자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Fiserv보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Fiserv Inc., 월별 수익률
| Fiserv Inc. (FISV) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값FISV,t1 | 피제수FISV,t1 | RFISV,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $53.72 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $57.70 | 7.41% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $57.65 | -0.09% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $59.57 | 3.33% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $96.52 | -2.00% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $103.79 | 7.53% | 4,766.18 | 4.36% | |
| 평균의 (R): | 1.32% | 1.36% | ||||
| 표준 편차: | 6.32% | 4.48% | ||||
| Fiserv Inc. (FISV) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값FISV,t1 | 피제수FISV,t1 | RFISV,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $53.72 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $57.70 | 7.41% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $57.65 | -0.09% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $59.57 | 3.33% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $62.64 | 5.15% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $61.17 | -2.35% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $64.25 | 5.04% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $61.86 | -3.72% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $64.48 | 4.24% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $64.71 | 0.36% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $65.72 | 1.56% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $65.57 | -0.23% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $70.42 | 7.40% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $71.70 | 1.82% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $71.31 | -0.54% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $70.86 | -0.63% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $72.60 | 2.46% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $74.09 | 2.05% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $75.48 | 1.88% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $80.07 | 6.08% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $82.38 | 2.88% | 2,913.98 | 0.43% | |
| 21. | 2018. 10. 31. | $79.30 | -3.74% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $79.13 | -0.21% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $73.49 | -7.13% | 2,506.85 | -9.18% | |
| 24. | 2019. 1. 31. | $82.93 | 12.85% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $84.69 | 2.12% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $88.28 | 4.24% | 2,834.40 | 1.79% | |
| 27. | 2019. 4. 30. | $87.24 | -1.18% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $85.86 | -1.58% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $91.16 | 6.17% | 2,941.76 | 6.89% | |
| 30. | 2019. 7. 31. | $105.43 | 15.65% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $106.94 | 1.43% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $103.59 | -3.13% | 2,976.74 | 1.72% | |
| 33. | 2019. 10. 31. | $106.14 | 2.46% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $116.24 | 9.52% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $115.63 | -0.52% | 3,230.78 | 2.86% | |
| 36. | 2020. 1. 31. | $118.61 | 2.58% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $109.36 | -7.80% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $94.99 | -13.14% | 2,584.59 | -12.51% | |
