자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Cisco보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Cisco Systems Inc., 월별 수익률
| Cisco Systems Inc. (CSCO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CSCO,t1 | 피제수CSCO,t1 | RCSCO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 8. 31. | $46.81 | 2,926.46 | ||||
| 1. | 2019. 9. 30. | $49.41 | 5.55% | 2,976.74 | 1.72% | |
| 2. | 2019. 10. 31. | $47.51 | $0.35 | -3.14% | 3,037.56 | 2.04% |
| 3. | 2019. 11. 30. | $45.31 | -4.63% | 3,140.98 | 3.40% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2025. 6. 30. | $69.38 | 10.06% | 6,204.95 | 4.96% | |
| 71. | 2025. 7. 31. | $68.08 | $0.41 | -1.28% | 6,339.39 | 2.17% |
| 평균의 (R): | 1.03% | 1.22% | ||||
| 표준 편차: | 7.02% | 4.97% | ||||
| Cisco Systems Inc. (CSCO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값CSCO,t1 | 피제수CSCO,t1 | RCSCO,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 8. 31. | $46.81 | 2,926.46 | ||||
| 1. | 2019. 9. 30. | $49.41 | 5.55% | 2,976.74 | 1.72% | |
| 2. | 2019. 10. 31. | $47.51 | $0.35 | -3.14% | 3,037.56 | 2.04% |
| 3. | 2019. 11. 30. | $45.31 | -4.63% | 3,140.98 | 3.40% | |
| 4. | 2019. 12. 31. | $47.96 | 5.85% | 3,230.78 | 2.86% | |
| 5. | 2020. 1. 31. | $45.97 | $0.35 | -3.42% | 3,225.52 | -0.16% |
| 6. | 2020. 2. 29. | $39.93 | -13.14% | 2,954.22 | -8.41% | |
| 7. | 2020. 3. 31. | $39.31 | -1.55% | 2,584.59 | -12.51% | |
| 8. | 2020. 4. 30. | $42.38 | $0.36 | 8.73% | 2,912.43 | 12.68% |
| 9. | 2020. 5. 31. | $47.82 | 12.84% | 3,044.31 | 4.53% | |
| 10. | 2020. 6. 30. | $46.64 | -2.47% | 3,100.29 | 1.84% | |
| 11. | 2020. 7. 31. | $47.10 | $0.36 | 1.76% | 3,271.12 | 5.51% |
| 12. | 2020. 8. 31. | $42.22 | -10.36% | 3,500.31 | 7.01% | |
| 13. | 2020. 9. 30. | $39.39 | -6.70% | 3,363.00 | -3.92% | |
| 14. | 2020. 10. 31. | $35.90 | $0.36 | -7.95% | 3,269.96 | -2.77% |
| 15. | 2020. 11. 30. | $43.02 | 19.83% | 3,621.63 | 10.75% | |
| 16. | 2020. 12. 31. | $44.75 | 4.02% | 3,756.07 | 3.71% | |
| 17. | 2021. 1. 31. | $44.58 | $0.36 | 0.42% | 3,714.24 | -1.11% |
| 18. | 2021. 2. 28. | $44.87 | 0.65% | 3,811.15 | 2.61% | |
| 19. | 2021. 3. 31. | $51.71 | 15.24% | 3,972.89 | 4.24% | |
| 20. | 2021. 4. 30. | $50.91 | $0.37 | -0.83% | 4,181.17 | 5.24% |
| 21. | 2021. 5. 31. | $52.90 | 3.91% | 4,204.11 | 0.55% | |
| 22. | 2021. 6. 30. | $53.00 | 0.19% | 4,297.50 | 2.22% | |
