자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Chipotle의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
Chipotle Mexican Grill Inc., 월별 수익률
| Chipotle Mexican Grill Inc. (CMG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CMG,t1 | 피제수CMG,t1 | RCMG,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $10.59 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $12.15 | 14.73% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $14.21 | 16.95% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $13.76 | -3.17% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $44.05 | 13.41% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $45.74 | 3.84% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.98% | 1.11% | ||||
| 표준 편차: | 10.06% | 5.31% | ||||
| Chipotle Mexican Grill Inc. (CMG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CMG,t1 | 피제수CMG,t1 | RCMG,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $10.59 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $12.15 | 14.73% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $14.21 | 16.95% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $13.76 | -3.17% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $13.20 | -4.07% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $14.66 | 11.06% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $15.91 | 8.53% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $16.77 | 5.41% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $16.81 | 0.24% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $15.56 | -7.44% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $16.28 | 4.63% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $16.74 | 2.83% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $17.34 | 3.58% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $15.47 | -10.78% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $13.09 | -15.38% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $17.57 | 34.22% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $20.08 | 14.29% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $21.05 | 4.83% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $23.10 | 9.74% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $26.21 | 13.46% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $24.87 | -5.11% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $24.03 | -3.38% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $25.79 | 7.32% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $27.73 | 7.52% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $29.60 | 6.74% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $28.84 | -2.57% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $28.42 | -1.46% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $29.84 | 5.00% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $27.44 | -8.04% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $31.01 | 13.01% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $37.27 | 20.19% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $38.07 | 2.15% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $36.35 | -4.52% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $35.58 | -2.12% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $32.87 | -7.62% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $34.97 | 6.39% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $29.71 | -15.04% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $30.47 | 2.56% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $31.64 | 