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 |
| 2020. 1. 31. | $37.62 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $35.22 | -6.38% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $29.15 | -17.23% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $30.47 | $0.52 | 6.31% | 2,912.43 | 12.68% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | $23.16 | 2.75% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $22.77 | -1.68% | 5,881.63 | -2.50% | |
| 평균의 (R): | -0.06% | 1.16% | ||||
| 표준 편차: | 7.20% | 5.28% | ||||
| 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 |
| 2020. 1. 31. | $37.62 | 3,225.52 | ||||
| 1. | 2020. 2. 29. | $35.22 | -6.38% | 2,954.22 | -8.41% | |
| 2. | 2020. 3. 31. | $29.15 | -17.23% | 2,584.59 | -12.51% | |
| 3. | 2020. 4. 30. | $30.47 | $0.52 | 6.31% | 2,912.43 | 12.68% |
| 4. | 2020. 5. 31. | $30.86 | 1.28% | 3,044.31 | 4.53% | |
| 5. | 2020. 6. 30. | $30.23 | -2.04% | 3,100.29 | 1.84% | |
| 6. | 2020. 7. 31. | $29.58 | $0.52 | -0.43% | 3,271.12 | 5.51% |
| 7. | 2020. 8. 31. | $29.81 | 0.78% | 3,500.31 | 7.01% | |
| 8. | 2020. 9. 30. | $28.51 | -4.36% | 3,363.00 | -3.92% | |
| 9. | 2020. 10. 31. | $27.02 | $0.52 | -3.40% | 3,269.96 | -2.77% |
| 10. | 2020. 11. 30. | $28.75 | 6.40% | 3,621.63 | 10.75% | |
| 11. | 2020. 12. 31. | $28.76 | 0.03% | 3,756.07 | 3.71% | |
| 12. | 2021. 1. 31. | $28.63 | $0.52 | 1.36% | 3,714.24 | -1.11% |
| 13. | 2021. 2. 28. | $27.89 | -2.58% | 3,811.15 | 2.61% | |
| 14. | 2021. 3. 31. | $30.27 | 8.53% | 3,972.89 | 4.24% | |
| 15. | 2021. 4. 30. | $31.41 | $0.52 | 5.48% | 4,181.17 | 5.24% |
| 16. | 2021. 5. 31. | $29.43 | -6.30% | 4,204.11 | 0.55% | |
| 17. | 2021. 6. 30. | $28.78 | -2.21% | 4,297.50 | 2.22% | |
| 18. | 2021. 7. 31. | $28.05 | $0.52 | -0.73% | 4,395.26 | 2.27% |
| 19. | 2021. 8. 31. | $27.42 | -2.25% | 4,522.68 | 2.90% | |
| 20. | 2021. 9. 30. | $27.01 | -1.50% | 4,307.54 | -4.76% | |
| 21. | 2021. 10. 31. | $25.26 | $0.52 | -4.55% | 4,605.38 | 6.91% |
| 22. | 2021. 11. 30. | $22.83 | -9.62% | 4,567.00 | -0.83% | |
| 23. | 2021. 12. 31. | $24.60 | 7.75% | 4,766.18 | 4.36% | |
| 24. | 2022. 1. 31. | $25.50 | $0.52 | 5.77% | 4,515.55 | -5.26% |
| 25. | 2022. 2. 28. | $23.69 | -7.10% | 4,373.94 | -3.14% | |
| 26. | 2022. 3. 31. | $23.63 | -0.25% | 4,530.41 | 3.58% | |
| 27. | 2022. 4. 30. | $18.86 | $0.2775 | -19.01% | 4,131.93 | -8.80% |
| 28. | 2022. 5. 31. | $21.29 | 12.88% | 4,132.15 | 0.01% | |
