 2021. 7. 31. | -1.77% | 2.27% | 8.81 | 1.37 | -3.47 |
| 31. | 2021. 8. 31. | -2.49% | 2.90% | 13.66 | 3.22 | -6.63 |
| 32. | 2021. 9. 30. | -4.09% | -4.76% | 27.96 | 34.37 | 31.00 |
| 33. | 2021. 10. 31. | -3.70% | 6.91% | 24.06 | 33.74 | -28.49 |
| 34. | 2021. 11. 30. | 1.14% | -0.83% | 0.00 | 3.76 | 0.11 |
| 35. | 2021. 12. 31. | 6.63% | 4.36% | 29.43 | 10.60 | 17.66 |
| 36. | 2022. 1. 31. | 9.49% | -5.26% | 68.65 | 40.51 | -52.73 |
| 37. | 2022. 2. 28. | 12.20% | -3.14% | 120.94 | 17.99 | -46.65 |
| 38. | 2022. 3. 31. | 1.75% | 3.58% | 0.30 | 6.11 | 1.36 |
| 39. | 2022. 4. 30. | -2.10% | -8.80% | 10.92 | 98.04 | 32.72 |
| 40. | 2022. 5. 31. | 2.50% | 0.01% | 1.68 | 1.21 | -1.43 |
| 41. | 2022. 6. 30. | -2.31% | -8.39% | 12.31 | 90.21 | 33.32 |
| 42. | 2022. 7. 31. | -3.76% | 9.11% | 24.58 | 64.09 | -39.69 |
| 43. | 2022. 8. 31. | 2.20% | -4.24% | 0.99 | 28.62 | -5.33 |
| 44. | 2022. 9. 30. | -8.05% | -9.34% | 85.60 | 109.11 | 96.64 |
| 45. | 2022. 10. 31. | 25.99% | 7.99% | 614.36 | 47.34 | 170.54 |
| 46. | 2022. 11. 30. | 0.31% | 5.38% | 0.79 | 18.23 | -3.81 |
| 47. | 2022. 12. 31. | 0.27% | -5.90% | 0.87 | 49.04 | 6.54 |
| 48. | 2023. 1. 31. | -4.78% | 6.18% | 35.72 | 25.70 | -30.30 |
| 49. | 2023. 2. 28. | 3.02% | -2.61% | 3.31 | 13.82 | -6.77 |
| 50. | 2023. 3. 31. | -0.32% | 3.51% | 2.32 | 5.76 | -3.66 |
| 51. | 2023. 4. 30. | -1.75% | 1.46% | 8.72 | 0.13 | -1.06 |
| 52. | 2023. 5. 31. | -3.75% | 0.25% | 24.57 | 0.74 | 4.25 |
| 53. | 2023. 6. 30. | 3.69% | 4.71% | 6.18 | 13.02 | 8.97 |
| 54. | 2023. 7. 31. | -3.04% | 4.85% | 18.02 | 13.99 | -15.88 |
| 55. | 2023. 8. 31. | 1.12% | -1.77% | 0.01 | 8.28 | 0.25 |
| 56. | 2023. 9. 30. | -8.79% | -4.87% | 99.75 | 35.73 | 59.70 |
| 57. | 2023. 10. 31. | 11.17% | -2.20% | 99.36 | 10.92 | -32.93 |
| 58. | 2023. 11. 30. | -0.82% | 8.92% | 4.08 | 61.03 | -15.78 |
| 59. | 2023. 12. 31. | 1.22% | 4.42% | 0.00 | 11.00 | 0.07 |
| 합계 (Σ): | 2,605.09 | 1,634.30 | 792.22 | |||
모두 보기
분산LMT = Σ(RLMT,t–RLMT)2 ÷ (59 – 1)
= 2,605.09 ÷ (59 – 1)
= 44.92
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산LMT, S&P 500 = Σ(RLMT,t–RLMT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 792.22 ÷ (59 – 1)
= 13.66
체계적인 위험 추정 (β)
| 분산LMT | 44.92 |
| 분산S&P 500 | 28.18 |
| 공분산LMT, S&P 500 | 13.66 |
| 상관 계수LMT, S&P 5001 | 0.38 |
| βLMT2 | 0.48 |
| αLMT3 | 0.67% |
계산
1 상관 계수LMT, S&P 500
= 공분산LMT, S&P 500 ÷ (표준 편차LMT × 표준 편차S&P 500)
= 13.66 ÷ (6.70% × 5.31%)
= 0.38
2 βLMT
= 공분산LMT, S&P 500 ÷ 분산S&P 500
= 13.66 ÷ 28.18
= 0.48
3 αLMT
= 평균의LMT – βLMT × 평균의S&P 500
= 1.20% – 0.48 × 1.11%
= 0.67%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.34% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.74% |
| 보통주의 체계적 위험Lockheed Martin | βLMT | 0.48 |
| Lockheed Martin 보통주의 예상 수익률3 | E(RLMT) | 8.90% |
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(RLMT) = RF + βLMT [E(RM) – RF]
= 4.34% + 0.48 [13.74% – 4.34%]
= 8.90%