자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Trane Technologies보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Trane Technologies plc, 월별 수익률
| Trane Technologies plc (TT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TT,t1 | 피제수TT,t1 | RTT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $94.63 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $88.80 | -6.16% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $85.51 | $0.45 | -3.20% | 2,640.87 | -2.69% |
| 3. | 2018. 4. 30. | $83.89 | -1.89% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $178.42 | 11.77% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $168.09 | $0.67 | -5.41% | 3,839.50 | -5.90% |
| 평균의 (R): | 1.92% | 0.67% | ||||
| 표준 편차: | 7.50% | 5.40% | ||||
| Trane Technologies plc (TT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값TT,t1 | 피제수TT,t1 | RTT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $94.63 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $88.80 | -6.16% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $85.51 | $0.45 | -3.20% | 2,640.87 | -2.69% |
| 3. | 2018. 4. 30. | $83.89 | -1.89% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $87.54 | 4.35% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $89.73 | $0.45 | 3.02% | 2,718.37 | 0.48% |
| 6. | 2018. 7. 31. | $98.51 | 9.78% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $101.29 | 2.82% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $102.30 | $0.53 | 1.52% | 2,913.98 | 0.43% |
| 9. | 2018. 10. 31. | $95.94 | -6.22% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $103.52 | 7.90% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $91.23 | $0.53 | -11.36% | 2,506.85 | -9.18% |
| 12. | 2019. 1. 31. | $100.04 | 9.66% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $105.56 | 5.52% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $107.95 | $0.53 | 2.77% | 2,834.40 | 1.79% |
| 15. | 2019. 4. 30. | $122.61 | 13.58% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $118.34 | -3.48% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $126.67 | $0.53 | 7.49% | 2,941.76 | 6.89% |
| 18. | 2019. 7. 31. | $123.66 | -2.38% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $121.09 | -2.08% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $123.21 | $0.53 | 2.19% | 2,976.74 | 1.72% |
| 21. | 2019. 10. 31. | $126.89 | 2.99% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $131.11 | 3.33% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $132.92 | $0.53 | 1.78% | 3,230.78 | 2.86% |
| 24. | 2020. 1. 31. | $133.23 | 0.23% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $129.04 | -3.14% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $82.59 | $29.46 | -13.17% | 2,584.59 | -12.51% |
| 27. | 2020. 4. 30. | $87.42 | 5.85% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $90.21 | 3.19% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $88.98 | $0.53 | -0.78% | 3,100.29 | 1.84% |
| 30. | 2020. 7. 31. | $111.87 | 25.72% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $118.39 | 5.83% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $121.25 | $0.53 | 2.86% | 3,363.00 | -3.92% |
| 33. | 2020. 10. 31. | $132.75 | 9.48% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $146.24 | 10.16% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $145.16 | $0.53 | -0.38% | 3,756.07 | 3.71% |
| 36. | 2021. 1. 31. | $143.35 | -1.25% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $153.24 | 6.90% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $165.56 | $0.59 | 8.42% | 3,972.89 | 4.24% |
