자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 ExxonMobil보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Exxon Mobil Corp., 월별 수익률
| Exxon Mobil Corp. (XOM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값XOM,t1 | 피제수XOM,t1 | RXOM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $44.84 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $54.37 | $0.87 | 23.19% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $55.83 | 2.69% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $57.24 | 2.53% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $115.92 | $1.03 | 2.26% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $120.34 | 3.81% | 6,845.50 | -0.05% | |
| 평균의 (R): | 2.32% | 1.14% | ||||
| 표준 편차: | 7.76% | 4.37% | ||||
| Exxon Mobil Corp. (XOM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값XOM,t1 | 피제수XOM,t1 | RXOM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $44.84 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $54.37 | $0.87 | 23.19% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $55.83 | 2.69% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $57.24 | 2.53% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $58.37 | $0.87 | 3.49% | 4,204.11 | 0.55% |
| 5. | 2021. 6. 30. | $63.08 | 8.07% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $57.57 | -8.73% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $54.52 | $0.87 | -3.79% | 4,522.68 | 2.90% |
| 8. | 2021. 9. 30. | $58.82 | 7.89% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $64.47 | 9.61% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $59.84 | $0.88 | -5.82% | 4,567.00 | -0.83% |
| 11. | 2021. 12. 31. | $61.19 | 2.26% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $75.96 | 24.14% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $78.42 | $0.88 | 4.40% | 4,373.94 | -3.14% |
| 14. | 2022. 3. 31. | $82.59 | 5.32% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $85.25 | 3.22% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $96.00 | $0.88 | 13.64% | 4,132.15 | 0.01% |
| 17. | 2022. 6. 30. | $85.64 | -10.79% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $96.93 | 13.18% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $95.59 | $0.88 | -0.47% | 3,955.00 | -4.24% |
| 20. | 2022. 9. 30. | $87.31 | -8.66% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $110.81 | 26.92% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $111.34 | $0.91 | 1.30% | 4,080.11 | 5.38% |
| 23. | 2022. 12. 31. | $110.30 | -0.93% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $116.01 | 5.18% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $109.91 | $0.91 | -4.47% | 3,970.15 | -2.61% |
| 26. | 2023. 3. 31. | $109.66 | -0.23% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $118.34 | 7.92% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $102.18 | $0.91 | -12.89% | 4,179.83 | 0.25% |
| 29. | 2023. 6. 30. | $107.25 | 4.96% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $107.24 | -0.01% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $111.19 | $0.91 | 4.53% | 4,507.66 | -1.77% |
| 32. | 2023. 9. 30. | $117.58 | 5.75% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $105.85 | -9.98% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $102.74 | $0.95 | -2.04% | 4,567.80 | 8.92% |
| 35. | 2023. 12. 31. | $99.98 | -2.69% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $102.81 | 2.83% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $104.52 | $0.95 | 2.59% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $116.24 | 11.21% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $118.27 | 1.75% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $117.26 | $0.95 | -0.05% | 5,277.51 | 4.80% |
