자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다 Paramount.
수익률
Paramount Global, 월별 수익률
| Paramount Global (PARA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PARA,t1 | 피제수PARA,t1 | RPARA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $57.61 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $52.97 | -8.05% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $51.39 | $0.18 | -2.64% | 2,640.87 | -2.69% |
| 3. | 2018. 4. 30. | $49.20 | -4.26% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $20.08 | 9.61% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $16.88 | $0.24 | -14.74% | 3,839.50 | -5.90% |
| 평균의 (R): | -0.66% | 0.67% | ||||
| 표준 편차: | 14.93% | 5.40% | ||||
| Paramount Global (PARA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PARA,t1 | 피제수PARA,t1 | RPARA,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $57.61 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $52.97 | -8.05% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $51.39 | $0.18 | -2.64% | 2,640.87 | -2.69% |
| 3. | 2018. 4. 30. | $49.20 | -4.26% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $50.37 | 2.38% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $56.22 | $0.18 | 11.97% | 2,718.37 | 0.48% |
| 6. | 2018. 7. 31. | $52.67 | -6.31% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $53.02 | 0.66% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $57.45 | $0.18 | 8.69% | 2,913.98 | 0.43% |
| 9. | 2018. 10. 31. | $57.35 | -0.17% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $54.18 | -5.53% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $43.72 | $0.18 | -18.97% | 2,506.85 | -9.18% |
| 12. | 2019. 1. 31. | $49.46 | 13.13% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $50.21 | 1.52% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $47.53 | $0.18 | -4.98% | 2,834.40 | 1.79% |
| 15. | 2019. 4. 30. | $51.27 | 7.87% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $48.28 | -5.83% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $49.90 | $0.18 | 3.73% | 2,941.76 | 6.89% |
| 18. | 2019. 7. 31. | $51.51 | 3.23% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $42.06 | -18.35% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $40.37 | $0.18 | -3.59% | 2,976.74 | 1.72% |
| 21. | 2019. 10. 31. | $36.04 | -10.73% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $40.38 | 12.04% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $41.97 | $0.24 | 4.53% | 3,230.78 | 2.86% |
| 24. | 2020. 1. 31. | $34.13 | -18.68% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $24.61 | -27.89% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $14.01 | $0.24 | -42.10% | 2,584.59 | -12.51% |
| 27. | 2020. 4. 30. | $17.26 | 23.20% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $20.74 | 20.16% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $23.32 | $0.24 | 13.60% | 3,100.29 | 1.84% |
| 30. | 2020. 7. 31. | $26.07 | 11.79% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $27.85 | 6.83% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $28.01 | $0.24 | 1.44% | 3,363.00 | -3.92% |
| 33. | 2020. 10. 31. | $28.57 | 2.00% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $35.28 | 23.49% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $37.26 | $0.24 | 6.29% | 3,756.07 | 3.71% |
| 36. | 2021. 1. 31. | $48.50 | 30.17% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $64.49 | 32.97% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $45.10 | $0.24 | -29.69% | 3,972.89 | 4.24% |