| 23. | 2021. 7. 31. | $55.37 | $0.37 | 5.17% | 4,395.26 | 2.27% |
| 24. | 2021. 8. 31. | $59.02 | 6.59% | 4,522.68 | 2.90% | |
| 25. | 2021. 9. 30. | $54.43 | -7.78% | 4,307.54 | -4.76% | |
| 26. | 2021. 10. 31. | $55.97 | $0.37 | 3.51% | 4,605.38 | 6.91% |
| 27. | 2021. 11. 30. | $54.84 | -2.02% | 4,567.00 | -0.83% | |
| 28. | 2021. 12. 31. | $63.37 | 15.55% | 4,766.18 | 4.36% | |
| 29. | 2022. 1. 31. | $55.67 | $0.37 | -11.57% | 4,515.55 | -5.26% |
| 30. | 2022. 2. 28. | $55.77 | 0.18% | 4,373.94 | -3.14% | |
| 31. | 2022. 3. 31. | $55.76 | -0.02% | 4,530.41 | 3.58% | |
| 32. | 2022. 4. 30. | $48.98 | $0.38 | -11.48% | 4,131.93 | -8.80% |
| 33. | 2022. 5. 31. | $45.05 | -8.02% | 4,132.15 | 0.01% | |
| 34. | 2022. 6. 30. | $42.64 | -5.35% | 3,785.38 | -8.39% | |
| 35. | 2022. 7. 31. | $45.37 | $0.38 | 7.29% | 4,130.29 | 9.11% |
| 36. | 2022. 8. 31. | $44.72 | -1.43% | 3,955.00 | -4.24% | |
| 37. | 2022. 9. 30. | $40.00 | -10.55% | 3,585.62 | -9.34% | |
| 38. | 2022. 10. 31. | $45.43 | $0.38 | 14.53% | 3,871.98 | 7.99% |
| 39. | 2022. 11. 30. | $49.72 | 9.44% | 4,080.11 | 5.38% | |
| 40. | 2022. 12. 31. | $47.64 | -4.18% | 3,839.50 | -5.90% | |
| 41. | 2023. 1. 31. | $48.67 | $0.38 | 2.96% | 4,076.60 | 6.18% |
| 42. | 2023. 2. 28. | $48.42 | -0.51% | 3,970.15 | -2.61% | |
| 43. | 2023. 3. 31. | $52.28 | 7.97% | 4,109.31 | 3.51% | |
| 44. | 2023. 4. 30. | $47.25 | $0.39 | -8.88% | 4,169.48 | 1.46% |
| 45. | 2023. 5. 31. | $49.67 | 5.12% | 4,179.83 | 0.25% | |
| 46. | 2023. 6. 30. | $51.74 | 4.17% | 4,376.86 | 4.71% | |
| 47. | 2023. 7. 31. | $52.04 | $0.39 | 1.33% | 4,588.96 | 4.85% |
| 48. | 2023. 8. 31. | $57.35 | 10.20% | 4,507.66 | -1.77% | |
| 49. | 2023. 9. 30. | $53.76 | -6.26% | 4,288.05 | -4.87% | |
| 50. | 2023. 10. 31. | $52.13 | $0.39 | -2.31% | 4,193.80 | -2.20% |
| 51. | 2023. 11. 30. | $48.38 | -7.19% | 4,567.80 | 8.92% | |
| 52. | 2023. 12. 31. | $50.52 | 4.42% | 4,769.83 | 4.42% | |
| 53. | 2024. 1. 31. | $50.18 | $0.39 | 0.10% | 4,845.65 | 1.59% |
| 54. | 2024. 2. 29. | $48.37 | -3.61% | 5,096.27 | 5.17% | |
| 55. | 2024. 3. 31. | $49.91 | 3.18% | 5,254.35 | 3.10% | |
| 56. | 2024. 4. 30. | $46.98 | $0.40 | -5.07% | 5,035.69 | -4.16% |
| 57. | 2024. 5. 31. | $46.50 | -1.02% | 5,277.51 | 4.80% | |
| 58. | 2024. 6. 30. | $47.51 | 2.17% | 5,460.48 | 3.47% | |
| 59. | 2024. 7. 31. | $48.45 | $0.40 | 2.82% | 5,522.30 | 1.13% |
| 60. | 2024. 8. 31. | $50.54 | 4.31% | 5,648.40 | 2.28% | |
