자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Marriott보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Marriott International Inc., 월별 수익률
| Marriott International Inc. (MAR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MAR,t1 | 피제수MAR,t1 | RMAR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $74.50 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $83.10 | $0.20 | 11.81% | 2,104.50 | 5.49% |
| 2. | 2015. 3. 31. | $80.32 | -3.35% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $80.05 | -0.34% | 2,085.51 | 0.85% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | $140.36 | $0.48 | 11.29% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $151.43 | 7.89% | 3,230.78 | 2.86% | |
| 평균의 (R): | 1.53% | 0.88% | ||||
| 표준 편차: | 6.56% | 3.45% | ||||
| Marriott International Inc. (MAR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MAR,t1 | 피제수MAR,t1 | RMAR,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2015. 1. 31. | $74.50 | 1,994.99 | ||||
| 1. | 2015. 2. 28. | $83.10 | $0.20 | 11.81% | 2,104.50 | 5.49% |
| 2. | 2015. 3. 31. | $80.32 | -3.35% | 2,067.89 | -1.74% | |
| 3. | 2015. 4. 30. | $80.05 | -0.34% | 2,085.51 | 0.85% | |
| 4. | 2015. 5. 31. | $77.99 | $0.25 | -2.26% | 2,107.39 | 1.05% |
| 5. | 2015. 6. 30. | $74.39 | -4.62% | 2,063.11 | -2.10% | |
| 6. | 2015. 7. 31. | $72.61 | -2.39% | 2,103.84 | 1.97% | |
| 7. | 2015. 8. 31. | $70.66 | $0.25 | -2.34% | 1,972.18 | -6.26% |
| 8. | 2015. 9. 30. | $68.20 | -3.48% | 1,920.03 | -2.64% | |
| 9. | 2015. 10. 31. | $76.78 | 12.58% | 2,079.36 | 8.30% | |
| 10. | 2015. 11. 30. | $70.91 | $0.25 | -7.32% | 2,080.41 | 0.05% |
| 11. | 2015. 12. 31. | $67.04 | -5.46% | 2,043.94 | -1.75% | |
| 12. | 2016. 1. 31. | $61.28 | -8.59% | 1,940.24 | -5.07% | |
| 13. | 2016. 2. 29. | $68.15 | $0.25 | 11.62% | 1,932.23 | -0.41% |
| 14. | 2016. 3. 31. | $71.18 | 4.45% | 2,059.74 | 6.60% | |
| 15. | 2016. 4. 30. | $70.09 | -1.53% | 2,065.30 | 0.27% | |
| 16. | 2016. 5. 31. | $66.04 | $0.30 | -5.35% | 2,096.95 | 1.53% |
| 17. | 2016. 6. 30. | $66.46 | 0.64% | 2,098.86 | 0.09% | |
| 18. | 2016. 7. 31. | $71.70 | 7.88% | 2,173.60 | 3.56% | |
| 19. | 2016. 8. 31. | $71.33 | -0.52% | 2,170.95 | -0.12% | |
| 20. | 2016. 9. 30. | $67.33 | $0.30 | -5.19% | 2,168.27 | -0.12% |
| 21. | 2016. 10. 31. | $68.70 | 2.03% | 2,126.15 | -1.94% | |
| 22. | 2016. 11. 30. | $78.78 | $0.30 | 15.11% | 2,198.81 | 3.42% |
| 23. | 2016. 12. 31. | $82.68 | 4.95% | 2,238.83 | 1.82% | |
| 24. | 2017. 1. 31. | $84.60 | 2.32% | 2,278.87 | 1.79% | |
| 25. | 2017. 2. 28. | $86.99 | $0.30 | 3.18% | 2,363.64 | 3.72% |
