자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Mastercard보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Mastercard Inc., 월별 수익률
| Mastercard Inc. (MA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MA,t1 | 피제수MA,t1 | RMA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $169.00 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $175.76 | 4.00% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $175.16 | -0.34% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $178.27 | $0.25 | 1.92% | 2,648.05 | 0.27% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $356.40 | 8.60% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $347.73 | -2.43% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.59% | 0.67% | ||||
| 표준 편차: | 8.04% | 5.40% | ||||
| Mastercard Inc. (MA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MA,t1 | 피제수MA,t1 | RMA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $169.00 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $175.76 | 4.00% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $175.16 | -0.34% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $178.27 | $0.25 | 1.92% | 2,648.05 | 0.27% |
| 4. | 2018. 5. 31. | $190.12 | 6.65% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $196.52 | 3.37% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $198.00 | $0.25 | 0.88% | 2,816.29 | 3.60% |
| 7. | 2018. 8. 31. | $215.56 | 8.87% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $222.61 | 3.27% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $197.67 | $0.25 | -11.09% | 2,711.74 | -6.94% |
| 10. | 2018. 11. 30. | $201.07 | 1.72% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $188.65 | -6.18% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $211.13 | $0.33 | 12.09% | 2,704.10 | 7.87% |
| 13. | 2019. 2. 28. | $224.77 | 6.46% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $235.45 | 4.75% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $254.24 | $0.33 | 8.12% | 2,945.83 | 3.93% |
| 16. | 2019. 5. 31. | $251.49 | -1.08% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $264.53 | 5.19% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $272.27 | $0.33 | 3.05% | 2,980.38 | 1.31% |
| 19. | 2019. 8. 31. | $281.37 | 3.34% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $271.57 | -3.48% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $276.81 | $0.33 | 2.05% | 3,037.56 | 2.04% |
| 22. | 2019. 11. 30. | $292.23 | 5.57% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $298.59 | 2.18% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $315.94 | $0.40 | 5.94% | 3,225.52 | -0.16% |
| 25. | 2020. 2. 29. | $290.25 | -8.13% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $241.56 | -16.78% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $274.97 | $0.40 | 14.00% | 2,912.43 | 12.68% |
| 28. | 2020. 5. 31. | $300.89 | 9.43% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $295.70 | -1.72% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $308.53 | $0.40 | 4.47% | 3,271.12 | 5.51% |
| 31. | 2020. 8. 31. | $358.19 | 16.10% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $338.17 | -5.59% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $288.64 | $0.40 | -14.53% | 3,269.96 | -2.77% |
| 34. | 2020. 11. 30. | $336.51 | 16.58% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $356.94 | 6.07% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $316.29 | $0.44 | -11.27% | 3,714.24 | -1.11% |
