자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 RTX의 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
RTX Corp., 월별 수익률
| RTX Corp. (RTX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값RTX,t1 | 피제수RTX,t1 | RRTX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $118.07 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $125.67 | $0.735 | 7.06% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $128.89 | 2.56% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $142.61 | 10.64% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $81.48 | $0.59 | 0.84% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $84.14 | 3.26% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.57% | 1.11% | ||||
| 표준 편차: | 8.83% | 5.31% | ||||
| RTX Corp. (RTX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값RTX,t1 | 피제수RTX,t1 | RRTX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $118.07 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $125.67 | $0.735 | 7.06% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $128.89 | 2.56% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $142.61 | 10.64% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $126.30 | $0.735 | -10.92% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $130.20 | 3.09% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $133.60 | 2.61% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $130.24 | $0.735 | -1.96% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $136.52 | 4.82% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $143.58 | 5.17% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $148.34 | $0.735 | 3.83% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $149.76 | 0.96% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $150.20 | 0.29% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $130.59 | $0.735 | -12.57% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $94.33 | $35.50 | -0.58% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $64.81 | -31.29% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $64.52 | $0.475 | 0.29% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $61.62 | -4.49% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $56.68 | -8.02% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $61.00 | $0.475 | 8.46% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $57.54 | -5.67% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $54.32 | -5.60% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $71.72 | $0.475 | 32.91% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $71.51 | -0.29% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $66.73 | -6.68% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $71.99 | $0.475 | 8.59% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $77.27 | 7.33% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $83.24 | 7.73% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $88.71 | $0.51 | 7.18% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $85.31 | -3.83% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $86.95 | 1.92% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $84.76 | $0.51 | -1.93% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $85.96 | 1.42% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $88.86 | 3.37% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $80.92 | $0.51 | -8.36% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $86.06 | 6.35% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $90.19 | 4.80% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $102.70 | $0.51 | 