자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Mosaic보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Mosaic Co., 월별 수익률
| Mosaic Co. (MOS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MOS,t1 | 피제수MOS,t1 | RMOS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $31.37 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $31.19 | $0.275 | 0.30% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $29.18 | -6.44% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $26.93 | -7.71% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $34.22 | -17.68% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $39.29 | $0.075 | 15.04% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.25% | 1.36% | ||||
| 표준 편차: | 12.24% | 4.48% | ||||
| Mosaic Co. (MOS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MOS,t1 | 피제수MOS,t1 | RMOS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $31.37 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $31.19 | $0.275 | 0.30% | 2,363.64 | 3.72% |
| 2. | 2017. 3. 31. | $29.18 | -6.44% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $26.93 | -7.71% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $22.63 | $0.15 | -15.41% | 2,411.80 | 1.16% |
| 5. | 2017. 6. 30. | $22.83 | 0.88% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $24.14 | 5.74% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $19.98 | -17.23% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $21.59 | $0.15 | 8.81% | 2,519.36 | 1.93% |
| 9. | 2017. 10. 31. | $22.34 | 3.47% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $24.29 | 8.73% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $25.66 | $0.025 | 5.74% | 2,673.61 | 0.98% |
| 12. | 2018. 1. 31. | $27.30 | 6.39% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $26.32 | $0.025 | -3.50% | 2,713.83 | -3.89% |
| 14. | 2018. 3. 31. | $24.28 | -7.75% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $26.95 | 11.00% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $27.49 | 2.00% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $28.05 | $0.025 | 2.13% | 2,718.37 | 0.48% |
| 18. | 2018. 7. 31. | $30.11 | 7.34% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $31.27 | 3.85% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $32.48 | $0.025 | 3.95% | 2,913.98 | 0.43% |
| 21. | 2018. 10. 31. | $30.94 | -4.74% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $36.00 | 16.35% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $29.21 | $0.025 | -18.79% | 2,506.85 | -9.18% |
| 24. | 2019. 1. 31. | $32.28 | 10.51% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $31.27 | -3.13% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $27.31 | $0.025 | -12.58% | 2,834.40 | 1.79% |
| 27. | 2019. 4. 30. | $26.11 | -4.39% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $21.47 | -17.77% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $25.03 | $0.05 | 16.81% | 2,941.76 | 6.89% |
| 30. | 2019. 7. 31. | $25.19 | 0.64% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $18.39 | -26.99% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $20.50 | $0.05 | 11.75% | 2,976.74 | 1.72% |
| 33. | 2019. 10. 31. | $19.88 | -3.02% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $19.05 | -4.18% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $21.64 | $0.05 | 13.86% | 3,230.78 | 2.86% |
| 36. | 2020. 1. 31. | $19.84 | -8.32% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $17.03 | -14.16% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $10.82 | $0.05 | -36.17% | 2,584.59 | -12.51% |