| 41. | 2024. 6. 30. | $115.12 | -1.83% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $118.59 | 3.01% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $117.94 | $0.95 | 0.25% | 5,648.40 | 2.28% |
| 44. | 2024. 9. 30. | $117.22 | -0.61% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $116.78 | -0.38% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $117.96 | $0.99 | 1.86% | 6,032.38 | 5.73% |
| 47. | 2024. 12. 31. | $107.57 | -8.81% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $106.83 | -0.69% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $111.33 | $0.99 | 5.14% | 5,954.50 | -1.42% |
| 50. | 2025. 3. 31. | $118.93 | 6.83% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $105.63 | -11.18% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $102.30 | $0.99 | -2.22% | 5,911.69 | 6.15% |
| 53. | 2025. 6. 30. | $107.80 | 5.38% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $111.64 | 3.56% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $114.29 | $0.99 | 3.26% | 6,460.26 | 1.91% |
| 56. | 2025. 9. 30. | $112.75 | -1.35% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $114.36 | 1.43% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $115.92 | $1.03 | 2.26% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $120.34 | 3.81% | 6,845.50 | -0.05% | |
| 평균의 (R): | 2.32% | 1.14% | ||||
| 표준 편차: | 7.76% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 XOM의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Exxon Mobil Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RXOM,t | RS&P 500,t | (RXOM,t–RXOM)2 | (RS&P 500,t–RS&P 500)2 | (RXOM,t–RXOM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 23.19% | 2.61% | 435.81 | 2.17 | 30.75 |
| 2. | 2021. 3. 31. | 2.69% | 4.24% | 0.14 | 9.66 | 1.14 |
| 3. | 2021. 4. 30. | 2.53% | 5.24% | 0.04 | 16.86 | 0.85 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 2.26% | 0.13% | 0.00 | 1.01 | 0.05 |
| 59. | 2025. 12. 31. | 3.81% | -0.05% | 2.24 | 1.41 | -1.78 |
| 합계 (Σ): | 3,496.66 | 1,108.23 | 424.12 | |||
| t | 날짜 | RXOM,t | RS&P 500,t | (RXOM,t–RXOM)2 | (RS&P 500,t–RS&P 500)2 | (RXOM,t–RXOM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 23.19% | 2.61% | 435.81 | 2.17 | 30.75 |
| 2. | 2021. 3. 31. | 2.69% | 4.24% | 0.14 | 9.66 | 1.14 |
| 3. | 2021. 4. 30. | 2.53% | 5.24% | 0.04 | 16.86 | 0.85 |
| 4. | 2021. 5. 31. | 3.49% | 0.55% | 1.38 | 0.35 | -0.69 |
| 5. | 2021. 6. 30. | 8.07% | 2.22% | 33.08 | 1.18 | 6.24 |
| 6. | 2021. 7. 31. | -8.73% | 2.27% | 122.16 | 1.30 | -12.59 |
| 7. | 2021. 8. 31. | -3.79% | 2.90% | 37.26 | 3.11 | -10.76 |
| 8. | 2021. 9. 30. | 7.89% | -4.76% | 31.02 | 34.73 | -32.82 |
| 9. | 2021. 10. 31. | 9.61% | 6.91% | 53.12 | 33.39 | 42.11 |
| 10. | 2021. 11. 30. | -5.82% | -0.83% | 66.16 | 3.88 | 16.02 |
| 11. | 2021. 12. 31. | 2.26% | 4.36% | 0.00 | 10.40 | -0.20 |
| 12. | 2022. 1. 31. | 24.14% | -5.26% | 476.13 | 40.89 | -139.53 |
| 13. | 2022. 2. 28. | 4.40% | -3.14% | 4.32 | 18.25 | -8.88 |
| 14. | 2022. 3. 31. | 5.32% | 3.58% | 9.00 | 5.96 | 7.32 |
| 15. | 2022. 4. 30. | 3.22% | -8.80% | 0.82 | 98.64 | -8.97 |
| 16. | 2022. 5. 31. | 13.64% | 0.01% | 128.25 | 1.28 | -12.81 |
| 17. | 2022. 6. 30. | -10.79% | -8.39% | 171.85 | 90.79 | 124.91 |
| 18. | 2022. 7. 31. | 13.18% | 9.11% | 118.06 | 63.61 | 86.66 |
| 19. | 2022. 8. 31. | -0.47% | -4.24% | 7.80 | 28.95 | 15.02 |
