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 |
| 2020. 1. 31. | $107.14 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $93.34 | $1.29 | -11.68% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $72.46 | -22.37% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $92.00 | 26.97% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $161.93 | $1.63 | 9.90% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $144.84 | -10.55% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.34% | 1.16% | ||||
| 표준 편차: | 9.70% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $107.14 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $93.34 | $1.29 | -11.68% | 2,954.22 | -8.41% |
| 2. | 2020. 3. 31. | $72.46 | -22.37% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $92.00 | 26.97% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $91.70 | $1.29 | 1.08% | 3,044.31 | 4.53% |
| 5. | 2020. 6. 30. | $89.23 | -2.69% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $83.94 | -5.93% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $83.93 | $1.29 | 1.52% | 3,500.31 | 7.01% |
| 8. | 2020. 9. 30. | $72.00 | -14.21% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $69.50 | -3.47% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $87.18 | $1.29 | 27.29% | 3,621.63 | 10.75% |
| 11. | 2020. 12. 31. | $84.45 | -3.13% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $85.20 | 0.89% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $100.00 | $1.29 | 18.88% | 3,811.15 | 2.61% |
| 14. | 2021. 3. 31. | $104.79 | 4.79% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $103.07 | -1.64% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $103.79 | $1.34 | 2.00% | 4,204.11 | 0.55% |
| 17. | 2021. 6. 30. | $104.74 | 0.92% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $101.81 | -2.80% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $96.77 | $1.34 | -3.63% | 4,522.68 | 2.90% |
| 20. | 2021. 9. 30. | $101.45 | 4.84% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $114.49 | 12.85% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $112.87 | $1.34 | -0.24% | 4,567.00 | -0.83% |
| 23. | 2021. 12. 31. | $117.35 | 3.97% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $131.33 | 11.91% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $144.00 | $1.42 | 10.73% | 4,373.94 | -3.14% |
| 26. | 2022. 3. 31. | $162.83 | 13.08% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $156.67 | -3.78% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $174.66 | $1.42 | 12.39% | 4,132.15 | 0.01% |
| 29. | 2022. 6. 30. | $144.78 | -17.11% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $163.78 | 13.12% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $158.06 | $1.42 | -2.63% | 3,955.00 | -4.24% |
| 32. | 2022. 9. 30. | $143.67 | -9.10% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $180.90 | 25.91% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $183.31 | $1.42 | 2.12% | 4,080.11 | 5.38% |
| 35. | 2022. 12. 31. | $179.49 | -2.08% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $174.02 | -3.05% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $160.77 | $1.51 | -6.75% | 3,970.15 | -2.61% |
| 38. | 2023. 3. 31. | $163.16 | 1.49% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $168.58 | 3.32% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $150.62 | $1.51 | -9.76% | 4,179.83 | 0.25% |
