자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 AT&T보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
AT&T Inc., 월별 수익률
| AT&T Inc. (T) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값T,t1 | 피제수T,t1 | RT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $28.63 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $27.89 | -2.58% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $30.27 | 8.53% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $31.41 | $0.52 | 5.48% | 4,181.17 | 5.24% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $26.02 | 5.13% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $24.84 | -4.53% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.51% | 1.14% | ||||
| 표준 편차: | 7.29% | 4.37% | ||||
| AT&T Inc. (T) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값T,t1 | 피제수T,t1 | RT,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $28.63 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $27.89 | -2.58% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $30.27 | 8.53% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $31.41 | $0.52 | 5.48% | 4,181.17 | 5.24% |
| 4. | 2021. 5. 31. | $29.43 | -6.30% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $28.78 | -2.21% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $28.05 | $0.52 | -0.73% | 4,395.26 | 2.27% |
| 7. | 2021. 8. 31. | $27.42 | -2.25% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $27.01 | -1.50% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $25.26 | $0.52 | -4.55% | 4,605.38 | 6.91% |
| 10. | 2021. 11. 30. | $22.83 | -9.62% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $24.60 | 7.75% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $25.50 | $0.52 | 5.77% | 4,515.55 | -5.26% |
| 13. | 2022. 2. 28. | $23.69 | -7.10% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $23.63 | -0.25% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $18.86 | $0.2775 | -19.01% | 4,131.93 | -8.80% |
| 16. | 2022. 5. 31. | $21.29 | 12.88% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $20.96 | -1.55% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $18.78 | $0.2775 | -9.08% | 4,130.29 | 9.11% |
| 19. | 2022. 8. 31. | $17.54 | -6.60% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $15.34 | -12.54% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $18.23 | $0.2775 | 20.65% | 3,871.98 | 7.99% |
| 22. | 2022. 11. 30. | $19.28 | 5.76% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $18.41 | -4.51% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $20.37 | $0.2775 | 12.15% | 4,076.60 | 6.18% |
| 25. | 2023. 2. 28. | $18.91 | -7.17% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $19.25 | 1.80% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $17.67 | $0.2775 | -6.77% | 4,169.48 | 1.46% |
| 28. | 2023. 5. 31. | $15.73 | -10.98% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $15.95 | 1.40% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $14.52 | $0.2775 | -7.23% | 4,588.96 | 4.85% |
| 31. | 2023. 8. 31. | $14.79 | 1.86% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $15.02 | 1.56% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $15.40 | $0.2775 | 4.38% | 4,193.80 | -2.20% |
| 34. | 2023. 11. 30. | $16.57 | 7.60% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $16.78 | 1.27% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $17.69 | $0.2775 | 7.08% | 4,845.65 | 1.59% |
