자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Verizon보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Verizon Communications Inc., 월별 수익률
| Verizon Communications Inc. (VZ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값VZ,t1 | 피제수VZ,t1 | RVZ,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $54.75 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $55.30 | 1.00% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $58.15 | 5.15% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $57.79 | $0.6275 | 0.46% | 4,181.17 | 5.24% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $41.11 | 3.45% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $40.73 | -0.92% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.14% | 1.14% | ||||
| 표준 편차: | 5.48% | 4.37% | ||||
| Verizon Communications Inc. (VZ) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값VZ,t1 | 피제수VZ,t1 | RVZ,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $54.75 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $55.30 | 1.00% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $58.15 | 5.15% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $57.79 | $0.6275 | 0.46% | 4,181.17 | 5.24% |
| 4. | 2021. 5. 31. | $56.49 | -2.25% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $56.03 | -0.81% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $55.78 | $0.6275 | 0.67% | 4,395.26 | 2.27% |
| 7. | 2021. 8. 31. | $55.00 | -1.40% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $54.01 | -1.80% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $52.99 | $0.64 | -0.70% | 4,605.38 | 6.91% |
| 10. | 2021. 11. 30. | $50.27 | -5.13% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $51.96 | 3.36% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $53.23 | $0.64 | 3.68% | 4,515.55 | -5.26% |
| 13. | 2022. 2. 28. | $53.67 | 0.83% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $50.94 | -5.09% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $46.30 | $0.64 | -7.85% | 4,131.93 | -8.80% |
| 16. | 2022. 5. 31. | $51.29 | 10.78% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $50.75 | -1.05% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $46.19 | $0.64 | -7.72% | 4,130.29 | 9.11% |
| 19. | 2022. 8. 31. | $41.81 | -9.48% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $37.97 | -9.18% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $37.37 | $0.6525 | 0.14% | 3,871.98 | 7.99% |
| 22. | 2022. 11. 30. | $38.98 | 4.31% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $39.40 | 1.08% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $41.57 | $0.6525 | 7.16% | 4,076.60 | 6.18% |
| 25. | 2023. 2. 28. | $38.81 | -6.64% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $38.89 | 0.21% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $38.83 | $0.6525 | 1.52% | 4,169.48 | 1.46% |
| 28. | 2023. 5. 31. | $35.63 | -8.24% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $37.19 | 4.38% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $34.08 | $0.6525 | -6.61% | 4,588.96 | 4.85% |
| 31. | 2023. 8. 31. | $34.98 | 2.64% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $32.41 | -7.35% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $35.13 | $0.665 | 10.44% | 4,193.80 | -2.20% |
| 34. | 2023. 11. 30. | $38.33 | 9.11% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $37.70 | -1.64% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $42.35 | $0.665 | 14.10% | 4,845.65 | 1.59% |
