자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Dell Technologies의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
Dell Technologies Inc., 월별 수익률
| Dell Technologies Inc. (DELL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DELL,t1 | 피제수DELL,t1 | RDELL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 2. 28. | $55.82 | 2,784.49 | ||||
| 1. | 2019. 3. 31. | $58.69 | 5.14% | 2,834.40 | 1.79% | |
| 2. | 2019. 4. 30. | $67.41 | 14.86% | 2,945.83 | 3.93% | |
| 3. | 2019. 5. 31. | $59.55 | -11.66% | 2,752.06 | -6.58% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 12. 31. | $115.24 | -9.68% | 5,881.63 | -2.50% | |
| 71. | 2025. 1. 31. | $103.60 | $0.445 | -9.71% | 6,040.53 | 2.70% |
| 평균의 (R): | 2.38% | 1.22% | ||||
| 표준 편차: | 9.43% | 4.99% | ||||
| Dell Technologies Inc. (DELL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값DELL,t1 | 피제수DELL,t1 | RDELL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 2. 28. | $55.82 | 2,784.49 | ||||
| 1. | 2019. 3. 31. | $58.69 | 5.14% | 2,834.40 | 1.79% | |
| 2. | 2019. 4. 30. | $67.41 | 14.86% | 2,945.83 | 3.93% | |
| 3. | 2019. 5. 31. | $59.55 | -11.66% | 2,752.06 | -6.58% | |
| 4. | 2019. 6. 30. | $50.80 | -14.69% | 2,941.76 | 6.89% | |
| 5. | 2019. 7. 31. | $57.74 | 13.66% | 2,980.38 | 1.31% | |
| 6. | 2019. 8. 31. | $51.53 | -10.76% | 2,926.46 | -1.81% | |
| 7. | 2019. 9. 30. | $51.86 | 0.64% | 2,976.74 | 1.72% | |
| 8. | 2019. 10. 31. | $52.89 | 1.99% | 3,037.56 | 2.04% | |
| 9. | 2019. 11. 30. | $48.49 | -8.32% | 3,140.98 | 3.40% | |
| 10. | 2019. 12. 31. | $51.39 | 5.98% | 3,230.78 | 2.86% | |
| 11. | 2020. 1. 31. | $48.77 | -5.10% | 3,225.52 | -0.16% | |
| 12. | 2020. 2. 29. | $40.46 | -17.04% | 2,954.22 | -8.41% | |
| 13. | 2020. 3. 31. | $39.55 | -2.25% | 2,584.59 | -12.51% | |
| 14. | 2020. 4. 30. | $42.69 | 7.94% | 2,912.43 | 12.68% | |
| 15. | 2020. 5. 31. | $49.64 | 16.28% | 3,044.31 | 4.53% | |
| 16. | 2020. 6. 30. | $54.94 | 10.68% | 3,100.29 | 1.84% | |
| 17. | 2020. 7. 31. | $59.83 | 8.90% | 3,271.12 | 5.51% | |
| 18. | 2020. 8. 31. | $66.08 | 10.45% | 3,500.31 | 7.01% | |
| 19. | 2020. 9. 30. | $67.69 | 2.44% | 3,363.00 | -3.92% | |
| 20. | 2020. 10. 31. | $60.26 | -10.98% | 3,269.96 | -2.77% | |
| 21. | 2020. 11. 30. | $69.03 | 14.55% | 3,621.63 | 10.75% | |
| 22. | 2020. 12. 31. | $73.29 | 6.17% | 3,756.07 | 3.71% | |
| 23. | 2021. 1. 31. | $72.89 | -0.55% | 3,714.24 | -1.11% | |
