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 |
| 2021. 1. 31. | $160.31 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $154.65 | -3.53% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $154.70 | 0.03% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $173.37 | 12.07% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $233.22 | -4.50% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $230.82 | -1.03% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.01% | 1.14% | ||||
| 표준 편차: | 9.02% | 4.37% | ||||
| 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 |
| 2021. 1. 31. | $160.31 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $154.65 | -3.53% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $154.70 | 0.03% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $173.37 | 12.07% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $161.15 | -7.05% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $172.01 | 6.74% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $166.38 | -3.27% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $173.54 | 4.30% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $164.25 | -5.35% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $168.62 | 2.66% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $175.35 | 3.99% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $166.72 | -4.92% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $149.57 | -10.29% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $153.56 | 2.67% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $163.00 | 6.15% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $124.28 | -23.75% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $120.21 | -3.27% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $106.21 | -11.65% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $134.95 | 27.06% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $126.77 | -6.06% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $113.00 | -10.86% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $102.44 | -9.35% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $96.54 | -5.76% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $84.00 | -12.99% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $103.13 | 22.77% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $94.23 | -8.63% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $103.29 | 9.61% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $105.45 | 2.09% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $120.58 | 14.35% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $130.36 | 8.11% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $133.68 | 2.55% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $138.01 | 3.24% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $127.12 | -7.89% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $133.09 | 4.70% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $146.09 | 9.77% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $151.94 | 4.00% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $155.20 | 2.15% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $176.76 | 13.89% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $180.38 | 2.05% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $175.00 | -2.98% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $176.44 | 0.82% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $193.25 | 9.53% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $186.98 | -3.24% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $178.50 | -4.54% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $186.33 | 4.39% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $186.40 | 0.04% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $207.89 | 11.53% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $219.39 | 5.53% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $237.68 | 8.34% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $212.28 | -10.69% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $190.26 | -10.37% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $184.42 | -3.07% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $205.01 | 11.16% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $219.39 | 7.01% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $234.11 | 6.71% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $229.00 | -2.18% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $219.57 | -4.12% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $244.22 | 11.23% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $233.22 | -4.50% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $230.82 | -1.03% | 6,845.50 | -0.05% | |
| 평균의 (R): | 1.01% | 1.14% | ||||
| 표준 편차: | 9.02% | 4.37% | ||||
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. | 2021. 2. 28. | -3.53% | 2.61% | 20.66 | 2.17 | -6.70 |
| 2. | 2021. 3. 31. | 0.03% | 4.24% | 0.97 | 9.66 | -3.05 |
