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 |
| 2019. 1. 31. | $30.06 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $31.12 | 3.53% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $31.36 | 0.77% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $30.96 | $0.51 | 0.35% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $16.57 | 7.60% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $16.78 | 1.27% | 4,769.83 | 4.42% | |
| 평균의 (R): | -0.20% | 1.11% | ||||
| 표준 편차: | 7.07% | 5.31% | ||||
| 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 |
| 2019. 1. 31. | $30.06 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $31.12 | 3.53% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $31.36 | 0.77% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $30.96 | $0.51 | 0.35% | 2,945.83 | 3.93% |
| 4. | 2019. 5. 31. | $30.58 | -1.23% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $33.51 | 9.58% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $34.05 | $0.51 | 3.13% | 2,980.38 | 1.31% |
| 7. | 2019. 8. 31. | $35.26 | 3.55% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $37.84 | 7.32% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $38.49 | $0.51 | 3.07% | 3,037.56 | 2.04% |
| 10. | 2019. 11. 30. | $37.38 | -2.88% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $39.08 | 4.55% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $37.62 | $0.52 | -2.41% | 3,225.52 | -0.16% |
| 13. | 2020. 2. 29. | $35.22 | -6.38% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $29.15 | -17.23% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $30.47 | $0.52 | 6.31% | 2,912.43 | 12.68% |
| 16. | 2020. 5. 31. | $30.86 | 1.28% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $30.23 | -2.04% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $29.58 | $0.52 | -0.43% | 3,271.12 | 5.51% |
| 19. | 2020. 8. 31. | $29.81 | 0.78% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $28.51 | -4.36% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $27.02 | $0.52 | -3.40% | 3,269.96 | -2.77% |
| 22. | 2020. 11. 30. | $28.75 | 6.40% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $28.76 | 0.03% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $28.63 | $0.52 | 1.36% | 3,714.24 | -1.11% |
| 25. | 2021. 2. 28. | $27.89 | -2.58% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $30.27 | 8.53% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $31.41 | $0.52 | 5.48% | 4,181.17 | 5.24% |
| 28. | 2021. 5. 31. | $29.43 | -6.30% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $28.78 | -2.21% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $28.05 | $0.52 | -0.73% | 4,395.26 | 2.27% |
| 31. | 2021. 8. 31. | $27.42 | -2.25% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $27.01 | -1.50% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $25.26 | $0.52 | -4.55% | 4,605.38 | 6.91% |
| 34. | 2021. 11. 30. | $22.83 | -9.62% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $24.60 | 7.75% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $25.50 | $0.52 | 5.77% | 4,515.55 | -5.26% |
| 37. | 2022. 2. 28. | $23.69 | -7.10% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $23.63 | -0.25% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $18.86 | $0.2775 | -19.01% | 4,131.93 | -8.80% |
