자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Apple보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Apple Inc., 월별 수익률
| Apple Inc. (AAPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AAPL,t1 | 피제수AAPL,t1 | RAAPL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 10. 31. | $62.19 | 3,037.56 | ||||
| 1. | 2019. 11. 30. | $66.81 | $0.1925 | 7.74% | 3,140.98 | 3.40% |
| 2. | 2019. 12. 31. | $73.41 | 9.88% | 3,230.78 | 2.86% | |
| 3. | 2020. 1. 31. | $77.38 | 5.41% | 3,225.52 | -0.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2025. 8. 31. | $232.14 | $0.26 | 11.96% | 6,460.26 | 1.91% |
| 71. | 2025. 9. 30. | $254.63 | 9.69% | 6,688.46 | 3.53% | |
| 평균의 (R): | 2.38% | 1.24% | ||||
| 표준 편차: | 8.13% | 4.98% | ||||
| Apple Inc. (AAPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값AAPL,t1 | 피제수AAPL,t1 | RAAPL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 10. 31. | $62.19 | 3,037.56 | ||||
| 1. | 2019. 11. 30. | $66.81 | $0.1925 | 7.74% | 3,140.98 | 3.40% |
| 2. | 2019. 12. 31. | $73.41 | 9.88% | 3,230.78 | 2.86% | |
| 3. | 2020. 1. 31. | $77.38 | 5.41% | 3,225.52 | -0.16% | |
| 4. | 2020. 2. 29. | $68.34 | $0.1925 | -11.43% | 2,954.22 | -8.41% |
| 5. | 2020. 3. 31. | $63.57 | -6.98% | 2,584.59 | -12.51% | |
| 6. | 2020. 4. 30. | $73.45 | 15.54% | 2,912.43 | 12.68% | |
| 7. | 2020. 5. 31. | $79.49 | $0.205 | 8.50% | 3,044.31 | 4.53% |
| 8. | 2020. 6. 30. | $91.20 | 14.73% | 3,100.29 | 1.84% | |
| 9. | 2020. 7. 31. | $106.26 | 16.51% | 3,271.12 | 5.51% | |
| 10. | 2020. 8. 31. | $129.04 | $0.205 | 21.63% | 3,500.31 | 7.01% |
| 11. | 2020. 9. 30. | $115.81 | -10.25% | 3,363.00 | -3.92% | |
| 12. | 2020. 10. 31. | $108.86 | -6.00% | 3,269.96 | -2.77% | |
| 13. | 2020. 11. 30. | $119.05 | $0.205 | 9.55% | 3,621.63 | 10.75% |
| 14. | 2020. 12. 31. | $132.69 | 11.46% | 3,756.07 | 3.71% | |
| 15. | 2021. 1. 31. | $131.96 | -0.55% | 3,714.24 | -1.11% | |
| 16. | 2021. 2. 28. | $121.26 | $0.205 | -7.95% | 3,811.15 | 2.61% |
| 17. | 2021. 3. 31. | $122.15 | 0.73% | 3,972.89 | 4.24% | |
| 18. | 2021. 4. 30. | $131.46 | 7.62% | 4,181.17 | 5.24% | |
| 19. | 2021. 5. 31. | $124.61 | $0.22 | -5.04% | 4,204.11 | 0.55% |
| 20. | 2021. 6. 30. | $136.96 | 9.91% | 4,297.50 | 2.22% | |
| 21. | 2021. 7. 31. | $145.86 | 6.50% | 4,395.26 | 2.27% | |
| 22. | 2021. 8. 31. | $151.83 | $0.22 | 4.24% | 4,522.68 | 2.90% |