| 37. | 2024. 2. 29. | $16.93 | -4.30% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $17.60 | 3.96% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $16.89 | $0.2775 | -2.46% | 5,035.69 | -4.16% |
| 40. | 2024. 5. 31. | $18.22 | 7.87% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $19.11 | 4.88% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $19.25 | $0.2775 | 2.18% | 5,522.30 | 1.13% |
| 43. | 2024. 8. 31. | $19.90 | 3.38% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $22.00 | 10.55% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $22.54 | $0.2775 | 3.72% | 5,705.45 | -0.99% |
| 46. | 2024. 11. 30. | $23.16 | 2.75% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $22.77 | -1.68% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $23.73 | $0.2775 | 5.43% | 6,040.53 | 2.70% |
| 49. | 2025. 2. 28. | $27.41 | 15.51% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $28.28 | 3.17% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $27.70 | $0.2775 | -1.07% | 5,569.06 | -0.76% |
| 52. | 2025. 5. 31. | $27.80 | 0.36% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $28.94 | 4.10% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $27.41 | $0.2775 | -4.33% | 6,339.39 | 2.17% |
| 55. | 2025. 8. 31. | $29.29 | 6.86% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $28.24 | -3.58% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $24.75 | $0.2775 | -11.38% | 6,840.20 | 2.27% |
| 58. | 2025. 11. 30. | $26.02 | 5.13% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $24.84 | -4.53% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.51% | 1.14% | ||||
| 표준 편차: | 7.29% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 T의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
AT&T Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RT,t | RS&P 500,t | (RT,t–RT)2 | (RS&P 500,t–RS&P 500)2 | (RT,t–RT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -2.58% | 2.61% | 9.56 | 2.17 | -4.55 |
| 2. | 2021. 3. 31. | 8.53% | 4.24% | 64.42 | 9.66 | 24.94 |
| 3. | 2021. 4. 30. | 5.48% | 5.24% | 24.77 | 16.86 | 20.44 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | 5.13% | 0.13% | 21.38 | 1.01 | -4.65 |
| 59. | 2025. 12. 31. | -4.53% | -0.05% | 25.42 | 1.41 | 5.99 |
| 합계 (Σ): | 3,085.20 | 1,108.23 | 671.17 | |||
| t | 날짜 | RT,t | RS&P 500,t | (RT,t–RT)2 | (RS&P 500,t–RS&P 500)2 | (RT,t–RT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -2.58% | 2.61% | 9.56 | 2.17 | -4.55 |
| 2. | 2021. 3. 31. | 8.53% | 4.24% | 64.42 | 9.66 | 24.94 |
| 3. | 2021. 4. 30. | 5.48% | 5.24% | 24.77 | 16.86 | 20.44 |
| 4. | 2021. 5. 31. | -6.30% | 0.55% | 46.39 | 0.35 | 4.00 |
| 5. | 2021. 6. 30. | -2.21% | 2.22% | 7.38 | 1.18 | -2.95 |
| 6. | 2021. 7. 31. | -0.73% | 2.27% | 1.53 | 1.30 | -1.41 |
| 7. | 2021. 8. 31. | -2.25% | 2.90% | 7.58 | 3.11 | -4.85 |
| 8. | 2021. 9. 30. | -1.50% | -4.76% | 4.01 | 34.73 | 11.80 |
| 9. | 2021. 10. 31. | -4.55% | 6.91% | 25.61 | 33.39 | -29.24 |
| 10. | 2021. 11. 30. | -9.62% | -0.83% | 102.56 | 3.88 | 19.95 |
| 11. | 2021. 12. 31. | 7.75% | 4.36% | 52.50 | 10.40 | 23.37 |
| 12. | 2022. 1. 31. | 5.77% | -5.26% | 27.72 | 40.89 | -33.67 |
| 13. | 2022. 2. 28. | -7.10% | -3.14% | 57.84 | 18.25 | 32.49 |
| 14. | 2022. 3. 31. | -0.25% | 3.58% | 0.58 | 5.96 | -1.86 |
| 15. | 2022. 4. 30. | -19.01% | -8.80% | 380.99 | 98.64 | 193.86 |
| 16. | 2022. 5. 31. | 12.88% | 0.01% | 153.19 | 1.28 | -14.00 |
| 17. | 2022. 6. 30. | -1.55% | -8.39% | 4.23 | 90.79 | 19.60 |
| 18. | 2022. 7. 31. | -9.08% | 9.11% | 91.85 | 63.61 | -76.44 |
| 19. | 2022. 8. 31. | -6.60% | -4.24% | 50.55 | 28.95 | 38.25 |
