자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 3M보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
3M Co., 월별 수익률
| 3M Co. (MMM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MMM,t1 | 피제수MMM,t1 | RMMM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $174.82 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $186.35 | $1.175 | 7.27% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $191.33 | 2.67% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $195.83 | 2.35% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $170.04 | $1.48 | -4.01% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $177.63 | 4.46% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.46% | 1.36% | ||||
| 표준 편차: | 6.03% | 4.48% | ||||
| 3M Co. (MMM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MMM,t1 | 피제수MMM,t1 | RMMM,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $174.82 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $186.35 | $1.175 | 7.27% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $191.33 | 2.67% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $195.83 | 2.35% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $204.47 | $1.175 | 5.01% | 2,411.80 | 1.16% |
| 5. | 2017. 6. 30. | $208.19 | 1.82% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $201.17 | -3.37% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $204.32 | $1.175 | 2.15% | 2,471.65 | 0.05% |
| 8. | 2017. 9. 30. | $209.90 | 2.73% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $230.19 | 9.67% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $243.14 | $1.175 | 6.14% | 2,647.58 | 2.81% |
| 11. | 2017. 12. 31. | $235.37 | -3.20% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $250.50 | 6.43% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $235.51 | $1.36 | -5.44% | 2,713.83 | -3.89% |
| 14. | 2018. 3. 31. | $219.52 | -6.79% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $194.39 | -11.45% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $197.23 | $1.36 | 2.16% | 2,705.27 | 2.16% |
| 17. | 2018. 6. 30. | $196.72 | -0.26% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $212.32 | 7.93% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $210.92 | $1.36 | -0.02% | 2,901.52 | 3.03% |
| 20. | 2018. 9. 30. | $210.71 | -0.10% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $190.26 | -9.71% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $207.92 | $1.36 | 10.00% | 2,760.17 | 1.79% |
| 23. | 2018. 12. 31. | $190.54 | -8.36% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $200.30 | 5.12% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $207.39 | $1.44 | 4.26% | 2,784.49 | 2.97% |
| 26. | 2019. 3. 31. | $207.78 | 0.19% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $189.51 | -8.79% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $159.75 | $1.44 | -14.94% | 2,752.06 | -6.58% |
| 29. | 2019. 6. 30. | $173.34 | 8.51% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $174.72 | 0.80% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $161.72 | $1.44 | -6.62% | 2,926.46 | -1.81% |
| 32. | 2019. 9. 30. | $164.40 | 1.66% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $164.99 | 0.36% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $169.77 | $1.44 | 3.77% | 3,140.98 | 3.40% |
| 35. | 2019. 12. 31. | $176.42 | 3.92% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $158.66 | -10.07% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $149.24 | $1.47 | -5.01% | 2,954.22 | -8.41% |
