자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Caterpillar보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Caterpillar Inc., 월별 수익률
| Caterpillar Inc. (CAT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CAT,t1 | 피제수CAT,t1 | RCAT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $131.35 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $124.24 | -5.41% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $116.04 | -6.60% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $116.38 | $1.03 | 1.18% | 2,912.43 | 12.68% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $406.11 | 7.95% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $362.76 | -10.67% | 5,881.63 | -2.50% | |
| 평균의 (R): | 2.32% | 1.16% | ||||
| 표준 편차: | 9.25% | 5.28% | ||||
| Caterpillar Inc. (CAT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CAT,t1 | 피제수CAT,t1 | RCAT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $131.35 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $124.24 | -5.41% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $116.04 | -6.60% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $116.38 | $1.03 | 1.18% | 2,912.43 | 12.68% |
| 4. | 2020. 5. 31. | $120.13 | 3.22% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $126.50 | 5.30% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $132.88 | $1.03 | 5.86% | 3,271.12 | 5.51% |
| 7. | 2020. 8. 31. | $142.31 | 7.10% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $149.15 | 4.81% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $157.05 | $1.03 | 5.99% | 3,269.96 | -2.77% |
| 10. | 2020. 11. 30. | $173.59 | 10.53% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $182.02 | 4.86% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $182.84 | $1.03 | 1.02% | 3,714.24 | -1.11% |
| 13. | 2021. 2. 28. | $215.88 | 18.07% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $231.87 | 7.41% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $228.11 | $1.03 | -1.18% | 4,181.17 | 5.24% |
| 16. | 2021. 5. 31. | $241.08 | 5.69% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $217.63 | -9.73% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $206.75 | $1.11 | -4.49% | 4,395.26 | 2.27% |
| 19. | 2021. 8. 31. | $210.87 | 1.99% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $191.97 | -8.96% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $204.01 | $1.11 | 6.85% | 4,605.38 | 6.91% |
| 22. | 2021. 11. 30. | $193.35 | -5.23% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $206.74 | 6.93% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $201.56 | $1.11 | -1.97% | 4,515.55 | -5.26% |
| 25. | 2022. 2. 28. | $187.58 | -6.94% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $222.82 | 18.79% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $210.54 | $1.11 | -5.01% | 4,131.93 | -8.80% |
| 28. | 2022. 5. 31. | $215.85 | 2.52% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $178.76 | -17.18% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $198.25 | $1.20 | 11.57% | 4,130.29 | 9.11% |
| 31. | 2022. 8. 31. | $184.71 | -6.83% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $164.08 | -11.17% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $216.46 | $1.20 | 32.65% | 3,871.98 | 7.99% |
| 34. | 2022. 11. 30. | $236.41 | 9.22% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $239.56 | 1.33% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $252.29 | $1.20 | 5.81% | 4,076.60 | 6.18% |
