자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Linde보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Linde plc, 월별 수익률
| Linde plc (LIN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LIN,t1 | 피제수LIN,t1 | RLIN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $203.13 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $191.01 | -5.97% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $173.00 | $0.963 | -8.92% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $183.99 | 6.35% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $460.99 | 1.06% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $418.67 | $1.39 | -8.88% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.57% | 1.16% | ||||
| 표준 편차: | 6.65% | 5.28% | ||||
| Linde plc (LIN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값LIN,t1 | 피제수LIN,t1 | RLIN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $203.13 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $191.01 | -5.97% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $173.00 | $0.963 | -8.92% | 2,584.59 | -12.51% |
| 3. | 2020. 4. 30. | $183.99 | 6.35% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $202.34 | 9.97% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $212.11 | $0.963 | 5.30% | 3,100.29 | 1.84% |
| 6. | 2020. 7. 31. | $245.11 | 15.56% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $249.74 | 1.89% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $238.13 | $0.963 | -4.26% | 3,363.00 | -3.92% |
| 9. | 2020. 10. 31. | $220.34 | -7.47% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $256.42 | 16.37% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $263.51 | $0.963 | 3.14% | 3,756.07 | 3.71% |
| 12. | 2021. 1. 31. | $245.40 | -6.87% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $244.27 | -0.46% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $280.14 | $1.06 | 15.12% | 3,972.89 | 4.24% |
| 15. | 2021. 4. 30. | $285.84 | 2.03% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $300.60 | 5.16% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $289.10 | $1.06 | -3.47% | 4,297.50 | 2.22% |
| 18. | 2021. 7. 31. | $307.39 | 6.33% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $314.59 | 2.34% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $293.38 | $1.06 | -6.41% | 4,307.54 | -4.76% |
| 21. | 2021. 10. 31. | $319.20 | 8.80% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $318.14 | -0.33% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $346.43 | $1.06 | 9.23% | 4,766.18 | 4.36% |
| 24. | 2022. 1. 31. | $318.68 | -8.01% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $293.24 | -7.98% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $319.43 | $1.17 | 9.33% | 4,530.41 | 3.58% |
| 27. | 2022. 4. 30. | $311.96 | -2.34% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $324.68 | 4.08% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $287.53 | $1.17 | -11.08% | 3,785.38 | -8.39% |
| 30. | 2022. 7. 31. | $302.00 | 5.03% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $282.86 | -6.34% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $269.59 | $1.17 | -4.28% | 3,585.62 | -9.34% |
| 33. | 2022. 10. 31. | $297.35 | 10.30% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $336.48 | 13.16% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $326.18 | $1.17 | -2.71% | 3,839.50 | -5.90% |
| 36. | 2023. 1. 31. | $330.94 | 1.46% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $348.37 | 5.27% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $355.44 | $1.275 | 2.40% | 4,109.31 | 3.51% |
