자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Valero보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Valero Energy Corp., 월별 수익률
| Valero Energy Corp. (VLO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값VLO,t1 | 피제수VLO,t1 | RVLO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $87.82 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $81.56 | $0.90 | -6.10% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $84.83 | 4.01% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $90.66 | 6.87% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $125.36 | $1.02 | -0.49% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $130.00 | 3.70% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.02% | 1.11% | ||||
| 표준 편차: | 14.24% | 5.31% | ||||
| Valero Energy Corp. (VLO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값VLO,t1 | 피제수VLO,t1 | RVLO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $87.82 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $81.56 | $0.90 | -6.10% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $84.83 | 4.01% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $90.66 | 6.87% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $70.40 | $0.90 | -21.35% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $85.61 | 21.61% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $85.25 | -0.42% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $75.28 | $0.90 | -10.64% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $85.24 | 13.23% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $96.98 | 13.77% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $95.49 | $0.90 | -0.61% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $93.65 | -1.93% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $84.31 | -9.97% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $66.25 | $0.98 | -20.26% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $45.36 | -31.53% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $63.35 | 39.66% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $66.64 | $0.98 | 6.74% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $58.82 | -11.73% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $56.23 | -4.40% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $52.59 | $0.98 | -4.73% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $43.32 | -17.63% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $38.61 | -10.87% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $53.77 | $0.98 | 41.80% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $56.57 | 5.21% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $56.43 | -0.25% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $76.98 | $0.98 | 38.15% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $71.60 | -6.99% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $73.96 | 3.30% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $80.40 | $0.98 | 10.03% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $78.08 | -2.89% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $66.97 | -14.23% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $66.31 | $0.98 | 0.48% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $70.57 | 6.42% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $77.33 | 9.58% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $66.94 | $0.98 | -12.17% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $75.11 | 12.20% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $82.97 | 10.46% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $83.51 | $0.98 | 