자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Cummins보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Cummins Inc., 월별 수익률
| Cummins Inc. (CMI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CMI,t1 | 피제수CMI,t1 | RCMI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $147.11 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $154.09 | $1.14 | 5.52% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $157.87 | 2.45% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $166.29 | 5.33% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $224.16 | $1.68 | 4.41% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $239.57 | 6.87% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.36% | 1.11% | ||||
| 표준 편차: | 7.89% | 5.31% | ||||
| Cummins Inc. (CMI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CMI,t1 | 피제수CMI,t1 | RCMI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $147.11 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $154.09 | $1.14 | 5.52% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $157.87 | 2.45% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $166.29 | 5.33% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $150.76 | $1.14 | -8.65% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $171.34 | 13.65% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $164.00 | -4.28% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $149.27 | $1.311 | -8.18% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $162.67 | 8.98% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $172.48 | 6.03% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $182.86 | $1.311 | 6.78% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $178.96 | -2.13% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $159.97 | -10.61% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $151.29 | $1.311 | -4.61% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $135.32 | -10.56% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $163.50 | 20.82% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $169.60 | $1.311 | 4.53% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $173.26 | 2.16% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $193.26 | 11.54% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $207.25 | $1.311 | 7.92% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $211.16 | 1.89% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $219.89 | 4.13% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $231.17 | $1.35 | 5.74% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $227.10 | -1.76% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $234.42 | 3.22% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $253.20 | $1.35 | 8.59% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $259.11 | 2.33% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $252.04 | -2.73% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $257.28 | $1.35 | 2.61% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $243.81 | -5.24% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $232.10 | -4.80% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $235.98 | $1.45 | 2.30% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $224.56 | -4.84% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $239.84 | 6.80% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $209.75 | $1.45 | -11.94% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $218.14 | 4.00% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $220.88 | 1.26% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $204.12 | $1.45 | -6.93% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $205.11 | 0.49% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $189.19 | -7.76% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $209.12 | $1.45 | 11.30% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $193.53 | -7.46% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $221.31 | 14.35% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $215.37 | $1.57 | -1.97% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $203.51 | -5.51% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $244.51 | 20.15% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $251.16 | $1.57 | 3.36% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $242.29 | -3.53% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $249.54 | 2.99% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $243.08 | $1.57 | -1.96% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $238.88 | -1.73% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $235.04 | -1.61% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $204.41 | $1.57 | -12.36% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $245.16 | 19.94% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $260.80 | 6.38% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $230.04 | $1.68 | -11.15% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $228.46 | -0.69% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $216.30 | -5.32% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $224.16 | $1.68 | 4.41% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $239.57 | 6.87% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.36% | 1.11% | ||||
| 표준 편차: | 7.89% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CMI의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Cummins Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCMI,t | RS&P 500,t | (RCMI,t–RCMI)2 | (RS&P 500,t–RS&P 500)2 | (RCMI,t–RCMI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.52% | 2.97% | 17.26 | 3.49 | 7.76 |
| 2. | 2019. 3. 31. | 2.45% | 1.79% | 1.18 | 0.47 | 0.75 |
| 3. | 2019. 4. 30. | 5.33% | 3.93% | 15.75 | 7.98 | 11.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 4.41% | 8.92% | 9.28 | 61.03 | 23.79 |
| 59. | 2023. 12. 31. | 6.87% | 4.42% | 30.36 | 11.00 | 18.28 |
| 합계 (Σ): | 3,606.22 | 1,634.30 | 1,651.43 | |||
| t | 날짜 | RCMI,t | RS&P 500,t | (RCMI,t–RCMI)2 | (RS&P 500,t–RS&P 500)2 | (RCMI,t–RCMI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 5.52% | 2.97% | 17.26 | 3.49 | 7.76 |
| 2. | 2019. 3. 31. | 2.45% | 1.79% | 1.18 | 0.47 | 0.75 |
| 3. | 2019. 4. 30. | 5.33% | 3.93% | 15.75 | 7.98 | 11.21 |
| 4. | 2019. 5. 31. | -8.65% | -6.58% | 100.37 | 59.04 | 76.98 |
| 5. | 2019. 6. 30. | 13.65% | 6.89% | 150.95 | 33.49 | 71.10 |
| 6. | 2019. 7. 31. | -4.28% | 1.31% | 31.91 | 0.04 | -1.17 |
| 7. | 2019. 8. 31. | -8.18% | -1.81% | 91.15 | 8.50 | 27.83 |
| 8. | 2019. 9. 30. | 8.98% | 1.72% | 57.95 | 0.37 | 4.66 |
| 9. | 2019. 10. 31. | 6.03% | 2.04% | 21.77 | 0.88 | 4.37 |
| 10. | 2019. 11. 30. | 6.78% | 3.40% | 29.30 | 5.28 | 12.44 |
| 11. | 2019. 12. 31. | -2.13% | 2.86% | 12.23 | 3.07 | -6.13 |
| 12. | 2020. 1. 31. | -10.61% | -0.16% | 143.43 | 1.61 | 15.19 |
| 13. | 2020. 2. 29. | -4.61% | -8.41% | 35.66 | 90.57 | 56.83 |
| 14. | 2020. 3. 31. | -10.56% | -12.51% | 142.10 | 185.44 | 162.33 |
| 15. | 2020. 4. 30. | 20.82% | 12.68% | 378.69 | 134.06 | 225.32 |
| 16. | 2020. 5. 31. | 4.53% | 4.53% | 10.04 | 11.71 | 10.84 |
| 17. | 2020. 6. 30. | 2.16% | 1.84% | 0.63 | 0.54 | 0.58 |