| 39. | 2021. 4. 30. | $173.83 | 5.00% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $186.40 | 7.23% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $184.14 | $0.59 | -0.90% | 4,297.50 | 2.22% |
| 42. | 2021. 7. 31. | $203.61 | 10.57% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $198.50 | -2.51% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $172.65 | $0.59 | -12.73% | 4,307.54 | -4.76% |
| 45. | 2021. 10. 31. | $180.93 | 4.80% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $186.65 | 3.16% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $202.03 | $0.59 | 8.56% | 4,766.18 | 4.36% |
| 48. | 2022. 1. 31. | $173.10 | -14.32% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $153.93 | -11.07% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $152.70 | $0.67 | -0.36% | 4,530.41 | 3.58% |
| 51. | 2022. 4. 30. | $139.89 | -8.39% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $138.06 | -1.31% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $129.87 | $0.67 | -5.45% | 3,785.38 | -8.39% |
| 54. | 2022. 7. 31. | $146.99 | 13.18% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $154.07 | 4.82% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $144.81 | $0.67 | -5.58% | 3,585.62 | -9.34% |
| 57. | 2022. 10. 31. | $159.63 | 10.23% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $178.42 | 11.77% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $168.09 | $0.67 | -5.41% | 3,839.50 | -5.90% |
| 평균의 (R): | 1.92% | 0.67% | ||||
| 표준 편차: | 7.50% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 TT의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Trane Technologies plc, 수익률의 분산 및 공분산 계산
| t | 날짜 | RTT,t | RS&P 500,t | (RTT,t–RTT)2 | (RS&P 500,t–RS&P 500)2 | (RTT,t–RTT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -6.16% | -3.89% | 65.27 | 20.81 | 36.85 |
| 2. | 2018. 3. 31. | -3.20% | -2.69% | 26.18 | 11.26 | 17.17 |
| 3. | 2018. 4. 30. | -1.89% | 0.27% | 14.54 | 0.16 | 1.51 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 11.77% | 5.38% | 97.08 | 22.17 | 46.39 |
| 59. | 2022. 12. 31. | -5.41% | -5.90% | 53.76 | 43.08 | 48.13 |
| 합계 (Σ): | 3,261.02 | 1,691.48 | 1,742.35 | |||
| t | 날짜 | RTT,t | RS&P 500,t | (RTT,t–RTT)2 | (RS&P 500,t–RS&P 500)2 | (RTT,t–RTT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -6.16% | -3.89% | 65.27 | 20.81 | 36.85 |
| 2. | 2018. 3. 31. | -3.20% | -2.69% | 26.18 | 11.26 | 17.17 |
| 3. | 2018. 4. 30. | -1.89% | 0.27% | 14.54 | 0.16 | 1.51 |
| 4. | 2018. 5. 31. | 4.35% | 2.16% | 5.92 | 2.23 | 3.64 |
| 5. | 2018. 6. 30. | 3.02% | 0.48% | 1.20 | 0.03 | -0.20 |
| 6. | 2018. 7. 31. | 9.78% | 3.60% | 61.89 | 8.62 | 23.09 |
| 7. | 2018. 8. 31. | 2.82% | 3.03% | 0.82 | 5.57 | 2.13 |
| 8. | 2018. 9. 30. | 1.52% | 0.43% | 0.16 | 0.06 | 0.09 |
| 9. | 2018. 10. 31. | -6.22% | -6.94% | 66.18 | 57.87 | 61.88 |
| 10. | 2018. 11. 30. | 7.90% | 1.79% | 35.79 | 1.25 | 6.70 |
| 11. | 2018. 12. 31. | -11.36% | -9.18% | 176.31 | 96.91 | 130.71 |
| 12. | 2019. 1. 31. | 9.66% | 7.87% | 59.89 | 51.87 | 55.73 |
| 13. | 2019. 2. 28. | 5.52% | 2.97% | 12.96 | 5.32 | 8.30 |
| 14. | 2019. 3. 31. | 2.77% | 1.79% | 0.72 | 1.27 | 0.95 |
| 15. | 2019. 4. 30. | 13.58% | 3.93% | 136.01 | 10.66 | 38.07 |
| 16. | 2019. 5. 31. | -3.48% | -6.58% | 29.17 | 52.48 | 39.12 |
| 17. | 2019. 6. 30. | 7.49% | 6.89% | 31.01 | 38.77 | 34.67 |
| 18. | 2019. 7. 31. | -2.38% | 1.31% | 18.44 | 0.42 | -2.77 |
| 19. | 2019. 8. 31. | -2.08% | -1.81% | 15.97 | 6.13 | 9.89 |
