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 |
| 2019. 1. 31. | $163.01 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $173.24 | 6.28% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $175.93 | $0.875 | 2.06% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $180.26 | 2.46% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $413.77 | 8.27% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $410.71 | $1.275 | -0.43% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.92% | 1.11% | ||||
| 표준 편차: | 6.50% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $163.01 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $173.24 | 6.28% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $175.93 | $0.875 | 2.06% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $180.26 | 2.46% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $180.55 | $0.875 | 0.65% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $200.80 | 11.22% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $191.28 | -4.74% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $188.91 | $0.875 | -0.78% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $193.72 | 2.55% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $198.35 | 2.39% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $206.21 | 3.96% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $212.90 | $0.875 | 3.67% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $203.13 | -4.59% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $191.01 | -5.97% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $173.00 | $0.963 | -8.92% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $183.99 | 6.35% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $202.34 | 9.97% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $212.11 | $0.963 | 5.30% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $245.11 | 15.56% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $249.74 | 1.89% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $238.13 | $0.963 | -4.26% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $220.34 | -7.47% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $256.42 | 16.37% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $263.51 | $0.963 | 3.14% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $245.40 | -6.87% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $244.27 | -0.46% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $280.14 | $1.06 | 15.12% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $285.84 | 2.03% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $300.60 | 5.16% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $289.10 | $1.06 | -3.47% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $307.39 | 6.33% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $314.59 | 2.34% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $293.38 | $1.06 | -6.41% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $319.20 | 8.80% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $318.14 | -0.33% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $346.43 | $1.06 | 9.23% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $318.68 | -8.01% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $293.24 | -7.98% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $319.43 | $1.17 | 9.33% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $311.96 | -2.34% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $324.68 | 4.08% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $287.53 | $1.17 | -11.08% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $302.00 | 5.03% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $282.86 | -6.34% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $269.59 | $1.17 | -4.28% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $297.35 | 10.30% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $336.48 | 13.16% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $326.18 | $1.17 | -2.71% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $330.94 | 1.46% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $348.37 | 5.27% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $355.44 | $1.275 | 2.40% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $369.45 | 3.94% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $353.66 | -4.27% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $381.08 | $1.275 | 8.11% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $390.67 | 2.52% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $387.04 | -0.93% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $372.35 | $1.275 | -3.47% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $382.16 | 2.63% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $413.77 | 8.27% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $410.71 | $1.275 | -0.43% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.92% | 1.11% | ||||
| 표준 편차: | 6.50% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 LIN의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 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. | 2019. 2. 28. | 6.28% | 2.97% | 18.98 | 3.49 | 8.13 |
| 2. | 2019. 3. 31. | 2.06% | 1.79% | 0.02 | 0.47 | 0.10 |
| 3. | 2019. 4. 30. | 2.46% | 3.93% | 0.29 | 7.98 | 1.53 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 8.27% | 8.92% | 40.36 | 61.03 | 49.63 |
| 59. | 2023. 12. 31. | -0.43% | 4.42% | 5.52 | 11.00 | -7.80 |
| 합계 (Σ): | 2,453.29 | 1,634.30 | 1,499.15 | |||
| 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. | 2019. 2. 28. | 6.28% | 2.97% | 18.98 | 3.49 | 8.13 |
| 2. | 2019. 3. 31. | 2.06% | 1.79% | 0.02 | 0.47 | 0.10 |
| 3. | 2019. 4. 30. | 2.46% | 3.93% | 0.29 | 7.98 | 1.53 |
| 4. | 2019. 5. 31. | 0.65% | -6.58% | 1.62 | 59.04 | 9.78 |
| 5. | 2019. 6. 30. | 11.22% | 6.89% | 86.44 | 33.49 | 53.80 |
| 6. | 2019. 7. 31. | -4.74% | 1.31% | 44.35 | 0.04 | -1.38 |
| 7. | 2019. 8. 31. | -0.78% | -1.81% | 7.29 | 8.50 | 7.87 |
| 8. | 2019. 9. 30. | 2.55% | 1.72% | 0.39 | 0.37 | 0.38 |
| 9. | 2019. 10. 31. | 2.39% | 2.04% | 0.22 | 0.88 | 0.44 |
| 10. | 2019. 11. 30. | 3.96% | 3.40% | 4.18 | 5.28 | 4.70 |
| 11. | 2019. 12. 31. | 3.67% | 2.86% | 3.06 | 3.07 | 3.07 |
| 12. | 2020. 1. 31. | -4.59% | -0.16% | 42.35 | 1.61 | 8.26 |
| 13. | 2020. 2. 29. | -5.97% | -8.41% | 62.18 | 90.57 | 75.04 |
| 14. | 2020. 3. 31. | -8.92% | -12.51% | 117.58 | 185.44 | 147.66 |
| 15. | 2020. 4. 30. | 6.35% | 12.68% | 19.66 | 134.06 | 51.34 |
| 16. | 2020. 5. 31. | 9.97% | 4.53% | 64.88 | 11.71 | 27.57 |
| 17. | 2020. 6. 30. | 5.30% | 1.84% | 11.46 | 0.54 | 2.48 |
| 18. | 2020. 7. 31. | 15.56% | 5.51% | 186.03 | 19.40 | 60.07 |
| 19. | 2020. 8. 31. | 1.89% | 7.01% | 0.00 | 34.82 | -0.18 |
| 20. | 2020. 9. 30. | -4.26% | -3.92% | 38.22 | 25.29 | 31.09 |
| 21. | 2020. 10. 31. | -7.47% | -2.77% | 88.16 | 15.00 | 36.36 |
