자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 McDonald’s보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
McDonald’s Corp., 월별 수익률
| McDonald’s Corp. (MCD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MCD,t1 | 피제수MCD,t1 | RMCD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $178.78 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $183.84 | $1.16 | 3.48% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $189.90 | 3.30% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $197.57 | 4.04% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $281.84 | $1.67 | 8.14% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $296.51 | 5.21% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.21% | 1.11% | ||||
| 표준 편차: | 5.57% | 5.31% | ||||
| McDonald’s Corp. (MCD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MCD,t1 | 피제수MCD,t1 | RMCD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $178.78 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $183.84 | $1.16 | 3.48% | 2,784.49 | 2.97% |
| 2. | 2019. 3. 31. | $189.90 | 3.30% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $197.57 | 4.04% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $198.27 | $1.16 | 0.94% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $207.66 | 4.74% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $210.72 | 1.47% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $217.97 | $1.16 | 3.99% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $214.71 | -1.50% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $196.70 | -8.39% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $194.48 | $1.25 | -0.49% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $197.61 | 1.61% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $213.97 | 8.28% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $194.17 | $1.25 | -8.67% | 2,954.22 | -8.41% |
| 14. | 2020. 3. 31. | $165.35 | -14.84% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $187.56 | 13.43% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $186.32 | $1.25 | 0.01% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $184.47 | -0.99% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $194.28 | 5.32% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $213.52 | $1.25 | 10.55% | 3,500.31 | 7.01% |
| 20. | 2020. 9. 30. | $219.49 | 2.80% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $213.00 | -2.96% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $217.44 | $1.29 | 2.69% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $214.58 | -1.32% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $207.84 | -3.14% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $206.14 | $1.29 | -0.20% | 3,811.15 | 2.61% |
| 26. | 2021. 3. 31. | $224.14 | 8.73% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $236.08 | 5.33% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $233.89 | $1.29 | -0.38% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $230.99 | -1.24% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $242.71 | 5.07% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $237.46 | $1.29 | -1.63% | 4,522.68 | 2.90% |
| 32. | 2021. 9. 30. | $241.11 | 1.54% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $245.55 | 1.84% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $244.60 | $1.38 | 0.18% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $268.07 | 9.60% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $259.45 | -3.22% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $244.77 | $1.38 | -5.13% | 4,373.94 | -3.14% |
