자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Amazon.com보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Amazon.com Inc., 월별 수익률
| Amazon.com Inc. (AMZN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AMZN,t1 | 피제수AMZN,t1 | RAMZN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $100.44 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $94.19 | -6.22% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $97.49 | 3.50% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $123.70 | 26.88% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $207.89 | 11.53% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $219.39 | 5.53% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.77% | 1.16% | ||||
| 표준 편차: | 9.53% | 5.28% | ||||
| Amazon.com Inc. (AMZN) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AMZN,t1 | 피제수AMZN,t1 | RAMZN,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2020. 1. 31. | $100.44 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $94.19 | -6.22% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $97.49 | 3.50% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $123.70 | 26.88% | 2,912.43 | 12.68% | |
| 4. | 2020. 5. 31. | $122.12 | -1.28% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $137.94 | 12.95% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $158.23 | 14.71% | 3,271.12 | 5.51% | |
| 7. | 2020. 8. 31. | $172.55 | 9.05% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $157.44 | -8.76% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $151.81 | -3.58% | 3,269.96 | -2.77% | |
| 10. | 2020. 11. 30. | $158.40 | 4.34% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $162.85 | 2.81% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $160.31 | -1.56% | 3,714.24 | -1.11% | |
| 13. | 2021. 2. 28. | $154.65 | -3.53% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $154.70 | 0.03% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $173.37 | 12.07% | 4,181.17 | 5.24% | |
| 16. | 2021. 5. 31. | $161.15 | -7.05% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $172.01 | 6.74% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $166.38 | -3.27% | 4,395.26 | 2.27% | |
| 19. | 2021. 8. 31. | $173.54 | 4.30% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $164.25 | -5.35% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $168.62 | 2.66% | 4,605.38 | 6.91% | |
| 22. | 2021. 11. 30. | $175.35 | 3.99% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $166.72 | -4.92% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $149.57 | -10.29% | 4,515.55 | -5.26% | |
| 25. | 2022. 2. 28. | $153.56 | 2.67% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $163.00 | 6.15% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $124.28 | -23.75% | 4,131.93 | -8.80% | |
| 28. | 2022. 5. 31. | $120.21 | -3.27% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $106.21 | -11.65% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $134.95 | 27.06% | 4,130.29 | 9.11% | |
| 31. | 2022. 8. 31. | $126.77 | -6.06% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $113.00 | -10.86% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $102.44 | -9.35% | 3,871.98 | 7.99% | |
| 34. | 2022. 11. 30. | $96.54 | -5.76% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $84.00 | -12.99% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $103.13 | 22.77% | 4,076.60 | 6.18% | |
| 37. | 2023. 2. 28. | $94.23 | -8.63% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $103.29 | 9.61% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $105.45 | 2.09% | 4,169.48 | 1.46% | |