| 20. | 2019. 9. 30. | 2.19% | 1.72% | 0.07 | 1.11 | 0.28 |
| 21. | 2019. 10. 31. | 2.99% | 2.04% | 1.14 | 1.89 | 1.47 |
| 22. | 2019. 11. 30. | 3.33% | 3.40% | 1.98 | 7.50 | 3.85 |
| 23. | 2019. 12. 31. | 1.78% | 2.86% | 0.02 | 4.81 | -0.29 |
| 24. | 2020. 1. 31. | 0.23% | -0.16% | 2.84 | 0.69 | 1.40 |
| 25. | 2020. 2. 29. | -3.14% | -8.41% | 25.63 | 82.40 | 45.96 |
| 26. | 2020. 3. 31. | -13.17% | -12.51% | 227.54 | 173.67 | 198.79 |
| 27. | 2020. 4. 30. | 5.85% | 12.68% | 15.45 | 144.43 | 47.23 |
| 28. | 2020. 5. 31. | 3.19% | 4.53% | 1.62 | 14.91 | 4.92 |
| 29. | 2020. 6. 30. | -0.78% | 1.84% | 7.26 | 1.37 | -3.16 |
| 30. | 2020. 7. 31. | 25.72% | 5.51% | 566.77 | 23.46 | 115.31 |
| 31. | 2020. 8. 31. | 5.83% | 7.01% | 15.29 | 40.19 | 24.79 |
| 32. | 2020. 9. 30. | 2.86% | -3.92% | 0.89 | 21.06 | -4.34 |
| 33. | 2020. 10. 31. | 9.48% | -2.77% | 57.25 | 11.79 | -25.98 |
| 34. | 2020. 11. 30. | 10.16% | 10.75% | 67.96 | 101.77 | 83.16 |
| 35. | 2020. 12. 31. | -0.38% | 3.71% | 5.26 | 9.28 | -6.99 |
| 36. | 2021. 1. 31. | -1.25% | -1.11% | 10.02 | 3.17 | 5.63 |
| 37. | 2021. 2. 28. | 6.90% | 2.61% | 24.81 | 3.77 | 9.68 |
| 38. | 2021. 3. 31. | 8.42% | 4.24% | 42.34 | 12.80 | 23.28 |
| 39. | 2021. 4. 30. | 5.00% | 5.24% | 9.47 | 20.94 | 14.08 |
| 40. | 2021. 5. 31. | 7.23% | 0.55% | 28.23 | 0.01 | -0.63 |
| 41. | 2021. 6. 30. | -0.90% | 2.22% | 7.92 | 2.42 | -4.38 |
| 42. | 2021. 7. 31. | 10.57% | 2.27% | 74.92 | 2.59 | 13.92 |
| 43. | 2021. 8. 31. | -2.51% | 2.90% | 19.60 | 4.98 | -9.88 |
| 44. | 2021. 9. 30. | -12.73% | -4.76% | 214.43 | 29.42 | 79.42 |
| 45. | 2021. 10. 31. | 4.80% | 6.91% | 8.28 | 39.03 | 17.98 |
| 46. | 2021. 11. 30. | 3.16% | -0.83% | 1.55 | 2.25 | -1.87 |
| 47. | 2021. 12. 31. | 8.56% | 4.36% | 44.06 | 13.65 | 24.53 |
| 48. | 2022. 1. 31. | -14.32% | -5.26% | 263.66 | 35.11 | 96.21 |
| 49. | 2022. 2. 28. | -11.07% | -3.14% | 168.81 | 14.46 | 49.41 |
| 50. | 2022. 3. 31. | -0.36% | 3.58% | 5.21 | 8.47 | -6.64 |
| 51. | 2022. 4. 30. | -8.39% | -8.80% | 106.24 | 89.54 | 97.53 |
| 52. | 2022. 5. 31. | -1.31% | 0.01% | 10.41 | 0.44 | 2.13 |
| 53. | 2022. 6. 30. | -5.45% | -8.39% | 54.24 | 82.06 | 66.72 |
| 54. | 2022. 7. 31. | 13.18% | 9.11% | 126.89 | 71.32 | 95.13 |
| 55. | 2022. 8. 31. | 4.82% | -4.24% | 8.40 | 24.11 | -14.23 |
| 56. | 2022. 9. 30. | -5.58% | -9.34% | 56.15 | 100.12 | 74.98 |
| 57. | 2022. 10. 31. | 10.23% | 7.99% | 69.16 | 53.58 | 60.87 |
| 58. | 2022. 11. 30. | 11.77% | 5.38% | 97.08 | 22.17 | 46.39 |
| 59. | 2022. 12. 31. | -5.41% | -5.90% | 53.76 | 43.08 | 48.13 |
| 합계 (Σ): | 3,261.02 | 1,691.48 | 1,742.35 | |||
모두 보기
분산TT = Σ(RTT,t–RTT)2 ÷ (59 – 1)
= 3,261.02 ÷ (59 – 1)
= 56.22
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산TT, S&P 500 = Σ(RTT,t–RTT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,742.35 ÷ (59 – 1)
= 30.04
체계적인 위험 추정 (β)
| 분산TT | 56.22 |
| 분산S&P 500 | 29.16 |
| 공분산TT, S&P 500 | 30.04 |
| 상관 계수TT, S&P 5001 | 0.74 |
| βTT2 | 1.03 |
| αTT3 | 1.23% |
계산
1 상관 계수TT, S&P 500
= 공분산TT, S&P 500 ÷ (표준 편차TT × 표준 편차S&P 500)
= 30.04 ÷ (7.50% × 5.40%)
= 0.74
2 βTT
= 공분산TT, S&P 500 ÷ 분산S&P 500
= 30.04 ÷ 29.16
= 1.03
3 αTT
= 평균의TT – βTT × 평균의S&P 500
= 1.92% – 1.03 × 0.67%
= 1.23%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.49% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.94% |
| 보통주의 체계적 위험Trane Technologies | βTT | 1.03 |
| Trane Technologies 보통주에 대한 예상 수익률3 | E(RTT) | 15.26% |
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(RTT) = RF + βTT [E(RM) – RF]
= 4.49% + 1.03 [14.94% – 4.49%]
= 15.26%