자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 ITW보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Illinois Tool Works Inc., 월별 수익률
| Illinois Tool Works Inc. (ITW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ITW,t1 | 피제수ITW,t1 | RITW,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $127.20 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $132.01 | 3.78% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $132.47 | $0.65 | 0.84% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $138.09 | 4.24% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $232.15 | 1.88% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $246.80 | $1.22 | 6.84% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.51% | 1.36% | ||||
| 표준 편차: | 5.99% | 4.48% | ||||
| Illinois Tool Works Inc. (ITW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값ITW,t1 | 피제수ITW,t1 | RITW,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $127.20 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $132.01 | 3.78% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $132.47 | $0.65 | 0.84% | 2,362.72 | -0.04% |
| 3. | 2017. 4. 30. | $138.09 | 4.24% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $141.22 | 2.27% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $143.25 | $0.65 | 1.90% | 2,423.41 | 0.48% |
| 6. | 2017. 7. 31. | $140.71 | -1.77% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $137.51 | -2.27% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $147.96 | $0.78 | 8.17% | 2,519.36 | 1.93% |
| 9. | 2017. 10. 31. | $156.52 | 5.79% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $169.25 | 8.13% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $166.85 | $0.78 | -0.96% | 2,673.61 | 0.98% |
| 12. | 2018. 1. 31. | $173.67 | 4.09% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $161.44 | -7.04% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $156.66 | $0.78 | -2.48% | 2,640.87 | -2.69% |
| 15. | 2018. 4. 30. | $142.02 | -9.35% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $143.70 | 1.18% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $138.54 | $0.78 | -3.05% | 2,718.37 | 0.48% |
| 18. | 2018. 7. 31. | $143.33 | 3.46% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $138.88 | -3.10% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $141.12 | $1.00 | 2.33% | 2,913.98 | 0.43% |
| 21. | 2018. 10. 31. | $127.57 | -9.60% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $139.05 | 9.00% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $126.69 | $1.00 | -8.17% | 2,506.85 | -9.18% |
| 24. | 2019. 1. 31. | $137.31 | 8.38% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $144.08 | 4.93% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $143.53 | $1.00 | 0.31% | 2,834.40 | 1.79% |
| 27. | 2019. 4. 30. | $155.63 | 8.43% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $139.64 | -10.27% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $150.81 | $1.00 | 8.72% | 2,941.76 | 6.89% |
| 30. | 2019. 7. 31. | $154.23 | 2.27% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $149.86 | -2.83% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $156.49 | $1.07 | 5.14% | 2,976.74 | 1.72% |
| 33. | 2019. 10. 31. | $168.58 | 7.73% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $174.33 | 3.41% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $179.63 | $1.07 | 3.65% | 3,230.78 | 2.86% |
| 36. | 2020. 1. 31. | $174.98 | -2.59% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $167.78 | -4.11% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $142.12 | $1.07 | -14.66% | 2,584.59 | -12.51% |