| 37. | 2024. 2. 29. | $40.02 | -5.50% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $41.96 | 4.85% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $39.49 | $0.665 | -4.30% | 5,035.69 | -4.16% |
| 40. | 2024. 5. 31. | $41.15 | 4.20% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $41.24 | 0.22% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $40.52 | $0.665 | -0.13% | 5,522.30 | 1.13% |
| 43. | 2024. 8. 31. | $41.78 | 3.11% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $44.91 | 7.49% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $42.13 | $0.6775 | -4.68% | 5,705.45 | -0.99% |
| 46. | 2024. 11. 30. | $44.34 | 5.25% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $39.99 | -9.81% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $39.39 | $0.6775 | 0.19% | 6,040.53 | 2.70% |
| 49. | 2025. 2. 28. | $43.10 | 9.42% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $45.36 | 5.24% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $44.06 | $0.6775 | -1.37% | 5,569.06 | -0.76% |
| 52. | 2025. 5. 31. | $43.96 | -0.23% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $43.27 | -1.57% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $42.76 | $0.6775 | 0.39% | 6,339.39 | 2.17% |
| 55. | 2025. 8. 31. | $44.23 | 3.44% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $43.95 | -0.63% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $39.74 | $0.69 | -8.01% | 6,840.20 | 2.27% |
| 58. | 2025. 11. 30. | $41.11 | 3.45% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $40.73 | -0.92% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.14% | 1.14% | ||||
| 표준 편차: | 5.48% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 VZ의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Verizon Communications Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RVZ,t | RS&P 500,t | (RVZ,t–RVZ)2 | (RS&P 500,t–RS&P 500)2 | (RVZ,t–RVZ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 1.00% | 2.61% | 0.75 | 2.17 | 1.28 |
| 2. | 2021. 3. 31. | 5.15% | 4.24% | 25.16 | 9.66 | 15.59 |
| 3. | 2021. 4. 30. | 0.46% | 5.24% | 0.10 | 16.86 | 1.32 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 3.45% | 0.13% | 10.95 | 1.01 | -3.33 |
| 59. | 2025. 12. 31. | -0.92% | -0.05% | 1.13 | 1.41 | 1.26 |
| 합계 (Σ): | 1,743.21 | 1,108.23 | 344.75 | |||
| t | 날짜 | RVZ,t | RS&P 500,t | (RVZ,t–RVZ)2 | (RS&P 500,t–RS&P 500)2 | (RVZ,t–RVZ)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | 1.00% | 2.61% | 0.75 | 2.17 | 1.28 |
| 2. | 2021. 3. 31. | 5.15% | 4.24% | 25.16 | 9.66 | 15.59 |
| 3. | 2021. 4. 30. | 0.46% | 5.24% | 0.10 | 16.86 | 1.32 |
| 4. | 2021. 5. 31. | -2.25% | 0.55% | 5.70 | 0.35 | 1.40 |
| 5. | 2021. 6. 30. | -0.81% | 2.22% | 0.91 | 1.18 | -1.03 |
| 6. | 2021. 7. 31. | 0.67% | 2.27% | 0.29 | 1.30 | 0.61 |
| 7. | 2021. 8. 31. | -1.40% | 2.90% | 2.36 | 3.11 | -2.71 |
| 8. | 2021. 9. 30. | -1.80% | -4.76% | 3.76 | 34.73 | 11.42 |
| 9. | 2021. 10. 31. | -0.70% | 6.91% | 0.71 | 33.39 | -4.86 |
| 10. | 2021. 11. 30. | -5.13% | -0.83% | 27.78 | 3.88 | 10.38 |
| 11. | 2021. 12. 31. | 3.36% | 4.36% | 10.39 | 10.40 | 10.40 |
| 12. | 2022. 1. 31. | 3.68% | -5.26% | 12.52 | 40.89 | -22.62 |
| 13. | 2022. 2. 28. | 0.83% | -3.14% | 0.47 | 18.25 | -2.94 |
| 14. | 2022. 3. 31. | -5.09% | 3.58% | 27.30 | 5.96 | -12.75 |
| 15. | 2022. 4. 30. | -7.85% | -8.80% | 63.85 | 98.64 | 79.36 |
| 16. | 2022. 5. 31. | 10.78% | 0.01% | 113.20 | 1.28 | -12.03 |
| 17. | 2022. 6. 30. | -1.05% | -8.39% | 1.42 | 90.79 | 11.35 |
| 18. | 2022. 7. 31. | -7.72% | 9.11% | 61.81 | 63.61 | -62.70 |
| 19. | 2022. 8. 31. | -9.48% | -4.24% | 92.56 | 28.95 | 51.76 |
