자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Altria보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Altria Group Inc., 월별 수익률
| Altria Group Inc. (MO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MO,t1 | 피제수MO,t1 | RMO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $49.35 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $52.41 | 6.20% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $57.43 | $0.80 | 11.10% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $54.33 | -5.40% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $42.04 | 4.66% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $40.34 | $0.98 | -1.71% | 4,769.83 | 4.42% |
| 평균의 (R): | 0.58% | 1.11% | ||||
| 표준 편차: | 7.13% | 5.31% | ||||
| Altria Group Inc. (MO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MO,t1 | 피제수MO,t1 | RMO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $49.35 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $52.41 | 6.20% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $57.43 | $0.80 | 11.10% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $54.33 | -5.40% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $49.06 | -9.70% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $47.35 | $0.80 | -1.85% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $47.07 | -0.59% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $43.74 | -7.07% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $40.90 | $0.84 | -4.57% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $44.79 | 9.51% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $49.70 | 10.96% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $49.91 | $0.84 | 2.11% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $47.53 | -4.77% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $40.37 | -15.06% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $38.67 | $0.84 | -2.13% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $39.25 | 1.50% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $39.05 | -0.51% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $39.25 | $0.84 | 2.66% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $41.15 | 4.84% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $43.74 | 6.29% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $38.64 | $0.86 | -9.69% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $36.08 | -6.63% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $39.83 | 10.39% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $41.00 | $0.86 | 5.10% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $41.08 | 0.20% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $43.60 | 6.13% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $51.16 | $0.86 | 19.31% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $47.75 | -6.67% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $49.22 | 3.08% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $47.68 | $0.86 | -1.38% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $48.04 | 0.76% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $50.23 | 4.56% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $45.52 | $0.90 | -7.59% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $44.11 | -3.10% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $42.64 | -3.33% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $47.39 | $0.90 | 13.25% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $50.88 | 7.36% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $51.29 | 