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 |
| 2020. 1. 31. | $59.44 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $54.16 | -8.88% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $53.73 | -0.79% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $57.45 | $0.615 | 8.07% | 2,912.43 | 12.68% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $44.34 | 5.25% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $39.99 | -9.81% | 5,881.63 | -2.50% | |
| 평균의 (R): | -0.06% | 1.16% | ||||
| 표준 편차: | 5.60% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $59.44 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $54.16 | -8.88% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $53.73 | -0.79% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $57.45 | $0.615 | 8.07% | 2,912.43 | 12.68% |
| 4. | 2020. 5. 31. | $57.38 | -0.12% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $55.13 | -3.92% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $57.48 | $0.615 | 5.38% | 3,271.12 | 5.51% |
| 7. | 2020. 8. 31. | $59.27 | 3.11% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $59.49 | 0.37% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $56.99 | $0.6275 | -3.15% | 3,269.96 | -2.77% |
| 10. | 2020. 11. 30. | $60.41 | 6.00% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $58.75 | -2.75% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $54.75 | $0.6275 | -5.74% | 3,714.24 | -1.11% |
| 13. | 2021. 2. 28. | $55.30 | 1.00% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $58.15 | 5.15% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $57.79 | $0.6275 | 0.46% | 4,181.17 | 5.24% |
| 16. | 2021. 5. 31. | $56.49 | -2.25% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $56.03 | -0.81% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $55.78 | $0.6275 | 0.67% | 4,395.26 | 2.27% |
| 19. | 2021. 8. 31. | $55.00 | -1.40% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $54.01 | -1.80% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $52.99 | $0.64 | -0.70% | 4,605.38 | 6.91% |
| 22. | 2021. 11. 30. | $50.27 | -5.13% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $51.96 | 3.36% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $53.23 | $0.64 | 3.68% | 4,515.55 | -5.26% |
| 25. | 2022. 2. 28. | $53.67 | 0.83% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $50.94 | -5.09% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $46.30 | $0.64 | -7.85% | 4,131.93 | -8.80% |
| 28. | 2022. 5. 31. | $51.29 | 10.78% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $50.75 | -1.05% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $46.19 | $0.64 | -7.72% | 4,130.29 | 9.11% |
| 31. | 2022. 8. 31. | $41.81 | -9.48% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $37.97 | -9.18% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $37.37 | $0.6525 | 0.14% | 3,871.98 | 7.99% |
| 34. | 2022. 11. 30. | $38.98 | 4.31% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $39.40 | 1.08% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $41.57 | $0.6525 | 7.16% | 4,076.60 | 6.18% |
| 37. | 2023. 2. 28. | $38.81 | -6.64% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $38.89 | 0.21% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $38.83 | $0.6525 | 1.52% | 4,169.48 | 1.46% |