| 40. | 2023. 5. 31. | $120.58 | 14.35% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $130.36 | 8.11% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $133.68 | 2.55% | 4,588.96 | 4.85% | |
| 43. | 2023. 8. 31. | $138.01 | 3.24% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $127.12 | -7.89% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $133.09 | 4.70% | 4,193.80 | -2.20% | |
| 46. | 2023. 11. 30. | $146.09 | 9.77% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $151.94 | 4.00% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $155.20 | 2.15% | 4,845.65 | 1.59% | |
| 49. | 2024. 2. 29. | $176.76 | 13.89% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $180.38 | 2.05% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $175.00 | -2.98% | 5,035.69 | -4.16% | |
| 52. | 2024. 5. 31. | $176.44 | 0.82% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $193.25 | 9.53% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $186.98 | -3.24% | 5,522.30 | 1.13% | |
| 55. | 2024. 8. 31. | $178.50 | -4.54% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $186.33 | 4.39% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $186.40 | 0.04% | 5,705.45 | -0.99% | |
| 58. | 2024. 11. 30. | $207.89 | 11.53% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $219.39 | 5.53% | 5,881.63 | -2.50% | |
| 평균의 (R): | 1.77% | 1.16% | ||||
| 표준 편차: | 9.53% | 5.28% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 AMZN의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Amazon.com Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RAMZN,t | RS&P 500,t | (RAMZN,t–RAMZN)2 | (RS&P 500,t–RS&P 500)2 | (RAMZN,t–RAMZN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.22% | -8.41% | 63.83 | 91.63 | 76.48 |
| 2. | 2020. 3. 31. | 3.50% | -12.51% | 3.02 | 186.96 | -23.74 |
| 3. | 2020. 4. 30. | 26.88% | 12.68% | 630.90 | 132.78 | 289.44 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 11.53% | 5.73% | 95.30 | 20.87 | 44.60 |
| 59. | 2024. 12. 31. | 5.53% | -2.50% | 14.17 | 13.40 | -13.78 |
| 합계 (Σ): | 5,262.12 | 1,618.62 | 1,861.87 | |||
| t | 날짜 | RAMZN,t | RS&P 500,t | (RAMZN,t–RAMZN)2 | (RS&P 500,t–RS&P 500)2 | (RAMZN,t–RAMZN)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2020. 2. 29. | -6.22% | -8.41% | 63.83 | 91.63 | 76.48 |
| 2. | 2020. 3. 31. | 3.50% | -12.51% | 3.02 | 186.96 | -23.74 |
| 3. | 2020. 4. 30. | 26.88% | 12.68% | 630.90 | 132.78 | 289.44 |
| 4. | 2020. 5. 31. | -1.28% | 4.53% | 9.27 | 11.34 | -10.25 |
| 5. | 2020. 6. 30. | 12.95% | 1.84% | 125.16 | 0.46 | 7.58 |
| 6. | 2020. 7. 31. | 14.71% | 5.51% | 167.50 | 18.91 | 56.28 |
| 7. | 2020. 8. 31. | 9.05% | 7.01% | 53.04 | 34.17 | 42.57 |
| 8. | 2020. 9. 30. | -8.76% | -3.92% | 110.75 | 25.85 | 53.50 |
| 9. | 2020. 10. 31. | -3.58% | -2.77% | 28.55 | 15.43 | 20.99 |
| 10. | 2020. 11. 30. | 4.34% | 10.75% | 6.63 | 92.03 | 24.69 |
| 11. | 2020. 12. 31. | 2.81% | 3.71% | 1.09 | 6.51 | 2.66 |
| 12. | 2021. 1. 31. | -1.56% | -1.11% | 11.07 | 5.18 | 7.57 |
| 13. | 2021. 2. 28. | -3.53% | 2.61% | 28.07 | 2.10 | -7.67 |
| 14. | 2021. 3. 31. | 0.03% | 4.24% | 3.01 | 9.50 | -5.35 |
| 15. | 2021. 4. 30. | 12.07% | 5.24% | 106.12 | 16.66 | 42.04 |
| 16. | 2021. 5. 31. | -7.05% | 0.55% | 77.71 | 0.38 | 5.40 |
| 17. | 2021. 6. 30. | 6.74% | 2.22% | 24.72 | 1.12 | 5.27 |
| 18. | 2021. 7. 31. | -3.27% | 2.27% | 25.40 | 1.24 | -5.61 |
| 19. | 2021. 8. 31. | 4.30% | 2.90% | 6.43 | 3.02 | 4.41 |
