자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 SLB보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Schlumberger Ltd., 월별 수익률
| Schlumberger Ltd. (SLB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SLB,t1 | 피제수SLB,t1 | RSLB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $44.21 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $44.06 | $0.50 | 0.79% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $43.57 | -1.11% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $42.68 | -2.04% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $52.04 | -6.50% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $52.04 | $0.25 | 0.48% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.67% | 1.11% | ||||
| 표준 편차: | 14.99% | 5.31% | ||||
| Schlumberger Ltd. (SLB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SLB,t1 | 피제수SLB,t1 | RSLB,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $44.21 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $44.06 | $0.50 | 0.79% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $43.57 | -1.11% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $42.68 | -2.04% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $34.69 | -18.72% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $39.74 | $0.50 | 16.00% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $39.97 | 0.58% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $32.43 | -18.86% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $34.17 | $0.50 | 6.91% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $32.69 | -4.33% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $36.20 | 10.74% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $40.20 | $0.50 | 12.43% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $33.51 | -16.64% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $27.09 | $0.50 | -17.67% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $13.49 | -50.20% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $16.82 | 24.68% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $18.47 | 9.81% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $18.39 | $0.125 | 0.24% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $18.14 | -1.36% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $19.01 | 4.80% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $15.56 | $0.125 | -17.49% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $14.94 | -3.98% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $20.79 | 39.16% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $21.83 | $0.125 | 5.60% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $22.21 | 1.74% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $27.91 | $0.125 | 26.23% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $27.19 | -2.58% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $27.05 | -0.51% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $31.33 | 15.82% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $32.01 | $0.125 | 2.57% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $28.83 | -9.93% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $28.04 | $0.125 | -2.31% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $29.64 | 5.71% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $32.26 | 8.84% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $28.68 | $0.125 | -10.71% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $29.95 | 4.43% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $39.07 | 30.45% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $39.24 | $0.125 | 0.76% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $41.31 | 5.28% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $39.01 | -5.57% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $45.96 | $0.175 | 18.26% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $35.76 | -22.19% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $37.03 | 3.55% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $38.15 | 3.02% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $35.90 | $0.175 | -5.44% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $52.03 | 44.93% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $51.55 | -0.92% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $53.46 | $0.175 | 4.04% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $56.98 | 6.58% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $53.21 | $0.25 | -6.18% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $49.10 | -7.72% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $49.35 | 0.51% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $42.83 | -13.21% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $49.12 | $0.25 | 15.27% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $58.34 | 18.77% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $58.96 | 1.06% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $58.30 | $0.25 | -0.70% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $55.66 | -4.53% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $52.04 | -6.50% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $52.04 | $0.25 | 0.48% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.67% | 1.11% | ||||
| 표준 편차: | 14.99% | 5.31% | ||||
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
Schlumberger Ltd., 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. | 2019. 2. 28. | 0.79% | 2.97% | 0.77 | 3.49 | -1.64 |
| 2. | 2019. 3. 31. | -1.11% | 1.79% | 7.75 | 0.47 | -1.91 |
| 3. | 2019. 4. 30. | -2.04% | 3.93% | 13.80 | 7.98 | -10.49 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -6.50% | 8.92% | 66.84 | 61.03 | -63.87 |
| 59. | 2023. 12. 31. | 0.48% | 4.42% | 1.42 | 11.00 | -3.95 |
| 합계 (Σ): | 13,036.39 | 1,634.30 | 2,649.68 | |||
| 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. | 2019. 2. 28. | 0.79% | 2.97% | 0.77 | 3.49 | -1.64 |
| 2. | 2019. 3. 31. | -1.11% | 1.79% | 7.75 | 0.47 | -1.91 |
| 3. | 2019. 4. 30. | -2.04% | 3.93% | 13.80 | 7.98 | -10.49 |
| 4. | 2019. 5. 31. | -18.72% | -6.58% | 415.84 | 59.04 | 156.69 |
| 5. | 2019. 6. 30. | 16.00% | 6.89% | 205.27 | 33.49 | 82.91 |
| 6. | 2019. 7. 31. | 0.58% | 1.31% | 1.19 | 0.04 | -0.23 |
| 7. | 2019. 8. 31. | -18.86% | -1.81% | 421.71 | 8.50 | 59.86 |
| 8. | 2019. 9. 30. | 6.91% | 1.72% | 27.41 | 0.37 | 3.21 |
| 9. | 2019. 10. 31. | -4.33% | 2.04% | 36.03 | 0.88 | -5.63 |
| 10. | 2019. 11. 30. | 10.74% | 3.40% | 82.19 | 5.28 | 20.84 |
| 11. | 2019. 12. 31. | 12.43% | 2.86% | 115.76 | 3.07 | 18.86 |
| 12. | 2020. 1. 31. | -16.64% | -0.16% | 335.38 | 1.61 | 23.23 |
| 13. | 2020. 2. 29. | -17.67% | -8.41% | 373.95 | 90.57 | 184.04 |
| 14. | 2020. 3. 31. | -50.20% | -12.51% | 2,690.97 | 185.44 | 706.42 |
| 15. | 2020. 4. 30. | 24.68% | 12.68% | 529.62 | 134.06 | 266.46 |
| 16. | 2020. 5. 31. | 9.81% | 4.53% | 66.23 | 11.71 | 27.85 |
| 17. | 2020. 6. 30. | 0.24% | 1.84% | 2.04 | 0.54 | -1.05 |
| 18. | 2020. 7. 31. | -1.36% | 5.51% | 9.19 | 19.40 | -13.35 |
| 19. | 2020. 8. 31. | 4.80% | 7.01% | 9.76 | 34.82 | 18.44 |