| 24. | 2021. 2. 28. | $81.07 | 11.22% | 3,811.15 | 2.61% | |
| 25. | 2021. 3. 31. | $88.15 | 8.73% | 3,972.89 | 4.24% | |
| 26. | 2021. 4. 30. | $98.33 | 11.55% | 4,181.17 | 5.24% | |
| 27. | 2021. 5. 31. | $98.64 | 0.32% | 4,204.11 | 0.55% | |
| 28. | 2021. 6. 30. | $99.67 | 1.04% | 4,297.50 | 2.22% | |
| 29. | 2021. 7. 31. | $96.62 | -3.06% | 4,395.26 | 2.27% | |
| 30. | 2021. 8. 31. | $97.46 | 0.87% | 4,522.68 | 2.90% | |
| 31. | 2021. 9. 30. | $104.04 | 6.75% | 4,307.54 | -4.76% | |
| 32. | 2021. 10. 31. | $109.99 | 5.72% | 4,605.38 | 6.91% | |
| 33. | 2021. 11. 30. | $56.47 | $54.85 | 1.21% | 4,567.00 | -0.83% |
| 34. | 2021. 12. 31. | $56.17 | -0.53% | 4,766.18 | 4.36% | |
| 35. | 2022. 1. 31. | $56.81 | 1.14% | 4,515.55 | -5.26% | |
| 36. | 2022. 2. 28. | $50.96 | -10.30% | 4,373.94 | -3.14% | |
| 37. | 2022. 3. 31. | $50.19 | -1.51% | 4,530.41 | 3.58% | |
| 38. | 2022. 4. 30. | $47.01 | $0.33 | -5.68% | 4,131.93 | -8.80% |
| 39. | 2022. 5. 31. | $49.94 | 6.23% | 4,132.15 | 0.01% | |
| 40. | 2022. 6. 30. | $46.21 | -7.47% | 3,785.38 | -8.39% | |
| 41. | 2022. 7. 31. | $45.06 | $0.33 | -1.77% | 4,130.29 | 9.11% |
| 42. | 2022. 8. 31. | $38.29 | -15.02% | 3,955.00 | -4.24% | |
| 43. | 2022. 9. 30. | $34.17 | -10.76% | 3,585.62 | -9.34% | |
| 44. | 2022. 10. 31. | $38.40 | $0.33 | 13.35% | 3,871.98 | 7.99% |
| 45. | 2022. 11. 30. | $44.79 | 16.64% | 4,080.11 | 5.38% | |
| 46. | 2022. 12. 31. | $40.22 | -10.20% | 3,839.50 | -5.90% | |
| 47. | 2023. 1. 31. | $40.62 | $0.33 | 1.82% | 4,076.60 | 6.18% |
| 48. | 2023. 2. 28. | $40.64 | 0.05% | 3,970.15 | -2.61% | |
| 49. | 2023. 3. 31. | $40.21 | -1.06% | 4,109.31 | 3.51% | |
| 50. | 2023. 4. 30. | $43.49 | $0.37 | 9.08% | 4,169.48 | 1.46% |
| 51. | 2023. 5. 31. | $44.81 | 3.04% | 4,179.83 | 0.25% | |
| 52. | 2023. 6. 30. | $54.11 | 20.75% | 4,376.86 | 4.71% | |
| 53. | 2023. 7. 31. | $52.92 | $0.37 | -1.52% | 4,588.96 | 4.85% |
| 54. | 2023. 8. 31. | $56.24 | 6.27% | 4,507.66 | -1.77% | |
| 55. | 2023. 9. 30. | $68.90 | 22.51% | 4,288.05 | -4.87% | |
| 56. | 2023. 10. 31. | $66.91 | $0.37 | -2.35% | 4,193.80 | -2.20% |
| 57. | 2023. 11. 30. | $75.87 | 13.39% | 4,567.80 | 8.92% | |
| 58. | 2023. 12. 31. | $76.50 | 0.83% | 4,769.83 | 4.42% | |
| 59. | 2024. 1. 31. | $82.88 | $0.37 | 8.82% | 4,845.65 | 1.59% |
| 60. | 2024. 2. 29. | $94.66 | 14.21% | 5,096.27 | 5.17% | |