| 39. | 2020. 4. 30. | $11.51 | 6.38% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $12.09 | 5.04% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $12.51 | $0.05 | 3.89% | 3,100.29 | 1.84% |
| 42. | 2020. 7. 31. | $13.47 | 7.67% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $18.23 | 35.34% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $18.27 | $0.05 | 0.49% | 3,363.00 | -3.92% |
| 45. | 2020. 10. 31. | $18.50 | 1.26% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $21.96 | 18.70% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $23.01 | $0.05 | 5.01% | 3,756.07 | 3.71% |
| 48. | 2021. 1. 31. | $25.96 | 12.82% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $29.40 | 13.25% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $31.61 | $0.05 | 7.69% | 3,972.89 | 4.24% |
| 51. | 2021. 4. 30. | $35.18 | 11.29% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $36.14 | 2.73% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $31.91 | $0.075 | -11.50% | 4,297.50 | 2.22% |
| 54. | 2021. 7. 31. | $31.23 | -2.13% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $32.18 | 3.04% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $35.72 | $0.075 | 11.23% | 4,307.54 | -4.76% |
| 57. | 2021. 10. 31. | $41.57 | 16.38% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $34.22 | -17.68% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $39.29 | $0.075 | 15.04% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.25% | 1.36% | ||||
| 표준 편차: | 12.24% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MOS의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Mosaic Co., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMOS,t | RS&P 500,t | (RMOS,t–RMOS)2 | (RS&P 500,t–RS&P 500)2 | (RMOS,t–RMOS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 0.30% | 3.72% | 0.90 | 5.58 | -2.24 |
| 2. | 2017. 3. 31. | -6.44% | -0.04% | 59.24 | 1.95 | 10.75 |
| 3. | 2017. 4. 30. | -7.71% | 0.91% | 80.34 | 0.20 | 4.02 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -17.68% | -0.83% | 358.48 | 4.80 | 41.49 |
| 59. | 2021. 12. 31. | 15.04% | 4.36% | 189.96 | 9.02 | 41.39 |
| 합계 (Σ): | 8,684.53 | 1,164.17 | 2,070.45 | |||
| t | 날짜 | RMOS,t | RS&P 500,t | (RMOS,t–RMOS)2 | (RS&P 500,t–RS&P 500)2 | (RMOS,t–RMOS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 0.30% | 3.72% | 0.90 | 5.58 | -2.24 |
| 2. | 2017. 3. 31. | -6.44% | -0.04% | 59.24 | 1.95 | 10.75 |
| 3. | 2017. 4. 30. | -7.71% | 0.91% | 80.34 | 0.20 | 4.02 |
| 4. | 2017. 5. 31. | -15.41% | 1.16% | 277.65 | 0.04 | 3.34 |
| 5. | 2017. 6. 30. | 0.88% | 0.48% | 0.14 | 0.77 | 0.32 |
| 6. | 2017. 7. 31. | 5.74% | 1.93% | 20.12 | 0.33 | 2.59 |
| 7. | 2017. 8. 31. | -17.23% | 0.05% | 341.71 | 1.70 | 24.09 |
| 8. | 2017. 9. 30. | 8.81% | 1.93% | 57.10 | 0.33 | 4.33 |
| 9. | 2017. 10. 31. | 3.47% | 2.22% | 4.93 | 0.74 | 1.91 |
| 10. | 2017. 11. 30. | 8.73% | 2.81% | 55.89 | 2.10 | 10.84 |
| 11. | 2017. 12. 31. | 5.74% | 0.98% | 20.16 | 0.14 | -1.68 |
| 12. | 2018. 1. 31. | 6.39% | 5.62% | 26.41 | 18.15 | 21.89 |
| 13. | 2018. 2. 28. | -3.50% | -3.89% | 22.57 | 27.59 | 24.95 |
| 14. | 2018. 3. 31. | -7.75% | -2.69% | 81.06 | 16.37 | 36.43 |
| 15. | 2018. 4. 30. | 11.00% | 0.27% | 94.95 | 1.18 | -10.58 |
| 16. | 2018. 5. 31. | 2.00% | 2.16% | 0.56 | 0.64 | 0.60 |
| 17. | 2018. 6. 30. | 2.13% | 0.48% | 0.77 | 0.76 | -0.76 |
| 18. | 2018. 7. 31. | 7.34% | 3.60% | 37.11 | 5.04 | 13.67 |
| 19. | 2018. 8. 31. | 3.85% | 3.03% | 6.76 | 2.78 | 4.34 |
