자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Pfizer보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Pfizer Inc., 월별 수익률
| Pfizer Inc. (PFE) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PFE,t1 | 피제수PFE,t1 | RPFE,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $42.45 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $43.35 | 2.12% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $42.47 | -2.03% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $40.61 | -4.38% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $30.47 | $0.41 | 1.05% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $28.79 | -5.51% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.03% | 1.11% | ||||
| 표준 편차: | 7.92% | 5.31% | ||||
| Pfizer Inc. (PFE) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PFE,t1 | 피제수PFE,t1 | RPFE,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $42.45 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $43.35 | 2.12% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $42.47 | -2.03% | 2,834.40 | 1.79% | |
| 3. | 2019. 4. 30. | $40.61 | -4.38% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $41.52 | $0.36 | 3.13% | 2,752.06 | -6.58% |
| 5. | 2019. 6. 30. | $43.32 | 4.34% | 2,941.76 | 6.89% | |
| 6. | 2019. 7. 31. | $38.84 | -10.34% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $35.55 | $0.36 | -7.54% | 2,926.46 | -1.81% |
| 8. | 2019. 9. 30. | $35.93 | 1.07% | 2,976.74 | 1.72% | |
| 9. | 2019. 10. 31. | $38.37 | 6.79% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $38.52 | $0.36 | 1.33% | 3,140.98 | 3.40% |
| 11. | 2019. 12. 31. | $39.18 | 1.71% | 3,230.78 | 2.86% | |
| 12. | 2020. 1. 31. | $37.24 | $0.38 | -3.98% | 3,225.52 | -0.16% |
| 13. | 2020. 2. 29. | $33.42 | -10.26% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $32.64 | -2.33% | 2,584.59 | -12.51% | |
| 15. | 2020. 4. 30. | $38.36 | 17.52% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $38.19 | $0.38 | 0.55% | 3,044.31 | 4.53% |
| 17. | 2020. 6. 30. | $32.70 | -14.38% | 3,100.29 | 1.84% | |
| 18. | 2020. 7. 31. | $38.48 | $0.38 | 18.84% | 3,271.12 | 5.51% |
| 19. | 2020. 8. 31. | $37.79 | -1.79% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $36.70 | -2.88% | 3,363.00 | -3.92% | |
| 21. | 2020. 10. 31. | $35.48 | -3.32% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $38.31 | $2.30819 | 14.48% | 3,621.63 | 10.75% |
| 23. | 2020. 12. 31. | $36.81 | -3.92% | 3,756.07 | 3.71% | |
| 24. | 2021. 1. 31. | $35.90 | $0.39 | -1.41% | 3,714.24 | -1.11% |
| 25. | 2021. 2. 28. | $33.49 | -6.71% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $36.23 | 8.18% | 3,972.89 | 4.24% | |
| 27. | 2021. 4. 30. | $38.65 | 6.68% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $38.73 | $0.39 | 1.22% | 4,204.11 | 0.55% |
| 29. | 2021. 6. 30. | $39.16 | 1.11% | 4,297.50 | 2.22% | |
| 30. | 2021. 7. 31. | $42.81 | $0.39 | 10.32% | 4,395.26 | 2.27% |
| 31. | 2021. 8. 31. | $46.07 | 7.62% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $43.01 | -6.64% | 4,307.54 | -4.76% | |
| 33. | 2021. 10. 31. | $43.74 | 1.70% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $53.73 | $0.39 | 23.73% | 4,567.00 | -0.83% |
| 35. | 2021. 12. 31. | $59.05 | 9.90% | 4,766.18 | 4.36% | |
| 36. | 2022. 1. 31. | $52.69 | $0.40 | -10.09% | 4,515.55 | -5.26% |
| 37. | 2022. 2. 28. | $46.94 | -10.91% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $51.77 | 10.29% | 4,530.41 | 3.58% | |