| 26. | 2017. 3. 31. | $94.18 | 8.27% | 2,362.72 | -0.04% | |
| 27. | 2017. 4. 30. | $94.42 | 0.25% | 2,384.20 | 0.91% | |
| 28. | 2017. 5. 31. | $107.65 | $0.33 | 14.36% | 2,411.80 | 1.16% |
| 29. | 2017. 6. 30. | $100.31 | -6.82% | 2,423.41 | 0.48% | |
| 30. | 2017. 7. 31. | $104.19 | 3.87% | 2,470.30 | 1.93% | |
| 31. | 2017. 8. 31. | $103.58 | $0.33 | -0.27% | 2,471.65 | 0.05% |
| 32. | 2017. 9. 30. | $110.26 | 6.45% | 2,519.36 | 1.93% | |
| 33. | 2017. 10. 31. | $119.48 | 8.36% | 2,575.26 | 2.22% | |
| 34. | 2017. 11. 30. | $127.00 | $0.33 | 6.57% | 2,647.58 | 2.81% |
| 35. | 2017. 12. 31. | $135.73 | 6.87% | 2,673.61 | 0.98% | |
| 36. | 2018. 1. 31. | $147.34 | 8.55% | 2,823.81 | 5.62% | |
| 37. | 2018. 2. 28. | $141.21 | $0.33 | -3.94% | 2,713.83 | -3.89% |
| 38. | 2018. 3. 31. | $135.98 | -3.70% | 2,640.87 | -2.69% | |
| 39. | 2018. 4. 30. | $136.68 | 0.51% | 2,648.05 | 0.27% | |
| 40. | 2018. 5. 31. | $135.36 | $0.41 | -0.67% | 2,705.27 | 2.16% |
| 41. | 2018. 6. 30. | $126.60 | -6.47% | 2,718.37 | 0.48% | |
| 42. | 2018. 7. 31. | $127.84 | 0.98% | 2,816.29 | 3.60% | |
| 43. | 2018. 8. 31. | $126.47 | $0.41 | -0.75% | 2,901.52 | 3.03% |
| 44. | 2018. 9. 30. | $132.03 | 4.40% | 2,913.98 | 0.43% | |
| 45. | 2018. 10. 31. | $116.89 | -11.47% | 2,711.74 | -6.94% | |
| 46. | 2018. 11. 30. | $115.03 | $0.41 | -1.24% | 2,760.17 | 1.79% |
| 47. | 2018. 12. 31. | $108.56 | -5.62% | 2,506.85 | -9.18% | |
| 48. | 2019. 1. 31. | $114.53 | 5.50% | 2,704.10 | 7.87% | |
| 49. | 2019. 2. 28. | $125.27 | $0.41 | 9.74% | 2,784.49 | 2.97% |
| 50. | 2019. 3. 31. | $125.09 | -0.14% | 2,834.40 | 1.79% | |
| 51. | 2019. 4. 30. | $136.42 | 9.06% | 2,945.83 | 3.93% | |
| 52. | 2019. 5. 31. | $124.84 | $0.48 | -8.14% | 2,752.06 | -6.58% |
| 53. | 2019. 6. 30. | $140.29 | 12.38% | 2,941.76 | 6.89% | |
| 54. | 2019. 7. 31. | $139.06 | -0.88% | 2,980.38 | 1.31% | |
| 55. | 2019. 8. 31. | $126.06 | $0.48 | -9.00% | 2,926.46 | -1.81% |
| 56. | 2019. 9. 30. | $124.37 | -1.34% | 2,976.74 | 1.72% | |
| 57. | 2019. 10. 31. | $126.55 | 1.75% | 3,037.56 | 2.04% | |
| 58. | 2019. 11. 30. | $140.36 | $0.48 | 11.29% | 3,140.98 | 3.40% |
| 59. | 2019. 12. 31. | $151.43 | 7.89% | 3,230.78 | 2.86% | |
| 평균의 (R): | 1.53% | 0.88% | ||||
| 표준 편차: | 6.56% | 3.45% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MAR의 보통주 수익률
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Marriott International Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMAR,t | RS&P 500,t | (RMAR,t–RMAR)2 | (RS&P 500,t–RS&P 500)2 | (RMAR,t–RMAR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 11.81% | 5.49% | 105.66 | 21.25 | 47.39 |