| 20. | 2021. 9. 30. | -5.35% | -4.76% | 50.70 | 35.02 | 42.14 |
| 21. | 2021. 10. 31. | 2.66% | 6.91% | 0.80 | 33.10 | 5.14 |
| 22. | 2021. 11. 30. | 3.99% | -0.83% | 4.95 | 3.98 | -4.44 |
| 23. | 2021. 12. 31. | -4.92% | 4.36% | 44.74 | 10.24 | -21.40 |
| 24. | 2022. 1. 31. | -10.29% | -5.26% | 145.29 | 41.21 | 77.38 |
| 25. | 2022. 2. 28. | 2.67% | -3.14% | 0.81 | 18.47 | -3.87 |
| 26. | 2022. 3. 31. | 6.15% | 3.58% | 19.19 | 5.84 | 10.58 |
| 27. | 2022. 4. 30. | -23.75% | -8.80% | 651.35 | 99.14 | 254.12 |
| 28. | 2022. 5. 31. | -3.27% | 0.01% | 25.42 | 1.34 | 5.83 |
| 29. | 2022. 6. 30. | -11.65% | -8.39% | 179.92 | 91.26 | 128.14 |
| 30. | 2022. 7. 31. | 27.06% | 9.11% | 639.72 | 63.21 | 201.09 |
| 31. | 2022. 8. 31. | -6.06% | -4.24% | 61.29 | 29.22 | 42.32 |
| 32. | 2022. 9. 30. | -10.86% | -9.34% | 159.50 | 110.27 | 132.62 |
| 33. | 2022. 10. 31. | -9.35% | 7.99% | 123.48 | 46.58 | -75.84 |
| 34. | 2022. 11. 30. | -5.76% | 5.38% | 56.65 | 17.76 | -31.72 |
| 35. | 2022. 12. 31. | -12.99% | -5.90% | 217.75 | 49.82 | 104.16 |
| 36. | 2023. 1. 31. | 22.77% | 6.18% | 441.29 | 25.14 | 105.33 |
| 37. | 2023. 2. 28. | -8.63% | -2.61% | 108.10 | 14.23 | 39.22 |
| 38. | 2023. 3. 31. | 9.61% | 3.51% | 61.59 | 5.49 | 18.39 |
| 39. | 2023. 4. 30. | 2.09% | 1.46% | 0.11 | 0.09 | 0.10 |
| 40. | 2023. 5. 31. | 14.35% | 0.25% | 158.28 | 0.83 | -11.49 |
| 41. | 2023. 6. 30. | 8.11% | 4.71% | 40.24 | 12.62 | 22.54 |
| 42. | 2023. 7. 31. | 2.55% | 4.85% | 0.61 | 13.58 | 2.87 |
| 43. | 2023. 8. 31. | 3.24% | -1.77% | 2.17 | 8.60 | -4.32 |
| 44. | 2023. 9. 30. | -7.89% | -4.87% | 93.27 | 36.40 | 58.27 |
| 45. | 2023. 10. 31. | 4.70% | -2.20% | 8.58 | 11.28 | -9.84 |
| 46. | 2023. 11. 30. | 9.77% | 8.92% | 64.01 | 60.17 | 62.06 |
| 47. | 2023. 12. 31. | 4.00% | 4.42% | 5.01 | 10.64 | 7.30 |
| 48. | 2024. 1. 31. | 2.15% | 1.59% | 0.14 | 0.18 | 0.16 |
| 49. | 2024. 2. 29. | 13.89% | 5.17% | 147.01 | 16.09 | 48.63 |
| 50. | 2024. 3. 31. | 2.05% | 3.10% | 0.08 | 3.77 | 0.55 |
| 51. | 2024. 4. 30. | -2.98% | -4.16% | 22.56 | 28.33 | 25.28 |
| 52. | 2024. 5. 31. | 0.82% | 4.80% | 0.89 | 13.26 | -3.44 |
| 53. | 2024. 6. 30. | 9.53% | 3.47% | 60.22 | 5.32 | 17.89 |
| 54. | 2024. 7. 31. | -3.24% | 1.13% | 25.12 | 0.00 | 0.15 |
| 55. | 2024. 8. 31. | -4.54% | 2.28% | 39.72 | 1.26 | -7.07 |
| 56. | 2024. 9. 30. | 4.39% | 2.02% | 6.86 | 0.74 | 2.25 |
| 57. | 2024. 10. 31. | 0.04% | -0.99% | 2.99 | 4.63 | 3.72 |
| 58. | 2024. 11. 30. | 11.53% | 5.73% | 95.30 | 20.87 | 44.60 |
| 59. | 2024. 12. 31. | 5.53% | -2.50% | 14.17 | 13.40 | -13.78 |
| 합계 (Σ): | 5,262.12 | 1,618.62 | 1,861.87 | |||
모두 보기
분산AMZN = Σ(RAMZN,t–RAMZN)2 ÷ (59 – 1)
= 5,262.12 ÷ (59 – 1)
= 90.73
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산AMZN, S&P 500 = Σ(RAMZN,t–RAMZN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,861.87 ÷ (59 – 1)
= 32.10
체계적인 위험 추정 (β)
| 분산AMZN | 90.73 |
| 분산S&P 500 | 27.91 |
| 공분산AMZN, S&P 500 | 32.10 |
| 상관 계수AMZN, S&P 5001 | 0.64 |
| βAMZN2 | 1.15 |
| αAMZN3 | 0.43% |
계산
1 상관 계수AMZN, S&P 500
= 공분산AMZN, S&P 500 ÷ (표준 편차AMZN × 표준 편차S&P 500)
= 32.10 ÷ (9.53% × 5.28%)
= 0.64
2 βAMZN
= 공분산AMZN, S&P 500 ÷ 분산S&P 500
= 32.10 ÷ 27.91
= 1.15
3 αAMZN
= 평균의AMZN – βAMZN × 평균의S&P 500
= 1.77% – 1.15 × 1.16%
= 0.43%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험Amazon.com | βAMZN | 1.15 |
| 보통주에 대한 기대 수익률 Amazon.com3 | E(RAMZN) | 16.43% |
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(RAMZN) = RF + βAMZN [E(RM) – RF]
= 4.60% + 1.15 [14.89% – 4.60%]
= 16.43%