자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Mondelēz International보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Mondelēz International Inc., 월별 수익률
| Mondelēz International Inc. (MDLZ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MDLZ,t1 | 피제수MDLZ,t1 | RMDLZ,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $46.26 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $47.16 | 1.95% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $49.92 | $0.26 | 6.40% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $50.85 | 1.86% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $71.06 | 7.33% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $72.43 | $0.425 | 2.53% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.08% | 1.11% | ||||
| 표준 편차: | 5.19% | 5.31% | ||||
| Mondelēz International Inc. (MDLZ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MDLZ,t1 | 피제수MDLZ,t1 | RMDLZ,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $46.26 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $47.16 | 1.95% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $49.92 | $0.26 | 6.40% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $50.85 | 1.86% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $50.85 | 0.00% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $53.90 | $0.26 | 6.51% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $53.49 | -0.76% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $55.22 | 3.23% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $55.32 | $0.285 | 0.70% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $52.45 | -5.19% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $52.54 | 0.17% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $55.08 | $0.285 | 5.38% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $57.38 | 4.18% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $52.80 | -7.98% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $50.08 | $0.285 | -4.61% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $51.44 | 2.72% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $52.12 | 1.32% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $51.13 | $0.285 | -1.35% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $55.49 | 8.53% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $58.42 | 5.28% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $57.45 | $0.315 | -1.12% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $53.12 | -7.54% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $57.45 | 8.15% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $58.47 | $0.315 | 2.32% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $55.44 | -5.18% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $53.16 | -4.11% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $58.53 | $0.315 | 10.69% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $60.81 | 3.90% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $63.53 | 4.47% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $62.44 | $0.315 | -1.22% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $63.26 | 1.31% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $62.07 | -1.88% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $58.18 | $0.35 | -5.70% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $60.74 | 4.40% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $58.94 | -2.96% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $66.31 | $0.35 | 13.10% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $67.03 | 1.09% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $65.48 | -2.31% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $62.78 | $0.35 | -3.59% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $64.48 | 2.71% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $63.56 | -1.43% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $62.09 | $0.35 | -1.76% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $64.04 | 3.14% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $61.86 | -3.40% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $54.83 | $0.385 | -10.74% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $61.48 | 12.13% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $67.61 | 9.97% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $66.65 | $0.385 | -0.85% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $65.44 | -1.82% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $65.18 | -0.40% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $69.72 | $0.385 | 7.56% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $76.72 | 10.04% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $73.41 | -4.31% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $72.94 | $0.385 | -0.12% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $74.13 | 1.63% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $71.26 | -3.87% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $69.40 | $0.425 | -2.01% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $66.21 | -4.60% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $71.06 | 7.33% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $72.43 | $0.425 | 2.53% | 4,769.83 | 4.42% |
| 평균의 (R): | 1.08% | 1.11% | ||||
| 표준 편차: | 5.19% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 MDLZ의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Mondelēz International Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMDLZ,t | RS&P 500,t | (RMDLZ,t–RMDLZ)2 | (RS&P 500,t–RS&P 500)2 | (RMDLZ,t–RMDLZ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 1.95% | 2.97% | 0.75 | 3.49 | 1.61 |
| 2. | 2019. 3. 31. | 6.40% | 1.79% | 28.32 | 0.47 | 3.65 |
| 3. | 2019. 4. 30. | 1.86% | 3.93% | 0.61 | 7.98 | 2.21 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 7.33% | 8.92% | 38.97 | 61.03 | 48.77 |
| 59. | 2023. 12. 31. | 2.53% | 4.42% | 2.08 | 11.00 | 4.79 |
| 합계 (Σ): | 1,563.88 | 1,634.30 | 960.54 | |||
| t | 날짜 | RMDLZ,t | RS&P 500,t | (RMDLZ,t–RMDLZ)2 | (RS&P 500,t–RS&P 500)2 | (RMDLZ,t–RMDLZ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 1.95% | 2.97% | 0.75 | 3.49 | 1.61 |
| 2. | 2019. 3. 31. | 6.40% | 1.79% | 28.32 | 0.47 | 3.65 |
| 3. | 2019. 4. 30. | 1.86% | 3.93% | 0.61 | 7.98 | 2.21 |
| 4. | 2019. 5. 31. | 0.00% | -6.58% | 1.17 | 59.04 | 8.32 |
| 5. | 2019. 6. 30. | 6.51% | 6.89% | 29.45 | 33.49 | 31.41 |
| 6. | 2019. 7. 31. | -0.76% | 1.31% | 3.40 | 0.04 | -0.38 |
| 7. | 2019. 8. 31. | 3.23% | -1.81% | 4.63 | 8.50 | -6.27 |
| 8. | 2019. 9. 30. | 0.70% | 1.72% | 0.15 | 0.37 | -0.24 |
| 9. | 2019. 10. 31. | -5.19% | 2.04% | 39.32 | 0.88 | -5.88 |
| 10. | 2019. 11. 30. | 0.17% | 3.40% | 0.83 | 5.28 | -2.09 |
| 11. | 2019. 12. 31. | 5.38% | 2.86% | 18.44 | 3.07 | 7.53 |
| 12. | 2020. 1. 31. | 4.18% | -0.16% | 9.57 | 1.61 | -3.92 |
| 13. | 2020. 2. 29. | -7.98% | -8.41% | 82.16 | 90.57 | 86.26 |
| 14. | 2020. 3. 31. | -4.61% | -12.51% | 32.42 | 185.44 | 77.54 |
| 15. | 2020. 4. 30. | 2.72% | 12.68% | 2.67 | 134.06 | 18.91 |
| 16. | 2020. 5. 31. | 1.32% | 4.53% | 0.06 | 11.71 | 0.82 |
| 17. | 2020. 6. 30. | -1.35% | 1.84% | 5.93 | 0.54 | -1.78 |
| 18. | 2020. 7. 31. | 8.53% | 5.51% | 55.43 | 19.40 | 32.79 |