| 23. | 2021. 9. 30. | $141.50 | -6.80% | 4,307.54 | -4.76% | |
| 24. | 2021. 10. 31. | $149.80 | 5.87% | 4,605.38 | 6.91% | |
| 25. | 2021. 11. 30. | $165.30 | $0.22 | 10.49% | 4,567.00 | -0.83% |
| 26. | 2021. 12. 31. | $177.57 | 7.42% | 4,766.18 | 4.36% | |
| 27. | 2022. 1. 31. | $174.78 | -1.57% | 4,515.55 | -5.26% | |
| 28. | 2022. 2. 28. | $165.12 | $0.22 | -5.40% | 4,373.94 | -3.14% |
| 29. | 2022. 3. 31. | $174.61 | 5.75% | 4,530.41 | 3.58% | |
| 30. | 2022. 4. 30. | $157.65 | -9.71% | 4,131.93 | -8.80% | |
| 31. | 2022. 5. 31. | $148.84 | $0.23 | -5.44% | 4,132.15 | 0.01% |
| 32. | 2022. 6. 30. | $136.72 | -8.14% | 3,785.38 | -8.39% | |
| 33. | 2022. 7. 31. | $162.51 | 18.86% | 4,130.29 | 9.11% | |
| 34. | 2022. 8. 31. | $157.22 | $0.23 | -3.11% | 3,955.00 | -4.24% |
| 35. | 2022. 9. 30. | $138.20 | -12.10% | 3,585.62 | -9.34% | |
| 36. | 2022. 10. 31. | $153.34 | 10.96% | 3,871.98 | 7.99% | |
| 37. | 2022. 11. 30. | $148.03 | $0.23 | -3.31% | 4,080.11 | 5.38% |
| 38. | 2022. 12. 31. | $129.93 | -12.23% | 3,839.50 | -5.90% | |
| 39. | 2023. 1. 31. | $144.29 | 11.05% | 4,076.60 | 6.18% | |
| 40. | 2023. 2. 28. | $147.41 | $0.23 | 2.32% | 3,970.15 | -2.61% |
| 41. | 2023. 3. 31. | $164.90 | 11.86% | 4,109.31 | 3.51% | |
| 42. | 2023. 4. 30. | $169.68 | 2.90% | 4,169.48 | 1.46% | |
| 43. | 2023. 5. 31. | $177.25 | $0.24 | 4.60% | 4,179.83 | 0.25% |
| 44. | 2023. 6. 30. | $193.97 | 9.43% | 4,376.86 | 4.71% | |
| 45. | 2023. 7. 31. | $196.45 | 1.28% | 4,588.96 | 4.85% | |
| 46. | 2023. 8. 31. | $187.87 | $0.24 | -4.25% | 4,507.66 | -1.77% |
| 47. | 2023. 9. 30. | $171.21 | -8.87% | 4,288.05 | -4.87% | |
| 48. | 2023. 10. 31. | $170.77 | -0.26% | 4,193.80 | -2.20% | |
| 49. | 2023. 11. 30. | $189.95 | $0.24 | 11.37% | 4,567.80 | 8.92% |
| 50. | 2023. 12. 31. | $192.53 | 1.36% | 4,769.83 | 4.42% | |
| 51. | 2024. 1. 31. | $184.40 | -4.22% | 4,845.65 | 1.59% | |
| 52. | 2024. 2. 29. | $180.75 | $0.24 | -1.85% | 5,096.27 | 5.17% |
| 53. | 2024. 3. 31. | $171.48 | -5.13% | 5,254.35 | 3.10% | |
| 54. | 2024. 4. 30. | $170.33 | -0.67% | 5,035.69 | -4.16% | |
| 55. | 2024. 5. 31. | $192.25 | $0.25 | 13.02% | 5,277.51 | 4.80% |
| 56. | 2024. 6. 30. | $210.62 | 9.56% | 5,460.48 | 3.47% | |
| 57. | 2024. 7. 31. | $222.08 | 5.44% | 5,522.30 | 1.13% | |
| 58. | 2024. 8. 31. | $229.00 | $0.25 | 3.23% | 5,648.40 | 2.28% |
| 59. | 2024. 9. 30. | $233.00 | 1.75% | 5,762.48 | 2.02% | |