0.81% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $52.25 | $0.90 | 3.63% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $55.57 | 6.35% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $54.09 | -2.66% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $41.77 | $0.90 | -21.11% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $43.86 | 5.00% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $45.12 | 2.87% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $40.38 | $0.94 | -8.42% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $46.27 | 14.59% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $46.58 | 0.67% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $45.71 | $0.94 | 0.15% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $45.04 | -1.47% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $46.43 | 3.09% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $44.62 | $0.94 | -1.87% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $47.51 | 6.48% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $44.42 | -6.50% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $45.30 | $0.94 | 4.10% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $45.42 | 0.26% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $44.22 | -2.64% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $42.05 | $0.98 | -2.69% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $40.17 | -4.47% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $42.04 | 4.66% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $40.34 | $0.98 | -1.71% | 4,769.83 | 4.42% |
| 평균의 (R): | 0.58% | 1.11% | ||||
| 표준 편차: | 7.13% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MO의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Altria Group Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMO,t | RS&P 500,t | (RMO,t–RMO)2 | (RS&P 500,t–RS&P 500)2 | (RMO,t–RMO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 6.20% | 2.97% | 31.56 | 3.49 | 10.49 |
| 2. | 2019. 3. 31. | 11.10% | 1.79% | 110.72 | 0.47 | 7.22 |
| 3. | 2019. 4. 30. | -5.40% | 3.93% | 35.77 | 7.98 | -16.90 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 4.66% | 8.92% | 16.59 | 61.03 | 31.82 |
| 59. | 2023. 12. 31. | -1.71% | 4.42% | 5.27 | 11.00 | -7.61 |
| 합계 (Σ): | 2,948.94 | 1,634.30 | 1,072.86 | |||
| t | 날짜 | RMO,t | RS&P 500,t | (RMO,t–RMO)2 | (RS&P 500,t–RS&P 500)2 | (RMO,t–RMO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 6.20% | 2.97% | 31.56 | 3.49 | 10.49 |
| 2. | 2019. 3. 31. | 11.10% | 1.79% | 110.72 | 0.47 | 7.22 |
| 3. | 2019. 4. 30. | -5.40% | 3.93% | 35.77 | 7.98 | -16.90 |
| 4. | 2019. 5. 31. | -9.70% | -6.58% | 105.73 | 59.04 | 79.01 |
| 5. | 2019. 6. 30. | -1.85% | 6.89% | 5.94 | 33.49 | -14.11 |
| 6. | 2019. 7. 31. | -0.59% | 1.31% | 1.38 | 0.04 | -0.24 |
| 7. | 2019. 8. 31. | -7.07% | -1.81% | 58.63 | 8.50 | 22.32 |
| 8. | 2019. 9. 30. | -4.57% | 1.72% | 26.58 | 0.37 | -3.16 |
| 9. | 2019. 10. 31. | 9.51% | 2.04% | 79.72 | 0.88 | 8.37 |
| 10. | 2019. 11. 30. | 10.96% | 3.40% | 107.74 | 5.28 | 23.86 |
| 11. | 2019. 12. 31. | 2.11% | 2.86% | 2.34 | 3.07 | 2.68 |
| 12. | 2020. 1. 31. | -4.77% | -0.16% | 28.64 | 1.61 | 6.79 |
| 13. | 2020. 2. 29. | -15.06% | -8.41% | 244.82 | 90.57 | 148.91 |
| 14. | 2020. 3. 31. | -2.13% | -12.51% | 7.36 | 185.44 | 36.94 |
| 15. | 2020. 4. 30. | 1.50% | 12.68% | 0.84 | 134.06 | 10.62 |
| 16. | 2020. 5. 31. | -0.51% | 4.53% | 1.19 | 11.71 | -3.74 |
| 17. | 2020. 6. 30. | 2.66% | 1.84% | 4.33 | 0.54 | 1.53 |
| 18. | 2020. 7. 31. | 4.84% | 5.51% | 18.13 | 19.40 | 18.75 |
