자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 SLB보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
SLB N.V., 월별 수익률
| SLB N.V. (SLB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SLB,t1 | 피제수SLB,t1 | RSLB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $22.21 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $27.91 | $0.125 | 26.23% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $27.19 | -2.58% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $27.05 | -0.51% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $36.24 | 0.50% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $38.38 | $0.285 | 6.69% | 6,845.50 | -0.05% |
| 평균의 (R): | 1.70% | 1.14% | ||||
| 표준 편차: | 11.32% | 4.37% | ||||
| SLB N.V. (SLB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SLB,t1 | 피제수SLB,t1 | RSLB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $22.21 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $27.91 | $0.125 | 26.23% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $27.19 | -2.58% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $27.05 | -0.51% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $31.33 | 15.82% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $32.01 | $0.125 | 2.57% | 4,297.50 | 2.22% |
| 6. | 2021. 7. 31. | $28.83 | -9.93% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $28.04 | $0.125 | -2.31% | 4,522.68 | 2.90% |
| 8. | 2021. 9. 30. | $29.64 | 5.71% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $32.26 | 8.84% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $28.68 | $0.125 | -10.71% | 4,567.00 | -0.83% |
| 11. | 2021. 12. 31. | $29.95 | 4.43% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $39.07 | 30.45% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $39.24 | $0.125 | 0.76% | 4,373.94 | -3.14% |
| 14. | 2022. 3. 31. | $41.31 | 5.28% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $39.01 | -5.57% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $45.96 | $0.175 | 18.26% | 4,132.15 | 0.01% |
| 17. | 2022. 6. 30. | $35.76 | -22.19% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $37.03 | 3.55% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $38.15 | 3.02% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $35.90 | $0.175 | -5.44% | 3,585.62 | -9.34% |
| 21. | 2022. 10. 31. | $52.03 | 44.93% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $51.55 | -0.92% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $53.46 | $0.175 | 4.04% | 3,839.50 | -5.90% |
| 24. | 2023. 1. 31. | $56.98 | 6.58% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $53.21 | $0.25 | -6.18% | 3,970.15 | -2.61% |
| 26. | 2023. 3. 31. | $49.10 | -7.72% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $49.35 | 0.51% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $42.83 | -13.21% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $49.12 | $0.25 | 15.27% | 4,376.86 | 4.71% |
| 30. | 2023. 7. 31. | $58.34 | 18.77% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $58.96 | 1.06% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $58.30 | $0.25 | -0.70% | 4,288.05 | -4.87% |
| 33. | 2023. 10. 31. | $55.66 | -4.53% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $52.04 | -6.50% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $52.04 | $0.25 | 0.48% | 4,769.83 | 4.42% |