| 39. | 2021. 4. 30. | $41.02 | -9.05% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $42.42 | 3.41% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $45.20 | $0.24 | 7.12% | 4,297.50 | 2.22% |
| 42. | 2021. 7. 31. | $40.93 | -9.45% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $41.45 | 1.27% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $39.51 | $0.24 | -4.10% | 4,307.54 | -4.76% |
| 45. | 2021. 10. 31. | $36.22 | -8.33% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $30.95 | -14.55% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $30.18 | $0.24 | -1.71% | 4,766.18 | 4.36% |
| 48. | 2022. 1. 31. | $33.45 | 10.83% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $30.61 | -8.49% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $37.81 | $0.24 | 24.31% | 4,530.41 | 3.58% |
| 51. | 2022. 4. 30. | $29.12 | -22.98% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $34.33 | 17.89% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $24.68 | $0.24 | -27.41% | 3,785.38 | -8.39% |
| 54. | 2022. 7. 31. | $23.65 | -4.17% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $23.39 | -1.10% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $19.04 | $0.24 | -17.57% | 3,585.62 | -9.34% |
| 57. | 2022. 10. 31. | $18.32 | -3.78% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $20.08 | 9.61% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $16.88 | $0.24 | -14.74% | 3,839.50 | -5.90% |
| 평균의 (R): | -0.66% | 0.67% | ||||
| 표준 편차: | 14.93% | 5.40% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 PARA의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Paramount Global, 수익률의 분산 및 공분산 계산
| t | 날짜 | RPARA,t | RS&P 500,t | (RPARA,t–RPARA)2 | (RS&P 500,t–RS&P 500)2 | (RPARA,t–RPARA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -8.05% | -3.89% | 54.63 | 20.81 | 33.72 |
| 2. | 2018. 3. 31. | -2.64% | -2.69% | 3.92 | 11.26 | 6.64 |
| 3. | 2018. 4. 30. | -4.26% | 0.27% | 12.95 | 0.16 | 1.42 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | 9.61% | 5.38% | 105.47 | 22.17 | 48.36 |
| 59. | 2022. 12. 31. | -14.74% | -5.90% | 198.20 | 43.08 | 92.41 |
| 합계 (Σ): | 12,926.67 | 1,691.48 | 2,605.93 | |||
| t | 날짜 | RPARA,t | RS&P 500,t | (RPARA,t–RPARA)2 | (RS&P 500,t–RS&P 500)2 | (RPARA,t–RPARA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -8.05% | -3.89% | 54.63 | 20.81 | 33.72 |
| 2. | 2018. 3. 31. | -2.64% | -2.69% | 3.92 | 11.26 | 6.64 |
| 3. | 2018. 4. 30. | -4.26% | 0.27% | 12.95 | 0.16 | 1.42 |
| 4. | 2018. 5. 31. | 2.38% | 2.16% | 9.25 | 2.23 | 4.54 |
| 5. | 2018. 6. 30. | 11.97% | 0.48% | 159.62 | 0.03 | -2.30 |
| 6. | 2018. 7. 31. | -6.31% | 3.60% | 31.94 | 8.62 | -16.59 |
| 7. | 2018. 8. 31. | 0.66% | 3.03% | 1.76 | 5.57 | 3.13 |
| 8. | 2018. 9. 30. | 8.69% | 0.43% | 87.56 | 0.06 | -2.22 |
| 9. | 2018. 10. 31. | -0.17% | -6.94% | 0.24 | 57.87 | -3.72 |
| 10. | 2018. 11. 30. | -5.53% | 1.79% | 23.67 | 1.25 | -5.45 |
| 11. | 2018. 12. 31. | -18.97% | -9.18% | 335.30 | 96.91 | 180.26 |
| 12. | 2019. 1. 31. | 13.13% | 7.87% | 190.21 | 51.87 | 99.33 |
| 13. | 2019. 2. 28. | 1.52% | 2.97% | 4.75 | 5.32 | 5.03 |
| 14. | 2019. 3. 31. | -4.98% | 1.79% | 18.63 | 1.27 | -4.86 |
| 15. | 2019. 4. 30. | 7.87% | 3.93% | 72.79 | 10.66 | 27.85 |
| 16. | 2019. 5. 31. | -5.83% | -6.58% | 26.72 | 52.48 | 37.45 |
| 17. | 2019. 6. 30. | 3.73% | 6.89% | 19.28 | 38.77 | 27.34 |
| 18. | 2019. 7. 31. | 3.23% | 1.31% | 15.13 | 0.42 | 2.51 |
| 19. | 2019. 8. 31. | -18.35% | -1.81% | 312.70 | 6.13 | 43.78 |
| 20. | 2019. 9. 30. | -3.59% | 1.72% | 8.57 | 1.11 | -3.08 |
| 21. | 2019. 10. 31. | -10.73% | 2.04% | 101.27 | 1.89 | -13.85 |