| 37. | 2021. 2. 28. | $353.85 | 11.88% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $356.05 | 0.62% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $382.06 | $0.44 | 7.43% | 4,181.17 | 5.24% |
| 40. | 2021. 5. 31. | $360.58 | -5.62% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $365.09 | 1.25% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $385.94 | $0.44 | 5.83% | 4,395.26 | 2.27% |
| 43. | 2021. 8. 31. | $346.23 | -10.29% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $347.68 | 0.42% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $335.52 | $0.44 | -3.37% | 4,605.38 | 6.91% |
| 46. | 2021. 11. 30. | $314.92 | -6.14% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $359.32 | 14.10% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $386.38 | $0.49 | 7.67% | 4,515.55 | -5.26% |
| 49. | 2022. 2. 28. | $360.82 | -6.62% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $357.38 | -0.95% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $363.38 | $0.49 | 1.82% | 4,131.93 | -8.80% |
| 52. | 2022. 5. 31. | $357.87 | -1.52% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $315.48 | -11.85% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $353.79 | $0.49 | 12.30% | 4,130.29 | 9.11% |
| 55. | 2022. 8. 31. | $324.37 | -8.32% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $284.34 | -12.34% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $328.18 | $0.49 | 15.59% | 3,871.98 | 7.99% |
| 58. | 2022. 11. 30. | $356.40 | 8.60% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $347.73 | -2.43% | 3,839.50 | -5.90% | |
| 평균의 (R): | 1.59% | 0.67% | ||||
| 표준 편차: | 8.04% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MA의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Mastercard Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMA,t | RS&P 500,t | (RMA,t–RMA)2 | (RS&P 500,t–RS&P 500)2 | (RMA,t–RMA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 4.00% | -3.89% | 5.80 | 20.81 | -10.98 |
| 2. | 2018. 3. 31. | -0.34% | -2.69% | 3.74 | 11.26 | 6.49 |
| 3. | 2018. 4. 30. | 1.92% | 0.27% | 0.11 | 0.16 | -0.13 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 8.60% | 5.38% | 49.10 | 22.17 | 32.99 |
| 59. | 2022. 12. 31. | -2.43% | -5.90% | 16.20 | 43.08 | 26.42 |
| 합계 (Σ): | 3,750.56 | 1,691.48 | 1,838.87 | |||
| t | 날짜 | RMA,t | RS&P 500,t | (RMA,t–RMA)2 | (RS&P 500,t–RS&P 500)2 | (RMA,t–RMA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 4.00% | -3.89% | 5.80 | 20.81 | -10.98 |
| 2. | 2018. 3. 31. | -0.34% | -2.69% | 3.74 | 11.26 | 6.49 |
| 3. | 2018. 4. 30. | 1.92% | 0.27% | 0.11 | 0.16 | -0.13 |
| 4. | 2018. 5. 31. | 6.65% | 2.16% | 25.55 | 2.23 | 7.55 |
| 5. | 2018. 6. 30. | 3.37% | 0.48% | 3.15 | 0.03 | -0.32 |
| 6. | 2018. 7. 31. | 0.88% | 3.60% | 0.51 | 8.62 | -2.09 |
| 7. | 2018. 8. 31. | 8.87% | 3.03% | 52.95 | 5.57 | 17.17 |
| 8. | 2018. 9. 30. | 3.27% | 0.43% | 2.82 | 0.06 | -0.40 |
| 9. | 2018. 10. 31. | -11.09% | -6.94% | 160.86 | 57.87 | 96.48 |
| 10. | 2018. 11. 30. | 1.72% | 1.79% | 0.02 | 1.25 | 0.14 |
| 11. | 2018. 12. 31. | -6.18% | -9.18% | 60.36 | 96.91 | 76.48 |
| 12. | 2019. 1. 31. | 12.09% | 7.87% | 110.23 | 51.87 | 75.61 |
| 13. | 2019. 2. 28. | 6.46% | 2.97% | 23.70 | 5.32 | 11.23 |
| 14. | 2019. 3. 31. | 4.75% | 1.79% | 9.98 | 1.27 | 3.56 |
| 15. | 2019. 4. 30. | 8.12% | 3.93% | 42.62 | 10.66 | 21.31 |
| 16. | 2019. 5. 31. | -1.08% | -6.58% | 7.15 | 52.48 | 19.37 |
| 17. | 2019. 6. 30. | 5.19% | 6.89% | 12.91 | 38.77 | 22.37 |
| 18. | 2019. 7. 31. | 3.05% | 1.31% | 2.13 | 0.42 | 0.94 |
| 19. | 2019. 8. 31. | 3.34% | -1.81% | 3.06 | 6.13 | -4.33 |
