자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Chevron보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Chevron Corp., 월별 수익률
| Chevron Corp. (CVX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CVX,t1 | 피제수CVX,t1 | RCVX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $85.20 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $100.00 | $1.29 | 18.88% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $104.79 | 4.79% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $103.07 | -1.64% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $151.13 | $1.71 | -3.09% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $152.41 | 0.85% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.65% | 1.14% | ||||
| 표준 편차: | 7.88% | 4.37% | ||||
| Chevron Corp. (CVX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CVX,t1 | 피제수CVX,t1 | RCVX,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $85.20 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $100.00 | $1.29 | 18.88% | 3,811.15 | 2.61% |
| 2. | 2021. 3. 31. | $104.79 | 4.79% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $103.07 | -1.64% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $103.79 | $1.34 | 2.00% | 4,204.11 | 0.55% |
| 5. | 2021. 6. 30. | $104.74 | 0.92% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $101.81 | -2.80% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $96.77 | $1.34 | -3.63% | 4,522.68 | 2.90% |
| 8. | 2021. 9. 30. | $101.45 | 4.84% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $114.49 | 12.85% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $112.87 | $1.34 | -0.24% | 4,567.00 | -0.83% |
| 11. | 2021. 12. 31. | $117.35 | 3.97% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $131.33 | 11.91% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $144.00 | $1.42 | 10.73% | 4,373.94 | -3.14% |
| 14. | 2022. 3. 31. | $162.83 | 13.08% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $156.67 | -3.78% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $174.66 | $1.42 | 12.39% | 4,132.15 | 0.01% |
| 17. | 2022. 6. 30. | $144.78 | -17.11% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $163.78 | 13.12% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $158.06 | $1.42 | -2.63% | 3,955.00 | -4.24% |
| 20. | 2022. 9. 30. | $143.67 | -9.10% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $180.90 | 25.91% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $183.31 | $1.42 | 2.12% | 4,080.11 | 5.38% |
| 23. | 2022. 12. 31. | $179.49 | -2.08% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $174.02 | -3.05% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $160.77 | $1.51 | -6.75% | 3,970.15 | -2.61% |
| 26. | 2023. 3. 31. | $163.16 | 1.49% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $168.58 | 3.32% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $150.62 | $1.51 | -9.76% | 4,179.83 | 0.25% |
| 29. | 2023. 6. 30. | $157.35 | 4.47% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $163.66 | 4.01% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $161.10 | $1.51 | -0.64% | 4,507.66 | -1.77% |
| 32. | 2023. 9. 30. | $168.62 | 4.67% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $145.73 | -13.57% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $143.60 | $1.51 | -0.43% | 4,567.80 | 8.92% |
| 35. | 2023. 12. 31. | $149.16 | 3.87% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $147.43 | -1.16% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $152.01 | $1.63 | 4.21% | 5,096.27 | 5.17% |