| 60. | 2024. 10. 31. | $225.91 | -3.04% | 5,705.45 | -0.99% | |
| 61. | 2024. 11. 30. | $237.33 | $0.25 | 5.17% | 6,032.38 | 5.73% |
| 62. | 2024. 12. 31. | $250.42 | 5.52% | 5,881.63 | -2.50% | |
| 63. | 2025. 1. 31. | $236.00 | -5.76% | 6,040.53 | 2.70% | |
| 64. | 2025. 2. 28. | $241.84 | $0.25 | 2.58% | 5,954.50 | -1.42% |
| 65. | 2025. 3. 31. | $222.13 | -8.15% | 5,611.85 | -5.75% | |
| 66. | 2025. 4. 30. | $212.50 | -4.34% | 5,569.06 | -0.76% | |
| 67. | 2025. 5. 31. | $200.85 | $0.26 | -5.36% | 5,911.69 | 6.15% |
| 68. | 2025. 6. 30. | $205.17 | 2.15% | 6,204.95 | 4.96% | |
| 69. | 2025. 7. 31. | $207.57 | 1.17% | 6,339.39 | 2.17% | |
| 70. | 2025. 8. 31. | $232.14 | $0.26 | 11.96% | 6,460.26 | 1.91% |
| 71. | 2025. 9. 30. | $254.63 | 9.69% | 6,688.46 | 3.53% | |
| 평균의 (R): | 2.38% | 1.24% | ||||
| 표준 편차: | 8.13% | 4.98% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 AAPL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Apple Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RAAPL,t | RS&P 500,t | (RAAPL,t–RAAPL)2 | (RS&P 500,t–RS&P 500)2 | (RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 11. 30. | 7.74% | 3.40% | 28.74 | 4.68 | 11.60 |
| 2. | 2019. 12. 31. | 9.88% | 2.86% | 56.27 | 2.62 | 12.14 |
| 3. | 2020. 1. 31. | 5.41% | -0.16% | 9.19 | 1.97 | -4.25 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2025. 8. 31. | 11.96% | 1.91% | 91.87 | 0.44 | 6.38 |
| 71. | 2025. 9. 30. | 9.69% | 3.53% | 53.45 | 5.25 | 16.75 |
| 합계 (Σ): | 4,630.57 | 1,734.96 | 2,029.19 | |||
| t | 날짜 | RAAPL,t | RS&P 500,t | (RAAPL,t–RAAPL)2 | (RS&P 500,t–RS&P 500)2 | (RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 11. 30. | 7.74% | 3.40% | 28.74 | 4.68 | 11.60 |
| 2. | 2019. 12. 31. | 9.88% | 2.86% | 56.27 | 2.62 | 12.14 |
| 3. | 2020. 1. 31. | 5.41% | -0.16% | 9.19 | 1.97 | -4.25 |
| 4. | 2020. 2. 29. | -11.43% | -8.41% | 190.75 | 93.16 | 133.30 |
| 5. | 2020. 3. 31. | -6.98% | -12.51% | 87.55 | 189.14 | 128.68 |
| 6. | 2020. 4. 30. | 15.54% | 12.68% | 173.31 | 130.96 | 150.65 |
| 7. | 2020. 5. 31. | 8.50% | 4.53% | 37.52 | 10.81 | 20.14 |
| 8. | 2020. 6. 30. | 14.73% | 1.84% | 152.63 | 0.36 | 7.39 |
| 9. | 2020. 7. 31. | 16.51% | 5.51% | 199.82 | 18.23 | 60.35 |
| 10. | 2020. 8. 31. | 21.63% | 7.01% | 370.70 | 33.24 | 111.01 |
| 11. | 2020. 9. 30. | -10.25% | -3.92% | 159.51 | 26.66 | 65.22 |
| 12. | 2020. 10. 31. | -6.00% | -2.77% | 70.20 | 16.06 | 33.58 |
