자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Warner Bros. Discovery보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Warner Bros. Discovery Inc., 월별 수익률
| Warner Bros. Discovery Inc. (WBD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값WBD,t1 | 피제수WBD,t1 | RWBD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $28.35 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $28.76 | 1.45% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $29.09 | 1.15% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $28.78 | -1.07% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $23.27 | -0.73% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $23.54 | 1.16% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.46% | 1.36% | ||||
| 표준 편차: | 12.92% | 4.48% | ||||
| Warner Bros. Discovery Inc. (WBD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값WBD,t1 | 피제수WBD,t1 | RWBD,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $28.35 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $28.76 | 1.45% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $29.09 | 1.15% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $28.78 | -1.07% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $26.50 | -7.92% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $25.83 | -2.53% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $24.60 | -4.76% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $22.21 | -9.72% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $21.29 | -4.14% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $18.88 | -11.32% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $19.02 | 0.74% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $22.38 | 17.67% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $25.07 | 12.02% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $24.32 | -2.99% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $21.43 | -11.88% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $23.65 | 10.36% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $21.09 | -10.82% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $27.50 | 30.39% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $26.58 | -3.35% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $27.83 | 4.70% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $32.00 | 14.98% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $32.39 | 1.22% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $30.72 | -5.16% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $24.74 | -19.47% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $28.38 | 14.71% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $28.90 | 1.83% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $27.02 | -6.51% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $30.90 | 14.36% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $27.26 | -11.78% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $30.70 | 12.62% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $30.31 | -1.27% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $27.60 | -8.94% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $26.63 | -3.51% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $26.96 | 1.24% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $32.94 | 22.18% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $32.74 | -0.61% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $29.26 | -10.63% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $25.70 | -12.17% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $19.44 | -24.36% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $22.42 | 15.33% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $21.75 | -2.99% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $21.10 | -2.99% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $21.10 | 0.00% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $22.07 | 4.60% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $21.77 | -1.36% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $20.24 | -7.03% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $26.91 | 32.95% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $30.09 | 11.82% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $41.42 | 37.65% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $53.03 | 28.03% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $43.46 | -18.05% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $37.66 | -13.35% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $32.11 | -14.74% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $30.68 | -4.45% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $29.01 | -5.44% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $28.84 | -0.59% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $25.38 | -12.00% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $23.44 | -7.64% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $23.27 | -0.73% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $23.54 | 1.16% | 4,766.18 | 4.36% | |
| 평균의 (R): | 0.46% | 1.36% | ||||
| 표준 편차: | 12.92% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 WBD의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Warner Bros. Discovery Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RWBD,t | RS&P 500,t | (RWBD,t–RWBD)2 | (RS&P 500,t–RS&P 500)2 | (RWBD,t–RWBD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 1.45% | 3.72% | 0.98 | 5.58 | 2.34 |
| 2. | 2017. 3. 31. | 1.15% | -0.04% | 0.48 | 1.95 | -0.97 |
| 3. | 2017. 4. 30. | -1.07% | 0.91% | 2.32 | 0.20 | 0.68 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -0.73% | -0.83% | 1.40 | 4.80 | 2.59 |
| 59. | 2021. 12. 31. | 1.16% | 4.36% | 0.50 | 9.02 | 2.11 |
| 합계 (Σ): | 9,681.94 | 1,164.17 | 1,526.12 | |||
| t | 날짜 | RWBD,t | RS&P 500,t | (RWBD,t–RWBD)2 | (RS&P 500,t–RS&P 500)2 | (RWBD,t–RWBD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 1.45% | 3.72% | 0.98 | 5.58 | 2.34 |
| 2. | 2017. 3. 31. | 1.15% | -0.04% | 0.48 | 1.95 | -0.97 |
| 3. | 2017. 4. 30. | -1.07% | 0.91% | 2.32 | 0.20 | 0.68 |
| 4. | 2017. 5. 31. | -7.92% | 1.16% | 70.20 | 0.04 | 1.68 |
| 5. | 2017. 6. 30. | -2.53% | 0.48% | 8.91 | 0.77 | 2.62 |
| 6. | 2017. 7. 31. | -4.76% | 1.93% | 27.23 | 0.33 | -3.01 |
| 7. | 2017. 8. 31. | -9.72% | 0.05% | 103.47 | 1.70 | 13.26 |
| 8. | 2017. 9. 30. | -4.14% | 1.93% | 21.15 | 0.33 | -2.63 |
| 9. | 2017. 10. 31. | -11.32% | 2.22% | 138.68 | 0.74 | -10.14 |
| 10. | 2017. 11. 30. | 0.74% | 2.81% | 0.08 | 2.10 | 0.41 |
| 11. | 2017. 12. 31. | 17.67% | 0.98% | 296.16 | 0.14 | -6.45 |
| 12. | 2018. 1. 31. | 12.02% | 5.62% | 133.71 | 18.15 | 49.26 |
| 13. | 2018. 2. 28. | -2.99% | -3.89% | 11.89 | 27.59 | 18.11 |
| 14. | 2018. 3. 31. | -11.88% | -2.69% | 152.27 | 16.37 | 49.93 |
| 15. | 2018. 4. 30. | 10.36% | 0.27% | 98.07 | 1.18 | -10.75 |
| 16. | 2018. 5. 31. | -10.82% | 2.16% | 127.26 | 0.64 | -9.06 |
| 17. | 2018. 6. 30. | 30.39% | 0.48% | 896.23 | 0.76 | -26.15 |
| 18. | 2018. 7. 31. | -3.35% | 3.60% | 14.45 | 5.04 | -8.53 |
| 19. | 2018. 8. 31. | 4.70% | 3.03% | 18.03 | 2.78 | 7.08 |