3.84% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $29.11 | -8.00% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $28.05 | -3.64% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $26.15 | -6.77% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $31.28 | 19.62% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $31.94 | 2.11% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $30.06 | -5.89% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $29.97 | -0.30% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $32.54 | 8.58% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $27.75 | -14.72% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $32.93 | 18.67% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $29.82 | -9.44% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $34.17 | 14.59% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $41.35 | 21.01% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $41.53 | 0.44% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $42.78 | 3.01% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $39.25 | -8.25% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $38.53 | -1.83% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $36.64 | -4.91% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $38.84 | 6.00% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $44.05 | 13.41% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $45.74 | 3.84% | 4,769.83 | 4.42% | |
| 평균의 (R): | 2.98% | 1.11% | ||||
| 표준 편차: | 10.06% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CMG의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Chipotle Mexican Grill Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCMG,t | RS&P 500,t | (RCMG,t–RCMG)2 | (RS&P 500,t–RS&P 500)2 | (RCMG,t–RCMG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 14.73% | 2.97% | 138.00 | 3.49 | 21.93 |
| 2. | 2019. 3. 31. | 16.95% | 1.79% | 195.19 | 0.47 | 9.59 |
| 3. | 2019. 4. 30. | -3.17% | 3.93% | 37.83 | 7.98 | -17.38 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 13.41% | 8.92% | 108.79 | 61.03 | 81.48 |
| 59. | 2023. 12. 31. | 3.84% | 4.42% | 0.73 | 11.00 | 2.83 |
| 합계 (Σ): | 5,864.53 | 1,634.30 | 2,092.35 | |||
| t | 날짜 | RCMG,t | RS&P 500,t | (RCMG,t–RCMG)2 | (RS&P 500,t–RS&P 500)2 | (RCMG,t–RCMG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 14.73% | 2.97% | 138.00 | 3.49 | 21.93 |
| 2. | 2019. 3. 31. | 16.95% | 1.79% | 195.19 | 0.47 | 9.59 |
| 3. | 2019. 4. 30. | -3.17% | 3.93% | 37.83 | 7.98 | -17.38 |
| 4. | 2019. 5. 31. | -4.07% | -6.58% | 49.75 | 59.04 | 54.20 |
| 5. | 2019. 6. 30. | 11.06% | 6.89% | 65.24 | 33.49 | 46.74 |
| 6. | 2019. 7. 31. | 8.53% | 1.31% | 30.72 | 0.04 | 1.15 |
| 7. | 2019. 8. 31. | 5.41% | -1.81% | 5.86 | 8.50 | -7.06 |
| 8. | 2019. 9. 30. | 0.24% | 1.72% | 7.54 | 0.37 | -1.68 |
| 9. | 2019. 10. 31. | -7.44% | 2.04% | 108.57 | 0.88 | -9.77 |
| 10. | 2019. 11. 30. | 4.63% | 3.40% | 2.70 | 5.28 | 3.78 |
| 11. | 2019. 12. 31. | 2.83% | 2.86% | 0.03 | 3.07 | -0.28 |
| 12. | 2020. 1. 31. | 3.58% | -0.16% | 0.36 | 1.61 | -0.76 |
| 13. | 2020. 2. 29. | -10.78% | -8.41% | 189.56 | 90.57 | 131.03 |
| 14. | 2020. 3. 31. | -15.38% | -12.51% | 337.39 | 185.44 | 250.14 |
| 15. | 2020. 4. 30. | 34.22% | 12.68% | 975.99 | 134.06 | 361.72 |
| 16. | 2020. 5. 31. | 14.29% | 4.53% | 127.74 | 11.71 | 38.68 |
| 17. | 2020. 6. 30. | 4.83% | 1.84% | 3.41 | 0.54 | 1.35 |
| 18. | 2020. 7. 31. | 9.74% | 5.51% | 45.63 | 19.40 | 29.75 |
| 19. | 2020. 8. 31. | 13.46% | 7.01% | 109.82 | 34.82 | 61.84 |