| 39. | 2022. 4. 30. | $49.07 | -5.22% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $53.04 | $0.40 | 8.91% | 4,132.15 | 0.01% |
| 41. | 2022. 6. 30. | $52.43 | -1.15% | 3,785.38 | -8.39% | |
| 42. | 2022. 7. 31. | $50.51 | $0.40 | -2.90% | 4,130.29 | 9.11% |
| 43. | 2022. 8. 31. | $45.23 | -10.45% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $43.76 | -3.25% | 3,585.62 | -9.34% | |
| 45. | 2022. 10. 31. | $46.55 | 6.38% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $50.13 | $0.40 | 8.55% | 4,080.11 | 5.38% |
| 47. | 2022. 12. 31. | $51.24 | 2.21% | 3,839.50 | -5.90% | |
| 48. | 2023. 1. 31. | $44.16 | $0.41 | -13.02% | 4,076.60 | 6.18% |
| 49. | 2023. 2. 28. | $40.57 | -8.13% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $40.80 | 0.57% | 4,109.31 | 3.51% | |
| 51. | 2023. 4. 30. | $38.89 | -4.68% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $38.02 | $0.41 | -1.18% | 4,179.83 | 0.25% |
| 53. | 2023. 6. 30. | $36.68 | -3.52% | 4,376.86 | 4.71% | |
| 54. | 2023. 7. 31. | $36.06 | $0.41 | -0.57% | 4,588.96 | 4.85% |
| 55. | 2023. 8. 31. | $35.38 | -1.89% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $33.17 | -6.25% | 4,288.05 | -4.87% | |
| 57. | 2023. 10. 31. | $30.56 | -7.87% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $30.47 | $0.41 | 1.05% | 4,567.80 | 8.92% |
| 59. | 2023. 12. 31. | $28.79 | -5.51% | 4,769.83 | 4.42% | |
| 평균의 (R): | 0.03% | 1.11% | ||||
| 표준 편차: | 7.92% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 PFE의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Pfizer Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RPFE,t | RS&P 500,t | (RPFE,t–RPFE)2 | (RS&P 500,t–RS&P 500)2 | (RPFE,t–RPFE)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 2.12% | 2.97% | 4.37 | 3.49 | 3.90 |
| 2. | 2019. 3. 31. | -2.03% | 1.79% | 4.24 | 0.47 | -1.41 |
| 3. | 2019. 4. 30. | -4.38% | 3.93% | 19.44 | 7.98 | -12.46 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 1.05% | 8.92% | 1.04 | 61.03 | 7.95 |
| 59. | 2023. 12. 31. | -5.51% | 4.42% | 30.73 | 11.00 | -18.39 |
| 합계 (Σ): | 3,638.66 | 1,634.30 | 1,018.78 | |||
| t | 날짜 | RPFE,t | RS&P 500,t | (RPFE,t–RPFE)2 | (RS&P 500,t–RS&P 500)2 | (RPFE,t–RPFE)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 2.12% | 2.97% | 4.37 | 3.49 | 3.90 |
| 2. | 2019. 3. 31. | -2.03% | 1.79% | 4.24 | 0.47 | -1.41 |
| 3. | 2019. 4. 30. | -4.38% | 3.93% | 19.44 | 7.98 | -12.46 |
| 4. | 2019. 5. 31. | 3.13% | -6.58% | 9.60 | 59.04 | -23.80 |
| 5. | 2019. 6. 30. | 4.34% | 6.89% | 18.54 | 33.49 | 24.92 |
| 6. | 2019. 7. 31. | -10.34% | 1.31% | 107.56 | 0.04 | -2.15 |
| 7. | 2019. 8. 31. | -7.54% | -1.81% | 57.36 | 8.50 | 22.08 |
| 8. | 2019. 9. 30. | 1.07% | 1.72% | 1.08 | 0.37 | 0.64 |
| 9. | 2019. 10. 31. | 6.79% | 2.04% | 45.72 | 0.88 | 6.34 |
| 10. | 2019. 11. 30. | 1.33% | 3.40% | 1.69 | 5.28 | 2.99 |
| 11. | 2019. 12. 31. | 1.71% | 2.86% | 2.83 | 3.07 | 2.95 |
| 12. | 2020. 1. 31. | -3.98% | -0.16% | 16.09 | 1.61 | 5.09 |
| 13. | 2020. 2. 29. | -10.26% | -8.41% | 105.83 | 90.57 | 97.90 |
| 14. | 2020. 3. 31. | -2.33% | -12.51% | 5.59 | 185.44 | 32.19 |
| 15. | 2020. 4. 30. | 17.52% | 12.68% | 306.07 | 134.06 | 202.57 |
| 16. | 2020. 5. 31. | 0.55% | 4.53% | 0.27 | 11.71 | 1.77 |
| 17. | 2020. 6. 30. | -14.38% | 1.84% | 207.51 | 0.54 | -10.56 |
| 18. | 2020. 7. 31. | 18.84% | 5.51% | 353.75 | 19.40 | 82.84 |
| 19. | 2020. 8. 31. | -1.79% | 7.01% | 3.32 | 34.82 | -10.76 |
| 20. | 2020. 9. 30. | -2.88% | -3.92% | 8.49 | 25.29 | 14.65 |