| 39. | 2020. 4. 30. | $103.06 | 8.50% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $106.77 | 3.60% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $97.62 | -8.57% | 3,100.29 | 1.84% | |
| 42. | 2020. 7. 31. | $99.79 | 2.22% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $99.58 | -0.21% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $103.05 | 3.48% | 3,363.00 | -3.92% | |
| 45. | 2020. 10. 31. | $95.47 | -7.36% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $115.18 | 20.65% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $113.86 | -1.15% | 3,756.07 | 3.71% | |
| 48. | 2021. 1. 31. | $102.69 | -9.81% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $115.37 | 12.35% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $119.04 | 3.18% | 3,972.89 | 4.24% | |
| 51. | 2021. 4. 30. | $120.12 | 0.91% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $115.20 | -4.10% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $106.89 | -7.21% | 4,297.50 | 2.22% | |
| 54. | 2021. 7. 31. | $115.11 | 7.69% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $117.79 | 2.33% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $108.50 | -7.89% | 4,307.54 | -4.76% | |
| 57. | 2021. 10. 31. | $98.49 | -9.23% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $96.52 | -2.00% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $103.79 | 7.53% | 4,766.18 | 4.36% | |
| 평균의 (R): | 1.32% | 1.36% | ||||
| 표준 편차: | 6.32% | 4.48% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 FISV의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Fiserv Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RFISV,t | RS&P 500,t | (RFISV,t–RFISV)2 | (RS&P 500,t–RS&P 500)2 | (RFISV,t–RFISV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 7.41% | 3.72% | 37.13 | 5.58 | 14.39 |
| 2. | 2017. 3. 31. | -0.09% | -0.04% | 1.96 | 1.95 | 1.96 |
| 3. | 2017. 4. 30. | 3.33% | 0.91% | 4.06 | 0.20 | -0.90 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | -2.00% | -0.83% | 10.99 | 4.80 | 7.26 |
| 59. | 2021. 12. 31. | 7.53% | 4.36% | 38.65 | 9.02 | 18.67 |
| 합계 (Σ): | 2,320.16 | 1,164.17 | 972.71 | |||
| t | 날짜 | RFISV,t | RS&P 500,t | (RFISV,t–RFISV)2 | (RS&P 500,t–RS&P 500)2 | (RFISV,t–RFISV)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 7.41% | 3.72% | 37.13 | 5.58 | 14.39 |
| 2. | 2017. 3. 31. | -0.09% | -0.04% | 1.96 | 1.95 | 1.96 |
| 3. | 2017. 4. 30. | 3.33% | 0.91% | 4.06 | 0.20 | -0.90 |
| 4. | 2017. 5. 31. | 5.15% | 1.16% | 14.73 | 0.04 | -0.77 |
| 5. | 2017. 6. 30. | -2.35% | 0.48% | 13.41 | 0.77 | 3.21 |
| 6. | 2017. 7. 31. | 5.04% | 1.93% | 13.84 | 0.33 | 2.15 |
| 7. | 2017. 8. 31. | -3.72% | 0.05% | 25.35 | 1.70 | 6.56 |
| 8. | 2017. 9. 30. | 4.24% | 1.93% | 8.53 | 0.33 | 1.67 |
| 9. | 2017. 10. 31. | 0.36% | 2.22% | 0.92 | 0.74 | -0.83 |
| 10. | 2017. 11. 30. | 1.56% | 2.81% | 0.06 | 2.10 | 0.36 |
| 11. | 2017. 12. 31. | -0.23% | 0.98% | 2.38 | 0.14 | 0.58 |
| 12. | 2018. 1. 31. | 7.40% | 5.62% | 36.99 | 18.15 | 25.91 |
| 13. | 2018. 2. 28. | 1.82% | -3.89% | 0.25 | 27.59 | -2.64 |
| 14. | 2018. 3. 31. | -0.54% | -2.69% | 3.46 | 16.37 | 7.52 |
| 15. | 2018. 4. 30. | -0.63% | 0.27% | 3.79 | 1.18 | 2.11 |
| 16. | 2018. 5. 31. | 2.46% | 2.16% | 1.30 | 0.64 | 0.92 |
| 17. | 2018. 6. 30. | 2.05% | 0.48% | 0.54 | 0.76 | -0.64 |
| 18. | 2018. 7. 31. | 1.88% | 3.60% | 0.31 | 5.04 | 1.26 |
| 19. | 2018. 8. 31. | 6.08% | 3.03% | 22.71 | 2.78 | 7.95 |
| 20. | 2018. 9. 30. | 2.88% | 0.43% | 2.46 | 0.86 | -1.46 |