| 38. | 2022. 3. 31. | $247.28 | 1.03% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $249.16 | 0.76% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $252.21 | 1.22% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $246.88 | $1.38 | -1.57% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $263.37 | 6.68% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $252.28 | $1.38 | -3.69% | 3,955.00 | -4.24% |
| 44. | 2022. 9. 30. | $230.74 | -8.54% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $272.66 | 18.17% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $272.79 | $1.52 | 0.61% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $263.53 | -3.39% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $267.40 | 1.47% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $263.91 | $1.52 | -0.74% | 3,970.15 | -2.61% |
| 50. | 2023. 3. 31. | $279.61 | 5.95% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $295.75 | 5.77% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $285.11 | -3.60% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $298.41 | $1.52 | 5.20% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $293.20 | -1.75% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $281.15 | $1.52 | -3.59% | 4,507.66 | -1.77% |
| 56. | 2023. 9. 30. | $263.44 | -6.30% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $262.17 | -0.48% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $281.84 | $1.67 | 8.14% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $296.51 | 5.21% | 4,769.83 | 4.42% | |
| 평균의 (R): | 1.21% | 1.11% | ||||
| 표준 편차: | 5.57% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 MCD의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
McDonald’s Corp., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMCD,t | RS&P 500,t | (RMCD,t–RMCD)2 | (RS&P 500,t–RS&P 500)2 | (RMCD,t–RMCD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 3.48% | 2.97% | 5.15 | 3.49 | 4.24 |
| 2. | 2019. 3. 31. | 3.30% | 1.79% | 4.35 | 0.47 | 1.43 |
| 3. | 2019. 4. 30. | 4.04% | 3.93% | 8.00 | 7.98 | 7.99 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 8.14% | 8.92% | 48.02 | 61.03 | 54.14 |
| 59. | 2023. 12. 31. | 5.21% | 4.42% | 15.96 | 11.00 | 13.25 |
| 합계 (Σ): | 1,798.52 | 1,634.30 | 1,183.72 | |||
| t | 날짜 | RMCD,t | RS&P 500,t | (RMCD,t–RMCD)2 | (RS&P 500,t–RS&P 500)2 | (RMCD,t–RMCD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 3.48% | 2.97% | 5.15 | 3.49 | 4.24 |
| 2. | 2019. 3. 31. | 3.30% | 1.79% | 4.35 | 0.47 | 1.43 |
| 3. | 2019. 4. 30. | 4.04% | 3.93% | 8.00 | 7.98 | 7.99 |
| 4. | 2019. 5. 31. | 0.94% | -6.58% | 0.07 | 59.04 | 2.06 |
| 5. | 2019. 6. 30. | 4.74% | 6.89% | 12.43 | 33.49 | 20.41 |
| 6. | 2019. 7. 31. | 1.47% | 1.31% | 0.07 | 0.04 | 0.05 |
| 7. | 2019. 8. 31. | 3.99% | -1.81% | 7.73 | 8.50 | -8.11 |
| 8. | 2019. 9. 30. | -1.50% | 1.72% | 7.32 | 0.37 | -1.66 |
| 9. | 2019. 10. 31. | -8.39% | 2.04% | 92.12 | 0.88 | -9.00 |
| 10. | 2019. 11. 30. | -0.49% | 3.40% | 2.90 | 5.28 | -3.92 |
| 11. | 2019. 12. 31. | 1.61% | 2.86% | 0.16 | 3.07 | 0.70 |
| 12. | 2020. 1. 31. | 8.28% | -0.16% | 49.97 | 1.61 | -8.97 |
| 13. | 2020. 2. 29. | -8.67% | -8.41% | 97.60 | 90.57 | 94.02 |
| 14. | 2020. 3. 31. | -14.84% | -12.51% | 257.68 | 185.44 | 218.60 |
| 15. | 2020. 4. 30. | 13.43% | 12.68% | 149.38 | 134.06 | 141.52 |
| 16. | 2020. 5. 31. | 0.01% | 4.53% | 1.45 | 11.71 | -4.12 |
| 17. | 2020. 6. 30. | -0.99% | 1.84% | 4.85 | 0.54 | -1.61 |
| 18. | 2020. 7. 31. | 5.32% | 5.51% | 16.88 | 19.40 | 18.09 |
| 19. | 2020. 8. 31. | 10.55% | 7.01% | 87.17 | 34.82 | 55.09 |