| 38. | 2024. 3. 31. | $157.74 | 3.77% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $161.27 | 2.24% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $162.30 | $1.63 | 1.65% | 5,277.51 | 4.80% |
| 41. | 2024. 6. 30. | $156.42 | -3.62% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $160.47 | 2.59% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $147.95 | $1.63 | -6.79% | 5,648.40 | 2.28% |
| 44. | 2024. 9. 30. | $147.27 | -0.46% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $148.82 | 1.05% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $161.93 | $1.63 | 9.90% | 6,032.38 | 5.73% |
| 47. | 2024. 12. 31. | $144.84 | -10.55% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $149.19 | 3.00% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $158.62 | $1.71 | 7.47% | 5,954.50 | -1.42% |
| 50. | 2025. 3. 31. | $167.29 | 5.47% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $136.06 | -18.67% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $136.70 | $1.71 | 1.73% | 5,911.69 | 6.15% |
| 53. | 2025. 6. 30. | $143.19 | 4.75% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $151.64 | 5.90% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $160.60 | $1.71 | 7.04% | 6,460.26 | 1.91% |
| 56. | 2025. 9. 30. | $155.29 | -3.31% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $157.72 | 1.56% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $151.13 | $1.71 | -3.09% | 6,849.09 | 0.13% |
| 59. | 2025. 12. 31. | $152.41 | 0.85% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.65% | 1.14% | ||||
| 표준 편차: | 7.88% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t기간 동안 CVX의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Chevron Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCVX,t | RS&P 500,t | (RCVX,t–RCVX)2 | (RS&P 500,t–RS&P 500)2 | (RCVX,t–RCVX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 18.88% | 2.61% | 296.87 | 2.17 | 25.38 |
| 2. | 2021. 3. 31. | 4.79% | 4.24% | 9.83 | 9.66 | 9.74 |
| 3. | 2021. 4. 30. | -1.64% | 5.24% | 10.87 | 16.86 | -13.54 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | -3.09% | 0.13% | 22.55 | 1.01 | 4.78 |
| 59. | 2025. 12. 31. | 0.85% | -0.05% | 0.65 | 1.41 | 0.96 |
| 합계 (Σ): | 3,597.15 | 1,108.23 | 780.29 | |||
| t | 날짜 | RCVX,t | RS&P 500,t | (RCVX,t–RCVX)2 | (RS&P 500,t–RS&P 500)2 | (RCVX,t–RCVX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 18.88% | 2.61% | 296.87 | 2.17 | 25.38 |
| 2. | 2021. 3. 31. | 4.79% | 4.24% | 9.83 | 9.66 | 9.74 |
| 3. | 2021. 4. 30. | -1.64% | 5.24% | 10.87 | 16.86 | -13.54 |
| 4. | 2021. 5. 31. | 2.00% | 0.55% | 0.12 | 0.35 | -0.20 |
| 5. | 2021. 6. 30. | 0.92% | 2.22% | 0.55 | 1.18 | -0.80 |
| 6. | 2021. 7. 31. | -2.80% | 2.27% | 19.82 | 1.30 | -5.07 |
| 7. | 2021. 8. 31. | -3.63% | 2.90% | 27.98 | 3.11 | -9.32 |
| 8. | 2021. 9. 30. | 4.84% | -4.76% | 10.12 | 34.73 | -18.75 |
| 9. | 2021. 10. 31. | 12.85% | 6.91% | 125.41 | 33.39 | 64.71 |
| 10. | 2021. 11. 30. | -0.24% | -0.83% | 3.61 | 3.88 | 3.74 |
| 11. | 2021. 12. 31. | 3.97% | 4.36% | 5.36 | 10.40 | 7.46 |
| 12. | 2022. 1. 31. | 11.91% | -5.26% | 105.23 | 40.89 | -65.60 |
| 13. | 2022. 2. 28. | 10.73% | -3.14% | 82.33 | 18.25 | -38.76 |
| 14. | 2022. 3. 31. | 13.08% | 3.58% | 130.45 | 5.96 | 27.88 |
| 15. | 2022. 4. 30. | -3.78% | -8.80% | 29.57 | 98.64 | 54.01 |
| 16. | 2022. 5. 31. | 12.39% | 0.01% | 115.22 | 1.28 | -12.14 |
| 17. | 2022. 6. 30. | -17.11% | -8.39% | 352.03 | 90.79 | 178.77 |
| 18. | 2022. 7. 31. | 13.12% | 9.11% | 131.52 | 63.61 | 91.47 |
| 19. | 2022. 8. 31. | -2.63% | -4.24% | 18.32 | 28.95 | 23.03 |