| 29. | 2022. 6. 30. | $20.96 | -1.55% | 3,785.38 | -8.39% | |
| 30. | 2022. 7. 31. | $18.78 | $0.2775 | -9.08% | 4,130.29 | 9.11% |
| 31. | 2022. 8. 31. | $17.54 | -6.60% | 3,955.00 | -4.24% | |
| 32. | 2022. 9. 30. | $15.34 | -12.54% | 3,585.62 | -9.34% | |
| 33. | 2022. 10. 31. | $18.23 | $0.2775 | 20.65% | 3,871.98 | 7.99% |
| 34. | 2022. 11. 30. | $19.28 | 5.76% | 4,080.11 | 5.38% | |
| 35. | 2022. 12. 31. | $18.41 | -4.51% | 3,839.50 | -5.90% | |
| 36. | 2023. 1. 31. | $20.37 | $0.2775 | 12.15% | 4,076.60 | 6.18% |
| 37. | 2023. 2. 28. | $18.91 | -7.17% | 3,970.15 | -2.61% | |
| 38. | 2023. 3. 31. | $19.25 | 1.80% | 4,109.31 | 3.51% | |
| 39. | 2023. 4. 30. | $17.67 | $0.2775 | -6.77% | 4,169.48 | 1.46% |
| 40. | 2023. 5. 31. | $15.73 | -10.98% | 4,179.83 | 0.25% | |
| 41. | 2023. 6. 30. | $15.95 | 1.40% | 4,376.86 | 4.71% | |
| 42. | 2023. 7. 31. | $14.52 | $0.2775 | -7.23% | 4,588.96 | 4.85% |
| 43. | 2023. 8. 31. | $14.79 | 1.86% | 4,507.66 | -1.77% | |
| 44. | 2023. 9. 30. | $15.02 | 1.56% | 4,288.05 | -4.87% | |
| 45. | 2023. 10. 31. | $15.40 | $0.2775 | 4.38% | 4,193.80 | -2.20% |
| 46. | 2023. 11. 30. | $16.57 | 7.60% | 4,567.80 | 8.92% | |
| 47. | 2023. 12. 31. | $16.78 | 1.27% | 4,769.83 | 4.42% | |
| 48. | 2024. 1. 31. | $17.69 | $0.2775 | 7.08% | 4,845.65 | 1.59% |
| 49. | 2024. 2. 29. | $16.93 | -4.30% | 5,096.27 | 5.17% | |
| 50. | 2024. 3. 31. | $17.60 | 3.96% | 5,254.35 | 3.10% | |
| 51. | 2024. 4. 30. | $16.89 | $0.2775 | -2.46% | 5,035.69 | -4.16% |
| 52. | 2024. 5. 31. | $18.22 | 7.87% | 5,277.51 | 4.80% | |
| 53. | 2024. 6. 30. | $19.11 | 4.88% | 5,460.48 | 3.47% | |
| 54. | 2024. 7. 31. | $19.25 | $0.2775 | 2.18% | 5,522.30 | 1.13% |
| 55. | 2024. 8. 31. | $19.90 | 3.38% | 5,648.40 | 2.28% | |
| 56. | 2024. 9. 30. | $22.00 | 10.55% | 5,762.48 | 2.02% | |
| 57. | 2024. 10. 31. | $22.54 | $0.2775 | 3.72% | 5,705.45 | -0.99% |
| 58. | 2024. 11. 30. | $23.16 | 2.75% | 6,032.38 | 5.73% | |
| 59. | 2024. 12. 31. | $22.77 | -1.68% | 5,881.63 | -2.50% | |
| 평균의 (R): | -0.06% | 1.16% | ||||
| 표준 편차: | 7.20% | 5.28% | ||||
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. | 2020. 2. 29. | -6.38% | -8.41% | 39.96 | 91.63 | 60.51 |
| 2. | 2020. 3. 31. | -17.23% | -12.51% | 295.03 | 186.96 | 234.86 |
| 3. | 2020. 4. 30. | 6.31% | 12.68% | 40.58 | 132.78 | 73.41 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2024. 11. 30. | 2.75% | 5.73% | 7.89 | 20.87 | 12.83 |