| 22. | 2019. 11. 30. | 12.04% | 3.40% | 161.41 | 7.50 | 34.79 |
| 23. | 2019. 12. 31. | 4.53% | 2.86% | 26.98 | 4.81 | 11.39 |
| 24. | 2020. 1. 31. | -18.68% | -0.16% | 324.62 | 0.69 | 14.94 |
| 25. | 2020. 2. 29. | -27.89% | -8.41% | 741.51 | 82.40 | 247.19 |
| 26. | 2020. 3. 31. | -42.10% | -12.51% | 1,716.78 | 173.67 | 546.04 |
| 27. | 2020. 4. 30. | 23.20% | 12.68% | 569.32 | 144.43 | 286.75 |
| 28. | 2020. 5. 31. | 20.16% | 4.53% | 433.68 | 14.91 | 80.42 |
| 29. | 2020. 6. 30. | 13.60% | 1.84% | 203.34 | 1.37 | 16.72 |
| 30. | 2020. 7. 31. | 11.79% | 5.51% | 155.13 | 23.46 | 60.33 |
| 31. | 2020. 8. 31. | 6.83% | 7.01% | 56.11 | 40.19 | 47.49 |
| 32. | 2020. 9. 30. | 1.44% | -3.92% | 4.41 | 21.06 | -9.63 |
| 33. | 2020. 10. 31. | 2.00% | -2.77% | 7.09 | 11.79 | -9.14 |
| 34. | 2020. 11. 30. | 23.49% | 10.75% | 583.17 | 101.77 | 243.61 |
| 35. | 2020. 12. 31. | 6.29% | 3.71% | 48.38 | 9.28 | 21.18 |
| 36. | 2021. 1. 31. | 30.17% | -1.11% | 950.43 | 3.17 | -54.89 |
| 37. | 2021. 2. 28. | 32.97% | 2.61% | 1,131.10 | 3.77 | 65.33 |
| 38. | 2021. 3. 31. | -29.69% | 4.24% | 842.85 | 12.80 | -103.85 |
| 39. | 2021. 4. 30. | -9.05% | 5.24% | 70.29 | 20.94 | -38.36 |
| 40. | 2021. 5. 31. | 3.41% | 0.55% | 16.61 | 0.01 | -0.48 |
| 41. | 2021. 6. 30. | 7.12% | 2.22% | 60.56 | 2.42 | 12.10 |
| 42. | 2021. 7. 31. | -9.45% | 2.27% | 77.16 | 2.59 | -14.13 |
| 43. | 2021. 8. 31. | 1.27% | 2.90% | 3.74 | 4.98 | 4.32 |
| 44. | 2021. 9. 30. | -4.10% | -4.76% | 11.82 | 29.42 | 18.65 |
| 45. | 2021. 10. 31. | -8.33% | 6.91% | 58.74 | 39.03 | -47.88 |
| 46. | 2021. 11. 30. | -14.55% | -0.83% | 192.86 | 2.25 | 20.83 |
| 47. | 2021. 12. 31. | -1.71% | 4.36% | 1.10 | 13.65 | -3.88 |
| 48. | 2022. 1. 31. | 10.83% | -5.26% | 132.20 | 35.11 | -68.13 |
| 49. | 2022. 2. 28. | -8.49% | -3.14% | 61.27 | 14.46 | 29.77 |
| 50. | 2022. 3. 31. | 24.31% | 3.58% | 623.43 | 8.47 | 72.68 |
| 51. | 2022. 4. 30. | -22.98% | -8.80% | 498.21 | 89.54 | 211.20 |
| 52. | 2022. 5. 31. | 17.89% | 0.01% | 344.26 | 0.44 | -12.27 |
| 53. | 2022. 6. 30. | -27.41% | -8.39% | 715.44 | 82.06 | 242.30 |
| 54. | 2022. 7. 31. | -4.17% | 9.11% | 12.32 | 71.32 | -29.65 |
| 55. | 2022. 8. 31. | -1.10% | -4.24% | 0.19 | 24.11 | 2.14 |
| 56. | 2022. 9. 30. | -17.57% | -9.34% | 285.91 | 100.12 | 169.19 |
| 57. | 2022. 10. 31. | -3.78% | 7.99% | 9.73 | 53.58 | -22.83 |
| 58. | 2022. 11. 30. | 9.61% | 5.38% | 105.47 | 22.17 | 48.36 |
| 59. | 2022. 12. 31. | -14.74% | -5.90% | 198.20 | 43.08 | 92.41 |
| 합계 (Σ): | 12,926.67 | 1,691.48 | 2,605.93 | |||
모두 표시
분산PARA = Σ(RPARA,t–RPARA)2 ÷ (59 – 1)
= 12,926.67 ÷ (59 – 1)
= 222.87
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산PARA, S&P 500 = Σ(RPARA,t–RPARA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,605.93 ÷ (59 – 1)
= 44.93
체계적인 위험 추정 (β)
| 분산PARA | 222.87 |
| 분산S&P 500 | 29.16 |
| 공분산PARA, S&P 500 | 44.93 |
| 상관 계수PARA, S&P 5001 | 0.56 |
| βPARA2 | 1.54 |
| αPARA3 | -1.69% |
계산
1 상관 계수PARA, S&P 500
= 공분산PARA, S&P 500 ÷ (표준 편차PARA × 표준 편차S&P 500)
= 44.93 ÷ (14.93% × 5.40%)
= 0.56
2 βPARA
= 공분산PARA, S&P 500 ÷ 분산S&P 500
= 44.93 ÷ 29.16
= 1.54
3 αPARA
= 평균의PARA – βPARA × 평균의S&P 500
= -0.66% – 1.54 × 0.67%
= -1.69%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.62% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.69% |
| 보통주 Paramount 의 체계적인 리스크 | βPARA | 1.54 |
| 파라마운트 보통주에 대한 예상 수익률3 | E(RPARA) | 18.59% |
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(RPARA) = RF + βPARA [E(RM) – RF]
= 4.62% + 1.54 [13.69% – 4.62%]
= 18.59%