14.44% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $99.07 | -3.53% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $94.91 | -4.20% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $95.12 | $0.55 | 0.80% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $96.11 | 1.04% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $93.21 | -3.02% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $89.75 | $0.55 | -3.12% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $81.86 | -8.79% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $94.82 | 15.83% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $98.72 | $0.55 | 4.69% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $100.92 | 2.23% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $99.85 | -1.06% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $98.09 | $0.55 | -1.21% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $97.93 | -0.16% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $99.90 | 2.01% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $92.14 | $0.59 | -7.18% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $97.96 | 6.32% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $87.93 | -10.24% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $86.04 | $0.59 | -1.48% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $71.97 | -16.35% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $81.39 | 13.09% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $81.48 | $0.59 | 0.84% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $84.14 | 3.26% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.57% | 1.11% | ||||
| 표준 편차: | 8.83% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 RTX의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
RTX Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RRTX,t | RS&P 500,t | (RRTX,t–RRTX)2 | (RS&P 500,t–RS&P 500)2 | (RRTX,t–RRTX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 7.06% | 2.97% | 42.17 | 3.49 | 12.12 |
| 2. | 2019. 3. 31. | 2.56% | 1.79% | 3.99 | 0.47 | 1.37 |
| 3. | 2019. 4. 30. | 10.64% | 3.93% | 101.59 | 7.98 | 28.48 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 0.84% | 8.92% | 0.07 | 61.03 | 2.11 |
| 59. | 2023. 12. 31. | 3.26% | 4.42% | 7.28 | 11.00 | 8.95 |
| 합계 (Σ): | 4,517.76 | 1,634.30 | 631.07 | |||
| t | 날짜 | RRTX,t | RS&P 500,t | (RRTX,t–RRTX)2 | (RS&P 500,t–RS&P 500)2 | (RRTX,t–RRTX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 7.06% | 2.97% | 42.17 | 3.49 | 12.12 |
| 2. | 2019. 3. 31. | 2.56% | 1.79% | 3.99 | 0.47 | 1.37 |
| 3. | 2019. 4. 30. | 10.64% | 3.93% | 101.59 | 7.98 | 28.48 |
| 4. | 2019. 5. 31. | -10.92% | -6.58% | 131.95 | 59.04 | 88.26 |
| 5. | 2019. 6. 30. | 3.09% | 6.89% | 6.36 | 33.49 | 14.60 |
| 6. | 2019. 7. 31. | 2.61% | 1.31% | 4.18 | 0.04 | 0.42 |
| 7. | 2019. 8. 31. | -1.96% | -1.81% | 6.40 | 8.50 | 7.38 |
| 8. | 2019. 9. 30. | 4.82% | 1.72% | 18.11 | 0.37 | 2.61 |
| 9. | 2019. 10. 31. | 5.17% | 2.04% | 21.21 | 0.88 | 4.32 |
| 10. | 2019. 11. 30. | 3.83% | 3.40% | 10.64 | 5.28 | 7.50 |
| 11. | 2019. 12. 31. | 0.96% | 2.86% | 0.15 | 3.07 | 0.69 |
| 12. | 2020. 1. 31. | 0.29% | -0.16% | 0.07 | 1.61 | 0.35 |
| 13. | 2020. 2. 29. | -12.57% | -8.41% | 172.46 | 90.57 | 124.98 |
| 14. | 2020. 3. 31. | -0.58% | -12.51% | 1.32 | 185.44 | 15.63 |
| 15. | 2020. 4. 30. | -31.29% | 12.68% | 1,015.07 | 134.06 | -368.89 |
| 16. | 2020. 5. 31. | 0.29% | 4.53% | 0.08 | 11.71 | -0.96 |
| 17. | 2020. 6. 30. | -4.49% | 1.84% | 25.61 | 0.54 | -3.71 |
| 18. | 2020. 7. 31. | -8.02% | 5.51% | 73.66 | 19.40 | -37.80 |
