자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 PayPal보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
PayPal Holdings Inc., 월별 수익률
| PayPal Holdings Inc. (PYPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PYPL,t1 | 피제수PYPL,t1 | RPYPL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $85.32 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $79.41 | -6.93% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $75.87 | -4.46% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $74.61 | -1.66% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $78.41 | -6.19% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $71.22 | -9.17% | 3,839.50 | -5.90% | |
| 평균의 (R): | 0.32% | 0.67% | ||||
| 표준 편차: | 11.11% | 5.40% | ||||
| PayPal Holdings Inc. (PYPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PYPL,t1 | 피제수PYPL,t1 | RPYPL,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $85.32 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $79.41 | -6.93% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $75.87 | -4.46% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $74.61 | -1.66% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $82.07 | 10.00% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $83.27 | 1.46% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $82.14 | -1.36% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $92.33 | 12.41% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $87.84 | -4.86% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $84.19 | -4.16% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $85.81 | 1.92% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $84.09 | -2.00% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $88.76 | 5.55% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $98.07 | 10.49% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $103.84 | 5.88% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $112.77 | 8.60% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $109.75 | -2.68% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $114.46 | 4.29% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $110.40 | -3.55% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $109.05 | -1.22% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $103.59 | -5.01% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $104.10 | 0.49% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $108.01 | 3.76% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $108.17 | 0.15% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $113.89 | 5.29% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $107.99 | -5.18% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $95.74 | -11.34% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $123.00 | 28.47% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $155.01 | 26.02% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $174.23 | 12.40% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $196.07 | 12.54% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $204.14 | 4.12% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $197.03 | -3.48% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $186.13 | -5.53% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $214.12 | 15.04% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $234.20 | 9.38% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $234.31 | 0.05% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $259.85 | 10.90% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $242.84 | -6.55% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $262.29 | 8.01% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $260.02 | -0.87% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $291.48 | 12.10% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $275.53 | -5.47% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $288.66 | 4.77% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $260.21 | -9.86% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $232.59 | -10.61% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $184.89 | -20.51% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $188.58 | 2.00% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $171.94 | -8.82% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $111.93 | -34.90% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $115.65 | 3.32% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $87.93 | -23.97% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $85.21 | -3.09% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $69.84 | -18.04% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $86.53 | 23.90% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $93.44 | 7.99% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $86.07 | -7.89% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $83.58 | -2.89% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $78.41 | -6.19% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $71.22 | -9.17% | 3,839.50 | -5.90% | |
| 평균의 (R): | 0.32% | 0.67% | ||||
| 표준 편차: | 11.11% | 5.40% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 t 기간 동안 PYPL의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
PayPal Holdings Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RPYPL,t | RS&P 500,t | (RPYPL,t–RPYPL)2 | (RS&P 500,t–RS&P 500)2 | (RPYPL,t–RPYPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -6.93% | -3.89% | 52.56 | 20.81 | 33.07 |
| 2. | 2018. 3. 31. | -4.46% | -2.69% | 22.85 | 11.26 | 16.04 |
| 3. | 2018. 4. 30. | -1.66% | 0.27% | 3.93 | 0.16 | 0.78 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | -6.19% | 5.38% | 42.36 | 22.17 | -30.65 |
| 59. | 2022. 12. 31. | -9.17% | -5.90% | 90.11 | 43.08 | 62.31 |
| 합계 (Σ): | 7,159.82 | 1,691.48 | 2,163.65 | |||
| t | 날짜 | RPYPL,t | RS&P 500,t | (RPYPL,t–RPYPL)2 | (RS&P 500,t–RS&P 500)2 | (RPYPL,t–RPYPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | -6.93% | -3.89% | 52.56 | 20.81 | 33.07 |
| 2. | 2018. 3. 31. | -4.46% | -2.69% | 22.85 | 11.26 | 16.04 |
| 3. | 2018. 4. 30. | -1.66% | 0.27% | 3.93 | 0.16 | 0.78 |
| 4. | 2018. 5. 31. | 10.00% | 2.16% | 93.63 | 2.23 | 14.46 |
| 5. | 2018. 6. 30. | 1.46% | 0.48% | 1.30 | 0.03 | -0.21 |
| 6. | 2018. 7. 31. | -1.36% | 3.60% | 2.82 | 8.62 | -4.93 |
| 7. | 2018. 8. 31. | 12.41% | 3.03% | 146.00 | 5.57 | 28.51 |
| 8. | 2018. 9. 30. | -4.86% | 0.43% | 26.89 | 0.06 | 1.23 |
| 9. | 2018. 10. 31. | -4.16% | -6.94% | 20.05 | 57.87 | 34.06 |
| 10. | 2018. 11. 30. | 1.92% | 1.79% | 2.57 | 1.25 | 1.79 |
| 11. | 2018. 12. 31. | -2.00% | -9.18% | 5.42 | 96.91 | 22.91 |
| 12. | 2019. 1. 31. | 5.55% | 7.87% | 27.36 | 51.87 | 37.67 |
| 13. | 2019. 2. 28. | 10.49% | 2.97% | 103.35 | 5.32 | 23.45 |
| 14. | 2019. 3. 31. | 5.88% | 1.79% | 30.92 | 1.27 | 6.26 |
| 15. | 2019. 4. 30. | 8.60% | 3.93% | 68.51 | 10.66 | 27.02 |
| 16. | 2019. 5. 31. | -2.68% | -6.58% | 9.00 | 52.48 | 21.74 |
| 17. | 2019. 6. 30. | 4.29% | 6.89% | 15.75 | 38.77 | 24.71 |
| 18. | 2019. 7. 31. | -3.55% | 1.31% | 14.97 | 0.42 | -2.50 |
| 19. | 2019. 8. 31. | -1.22% | -1.81% | 2.39 | 6.13 | 3.83 |
| 20. | 2019. 9. 30. | -5.01% | 1.72% | 28.40 | 1.11 | -5.60 |