| 20. | 2022. 9. 30. | -9.18% | -9.34% | 86.91 | 109.74 | 97.66 |
| 21. | 2022. 10. 31. | 0.14% | 7.99% | 0.00 | 46.93 | 0.00 |
| 22. | 2022. 11. 30. | 4.31% | 5.38% | 17.39 | 17.97 | 17.68 |
| 23. | 2022. 12. 31. | 1.08% | -5.90% | 0.88 | 49.47 | -6.61 |
| 24. | 2023. 1. 31. | 7.16% | 6.18% | 49.36 | 25.39 | 35.40 |
| 25. | 2023. 2. 28. | -6.64% | -2.61% | 45.93 | 14.04 | 25.40 |
| 26. | 2023. 3. 31. | 0.21% | 3.51% | 0.00 | 5.61 | 0.16 |
| 27. | 2023. 4. 30. | 1.52% | 1.46% | 1.92 | 0.11 | 0.45 |
| 28. | 2023. 5. 31. | -8.24% | 0.25% | 70.21 | 0.79 | 7.44 |
| 29. | 2023. 6. 30. | 4.38% | 4.71% | 17.98 | 12.80 | 15.17 |
| 30. | 2023. 7. 31. | -6.61% | 4.85% | 45.51 | 13.76 | -25.03 |
| 31. | 2023. 8. 31. | 2.64% | -1.77% | 6.26 | 8.46 | -7.28 |
| 32. | 2023. 9. 30. | -7.35% | -4.87% | 56.03 | 36.10 | 44.97 |
| 33. | 2023. 10. 31. | 10.44% | -2.20% | 106.22 | 11.12 | -34.36 |
| 34. | 2023. 11. 30. | 9.11% | 8.92% | 80.48 | 60.56 | 69.81 |
| 35. | 2023. 12. 31. | -1.64% | 4.42% | 3.17 | 10.80 | -5.86 |
| 36. | 2024. 1. 31. | 14.10% | 1.59% | 194.89 | 0.21 | 6.33 |
| 37. | 2024. 2. 29. | -5.50% | 5.17% | 31.81 | 16.29 | -22.76 |
| 38. | 2024. 3. 31. | 4.85% | 3.10% | 22.18 | 3.86 | 9.26 |
| 39. | 2024. 4. 30. | -4.30% | -4.16% | 19.71 | 28.06 | 23.52 |
| 40. | 2024. 5. 31. | 4.20% | 4.80% | 16.53 | 13.44 | 14.90 |
| 41. | 2024. 6. 30. | 0.22% | 3.47% | 0.01 | 5.43 | 0.19 |
| 42. | 2024. 7. 31. | -0.13% | 1.13% | 0.07 | 0.00 | 0.00 |
| 43. | 2024. 8. 31. | 3.11% | 2.28% | 8.83 | 1.32 | 3.41 |
| 44. | 2024. 9. 30. | 7.49% | 2.02% | 54.08 | 0.78 | 6.50 |
| 45. | 2024. 10. 31. | -4.68% | -0.99% | 23.23 | 4.52 | 10.25 |
| 46. | 2024. 11. 30. | 5.25% | 5.73% | 26.09 | 21.10 | 23.46 |
| 47. | 2024. 12. 31. | -9.81% | -2.50% | 98.97 | 13.21 | 36.16 |
| 48. | 2025. 1. 31. | 0.19% | 2.70% | 0.00 | 2.45 | 0.09 |
| 49. | 2025. 2. 28. | 9.42% | -1.42% | 86.13 | 6.56 | -23.76 |
| 50. | 2025. 3. 31. | 5.24% | -5.75% | 26.07 | 47.48 | -35.18 |
| 51. | 2025. 4. 30. | -1.37% | -0.76% | 2.28 | 3.60 | 2.87 |
| 52. | 2025. 5. 31. | -0.23% | 6.15% | 0.13 | 25.16 | -1.83 |
| 53. | 2025. 6. 30. | -1.57% | 4.96% | 2.92 | 14.63 | -6.53 |
| 54. | 2025. 7. 31. | 0.39% | 2.17% | 0.06 | 1.06 | 0.26 |
| 55. | 2025. 8. 31. | 3.44% | 1.91% | 10.89 | 0.59 | 2.54 |
| 56. | 2025. 9. 30. | -0.63% | 3.53% | 0.59 | 5.74 | -1.85 |
| 57. | 2025. 10. 31. | -8.01% | 2.27% | 66.38 | 1.28 | -9.23 |
| 58. | 2025. 11. 30. | 3.45% | 0.13% | 10.95 | 1.01 | -3.33 |
| 59. | 2025. 12. 31. | -0.92% | -0.05% | 1.13 | 1.41 | 1.26 |
| 합계 (Σ): | 1,743.21 | 1,108.23 | 344.75 | |||
모두 보기
분산VZ = Σ(RVZ,t–RVZ)2 ÷ (59 – 1)
= 1,743.21 ÷ (59 – 1)
= 30.06
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산VZ, S&P 500 = Σ(RVZ,t–RVZ)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 344.75 ÷ (59 – 1)
= 5.94
체계적인 위험 추정 (β)
| 분산VZ | 30.06 |
| 분산S&P 500 | 19.11 |
| 공분산VZ, S&P 500 | 5.94 |
| 상관 계수VZ, S&P 5001 | 0.25 |
| βVZ2 | 0.31 |
| αVZ3 | -0.22% |
계산
1 상관 계수VZ, S&P 500
= 공분산VZ, S&P 500 ÷ (표준 편차VZ × 표준 편차S&P 500)
= 5.94 ÷ (5.48% × 4.37%)
= 0.25
2 βVZ
= 공분산VZ, S&P 500 ÷ 분산S&P 500
= 5.94 ÷ 19.11
= 0.31
3 αVZ
= 평균의VZ – βVZ × 평균의S&P 500
= 0.14% – 0.31 × 1.14%
= -0.22%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.54% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.37% |
| 보통주의 체계적 위험Verizon | βVZ | 0.31 |
| Verizon 보통주에 대한 예상 수익률3 | E(RVZ) | 8.53% |
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(RVZ) = RF + βVZ [E(RM) – RF]
= 4.54% + 0.31 [17.37% – 4.54%]
= 8.53%