| 41. | 2023. 6. 30. | $157.35 | 4.47% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $163.66 | 4.01% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $161.10 | $1.51 | -0.64% | 4,507.66 | -1.77% |
| 44. | 2023. 9. 30. | $168.62 | 4.67% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $145.73 | -13.57% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $143.60 | $1.51 | -0.43% | 4,567.80 | 8.92% |
| 47. | 2023. 12. 31. | $149.16 | 3.87% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $147.43 | -1.16% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $152.01 | $1.63 | 4.21% | 5,096.27 | 5.17% |
| 50. | 2024. 3. 31. | $157.74 | 3.77% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $161.27 | 2.24% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $162.30 | $1.63 | 1.65% | 5,277.51 | 4.80% |
| 53. | 2024. 6. 30. | $156.42 | -3.62% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $160.47 | 2.59% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $147.95 | $1.63 | -6.79% | 5,648.40 | 2.28% |
| 56. | 2024. 9. 30. | $147.27 | -0.46% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $148.82 | 1.05% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $161.93 | $1.63 | 9.90% | 6,032.38 | 5.73% |
| 59. | 2024. 12. 31. | $144.84 | -10.55% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.34% | 1.16% | ||||
| 표준 편차: | 9.70% | 5.28% | ||||
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. | 2020. 2. 29. | -11.68% | -8.41% | 169.49 | 91.63 | 124.62 |
| 2. | 2020. 3. 31. | -22.37% | -12.51% | 562.28 | 186.96 | 324.23 |
| 3. | 2020. 4. 30. | 26.97% | 12.68% | 656.59 | 132.78 | 295.27 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 9.90% | 5.73% | 73.31 | 20.87 | 39.12 |
| 59. | 2024. 12. 31. | -10.55% | -2.50% | 141.53 | 13.40 | 43.55 |
| 합계 (Σ): | 5,455.24 | 1,618.62 | 1,811.56 | |||
| 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. | 2020. 2. 29. | -11.68% | -8.41% | 169.49 | 91.63 | 124.62 |
| 2. | 2020. 3. 31. | -22.37% | -12.51% | 562.28 | 186.96 | 324.23 |
| 3. | 2020. 4. 30. | 26.97% | 12.68% | 656.59 | 132.78 | 295.27 |
| 4. | 2020. 5. 31. | 1.08% | 4.53% | 0.07 | 11.34 | -0.90 |
| 5. | 2020. 6. 30. | -2.69% | 1.84% | 16.29 | 0.46 | -2.73 |
| 6. | 2020. 7. 31. | -5.93% | 5.51% | 52.87 | 18.91 | -31.62 |
| 7. | 2020. 8. 31. | 1.52% | 7.01% | 0.03 | 34.17 | 1.07 |
| 8. | 2020. 9. 30. | -14.21% | -3.92% | 242.02 | 25.85 | 79.09 |
| 9. | 2020. 10. 31. | -3.47% | -2.77% | 23.18 | 15.43 | 18.91 |
| 10. | 2020. 11. 30. | 27.29% | 10.75% | 673.52 | 92.03 | 248.97 |
| 11. | 2020. 12. 31. | -3.13% | 3.71% | 20.02 | 6.51 | -11.41 |
| 12. | 2021. 1. 31. | 0.89% | -1.11% | 0.21 | 5.18 | 1.03 |
| 13. | 2021. 2. 28. | 18.88% | 2.61% | 307.73 | 2.10 | 25.40 |
| 14. | 2021. 3. 31. | 4.79% | 4.24% | 11.88 | 9.50 | 10.63 |
| 15. | 2021. 4. 30. | -1.64% | 5.24% | 8.90 | 16.66 | -12.18 |
| 16. | 2021. 5. 31. | 2.00% | 0.55% | 0.43 | 0.38 | -0.40 |
| 17. | 2021. 6. 30. | 0.92% | 2.22% | 0.18 | 1.12 | -0.45 |
| 18. | 2021. 7. 31. | -2.80% | 2.27% | 17.14 | 1.24 | -4.61 |
| 19. | 2021. 8. 31. | -3.63% | 2.90% | 24.77 | 3.02 | -8.65 |
| 20. | 2021. 9. 30. | 4.84% | -4.76% | 12.20 | 35.02 | -20.68 |
| 21. | 2021. 10. 31. | 12.85% | 6.91% | 132.50 | 33.10 | 66.22 |
| 22. | 2021. 11. 30. | -0.24% | -0.83% | 2.52 | 3.98 | 3.17 |