1.83% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $101.54 | 21.59% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $111.48 | 9.79% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $129.60 | $0.98 | 17.13% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $106.28 | -17.99% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $110.77 | 4.22% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $117.12 | $0.98 | 6.62% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $106.85 | -8.77% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $125.55 | 17.50% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $133.62 | $0.98 | 7.21% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $126.86 | -5.06% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $140.03 | 10.38% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $131.73 | $1.02 | -5.20% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $139.60 | 5.97% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $114.67 | -17.86% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $107.04 | $1.02 | -5.76% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $117.30 | 9.59% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $128.91 | 9.90% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $129.90 | $1.02 | 1.56% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $141.71 | 9.09% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $127.00 | -10.38% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $125.36 | $1.02 | -0.49% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $130.00 | 3.70% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.02% | 1.11% | ||||
| 표준 편차: | 14.24% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 VLO의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Valero Energy Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RVLO,t | RS&P 500,t | (RVLO,t–RVLO)2 | (RS&P 500,t–RS&P 500)2 | (RVLO,t–RVLO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -6.10% | 2.97% | 66.05 | 3.49 | -15.17 |
| 2. | 2019. 3. 31. | 4.01% | 1.79% | 3.94 | 0.47 | 1.36 |
| 3. | 2019. 4. 30. | 6.87% | 3.93% | 23.51 | 7.98 | 13.70 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | -0.49% | 8.92% | 6.31 | 61.03 | -19.62 |
| 59. | 2023. 12. 31. | 3.70% | 4.42% | 2.81 | 11.00 | 5.56 |
| 합계 (Σ): | 11,760.38 | 1,634.30 | 2,513.35 | |||
| t | 날짜 | RVLO,t | RS&P 500,t | (RVLO,t–RVLO)2 | (RS&P 500,t–RS&P 500)2 | (RVLO,t–RVLO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | -6.10% | 2.97% | 66.05 | 3.49 | -15.17 |
| 2. | 2019. 3. 31. | 4.01% | 1.79% | 3.94 | 0.47 | 1.36 |
| 3. | 2019. 4. 30. | 6.87% | 3.93% | 23.51 | 7.98 | 13.70 |
| 4. | 2019. 5. 31. | -21.35% | -6.58% | 546.55 | 59.04 | 179.63 |
| 5. | 2019. 6. 30. | 21.61% | 6.89% | 383.43 | 33.49 | 113.32 |
| 6. | 2019. 7. 31. | -0.42% | 1.31% | 5.97 | 0.04 | -0.51 |
| 7. | 2019. 8. 31. | -10.64% | -1.81% | 160.35 | 8.50 | 36.91 |
| 8. | 2019. 9. 30. | 13.23% | 1.72% | 125.59 | 0.37 | 6.86 |
| 9. | 2019. 10. 31. | 13.77% | 2.04% | 138.04 | 0.88 | 11.01 |
| 10. | 2019. 11. 30. | -0.61% | 3.40% | 6.93 | 5.28 | -6.05 |
| 11. | 2019. 12. 31. | -1.93% | 2.86% | 15.61 | 3.07 | -6.93 |
| 12. | 2020. 1. 31. | -9.97% | -0.16% | 143.93 | 1.61 | 15.22 |
| 13. | 2020. 2. 29. | -20.26% | -8.41% | 496.50 | 90.57 | 212.06 |
| 14. | 2020. 3. 31. | -31.53% | -12.51% | 1,126.00 | 185.44 | 456.96 |
| 15. | 2020. 4. 30. | 39.66% | 12.68% | 1,416.52 | 134.06 | 435.78 |
| 16. | 2020. 5. 31. | 6.74% | 4.53% | 22.25 | 11.71 | 16.14 |
| 17. | 2020. 6. 30. | -11.73% | 1.84% | 189.30 | 0.54 | -10.08 |
| 18. | 2020. 7. 31. | -4.40% | 5.51% | 41.31 | 19.40 | -28.31 |