| 20. | 2022. 9. 30. | -8.66% | -9.34% | 120.55 | 109.74 | 115.02 |
| 21. | 2022. 10. 31. | 26.92% | 7.99% | 605.07 | 46.93 | 168.50 |
| 22. | 2022. 11. 30. | 1.30% | 5.38% | 1.04 | 17.97 | -4.32 |
| 23. | 2022. 12. 31. | -0.93% | -5.90% | 10.57 | 49.47 | 22.87 |
| 24. | 2023. 1. 31. | 5.18% | 6.18% | 8.18 | 25.39 | 14.41 |
| 25. | 2023. 2. 28. | -4.47% | -2.61% | 46.12 | 14.04 | 25.45 |
| 26. | 2023. 3. 31. | -0.23% | 3.51% | 6.48 | 5.61 | -6.03 |
| 27. | 2023. 4. 30. | 7.92% | 1.46% | 31.34 | 0.11 | 1.84 |
| 28. | 2023. 5. 31. | -12.89% | 0.25% | 231.16 | 0.79 | 13.50 |
| 29. | 2023. 6. 30. | 4.96% | 4.71% | 6.99 | 12.80 | 9.46 |
| 30. | 2023. 7. 31. | -0.01% | 4.85% | 5.41 | 13.76 | -8.63 |
| 31. | 2023. 8. 31. | 4.53% | -1.77% | 4.90 | 8.46 | -6.44 |
| 32. | 2023. 9. 30. | 5.75% | -4.87% | 11.76 | 36.10 | -20.60 |
| 33. | 2023. 10. 31. | -9.98% | -2.20% | 151.13 | 11.12 | 40.99 |
| 34. | 2023. 11. 30. | -2.04% | 8.92% | 18.99 | 60.56 | -33.91 |
| 35. | 2023. 12. 31. | -2.69% | 4.42% | 25.04 | 10.80 | -16.45 |
| 36. | 2024. 1. 31. | 2.83% | 1.59% | 0.26 | 0.21 | 0.23 |
| 37. | 2024. 2. 29. | 2.59% | 5.17% | 0.07 | 16.29 | 1.09 |
| 38. | 2024. 3. 31. | 11.21% | 3.10% | 79.13 | 3.86 | 17.49 |
| 39. | 2024. 4. 30. | 1.75% | -4.16% | 0.33 | 28.06 | 3.03 |
| 40. | 2024. 5. 31. | -0.05% | 4.80% | 5.61 | 13.44 | -8.68 |
| 41. | 2024. 6. 30. | -1.83% | 3.47% | 17.16 | 5.43 | -9.66 |
| 42. | 2024. 7. 31. | 3.01% | 1.13% | 0.49 | 0.00 | 0.00 |
| 43. | 2024. 8. 31. | 0.25% | 2.28% | 4.26 | 1.32 | -2.37 |
| 44. | 2024. 9. 30. | -0.61% | 2.02% | 8.57 | 0.78 | -2.59 |
| 45. | 2024. 10. 31. | -0.38% | -0.99% | 7.25 | 4.52 | 5.72 |
| 46. | 2024. 11. 30. | 1.86% | 5.73% | 0.21 | 21.10 | -2.11 |
| 47. | 2024. 12. 31. | -8.81% | -2.50% | 123.78 | 13.21 | 40.44 |
| 48. | 2025. 1. 31. | -0.69% | 2.70% | 9.03 | 2.45 | -4.70 |
| 49. | 2025. 2. 28. | 5.14% | -1.42% | 7.96 | 6.56 | -7.22 |
| 50. | 2025. 3. 31. | 6.83% | -5.75% | 20.33 | 47.48 | -31.07 |
| 51. | 2025. 4. 30. | -11.18% | -0.76% | 182.26 | 3.60 | 25.63 |
| 52. | 2025. 5. 31. | -2.22% | 6.15% | 20.55 | 25.16 | -22.74 |
| 53. | 2025. 6. 30. | 5.38% | 4.96% | 9.36 | 14.63 | 11.70 |
| 54. | 2025. 7. 31. | 3.56% | 2.17% | 1.55 | 1.06 | 1.28 |
| 55. | 2025. 8. 31. | 3.26% | 1.91% | 0.89 | 0.59 | 0.73 |
| 56. | 2025. 9. 30. | -1.35% | 3.53% | 13.43 | 5.74 | -8.78 |
| 57. | 2025. 10. 31. | 1.43% | 2.27% | 0.79 | 1.28 | -1.01 |
| 58. | 2025. 11. 30. | 2.26% | 0.13% | 0.00 | 1.01 | 0.05 |
| 59. | 2025. 12. 31. | 3.81% | -0.05% | 2.24 | 1.41 | -1.78 |
| 합계 (Σ): | 3,496.66 | 1,108.23 | 424.12 | |||
모두 보기
분산XOM = Σ(RXOM,t–RXOM)2 ÷ (59 – 1)
= 3,496.66 ÷ (59 – 1)
= 60.29
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산XOM, S&P 500 = Σ(RXOM,t–RXOM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 424.12 ÷ (59 – 1)
= 7.31
체계적인 위험 추정 (β)
| 분산XOM | 60.29 |
| 분산S&P 500 | 19.11 |
| 공분산XOM, S&P 500 | 7.31 |
| 상관 계수XOM, S&P 5001 | 0.22 |
| βXOM2 | 0.38 |
| αXOM3 | 1.88% |
계산
1 상관 계수XOM, S&P 500
= 공분산XOM, S&P 500 ÷ (표준 편차XOM × 표준 편차S&P 500)
= 7.31 ÷ (7.76% × 4.37%)
= 0.22
2 βXOM
= 공분산XOM, S&P 500 ÷ 분산S&P 500
= 7.31 ÷ 19.11
= 0.38
3 αXOM
= 평균의XOM – βXOM × 평균의S&P 500
= 2.32% – 0.38 × 1.14%
= 1.88%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.95% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.36% |
| 보통주의 체계적 위험ExxonMobil | βXOM | 0.38 |
| ExxonMobil 보통주 예상 수익률3 | E(RXOM) | 9.70% |
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(RXOM) = RF + βXOM [E(RM) – RF]
= 4.95% + 0.38 [17.36% – 4.95%]
= 9.70%