| 20. | 2018. 9. 30. | 14.98% | 0.43% | 211.05 | 0.86 | -13.49 |
| 21. | 2018. 10. 31. | 1.22% | -6.94% | 0.58 | 68.86 | -6.33 |
| 22. | 2018. 11. 30. | -5.16% | 1.79% | 31.50 | 0.18 | -2.40 |
| 23. | 2018. 12. 31. | -19.47% | -9.18% | 396.91 | 111.00 | 209.90 |
| 24. | 2019. 1. 31. | 14.71% | 7.87% | 203.25 | 42.39 | 92.82 |
| 25. | 2019. 2. 28. | 1.83% | 2.97% | 1.89 | 2.61 | 2.22 |
| 26. | 2019. 3. 31. | -6.51% | 1.79% | 48.46 | 0.19 | -3.02 |
| 27. | 2019. 4. 30. | 14.36% | 3.93% | 193.30 | 6.62 | 35.78 |
| 28. | 2019. 5. 31. | -11.78% | -6.58% | 149.73 | 62.97 | 97.10 |
| 29. | 2019. 6. 30. | 12.62% | 6.89% | 147.93 | 30.64 | 67.32 |
| 30. | 2019. 7. 31. | -1.27% | 1.31% | 2.98 | 0.00 | 0.08 |
| 31. | 2019. 8. 31. | -8.94% | -1.81% | 88.31 | 10.03 | 29.76 |
| 32. | 2019. 9. 30. | -3.51% | 1.72% | 15.77 | 0.13 | -1.43 |
| 33. | 2019. 10. 31. | 1.24% | 2.04% | 0.61 | 0.47 | 0.54 |
| 34. | 2019. 11. 30. | 22.18% | 3.40% | 471.96 | 4.19 | 44.47 |
| 35. | 2019. 12. 31. | -0.61% | 2.86% | 1.13 | 2.25 | -1.60 |
| 36. | 2020. 1. 31. | -10.63% | -0.16% | 122.89 | 2.31 | 16.86 |
| 37. | 2020. 2. 29. | -12.17% | -8.41% | 159.34 | 95.43 | 123.32 |
| 38. | 2020. 3. 31. | -24.36% | -12.51% | 615.75 | 192.37 | 344.17 |
| 39. | 2020. 4. 30. | 15.33% | 12.68% | 221.20 | 128.29 | 168.46 |
| 40. | 2020. 5. 31. | -2.99% | 4.53% | 11.87 | 10.05 | -10.92 |
| 41. | 2020. 6. 30. | -2.99% | 1.84% | 11.87 | 0.23 | -1.66 |
| 42. | 2020. 7. 31. | 0.00% | 5.51% | 0.21 | 17.24 | -1.90 |
| 43. | 2020. 8. 31. | 4.60% | 7.01% | 17.15 | 31.91 | 23.39 |
| 44. | 2020. 9. 30. | -1.36% | -3.92% | 3.30 | 27.89 | 9.59 |
| 45. | 2020. 10. 31. | -7.03% | -2.77% | 56.02 | 17.01 | 30.87 |
| 46. | 2020. 11. 30. | 32.95% | 10.75% | 1,056.13 | 88.30 | 305.37 |
| 47. | 2020. 12. 31. | 11.82% | 3.71% | 129.07 | 5.54 | 26.75 |
| 48. | 2021. 1. 31. | 37.65% | -1.11% | 1,383.64 | 6.11 | -91.94 |
| 49. | 2021. 2. 28. | 28.03% | 2.61% | 760.30 | 1.57 | 34.50 |
| 50. | 2021. 3. 31. | -18.05% | 4.24% | 342.35 | 8.33 | -53.40 |
| 51. | 2021. 4. 30. | -13.35% | 5.24% | 190.50 | 15.09 | -53.62 |
| 52. | 2021. 5. 31. | -14.74% | 0.55% | 230.84 | 0.65 | 12.30 |
| 53. | 2021. 6. 30. | -4.45% | 2.22% | 24.11 | 0.75 | -4.24 |
| 54. | 2021. 7. 31. | -5.44% | 2.27% | 34.81 | 0.84 | -5.41 |
| 55. | 2021. 8. 31. | -0.59% | 2.90% | 1.09 | 2.38 | -1.61 |
| 56. | 2021. 9. 30. | -12.00% | -4.76% | 155.09 | 37.39 | 76.15 |
| 57. | 2021. 10. 31. | -7.64% | 6.91% | 65.61 | 30.87 | -45.01 |
| 58. | 2021. 11. 30. | -0.73% | -0.83% | 1.40 | 4.80 | 2.59 |
| 59. | 2021. 12. 31. | 1.16% | 4.36% | 0.50 | 9.02 | 2.11 |
| 합계 (Σ): | 9,681.94 | 1,164.17 | 1,526.12 | |||
모두 보기
분산WBD = Σ(RWBD,t–RWBD)2 ÷ (59 – 1)
= 9,681.94 ÷ (59 – 1)
= 166.93
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산WBD, S&P 500 = Σ(RWBD,t–RWBD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,526.12 ÷ (59 – 1)
= 26.31
체계적인 위험 추정 (β)
| 분산WBD | 166.93 |
| 분산S&P 500 | 20.07 |
| 공분산WBD, S&P 500 | 26.31 |
| 상관 계수WBD, S&P 5001 | 0.45 |
| βWBD2 | 1.31 |
| αWBD3 | -1.32% |
계산
1 상관 계수WBD, S&P 500
= 공분산WBD, S&P 500 ÷ (표준 편차WBD × 표준 편차S&P 500)
= 26.31 ÷ (12.92% × 4.48%)
= 0.45
2 βWBD
= 공분산WBD, S&P 500 ÷ 분산S&P 500
= 26.31 ÷ 20.07
= 1.31
3 αWBD
= 평균의WBD – βWBD × 평균의S&P 500
= 0.46% – 1.31 × 1.36%
= -1.32%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.84% |
| 보통주의 체계적 위험Warner Bros. Discovery | βWBD | 1.31 |
| 워너브라더스 디스커버리 보통주 기대수익률3 | E(RWBD) | 17.93% |
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(RWBD) = RF + βWBD [E(RM) – RF]
= 4.91% + 1.31 [14.84% – 4.91%]
= 17.93%