| 19. | 2020. 8. 31. | 5.28% | 7.01% | 17.62 | 34.82 | 24.77 |
| 20. | 2020. 9. 30. | -1.12% | -3.92% | 4.86 | 25.29 | 11.08 |
| 21. | 2020. 10. 31. | -7.54% | -2.77% | 74.29 | 15.00 | 33.38 |
| 22. | 2020. 11. 30. | 8.15% | 10.75% | 49.97 | 93.10 | 68.21 |
| 23. | 2020. 12. 31. | 2.32% | 3.71% | 1.54 | 6.79 | 3.24 |
| 24. | 2021. 1. 31. | -5.18% | -1.11% | 39.24 | 4.93 | 13.90 |
| 25. | 2021. 2. 28. | -4.11% | 2.61% | 26.99 | 2.26 | -7.81 |
| 26. | 2021. 3. 31. | 10.69% | 4.24% | 92.39 | 9.85 | 30.16 |
| 27. | 2021. 4. 30. | 3.90% | 5.24% | 7.91 | 17.11 | 11.64 |
| 28. | 2021. 5. 31. | 4.47% | 0.55% | 11.50 | 0.31 | -1.89 |
| 29. | 2021. 6. 30. | -1.22% | 2.22% | 5.30 | 1.24 | -2.57 |
| 30. | 2021. 7. 31. | 1.31% | 2.27% | 0.05 | 1.37 | 0.27 |
| 31. | 2021. 8. 31. | -1.88% | 2.90% | 8.78 | 3.22 | -5.31 |
| 32. | 2021. 9. 30. | -5.70% | -4.76% | 46.04 | 34.37 | 39.78 |
| 33. | 2021. 10. 31. | 4.40% | 6.91% | 11.01 | 33.74 | 19.27 |
| 34. | 2021. 11. 30. | -2.96% | -0.83% | 16.37 | 3.76 | 7.85 |
| 35. | 2021. 12. 31. | 13.10% | 4.36% | 144.38 | 10.60 | 39.12 |
| 36. | 2022. 1. 31. | 1.09% | -5.26% | 0.00 | 40.51 | -0.02 |
| 37. | 2022. 2. 28. | -2.31% | -3.14% | 11.52 | 17.99 | 14.40 |
| 38. | 2022. 3. 31. | -3.59% | 3.58% | 21.82 | 6.11 | -11.54 |
| 39. | 2022. 4. 30. | 2.71% | -8.80% | 2.64 | 98.04 | -16.10 |
| 40. | 2022. 5. 31. | -1.43% | 0.01% | 6.30 | 1.21 | 2.76 |
| 41. | 2022. 6. 30. | -1.76% | -8.39% | 8.09 | 90.21 | 27.02 |
| 42. | 2022. 7. 31. | 3.14% | 9.11% | 4.24 | 64.09 | 16.48 |
| 43. | 2022. 8. 31. | -3.40% | -4.24% | 20.13 | 28.62 | 24.00 |
| 44. | 2022. 9. 30. | -10.74% | -9.34% | 139.81 | 109.11 | 123.51 |
| 45. | 2022. 10. 31. | 12.13% | 7.99% | 122.02 | 47.34 | 76.00 |
| 46. | 2022. 11. 30. | 9.97% | 5.38% | 79.00 | 18.23 | 37.95 |
| 47. | 2022. 12. 31. | -0.85% | -5.90% | 3.74 | 49.04 | 13.54 |
| 48. | 2023. 1. 31. | -1.82% | 6.18% | 8.40 | 25.70 | -14.69 |
| 49. | 2023. 2. 28. | -0.40% | -2.61% | 2.19 | 13.82 | 5.50 |
| 50. | 2023. 3. 31. | 7.56% | 3.51% | 41.91 | 5.76 | 15.53 |
| 51. | 2023. 4. 30. | 10.04% | 1.46% | 80.24 | 0.13 | 3.21 |
| 52. | 2023. 5. 31. | -4.31% | 0.25% | 29.12 | 0.74 | 4.63 |
| 53. | 2023. 6. 30. | -0.12% | 4.71% | 1.44 | 13.02 | -4.32 |
| 54. | 2023. 7. 31. | 1.63% | 4.85% | 0.30 | 13.99 | 2.05 |
| 55. | 2023. 8. 31. | -3.87% | -1.77% | 24.54 | 8.28 | 14.25 |
| 56. | 2023. 9. 30. | -2.01% | -4.87% | 9.59 | 35.73 | 18.51 |
| 57. | 2023. 10. 31. | -4.60% | -2.20% | 32.25 | 10.92 | 18.76 |
| 58. | 2023. 11. 30. | 7.33% | 8.92% | 38.97 | 61.03 | 48.77 |
| 59. | 2023. 12. 31. | 2.53% | 4.42% | 2.08 | 11.00 | 4.79 |
| 합계 (Σ): | 1,563.88 | 1,634.30 | 960.54 | |||
모두 표시
분산MDLZ = Σ(RMDLZ,t–RMDLZ)2 ÷ (59 – 1)
= 1,563.88 ÷ (59 – 1)
= 26.96
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산MDLZ, S&P 500 = Σ(RMDLZ,t–RMDLZ)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 960.54 ÷ (59 – 1)
= 16.56
체계적인 위험 추정 (β)
| 분산MDLZ | 26.96 |
| 분산S&P 500 | 28.18 |
| 공분산MDLZ, S&P 500 | 16.56 |
| 상관 계수MDLZ, S&P 5001 | 0.60 |
| βMDLZ2 | 0.59 |
| αMDLZ3 | 0.43% |
계산
1 상관 계수MDLZ, S&P 500
= 공분산MDLZ, S&P 500 ÷ (표준 편차MDLZ × 표준 편차S&P 500)
= 16.56 ÷ (5.19% × 5.31%)
= 0.60
2 βMDLZ
= 공분산MDLZ, S&P 500 ÷ 분산S&P 500
= 16.56 ÷ 28.18
= 0.59
3 αMDLZ
= 평균의MDLZ – βMDLZ × 평균의S&P 500
= 1.08% – 0.59 × 1.11%
= 0.43%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주의 체계적 위험Mondelēz International | βMDLZ | 0.59 |
| Mondelēz International 보통주의 예상 수익률3 | E(RMDLZ) | 9.97% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RMDLZ) = RF + βMDLZ [E(RM) – RF]
= 4.56% + 0.59 [13.77% – 4.56%]
= 9.97%