| 59. | 2024. 12. 31. | -1.68% | -2.50% | 2.64 | 13.40 | 5.95 |
| 합계 (Σ): | 3,004.65 | 1,618.62 | 1,193.80 | |||
| 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. | 2020. 2. 29. | -6.38% | -8.41% | 39.96 | 91.63 | 60.51 |
| 2. | 2020. 3. 31. | -17.23% | -12.51% | 295.03 | 186.96 | 234.86 |
| 3. | 2020. 4. 30. | 6.31% | 12.68% | 40.58 | 132.78 | 73.41 |
| 4. | 2020. 5. 31. | 1.28% | 4.53% | 1.79 | 11.34 | 4.51 |
| 5. | 2020. 6. 30. | -2.04% | 1.84% | 3.93 | 0.46 | -1.34 |
| 6. | 2020. 7. 31. | -0.43% | 5.51% | 0.14 | 18.91 | -1.62 |
| 7. | 2020. 8. 31. | 0.78% | 7.01% | 0.70 | 34.17 | 4.89 |
| 8. | 2020. 9. 30. | -4.36% | -3.92% | 18.51 | 25.85 | 21.88 |
| 9. | 2020. 10. 31. | -3.40% | -2.77% | 11.18 | 15.43 | 13.14 |
| 10. | 2020. 11. 30. | 6.40% | 10.75% | 41.74 | 92.03 | 61.98 |
| 11. | 2020. 12. 31. | 0.03% | 3.71% | 0.01 | 6.51 | 0.24 |
| 12. | 2021. 1. 31. | 1.36% | -1.11% | 2.00 | 5.18 | -3.22 |
| 13. | 2021. 2. 28. | -2.58% | 2.61% | 6.38 | 2.10 | -3.66 |
| 14. | 2021. 3. 31. | 8.53% | 4.24% | 73.82 | 9.50 | 26.48 |
| 15. | 2021. 4. 30. | 5.48% | 5.24% | 30.72 | 16.66 | 22.62 |
| 16. | 2021. 5. 31. | -6.30% | 0.55% | 39.01 | 0.38 | 3.83 |
| 17. | 2021. 6. 30. | -2.21% | 2.22% | 4.62 | 1.12 | -2.28 |
| 18. | 2021. 7. 31. | -0.73% | 2.27% | 0.45 | 1.24 | -0.75 |
| 19. | 2021. 8. 31. | -2.25% | 2.90% | 4.79 | 3.02 | -3.80 |
| 20. | 2021. 9. 30. | -1.50% | -4.76% | 2.07 | 35.02 | 8.50 |
| 21. | 2021. 10. 31. | -4.55% | 6.91% | 20.21 | 33.10 | -25.86 |
| 22. | 2021. 11. 30. | -9.62% | -0.83% | 91.43 | 3.98 | 19.07 |
| 23. | 2021. 12. 31. | 7.75% | 4.36% | 61.01 | 10.24 | 25.00 |
| 24. | 2022. 1. 31. | 5.77% | -5.26% | 34.00 | 41.21 | -37.43 |
| 25. | 2022. 2. 28. | -7.10% | -3.14% | 49.56 | 18.47 | 30.25 |
| 26. | 2022. 3. 31. | -0.25% | 3.58% | 0.04 | 5.84 | -0.47 |
| 27. | 2022. 4. 30. | -19.01% | -8.80% | 359.24 | 99.14 | 188.72 |
| 28. | 2022. 5. 31. | 12.88% | 0.01% | 167.51 | 1.34 | -14.96 |
| 29. | 2022. 6. 30. | -1.55% | -8.39% | 2.23 | 91.26 | 14.25 |
| 30. | 2022. 7. 31. | -9.08% | 9.11% | 81.34 | 63.21 | -71.70 |
| 31. | 2022. 8. 31. | -6.60% | -4.24% | 42.83 | 29.22 | 35.38 |
| 32. | 2022. 9. 30. | -12.54% | -9.34% | 155.86 | 110.27 | 131.10 |
| 33. | 2022. 10. 31. | 20.65% | 7.99% | 428.77 | 46.58 | 141.33 |
| 34. | 2022. 11. 30. | 5.76% | 5.38% | 33.85 | 17.76 | 24.52 |
| 35. | 2022. 12. 31. | -4.51% | -5.90% | 19.84 | 49.82 | 31.44 |