| 40. | 2023. 5. 31. | $35.63 | -8.24% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $37.19 | 4.38% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $34.08 | $0.6525 | -6.61% | 4,588.96 | 4.85% |
| 43. | 2023. 8. 31. | $34.98 | 2.64% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $32.41 | -7.35% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $35.13 | $0.665 | 10.44% | 4,193.80 | -2.20% |
| 46. | 2023. 11. 30. | $38.33 | 9.11% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $37.70 | -1.64% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $42.35 | $0.665 | 14.10% | 4,845.65 | 1.59% |
| 49. | 2024. 2. 29. | $40.02 | -5.50% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $41.96 | 4.85% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $39.49 | $0.665 | -4.30% | 5,035.69 | -4.16% |
| 52. | 2024. 5. 31. | $41.15 | 4.20% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $41.24 | 0.22% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $40.52 | $0.665 | -0.13% | 5,522.30 | 1.13% |
| 55. | 2024. 8. 31. | $41.78 | 3.11% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $44.91 | 7.49% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $42.13 | $0.6775 | -4.68% | 5,705.45 | -0.99% |
| 58. | 2024. 11. 30. | $44.34 | 5.25% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $39.99 | -9.81% | 5,881.63 | -2.50% | |
| 평균의 (R): | -0.06% | 1.16% | ||||
| 표준 편차: | 5.60% | 5.28% | ||||
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. | 2020. 2. 29. | -8.88% | -8.41% | 77.80 | 91.63 | 84.43 |
| 2. | 2020. 3. 31. | -0.79% | -12.51% | 0.54 | 186.96 | 10.00 |
| 3. | 2020. 4. 30. | 8.07% | 12.68% | 66.10 | 132.78 | 93.69 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 5.25% | 5.73% | 28.17 | 20.87 | 24.25 |
| 59. | 2024. 12. 31. | -9.81% | -2.50% | 95.03 | 13.40 | 35.68 |
| 합계 (Σ): | 1,819.41 | 1,618.62 | 720.65 | |||
| 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. | 2020. 2. 29. | -8.88% | -8.41% | 77.80 | 91.63 | 84.43 |
| 2. | 2020. 3. 31. | -0.79% | -12.51% | 0.54 | 186.96 | 10.00 |
| 3. | 2020. 4. 30. | 8.07% | 12.68% | 66.10 | 132.78 | 93.69 |
| 4. | 2020. 5. 31. | -0.12% | 4.53% | 0.00 | 11.34 | -0.20 |
| 5. | 2020. 6. 30. | -3.92% | 1.84% | 14.89 | 0.46 | -2.61 |
| 6. | 2020. 7. 31. | 5.38% | 5.51% | 29.60 | 18.91 | 23.66 |
| 7. | 2020. 8. 31. | 3.11% | 7.01% | 10.09 | 34.17 | 18.57 |
| 8. | 2020. 9. 30. | 0.37% | -3.92% | 0.19 | 25.85 | -2.20 |
| 9. | 2020. 10. 31. | -3.15% | -2.77% | 9.52 | 15.43 | 12.12 |
| 10. | 2020. 11. 30. | 6.00% | 10.75% | 36.76 | 92.03 | 58.17 |
| 11. | 2020. 12. 31. | -2.75% | 3.71% | 7.21 | 6.51 | -6.85 |
| 12. | 2021. 1. 31. | -5.74% | -1.11% | 32.24 | 5.18 | 12.92 |
| 13. | 2021. 2. 28. | 1.00% | 2.61% | 1.14 | 2.10 | 1.54 |
| 14. | 2021. 3. 31. | 5.15% | 4.24% | 27.21 | 9.50 | 16.08 |
| 15. | 2021. 4. 30. | 0.46% | 5.24% | 0.27 | 16.66 | 2.13 |
| 16. | 2021. 5. 31. | -2.25% | 0.55% | 4.78 | 0.38 | 1.34 |
| 17. | 2021. 6. 30. | -0.81% | 2.22% | 0.57 | 1.12 | -0.80 |
| 18. | 2021. 7. 31. | 0.67% | 2.27% | 0.54 | 1.24 | 0.82 |
| 19. | 2021. 8. 31. | -1.40% | 2.90% | 1.79 | 3.02 | -2.32 |
| 20. | 2021. 9. 30. | -1.80% | -4.76% | 3.02 | 35.02 | 10.28 |
| 21. | 2021. 10. 31. | -0.70% | 6.91% | 0.41 | 33.10 | -3.69 |
| 22. | 2021. 11. 30. | -5.13% | -0.83% | 25.71 | 3.98 | 10.11 |