| 40. | 2022. 5. 31. | $21.29 | 12.88% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $20.96 | -1.55% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $18.78 | $0.2775 | -9.08% | 4,130.29 | 9.11% |
| 43. | 2022. 8. 31. | $17.54 | -6.60% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $15.34 | -12.54% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $18.23 | $0.2775 | 20.65% | 3,871.98 | 7.99% |
| 46. | 2022. 11. 30. | $19.28 | 5.76% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $18.41 | -4.51% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $20.37 | $0.2775 | 12.15% | 4,076.60 | 6.18% |
| 49. | 2023. 2. 28. | $18.91 | -7.17% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $19.25 | 1.80% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $17.67 | $0.2775 | -6.77% | 4,169.48 | 1.46% |
| 52. | 2023. 5. 31. | $15.73 | -10.98% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $15.95 | 1.40% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $14.52 | $0.2775 | -7.23% | 4,588.96 | 4.85% |
| 55. | 2023. 8. 31. | $14.79 | 1.86% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $15.02 | 1.56% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $15.40 | $0.2775 | 4.38% | 4,193.80 | -2.20% |
| 58. | 2023. 11. 30. | $16.57 | 7.60% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $16.78 | 1.27% | 4,769.83 | 4.42% | |
| 평균의 (R): | -0.20% | 1.11% | ||||
| 표준 편차: | 7.07% | 5.31% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 T의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 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. | 2019. 2. 28. | 3.53% | 2.97% | 13.92 | 3.49 | 6.96 |
| 2. | 2019. 3. 31. | 0.77% | 1.79% | 0.95 | 0.47 | 0.67 |
| 3. | 2019. 4. 30. | 0.35% | 3.93% | 0.31 | 7.98 | 1.57 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 7.60% | 8.92% | 60.86 | 61.03 | 60.95 |
| 59. | 2023. 12. 31. | 1.27% | 4.42% | 2.17 | 11.00 | 4.88 |
| 합계 (Σ): | 2,901.17 | 1,634.30 | 1,196.51 | |||
| 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. | 2019. 2. 28. | 3.53% | 2.97% | 13.92 | 3.49 | 6.96 |
| 2. | 2019. 3. 31. | 0.77% | 1.79% | 0.95 | 0.47 | 0.67 |
| 3. | 2019. 4. 30. | 0.35% | 3.93% | 0.31 | 7.98 | 1.57 |
| 4. | 2019. 5. 31. | -1.23% | -6.58% | 1.05 | 59.04 | 7.86 |
| 5. | 2019. 6. 30. | 9.58% | 6.89% | 95.76 | 33.49 | 56.63 |
| 6. | 2019. 7. 31. | 3.13% | 1.31% | 11.14 | 0.04 | 0.69 |
| 7. | 2019. 8. 31. | 3.55% | -1.81% | 14.12 | 8.50 | -10.95 |
| 8. | 2019. 9. 30. | 7.32% | 1.72% | 56.57 | 0.37 | 4.60 |
| 9. | 2019. 10. 31. | 3.07% | 2.04% | 10.69 | 0.88 | 3.06 |
| 10. | 2019. 11. 30. | -2.88% | 3.40% | 7.18 | 5.28 | -6.16 |
| 11. | 2019. 12. 31. | 4.55% | 2.86% | 22.58 | 3.07 | 8.33 |
| 12. | 2020. 1. 31. | -2.41% | -0.16% | 4.85 | 1.61 | 2.79 |
| 13. | 2020. 2. 29. | -6.38% | -8.41% | 38.14 | 90.57 | 58.77 |
| 14. | 2020. 3. 31. | -17.23% | -12.51% | 290.04 | 185.44 | 231.92 |
| 15. | 2020. 4. 30. | 6.31% | 12.68% | 42.46 | 134.06 | 75.45 |
| 16. | 2020. 5. 31. | 1.28% | 4.53% | 2.20 | 11.71 | 5.08 |
| 17. | 2020. 6. 30. | -2.04% | 1.84% | 3.38 | 0.54 | -1.35 |
| 18. | 2020. 7. 31. | -0.43% | 5.51% | 0.05 | 19.40 | -1.00 |
| 19. | 2020. 8. 31. | 0.78% | 7.01% | 0.96 | 34.82 | 5.79 |
| 20. | 2020. 9. 30. | -4.36% | -3.92% | 17.28 | 25.29 | 20.90 |
| 21. | 2020. 10. 31. | -3.40% | -2.77% | 10.23 | 15.00 | 12.38 |