| 23. | 2021. 12. 31. | 3.97% | 4.36% | 6.90 | 10.24 | 8.40 |
| 24. | 2022. 1. 31. | 11.91% | -5.26% | 111.73 | 41.21 | -67.86 |
| 25. | 2022. 2. 28. | 10.73% | -3.14% | 88.10 | 18.47 | -40.33 |
| 26. | 2022. 3. 31. | 13.08% | 3.58% | 137.68 | 5.84 | 28.35 |
| 27. | 2022. 4. 30. | -3.78% | -8.80% | 26.27 | 99.14 | 51.04 |
| 28. | 2022. 5. 31. | 12.39% | 0.01% | 122.02 | 1.34 | -12.77 |
| 29. | 2022. 6. 30. | -17.11% | -8.39% | 340.41 | 91.26 | 176.26 |
| 30. | 2022. 7. 31. | 13.12% | 9.11% | 138.78 | 63.21 | 93.66 |
| 31. | 2022. 8. 31. | -2.63% | -4.24% | 15.75 | 29.22 | 21.45 |
| 32. | 2022. 9. 30. | -9.10% | -9.34% | 109.14 | 110.27 | 109.70 |
| 33. | 2022. 10. 31. | 25.91% | 7.99% | 603.73 | 46.58 | 167.70 |
| 34. | 2022. 11. 30. | 2.12% | 5.38% | 0.60 | 17.76 | 3.26 |
| 35. | 2022. 12. 31. | -2.08% | -5.90% | 11.74 | 49.82 | 24.19 |
| 36. | 2023. 1. 31. | -3.05% | 6.18% | 19.27 | 25.14 | -22.01 |
| 37. | 2023. 2. 28. | -6.75% | -2.61% | 65.43 | 14.23 | 30.52 |
| 38. | 2023. 3. 31. | 1.49% | 3.51% | 0.02 | 5.49 | 0.34 |
| 39. | 2023. 4. 30. | 3.32% | 1.46% | 3.92 | 0.09 | 0.60 |
| 40. | 2023. 5. 31. | -9.76% | 0.25% | 123.22 | 0.83 | 10.14 |
| 41. | 2023. 6. 30. | 4.47% | 4.71% | 9.77 | 12.62 | 11.10 |
| 42. | 2023. 7. 31. | 4.01% | 4.85% | 7.12 | 13.58 | 9.83 |
| 43. | 2023. 8. 31. | -0.64% | -1.77% | 3.94 | 8.60 | 5.82 |
| 44. | 2023. 9. 30. | 4.67% | -4.87% | 11.06 | 36.40 | -20.06 |
| 45. | 2023. 10. 31. | -13.57% | -2.20% | 222.53 | 11.28 | 50.11 |
| 46. | 2023. 11. 30. | -0.43% | 8.92% | 3.13 | 60.17 | -13.71 |
| 47. | 2023. 12. 31. | 3.87% | 4.42% | 6.40 | 10.64 | 8.25 |
| 48. | 2024. 1. 31. | -1.16% | 1.59% | 6.26 | 0.18 | -1.07 |
| 49. | 2024. 2. 29. | 4.21% | 5.17% | 8.23 | 16.09 | 11.51 |
| 50. | 2024. 3. 31. | 3.77% | 3.10% | 5.89 | 3.77 | 4.71 |
| 51. | 2024. 4. 30. | 2.24% | -4.16% | 0.80 | 28.33 | -4.76 |
| 52. | 2024. 5. 31. | 1.65% | 4.80% | 0.09 | 13.26 | 1.12 |
| 53. | 2024. 6. 30. | -3.62% | 3.47% | 24.66 | 5.32 | -11.45 |
| 54. | 2024. 7. 31. | 2.59% | 1.13% | 1.55 | 0.00 | -0.04 |
| 55. | 2024. 8. 31. | -6.79% | 2.28% | 66.08 | 1.26 | -9.12 |
| 56. | 2024. 9. 30. | -0.46% | 2.02% | 3.25 | 0.74 | -1.55 |
| 57. | 2024. 10. 31. | 1.05% | -0.99% | 0.08 | 4.63 | 0.62 |
| 58. | 2024. 11. 30. | 9.90% | 5.73% | 73.31 | 20.87 | 39.12 |
| 59. | 2024. 12. 31. | -10.55% | -2.50% | 141.53 | 13.40 | 43.55 |
| 합계 (Σ): | 5,455.24 | 1,618.62 | 1,811.56 | |||
모두 보기
분산CVX = Σ(RCVX,t–RCVX)2 ÷ (59 – 1)
= 5,455.24 ÷ (59 – 1)
= 94.06
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산CVX, S&P 500 = Σ(RCVX,t–RCVX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,811.56 ÷ (59 – 1)
= 31.23
체계적인 위험 추정 (β)
| 분산CVX | 94.06 |
| 분산S&P 500 | 27.91 |
| 공분산CVX, S&P 500 | 31.23 |
| 상관 계수CVX, S&P 5001 | 0.61 |
| βCVX2 | 1.12 |
| αCVX3 | 0.04% |
계산
1 상관 계수CVX, S&P 500
= 공분산CVX, S&P 500 ÷ (표준 편차CVX × 표준 편차S&P 500)
= 31.23 ÷ (9.70% × 5.28%)
= 0.61
2 βCVX
= 공분산CVX, S&P 500 ÷ 분산S&P 500
= 31.23 ÷ 27.91
= 1.12
3 αCVX
= 평균의CVX – βCVX × 평균의S&P 500
= 1.34% – 1.12 × 1.16%
= 0.04%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.49% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.87% |
| 보통주의 체계적 위험Chevron | βCVX | 1.12 |
| Chevron 보통주에 대한 예상 수익률3 | E(RCVX) | 16.11% |
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]
= 4.49% + 1.12 [14.87% – 4.49%]
= 16.11%