| 23. | 2021. 12. 31. | 3.36% | 4.36% | 11.72 | 10.24 | 10.96 |
| 24. | 2022. 1. 31. | 3.68% | -5.26% | 13.97 | 41.21 | -24.00 |
| 25. | 2022. 2. 28. | 0.83% | -3.14% | 0.79 | 18.47 | -3.82 |
| 26. | 2022. 3. 31. | -5.09% | 3.58% | 25.24 | 5.84 | -12.14 |
| 27. | 2022. 4. 30. | -7.85% | -8.80% | 60.69 | 99.14 | 77.57 |
| 28. | 2022. 5. 31. | 10.78% | 0.01% | 117.50 | 1.34 | -12.53 |
| 29. | 2022. 6. 30. | -1.05% | -8.39% | 0.98 | 91.26 | 9.46 |
| 30. | 2022. 7. 31. | -7.72% | 9.11% | 58.70 | 63.21 | -60.91 |
| 31. | 2022. 8. 31. | -9.48% | -4.24% | 88.74 | 29.22 | 50.92 |
| 32. | 2022. 9. 30. | -9.18% | -9.34% | 83.21 | 110.27 | 95.79 |
| 33. | 2022. 10. 31. | 0.14% | 7.99% | 0.04 | 46.58 | 1.37 |
| 34. | 2022. 11. 30. | 4.31% | 5.38% | 19.10 | 17.76 | 18.42 |
| 35. | 2022. 12. 31. | 1.08% | -5.90% | 1.30 | 49.82 | -8.04 |
| 36. | 2023. 1. 31. | 7.16% | 6.18% | 52.21 | 25.14 | 36.23 |
| 37. | 2023. 2. 28. | -6.64% | -2.61% | 43.26 | 14.23 | 24.81 |
| 38. | 2023. 3. 31. | 0.21% | 3.51% | 0.07 | 5.49 | 0.63 |
| 39. | 2023. 4. 30. | 1.52% | 1.46% | 2.51 | 0.09 | 0.48 |
| 40. | 2023. 5. 31. | -8.24% | 0.25% | 66.89 | 0.83 | 7.47 |
| 41. | 2023. 6. 30. | 4.38% | 4.71% | 19.72 | 12.62 | 15.78 |
| 42. | 2023. 7. 31. | -6.61% | 4.85% | 42.85 | 13.58 | -24.12 |
| 43. | 2023. 8. 31. | 2.64% | -1.77% | 7.31 | 8.60 | -7.93 |
| 44. | 2023. 9. 30. | -7.35% | -4.87% | 53.07 | 36.40 | 43.95 |
| 45. | 2023. 10. 31. | 10.44% | -2.20% | 110.39 | 11.28 | -35.29 |
| 46. | 2023. 11. 30. | 9.11% | 8.92% | 84.11 | 60.17 | 71.14 |
| 47. | 2023. 12. 31. | -1.64% | 4.42% | 2.50 | 10.64 | -5.16 |
| 48. | 2024. 1. 31. | 14.10% | 1.59% | 200.52 | 0.18 | 6.06 |
| 49. | 2024. 2. 29. | -5.50% | 5.17% | 29.59 | 16.09 | -21.82 |
| 50. | 2024. 3. 31. | 4.85% | 3.10% | 24.11 | 3.77 | 9.53 |
| 51. | 2024. 4. 30. | -4.30% | -4.16% | 17.97 | 28.33 | 22.57 |
| 52. | 2024. 5. 31. | 4.20% | 4.80% | 18.20 | 13.26 | 15.53 |
| 53. | 2024. 6. 30. | 0.22% | 3.47% | 0.08 | 5.32 | 0.65 |
| 54. | 2024. 7. 31. | -0.13% | 1.13% | 0.01 | 0.00 | 0.00 |
| 55. | 2024. 8. 31. | 3.11% | 2.28% | 10.06 | 1.26 | 3.56 |
| 56. | 2024. 9. 30. | 7.49% | 2.02% | 57.06 | 0.74 | 6.48 |
| 57. | 2024. 10. 31. | -4.68% | -0.99% | 21.34 | 4.63 | 9.94 |
| 58. | 2024. 11. 30. | 5.25% | 5.73% | 28.17 | 20.87 | 24.25 |
| 59. | 2024. 12. 31. | -9.81% | -2.50% | 95.03 | 13.40 | 35.68 |
| 합계 (Σ): | 1,819.41 | 1,618.62 | 720.65 | |||
모두 보기
분산VZ = Σ(RVZ,t–RVZ)2 ÷ (59 – 1)
= 1,819.41 ÷ (59 – 1)
= 31.37
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산VZ, S&P 500 = Σ(RVZ,t–RVZ)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 720.65 ÷ (59 – 1)
= 12.42
체계적인 위험 추정 (β)
| 분산VZ | 31.37 |
| 분산S&P 500 | 27.91 |
| 공분산VZ, S&P 500 | 12.42 |
| 상관 계수VZ, S&P 5001 | 0.42 |
| βVZ2 | 0.45 |
| αVZ3 | -0.58% |
계산
1 상관 계수VZ, S&P 500
= 공분산VZ, S&P 500 ÷ (표준 편차VZ × 표준 편차S&P 500)
= 12.42 ÷ (5.60% × 5.28%)
= 0.42
2 βVZ
= 공분산VZ, S&P 500 ÷ 분산S&P 500
= 12.42 ÷ 27.91
= 0.45
3 αVZ
= 평균의VZ – βVZ × 평균의S&P 500
= -0.06% – 0.45 × 1.16%
= -0.58%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.79% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.38% |
| 보통주의 체계적 위험Verizon | βVZ | 0.45 |
| Verizon 보통주에 대한 예상 수익률3 | E(RVZ) | 10.40% |
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]
= 4.79% + 0.45 [17.38% – 4.79%]
= 10.40%