| 39. | 2020. 4. 30. | $162.50 | 14.34% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $172.46 | 6.13% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $174.85 | $1.07 | 2.01% | 3,100.29 | 1.84% |
| 42. | 2020. 7. 31. | $184.99 | 5.80% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $197.55 | 6.79% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $193.21 | $1.14 | -1.62% | 3,363.00 | -3.92% |
| 45. | 2020. 10. 31. | $195.88 | 1.38% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $211.09 | 7.76% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $203.88 | $1.14 | -2.88% | 3,756.07 | 3.71% |
| 48. | 2021. 1. 31. | $194.21 | -4.74% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $202.18 | 4.10% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $221.52 | $1.14 | 10.13% | 3,972.89 | 4.24% |
| 51. | 2021. 4. 30. | $230.46 | 4.04% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $231.76 | 0.56% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $223.56 | $1.14 | -3.05% | 4,297.50 | 2.22% |
| 54. | 2021. 7. 31. | $226.67 | 1.39% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $232.86 | 2.73% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $206.63 | $1.22 | -10.74% | 4,307.54 | -4.76% |
| 57. | 2021. 10. 31. | $227.87 | 10.28% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $232.15 | 1.88% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $246.80 | $1.22 | 6.84% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.51% | 1.36% | ||||
| 표준 편차: | 5.99% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 ITW의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Illinois Tool Works Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RITW,t | RS&P 500,t | (RITW,t–RITW)2 | (RS&P 500,t–RS&P 500)2 | (RITW,t–RITW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 3.78% | 3.72% | 5.17 | 5.58 | 5.37 |
| 2. | 2017. 3. 31. | 0.84% | -0.04% | 0.45 | 1.95 | 0.93 |
| 3. | 2017. 4. 30. | 4.24% | 0.91% | 7.47 | 0.20 | -1.23 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | 1.88% | -0.83% | 0.14 | 4.80 | -0.81 |
| 59. | 2021. 12. 31. | 6.84% | 4.36% | 28.38 | 9.02 | 16.00 |
| 합계 (Σ): | 2,078.90 | 1,164.17 | 1,283.40 | |||
| t | 날짜 | RITW,t | RS&P 500,t | (RITW,t–RITW)2 | (RS&P 500,t–RS&P 500)2 | (RITW,t–RITW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 3.78% | 3.72% | 5.17 | 5.58 | 5.37 |
| 2. | 2017. 3. 31. | 0.84% | -0.04% | 0.45 | 1.95 | 0.93 |
| 3. | 2017. 4. 30. | 4.24% | 0.91% | 7.47 | 0.20 | -1.23 |
| 4. | 2017. 5. 31. | 2.27% | 1.16% | 0.57 | 0.04 | -0.15 |
| 5. | 2017. 6. 30. | 1.90% | 0.48% | 0.15 | 0.77 | -0.34 |
| 6. | 2017. 7. 31. | -1.77% | 1.93% | 10.77 | 0.33 | -1.89 |
| 7. | 2017. 8. 31. | -2.27% | 0.05% | 14.31 | 1.70 | 4.93 |
| 8. | 2017. 9. 30. | 8.17% | 1.93% | 44.33 | 0.33 | 3.81 |
| 9. | 2017. 10. 31. | 5.79% | 2.22% | 18.29 | 0.74 | 3.68 |
| 10. | 2017. 11. 30. | 8.13% | 2.81% | 43.88 | 2.10 | 9.61 |
| 11. | 2017. 12. 31. | -0.96% | 0.98% | 6.08 | 0.14 | 0.92 |
| 12. | 2018. 1. 31. | 4.09% | 5.62% | 6.65 | 18.15 | 10.99 |
| 13. | 2018. 2. 28. | -7.04% | -3.89% | 73.12 | 27.59 | 44.91 |
| 14. | 2018. 3. 31. | -2.48% | -2.69% | 15.89 | 16.37 | 16.13 |
| 15. | 2018. 4. 30. | -9.35% | 0.27% | 117.81 | 1.18 | 11.79 |
| 16. | 2018. 5. 31. | 1.18% | 2.16% | 0.11 | 0.64 | -0.26 |
| 17. | 2018. 6. 30. | -3.05% | 0.48% | 20.76 | 0.76 | 3.98 |
| 18. | 2018. 7. 31. | 3.46% | 3.60% | 3.80 | 5.04 | 4.37 |
| 19. | 2018. 8. 31. | -3.10% | 3.03% | 21.28 | 2.78 | -7.70 |