| 61. | 2024. 9. 30. | $53.22 | 5.30% | 5,762.48 | 2.02% | |
| 62. | 2024. 10. 31. | $54.77 | $0.40 | 3.66% | 5,705.45 | -0.99% |
| 63. | 2024. 11. 30. | $59.21 | 8.11% | 6,032.38 | 5.73% | |
| 64. | 2024. 12. 31. | $59.20 | -0.02% | 5,881.63 | -2.50% | |
| 65. | 2025. 1. 31. | $60.60 | $0.40 | 3.04% | 6,040.53 | 2.70% |
| 66. | 2025. 2. 28. | $64.11 | 5.79% | 5,954.50 | -1.42% | |
| 67. | 2025. 3. 31. | $61.71 | -3.74% | 5,611.85 | -5.75% | |
| 68. | 2025. 4. 30. | $57.73 | $0.41 | -5.79% | 5,569.06 | -0.76% |
| 69. | 2025. 5. 31. | $63.04 | 9.20% | 5,911.69 | 6.15% | |
| 70. | 2025. 6. 30. | $69.38 | 10.06% | 6,204.95 | 4.96% | |
| 71. | 2025. 7. 31. | $68.08 | $0.41 | -1.28% | 6,339.39 | 2.17% |
| 평균의 (R): | 1.03% | 1.22% | ||||
| 표준 편차: | 7.02% | 4.97% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 CSCO의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Cisco Systems Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RCSCO,t | RS&P 500,t | (RCSCO,t–RCSCO)2 | (RS&P 500,t–RS&P 500)2 | (RCSCO,t–RCSCO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 9. 30. | 5.55% | 1.72% | 20.50 | 0.25 | 2.27 |
| 2. | 2019. 10. 31. | -3.14% | 2.04% | 17.34 | 0.68 | -3.44 |
| 3. | 2019. 11. 30. | -4.63% | 3.40% | 32.01 | 4.79 | -12.38 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2025. 6. 30. | 10.06% | 4.96% | 81.54 | 14.01 | 33.80 |
| 71. | 2025. 7. 31. | -1.28% | 2.17% | 5.34 | 0.90 | -2.19 |
| 합계 (Σ): | 3,446.80 | 1,730.09 | 1,464.18 | |||
| t | 날짜 | RCSCO,t | RS&P 500,t | (RCSCO,t–RCSCO)2 | (RS&P 500,t–RS&P 500)2 | (RCSCO,t–RCSCO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 9. 30. | 5.55% | 1.72% | 20.50 | 0.25 | 2.27 |
| 2. | 2019. 10. 31. | -3.14% | 2.04% | 17.34 | 0.68 | -3.44 |
| 3. | 2019. 11. 30. | -4.63% | 3.40% | 32.01 | 4.79 | -12.38 |
| 4. | 2019. 12. 31. | 5.85% | 2.86% | 23.25 | 2.70 | 7.92 |
| 5. | 2020. 1. 31. | -3.42% | -0.16% | 19.77 | 1.90 | 6.14 |
| 6. | 2020. 2. 29. | -13.14% | -8.41% | 200.68 | 92.70 | 136.39 |
| 7. | 2020. 3. 31. | -1.55% | -12.51% | 6.66 | 188.49 | 35.42 |
| 8. | 2020. 4. 30. | 8.73% | 12.68% | 59.27 | 131.50 | 88.28 |
| 9. | 2020. 5. 31. | 12.84% | 4.53% | 139.46 | 10.96 | 39.10 |
| 10. | 2020. 6. 30. | -2.47% | 1.84% | 12.21 | 0.39 | -2.17 |
| 11. | 2020. 7. 31. | 1.76% | 5.51% | 0.53 | 18.43 | 3.14 |
| 12. | 2020. 8. 31. | -10.36% | 7.01% | 129.69 | 33.52 | -65.93 |