| 20. | 2022. 9. 30. | -12.54% | -9.34% | 170.30 | 109.74 | 136.71 |
| 21. | 2022. 10. 31. | 20.65% | 7.99% | 405.68 | 46.93 | 137.97 |
| 22. | 2022. 11. 30. | 5.76% | 5.38% | 27.59 | 17.97 | 22.27 |
| 23. | 2022. 12. 31. | -4.51% | -5.90% | 25.20 | 49.47 | 35.30 |
| 24. | 2023. 1. 31. | 12.15% | 6.18% | 135.64 | 25.39 | 58.69 |
| 25. | 2023. 2. 28. | -7.17% | -2.61% | 58.90 | 14.04 | 28.76 |
| 26. | 2023. 3. 31. | 1.80% | 3.51% | 1.67 | 5.61 | 3.06 |
| 27. | 2023. 4. 30. | -6.77% | 1.46% | 52.90 | 0.11 | -2.39 |
| 28. | 2023. 5. 31. | -10.98% | 0.25% | 131.93 | 0.79 | 10.20 |
| 29. | 2023. 6. 30. | 1.40% | 4.71% | 0.79 | 12.80 | 3.19 |
| 30. | 2023. 7. 31. | -7.23% | 4.85% | 59.80 | 13.76 | -28.69 |
| 31. | 2023. 8. 31. | 1.86% | -1.77% | 1.83 | 8.46 | -3.93 |
| 32. | 2023. 9. 30. | 1.56% | -4.87% | 1.10 | 36.10 | -6.30 |
| 33. | 2023. 10. 31. | 4.38% | -2.20% | 14.98 | 11.12 | -12.90 |
| 34. | 2023. 11. 30. | 7.60% | 8.92% | 50.27 | 60.56 | 55.17 |
| 35. | 2023. 12. 31. | 1.27% | 4.42% | 0.58 | 10.80 | 2.50 |
| 36. | 2024. 1. 31. | 7.08% | 1.59% | 43.16 | 0.21 | 2.98 |
| 37. | 2024. 2. 29. | -4.30% | 5.17% | 23.07 | 16.29 | -19.39 |
| 38. | 2024. 3. 31. | 3.96% | 3.10% | 11.90 | 3.86 | 6.78 |
| 39. | 2024. 4. 30. | -2.46% | -4.16% | 8.79 | 28.06 | 15.71 |
| 40. | 2024. 5. 31. | 7.87% | 4.80% | 54.28 | 13.44 | 27.01 |
| 41. | 2024. 6. 30. | 4.88% | 3.47% | 19.16 | 5.43 | 10.20 |
| 42. | 2024. 7. 31. | 2.18% | 1.13% | 2.81 | 0.00 | -0.01 |
| 43. | 2024. 8. 31. | 3.38% | 2.28% | 8.23 | 1.32 | 3.29 |
| 44. | 2024. 9. 30. | 10.55% | 2.02% | 100.91 | 0.78 | 8.88 |
| 45. | 2024. 10. 31. | 3.72% | -0.99% | 10.30 | 4.52 | -6.82 |
| 46. | 2024. 11. 30. | 2.75% | 5.73% | 5.03 | 21.10 | 10.31 |
| 47. | 2024. 12. 31. | -1.68% | -2.50% | 4.80 | 13.21 | 7.97 |
| 48. | 2025. 1. 31. | 5.43% | 2.70% | 24.28 | 2.45 | 7.71 |
| 49. | 2025. 2. 28. | 15.51% | -1.42% | 225.02 | 6.56 | -38.41 |
| 50. | 2025. 3. 31. | 3.17% | -5.75% | 7.11 | 47.48 | -18.38 |
| 51. | 2025. 4. 30. | -1.07% | -0.76% | 2.49 | 3.60 | 2.99 |
| 52. | 2025. 5. 31. | 0.36% | 6.15% | 0.02 | 25.16 | -0.73 |
| 53. | 2025. 6. 30. | 4.10% | 4.96% | 12.91 | 14.63 | 13.74 |
| 54. | 2025. 7. 31. | -4.33% | 2.17% | 23.38 | 1.06 | -4.98 |
| 55. | 2025. 8. 31. | 6.86% | 1.91% | 40.34 | 0.59 | 4.89 |
| 56. | 2025. 9. 30. | -3.58% | 3.53% | 16.75 | 5.74 | -9.81 |
| 57. | 2025. 10. 31. | -11.38% | 2.27% | 141.20 | 1.28 | -13.46 |
| 58. | 2025. 11. 30. | 5.13% | 0.13% | 21.38 | 1.01 | -4.65 |
| 59. | 2025. 12. 31. | -4.53% | -0.05% | 25.42 | 1.41 | 5.99 |
| 합계 (Σ): | 3,085.20 | 1,108.23 | 671.17 | |||
모두 보기
분산T = Σ(RT,t–RT)2 ÷ (59 – 1)
= 3,085.20 ÷ (59 – 1)
= 53.19
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산T, S&P 500 = Σ(RT,t–RT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 671.17 ÷ (59 – 1)
= 11.57
체계적인 위험 추정 (β)
| 분산T | 53.19 |
| 분산S&P 500 | 19.11 |
| 공분산T, S&P 500 | 11.57 |
| 상관 계수T, S&P 5001 | 0.36 |
| βT2 | 0.61 |
| αT3 | -0.18% |
계산
1 상관 계수T, S&P 500
= 공분산T, S&P 500 ÷ (표준 편차T × 표준 편차S&P 500)
= 11.57 ÷ (7.29% × 4.37%)
= 0.36
2 βT
= 공분산T, S&P 500 ÷ 분산S&P 500
= 11.57 ÷ 19.11
= 0.61
3 αT
= 평균의T – βT × 평균의S&P 500
= 0.51% – 0.61 × 1.14%
= -0.18%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.79% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.38% |
| 보통주의 체계적 위험AT&T | βT | 0.61 |
| AT&T 보통주 예상 수익률3 | E(RT) | 12.42% |
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(RT) = RF + βT [E(RM) – RF]
= 4.79% + 0.61 [17.38% – 4.79%]
= 12.42%