| 38. | 2020. 3. 31. | $136.51 | -8.53% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $151.92 | 11.29% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $156.44 | $1.47 | 3.94% | 3,044.31 | 4.53% |
| 41. | 2020. 6. 30. | $155.99 | -0.29% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $150.47 | -3.54% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $163.02 | $1.47 | 9.32% | 3,500.31 | 7.01% |
| 44. | 2020. 9. 30. | $160.18 | -1.74% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $159.96 | -0.14% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $172.73 | $1.47 | 8.90% | 3,621.63 | 10.75% |
| 47. | 2020. 12. 31. | $174.79 | 1.19% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $175.66 | 0.50% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $175.06 | $1.48 | 0.50% | 3,811.15 | 2.61% |
| 50. | 2021. 3. 31. | $192.68 | 10.07% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $197.14 | 2.31% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $203.04 | $1.48 | 3.74% | 4,204.11 | 0.55% |
| 53. | 2021. 6. 30. | $198.63 | -2.17% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $197.94 | -0.35% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $194.74 | $1.48 | -0.87% | 4,522.68 | 2.90% |
| 56. | 2021. 9. 30. | $175.42 | -9.92% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $178.68 | 1.86% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $170.04 | $1.48 | -4.01% | 4,567.00 | -0.83% |
| 59. | 2021. 12. 31. | $177.63 | 4.46% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.46% | 1.36% | ||||
| 표준 편차: | 6.03% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MMM의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
3M Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMMM,t | RS&P 500,t | (RMMM,t–RMMM)2 | (RS&P 500,t–RS&P 500)2 | (RMMM,t–RMMM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 7.27% | 3.72% | 46.30 | 5.58 | 16.07 |
| 2. | 2017. 3. 31. | 2.67% | -0.04% | 4.88 | 1.95 | -3.09 |
| 3. | 2017. 4. 30. | 2.35% | 0.91% | 3.57 | 0.20 | -0.85 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -4.01% | -0.83% | 19.98 | 4.80 | 9.80 |
| 59. | 2021. 12. 31. | 4.46% | 4.36% | 16.01 | 9.02 | 12.02 |
| 합계 (Σ): | 2,109.95 | 1,164.17 | 1,113.30 | |||
| t | 날짜 | RMMM,t | RS&P 500,t | (RMMM,t–RMMM)2 | (RS&P 500,t–RS&P 500)2 | (RMMM,t–RMMM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 7.27% | 3.72% | 46.30 | 5.58 | 16.07 |
| 2. | 2017. 3. 31. | 2.67% | -0.04% | 4.88 | 1.95 | -3.09 |
| 3. | 2017. 4. 30. | 2.35% | 0.91% | 3.57 | 0.20 | -0.85 |
| 4. | 2017. 5. 31. | 5.01% | 1.16% | 20.69 | 0.04 | -0.91 |
| 5. | 2017. 6. 30. | 1.82% | 0.48% | 1.84 | 0.77 | -1.19 |
| 6. | 2017. 7. 31. | -3.37% | 1.93% | 14.71 | 0.33 | -2.21 |
| 7. | 2017. 8. 31. | 2.15% | 0.05% | 2.85 | 1.70 | -2.20 |
| 8. | 2017. 9. 30. | 2.73% | 1.93% | 5.14 | 0.33 | 1.30 |
| 9. | 2017. 10. 31. | 9.67% | 2.22% | 84.70 | 0.74 | 7.92 |
| 10. | 2017. 11. 30. | 6.14% | 2.81% | 32.19 | 2.10 | 8.23 |
| 11. | 2017. 12. 31. | -3.20% | 0.98% | 13.39 | 0.14 | 1.37 |
| 12. | 2018. 1. 31. | 6.43% | 5.62% | 35.58 | 18.15 | 25.41 |
| 13. | 2018. 2. 28. | -5.44% | -3.89% | 34.86 | 27.59 | 31.01 |
| 14. | 2018. 3. 31. | -6.79% | -2.69% | 52.60 | 16.37 | 29.35 |
| 15. | 2018. 4. 30. | -11.45% | 0.27% | 141.86 | 1.18 | 12.94 |
| 16. | 2018. 5. 31. | 2.16% | 2.16% | 2.88 | 0.64 | 1.36 |
| 17. | 2018. 6. 30. | -0.26% | 0.48% | 0.52 | 0.76 | 0.63 |
| 18. | 2018. 7. 31. | 7.93% | 3.60% | 55.76 | 5.04 | 16.76 |