| 2. | 2015. 3. 31. | -3.35% | -1.74% | 23.80 | 6.86 | 12.78 |
| 3. | 2015. 4. 30. | -0.34% | 0.85% | 3.49 | 0.00 | 0.05 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2019. 11. 30. | 11.29% | 3.40% | 95.24 | 6.38 | 24.65 |
| 59. | 2019. 12. 31. | 7.89% | 2.86% | 40.37 | 3.92 | 12.58 |
| 합계 (Σ): | 2,496.73 | 688.77 | 893.73 | |||
| t | 날짜 | RMAR,t | RS&P 500,t | (RMAR,t–RMAR)2 | (RS&P 500,t–RS&P 500)2 | (RMAR,t–RMAR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2015. 2. 28. | 11.81% | 5.49% | 105.66 | 21.25 | 47.39 |
| 2. | 2015. 3. 31. | -3.35% | -1.74% | 23.80 | 6.86 | 12.78 |
| 3. | 2015. 4. 30. | -0.34% | 0.85% | 3.49 | 0.00 | 0.05 |
| 4. | 2015. 5. 31. | -2.26% | 1.05% | 14.39 | 0.03 | -0.65 |
| 5. | 2015. 6. 30. | -4.62% | -2.10% | 37.81 | 8.88 | 18.33 |
| 6. | 2015. 7. 31. | -2.39% | 1.97% | 15.41 | 1.20 | -4.30 |
| 7. | 2015. 8. 31. | -2.34% | -6.26% | 15.01 | 50.94 | 27.65 |
| 8. | 2015. 9. 30. | -3.48% | -2.64% | 25.14 | 12.41 | 17.67 |
| 9. | 2015. 10. 31. | 12.58% | 8.30% | 122.05 | 55.04 | 81.96 |
| 10. | 2015. 11. 30. | -7.32% | 0.05% | 78.37 | 0.69 | 7.34 |
| 11. | 2015. 12. 31. | -5.46% | -1.75% | 48.87 | 6.93 | 18.40 |
| 12. | 2016. 1. 31. | -8.59% | -5.07% | 102.51 | 35.43 | 60.27 |
| 13. | 2016. 2. 29. | 11.62% | -0.41% | 101.72 | 1.67 | -13.03 |
| 14. | 2016. 3. 31. | 4.45% | 6.60% | 8.49 | 32.72 | 16.66 |
| 15. | 2016. 4. 30. | -1.53% | 0.27% | 9.39 | 0.37 | 1.87 |
| 16. | 2016. 5. 31. | -5.35% | 1.53% | 47.38 | 0.43 | -4.50 |
| 17. | 2016. 6. 30. | 0.64% | 0.09% | 0.80 | 0.62 | 0.71 |
| 18. | 2016. 7. 31. | 7.88% | 3.56% | 40.34 | 7.19 | 17.03 |
| 19. | 2016. 8. 31. | -0.52% | -0.12% | 4.20 | 1.00 | 2.05 |
| 20. | 2016. 9. 30. | -5.19% | -0.12% | 45.16 | 1.01 | 6.74 |
| 21. | 2016. 10. 31. | 2.03% | -1.94% | 0.25 | 7.96 | -1.42 |
| 22. | 2016. 11. 30. | 15.11% | 3.42% | 184.31 | 6.44 | 34.46 |
| 23. | 2016. 12. 31. | 4.95% | 1.82% | 11.68 | 0.89 | 3.22 |
| 24. | 2017. 1. 31. | 2.32% | 1.79% | 0.62 | 0.83 | 0.72 |
| 25. | 2017. 2. 28. | 3.18% | 3.72% | 2.71 | 8.07 | 4.68 |
| 26. | 2017. 3. 31. | 8.27% | -0.04% | 45.32 | 0.84 | -6.18 |
| 27. | 2017. 4. 30. | 0.25% | 0.91% | 1.63 | 0.00 | -0.04 |
| 28. | 2017. 5. 31. | 14.36% | 1.16% | 164.57 | 0.08 | 3.57 |
| 29. | 2017. 6. 30. | -6.82% | 0.48% | 69.75 | 0.16 | 3.32 |
| 30. | 2017. 7. 31. | 3.87% | 1.93% | 5.45 | 1.11 | 2.47 |
| 31. | 2017. 8. 31. | -0.27% | 0.05% | 3.25 | 0.68 | 1.49 |
| 32. | 2017. 9. 30. | 6.45% | 1.93% | 24.17 | 1.10 | 5.17 |
| 33. | 2017. 10. 31. | 8.36% | 2.22% | 46.64 | 1.79 | 9.15 |