| 37. | 2023. 2. 28. | $239.55 | -5.05% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $228.84 | -4.47% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $218.80 | $1.20 | -3.86% | 4,169.48 | 1.46% |
| 40. | 2023. 5. 31. | $205.75 | -5.96% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $246.05 | 19.59% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $265.17 | $1.30 | 8.30% | 4,588.96 | 4.85% |
| 43. | 2023. 8. 31. | $281.13 | 6.02% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $273.00 | -2.89% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $226.05 | $1.30 | -16.72% | 4,193.80 | -2.20% |
| 46. | 2023. 11. 30. | $250.72 | 10.91% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $295.67 | 17.93% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $300.31 | $1.30 | 2.01% | 4,845.65 | 1.59% |
| 49. | 2024. 2. 29. | $333.96 | 11.21% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $366.43 | 9.72% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $334.57 | $1.30 | -8.34% | 5,035.69 | -4.16% |
| 52. | 2024. 5. 31. | $338.52 | 1.18% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $333.10 | -1.60% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $346.20 | $1.41 | 4.36% | 5,522.30 | 1.13% |
| 55. | 2024. 8. 31. | $356.10 | 2.86% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $391.12 | 9.83% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $376.20 | $1.41 | -3.45% | 5,705.45 | -0.99% |
| 58. | 2024. 11. 30. | $406.11 | 7.95% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $362.76 | -10.67% | 5,881.63 | -2.50% | |
| 평균의 (R): | 2.32% | 1.16% | ||||
| 표준 편차: | 9.25% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CAT의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Caterpillar Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCAT,t | RS&P 500,t | (RCAT,t–RCAT)2 | (RS&P 500,t–RS&P 500)2 | (RCAT,t–RCAT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -5.41% | -8.41% | 59.79 | 91.63 | 74.01 |
| 2. | 2020. 3. 31. | -6.60% | -12.51% | 79.55 | 186.96 | 121.96 |
| 3. | 2020. 4. 30. | 1.18% | 12.68% | 1.30 | 132.78 | -13.12 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 7.95% | 5.73% | 31.71 | 20.87 | 25.73 |
| 59. | 2024. 12. 31. | -10.67% | -2.50% | 168.83 | 13.40 | 47.56 |
| 합계 (Σ): | 4,958.68 | 1,618.62 | 1,796.90 | |||
| t | 날짜 | RCAT,t | RS&P 500,t | (RCAT,t–RCAT)2 | (RS&P 500,t–RS&P 500)2 | (RCAT,t–RCAT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -5.41% | -8.41% | 59.79 | 91.63 | 74.01 |
| 2. | 2020. 3. 31. | -6.60% | -12.51% | 79.55 | 186.96 | 121.96 |
| 3. | 2020. 4. 30. | 1.18% | 12.68% | 1.30 | 132.78 | -13.12 |
| 4. | 2020. 5. 31. | 3.22% | 4.53% | 0.82 | 11.34 | 3.04 |
| 5. | 2020. 6. 30. | 5.30% | 1.84% | 8.90 | 0.46 | 2.02 |
| 6. | 2020. 7. 31. | 5.86% | 5.51% | 12.52 | 18.91 | 15.39 |
| 7. | 2020. 8. 31. | 7.10% | 7.01% | 22.82 | 34.17 | 27.93 |
| 8. | 2020. 9. 30. | 4.81% | -3.92% | 6.19 | 25.85 | -12.65 |
| 9. | 2020. 10. 31. | 5.99% | -2.77% | 13.46 | 15.43 | -14.41 |
| 10. | 2020. 11. 30. | 10.53% | 10.75% | 67.45 | 92.03 | 78.79 |
| 11. | 2020. 12. 31. | 4.86% | 3.71% | 6.44 | 6.51 | 6.47 |
| 12. | 2021. 1. 31. | 1.02% | -1.11% | 1.70 | 5.18 | 2.96 |
| 13. | 2021. 2. 28. | 18.07% | 2.61% | 248.10 | 2.10 | 22.81 |
| 14. | 2021. 3. 31. | 7.41% | 4.24% | 25.89 | 9.50 | 15.68 |
| 15. | 2021. 4. 30. | -1.18% | 5.24% | 12.23 | 16.66 | -14.27 |
| 16. | 2021. 5. 31. | 5.69% | 0.55% | 11.33 | 0.38 | -2.06 |
| 17. | 2021. 6. 30. | -9.73% | 2.22% | 145.11 | 1.12 | -12.77 |
| 18. | 2021. 7. 31. | -4.49% | 2.27% | 46.35 | 1.24 | -7.58 |