| 13. | 2020. 11. 30. | 9.55% | 10.75% | 51.43 | 90.51 | 68.23 |
| 14. | 2020. 12. 31. | 11.46% | 3.71% | 82.45 | 6.11 | 22.44 |
| 15. | 2021. 1. 31. | -0.55% | -1.11% | 8.57 | 5.54 | 6.89 |
| 16. | 2021. 2. 28. | -7.95% | 2.61% | 106.72 | 1.87 | -14.14 |
| 17. | 2021. 3. 31. | 0.73% | 4.24% | 2.70 | 9.02 | -4.93 |
| 18. | 2021. 4. 30. | 7.62% | 5.24% | 27.51 | 16.01 | 20.99 |
| 19. | 2021. 5. 31. | -5.04% | 0.55% | 55.07 | 0.48 | 5.14 |
| 20. | 2021. 6. 30. | 9.91% | 2.22% | 56.76 | 0.96 | 7.39 |
| 21. | 2021. 7. 31. | 6.50% | 2.27% | 16.98 | 1.07 | 4.26 |
| 22. | 2021. 8. 31. | 4.24% | 2.90% | 3.48 | 2.75 | 3.10 |
| 23. | 2021. 9. 30. | -6.80% | -4.76% | 84.29 | 35.97 | 55.06 |
| 24. | 2021. 10. 31. | 5.87% | 6.91% | 12.17 | 32.19 | 19.79 |
| 25. | 2021. 11. 30. | 10.49% | -0.83% | 65.88 | 4.30 | -16.84 |
| 26. | 2021. 12. 31. | 7.42% | 4.36% | 25.46 | 9.74 | 15.74 |
| 27. | 2022. 1. 31. | -1.57% | -5.26% | 15.59 | 42.24 | 25.66 |
| 28. | 2022. 2. 28. | -5.40% | -3.14% | 60.50 | 19.16 | 34.04 |
| 29. | 2022. 3. 31. | 5.75% | 3.58% | 11.36 | 5.46 | 7.87 |
| 30. | 2022. 4. 30. | -9.71% | -8.80% | 146.18 | 100.73 | 121.34 |
| 31. | 2022. 5. 31. | -5.44% | 0.01% | 61.15 | 1.53 | 9.66 |
| 32. | 2022. 6. 30. | -8.14% | -8.39% | 110.67 | 92.79 | 101.34 |
| 33. | 2022. 7. 31. | 18.86% | 9.11% | 271.79 | 61.95 | 129.76 |
| 34. | 2022. 8. 31. | -3.11% | -4.24% | 30.15 | 30.08 | 30.12 |
| 35. | 2022. 9. 30. | -12.10% | -9.34% | 209.52 | 111.94 | 153.15 |
| 36. | 2022. 10. 31. | 10.96% | 7.99% | 73.58 | 45.50 | 57.86 |
| 37. | 2022. 11. 30. | -3.31% | 5.38% | 32.38 | 17.09 | -23.53 |
| 38. | 2022. 12. 31. | -12.23% | -5.90% | 213.29 | 50.95 | 104.25 |
| 39. | 2023. 1. 31. | 11.05% | 6.18% | 75.25 | 24.35 | 42.81 |
| 40. | 2023. 2. 28. | 2.32% | -2.61% | 0.00 | 14.84 | 0.21 |
| 41. | 2023. 3. 31. | 11.86% | 3.51% | 90.02 | 5.13 | 21.48 |
| 42. | 2023. 4. 30. | 2.90% | 1.46% | 0.27 | 0.05 | 0.12 |
| 43. | 2023. 5. 31. | 4.60% | 0.25% | 4.95 | 0.99 | -2.21 |
| 44. | 2023. 6. 30. | 9.43% | 4.71% | 49.78 | 12.06 | 24.51 |
| 45. | 2023. 7. 31. | 1.28% | 4.85% | 1.21 | 13.00 | -3.96 |
| 46. | 2023. 8. 31. | -4.25% | -1.77% | 43.86 | 9.07 | 19.95 |
| 47. | 2023. 9. 30. | -8.87% | -4.87% | 126.45 | 37.37 | 68.74 |
| 48. | 2023. 10. 31. | -0.26% | -2.20% | 6.94 | 11.82 | 9.06 |
| 49. | 2023. 11. 30. | 11.37% | 8.92% | 80.91 | 58.94 | 69.05 |