| 36. | 2024. 1. 31. | $48.70 | -6.42% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $48.33 | $0.275 | -0.20% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $54.81 | 13.41% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $47.48 | -13.37% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $45.89 | -3.35% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $47.18 | $0.275 | 3.41% | 5,460.48 | 3.47% |
| 42. | 2024. 7. 31. | $48.29 | 2.35% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $43.99 | -8.90% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $41.95 | $0.275 | -4.01% | 5,762.48 | 2.02% |
| 45. | 2024. 10. 31. | $40.07 | -4.48% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $43.94 | 9.66% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $38.34 | $0.275 | -12.12% | 5,881.63 | -2.50% |
| 48. | 2025. 1. 31. | $40.28 | 5.06% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $41.66 | $0.285 | 4.13% | 5,954.50 | -1.42% |
| 50. | 2025. 3. 31. | $41.80 | 0.34% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $33.25 | -20.45% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $33.05 | -0.60% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $33.80 | $0.285 | 3.13% | 6,204.95 | 4.96% |
| 54. | 2025. 7. 31. | $33.80 | 0.00% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $36.84 | 8.99% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $34.37 | $0.285 | -5.93% | 6,688.46 | 3.53% |
| 57. | 2025. 10. 31. | $36.06 | 4.92% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $36.24 | 0.50% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $38.38 | $0.285 | 6.69% | 6,845.50 | -0.05% |
| 평균의 (R): | 1.70% | 1.14% | ||||
| 표준 편차: | 11.32% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 SLB의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
SLB N.V., 수익률의 분산 및 공분산 계산
| t | 날짜 | RSLB,t | RS&P 500,t | (RSLB,t–RSLB)2 | (RS&P 500,t–RS&P 500)2 | (RSLB,t–RSLB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 26.23% | 2.61% | 601.56 | 2.17 | 36.13 |
| 2. | 2021. 3. 31. | -2.58% | 4.24% | 18.32 | 9.66 | -13.30 |
| 3. | 2021. 4. 30. | -0.51% | 5.24% | 4.91 | 16.86 | -9.10 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 0.50% | 0.13% | 1.44 | 1.01 | 1.21 |
| 59. | 2025. 12. 31. | 6.69% | -0.05% | 24.91 | 1.41 | -5.93 |
| 합계 (Σ): | 7,436.88 | 1,108.23 | 812.28 | |||
| t | 날짜 | RSLB,t | RS&P 500,t | (RSLB,t–RSLB)2 | (RS&P 500,t–RS&P 500)2 | (RSLB,t–RSLB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 26.23% | 2.61% | 601.56 | 2.17 | 36.13 |
| 2. | 2021. 3. 31. | -2.58% | 4.24% | 18.32 | 9.66 | -13.30 |
| 3. | 2021. 4. 30. | -0.51% | 5.24% | 4.91 | 16.86 | -9.10 |
| 4. | 2021. 5. 31. | 15.82% | 0.55% | 199.44 | 0.35 | -8.30 |
| 5. | 2021. 6. 30. | 2.57% | 2.22% | 0.76 | 1.18 | 0.94 |
| 6. | 2021. 7. 31. | -9.93% | 2.27% | 135.36 | 1.30 | -13.25 |
| 7. | 2021. 8. 31. | -2.31% | 2.90% | 16.05 | 3.11 | -7.06 |
| 8. | 2021. 9. 30. | 5.71% | -4.76% | 16.05 | 34.73 | -23.61 |
| 9. | 2021. 10. 31. | 8.84% | 6.91% | 50.97 | 33.39 | 41.25 |
| 10. | 2021. 11. 30. | -10.71% | -0.83% | 154.01 | 3.88 | 24.44 |
| 11. | 2021. 12. 31. | 4.43% | 4.36% | 7.44 | 10.40 | 8.80 |
| 12. | 2022. 1. 31. | 30.45% | -5.26% | 826.60 | 40.89 | -183.85 |
| 13. | 2022. 2. 28. | 0.76% | -3.14% | 0.89 | 18.25 | 4.04 |
| 14. | 2022. 3. 31. | 5.28% | 3.58% | 12.78 | 5.96 | 8.73 |
| 15. | 2022. 4. 30. | -5.57% | -8.80% | 52.82 | 98.64 | 72.18 |
| 16. | 2022. 5. 31. | 18.26% | 0.01% | 274.38 | 1.28 | -18.73 |
| 17. | 2022. 6. 30. | -22.19% | -8.39% | 570.89 | 90.79 | 227.66 |
| 18. | 2022. 7. 31. | 3.55% | 9.11% | 3.43 | 63.61 | 14.77 |
| 19. | 2022. 8. 31. | 3.02% | -4.24% | 1.75 | 28.95 | -7.13 |