| 39. | 2023. 4. 30. | $369.45 | 3.94% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $353.66 | -4.27% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $381.08 | $1.275 | 8.11% | 4,376.86 | 4.71% |
| 42. | 2023. 7. 31. | $390.67 | 2.52% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $387.04 | -0.93% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $372.35 | $1.275 | -3.47% | 4,288.05 | -4.87% |
| 45. | 2023. 10. 31. | $382.16 | 2.63% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $413.77 | 8.27% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $410.71 | $1.275 | -0.43% | 4,769.83 | 4.42% |
| 48. | 2024. 1. 31. | $404.83 | -1.43% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $448.82 | 10.87% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $464.32 | $1.39 | 3.76% | 5,254.35 | 3.10% |
| 51. | 2024. 4. 30. | $440.96 | -5.03% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $435.52 | -1.23% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $438.81 | $1.39 | 1.07% | 5,460.48 | 3.47% |
| 54. | 2024. 7. 31. | $453.50 | 3.35% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $478.25 | 5.46% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $476.86 | $1.39 | 0.00% | 5,762.48 | 2.02% |
| 57. | 2024. 10. 31. | $456.15 | -4.34% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $460.99 | 1.06% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $418.67 | $1.39 | -8.88% | 5,881.63 | -2.50% |
| 평균의 (R): | 1.57% | 1.16% | ||||
| 표준 편차: | 6.65% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 LIN의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Linde plc, 수익률의 분산 및 공분산 계산
| t | 날짜 | RLIN,t | RS&P 500,t | (RLIN,t–RLIN)2 | (RS&P 500,t–RS&P 500)2 | (RLIN,t–RLIN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -5.97% | -8.41% | 56.83 | 91.63 | 72.16 |
| 2. | 2020. 3. 31. | -8.92% | -12.51% | 110.18 | 186.96 | 143.52 |
| 3. | 2020. 4. 30. | 6.35% | 12.68% | 22.86 | 132.78 | 55.09 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 1.06% | 5.73% | 0.26 | 20.87 | -2.33 |
| 59. | 2024. 12. 31. | -8.88% | -2.50% | 109.22 | 13.40 | 38.25 |
| 합계 (Σ): | 2,565.41 | 1,618.62 | 1,515.53 | |||
| t | 날짜 | RLIN,t | RS&P 500,t | (RLIN,t–RLIN)2 | (RS&P 500,t–RS&P 500)2 | (RLIN,t–RLIN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -5.97% | -8.41% | 56.83 | 91.63 | 72.16 |
| 2. | 2020. 3. 31. | -8.92% | -12.51% | 110.18 | 186.96 | 143.52 |
| 3. | 2020. 4. 30. | 6.35% | 12.68% | 22.86 | 132.78 | 55.09 |
| 4. | 2020. 5. 31. | 9.97% | 4.53% | 70.58 | 11.34 | 28.29 |
| 5. | 2020. 6. 30. | 5.30% | 1.84% | 13.93 | 0.46 | 2.53 |
| 6. | 2020. 7. 31. | 15.56% | 5.51% | 195.61 | 18.91 | 60.82 |
| 7. | 2020. 8. 31. | 1.89% | 7.01% | 0.10 | 34.17 | 1.85 |
| 8. | 2020. 9. 30. | -4.26% | -3.92% | 34.05 | 25.85 | 29.67 |
| 9. | 2020. 10. 31. | -7.47% | -2.77% | 81.77 | 15.43 | 35.52 |
| 10. | 2020. 11. 30. | 16.37% | 10.75% | 219.12 | 92.03 | 142.01 |
| 11. | 2020. 12. 31. | 3.14% | 3.71% | 2.46 | 6.51 | 4.00 |
| 12. | 2021. 1. 31. | -6.87% | -1.11% | 71.31 | 5.18 | 19.21 |
| 13. | 2021. 2. 28. | -0.46% | 2.61% | 4.13 | 2.10 | -2.94 |
| 14. | 2021. 3. 31. | 15.12% | 4.24% | 183.51 | 9.50 | 41.76 |
| 15. | 2021. 4. 30. | 2.03% | 5.24% | 0.21 | 16.66 | 1.89 |
| 16. | 2021. 5. 31. | 5.16% | 0.55% | 12.90 | 0.38 | -2.20 |
| 17. | 2021. 6. 30. | -3.47% | 2.22% | 25.45 | 1.12 | -5.35 |
| 18. | 2021. 7. 31. | 6.33% | 2.27% | 22.61 | 1.24 | 5.29 |
| 19. | 2021. 8. 31. | 2.34% | 2.90% | 0.59 | 3.02 | 1.34 |