| 34. | 2017. 11. 30. | 6.57% | 2.81% | 25.37 | 3.72 | 9.72 |
| 35. | 2017. 12. 31. | 6.87% | 0.98% | 28.53 | 0.01 | 0.56 |
| 36. | 2018. 1. 31. | 8.55% | 5.62% | 49.29 | 22.46 | 33.27 |
| 37. | 2018. 2. 28. | -3.94% | -3.89% | 29.91 | 22.79 | 26.11 |
| 38. | 2018. 3. 31. | -3.70% | -2.69% | 27.42 | 12.73 | 18.68 |
| 39. | 2018. 4. 30. | 0.51% | 0.27% | 1.04 | 0.37 | 0.62 |
| 40. | 2018. 5. 31. | -0.67% | 2.16% | 4.83 | 1.64 | -2.82 |
| 41. | 2018. 6. 30. | -6.47% | 0.48% | 64.07 | 0.16 | 3.16 |
| 42. | 2018. 7. 31. | 0.98% | 3.60% | 0.31 | 7.41 | -1.51 |
| 43. | 2018. 8. 31. | -0.75% | 3.03% | 5.22 | 4.61 | -4.90 |
| 44. | 2018. 9. 30. | 4.40% | 0.43% | 8.20 | 0.20 | -1.29 |
| 45. | 2018. 10. 31. | -11.47% | -6.94% | 169.00 | 61.14 | 101.65 |
| 46. | 2018. 11. 30. | -1.24% | 1.79% | 7.69 | 0.82 | -2.52 |
| 47. | 2018. 12. 31. | -5.62% | -9.18% | 51.23 | 101.14 | 71.98 |
| 48. | 2019. 1. 31. | 5.50% | 7.87% | 15.73 | 48.85 | 27.72 |
| 49. | 2019. 2. 28. | 9.74% | 2.97% | 67.28 | 4.38 | 17.17 |
| 50. | 2019. 3. 31. | -0.14% | 1.79% | 2.81 | 0.83 | -1.53 |
| 51. | 2019. 4. 30. | 9.06% | 3.93% | 56.62 | 9.32 | 22.97 |
| 52. | 2019. 5. 31. | -8.14% | -6.58% | 93.50 | 55.61 | 72.11 |
| 53. | 2019. 6. 30. | 12.38% | 6.89% | 117.57 | 36.17 | 65.21 |
| 54. | 2019. 7. 31. | -0.88% | 1.31% | 5.81 | 0.19 | -1.05 |
| 55. | 2019. 8. 31. | -9.00% | -1.81% | 111.01 | 7.23 | 28.32 |
| 56. | 2019. 9. 30. | -1.34% | 1.72% | 8.26 | 0.70 | -2.41 |
| 57. | 2019. 10. 31. | 1.75% | 2.04% | 0.05 | 1.36 | 0.26 |
| 58. | 2019. 11. 30. | 11.29% | 3.40% | 95.24 | 6.38 | 24.65 |
| 59. | 2019. 12. 31. | 7.89% | 2.86% | 40.37 | 3.92 | 12.58 |
| 합계 (Σ): | 2,496.73 | 688.77 | 893.73 | |||
모두 보기
분산MAR = Σ(RMAR,t–RMAR)2 ÷ (59 – 1)
= 2,496.73 ÷ (59 – 1)
= 43.05
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88
공분산MAR, S&P 500 = Σ(RMAR,t–RMAR)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 893.73 ÷ (59 – 1)
= 15.41
체계적인 위험 추정 (β)
| 분산MAR | 43.05 |
| 분산S&P 500 | 11.88 |
| 공분산MAR, S&P 500 | 15.41 |
| 상관 계수MAR, S&P 5001 | 0.68 |
| βMAR2 | 1.30 |
| αMAR3 | 0.39% |
계산
1 상관 계수MAR, S&P 500
= 공분산MAR, S&P 500 ÷ (표준 편차MAR × 표준 편차S&P 500)
= 15.41 ÷ (6.56% × 3.45%)
= 0.68
2 βMAR
= 공분산MAR, S&P 500 ÷ 분산S&P 500
= 15.41 ÷ 11.88
= 1.30
3 αMAR
= 평균의MAR – βMAR × 평균의S&P 500
= 1.53% – 1.30 × 0.88%
= 0.39%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.85% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.71% |
| 보통주의 체계적 위험Marriott | βMAR | 1.30 |
| 메리어트 보통주에 대한 기대 수익률3 | E(RMAR) | 17.64% |
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(RMAR) = RF + βMAR [E(RM) – RF]
= 4.85% + 1.30 [14.71% – 4.85%]
= 17.64%