| 3. | 2021. 4. 30. | 12.07% | 5.24% | 122.18 | 16.86 | 45.39 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | -4.50% | 0.13% | 30.46 | 1.01 | 5.55 |
| 59. | 2025. 12. 31. | -1.03% | -0.05% | 4.18 | 1.41 | 2.43 |
| 합계 (Σ): | 4,714.11 | 1,108.23 | 1,523.81 | |||
| 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. | 2021. 2. 28. | -3.53% | 2.61% | 20.66 | 2.17 | -6.70 |
| 2. | 2021. 3. 31. | 0.03% | 4.24% | 0.97 | 9.66 | -3.05 |
| 3. | 2021. 4. 30. | 12.07% | 5.24% | 122.18 | 16.86 | 45.39 |
| 4. | 2021. 5. 31. | -7.05% | 0.55% | 65.02 | 0.35 | 4.74 |
| 5. | 2021. 6. 30. | 6.74% | 2.22% | 32.77 | 1.18 | 6.21 |
| 6. | 2021. 7. 31. | -3.27% | 2.27% | 18.39 | 1.30 | -4.88 |
| 7. | 2021. 8. 31. | 4.30% | 2.90% | 10.81 | 3.11 | 5.80 |
| 8. | 2021. 9. 30. | -5.35% | -4.76% | 40.55 | 34.73 | 37.53 |
| 9. | 2021. 10. 31. | 2.66% | 6.91% | 2.71 | 33.39 | 9.51 |
| 10. | 2021. 11. 30. | 3.99% | -0.83% | 8.86 | 3.88 | -5.86 |
| 11. | 2021. 12. 31. | -4.92% | 4.36% | 35.24 | 10.40 | -19.15 |
| 12. | 2022. 1. 31. | -10.29% | -5.26% | 127.73 | 40.89 | 72.27 |
| 13. | 2022. 2. 28. | 2.67% | -3.14% | 2.73 | 18.25 | -7.06 |
| 14. | 2022. 3. 31. | 6.15% | 3.58% | 26.34 | 5.96 | 12.53 |
| 15. | 2022. 4. 30. | -23.75% | -8.80% | 613.53 | 98.64 | 246.01 |
| 16. | 2022. 5. 31. | -3.27% | 0.01% | 18.40 | 1.28 | 4.85 |
| 17. | 2022. 6. 30. | -11.65% | -8.39% | 160.31 | 90.79 | 120.64 |
| 18. | 2022. 7. 31. | 27.06% | 9.11% | 678.32 | 63.61 | 207.72 |
| 19. | 2022. 8. 31. | -6.06% | -4.24% | 50.08 | 28.95 | 38.07 |
| 20. | 2022. 9. 30. | -10.86% | -9.34% | 141.07 | 109.74 | 124.42 |
| 21. | 2022. 10. 31. | -9.35% | 7.99% | 107.33 | 46.93 | -70.97 |
| 22. | 2022. 11. 30. | -5.76% | 5.38% | 45.89 | 17.97 | -28.72 |
| 23. | 2022. 12. 31. | -12.99% | -5.90% | 196.12 | 49.47 | 98.50 |
| 24. | 2023. 1. 31. | 22.77% | 6.18% | 473.45 | 25.39 | 109.65 |
| 25. | 2023. 2. 28. | -8.63% | -2.61% | 93.02 | 14.04 | 36.14 |
| 26. | 2023. 3. 31. | 9.61% | 3.51% | 73.96 | 5.61 | 20.37 |
| 27. | 2023. 4. 30. | 2.09% | 1.46% | 1.16 | 0.11 | 0.35 |
| 28. | 2023. 5. 31. | 14.35% | 0.25% | 177.77 | 0.79 | -11.84 |
| 29. | 2023. 6. 30. | 8.11% | 4.71% | 50.35 | 12.80 | 25.39 |
| 30. | 2023. 7. 31. | 2.55% | 4.85% | 2.35 | 13.76 | 5.68 |
| 31. | 2023. 8. 31. | 3.24% | -1.77% | 4.95 | 8.46 | -6.47 |
| 32. | 2023. 9. 30. | -7.89% | -4.87% | 79.31 | 36.10 | 53.51 |
| 33. | 2023. 10. 31. | 4.70% | -2.20% | 13.55 | 11.12 | -12.27 |
| 34. | 2023. 11. 30. | 9.77% | 8.92% | 76.61 | 60.56 | 68.11 |
| 35. | 2023. 12. 31. | 4.00% | 4.42% | 8.94 | 10.80 | 9.83 |
| 36. | 2024. 1. 31. | 2.15% | 1.59% | 1.28 | 0.21 | 0.51 |
| 37. | 2024. 2. 29. | 13.89% | 5.17% | 165.81 | 16.29 | 51.97 |
| 38. | 2024. 3. 31. | 2.05% | 3.10% | 1.07 | 3.86 | 2.03 |
| 39. | 2024. 4. 30. | -2.98% | -4.16% | 15.98 | 28.06 | 21.18 |
| 40. | 2024. 5. 31. | 0.82% | 4.80% | 0.04 | 13.44 | -0.70 |
| 41. | 2024. 6. 30. | 9.53% | 3.47% | 72.46 | 5.43 | 19.84 |
| 42. | 2024. 7. 31. | -3.24% | 1.13% | 18.14 | 0.00 | 0.02 |
| 43. | 2024. 8. 31. | -4.54% | 2.28% | 30.80 | 1.32 | -6.37 |
| 44. | 2024. 9. 30. | 4.39% | 2.02% | 11.37 | 0.78 | 2.98 |
| 45. | 2024. 10. 31. | 0.04% | -0.99% | 0.96 | 4.52 | 2.08 |
| 46. | 2024. 11. 30. | 11.53% | 5.73% | 110.54 | 21.10 | 48.30 |
| 47. | 2024. 12. 31. | 5.53% | -2.50% | 20.40 | 13.21 | -16.42 |
| 48. | 2025. 1. 31. | 8.34% | 2.70% | 53.61 | 2.45 | 11.46 |
| 49. | 2025. 2. 28. | -10.69% | -1.42% | 136.93 | 6.56 | 29.96 |
| 50. | 2025. 3. 31. | -10.37% | -5.75% | 129.69 | 47.48 | 78.47 |
| 51. | 2025. 4. 30. | -3.07% | -0.76% | 16.68 | 3.60 | 7.75 |
| 52. | 2025. 5. 31. | 11.16% | 6.15% | 103.02 | 25.16 | 50.91 |
| 53. | 2025. 6. 30. | 7.01% | 4.96% | 35.99 | 14.63 | 22.94 |
| 54. | 2025. 7. 31. | 6.71% | 2.17% | 32.43 | 1.06 | 5.87 |
| 55. | 2025. 8. 31. | -2.18% | 1.91% | 10.23 | 0.59 | -2.46 |
| 56. | 2025. 9. 30. | -4.12% | 3.53% | 26.35 | 5.74 | -12.30 |
| 57. | 2025. 10. 31. | 11.23% | 2.27% | 104.28 | 1.28 | 11.57 |
| 58. | 2025. 11. 30. | -4.50% | 0.13% | 30.46 | 1.01 | 5.55 |
| 59. | 2025. 12. 31. | -1.03% | -0.05% | 4.18 | 1.41 | 2.43 |
| 합계 (Σ): | 4,714.11 | 1,108.23 | 1,523.81 | |||
모두 보기
분산AMZN = Σ(RAMZN,t–RAMZN)2 ÷ (59 – 1)
= 4,714.11 ÷ (59 – 1)
= 81.28
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산AMZN, S&P 500 = Σ(RAMZN,t–RAMZN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,523.81 ÷ (59 – 1)
= 26.27
체계적인 위험 추정 (β)
| 분산AMZN | 81.28 |
| 분산S&P 500 | 19.11 |
| 공분산AMZN, S&P 500 | 26.27 |
| 상관 계수AMZN, S&P 5001 | 0.67 |
| βAMZN2 | 1.37 |
| αAMZN3 | -0.55% |
계산
1 상관 계수AMZN, S&P 500
= 공분산AMZN, S&P 500 ÷ (표준 편차AMZN × 표준 편차S&P 500)
= 26.27 ÷ (9.02% × 4.37%)
= 0.67
2 βAMZN
= 공분산AMZN, S&P 500 ÷ 분산S&P 500
= 26.27 ÷ 19.11
= 1.37
3 αAMZN
= 평균의AMZN – βAMZN × 평균의S&P 500
= 1.01% – 1.37 × 1.14%
= -0.55%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.79% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.38% |
| 보통주의 체계적 위험Amazon.com | βAMZN | 1.37 |
| 보통주에 대한 기대 수익률 Amazon.com3 | E(RAMZN) | 22.10% |
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]
= 4.79% + 1.37 [17.38% – 4.79%]
= 22.10%