| 61. | 2024. 3. 31. | $114.11 | 20.55% | 5,254.35 | 3.10% | |
| 62. | 2024. 4. 30. | $124.64 | $0.445 | 9.62% | 5,035.69 | -4.16% |
| 63. | 2024. 5. 31. | $139.56 | 11.97% | 5,277.51 | 4.80% | |
| 64. | 2024. 6. 30. | $137.91 | -1.18% | 5,460.48 | 3.47% | |
| 65. | 2024. 7. 31. | $113.68 | $0.445 | -17.25% | 5,522.30 | 1.13% |
| 66. | 2024. 8. 31. | $115.54 | 1.64% | 5,648.40 | 2.28% | |
| 67. | 2024. 9. 30. | $118.54 | 2.60% | 5,762.48 | 2.02% | |
| 68. | 2024. 10. 31. | $123.63 | $0.445 | 4.67% | 5,705.45 | -0.99% |
| 69. | 2024. 11. 30. | $127.59 | 3.20% | 6,032.38 | 5.73% | |
| 70. | 2024. 12. 31. | $115.24 | -9.68% | 5,881.63 | -2.50% | |
| 71. | 2025. 1. 31. | $103.60 | $0.445 | -9.71% | 6,040.53 | 2.70% |
| 평균의 (R): | 2.38% | 1.22% | ||||
| 표준 편차: | 9.43% | 4.99% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 DELL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Dell Technologies Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RDELL,t | RS&P 500,t | (RDELL,t–RDELL)2 | (RS&P 500,t–RS&P 500)2 | (RDELL,t–RDELL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 3. 31. | 5.14% | 1.79% | 7.62 | 0.33 | 1.58 |
| 2. | 2019. 4. 30. | 14.86% | 3.93% | 155.66 | 7.35 | 33.83 |
| 3. | 2019. 5. 31. | -11.66% | -6.58% | 197.15 | 60.81 | 109.49 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2024. 12. 31. | -9.68% | -2.50% | 145.46 | 13.83 | 44.85 |
| 71. | 2025. 1. 31. | -9.71% | 2.70% | 146.31 | 2.20 | -17.92 |
| 합계 (Σ): | 6,230.65 | 1,741.16 | 1,509.56 | |||
| t | 날짜 | RDELL,t | RS&P 500,t | (RDELL,t–RDELL)2 | (RS&P 500,t–RS&P 500)2 | (RDELL,t–RDELL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 3. 31. | 5.14% | 1.79% | 7.62 | 0.33 | 1.58 |
| 2. | 2019. 4. 30. | 14.86% | 3.93% | 155.66 | 7.35 | 33.83 |
| 3. | 2019. 5. 31. | -11.66% | -6.58% | 197.15 | 60.81 | 109.49 |
| 4. | 2019. 6. 30. | -14.69% | 6.89% | 291.55 | 32.18 | -96.86 |
| 5. | 2019. 7. 31. | 13.66% | 1.31% | 127.24 | 0.01 | 1.05 |
| 6. | 2019. 8. 31. | -10.76% | -1.81% | 172.56 | 9.18 | 39.79 |
| 7. | 2019. 9. 30. | 0.64% | 1.72% | 3.03 | 0.25 | -0.87 |
| 8. | 2019. 10. 31. | 1.99% | 2.04% | 0.16 | 0.68 | -0.33 |
| 9. | 2019. 11. 30. | -8.32% | 3.40% | 114.50 | 4.77 | -23.38 |
| 10. | 2019. 12. 31. | 5.98% | 2.86% | 12.96 | 2.69 | 5.90 |
| 11. | 2020. 1. 31. | -5.10% | -0.16% | 55.94 | 1.91 | 10.34 |
| 12. | 2020. 2. 29. | -17.04% | -8.41% | 377.15 | 92.76 | 187.04 |
| 13. | 2020. 3. 31. | -2.25% | -12.51% | 21.44 | 188.57 | 63.58 |