| 20. | 2020. 9. 30. | -5.11% | -3.92% | 65.55 | 25.29 | 40.71 |
| 21. | 2020. 10. 31. | -3.38% | -2.77% | 40.47 | 15.00 | 24.63 |
| 22. | 2020. 11. 30. | 7.32% | 10.75% | 18.84 | 93.10 | 41.88 |
| 23. | 2020. 12. 31. | 7.52% | 3.71% | 20.60 | 6.79 | 11.83 |
| 24. | 2021. 1. 31. | 6.74% | -1.11% | 14.14 | 4.93 | -8.35 |
| 25. | 2021. 2. 28. | -2.57% | 2.61% | 30.82 | 2.26 | -8.35 |
| 26. | 2021. 3. 31. | -1.46% | 4.24% | 19.71 | 9.85 | -13.93 |
| 27. | 2021. 4. 30. | 5.00% | 5.24% | 4.05 | 17.11 | 8.33 |
| 28. | 2021. 5. 31. | -8.04% | 0.55% | 121.59 | 0.31 | 6.14 |
| 29. | 2021. 6. 30. | 13.01% | 2.22% | 100.53 | 1.24 | 11.19 |
| 30. | 2021. 7. 31. | 20.19% | 2.27% | 295.95 | 1.37 | 20.11 |
| 31. | 2021. 8. 31. | 2.15% | 2.90% | 0.70 | 3.22 | -1.50 |
| 32. | 2021. 9. 30. | -4.52% | -4.76% | 56.28 | 34.37 | 43.98 |
| 33. | 2021. 10. 31. | -2.12% | 6.91% | 26.03 | 33.74 | -29.64 |
| 34. | 2021. 11. 30. | -7.62% | -0.83% | 112.37 | 3.76 | 20.56 |
| 35. | 2021. 12. 31. | 6.39% | 4.36% | 11.59 | 10.60 | 11.09 |
| 36. | 2022. 1. 31. | -15.04% | -5.26% | 324.91 | 40.51 | 114.72 |
| 37. | 2022. 2. 28. | 2.56% | -3.14% | 0.18 | 17.99 | 1.81 |
| 38. | 2022. 3. 31. | 3.84% | 3.58% | 0.73 | 6.11 | 2.12 |
| 39. | 2022. 4. 30. | -8.00% | -8.80% | 120.56 | 98.04 | 108.72 |
| 40. | 2022. 5. 31. | -3.64% | 0.01% | 43.89 | 1.21 | 7.29 |
| 41. | 2022. 6. 30. | -6.77% | -8.39% | 95.21 | 90.21 | 92.67 |
| 42. | 2022. 7. 31. | 19.62% | 9.11% | 276.69 | 64.09 | 133.17 |
| 43. | 2022. 8. 31. | 2.11% | -4.24% | 0.76 | 28.62 | 4.67 |
| 44. | 2022. 9. 30. | -5.89% | -9.34% | 78.67 | 109.11 | 92.65 |
| 45. | 2022. 10. 31. | -0.30% | 7.99% | 10.78 | 47.34 | -22.59 |
| 46. | 2022. 11. 30. | 8.58% | 5.38% | 31.27 | 18.23 | 23.87 |
| 47. | 2022. 12. 31. | -14.72% | -5.90% | 313.43 | 49.04 | 123.98 |
| 48. | 2023. 1. 31. | 18.67% | 6.18% | 245.96 | 25.70 | 79.50 |
| 49. | 2023. 2. 28. | -9.44% | -2.61% | 154.45 | 13.82 | 46.20 |
| 50. | 2023. 3. 31. | 14.59% | 3.51% | 134.65 | 5.76 | 27.84 |
| 51. | 2023. 4. 30. | 21.01% | 1.46% | 325.04 | 0.13 | 6.46 |
| 52. | 2023. 5. 31. | 0.44% | 0.25% | 6.49 | 0.74 | 2.19 |
| 53. | 2023. 6. 30. | 3.01% | 4.71% | 0.00 | 13.02 | 0.09 |
| 54. | 2023. 7. 31. | -8.25% | 4.85% | 126.23 | 13.99 | -42.02 |
| 55. | 2023. 8. 31. | -1.83% | -1.77% | 23.21 | 8.28 | 13.86 |
| 56. | 2023. 9. 30. | -4.91% | -4.87% | 62.24 | 35.73 | 47.16 |
| 57. | 2023. 10. 31. | 6.00% | -2.20% | 9.12 | 10.92 | -9.98 |
| 58. | 2023. 11. 30. | 13.41% | 8.92% | 108.79 | 61.03 | 81.48 |
| 59. | 2023. 12. 31. | 3.84% | 4.42% | 0.73 | 11.00 | 2.83 |
| 합계 (Σ): | 5,864.53 | 1,634.30 | 2,092.35 | |||
모두 보기
분산CMG = Σ(RCMG,t–RCMG)2 ÷ (59 – 1)
= 5,864.53 ÷ (59 – 1)
= 101.11
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산CMG, S&P 500 = Σ(RCMG,t–RCMG)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,092.35 ÷ (59 – 1)
= 36.07
체계적인 위험 추정 (β)
| 분산CMG | 101.11 |
| 분산S&P 500 | 28.18 |
| 공분산CMG, S&P 500 | 36.07 |
| 상관 계수CMG, S&P 5001 | 0.68 |
| βCMG2 | 1.28 |
| αCMG3 | 1.57% |
계산
1 상관 계수CMG, S&P 500
= 공분산CMG, S&P 500 ÷ (표준 편차CMG × 표준 편차S&P 500)
= 36.07 ÷ (10.06% × 5.31%)
= 0.68
2 βCMG
= 공분산CMG, S&P 500 ÷ 분산S&P 500
= 36.07 ÷ 28.18
= 1.28
3 αCMG
= 평균의CMG – βCMG × 평균의S&P 500
= 2.98% – 1.28 × 1.11%
= 1.57%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.48% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.84% |
| 보통주의 체계적 위험Chipotle | βCMG | 1.28 |
| Chipotle 보통주에 대한 예상 수익률3 | E(RCMG) | 16.47% |
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(RCMG) = RF + βCMG [E(RM) – RF]
= 4.48% + 1.28 [13.84% – 4.48%]
= 16.47%