| 19. | 2020. 8. 31. | 8.46% | 7.01% | 62.32 | 34.82 | 46.58 |
| 20. | 2020. 9. 30. | -5.67% | -3.92% | 38.91 | 25.29 | 31.37 |
| 21. | 2020. 10. 31. | -5.60% | -2.77% | 37.97 | 15.00 | 23.86 |
| 22. | 2020. 11. 30. | 32.91% | 10.75% | 1,045.95 | 93.10 | 312.05 |
| 23. | 2020. 12. 31. | -0.29% | 3.71% | 0.74 | 6.79 | -2.24 |
| 24. | 2021. 1. 31. | -6.68% | -1.11% | 52.56 | 4.93 | 16.09 |
| 25. | 2021. 2. 28. | 8.59% | 2.61% | 64.46 | 2.26 | 12.07 |
| 26. | 2021. 3. 31. | 7.33% | 4.24% | 45.81 | 9.85 | 21.24 |
| 27. | 2021. 4. 30. | 7.73% | 5.24% | 51.27 | 17.11 | 29.62 |
| 28. | 2021. 5. 31. | 7.18% | 0.55% | 43.80 | 0.31 | -3.69 |
| 29. | 2021. 6. 30. | -3.83% | 2.22% | 19.35 | 1.24 | -4.91 |
| 30. | 2021. 7. 31. | 1.92% | 2.27% | 1.84 | 1.37 | 1.59 |
| 31. | 2021. 8. 31. | -1.93% | 2.90% | 6.24 | 3.22 | -4.48 |
| 32. | 2021. 9. 30. | 1.42% | -4.76% | 0.72 | 34.37 | -4.98 |
| 33. | 2021. 10. 31. | 3.37% | 6.91% | 7.88 | 33.74 | 16.31 |
| 34. | 2021. 11. 30. | -8.36% | -0.83% | 79.70 | 3.76 | 17.31 |
| 35. | 2021. 12. 31. | 6.35% | 4.36% | 33.48 | 10.60 | 18.84 |
| 36. | 2022. 1. 31. | 4.80% | -5.26% | 17.92 | 40.51 | -26.94 |
| 37. | 2022. 2. 28. | 14.44% | -3.14% | 192.39 | 17.99 | -58.84 |
| 38. | 2022. 3. 31. | -3.53% | 3.58% | 16.81 | 6.11 | -10.13 |
| 39. | 2022. 4. 30. | -4.20% | -8.80% | 22.70 | 98.04 | 47.18 |
| 40. | 2022. 5. 31. | 0.80% | 0.01% | 0.06 | 1.21 | -0.26 |
| 41. | 2022. 6. 30. | 1.04% | -8.39% | 0.23 | 90.21 | -4.51 |
| 42. | 2022. 7. 31. | -3.02% | 9.11% | 12.84 | 64.09 | -28.69 |
| 43. | 2022. 8. 31. | -3.12% | -4.24% | 13.60 | 28.62 | 19.73 |
| 44. | 2022. 9. 30. | -8.79% | -9.34% | 87.55 | 109.11 | 97.74 |
| 45. | 2022. 10. 31. | 15.83% | 7.99% | 233.06 | 47.34 | 105.04 |
| 46. | 2022. 11. 30. | 4.69% | 5.38% | 17.03 | 18.23 | 17.62 |
| 47. | 2022. 12. 31. | 2.23% | -5.90% | 2.76 | 49.04 | -11.64 |
| 48. | 2023. 1. 31. | -1.06% | 6.18% | 2.64 | 25.70 | -8.24 |
| 49. | 2023. 2. 28. | -1.21% | -2.61% | 3.16 | 13.82 | 6.61 |
| 50. | 2023. 3. 31. | -0.16% | 3.51% | 0.53 | 5.76 | -1.75 |
| 51. | 2023. 4. 30. | 2.01% | 1.46% | 2.09 | 0.13 | 0.52 |
| 52. | 2023. 5. 31. | -7.18% | 0.25% | 59.95 | 0.74 | 6.64 |
| 53. | 2023. 6. 30. | 6.32% | 4.71% | 33.07 | 13.02 | 20.75 |
| 54. | 2023. 7. 31. | -10.24% | 4.85% | 116.74 | 13.99 | -40.41 |
| 55. | 2023. 8. 31. | -1.48% | -1.77% | 4.18 | 8.28 | 5.88 |
| 56. | 2023. 9. 30. | -16.35% | -4.87% | 286.24 | 35.73 | 101.14 |
| 57. | 2023. 10. 31. | 13.09% | -2.20% | 156.83 | 10.92 | -41.37 |
| 58. | 2023. 11. 30. | 0.84% | 8.92% | 0.07 | 61.03 | 2.11 |
| 59. | 2023. 12. 31. | 3.26% | 4.42% | 7.28 | 11.00 | 8.95 |
| 합계 (Σ): | 4,517.76 | 1,634.30 | 631.07 | |||
모두 보기
분산RTX = Σ(RRTX,t–RRTX)2 ÷ (59 – 1)
= 4,517.76 ÷ (59 – 1)
= 77.89
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산RTX, S&P 500 = Σ(RRTX,t–RRTX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 631.07 ÷ (59 – 1)
= 10.88
체계적인 위험 추정 (β)
| 분산RTX | 77.89 |
| 분산S&P 500 | 28.18 |
| 공분산RTX, S&P 500 | 10.88 |
| 상관 계수RTX, S&P 5001 | 0.23 |
| βRTX2 | 0.39 |
| αRTX3 | 0.14% |
계산
1 상관 계수RTX, S&P 500
= 공분산RTX, S&P 500 ÷ (표준 편차RTX × 표준 편차S&P 500)
= 10.88 ÷ (8.83% × 5.31%)
= 0.23
2 βRTX
= 공분산RTX, S&P 500 ÷ 분산S&P 500
= 10.88 ÷ 28.18
= 0.39
3 αRTX
= 평균의RTX – βRTX × 평균의S&P 500
= 0.57% – 0.39 × 1.11%
= 0.14%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.65% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험RTX | βRTX | 0.39 |
| RTX 보통주에 대한 예상 수익률3 | E(RRTX) | 8.18% |
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(RRTX) = RF + βRTX [E(RM) – RF]
= 4.65% + 0.39 [13.79% – 4.65%]
= 8.18%