| 21. | 2019. 10. 31. | 0.49% | 2.04% | 0.03 | 1.89 | 0.23 |
| 22. | 2019. 11. 30. | 3.76% | 3.40% | 11.79 | 7.50 | 9.40 |
| 23. | 2019. 12. 31. | 0.15% | 2.86% | 0.03 | 4.81 | -0.38 |
| 24. | 2020. 1. 31. | 5.29% | -0.16% | 24.65 | 0.69 | -4.12 |
| 25. | 2020. 2. 29. | -5.18% | -8.41% | 30.28 | 82.40 | 49.96 |
| 26. | 2020. 3. 31. | -11.34% | -12.51% | 136.10 | 173.67 | 153.75 |
| 27. | 2020. 4. 30. | 28.47% | 12.68% | 792.44 | 144.43 | 338.30 |
| 28. | 2020. 5. 31. | 26.02% | 4.53% | 660.58 | 14.91 | 99.25 |
| 29. | 2020. 6. 30. | 12.40% | 1.84% | 145.84 | 1.37 | 14.16 |
| 30. | 2020. 7. 31. | 12.54% | 5.51% | 149.15 | 23.46 | 59.15 |
| 31. | 2020. 8. 31. | 4.12% | 7.01% | 14.39 | 40.19 | 24.05 |
| 32. | 2020. 9. 30. | -3.48% | -3.92% | 14.48 | 21.06 | 17.47 |
| 33. | 2020. 10. 31. | -5.53% | -2.77% | 34.28 | 11.79 | 20.10 |
| 34. | 2020. 11. 30. | 15.04% | 10.75% | 216.54 | 101.77 | 148.45 |
| 35. | 2020. 12. 31. | 9.38% | 3.71% | 82.00 | 9.28 | 27.58 |
| 36. | 2021. 1. 31. | 0.05% | -1.11% | 0.08 | 3.17 | 0.49 |
| 37. | 2021. 2. 28. | 10.90% | 2.61% | 111.88 | 3.77 | 20.55 |
| 38. | 2021. 3. 31. | -6.55% | 4.24% | 47.18 | 12.80 | -24.57 |
| 39. | 2021. 4. 30. | 8.01% | 5.24% | 59.09 | 20.94 | 35.17 |
| 40. | 2021. 5. 31. | -0.87% | 0.55% | 1.41 | 0.01 | 0.14 |
| 41. | 2021. 6. 30. | 12.10% | 2.22% | 138.68 | 2.42 | 18.31 |
| 42. | 2021. 7. 31. | -5.47% | 2.27% | 33.58 | 2.59 | -9.32 |
| 43. | 2021. 8. 31. | 4.77% | 2.90% | 19.74 | 4.98 | 9.92 |
| 44. | 2021. 9. 30. | -9.86% | -4.76% | 103.60 | 29.42 | 55.20 |
| 45. | 2021. 10. 31. | -10.61% | 6.91% | 119.62 | 39.03 | -68.33 |
| 46. | 2021. 11. 30. | -20.51% | -0.83% | 433.92 | 2.25 | 31.25 |
| 47. | 2021. 12. 31. | 2.00% | 4.36% | 2.80 | 13.65 | 6.18 |
| 48. | 2022. 1. 31. | -8.82% | -5.26% | 83.66 | 35.11 | 54.19 |
| 49. | 2022. 2. 28. | -34.90% | -3.14% | 1,240.76 | 14.46 | 133.95 |
| 50. | 2022. 3. 31. | 3.32% | 3.58% | 9.01 | 8.47 | 8.73 |
| 51. | 2022. 4. 30. | -23.97% | -8.80% | 590.08 | 89.54 | 229.85 |
| 52. | 2022. 5. 31. | -3.09% | 0.01% | 11.67 | 0.44 | 2.26 |
| 53. | 2022. 6. 30. | -18.04% | -8.39% | 337.11 | 82.06 | 166.32 |
| 54. | 2022. 7. 31. | 23.90% | 9.11% | 555.77 | 71.32 | 199.09 |
| 55. | 2022. 8. 31. | 7.99% | -4.24% | 58.72 | 24.11 | -37.63 |
| 56. | 2022. 9. 30. | -7.89% | -9.34% | 67.41 | 100.12 | 82.15 |
| 57. | 2022. 10. 31. | -2.89% | 7.99% | 10.34 | 53.58 | -23.54 |
| 58. | 2022. 11. 30. | -6.19% | 5.38% | 42.36 | 22.17 | -30.65 |
| 59. | 2022. 12. 31. | -9.17% | -5.90% | 90.11 | 43.08 | 62.31 |
| 합계 (Σ): | 7,159.82 | 1,691.48 | 2,163.65 | |||
모두 보기
분산PYPL = Σ(RPYPL,t–RPYPL)2 ÷ (59 – 1)
= 7,159.82 ÷ (59 – 1)
= 123.45
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산PYPL, S&P 500 = Σ(RPYPL,t–RPYPL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,163.65 ÷ (59 – 1)
= 37.30
체계적인 위험 추정 (β)
| 분산PYPL | 123.45 |
| 분산S&P 500 | 29.16 |
| 공분산PYPL, S&P 500 | 37.30 |
| 상관 계수PYPL, S&P 5001 | 0.62 |
| βPYPL2 | 1.28 |
| αPYPL3 | -0.53% |
계산
1 상관 계수PYPL, S&P 500
= 공분산PYPL, S&P 500 ÷ (표준 편차PYPL × 표준 편차S&P 500)
= 37.30 ÷ (11.11% × 5.40%)
= 0.62
2 βPYPL
= 공분산PYPL, S&P 500 ÷ 분산S&P 500
= 37.30 ÷ 29.16
= 1.28
3 αPYPL
= 평균의PYPL – βPYPL × 평균의S&P 500
= 0.32% – 1.28 × 0.67%
= -0.53%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.79% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.38% |
| 보통주의 체계적 위험PayPal | βPYPL | 1.28 |
| PayPal 보통주에 대한 예상 수익률3 | E(RPYPL) | 20.90% |
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(RPYPL) = RF + βPYPL [E(RM) – RF]
= 4.79% + 1.28 [17.38% – 4.79%]
= 20.90%