| 20. | 2022. 9. 30. | -9.10% | -9.34% | 115.76 | 109.74 | 112.71 |
| 21. | 2022. 10. 31. | 25.91% | 7.99% | 588.48 | 46.93 | 166.18 |
| 22. | 2022. 11. 30. | 2.12% | 5.38% | 0.21 | 17.97 | 1.96 |
| 23. | 2022. 12. 31. | -2.08% | -5.90% | 13.98 | 49.47 | 26.30 |
| 24. | 2023. 1. 31. | -3.05% | 6.18% | 22.11 | 25.39 | -23.70 |
| 25. | 2023. 2. 28. | -6.75% | -2.61% | 70.58 | 14.04 | 31.48 |
| 26. | 2023. 3. 31. | 1.49% | 3.51% | 0.03 | 5.61 | -0.40 |
| 27. | 2023. 4. 30. | 3.32% | 1.46% | 2.78 | 0.11 | 0.55 |
| 28. | 2023. 5. 31. | -9.76% | 0.25% | 130.26 | 0.79 | 10.13 |
| 29. | 2023. 6. 30. | 4.47% | 4.71% | 7.91 | 12.80 | 10.06 |
| 30. | 2023. 7. 31. | 4.01% | 4.85% | 5.55 | 13.76 | 8.74 |
| 31. | 2023. 8. 31. | -0.64% | -1.77% | 5.27 | 8.46 | 6.68 |
| 32. | 2023. 9. 30. | 4.67% | -4.87% | 9.08 | 36.10 | -18.10 |
| 33. | 2023. 10. 31. | -13.57% | -2.20% | 231.95 | 11.12 | 50.78 |
| 34. | 2023. 11. 30. | -0.43% | 8.92% | 4.33 | 60.56 | -16.19 |
| 35. | 2023. 12. 31. | 3.87% | 4.42% | 4.91 | 10.80 | 7.29 |
| 36. | 2024. 1. 31. | -1.16% | 1.59% | 7.92 | 0.21 | -1.28 |
| 37. | 2024. 2. 29. | 4.21% | 5.17% | 6.54 | 16.29 | 10.32 |
| 38. | 2024. 3. 31. | 3.77% | 3.10% | 4.47 | 3.86 | 4.16 |
| 39. | 2024. 4. 30. | 2.24% | -4.16% | 0.34 | 28.06 | -3.09 |
| 40. | 2024. 5. 31. | 1.65% | 4.80% | 0.00 | 13.44 | -0.02 |
| 41. | 2024. 6. 30. | -3.62% | 3.47% | 27.86 | 5.43 | -12.30 |
| 42. | 2024. 7. 31. | 2.59% | 1.13% | 0.87 | 0.00 | 0.00 |
| 43. | 2024. 8. 31. | -6.79% | 2.28% | 71.26 | 1.32 | -9.69 |
| 44. | 2024. 9. 30. | -0.46% | 2.02% | 4.47 | 0.78 | -1.87 |
| 45. | 2024. 10. 31. | 1.05% | -0.99% | 0.36 | 4.52 | 1.28 |
| 46. | 2024. 11. 30. | 9.90% | 5.73% | 68.06 | 21.10 | 37.90 |
| 47. | 2024. 12. 31. | -10.55% | -2.50% | 149.06 | 13.21 | 44.38 |
| 48. | 2025. 1. 31. | 3.00% | 2.70% | 1.82 | 2.45 | 2.11 |
| 49. | 2025. 2. 28. | 7.47% | -1.42% | 33.78 | 6.56 | -14.88 |
| 50. | 2025. 3. 31. | 5.47% | -5.75% | 14.52 | 47.48 | -26.26 |
| 51. | 2025. 4. 30. | -18.67% | -0.76% | 413.03 | 3.60 | 38.59 |
| 52. | 2025. 5. 31. | 1.73% | 6.15% | 0.01 | 25.16 | 0.36 |
| 53. | 2025. 6. 30. | 4.75% | 4.96% | 9.56 | 14.63 | 11.83 |
| 54. | 2025. 7. 31. | 5.90% | 2.17% | 18.03 | 1.06 | 4.38 |
| 55. | 2025. 8. 31. | 7.04% | 1.91% | 28.96 | 0.59 | 4.15 |
| 56. | 2025. 9. 30. | -3.31% | 3.53% | 24.61 | 5.74 | -11.89 |
| 57. | 2025. 10. 31. | 1.56% | 2.27% | 0.01 | 1.28 | -0.10 |
| 58. | 2025. 11. 30. | -3.09% | 0.13% | 22.55 | 1.01 | 4.78 |
| 59. | 2025. 12. 31. | 0.85% | -0.05% | 0.65 | 1.41 | 0.96 |
| 합계 (Σ): | 3,597.15 | 1,108.23 | 780.29 | |||
모두 보기
분산CVX = Σ(RCVX,t–RCVX)2 ÷ (59 – 1)
= 3,597.15 ÷ (59 – 1)
= 62.02
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산CVX, S&P 500 = Σ(RCVX,t–RCVX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 780.29 ÷ (59 – 1)
= 13.45
체계적인 위험 추정 (β)
| 분산CVX | 62.02 |
| 분산S&P 500 | 19.11 |
| 공분산CVX, S&P 500 | 13.45 |
| 상관 계수CVX, S&P 5001 | 0.39 |
| βCVX2 | 0.70 |
| αCVX3 | 0.86% |
계산
1 상관 계수CVX, S&P 500
= 공분산CVX, S&P 500 ÷ (표준 편차CVX × 표준 편차S&P 500)
= 13.45 ÷ (7.88% × 4.37%)
= 0.39
2 βCVX
= 공분산CVX, S&P 500 ÷ 분산S&P 500
= 13.45 ÷ 19.11
= 0.70
3 αCVX
= 평균의CVX – βCVX × 평균의S&P 500
= 1.65% – 0.70 × 1.14%
= 0.86%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.84% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Chevron | βCVX | 0.70 |
| Chevron 보통주에 대한 예상 수익률3 | E(RCVX) | 13.66% |
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(RCVX) = RF + βCVX [E(RM) – RF]
= 4.84% + 0.70 [17.37% – 4.84%]
= 13.66%