| 14. | 2020. 4. 30. | 7.94% | 12.68% | 30.89 | 131.43 | 63.72 |
| 15. | 2020. 5. 31. | 16.28% | 4.53% | 193.18 | 10.94 | 45.98 |
| 16. | 2020. 6. 30. | 10.68% | 1.84% | 68.82 | 0.38 | 5.13 |
| 17. | 2020. 7. 31. | 8.90% | 5.51% | 42.50 | 18.41 | 27.97 |
| 18. | 2020. 8. 31. | 10.45% | 7.01% | 65.05 | 33.48 | 46.67 |
| 19. | 2020. 9. 30. | 2.44% | -3.92% | 0.00 | 26.45 | -0.28 |
| 20. | 2020. 10. 31. | -10.98% | -2.77% | 178.43 | 15.89 | 53.25 |
| 21. | 2020. 11. 30. | 14.55% | 10.75% | 148.17 | 90.91 | 116.06 |
| 22. | 2020. 12. 31. | 6.17% | 3.71% | 14.36 | 6.21 | 9.45 |
| 23. | 2021. 1. 31. | -0.55% | -1.11% | 8.57 | 5.45 | 6.83 |
| 24. | 2021. 2. 28. | 11.22% | 2.61% | 78.17 | 1.93 | 12.28 |
| 25. | 2021. 3. 31. | 8.73% | 4.24% | 40.35 | 9.14 | 19.21 |
| 26. | 2021. 4. 30. | 11.55% | 5.24% | 84.04 | 16.18 | 36.88 |
| 27. | 2021. 5. 31. | 0.32% | 0.55% | 4.27 | 0.45 | 1.39 |
| 28. | 2021. 6. 30. | 1.04% | 2.22% | 1.79 | 1.00 | -1.34 |
| 29. | 2021. 7. 31. | -3.06% | 2.27% | 29.61 | 1.11 | -5.74 |
| 30. | 2021. 8. 31. | 0.87% | 2.90% | 2.29 | 2.82 | -2.54 |
| 31. | 2021. 9. 30. | 6.75% | -4.76% | 19.10 | 35.72 | -26.12 |
| 32. | 2021. 10. 31. | 5.72% | 6.91% | 11.14 | 32.43 | 19.01 |
| 33. | 2021. 11. 30. | 1.21% | -0.83% | 1.37 | 4.22 | 2.41 |
| 34. | 2021. 12. 31. | -0.53% | 4.36% | 8.48 | 9.87 | -9.15 |
| 35. | 2022. 1. 31. | 1.14% | -5.26% | 1.54 | 41.97 | 8.04 |
| 36. | 2022. 2. 28. | -10.30% | -3.14% | 160.75 | 18.98 | 55.23 |
| 37. | 2022. 3. 31. | -1.51% | 3.58% | 15.15 | 5.56 | -9.18 |
| 38. | 2022. 4. 30. | -5.68% | -8.80% | 64.96 | 100.31 | 80.72 |
| 39. | 2022. 5. 31. | 6.23% | 0.01% | 14.83 | 1.48 | -4.68 |
| 40. | 2022. 6. 30. | -7.47% | -8.39% | 97.03 | 92.39 | 94.68 |
| 41. | 2022. 7. 31. | -1.77% | 9.11% | 17.27 | 62.28 | -32.80 |
| 42. | 2022. 8. 31. | -15.02% | -4.24% | 302.95 | 29.86 | 95.10 |
| 43. | 2022. 9. 30. | -10.76% | -9.34% | 172.69 | 111.50 | 138.77 |
| 44. | 2022. 10. 31. | 13.35% | 7.99% | 120.21 | 45.78 | 74.19 |
| 45. | 2022. 11. 30. | 16.64% | 5.38% | 203.33 | 17.27 | 59.25 |
| 46. | 2022. 12. 31. | -10.20% | -5.90% | 158.37 | 50.65 | 89.56 |
| 47. | 2023. 1. 31. | 1.82% | 6.18% | 0.32 | 24.55 | -2.81 |
| 48. | 2023. 2. 28. | 0.05% | -2.61% | 5.44 | 14.68 | 8.93 |
| 49. | 2023. 3. 31. | -1.06% | 3.51% | 11.83 | 5.22 | -7.86 |
| 50. | 2023. 4. 30. | 9.08% | 1.46% | 44.84 | 0.06 | 1.64 |