| 20. | 2020. 9. 30. | -17.49% | -3.92% | 367.19 | 25.29 | 96.36 |
| 21. | 2020. 10. 31. | -3.98% | -2.77% | 31.99 | 15.00 | 21.90 |
| 22. | 2020. 11. 30. | 39.16% | 10.75% | 1,405.13 | 93.10 | 361.68 |
| 23. | 2020. 12. 31. | 5.60% | 3.71% | 15.46 | 6.79 | 10.25 |
| 24. | 2021. 1. 31. | 1.74% | -1.11% | 0.00 | 4.93 | -0.15 |
| 25. | 2021. 2. 28. | 26.23% | 2.61% | 602.97 | 2.26 | 36.91 |
| 26. | 2021. 3. 31. | -2.58% | 4.24% | 18.07 | 9.85 | -13.34 |
| 27. | 2021. 4. 30. | -0.51% | 5.24% | 4.78 | 17.11 | -9.04 |
| 28. | 2021. 5. 31. | 15.82% | 0.55% | 200.25 | 0.31 | -7.88 |
| 29. | 2021. 6. 30. | 2.57% | 2.22% | 0.81 | 1.24 | 1.00 |
| 30. | 2021. 7. 31. | -9.93% | 2.27% | 134.70 | 1.37 | -13.57 |
| 31. | 2021. 8. 31. | -2.31% | 2.90% | 15.83 | 3.22 | -7.13 |
| 32. | 2021. 9. 30. | 5.71% | -4.76% | 16.28 | 34.37 | -23.65 |
| 33. | 2021. 10. 31. | 8.84% | 6.91% | 51.38 | 33.74 | 41.63 |
| 34. | 2021. 11. 30. | -10.71% | -0.83% | 153.30 | 3.76 | 24.01 |
| 35. | 2021. 12. 31. | 4.43% | 4.36% | 7.60 | 10.60 | 8.97 |
| 36. | 2022. 1. 31. | 30.45% | -5.26% | 828.24 | 40.51 | -183.16 |
| 37. | 2022. 2. 28. | 0.76% | -3.14% | 0.84 | 17.99 | 3.89 |
| 38. | 2022. 3. 31. | 5.28% | 3.58% | 12.99 | 6.11 | 8.91 |
| 39. | 2022. 4. 30. | -5.57% | -8.80% | 52.41 | 98.04 | 71.68 |
| 40. | 2022. 5. 31. | 18.26% | 0.01% | 275.33 | 1.21 | -18.26 |
| 41. | 2022. 6. 30. | -22.19% | -8.39% | 569.53 | 90.21 | 226.66 |
| 42. | 2022. 7. 31. | 3.55% | 9.11% | 3.53 | 64.09 | 15.05 |
| 43. | 2022. 8. 31. | 3.02% | -4.24% | 1.83 | 28.62 | -7.24 |
| 44. | 2022. 9. 30. | -5.44% | -9.34% | 50.56 | 109.11 | 74.27 |
| 45. | 2022. 10. 31. | 44.93% | 7.99% | 1,871.33 | 47.34 | 297.64 |
| 46. | 2022. 11. 30. | -0.92% | 5.38% | 6.73 | 18.23 | -11.08 |
| 47. | 2022. 12. 31. | 4.04% | -5.90% | 5.63 | 49.04 | -16.62 |
| 48. | 2023. 1. 31. | 6.58% | 6.18% | 24.14 | 25.70 | 24.91 |
| 49. | 2023. 2. 28. | -6.18% | -2.61% | 61.61 | 13.82 | 29.18 |
| 50. | 2023. 3. 31. | -7.72% | 3.51% | 88.28 | 5.76 | -22.54 |
| 51. | 2023. 4. 30. | 0.51% | 1.46% | 1.35 | 0.13 | -0.42 |
| 52. | 2023. 5. 31. | -13.21% | 0.25% | 221.51 | 0.74 | 12.76 |
| 53. | 2023. 6. 30. | 15.27% | 4.71% | 184.91 | 13.02 | 49.06 |
| 54. | 2023. 7. 31. | 18.77% | 4.85% | 292.37 | 13.99 | 63.95 |
| 55. | 2023. 8. 31. | 1.06% | -1.77% | 0.37 | 8.28 | 1.75 |
| 56. | 2023. 9. 30. | -0.70% | -4.87% | 5.60 | 35.73 | 14.15 |
| 57. | 2023. 10. 31. | -4.53% | -2.20% | 38.44 | 10.92 | 20.48 |
| 58. | 2023. 11. 30. | -6.50% | 8.92% | 66.84 | 61.03 | -63.87 |
| 59. | 2023. 12. 31. | 0.48% | 4.42% | 1.42 | 11.00 | -3.95 |
| 합계 (Σ): | 13,036.39 | 1,634.30 | 2,649.68 | |||
모두 보기
분산SLB = Σ(RSLB,t–RSLB)2 ÷ (59 – 1)
= 13,036.39 ÷ (59 – 1)
= 224.77
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산SLB, S&P 500 = Σ(RSLB,t–RSLB)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,649.68 ÷ (59 – 1)
= 45.68
체계적인 위험 추정 (β)
| 분산SLB | 224.77 |
| 분산S&P 500 | 28.18 |
| 공분산SLB, S&P 500 | 45.68 |
| 상관 계수SLB, S&P 5001 | 0.57 |
| βSLB2 | 1.62 |
| αSLB3 | -0.12% |
계산
1 상관 계수SLB, S&P 500
= 공분산SLB, S&P 500 ÷ (표준 편차SLB × 표준 편차S&P 500)
= 45.68 ÷ (14.99% × 5.31%)
= 0.57
2 βSLB
= 공분산SLB, S&P 500 ÷ 분산S&P 500
= 45.68 ÷ 28.18
= 1.62
3 αSLB
= 평균의SLB – βSLB × 평균의S&P 500
= 1.67% – 1.62 × 1.11%
= -0.12%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.34% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.74% |
| 보통주의 체계적 위험SLB | βSLB | 1.62 |
| SLB 보통주에 대한 기대 수익률3 | E(RSLB) | 19.59% |
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]
= 4.34% + 1.62 [13.74% – 4.34%]
= 19.59%