| 21. | 2018. 10. 31. | -3.74% | -6.94% | 25.54 | 68.86 | 41.94 |
| 22. | 2018. 11. 30. | -0.21% | 1.79% | 2.34 | 0.18 | -0.65 |
| 23. | 2018. 12. 31. | -7.13% | -9.18% | 71.28 | 111.00 | 88.95 |
| 24. | 2019. 1. 31. | 12.85% | 7.87% | 132.94 | 42.39 | 75.07 |
| 25. | 2019. 2. 28. | 2.12% | 2.97% | 0.65 | 2.61 | 1.30 |
| 26. | 2019. 3. 31. | 4.24% | 1.79% | 8.55 | 0.19 | 1.27 |
| 27. | 2019. 4. 30. | -1.18% | 3.93% | 6.22 | 6.62 | -6.42 |
| 28. | 2019. 5. 31. | -1.58% | -6.58% | 8.39 | 62.97 | 22.99 |
| 29. | 2019. 6. 30. | 6.17% | 6.89% | 23.60 | 30.64 | 26.89 |
| 30. | 2019. 7. 31. | 15.65% | 1.31% | 205.60 | 0.00 | -0.65 |
| 31. | 2019. 8. 31. | 1.43% | -1.81% | 0.01 | 10.03 | -0.37 |
| 32. | 2019. 9. 30. | -3.13% | 1.72% | 19.78 | 0.13 | -1.60 |
| 33. | 2019. 10. 31. | 2.46% | 2.04% | 1.31 | 0.47 | 0.79 |
| 34. | 2019. 11. 30. | 9.52% | 3.40% | 67.25 | 4.19 | 16.79 |
| 35. | 2019. 12. 31. | -0.52% | 2.86% | 3.39 | 2.25 | -2.76 |
| 36. | 2020. 1. 31. | 2.58% | -0.16% | 1.59 | 2.31 | -1.92 |
| 37. | 2020. 2. 29. | -7.80% | -8.41% | 83.06 | 95.43 | 89.03 |
| 38. | 2020. 3. 31. | -13.14% | -12.51% | 208.95 | 192.37 | 200.49 |
| 39. | 2020. 4. 30. | 8.50% | 12.68% | 51.56 | 128.29 | 81.33 |
| 40. | 2020. 5. 31. | 3.60% | 4.53% | 5.22 | 10.05 | 7.24 |
| 41. | 2020. 6. 30. | -8.57% | 1.84% | 97.71 | 0.23 | -4.75 |
| 42. | 2020. 7. 31. | 2.22% | 5.51% | 0.82 | 17.24 | 3.77 |
| 43. | 2020. 8. 31. | -0.21% | 7.01% | 2.33 | 31.91 | -8.62 |
| 44. | 2020. 9. 30. | 3.48% | -3.92% | 4.71 | 27.89 | -11.46 |
| 45. | 2020. 10. 31. | -7.36% | -2.77% | 75.18 | 17.01 | 35.76 |
| 46. | 2020. 11. 30. | 20.65% | 10.75% | 373.65 | 88.30 | 181.64 |
| 47. | 2020. 12. 31. | -1.15% | 3.71% | 6.06 | 5.54 | -5.79 |
| 48. | 2021. 1. 31. | -9.81% | -1.11% | 123.77 | 6.11 | 27.50 |
| 49. | 2021. 2. 28. | 12.35% | 2.61% | 121.72 | 1.57 | 13.80 |
| 50. | 2021. 3. 31. | 3.18% | 4.24% | 3.48 | 8.33 | 5.39 |
| 51. | 2021. 4. 30. | 0.91% | 5.24% | 0.17 | 15.09 | -1.58 |
| 52. | 2021. 5. 31. | -4.10% | 0.55% | 29.28 | 0.65 | 4.38 |
| 53. | 2021. 6. 30. | -7.21% | 2.22% | 72.74 | 0.75 | -7.36 |
| 54. | 2021. 7. 31. | 7.69% | 2.27% | 40.64 | 0.84 | 5.85 |
| 55. | 2021. 8. 31. | 2.33% | 2.90% | 1.03 | 2.38 | 1.56 |
| 56. | 2021. 9. 30. | -7.89% | -4.76% | 84.68 | 37.39 | 56.27 |
| 57. | 2021. 10. 31. | -9.23% | 6.91% | 111.11 | 30.87 | -58.57 |
| 58. | 2021. 11. 30. | -2.00% | -0.83% | 10.99 | 4.80 | 7.26 |
| 59. | 2021. 12. 31. | 7.53% | 4.36% | 38.65 | 9.02 | 18.67 |
| 합계 (Σ): | 2,320.16 | 1,164.17 | 972.71 | |||
모두 보기
분산FISV = Σ(RFISV,t–RFISV)2 ÷ (59 – 1)
= 2,320.16 ÷ (59 – 1)
= 40.00
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산FISV, S&P 500 = Σ(RFISV,t–RFISV)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 972.71 ÷ (59 – 1)
= 16.77
체계적인 위험 추정 (β)
| 분산FISV | 40.00 |
| 분산S&P 500 | 20.07 |
| 공분산FISV, S&P 500 | 16.77 |
| 상관 계수FISV, S&P 5001 | 0.59 |
| βFISV2 | 0.84 |
| αFISV3 | 0.18% |
계산
1 상관 계수FISV, S&P 500
= 공분산FISV, S&P 500 ÷ (표준 편차FISV × 표준 편차S&P 500)
= 16.77 ÷ (6.32% × 4.48%)
= 0.59
2 βFISV
= 공분산FISV, S&P 500 ÷ 분산S&P 500
= 16.77 ÷ 20.07
= 0.84
3 αFISV
= 평균의FISV – βFISV × 평균의S&P 500
= 1.32% – 0.84 × 1.36%
= 0.18%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.67% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.79% |
| 보통주의 체계적 위험Fiserv | βFISV | 0.84 |
| Fiserv 보통주의 예상 수익률3 | E(RFISV) | 12.29% |
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(RFISV) = RF + βFISV [E(RM) – RF]
= 4.67% + 0.84 [13.79% – 4.67%]
= 12.29%