| 20. | 2020. 9. 30. | 2.80% | -3.92% | 2.52 | 25.29 | -7.98 |
| 21. | 2020. 10. 31. | -2.96% | -2.77% | 17.36 | 15.00 | 16.14 |
| 22. | 2020. 11. 30. | 2.69% | 10.75% | 2.19 | 93.10 | 14.28 |
| 23. | 2020. 12. 31. | -1.32% | 3.71% | 6.38 | 6.79 | -6.58 |
| 24. | 2021. 1. 31. | -3.14% | -1.11% | 18.93 | 4.93 | 9.66 |
| 25. | 2021. 2. 28. | -0.20% | 2.61% | 1.98 | 2.26 | -2.12 |
| 26. | 2021. 3. 31. | 8.73% | 4.24% | 56.58 | 9.85 | 23.60 |
| 27. | 2021. 4. 30. | 5.33% | 5.24% | 16.95 | 17.11 | 17.03 |
| 28. | 2021. 5. 31. | -0.38% | 0.55% | 2.53 | 0.31 | 0.89 |
| 29. | 2021. 6. 30. | -1.24% | 2.22% | 6.00 | 1.24 | -2.73 |
| 30. | 2021. 7. 31. | 5.07% | 2.27% | 14.93 | 1.37 | 4.52 |
| 31. | 2021. 8. 31. | -1.63% | 2.90% | 8.07 | 3.22 | -5.10 |
| 32. | 2021. 9. 30. | 1.54% | -4.76% | 0.11 | 34.37 | -1.92 |
| 33. | 2021. 10. 31. | 1.84% | 6.91% | 0.40 | 33.74 | 3.67 |
| 34. | 2021. 11. 30. | 0.18% | -0.83% | 1.07 | 3.76 | 2.01 |
| 35. | 2021. 12. 31. | 9.60% | 4.36% | 70.31 | 10.60 | 27.30 |
| 36. | 2022. 1. 31. | -3.22% | -5.26% | 19.58 | 40.51 | 28.17 |
| 37. | 2022. 2. 28. | -5.13% | -3.14% | 40.15 | 17.99 | 26.88 |
| 38. | 2022. 3. 31. | 1.03% | 3.58% | 0.03 | 6.11 | -0.46 |
| 39. | 2022. 4. 30. | 0.76% | -8.80% | 0.20 | 98.04 | 4.45 |
| 40. | 2022. 5. 31. | 1.22% | 0.01% | 0.00 | 1.21 | -0.02 |
| 41. | 2022. 6. 30. | -1.57% | -8.39% | 7.71 | 90.21 | 26.37 |
| 42. | 2022. 7. 31. | 6.68% | 9.11% | 29.91 | 64.09 | 43.79 |
| 43. | 2022. 8. 31. | -3.69% | -4.24% | 23.98 | 28.62 | 26.20 |
| 44. | 2022. 9. 30. | -8.54% | -9.34% | 95.02 | 109.11 | 101.82 |
| 45. | 2022. 10. 31. | 18.17% | 7.99% | 287.56 | 47.34 | 116.68 |
| 46. | 2022. 11. 30. | 0.61% | 5.38% | 0.37 | 18.23 | -2.58 |
| 47. | 2022. 12. 31. | -3.39% | -5.90% | 21.20 | 49.04 | 32.24 |
| 48. | 2023. 1. 31. | 1.47% | 6.18% | 0.07 | 25.70 | 1.31 |
| 49. | 2023. 2. 28. | -0.74% | -2.61% | 3.79 | 13.82 | 7.24 |
| 50. | 2023. 3. 31. | 5.95% | 3.51% | 22.46 | 5.76 | 11.37 |
| 51. | 2023. 4. 30. | 5.77% | 1.46% | 20.82 | 0.13 | 1.64 |
| 52. | 2023. 5. 31. | -3.60% | 0.25% | 23.11 | 0.74 | 4.12 |
| 53. | 2023. 6. 30. | 5.20% | 4.71% | 15.90 | 13.02 | 14.39 |
| 54. | 2023. 7. 31. | -1.75% | 4.85% | 8.74 | 13.99 | -11.06 |
| 55. | 2023. 8. 31. | -3.59% | -1.77% | 23.05 | 8.28 | 13.82 |
| 56. | 2023. 9. 30. | -6.30% | -4.87% | 56.39 | 35.73 | 44.89 |
| 57. | 2023. 10. 31. | -0.48% | -2.20% | 2.86 | 10.92 | 5.59 |
| 58. | 2023. 11. 30. | 8.14% | 8.92% | 48.02 | 61.03 | 54.14 |
| 59. | 2023. 12. 31. | 5.21% | 4.42% | 15.96 | 11.00 | 13.25 |
| 합계 (Σ): | 1,798.52 | 1,634.30 | 1,183.72 | |||
모두 표시
분산MCD = Σ(RMCD,t–RMCD)2 ÷ (59 – 1)
= 1,798.52 ÷ (59 – 1)
= 31.01
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산MCD, S&P 500 = Σ(RMCD,t–RMCD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,183.72 ÷ (59 – 1)
= 20.41
체계적인 위험 추정 (β)
| 분산MCD | 31.01 |
| 분산S&P 500 | 28.18 |
| 공분산MCD, S&P 500 | 20.41 |
| 상관 계수MCD, S&P 5001 | 0.69 |
| βMCD2 | 0.72 |
| αMCD3 | 0.41% |
계산
1 상관 계수MCD, S&P 500
= 공분산MCD, S&P 500 ÷ (표준 편차MCD × 표준 편차S&P 500)
= 20.41 ÷ (5.57% × 5.31%)
= 0.69
2 βMCD
= 공분산MCD, S&P 500 ÷ 분산S&P 500
= 20.41 ÷ 28.18
= 0.72
3 αMCD
= 평균의MCD – βMCD × 평균의S&P 500
= 1.21% – 0.72 × 1.11%
= 0.41%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.82% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.46% |
| 보통주의 체계적 위험McDonald’s | βMCD | 0.72 |
| 맥도날드 보통주 예상 수익률3 | E(RMCD) | 11.08% |
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(RMCD) = RF + βMCD [E(RM) – RF]
= 4.82% + 0.72 [13.46% – 4.82%]
= 11.08%