| 20. | 2018. 9. 30. | 2.33% | 0.43% | 0.68 | 0.86 | -0.77 |
| 21. | 2018. 10. 31. | -9.60% | -6.94% | 123.44 | 68.86 | 92.20 |
| 22. | 2018. 11. 30. | 9.00% | 1.79% | 56.10 | 0.18 | 3.21 |
| 23. | 2018. 12. 31. | -8.17% | -9.18% | 93.67 | 111.00 | 101.97 |
| 24. | 2019. 1. 31. | 8.38% | 7.87% | 47.25 | 42.39 | 44.75 |
| 25. | 2019. 2. 28. | 4.93% | 2.97% | 11.71 | 2.61 | 5.53 |
| 26. | 2019. 3. 31. | 0.31% | 1.79% | 1.43 | 0.19 | -0.52 |
| 27. | 2019. 4. 30. | 8.43% | 3.93% | 47.91 | 6.62 | 17.81 |
| 28. | 2019. 5. 31. | -10.27% | -6.58% | 138.84 | 62.97 | 93.51 |
| 29. | 2019. 6. 30. | 8.72% | 6.89% | 51.93 | 30.64 | 39.89 |
| 30. | 2019. 7. 31. | 2.27% | 1.31% | 0.58 | 0.00 | -0.03 |
| 31. | 2019. 8. 31. | -2.83% | -1.81% | 18.85 | 10.03 | 13.75 |
| 32. | 2019. 9. 30. | 5.14% | 1.72% | 13.17 | 0.13 | 1.31 |
| 33. | 2019. 10. 31. | 7.73% | 2.04% | 38.65 | 0.47 | 4.26 |
| 34. | 2019. 11. 30. | 3.41% | 3.40% | 3.62 | 4.19 | 3.89 |
| 35. | 2019. 12. 31. | 3.65% | 2.86% | 4.60 | 2.25 | 3.22 |
| 36. | 2020. 1. 31. | -2.59% | -0.16% | 16.79 | 2.31 | 6.23 |
| 37. | 2020. 2. 29. | -4.11% | -8.41% | 31.62 | 95.43 | 54.94 |
| 38. | 2020. 3. 31. | -14.66% | -12.51% | 261.30 | 192.37 | 224.20 |
| 39. | 2020. 4. 30. | 14.34% | 12.68% | 164.64 | 128.29 | 145.33 |
| 40. | 2020. 5. 31. | 6.13% | 4.53% | 21.35 | 10.05 | 14.65 |
| 41. | 2020. 6. 30. | 2.01% | 1.84% | 0.25 | 0.23 | 0.24 |
| 42. | 2020. 7. 31. | 5.80% | 5.51% | 18.41 | 17.24 | 17.82 |
| 43. | 2020. 8. 31. | 6.79% | 7.01% | 27.89 | 31.91 | 29.83 |
| 44. | 2020. 9. 30. | -1.62% | -3.92% | 9.79 | 27.89 | 16.52 |
| 45. | 2020. 10. 31. | 1.38% | -2.77% | 0.02 | 17.01 | 0.52 |
| 46. | 2020. 11. 30. | 7.76% | 10.75% | 39.14 | 88.30 | 58.79 |
| 47. | 2020. 12. 31. | -2.88% | 3.71% | 19.22 | 5.54 | -10.32 |
| 48. | 2021. 1. 31. | -4.74% | -1.11% | 39.08 | 6.11 | 15.45 |
| 49. | 2021. 2. 28. | 4.10% | 2.61% | 6.73 | 1.57 | 3.25 |
| 50. | 2021. 3. 31. | 10.13% | 4.24% | 74.32 | 8.33 | 24.88 |
| 51. | 2021. 4. 30. | 4.04% | 5.24% | 6.39 | 15.09 | 9.82 |
| 52. | 2021. 5. 31. | 0.56% | 0.55% | 0.89 | 0.65 | 0.76 |
| 53. | 2021. 6. 30. | -3.05% | 2.22% | 20.75 | 0.75 | -3.93 |
| 54. | 2021. 7. 31. | 1.39% | 2.27% | 0.01 | 0.84 | -0.11 |
| 55. | 2021. 8. 31. | 2.73% | 2.90% | 1.49 | 2.38 | 1.88 |
| 56. | 2021. 9. 30. | -10.74% | -4.76% | 150.04 | 37.39 | 74.90 |
| 57. | 2021. 10. 31. | 10.28% | 6.91% | 76.92 | 30.87 | 48.73 |
| 58. | 2021. 11. 30. | 1.88% | -0.83% | 0.14 | 4.80 | -0.81 |
| 59. | 2021. 12. 31. | 6.84% | 4.36% | 28.38 | 9.02 | 16.00 |
| 합계 (Σ): | 2,078.90 | 1,164.17 | 1,283.40 | |||
모두 보기
분산ITW = Σ(RITW,t–RITW)2 ÷ (59 – 1)
= 2,078.90 ÷ (59 – 1)
= 35.84
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산ITW, S&P 500 = Σ(RITW,t–RITW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,283.40 ÷ (59 – 1)
= 22.13
체계적인 위험 추정 (β)
| 분산ITW | 35.84 |
| 분산S&P 500 | 20.07 |
| 공분산ITW, S&P 500 | 22.13 |
| 상관 계수ITW, S&P 5001 | 0.82 |
| βITW2 | 1.10 |
| αITW3 | 0.01% |
계산
1 상관 계수ITW, S&P 500
= 공분산ITW, S&P 500 ÷ (표준 편차ITW × 표준 편차S&P 500)
= 22.13 ÷ (5.99% × 4.48%)
= 0.82
2 βITW
= 공분산ITW, S&P 500 ÷ 분산S&P 500
= 22.13 ÷ 20.07
= 1.10
3 αITW
= 평균의ITW – βITW × 평균의S&P 500
= 1.51% – 1.10 × 1.36%
= 0.01%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.89% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험ITW | βITW | 1.10 |
| ITW 보통주에 대한 예상 수익률3 | E(RITW) | 15.90% |
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(RITW) = RF + βITW [E(RM) – RF]
= 4.89% + 1.10 [14.88% – 4.89%]
= 15.90%