| 19. | 2021. 8. 31. | 1.99% | 2.90% | 0.11 | 3.02 | -0.57 |
| 20. | 2021. 9. 30. | -8.96% | -4.76% | 127.28 | 35.02 | 66.77 |
| 21. | 2021. 10. 31. | 6.85% | 6.91% | 20.53 | 33.10 | 26.07 |
| 22. | 2021. 11. 30. | -5.23% | -0.83% | 56.92 | 3.98 | 15.05 |
| 23. | 2021. 12. 31. | 6.93% | 4.36% | 21.22 | 10.24 | 14.74 |
| 24. | 2022. 1. 31. | -1.97% | -5.26% | 18.39 | 41.21 | 27.53 |
| 25. | 2022. 2. 28. | -6.94% | -3.14% | 85.66 | 18.47 | 39.77 |
| 26. | 2022. 3. 31. | 18.79% | 3.58% | 271.18 | 5.84 | 39.79 |
| 27. | 2022. 4. 30. | -5.01% | -8.80% | 53.76 | 99.14 | 73.01 |
| 28. | 2022. 5. 31. | 2.52% | 0.01% | 0.04 | 1.34 | -0.23 |
| 29. | 2022. 6. 30. | -17.18% | -8.39% | 380.34 | 91.26 | 186.31 |
| 30. | 2022. 7. 31. | 11.57% | 9.11% | 85.66 | 63.21 | 73.58 |
| 31. | 2022. 8. 31. | -6.83% | -4.24% | 83.70 | 29.22 | 49.45 |
| 32. | 2022. 9. 30. | -11.17% | -9.34% | 181.93 | 110.27 | 141.64 |
| 33. | 2022. 10. 31. | 32.65% | 7.99% | 920.25 | 46.58 | 207.04 |
| 34. | 2022. 11. 30. | 9.22% | 5.38% | 47.57 | 17.76 | 29.07 |
| 35. | 2022. 12. 31. | 1.33% | -5.90% | 0.97 | 49.82 | 6.96 |
| 36. | 2023. 1. 31. | 5.81% | 6.18% | 12.22 | 25.14 | 17.53 |
| 37. | 2023. 2. 28. | -5.05% | -2.61% | 54.30 | 14.23 | 27.80 |
| 38. | 2023. 3. 31. | -4.47% | 3.51% | 46.10 | 5.49 | -15.92 |
| 39. | 2023. 4. 30. | -3.86% | 1.46% | 38.22 | 0.09 | -1.87 |
| 40. | 2023. 5. 31. | -5.96% | 0.25% | 68.62 | 0.83 | 7.56 |
| 41. | 2023. 6. 30. | 19.59% | 4.71% | 298.17 | 12.62 | 61.34 |
| 42. | 2023. 7. 31. | 8.30% | 4.85% | 35.76 | 13.58 | 22.03 |
| 43. | 2023. 8. 31. | 6.02% | -1.77% | 13.69 | 8.60 | -10.85 |
| 44. | 2023. 9. 30. | -2.89% | -4.87% | 27.16 | 36.40 | 31.44 |
| 45. | 2023. 10. 31. | -16.72% | -2.20% | 362.55 | 11.28 | 63.96 |
| 46. | 2023. 11. 30. | 10.91% | 8.92% | 73.86 | 60.17 | 66.66 |
| 47. | 2023. 12. 31. | 17.93% | 4.42% | 243.65 | 10.64 | 50.91 |
| 48. | 2024. 1. 31. | 2.01% | 1.59% | 0.10 | 0.18 | -0.13 |
| 49. | 2024. 2. 29. | 11.21% | 5.17% | 78.96 | 16.09 | 35.64 |
| 50. | 2024. 3. 31. | 9.72% | 3.10% | 54.81 | 3.77 | 14.37 |
| 51. | 2024. 4. 30. | -8.34% | -4.16% | 113.62 | 28.33 | 56.74 |
| 52. | 2024. 5. 31. | 1.18% | 4.80% | 1.30 | 13.26 | -4.15 |
| 53. | 2024. 6. 30. | -1.60% | 3.47% | 15.37 | 5.32 | -9.04 |
| 54. | 2024. 7. 31. | 4.36% | 1.13% | 4.15 | 0.00 | -0.06 |
| 55. | 2024. 8. 31. | 2.86% | 2.28% | 0.29 | 1.26 | 0.61 |
| 56. | 2024. 9. 30. | 9.83% | 2.02% | 56.48 | 0.74 | 6.45 |
| 57. | 2024. 10. 31. | -3.45% | -0.99% | 33.33 | 4.63 | 12.42 |
| 58. | 2024. 11. 30. | 7.95% | 5.73% | 31.71 | 20.87 | 25.73 |
| 59. | 2024. 12. 31. | -10.67% | -2.50% | 168.83 | 13.40 | 47.56 |
| 합계 (Σ): | 4,958.68 | 1,618.62 | 1,796.90 | |||
모두 보기
분산CAT = Σ(RCAT,t–RCAT)2 ÷ (59 – 1)
= 4,958.68 ÷ (59 – 1)
= 85.49
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산CAT, S&P 500 = Σ(RCAT,t–RCAT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,796.90 ÷ (59 – 1)
= 30.98
체계적인 위험 추정 (β)
| 분산CAT | 85.49 |
| 분산S&P 500 | 27.91 |
| 공분산CAT, S&P 500 | 30.98 |
| 상관 계수CAT, S&P 5001 | 0.63 |
| βCAT2 | 1.11 |
| αCAT3 | 1.03% |
계산
1 상관 계수CAT, S&P 500
= 공분산CAT, S&P 500 ÷ (표준 편차CAT × 표준 편차S&P 500)
= 30.98 ÷ (9.25% × 5.28%)
= 0.63
2 βCAT
= 공분산CAT, S&P 500 ÷ 분산S&P 500
= 30.98 ÷ 27.91
= 1.11
3 αCAT
= 평균의CAT – βCAT × 평균의S&P 500
= 2.32% – 1.11 × 1.16%
= 1.03%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Caterpillar | βCAT | 1.11 |
| Caterpillar 보통주에 대한 예상 수익률3 | E(RCAT) | 16.02% |
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(RCAT) = RF + βCAT [E(RM) – RF]
= 4.60% + 1.11 [14.89% – 4.60%]
= 16.02%