| 20. | 2021. 9. 30. | -6.41% | -4.76% | 63.63 | 35.02 | 47.21 |
| 21. | 2021. 10. 31. | 8.80% | 6.91% | 52.26 | 33.10 | 41.59 |
| 22. | 2021. 11. 30. | -0.33% | -0.83% | 3.63 | 3.98 | 3.80 |
| 23. | 2021. 12. 31. | 9.23% | 4.36% | 58.58 | 10.24 | 24.49 |
| 24. | 2022. 1. 31. | -8.01% | -5.26% | 91.82 | 41.21 | 61.52 |
| 25. | 2022. 2. 28. | -7.98% | -3.14% | 91.29 | 18.47 | 41.06 |
| 26. | 2022. 3. 31. | 9.33% | 3.58% | 60.19 | 5.84 | 18.74 |
| 27. | 2022. 4. 30. | -2.34% | -8.80% | 15.29 | 99.14 | 38.94 |
| 28. | 2022. 5. 31. | 4.08% | 0.01% | 6.28 | 1.34 | -2.90 |
| 29. | 2022. 6. 30. | -11.08% | -8.39% | 160.11 | 91.26 | 120.88 |
| 30. | 2022. 7. 31. | 5.03% | 9.11% | 11.98 | 63.21 | 27.51 |
| 31. | 2022. 8. 31. | -6.34% | -4.24% | 62.56 | 29.22 | 42.75 |
| 32. | 2022. 9. 30. | -4.28% | -9.34% | 34.22 | 110.27 | 61.43 |
| 33. | 2022. 10. 31. | 10.30% | 7.99% | 76.13 | 46.58 | 59.55 |
| 34. | 2022. 11. 30. | 13.16% | 5.38% | 134.27 | 17.76 | 48.83 |
| 35. | 2022. 12. 31. | -2.71% | -5.90% | 18.36 | 49.82 | 30.25 |
| 36. | 2023. 1. 31. | 1.46% | 6.18% | 0.01 | 25.14 | -0.56 |
| 37. | 2023. 2. 28. | 5.27% | -2.61% | 13.65 | 14.23 | -13.94 |
| 38. | 2023. 3. 31. | 2.40% | 3.51% | 0.68 | 5.49 | 1.93 |
| 39. | 2023. 4. 30. | 3.94% | 1.46% | 5.62 | 0.09 | 0.72 |
| 40. | 2023. 5. 31. | -4.27% | 0.25% | 34.17 | 0.83 | 5.34 |
| 41. | 2023. 6. 30. | 8.11% | 4.71% | 42.80 | 12.62 | 23.24 |
| 42. | 2023. 7. 31. | 2.52% | 4.85% | 0.89 | 13.58 | 3.48 |
| 43. | 2023. 8. 31. | -0.93% | -1.77% | 6.26 | 8.60 | 7.34 |
| 44. | 2023. 9. 30. | -3.47% | -4.87% | 25.38 | 36.40 | 30.39 |
| 45. | 2023. 10. 31. | 2.63% | -2.20% | 1.13 | 11.28 | -3.57 |
| 46. | 2023. 11. 30. | 8.27% | 8.92% | 44.88 | 60.17 | 51.97 |
| 47. | 2023. 12. 31. | -0.43% | 4.42% | 4.01 | 10.64 | -6.53 |
| 48. | 2024. 1. 31. | -1.43% | 1.59% | 9.02 | 0.18 | -1.29 |
| 49. | 2024. 2. 29. | 10.87% | 5.17% | 86.39 | 16.09 | 37.28 |
| 50. | 2024. 3. 31. | 3.76% | 3.10% | 4.80 | 3.77 | 4.25 |
| 51. | 2024. 4. 30. | -5.03% | -4.16% | 43.60 | 28.33 | 35.15 |
| 52. | 2024. 5. 31. | -1.23% | 4.80% | 7.87 | 13.26 | -10.21 |
| 53. | 2024. 6. 30. | 1.07% | 3.47% | 0.25 | 5.32 | -1.15 |
| 54. | 2024. 7. 31. | 3.35% | 1.13% | 3.15 | 0.00 | -0.05 |
| 55. | 2024. 8. 31. | 5.46% | 2.28% | 15.10 | 1.26 | 4.36 |
| 56. | 2024. 9. 30. | 0.00% | 2.02% | 2.47 | 0.74 | -1.35 |
| 57. | 2024. 10. 31. | -4.34% | -0.99% | 34.99 | 4.63 | 12.72 |
| 58. | 2024. 11. 30. | 1.06% | 5.73% | 0.26 | 20.87 | -2.33 |
| 59. | 2024. 12. 31. | -8.88% | -2.50% | 109.22 | 13.40 | 38.25 |
| 합계 (Σ): | 2,565.41 | 1,618.62 | 1,515.53 | |||
모두 보기
분산LIN = Σ(RLIN,t–RLIN)2 ÷ (59 – 1)
= 2,565.41 ÷ (59 – 1)
= 44.23
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산LIN, S&P 500 = Σ(RLIN,t–RLIN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,515.53 ÷ (59 – 1)
= 26.13
체계적인 위험 추정 (β)
| 분산LIN | 44.23 |
| 분산S&P 500 | 27.91 |
| 공분산LIN, S&P 500 | 26.13 |
| 상관 계수LIN, S&P 5001 | 0.74 |
| βLIN2 | 0.94 |
| αLIN3 | 0.48% |
계산
1 상관 계수LIN, S&P 500
= 공분산LIN, S&P 500 ÷ (표준 편차LIN × 표준 편차S&P 500)
= 26.13 ÷ (6.65% × 5.28%)
= 0.74
2 βLIN
= 공분산LIN, S&P 500 ÷ 분산S&P 500
= 26.13 ÷ 27.91
= 0.94
3 αLIN
= 평균의LIN – βLIN × 평균의S&P 500
= 1.57% – 0.94 × 1.16%
= 0.48%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.53% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.88% |
| 보통주의 체계적 위험Linde | βLIN | 0.94 |
| Linde 보통주의 예상 수익률3 | E(RLIN) | 14.22% |
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(RLIN) = RF + βLIN [E(RM) – RF]
= 4.53% + 0.94 [14.88% – 4.53%]
= 14.22%