| 19. | 2020. 8. 31. | 6.29% | 7.01% | 32.62 | 34.82 | 33.70 |
| 20. | 2020. 9. 30. | -9.69% | -3.92% | 105.60 | 25.29 | 51.68 |
| 21. | 2020. 10. 31. | -6.63% | -2.77% | 51.95 | 15.00 | 27.91 |
| 22. | 2020. 11. 30. | 10.39% | 10.75% | 96.25 | 93.10 | 94.66 |
| 23. | 2020. 12. 31. | 5.10% | 3.71% | 20.38 | 6.79 | 11.76 |
| 24. | 2021. 1. 31. | 0.20% | -1.11% | 0.15 | 4.93 | 0.86 |
| 25. | 2021. 2. 28. | 6.13% | 2.61% | 30.82 | 2.26 | 8.35 |
| 26. | 2021. 3. 31. | 19.31% | 4.24% | 350.79 | 9.85 | 58.77 |
| 27. | 2021. 4. 30. | -6.67% | 5.24% | 52.53 | 17.11 | -29.98 |
| 28. | 2021. 5. 31. | 3.08% | 0.55% | 6.23 | 0.31 | -1.39 |
| 29. | 2021. 6. 30. | -1.38% | 2.22% | 3.86 | 1.24 | -2.19 |
| 30. | 2021. 7. 31. | 0.76% | 2.27% | 0.03 | 1.37 | 0.20 |
| 31. | 2021. 8. 31. | 4.56% | 2.90% | 15.81 | 3.22 | 7.13 |
| 32. | 2021. 9. 30. | -7.59% | -4.76% | 66.71 | 34.37 | 47.89 |
| 33. | 2021. 10. 31. | -3.10% | 6.91% | 13.54 | 33.74 | -21.38 |
| 34. | 2021. 11. 30. | -3.33% | -0.83% | 15.33 | 3.76 | 7.59 |
| 35. | 2021. 12. 31. | 13.25% | 4.36% | 160.47 | 10.60 | 41.24 |
| 36. | 2022. 1. 31. | 7.36% | -5.26% | 45.99 | 40.51 | -43.16 |
| 37. | 2022. 2. 28. | 0.81% | -3.14% | 0.05 | 17.99 | -0.95 |
| 38. | 2022. 3. 31. | 3.63% | 3.58% | 9.26 | 6.11 | 7.52 |
| 39. | 2022. 4. 30. | 6.35% | -8.80% | 33.31 | 98.04 | -57.15 |
| 40. | 2022. 5. 31. | -2.66% | 0.01% | 10.54 | 1.21 | 3.57 |
| 41. | 2022. 6. 30. | -21.11% | -8.39% | 470.70 | 90.21 | 206.06 |
| 42. | 2022. 7. 31. | 5.00% | 9.11% | 19.54 | 64.09 | 35.39 |
| 43. | 2022. 8. 31. | 2.87% | -4.24% | 5.24 | 28.62 | -12.25 |
| 44. | 2022. 9. 30. | -8.42% | -9.34% | 81.08 | 109.11 | 94.06 |
| 45. | 2022. 10. 31. | 14.59% | 7.99% | 196.11 | 47.34 | 96.35 |
| 46. | 2022. 11. 30. | 0.67% | 5.38% | 0.01 | 18.23 | 0.37 |
| 47. | 2022. 12. 31. | 0.15% | -5.90% | 0.19 | 49.04 | 3.03 |
| 48. | 2023. 1. 31. | -1.47% | 6.18% | 4.20 | 25.70 | -10.38 |
| 49. | 2023. 2. 28. | 3.09% | -2.61% | 6.27 | 13.82 | -9.31 |
| 50. | 2023. 3. 31. | -1.87% | 3.51% | 6.03 | 5.76 | -5.89 |
| 51. | 2023. 4. 30. | 6.48% | 1.46% | 34.74 | 0.13 | 2.11 |
| 52. | 2023. 5. 31. | -6.50% | 0.25% | 50.22 | 0.74 | 6.08 |
| 53. | 2023. 6. 30. | 4.10% | 4.71% | 12.35 | 13.02 | 12.68 |
| 54. | 2023. 7. 31. | 0.26% | 4.85% | 0.10 | 13.99 | -1.19 |
| 55. | 2023. 8. 31. | -2.64% | -1.77% | 10.40 | 8.28 | 9.28 |
| 56. | 2023. 9. 30. | -2.69% | -4.87% | 10.72 | 35.73 | 19.57 |
| 57. | 2023. 10. 31. | -4.47% | -2.20% | 25.54 | 10.92 | 16.70 |
| 58. | 2023. 11. 30. | 4.66% | 8.92% | 16.59 | 61.03 | 31.82 |
| 59. | 2023. 12. 31. | -1.71% | 4.42% | 5.27 | 11.00 | -7.61 |
| 합계 (Σ): | 2,948.94 | 1,634.30 | 1,072.86 | |||
모두 보기
분산MO = Σ(RMO,t–RMO)2 ÷ (59 – 1)
= 2,948.94 ÷ (59 – 1)
= 50.84
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산MO, S&P 500 = Σ(RMO,t–RMO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,072.86 ÷ (59 – 1)
= 18.50
체계적인 위험 추정 (β)
| 분산MO | 50.84 |
| 분산S&P 500 | 28.18 |
| 공분산MO, S&P 500 | 18.50 |
| 상관 계수MO, S&P 5001 | 0.49 |
| βMO2 | 0.66 |
| αMO3 | -0.14% |
계산
1 상관 계수MO, S&P 500
= 공분산MO, S&P 500 ÷ (표준 편차MO × 표준 편차S&P 500)
= 18.50 ÷ (7.13% × 5.31%)
= 0.49
2 βMO
= 공분산MO, S&P 500 ÷ 분산S&P 500
= 18.50 ÷ 28.18
= 0.66
3 αMO
= 평균의MO – βMO × 평균의S&P 500
= 0.58% – 0.66 × 1.11%
= -0.14%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Altria | βMO | 0.66 |
| Altria 보통주의 예상 수익률3 | E(RMO) | 11.35% |
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(RMO) = RF + βMO [E(RM) – RF]
= 4.60% + 0.66 [14.89% – 4.60%]
= 11.35%