| 21. | 2020. 10. 31. | -3.32% | -2.77% | 11.25 | 15.00 | 12.99 |
| 22. | 2020. 11. 30. | 14.48% | 10.75% | 208.87 | 93.10 | 139.45 |
| 23. | 2020. 12. 31. | -3.92% | 3.71% | 15.56 | 6.79 | -10.28 |
| 24. | 2021. 1. 31. | -1.41% | -1.11% | 2.08 | 4.93 | 3.20 |
| 25. | 2021. 2. 28. | -6.71% | 2.61% | 45.46 | 2.26 | -10.14 |
| 26. | 2021. 3. 31. | 8.18% | 4.24% | 66.45 | 9.85 | 25.58 |
| 27. | 2021. 4. 30. | 6.68% | 5.24% | 44.22 | 17.11 | 27.51 |
| 28. | 2021. 5. 31. | 1.22% | 0.55% | 1.41 | 0.31 | -0.66 |
| 29. | 2021. 6. 30. | 1.11% | 2.22% | 1.17 | 1.24 | 1.21 |
| 30. | 2021. 7. 31. | 10.32% | 2.27% | 105.82 | 1.37 | 12.03 |
| 31. | 2021. 8. 31. | 7.62% | 2.90% | 57.54 | 3.22 | 13.60 |
| 32. | 2021. 9. 30. | -6.64% | -4.76% | 44.51 | 34.37 | 39.11 |
| 33. | 2021. 10. 31. | 1.70% | 6.91% | 2.78 | 33.74 | 9.69 |
| 34. | 2021. 11. 30. | 23.73% | -0.83% | 561.76 | 3.76 | -45.96 |
| 35. | 2021. 12. 31. | 9.90% | 4.36% | 97.45 | 10.60 | 32.14 |
| 36. | 2022. 1. 31. | -10.09% | -5.26% | 102.47 | 40.51 | 64.43 |
| 37. | 2022. 2. 28. | -10.91% | -3.14% | 119.74 | 17.99 | 46.42 |
| 38. | 2022. 3. 31. | 10.29% | 3.58% | 105.27 | 6.11 | 25.36 |
| 39. | 2022. 4. 30. | -5.22% | -8.80% | 27.51 | 98.04 | 51.93 |
| 40. | 2022. 5. 31. | 8.91% | 0.01% | 78.78 | 1.21 | -9.77 |
| 41. | 2022. 6. 30. | -1.15% | -8.39% | 1.39 | 90.21 | 11.20 |
| 42. | 2022. 7. 31. | -2.90% | 9.11% | 8.58 | 64.09 | -23.45 |
| 43. | 2022. 8. 31. | -10.45% | -4.24% | 109.89 | 28.62 | 56.08 |
| 44. | 2022. 9. 30. | -3.25% | -9.34% | 10.76 | 109.11 | 34.26 |
| 45. | 2022. 10. 31. | 6.38% | 7.99% | 40.27 | 47.34 | 43.66 |
| 46. | 2022. 11. 30. | 8.55% | 5.38% | 72.60 | 18.23 | 36.38 |
| 47. | 2022. 12. 31. | 2.21% | -5.90% | 4.77 | 49.04 | -15.30 |
| 48. | 2023. 1. 31. | -13.02% | 6.18% | 170.22 | 25.70 | -66.14 |
| 49. | 2023. 2. 28. | -8.13% | -2.61% | 66.57 | 13.82 | 30.33 |
| 50. | 2023. 3. 31. | 0.57% | 3.51% | 0.29 | 5.76 | 1.29 |
| 51. | 2023. 4. 30. | -4.68% | 1.46% | 22.19 | 0.13 | -1.69 |
| 52. | 2023. 5. 31. | -1.18% | 0.25% | 1.47 | 0.74 | 1.04 |
| 53. | 2023. 6. 30. | -3.52% | 4.71% | 12.63 | 13.02 | -12.82 |
| 54. | 2023. 7. 31. | -0.57% | 4.85% | 0.36 | 13.99 | -2.25 |
| 55. | 2023. 8. 31. | -1.89% | -1.77% | 3.67 | 8.28 | 5.51 |
| 56. | 2023. 9. 30. | -6.25% | -4.87% | 39.39 | 35.73 | 37.52 |
| 57. | 2023. 10. 31. | -7.87% | -2.20% | 62.38 | 10.92 | 26.09 |
| 58. | 2023. 11. 30. | 1.05% | 8.92% | 1.04 | 61.03 | 7.95 |
| 59. | 2023. 12. 31. | -5.51% | 4.42% | 30.73 | 11.00 | -18.39 |
| 합계 (Σ): | 3,638.66 | 1,634.30 | 1,018.78 | |||
모두 보기
분산PFE = Σ(RPFE,t–RPFE)2 ÷ (59 – 1)
= 3,638.66 ÷ (59 – 1)
= 62.74
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산PFE, S&P 500 = Σ(RPFE,t–RPFE)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,018.78 ÷ (59 – 1)
= 17.57
체계적인 위험 추정 (β)
| 분산PFE | 62.74 |
| 분산S&P 500 | 28.18 |
| 공분산PFE, S&P 500 | 17.57 |
| 상관 계수PFE, S&P 5001 | 0.42 |
| βPFE2 | 0.62 |
| αPFE3 | -0.66% |
계산
1 상관 계수PFE, S&P 500
= 공분산PFE, S&P 500 ÷ (표준 편차PFE × 표준 편차S&P 500)
= 17.57 ÷ (7.92% × 5.31%)
= 0.42
2 βPFE
= 공분산PFE, S&P 500 ÷ 분산S&P 500
= 17.57 ÷ 28.18
= 0.62
3 αPFE
= 평균의PFE – βPFE × 평균의S&P 500
= 0.03% – 0.62 × 1.11%
= -0.66%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.90% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.94% |
| 보통주의 체계적 위험Pfizer | βPFE | 0.62 |
| Pfizer 보통주 예상 수익률3 | E(RPFE) | 10.54% |
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(RPFE) = RF + βPFE [E(RM) – RF]
= 4.90% + 0.62 [13.94% – 4.90%]
= 10.54%