| 18. | 2020. 7. 31. | 11.54% | 5.51% | 103.60 | 19.40 | 44.83 |
| 19. | 2020. 8. 31. | 7.92% | 7.01% | 42.93 | 34.82 | 38.66 |
| 20. | 2020. 9. 30. | 1.89% | -3.92% | 0.27 | 25.29 | -2.62 |
| 21. | 2020. 10. 31. | 4.13% | -2.77% | 7.67 | 15.00 | -10.72 |
| 22. | 2020. 11. 30. | 5.74% | 10.75% | 19.17 | 93.10 | 42.25 |
| 23. | 2020. 12. 31. | -1.76% | 3.71% | 9.77 | 6.79 | -8.15 |
| 24. | 2021. 1. 31. | 3.22% | -1.11% | 3.45 | 4.93 | -4.12 |
| 25. | 2021. 2. 28. | 8.59% | 2.61% | 52.16 | 2.26 | 10.86 |
| 26. | 2021. 3. 31. | 2.33% | 4.24% | 0.94 | 9.85 | 3.04 |
| 27. | 2021. 4. 30. | -2.73% | 5.24% | 16.76 | 17.11 | -16.93 |
| 28. | 2021. 5. 31. | 2.61% | 0.55% | 1.56 | 0.31 | -0.70 |
| 29. | 2021. 6. 30. | -5.24% | 2.22% | 43.57 | 1.24 | -7.36 |
| 30. | 2021. 7. 31. | -4.80% | 2.27% | 38.04 | 1.37 | -7.21 |
| 31. | 2021. 8. 31. | 2.30% | 2.90% | 0.87 | 3.22 | 1.67 |
| 32. | 2021. 9. 30. | -4.84% | -4.76% | 38.49 | 34.37 | 36.37 |
| 33. | 2021. 10. 31. | 6.80% | 6.91% | 29.59 | 33.74 | 31.60 |
| 34. | 2021. 11. 30. | -11.94% | -0.83% | 177.05 | 3.76 | 25.80 |
| 35. | 2021. 12. 31. | 4.00% | 4.36% | 6.94 | 10.60 | 8.58 |
| 36. | 2022. 1. 31. | 1.26% | -5.26% | 0.01 | 40.51 | 0.69 |
| 37. | 2022. 2. 28. | -6.93% | -3.14% | 68.83 | 17.99 | 35.19 |
| 38. | 2022. 3. 31. | 0.49% | 3.58% | 0.77 | 6.11 | -2.17 |
| 39. | 2022. 4. 30. | -7.76% | -8.80% | 83.29 | 98.04 | 90.37 |
| 40. | 2022. 5. 31. | 11.30% | 0.01% | 98.72 | 1.21 | -10.93 |
| 41. | 2022. 6. 30. | -7.46% | -8.39% | 77.79 | 90.21 | 83.77 |
| 42. | 2022. 7. 31. | 14.35% | 9.11% | 168.73 | 64.09 | 103.99 |
| 43. | 2022. 8. 31. | -1.97% | -4.24% | 11.15 | 28.62 | 17.87 |
| 44. | 2022. 9. 30. | -5.51% | -9.34% | 47.22 | 109.11 | 71.78 |
| 45. | 2022. 10. 31. | 20.15% | 7.99% | 352.75 | 47.34 | 129.23 |
| 46. | 2022. 11. 30. | 3.36% | 5.38% | 3.99 | 18.23 | 8.53 |
| 47. | 2022. 12. 31. | -3.53% | -5.90% | 23.98 | 49.04 | 34.29 |
| 48. | 2023. 1. 31. | 2.99% | 6.18% | 2.65 | 25.70 | 8.25 |
| 49. | 2023. 2. 28. | -1.96% | -2.61% | 11.05 | 13.82 | 12.36 |
| 50. | 2023. 3. 31. | -1.73% | 3.51% | 9.56 | 5.76 | -7.42 |
| 51. | 2023. 4. 30. | -1.61% | 1.46% | 8.83 | 0.13 | -1.07 |
| 52. | 2023. 5. 31. | -12.36% | 0.25% | 188.48 | 0.74 | 11.77 |
| 53. | 2023. 6. 30. | 19.94% | 4.71% | 344.87 | 13.02 | 67.00 |
| 54. | 2023. 7. 31. | 6.38% | 4.85% | 25.15 | 13.99 | 18.76 |
| 55. | 2023. 8. 31. | -11.15% | -1.77% | 156.63 | 8.28 | 36.01 |
| 56. | 2023. 9. 30. | -0.69% | -4.87% | 4.21 | 35.73 | 12.26 |
| 57. | 2023. 10. 31. | -5.32% | -2.20% | 44.72 | 10.92 | 22.09 |
| 58. | 2023. 11. 30. | 4.41% | 8.92% | 9.28 | 61.03 | 23.79 |
| 59. | 2023. 12. 31. | 6.87% | 4.42% | 30.36 | 11.00 | 18.28 |
| 합계 (Σ): | 3,606.22 | 1,634.30 | 1,651.43 | |||
모두 보기
분산CMI = Σ(RCMI,t–RCMI)2 ÷ (59 – 1)
= 3,606.22 ÷ (59 – 1)
= 62.18
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산CMI, S&P 500 = Σ(RCMI,t–RCMI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,651.43 ÷ (59 – 1)
= 28.47
체계적인 위험 추정 (β)
| 분산CMI | 62.18 |
| 분산S&P 500 | 28.18 |
| 공분산CMI, S&P 500 | 28.47 |
| 상관 계수CMI, S&P 5001 | 0.68 |
| βCMI2 | 1.01 |
| αCMI3 | 0.25% |
계산
1 상관 계수CMI, S&P 500
= 공분산CMI, S&P 500 ÷ (표준 편차CMI × 표준 편차S&P 500)
= 28.47 ÷ (7.89% × 5.31%)
= 0.68
2 βCMI
= 공분산CMI, S&P 500 ÷ 분산S&P 500
= 28.47 ÷ 28.18
= 1.01
3 αCMI
= 평균의CMI – βCMI × 평균의S&P 500
= 1.36% – 1.01 × 1.11%
= 0.25%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Cummins | βCMI | 1.01 |
| 커민스 보통주에 대한 예상 수익률3 | E(RCMI) | 13.88% |
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(RCMI) = RF + βCMI [E(RM) – RF]
= 4.67% + 1.01 [13.79% – 4.67%]
= 13.88%