| 22. | 2020. 11. 30. | 6.40% | 10.75% | 43.65 | 93.10 | 63.75 |
| 23. | 2020. 12. 31. | 0.03% | 3.71% | 0.06 | 6.79 | 0.62 |
| 24. | 2021. 1. 31. | 1.36% | -1.11% | 2.43 | 4.93 | -3.46 |
| 25. | 2021. 2. 28. | -2.58% | 2.61% | 5.67 | 2.26 | -3.58 |
| 26. | 2021. 3. 31. | 8.53% | 4.24% | 76.35 | 9.85 | 27.42 |
| 27. | 2021. 4. 30. | 5.48% | 5.24% | 32.35 | 17.11 | 23.53 |
| 28. | 2021. 5. 31. | -6.30% | 0.55% | 37.21 | 0.31 | 3.40 |
| 29. | 2021. 6. 30. | -2.21% | 2.22% | 4.02 | 1.24 | -2.24 |
| 30. | 2021. 7. 31. | -0.73% | 2.27% | 0.28 | 1.37 | -0.61 |
| 31. | 2021. 8. 31. | -2.25% | 2.90% | 4.17 | 3.22 | -3.66 |
| 32. | 2021. 9. 30. | -1.50% | -4.76% | 1.67 | 34.37 | 7.57 |
| 33. | 2021. 10. 31. | -4.55% | 6.91% | 18.92 | 33.74 | -25.27 |
| 34. | 2021. 11. 30. | -9.62% | -0.83% | 88.66 | 3.76 | 18.26 |
| 35. | 2021. 12. 31. | 7.75% | 4.36% | 63.31 | 10.60 | 25.90 |
| 36. | 2022. 1. 31. | 5.77% | -5.26% | 35.72 | 40.51 | -38.04 |
| 37. | 2022. 2. 28. | -7.10% | -3.14% | 47.53 | 17.99 | 29.24 |
| 38. | 2022. 3. 31. | -0.25% | 3.58% | 0.00 | 6.11 | -0.12 |
| 39. | 2022. 4. 30. | -19.01% | -8.80% | 353.73 | 98.04 | 186.23 |
| 40. | 2022. 5. 31. | 12.88% | 0.01% | 171.31 | 1.21 | -14.40 |
| 41. | 2022. 6. 30. | -1.55% | -8.39% | 1.81 | 90.21 | 12.78 |
| 42. | 2022. 7. 31. | -9.08% | 9.11% | 78.73 | 64.09 | -71.03 |
| 43. | 2022. 8. 31. | -6.60% | -4.24% | 40.94 | 28.62 | 34.23 |
| 44. | 2022. 9. 30. | -12.54% | -9.34% | 152.24 | 109.11 | 128.88 |
| 45. | 2022. 10. 31. | 20.65% | 7.99% | 434.84 | 47.34 | 143.48 |
| 46. | 2022. 11. 30. | 5.76% | 5.38% | 35.57 | 18.23 | 25.46 |
| 47. | 2022. 12. 31. | -4.51% | -5.90% | 18.56 | 49.04 | 30.17 |
| 48. | 2023. 1. 31. | 12.15% | 6.18% | 152.72 | 25.70 | 62.65 |
| 49. | 2023. 2. 28. | -7.17% | -2.61% | 48.49 | 13.82 | 25.88 |
| 50. | 2023. 3. 31. | 1.80% | 3.51% | 4.01 | 5.76 | 4.80 |
| 51. | 2023. 4. 30. | -6.77% | 1.46% | 43.06 | 0.13 | -2.35 |
| 52. | 2023. 5. 31. | -10.98% | 0.25% | 116.10 | 0.74 | 9.24 |
| 53. | 2023. 6. 30. | 1.40% | 4.71% | 2.57 | 13.02 | 5.78 |
| 54. | 2023. 7. 31. | -7.23% | 4.85% | 49.30 | 13.99 | -26.26 |
| 55. | 2023. 8. 31. | 1.86% | -1.77% | 4.26 | 8.28 | -5.94 |
| 56. | 2023. 9. 30. | 1.56% | -4.87% | 3.09 | 35.73 | -10.52 |
| 57. | 2023. 10. 31. | 4.38% | -2.20% | 20.99 | 10.92 | -15.14 |
| 58. | 2023. 11. 30. | 7.60% | 8.92% | 60.86 | 61.03 | 60.95 |
| 59. | 2023. 12. 31. | 1.27% | 4.42% | 2.17 | 11.00 | 4.88 |
| 합계 (Σ): | 2,901.17 | 1,634.30 | 1,196.51 | |||
모두 표시
분산T = Σ(RT,t–RT)2 ÷ (59 – 1)
= 2,901.17 ÷ (59 – 1)
= 50.02
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산T, S&P 500 = Σ(RT,t–RT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,196.51 ÷ (59 – 1)
= 20.63
체계적인 위험 추정 (β)
| 분산T | 50.02 |
| 분산S&P 500 | 28.18 |
| 공분산T, S&P 500 | 20.63 |
| 상관 계수T, S&P 5001 | 0.55 |
| βT2 | 0.73 |
| αT3 | -1.01% |
계산
1 상관 계수T, S&P 500
= 공분산T, S&P 500 ÷ (표준 편차T × 표준 편차S&P 500)
= 20.63 ÷ (7.07% × 5.31%)
= 0.55
2 βT
= 공분산T, S&P 500 ÷ 분산S&P 500
= 20.63 ÷ 28.18
= 0.73
3 αT
= 평균의T – βT × 평균의S&P 500
= -0.20% – 0.73 × 1.11%
= -1.01%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주의 체계적 위험AT&T | βT | 0.73 |
| AT&T 보통주 예상 수익률3 | E(RT) | 11.30% |
1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).
2 자세히 보기 »
3 E(RT) = RF + βT [E(RM) – RF]
= 4.56% + 0.73 [13.77% – 4.56%]
= 11.30%