| 20. | 2019. 9. 30. | -3.48% | 1.72% | 25.76 | 1.11 | -5.34 |
| 21. | 2019. 10. 31. | 2.05% | 2.04% | 0.21 | 1.89 | 0.63 |
| 22. | 2019. 11. 30. | 5.57% | 3.40% | 15.83 | 7.50 | 10.89 |
| 23. | 2019. 12. 31. | 2.18% | 2.86% | 0.34 | 4.81 | 1.28 |
| 24. | 2020. 1. 31. | 5.94% | -0.16% | 18.94 | 0.69 | -3.61 |
| 25. | 2020. 2. 29. | -8.13% | -8.41% | 94.54 | 82.40 | 88.27 |
| 26. | 2020. 3. 31. | -16.78% | -12.51% | 337.36 | 173.67 | 242.05 |
| 27. | 2020. 4. 30. | 14.00% | 12.68% | 153.87 | 144.43 | 149.07 |
| 28. | 2020. 5. 31. | 9.43% | 4.53% | 61.38 | 14.91 | 30.25 |
| 29. | 2020. 6. 30. | -1.72% | 1.84% | 11.00 | 1.37 | -3.89 |
| 30. | 2020. 7. 31. | 4.47% | 5.51% | 8.31 | 23.46 | 13.96 |
| 31. | 2020. 8. 31. | 16.10% | 7.01% | 210.35 | 40.19 | 91.95 |
| 32. | 2020. 9. 30. | -5.59% | -3.92% | 51.57 | 21.06 | 32.96 |
| 33. | 2020. 10. 31. | -14.53% | -2.77% | 259.86 | 11.79 | 55.34 |
| 34. | 2020. 11. 30. | 16.58% | 10.75% | 224.78 | 101.77 | 151.24 |
| 35. | 2020. 12. 31. | 6.07% | 3.71% | 20.06 | 9.28 | 13.64 |
| 36. | 2021. 1. 31. | -11.27% | -1.11% | 165.31 | 3.17 | 22.89 |
| 37. | 2021. 2. 28. | 11.88% | 2.61% | 105.74 | 3.77 | 19.97 |
| 38. | 2021. 3. 31. | 0.62% | 4.24% | 0.94 | 12.80 | -3.47 |
| 39. | 2021. 4. 30. | 7.43% | 5.24% | 34.07 | 20.94 | 26.71 |
| 40. | 2021. 5. 31. | -5.62% | 0.55% | 52.05 | 0.01 | 0.85 |
| 41. | 2021. 6. 30. | 1.25% | 2.22% | 0.12 | 2.42 | -0.53 |
| 42. | 2021. 7. 31. | 5.83% | 2.27% | 17.97 | 2.59 | 6.82 |
| 43. | 2021. 8. 31. | -10.29% | 2.90% | 141.16 | 4.98 | -26.52 |
| 44. | 2021. 9. 30. | 0.42% | -4.76% | 1.38 | 29.42 | 6.36 |
| 45. | 2021. 10. 31. | -3.37% | 6.91% | 24.63 | 39.03 | -31.01 |
| 46. | 2021. 11. 30. | -6.14% | -0.83% | 59.78 | 2.25 | 11.60 |
| 47. | 2021. 12. 31. | 14.10% | 4.36% | 156.42 | 13.65 | 46.21 |
| 48. | 2022. 1. 31. | 7.67% | -5.26% | 36.91 | 35.11 | -36.00 |
| 49. | 2022. 2. 28. | -6.62% | -3.14% | 67.36 | 14.46 | 31.21 |
| 50. | 2022. 3. 31. | -0.95% | 3.58% | 6.48 | 8.47 | -7.41 |
| 51. | 2022. 4. 30. | 1.82% | -8.80% | 0.05 | 89.54 | -2.12 |
| 52. | 2022. 5. 31. | -1.52% | 0.01% | 9.66 | 0.44 | 2.06 |
| 53. | 2022. 6. 30. | -11.85% | -8.39% | 180.56 | 82.06 | 121.72 |
| 54. | 2022. 7. 31. | 12.30% | 9.11% | 114.63 | 71.32 | 90.42 |
| 55. | 2022. 8. 31. | -8.32% | -4.24% | 98.16 | 24.11 | 48.65 |
| 56. | 2022. 9. 30. | -12.34% | -9.34% | 194.13 | 100.12 | 139.42 |
| 57. | 2022. 10. 31. | 15.59% | 7.99% | 195.96 | 53.58 | 102.46 |
| 58. | 2022. 11. 30. | 8.60% | 5.38% | 49.10 | 22.17 | 32.99 |
| 59. | 2022. 12. 31. | -2.43% | -5.90% | 16.20 | 43.08 | 26.42 |
| 합계 (Σ): | 3,750.56 | 1,691.48 | 1,838.87 | |||
모두 보기
분산MA = Σ(RMA,t–RMA)2 ÷ (59 – 1)
= 3,750.56 ÷ (59 – 1)
= 64.66
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산MA, S&P 500 = Σ(RMA,t–RMA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,838.87 ÷ (59 – 1)
= 31.70
체계적인 위험 추정 (β)
| 분산MA | 64.66 |
| 분산S&P 500 | 29.16 |
| 공분산MA, S&P 500 | 31.70 |
| 상관 계수MA, S&P 5001 | 0.73 |
| βMA2 | 1.09 |
| αMA3 | 0.87% |
계산
1 상관 계수MA, S&P 500
= 공분산MA, S&P 500 ÷ (표준 편차MA × 표준 편차S&P 500)
= 31.70 ÷ (8.04% × 5.40%)
= 0.73
2 βMA
= 공분산MA, S&P 500 ÷ 분산S&P 500
= 31.70 ÷ 29.16
= 1.09
3 αMA
= 평균의MA – βMA × 평균의S&P 500
= 1.59% – 1.09 × 0.67%
= 0.87%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.85% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.71% |
| 보통주의 체계적 위험Mastercard | βMA | 1.09 |
| 마스터카드 보통주의 예상 수익률3 | E(RMA) | 15.57% |
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(RMA) = RF + βMA [E(RM) – RF]
= 4.85% + 1.09 [14.71% – 4.85%]
= 15.57%