| 36. | 2023. 1. 31. | 12.15% | 6.18% | 149.13 | 25.14 | 61.23 |
| 37. | 2023. 2. 28. | -7.17% | -2.61% | 50.54 | 14.23 | 26.82 |
| 38. | 2023. 3. 31. | 1.80% | 3.51% | 3.45 | 5.49 | 4.35 |
| 39. | 2023. 4. 30. | -6.77% | 1.46% | 45.00 | 0.09 | -2.03 |
| 40. | 2023. 5. 31. | -10.98% | 0.25% | 119.26 | 0.83 | 9.97 |
| 41. | 2023. 6. 30. | 1.40% | 4.71% | 2.12 | 12.62 | 5.18 |
| 42. | 2023. 7. 31. | -7.23% | 4.85% | 51.37 | 13.58 | -26.41 |
| 43. | 2023. 8. 31. | 1.86% | -1.77% | 3.68 | 8.60 | -5.62 |
| 44. | 2023. 9. 30. | 1.56% | -4.87% | 2.60 | 36.40 | -9.73 |
| 45. | 2023. 10. 31. | 4.38% | -2.20% | 19.68 | 11.28 | -14.90 |
| 46. | 2023. 11. 30. | 7.60% | 8.92% | 58.61 | 60.17 | 59.38 |
| 47. | 2023. 12. 31. | 1.27% | 4.42% | 1.76 | 10.64 | 4.32 |
| 48. | 2024. 1. 31. | 7.08% | 1.59% | 50.91 | 0.18 | 3.06 |
| 49. | 2024. 2. 29. | -4.30% | 5.17% | 17.96 | 16.09 | -17.00 |
| 50. | 2024. 3. 31. | 3.96% | 3.10% | 16.13 | 3.77 | 7.79 |
| 51. | 2024. 4. 30. | -2.46% | -4.16% | 5.76 | 28.33 | 12.77 |
| 52. | 2024. 5. 31. | 7.87% | 4.80% | 62.93 | 13.26 | 28.88 |
| 53. | 2024. 6. 30. | 4.88% | 3.47% | 24.43 | 5.32 | 11.40 |
| 54. | 2024. 7. 31. | 2.18% | 1.13% | 5.03 | 0.00 | -0.07 |
| 55. | 2024. 8. 31. | 3.38% | 2.28% | 11.80 | 1.26 | 3.85 |
| 56. | 2024. 9. 30. | 10.55% | 2.02% | 112.59 | 0.74 | 9.11 |
| 57. | 2024. 10. 31. | 3.72% | -0.99% | 14.24 | 4.63 | -8.12 |
| 58. | 2024. 11. 30. | 2.75% | 5.73% | 7.89 | 20.87 | 12.83 |
| 59. | 2024. 12. 31. | -1.68% | -2.50% | 2.64 | 13.40 | 5.95 |
| 합계 (Σ): | 3,004.65 | 1,618.62 | 1,193.80 | |||
모두 보기
분산T = Σ(RT,t–RT)2 ÷ (59 – 1)
= 3,004.65 ÷ (59 – 1)
= 51.80
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
공분산T, S&P 500 = Σ(RT,t–RT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,193.80 ÷ (59 – 1)
= 20.58
체계적인 위험 추정 (β)
| 분산T | 51.80 |
| 분산S&P 500 | 27.91 |
| 공분산T, S&P 500 | 20.58 |
| 상관 계수T, S&P 5001 | 0.54 |
| βT2 | 0.74 |
| αT3 | -0.91% |
계산
1 상관 계수T, S&P 500
= 공분산T, S&P 500 ÷ (표준 편차T × 표준 편차S&P 500)
= 20.58 ÷ (7.20% × 5.28%)
= 0.54
2 βT
= 공분산T, S&P 500 ÷ 분산S&P 500
= 20.58 ÷ 27.91
= 0.74
3 αT
= 평균의T – βT × 평균의S&P 500
= -0.06% – 0.74 × 1.16%
= -0.91%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.60% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.89% |
| 보통주의 체계적 위험AT&T | βT | 0.74 |
| AT&T 보통주 예상 수익률3 | E(RT) | 12.19% |
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]
= 4.60% + 0.74 [14.89% – 4.60%]
= 12.19%