| 20. | 2018. 9. 30. | 3.95% | 0.43% | 7.27 | 0.86 | -2.50 |
| 21. | 2018. 10. 31. | -4.74% | -6.94% | 35.93 | 68.86 | 49.74 |
| 22. | 2018. 11. 30. | 16.35% | 1.79% | 228.06 | 0.18 | 6.46 |
| 23. | 2018. 12. 31. | -18.79% | -9.18% | 401.77 | 111.00 | 211.18 |
| 24. | 2019. 1. 31. | 10.51% | 7.87% | 85.70 | 42.39 | 60.27 |
| 25. | 2019. 2. 28. | -3.13% | 2.97% | 19.20 | 2.61 | -7.08 |
| 26. | 2019. 3. 31. | -12.58% | 1.79% | 191.45 | 0.19 | -6.01 |
| 27. | 2019. 4. 30. | -4.39% | 3.93% | 31.88 | 6.62 | -14.53 |
| 28. | 2019. 5. 31. | -17.77% | -6.58% | 361.90 | 62.97 | 150.96 |
| 29. | 2019. 6. 30. | 16.81% | 6.89% | 242.16 | 30.64 | 86.14 |
| 30. | 2019. 7. 31. | 0.64% | 1.31% | 0.38 | 0.00 | 0.03 |
| 31. | 2019. 8. 31. | -26.99% | -1.81% | 797.92 | 10.03 | 89.46 |
| 32. | 2019. 9. 30. | 11.75% | 1.72% | 110.10 | 0.13 | 3.78 |
| 33. | 2019. 10. 31. | -3.02% | 2.04% | 18.29 | 0.47 | -2.93 |
| 34. | 2019. 11. 30. | -4.18% | 3.40% | 29.46 | 4.19 | -11.11 |
| 35. | 2019. 12. 31. | 13.86% | 2.86% | 158.90 | 2.25 | 18.92 |
| 36. | 2020. 1. 31. | -8.32% | -0.16% | 91.59 | 2.31 | 14.55 |
| 37. | 2020. 2. 29. | -14.16% | -8.41% | 237.65 | 95.43 | 150.60 |
| 38. | 2020. 3. 31. | -36.17% | -12.51% | 1,400.56 | 192.37 | 519.07 |
| 39. | 2020. 4. 30. | 6.38% | 12.68% | 26.26 | 128.29 | 58.04 |
| 40. | 2020. 5. 31. | 5.04% | 4.53% | 14.34 | 10.05 | 12.00 |
| 41. | 2020. 6. 30. | 3.89% | 1.84% | 6.94 | 0.23 | 1.27 |
| 42. | 2020. 7. 31. | 7.67% | 5.51% | 41.23 | 17.24 | 26.66 |
| 43. | 2020. 8. 31. | 35.34% | 7.01% | 1,161.80 | 31.91 | 192.53 |
| 44. | 2020. 9. 30. | 0.49% | -3.92% | 0.58 | 27.89 | 4.01 |
| 45. | 2020. 10. 31. | 1.26% | -2.77% | 0.00 | 17.01 | -0.03 |
| 46. | 2020. 11. 30. | 18.70% | 10.75% | 304.51 | 88.30 | 163.97 |
| 47. | 2020. 12. 31. | 5.01% | 3.71% | 14.11 | 5.54 | 8.84 |
| 48. | 2021. 1. 31. | 12.82% | -1.11% | 133.82 | 6.11 | -28.59 |
| 49. | 2021. 2. 28. | 13.25% | 2.61% | 143.97 | 1.57 | 15.01 |
| 50. | 2021. 3. 31. | 7.69% | 4.24% | 41.40 | 8.33 | 18.57 |
| 51. | 2021. 4. 30. | 11.29% | 5.24% | 100.83 | 15.09 | 39.01 |
| 52. | 2021. 5. 31. | 2.73% | 0.55% | 2.18 | 0.65 | -1.19 |
| 53. | 2021. 6. 30. | -11.50% | 2.22% | 162.55 | 0.75 | -11.01 |
| 54. | 2021. 7. 31. | -2.13% | 2.27% | 11.45 | 0.84 | -3.10 |
| 55. | 2021. 8. 31. | 3.04% | 2.90% | 3.20 | 2.38 | 2.76 |
| 56. | 2021. 9. 30. | 11.23% | -4.76% | 99.62 | 37.39 | -61.03 |
| 57. | 2021. 10. 31. | 16.38% | 6.91% | 228.76 | 30.87 | 84.04 |
| 58. | 2021. 11. 30. | -17.68% | -0.83% | 358.48 | 4.80 | 41.49 |
| 59. | 2021. 12. 31. | 15.04% | 4.36% | 189.96 | 9.02 | 41.39 |
| 합계 (Σ): | 8,684.53 | 1,164.17 | 2,070.45 | |||
모두 보기
분산MOS = Σ(RMOS,t–RMOS)2 ÷ (59 – 1)
= 8,684.53 ÷ (59 – 1)
= 149.73
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산MOS, S&P 500 = Σ(RMOS,t–RMOS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,070.45 ÷ (59 – 1)
= 35.70
체계적인 위험 추정 (β)
| 분산MOS | 149.73 |
| 분산S&P 500 | 20.07 |
| 공분산MOS, S&P 500 | 35.70 |
| 상관 계수MOS, S&P 5001 | 0.65 |
| βMOS2 | 1.78 |
| αMOS3 | -1.16% |
계산
1 상관 계수MOS, S&P 500
= 공분산MOS, S&P 500 ÷ (표준 편차MOS × 표준 편차S&P 500)
= 35.70 ÷ (12.24% × 4.48%)
= 0.65
2 βMOS
= 공분산MOS, S&P 500 ÷ 분산S&P 500
= 35.70 ÷ 20.07
= 1.78
3 αMOS
= 평균의MOS – βMOS × 평균의S&P 500
= 1.25% – 1.78 × 1.36%
= -1.16%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험Mosaic | βMOS | 1.78 |
| Mosaic 보통주에 대한 예상 수익률3 | E(RMOS) | 22.57% |
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(RMOS) = RF + βMOS [E(RM) – RF]
= 4.91% + 1.78 [14.84% – 4.91%]
= 22.57%