| 22. | 2020. 11. 30. | 16.37% | 10.75% | 208.98 | 93.10 | 139.48 |
| 23. | 2020. 12. 31. | 3.14% | 3.71% | 1.49 | 6.79 | 3.18 |
| 24. | 2021. 1. 31. | -6.87% | -1.11% | 77.29 | 4.93 | 19.51 |
| 25. | 2021. 2. 28. | -0.46% | 2.61% | 5.66 | 2.26 | -3.58 |
| 26. | 2021. 3. 31. | 15.12% | 4.24% | 174.24 | 9.85 | 41.42 |
| 27. | 2021. 4. 30. | 2.03% | 5.24% | 0.01 | 17.11 | 0.48 |
| 28. | 2021. 5. 31. | 5.16% | 0.55% | 10.53 | 0.31 | -1.81 |
| 29. | 2021. 6. 30. | -3.47% | 2.22% | 29.07 | 1.24 | -6.01 |
| 30. | 2021. 7. 31. | 6.33% | 2.27% | 19.43 | 1.37 | 5.15 |
| 31. | 2021. 8. 31. | 2.34% | 2.90% | 0.18 | 3.22 | 0.76 |
| 32. | 2021. 9. 30. | -6.41% | -4.76% | 69.29 | 34.37 | 48.80 |
| 33. | 2021. 10. 31. | 8.80% | 6.91% | 47.36 | 33.74 | 39.98 |
| 34. | 2021. 11. 30. | -0.33% | -0.83% | 5.07 | 3.76 | 4.36 |
| 35. | 2021. 12. 31. | 9.23% | 4.36% | 53.39 | 10.60 | 23.79 |
| 36. | 2022. 1. 31. | -8.01% | -5.26% | 98.58 | 40.51 | 63.19 |
| 37. | 2022. 2. 28. | -7.98% | -3.14% | 98.04 | 17.99 | 42.00 |
| 38. | 2022. 3. 31. | 9.33% | 3.58% | 54.93 | 6.11 | 18.32 |
| 39. | 2022. 4. 30. | -2.34% | -8.80% | 18.12 | 98.04 | 42.15 |
| 40. | 2022. 5. 31. | 4.08% | 0.01% | 4.66 | 1.21 | -2.38 |
| 41. | 2022. 6. 30. | -11.08% | -8.39% | 169.01 | 90.21 | 123.48 |
| 42. | 2022. 7. 31. | 5.03% | 9.11% | 9.70 | 64.09 | 24.93 |
| 43. | 2022. 8. 31. | -6.34% | -4.24% | 68.17 | 28.62 | 44.17 |
| 44. | 2022. 9. 30. | -4.28% | -9.34% | 38.40 | 109.11 | 64.72 |
| 45. | 2022. 10. 31. | 10.30% | 7.99% | 70.20 | 47.34 | 57.65 |
| 46. | 2022. 11. 30. | 13.16% | 5.38% | 126.36 | 18.23 | 47.99 |
| 47. | 2022. 12. 31. | -2.71% | -5.90% | 21.46 | 49.04 | 32.44 |
| 48. | 2023. 1. 31. | 1.46% | 6.18% | 0.21 | 25.70 | -2.33 |
| 49. | 2023. 2. 28. | 5.27% | -2.61% | 11.21 | 13.82 | -12.45 |
| 50. | 2023. 3. 31. | 2.40% | 3.51% | 0.23 | 5.76 | 1.14 |
| 51. | 2023. 4. 30. | 3.94% | 1.46% | 4.09 | 0.13 | 0.72 |
| 52. | 2023. 5. 31. | -4.27% | 0.25% | 38.35 | 0.74 | 5.31 |
| 53. | 2023. 6. 30. | 8.11% | 4.71% | 38.38 | 13.02 | 22.35 |
| 54. | 2023. 7. 31. | 2.52% | 4.85% | 0.36 | 13.99 | 2.24 |
| 55. | 2023. 8. 31. | -0.93% | -1.77% | 8.11 | 8.28 | 8.19 |
| 56. | 2023. 9. 30. | -3.47% | -4.87% | 29.00 | 35.73 | 32.19 |
| 57. | 2023. 10. 31. | 2.63% | -2.20% | 0.51 | 10.92 | -2.37 |
| 58. | 2023. 11. 30. | 8.27% | 8.92% | 40.36 | 61.03 | 49.63 |
| 59. | 2023. 12. 31. | -0.43% | 4.42% | 5.52 | 11.00 | -7.80 |
| 합계 (Σ): | 2,453.29 | 1,634.30 | 1,499.15 | |||
모두 표시
분산LIN = Σ(RLIN,t–RLIN)2 ÷ (59 – 1)
= 2,453.29 ÷ (59 – 1)
= 42.30
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산LIN, S&P 500 = Σ(RLIN,t–RLIN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,499.15 ÷ (59 – 1)
= 25.85
체계적인 위험 추정 (β)
| 분산LIN | 42.30 |
| 분산S&P 500 | 28.18 |
| 공분산LIN, S&P 500 | 25.85 |
| 상관 계수LIN, S&P 5001 | 0.75 |
| βLIN2 | 0.92 |
| αLIN3 | 0.90% |
계산
1 상관 계수LIN, S&P 500
= 공분산LIN, S&P 500 ÷ (표준 편차LIN × 표준 편차S&P 500)
= 25.85 ÷ (6.50% × 5.31%)
= 0.75
2 βLIN
= 공분산LIN, S&P 500 ÷ 분산S&P 500
= 25.85 ÷ 28.18
= 0.92
3 αLIN
= 평균의LIN – βLIN × 평균의S&P 500
= 1.92% – 0.92 × 1.11%
= 0.90%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.86% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.52% |
| 보통주의 체계적 위험Linde | βLIN | 0.92 |
| Linde 보통주의 예상 수익률3 | E(RLIN) | 12.81% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RLIN) = RF + βLIN [E(RM) – RF]
= 4.86% + 0.92 [13.52% – 4.86%]
= 12.81%