| 20. | 2022. 9. 30. | -5.44% | -9.34% | 50.97 | 109.74 | 74.79 |
| 21. | 2022. 10. 31. | 44.93% | 7.99% | 1,868.85 | 46.93 | 296.14 |
| 22. | 2022. 11. 30. | -0.92% | 5.38% | 6.88 | 17.97 | -11.12 |
| 23. | 2022. 12. 31. | 4.04% | -5.90% | 5.50 | 49.47 | -16.49 |
| 24. | 2023. 1. 31. | 6.58% | 6.18% | 23.86 | 25.39 | 24.61 |
| 25. | 2023. 2. 28. | -6.18% | -2.61% | 62.06 | 14.04 | 29.52 |
| 26. | 2023. 3. 31. | -7.72% | 3.51% | 88.82 | 5.61 | -22.33 |
| 27. | 2023. 4. 30. | 0.51% | 1.46% | 1.42 | 0.11 | -0.39 |
| 28. | 2023. 5. 31. | -13.21% | 0.25% | 222.37 | 0.79 | 13.24 |
| 29. | 2023. 6. 30. | 15.27% | 4.71% | 184.13 | 12.80 | 48.55 |
| 30. | 2023. 7. 31. | 18.77% | 4.85% | 291.39 | 13.76 | 63.33 |
| 31. | 2023. 8. 31. | 1.06% | -1.77% | 0.41 | 8.46 | 1.85 |
| 32. | 2023. 9. 30. | -0.70% | -4.87% | 5.74 | 36.10 | 14.39 |
| 33. | 2023. 10. 31. | -4.53% | -2.20% | 38.79 | 11.12 | 20.77 |
| 34. | 2023. 11. 30. | -6.50% | 8.92% | 67.30 | 60.56 | -63.84 |
| 35. | 2023. 12. 31. | 0.48% | 4.42% | 1.49 | 10.80 | -4.01 |
| 36. | 2024. 1. 31. | -6.42% | 1.59% | 65.91 | 0.21 | -3.68 |
| 37. | 2024. 2. 29. | -0.20% | 5.17% | 3.59 | 16.29 | -7.65 |
| 38. | 2024. 3. 31. | 13.41% | 3.10% | 137.07 | 3.86 | 23.01 |
| 39. | 2024. 4. 30. | -13.37% | -4.16% | 227.21 | 28.06 | 79.85 |
| 40. | 2024. 5. 31. | -3.35% | 4.80% | 25.49 | 13.44 | -18.51 |
| 41. | 2024. 6. 30. | 3.41% | 3.47% | 2.92 | 5.43 | 3.99 |
| 42. | 2024. 7. 31. | 2.35% | 1.13% | 0.43 | 0.00 | 0.00 |
| 43. | 2024. 8. 31. | -8.90% | 2.28% | 112.46 | 1.32 | -12.17 |
| 44. | 2024. 9. 30. | -4.01% | 2.02% | 32.63 | 0.78 | -5.05 |
| 45. | 2024. 10. 31. | -4.48% | -0.99% | 38.21 | 4.52 | 13.14 |
| 46. | 2024. 11. 30. | 9.66% | 5.73% | 63.33 | 21.10 | 36.56 |
| 47. | 2024. 12. 31. | -12.12% | -2.50% | 190.96 | 13.21 | 50.23 |
| 48. | 2025. 1. 31. | 5.06% | 2.70% | 11.29 | 2.45 | 5.26 |
| 49. | 2025. 2. 28. | 4.13% | -1.42% | 5.92 | 6.56 | -6.23 |
| 50. | 2025. 3. 31. | 0.34% | -5.75% | 1.86 | 47.48 | 9.40 |
| 51. | 2025. 4. 30. | -20.45% | -0.76% | 490.83 | 3.60 | 42.06 |
| 52. | 2025. 5. 31. | -0.60% | 6.15% | 5.30 | 25.16 | -11.55 |
| 53. | 2025. 6. 30. | 3.13% | 4.96% | 2.05 | 14.63 | 5.47 |
| 54. | 2025. 7. 31. | 0.00% | 2.17% | 2.89 | 1.06 | -1.75 |
| 55. | 2025. 8. 31. | 8.99% | 1.91% | 53.20 | 0.59 | 5.62 |
| 56. | 2025. 9. 30. | -5.93% | 3.53% | 58.24 | 5.74 | -18.29 |
| 57. | 2025. 10. 31. | 4.92% | 2.27% | 10.35 | 1.28 | 3.64 |
| 58. | 2025. 11. 30. | 0.50% | 0.13% | 1.44 | 1.01 | 1.21 |
| 59. | 2025. 12. 31. | 6.69% | -0.05% | 24.91 | 1.41 | -5.93 |
| 합계 (Σ): | 7,436.88 | 1,108.23 | 812.28 | |||
모두 보기
분산SLB = Σ(RSLB,t–RSLB)2 ÷ (59 – 1)
= 7,436.88 ÷ (59 – 1)
= 128.22
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산SLB, S&P 500 = Σ(RSLB,t–RSLB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 812.28 ÷ (59 – 1)
= 14.00
체계적인 위험 추정 (β)
| 분산SLB | 128.22 |
| 분산S&P 500 | 19.11 |
| 공분산SLB, S&P 500 | 14.00 |
| 상관 계수SLB, S&P 5001 | 0.28 |
| βSLB2 | 0.73 |
| αSLB3 | 0.87% |
계산
1 상관 계수SLB, S&P 500
= 공분산SLB, S&P 500 ÷ (표준 편차SLB × 표준 편차S&P 500)
= 14.00 ÷ (11.32% × 4.37%)
= 0.28
2 βSLB
= 공분산SLB, S&P 500 ÷ 분산S&P 500
= 14.00 ÷ 19.11
= 0.73
3 αSLB
= 평균의SLB – βSLB × 평균의S&P 500
= 1.70% – 0.73 × 1.14%
= 0.87%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.79% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.38% |
| 보통주의 체계적 위험SLB | βSLB | 0.73 |
| SLB 보통주에 대한 기대 수익률3 | E(RSLB) | 14.02% |
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(RSLB) = RF + βSLB [E(RM) – RF]
= 4.79% + 0.73 [17.38% – 4.79%]
= 14.02%