| 19. | 2018. 8. 31. | -0.02% | 3.03% | 0.23 | 2.78 | -0.80 |
| 20. | 2018. 9. 30. | -0.10% | 0.43% | 0.32 | 0.86 | 0.52 |
| 21. | 2018. 10. 31. | -9.71% | -6.94% | 103.39 | 68.86 | 84.38 |
| 22. | 2018. 11. 30. | 10.00% | 1.79% | 90.89 | 0.18 | 4.08 |
| 23. | 2018. 12. 31. | -8.36% | -9.18% | 77.83 | 111.00 | 92.94 |
| 24. | 2019. 1. 31. | 5.12% | 7.87% | 21.71 | 42.39 | 30.33 |
| 25. | 2019. 2. 28. | 4.26% | 2.97% | 14.41 | 2.61 | 6.13 |
| 26. | 2019. 3. 31. | 0.19% | 1.79% | 0.08 | 0.19 | -0.12 |
| 27. | 2019. 4. 30. | -8.79% | 3.93% | 85.67 | 6.62 | -23.82 |
| 28. | 2019. 5. 31. | -14.94% | -6.58% | 237.37 | 62.97 | 122.26 |
| 29. | 2019. 6. 30. | 8.51% | 6.89% | 64.71 | 30.64 | 44.52 |
| 30. | 2019. 7. 31. | 0.80% | 1.31% | 0.11 | 0.00 | -0.02 |
| 31. | 2019. 8. 31. | -6.62% | -1.81% | 50.12 | 10.03 | 22.42 |
| 32. | 2019. 9. 30. | 1.66% | 1.72% | 1.43 | 0.13 | 0.43 |
| 33. | 2019. 10. 31. | 0.36% | 2.04% | 0.01 | 0.47 | -0.07 |
| 34. | 2019. 11. 30. | 3.77% | 3.40% | 10.94 | 4.19 | 6.77 |
| 35. | 2019. 12. 31. | 3.92% | 2.86% | 11.93 | 2.25 | 5.18 |
| 36. | 2020. 1. 31. | -10.07% | -0.16% | 110.88 | 2.31 | 16.01 |
| 37. | 2020. 2. 29. | -5.01% | -8.41% | 29.96 | 95.43 | 53.47 |
| 38. | 2020. 3. 31. | -8.53% | -12.51% | 80.87 | 192.37 | 124.73 |
| 39. | 2020. 4. 30. | 11.29% | 12.68% | 117.19 | 128.29 | 122.62 |
| 40. | 2020. 5. 31. | 3.94% | 4.53% | 12.11 | 10.05 | 11.03 |
| 41. | 2020. 6. 30. | -0.29% | 1.84% | 0.56 | 0.23 | -0.36 |
| 42. | 2020. 7. 31. | -3.54% | 5.51% | 16.01 | 17.24 | -16.62 |
| 43. | 2020. 8. 31. | 9.32% | 7.01% | 78.40 | 31.91 | 50.02 |
| 44. | 2020. 9. 30. | -1.74% | -3.92% | 4.86 | 27.89 | 11.64 |
| 45. | 2020. 10. 31. | -0.14% | -2.77% | 0.36 | 17.01 | 2.48 |
| 46. | 2020. 11. 30. | 8.90% | 10.75% | 71.22 | 88.30 | 79.30 |
| 47. | 2020. 12. 31. | 1.19% | 3.71% | 0.53 | 5.54 | 1.72 |
| 48. | 2021. 1. 31. | 0.50% | -1.11% | 0.00 | 6.11 | -0.09 |
| 49. | 2021. 2. 28. | 0.50% | 2.61% | 0.00 | 1.57 | 0.05 |
| 50. | 2021. 3. 31. | 10.07% | 4.24% | 92.20 | 8.33 | 27.71 |
| 51. | 2021. 4. 30. | 2.31% | 5.24% | 3.43 | 15.09 | 7.19 |
| 52. | 2021. 5. 31. | 3.74% | 0.55% | 10.76 | 0.65 | -2.65 |
| 53. | 2021. 6. 30. | -2.17% | 2.22% | 6.94 | 0.75 | -2.28 |
| 54. | 2021. 7. 31. | -0.35% | 2.27% | 0.66 | 0.84 | -0.74 |
| 55. | 2021. 8. 31. | -0.87% | 2.90% | 1.77 | 2.38 | -2.05 |
| 56. | 2021. 9. 30. | -9.92% | -4.76% | 107.83 | 37.39 | 63.50 |
| 57. | 2021. 10. 31. | 1.86% | 6.91% | 1.95 | 30.87 | 7.75 |
| 58. | 2021. 11. 30. | -4.01% | -0.83% | 19.98 | 4.80 | 9.80 |
| 59. | 2021. 12. 31. | 4.46% | 4.36% | 16.01 | 9.02 | 12.02 |
| 합계 (Σ): | 2,109.95 | 1,164.17 | 1,113.30 | |||
모두 보기
분산MMM = Σ(RMMM,t–RMMM)2 ÷ (59 – 1)
= 2,109.95 ÷ (59 – 1)
= 36.38
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산MMM, S&P 500 = Σ(RMMM,t–RMMM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,113.30 ÷ (59 – 1)
= 19.19
체계적인 위험 추정 (β)
| 분산MMM | 36.38 |
| 분산S&P 500 | 20.07 |
| 공분산MMM, S&P 500 | 19.19 |
| 상관 계수MMM, S&P 5001 | 0.71 |
| βMMM2 | 0.96 |
| αMMM3 | -0.84% |
계산
1 상관 계수MMM, S&P 500
= 공분산MMM, S&P 500 ÷ (표준 편차MMM × 표준 편차S&P 500)
= 19.19 ÷ (6.03% × 4.48%)
= 0.71
2 βMMM
= 공분산MMM, S&P 500 ÷ 분산S&P 500
= 19.19 ÷ 20.07
= 0.96
3 αMMM
= 평균의MMM – βMMM × 평균의S&P 500
= 0.46% – 0.96 × 1.36%
= -0.84%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험3M | βMMM | 0.96 |
| 3M 보통주에 대한 예상 수익률3 | E(RMMM) | 13.39% |
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(RMMM) = RF + βMMM [E(RM) – RF]
= 4.67% + 0.96 [13.79% – 4.67%]
= 13.39%