| 19. | 2020. 8. 31. | -4.73% | 7.01% | 45.62 | 34.82 | -39.86 |
| 20. | 2020. 9. 30. | -17.63% | -3.92% | 386.15 | 25.29 | 98.82 |
| 21. | 2020. 10. 31. | -10.87% | -2.77% | 166.32 | 15.00 | 49.94 |
| 22. | 2020. 11. 30. | 41.80% | 10.75% | 1,582.36 | 93.10 | 383.81 |
| 23. | 2020. 12. 31. | 5.21% | 3.71% | 10.13 | 6.79 | 8.30 |
| 24. | 2021. 1. 31. | -0.25% | -1.11% | 5.16 | 4.93 | 5.04 |
| 25. | 2021. 2. 28. | 38.15% | 2.61% | 1,305.35 | 2.26 | 54.31 |
| 26. | 2021. 3. 31. | -6.99% | 4.24% | 81.23 | 9.85 | -28.28 |
| 27. | 2021. 4. 30. | 3.30% | 5.24% | 1.62 | 17.11 | 5.26 |
| 28. | 2021. 5. 31. | 10.03% | 0.55% | 64.14 | 0.31 | -4.46 |
| 29. | 2021. 6. 30. | -2.89% | 2.22% | 24.10 | 1.24 | -5.48 |
| 30. | 2021. 7. 31. | -14.23% | 2.27% | 264.15 | 1.37 | -19.00 |
| 31. | 2021. 8. 31. | 0.48% | 2.90% | 2.39 | 3.22 | -2.77 |
| 32. | 2021. 9. 30. | 6.42% | -4.76% | 19.36 | 34.37 | -25.80 |
| 33. | 2021. 10. 31. | 9.58% | 6.91% | 57.08 | 33.74 | 43.89 |
| 34. | 2021. 11. 30. | -12.17% | -0.83% | 201.43 | 3.76 | 27.52 |
| 35. | 2021. 12. 31. | 12.20% | 4.36% | 103.66 | 10.60 | 33.14 |
| 36. | 2022. 1. 31. | 10.46% | -5.26% | 71.25 | 40.51 | -53.72 |
| 37. | 2022. 2. 28. | 1.83% | -3.14% | 0.04 | 17.99 | 0.81 |
| 38. | 2022. 3. 31. | 21.59% | 3.58% | 382.84 | 6.11 | 48.36 |
| 39. | 2022. 4. 30. | 9.79% | -8.80% | 60.30 | 98.04 | -76.89 |
| 40. | 2022. 5. 31. | 17.13% | 0.01% | 228.29 | 1.21 | -16.63 |
| 41. | 2022. 6. 30. | -17.99% | -8.39% | 400.71 | 90.21 | 190.12 |
| 42. | 2022. 7. 31. | 4.22% | 9.11% | 4.84 | 64.09 | 17.62 |
| 43. | 2022. 8. 31. | 6.62% | -4.24% | 21.10 | 28.62 | -24.57 |
| 44. | 2022. 9. 30. | -8.77% | -9.34% | 116.48 | 109.11 | 112.73 |
| 45. | 2022. 10. 31. | 17.50% | 7.99% | 239.55 | 47.34 | 106.49 |
| 46. | 2022. 11. 30. | 7.21% | 5.38% | 26.88 | 18.23 | 22.13 |
| 47. | 2022. 12. 31. | -5.06% | -5.90% | 50.17 | 49.04 | 49.60 |
| 48. | 2023. 1. 31. | 10.38% | 6.18% | 69.85 | 25.70 | 42.37 |
| 49. | 2023. 2. 28. | -5.20% | -2.61% | 52.17 | 13.82 | 26.85 |
| 50. | 2023. 3. 31. | 5.97% | 3.51% | 15.61 | 5.76 | 9.48 |
| 51. | 2023. 4. 30. | -17.86% | 1.46% | 395.29 | 0.13 | -7.13 |
| 52. | 2023. 5. 31. | -5.76% | 0.25% | 60.66 | 0.74 | 6.68 |
| 53. | 2023. 6. 30. | 9.59% | 4.71% | 57.17 | 13.02 | 27.28 |
| 54. | 2023. 7. 31. | 9.90% | 4.85% | 62.00 | 13.99 | 29.45 |
| 55. | 2023. 8. 31. | 1.56% | -1.77% | 0.22 | 8.28 | 1.34 |
| 56. | 2023. 9. 30. | 9.09% | -4.87% | 49.95 | 35.73 | -42.25 |
| 57. | 2023. 10. 31. | -10.38% | -2.20% | 153.86 | 10.92 | 40.98 |
| 58. | 2023. 11. 30. | -0.49% | 8.92% | 6.31 | 61.03 | -19.62 |
| 59. | 2023. 12. 31. | 3.70% | 4.42% | 2.81 | 11.00 | 5.56 |
| 합계 (Σ): | 11,760.38 | 1,634.30 | 2,513.35 | |||
모두 보기
분산VLO = Σ(RVLO,t–RVLO)2 ÷ (59 – 1)
= 11,760.38 ÷ (59 – 1)
= 202.77
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산VLO, S&P 500 = Σ(RVLO,t–RVLO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,513.35 ÷ (59 – 1)
= 43.33
체계적인 위험 추정 (β)
| 분산VLO | 202.77 |
| 분산S&P 500 | 28.18 |
| 공분산VLO, S&P 500 | 43.33 |
| 상관 계수VLO, S&P 5001 | 0.57 |
| βVLO2 | 1.54 |
| αVLO3 | 0.32% |
계산
1 상관 계수VLO, S&P 500
= 공분산VLO, S&P 500 ÷ (표준 편차VLO × 표준 편차S&P 500)
= 43.33 ÷ (14.24% × 5.31%)
= 0.57
2 βVLO
= 공분산VLO, S&P 500 ÷ 분산S&P 500
= 43.33 ÷ 28.18
= 1.54
3 αVLO
= 평균의VLO – βVLO × 평균의S&P 500
= 2.02% – 1.54 × 1.11%
= 0.32%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Valero | βVLO | 1.54 |
| Valero 보통주의 예상 수익률3 | E(RVLO) | 24.27% |
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(RVLO) = RF + βVLO [E(RM) – RF]
= 4.54% + 1.54 [17.37% – 4.54%]
= 24.27%