| 13. | 2020. 9. 30. | -6.70% | -3.92% | 59.75 | 26.42 | 39.73 |
| 14. | 2020. 10. 31. | -7.95% | -2.77% | 80.52 | 15.87 | 35.75 |
| 15. | 2020. 11. 30. | 19.83% | 10.75% | 353.66 | 90.96 | 179.36 |
| 16. | 2020. 12. 31. | 4.02% | 3.71% | 8.97 | 6.22 | 7.47 |
| 17. | 2021. 1. 31. | 0.42% | -1.11% | 0.36 | 5.43 | 1.40 |
| 18. | 2021. 2. 28. | 0.65% | 2.61% | 0.14 | 1.94 | -0.52 |
| 19. | 2021. 3. 31. | 15.24% | 4.24% | 202.12 | 9.16 | 43.03 |
| 20. | 2021. 4. 30. | -0.83% | 5.24% | 3.45 | 16.20 | -7.48 |
| 21. | 2021. 5. 31. | 3.91% | 0.55% | 8.30 | 0.45 | -1.93 |
| 22. | 2021. 6. 30. | 0.19% | 2.22% | 0.70 | 1.01 | -0.84 |
| 23. | 2021. 7. 31. | 5.17% | 2.27% | 17.16 | 1.12 | 4.38 |
| 24. | 2021. 8. 31. | 6.59% | 2.90% | 30.97 | 2.83 | 9.36 |
| 25. | 2021. 9. 30. | -7.78% | -4.76% | 77.51 | 35.69 | 52.60 |
| 26. | 2021. 10. 31. | 3.51% | 6.91% | 6.16 | 32.46 | 14.14 |
| 27. | 2021. 11. 30. | -2.02% | -0.83% | 9.28 | 4.20 | 6.25 |
| 28. | 2021. 12. 31. | 15.55% | 4.36% | 211.04 | 9.89 | 45.68 |
| 29. | 2022. 1. 31. | -11.57% | -5.26% | 158.61 | 41.93 | 81.56 |
| 30. | 2022. 2. 28. | 0.18% | -3.14% | 0.72 | 18.95 | 3.69 |
| 31. | 2022. 3. 31. | -0.02% | 3.58% | 1.09 | 5.57 | -2.47 |
| 32. | 2022. 4. 30. | -11.48% | -8.80% | 156.37 | 100.26 | 125.21 |
| 33. | 2022. 5. 31. | -8.02% | 0.01% | 81.92 | 1.47 | 10.97 |
| 34. | 2022. 6. 30. | -5.35% | -8.39% | 40.66 | 92.34 | 61.28 |
| 35. | 2022. 7. 31. | 7.29% | 9.11% | 39.27 | 62.32 | 49.47 |
| 36. | 2022. 8. 31. | -1.43% | -4.24% | 6.05 | 29.82 | 13.43 |
| 37. | 2022. 9. 30. | -10.55% | -9.34% | 134.14 | 111.44 | 122.26 |
| 38. | 2022. 10. 31. | 14.53% | 7.99% | 182.19 | 45.82 | 91.37 |
| 39. | 2022. 11. 30. | 9.44% | 5.38% | 70.83 | 17.29 | 34.99 |
| 40. | 2022. 12. 31. | -4.18% | -5.90% | 27.15 | 50.61 | 37.07 |
| 41. | 2023. 1. 31. | 2.96% | 6.18% | 3.73 | 24.58 | 9.58 |
| 42. | 2023. 2. 28. | -0.51% | -2.61% | 2.37 | 14.66 | 5.90 |
| 43. | 2023. 3. 31. | 7.97% | 3.51% | 48.23 | 5.23 | 15.89 |
| 44. | 2023. 4. 30. | -8.88% | 1.46% | 98.06 | 0.06 | -2.45 |
| 45. | 2023. 5. 31. | 5.12% | 0.25% | 16.77 | 0.94 | -3.97 |
| 46. | 2023. 6. 30. | 4.17% | 4.71% | 9.86 | 12.23 | 10.98 |
| 47. | 2023. 7. 31. | 1.33% | 4.85% | 0.09 | 13.17 | 1.11 |
| 48. | 2023. 8. 31. | 10.20% | -1.77% | 84.21 | 8.93 | -27.43 |
| 49. | 2023. 9. 30. | -6.26% | -4.87% | 53.10 | 37.08 | 44.37 |