| 51. | 2023. 5. 31. | 3.04% | 0.25% | 0.43 | 0.94 | -0.64 |
| 52. | 2023. 6. 30. | 20.75% | 4.71% | 337.57 | 12.21 | 64.19 |
| 53. | 2023. 7. 31. | -1.52% | 4.85% | 15.18 | 13.15 | -14.13 |
| 54. | 2023. 8. 31. | 6.27% | -1.77% | 15.15 | 8.95 | -11.64 |
| 55. | 2023. 9. 30. | 22.51% | -4.87% | 405.20 | 37.11 | -122.63 |
| 56. | 2023. 10. 31. | -2.35% | -2.20% | 22.40 | 11.68 | 16.18 |
| 57. | 2023. 11. 30. | 13.39% | 8.92% | 121.22 | 59.26 | 84.75 |
| 58. | 2023. 12. 31. | 0.83% | 4.42% | 2.41 | 10.26 | -4.97 |
| 59. | 2024. 1. 31. | 8.82% | 1.59% | 41.50 | 0.14 | 2.38 |
| 60. | 2024. 2. 29. | 14.21% | 5.17% | 140.00 | 15.62 | 46.76 |
| 61. | 2024. 3. 31. | 20.55% | 3.10% | 330.01 | 3.54 | 34.19 |
| 62. | 2024. 4. 30. | 9.62% | -4.16% | 52.37 | 28.96 | -38.94 |
| 63. | 2024. 5. 31. | 11.97% | 4.80% | 91.95 | 12.83 | 34.35 |
| 64. | 2024. 6. 30. | -1.18% | 3.47% | 12.70 | 5.05 | -8.01 |
| 65. | 2024. 7. 31. | -17.25% | 1.13% | 385.26 | 0.01 | 1.73 |
| 66. | 2024. 8. 31. | 1.64% | 2.28% | 0.56 | 1.13 | -0.79 |
| 67. | 2024. 9. 30. | 2.60% | 2.02% | 0.05 | 0.64 | 0.17 |
| 68. | 2024. 10. 31. | 4.67% | -0.99% | 5.24 | 4.88 | -5.06 |
| 69. | 2024. 11. 30. | 3.20% | 5.73% | 0.68 | 20.34 | 3.71 |
| 70. | 2024. 12. 31. | -9.68% | -2.50% | 145.46 | 13.83 | 44.85 |
| 71. | 2025. 1. 31. | -9.71% | 2.70% | 146.31 | 2.20 | -17.92 |
| 합계 (Σ): | 6,230.65 | 1,741.16 | 1,509.56 | |||
모두 보기
분산DELL = Σ(RDELL,t–RDELL)2 ÷ (71 – 1)
= 6,230.65 ÷ (71 – 1)
= 89.01
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,741.16 ÷ (71 – 1)
= 24.87
공분산DELL, S&P 500 = Σ(RDELL,t–RDELL)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,509.56 ÷ (71 – 1)
= 21.57
체계적인 위험 추정 (β)
| 분산DELL | 89.01 |
| 분산S&P 500 | 24.87 |
| 공분산DELL, S&P 500 | 21.57 |
| 상관 계수DELL, S&P 5001 | 0.46 |
| βDELL2 | 0.87 |
| αDELL3 | 1.32% |
계산
1 상관 계수DELL, S&P 500
= 공분산DELL, S&P 500 ÷ (표준 편차DELL × 표준 편차S&P 500)
= 21.57 ÷ (9.43% × 4.99%)
= 0.46
2 βDELL
= 공분산DELL, S&P 500 ÷ 분산S&P 500
= 21.57 ÷ 24.87
= 0.87
3 αDELL
= 평균의DELL – βDELL × 평균의S&P 500
= 2.38% – 0.87 × 1.22%
= 1.32%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.69% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.90% |
| 보통주의 체계적 위험Dell Technologies | βDELL | 0.87 |
| Dell Technologies 보통주에 대한 예상 수익률3 | E(RDELL) | 13.54% |
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(RDELL) = RF + βDELL [E(RM) – RF]
= 4.69% + 0.87 [14.90% – 4.69%]
= 13.54%