| 50. | 2023. 12. 31. | 1.36% | 4.42% | 1.04 | 10.13 | -3.24 |
| 51. | 2024. 1. 31. | -4.22% | 1.59% | 43.56 | 0.12 | -2.30 |
| 52. | 2024. 2. 29. | -1.85% | 5.17% | 17.86 | 15.46 | -16.62 |
| 53. | 2024. 3. 31. | -5.13% | 3.10% | 56.34 | 3.46 | -13.97 |
| 54. | 2024. 4. 30. | -0.67% | -4.16% | 9.29 | 29.18 | 16.47 |
| 55. | 2024. 5. 31. | 13.02% | 4.80% | 113.18 | 12.68 | 37.89 |
| 56. | 2024. 6. 30. | 9.56% | 3.47% | 51.52 | 4.96 | 15.98 |
| 57. | 2024. 7. 31. | 5.44% | 1.13% | 9.39 | 0.01 | -0.33 |
| 58. | 2024. 8. 31. | 3.23% | 2.28% | 0.72 | 1.09 | 0.89 |
| 59. | 2024. 9. 30. | 1.75% | 2.02% | 0.40 | 0.61 | -0.49 |
| 60. | 2024. 10. 31. | -3.04% | -0.99% | 29.38 | 4.97 | 12.09 |
| 61. | 2024. 11. 30. | 5.17% | 5.73% | 7.78 | 20.15 | 12.52 |
| 62. | 2024. 12. 31. | 5.52% | -2.50% | 9.85 | 13.99 | -11.74 |
| 63. | 2025. 1. 31. | -5.76% | 2.70% | 66.19 | 2.13 | -11.88 |
| 64. | 2025. 2. 28. | 2.58% | -1.42% | 0.04 | 7.10 | -0.54 |
| 65. | 2025. 3. 31. | -8.15% | -5.75% | 110.82 | 48.93 | 73.64 |
| 66. | 2025. 4. 30. | -4.34% | -0.76% | 45.06 | 4.01 | 13.45 |
| 67. | 2025. 5. 31. | -5.36% | 6.15% | 59.86 | 24.12 | -38.00 |
| 68. | 2025. 6. 30. | 2.15% | 4.96% | 0.05 | 13.84 | -0.84 |
| 69. | 2025. 7. 31. | 1.17% | 2.17% | 1.46 | 0.86 | -1.12 |
| 70. | 2025. 8. 31. | 11.96% | 1.91% | 91.87 | 0.44 | 6.38 |
| 71. | 2025. 9. 30. | 9.69% | 3.53% | 53.45 | 5.25 | 16.75 |
| 합계 (Σ): | 4,630.57 | 1,734.96 | 2,029.19 | |||
모두 보기
분산AAPL = Σ(RAAPL,t–RAAPL)2 ÷ (71 – 1)
= 4,630.57 ÷ (71 – 1)
= 66.15
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,734.96 ÷ (71 – 1)
= 24.79
공분산AAPL, S&P 500 = Σ(RAAPL,t–RAAPL)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,029.19 ÷ (71 – 1)
= 28.99
체계적인 위험 추정 (β)
| 분산AAPL | 66.15 |
| 분산S&P 500 | 24.79 |
| 공분산AAPL, S&P 500 | 28.99 |
| 상관 계수AAPL, S&P 5001 | 0.72 |
| βAAPL2 | 1.17 |
| αAAPL3 | 0.93% |
계산
1 상관 계수AAPL, S&P 500
= 공분산AAPL, S&P 500 ÷ (표준 편차AAPL × 표준 편차S&P 500)
= 28.99 ÷ (8.13% × 4.98%)
= 0.72
2 βAAPL
= 공분산AAPL, S&P 500 ÷ 분산S&P 500
= 28.99 ÷ 24.79
= 1.17
3 αAAPL
= 평균의AAPL – βAAPL × 평균의S&P 500
= 2.38% – 1.17 × 1.24%
= 0.93%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.69% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.90% |
| 보통주의 체계적 위험Apple | βAAPL | 1.17 |
| Apple 보통주 예상 수익률3 | E(RAAPL) | 16.64% |
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(RAAPL) = RF + βAAPL [E(RM) – RF]
= 4.69% + 1.17 [14.90% – 4.69%]
= 16.64%