| 50. | 2023. 10. 31. | -2.31% | -2.20% | 11.11 | 11.66 | 11.38 |
| 51. | 2023. 11. 30. | -7.19% | 8.92% | 67.58 | 59.30 | -63.31 |
| 52. | 2023. 12. 31. | 4.42% | 4.42% | 11.53 | 10.28 | 10.89 |
| 53. | 2024. 1. 31. | 0.10% | 1.59% | 0.86 | 0.14 | -0.35 |
| 54. | 2024. 2. 29. | -3.61% | 5.17% | 21.48 | 15.64 | -18.33 |
| 55. | 2024. 3. 31. | 3.18% | 3.10% | 4.65 | 3.55 | 4.06 |
| 56. | 2024. 4. 30. | -5.07% | -4.16% | 37.16 | 28.93 | 32.79 |
| 57. | 2024. 5. 31. | -1.02% | 4.80% | 4.20 | 12.85 | -7.35 |
| 58. | 2024. 6. 30. | 2.17% | 3.47% | 1.31 | 5.06 | 2.58 |
| 59. | 2024. 7. 31. | 2.82% | 1.13% | 3.22 | 0.01 | -0.15 |
| 60. | 2024. 8. 31. | 4.31% | 2.28% | 10.80 | 1.14 | 3.50 |
| 61. | 2024. 9. 30. | 5.30% | 2.02% | 18.28 | 0.64 | 3.43 |
| 62. | 2024. 10. 31. | 3.66% | -0.99% | 6.95 | 4.87 | -5.82 |
| 63. | 2024. 11. 30. | 8.11% | 5.73% | 50.12 | 20.37 | 31.95 |
| 64. | 2024. 12. 31. | -0.02% | -2.50% | 1.09 | 13.81 | 3.88 |
| 65. | 2025. 1. 31. | 3.04% | 2.70% | 4.05 | 2.20 | 2.99 |
| 66. | 2025. 2. 28. | 5.79% | -1.42% | 22.70 | 6.98 | -12.59 |
| 67. | 2025. 3. 31. | -3.74% | -5.75% | 22.76 | 48.60 | 33.26 |
| 68. | 2025. 4. 30. | -5.79% | -0.76% | 46.41 | 3.92 | 13.49 |
| 69. | 2025. 5. 31. | 9.20% | 6.15% | 66.76 | 24.36 | 40.33 |
| 70. | 2025. 6. 30. | 10.06% | 4.96% | 81.54 | 14.01 | 33.80 |
| 71. | 2025. 7. 31. | -1.28% | 2.17% | 5.34 | 0.90 | -2.19 |
| 합계 (Σ): | 3,446.80 | 1,730.09 | 1,464.18 | |||
모두 보기
분산CSCO = Σ(RCSCO,t–RCSCO)2 ÷ (71 – 1)
= 3,446.80 ÷ (71 – 1)
= 49.24
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,730.09 ÷ (71 – 1)
= 24.72
공분산CSCO, S&P 500 = Σ(RCSCO,t–RCSCO)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,464.18 ÷ (71 – 1)
= 20.92
체계적인 위험 추정 (β)
| 분산CSCO | 49.24 |
| 분산S&P 500 | 24.72 |
| 공분산CSCO, S&P 500 | 20.92 |
| 상관 계수CSCO, S&P 5001 | 0.60 |
| βCSCO2 | 0.85 |
| αCSCO3 | 0.00% |
계산
1 상관 계수CSCO, S&P 500
= 공분산CSCO, S&P 500 ÷ (표준 편차CSCO × 표준 편차S&P 500)
= 20.92 ÷ (7.02% × 4.97%)
= 0.60
2 βCSCO
= 공분산CSCO, S&P 500 ÷ 분산S&P 500
= 20.92 ÷ 24.72
= 0.85
3 αCSCO
= 평균의CSCO – βCSCO × 평균의S&P 500
= 1.03% – 0.85 × 1.22%
= 0.00%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.71% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.85% |
| 보통주의 체계적 위험Cisco | βCSCO | 0.85 |
| Cisco 보통주에 대한 예상 수익률3 | E(RCSCO) | 13.29% |
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(RCSCO) = RF + βCSCO [E(RM) – RF]
= 4.71% + 0.85 [14.85% – 4.71%]
= 13.29%