자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Paycom보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Paycom Software Inc., 월별 수익률
| Paycom Software Inc. (PAYC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PAYC,t1 | 피제수PAYC,t1 | RPAYC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $91.64 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $98.92 | 7.94% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $107.39 | 8.56% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $114.21 | 6.35% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | $339.10 | -1.99% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $310.31 | -8.49% | 3,839.50 | -5.90% | |
| 평균의 (R): | 2.98% | 0.67% | ||||
| 표준 편차: | 13.66% | 5.40% | ||||
| Paycom Software Inc. (PAYC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값PAYC,t1 | 피제수PAYC,t1 | RPAYC,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2018. 1. 31. | $91.64 | 2,823.81 | ||||
| 1. | 2018. 2. 28. | $98.92 | 7.94% | 2,713.83 | -3.89% | |
| 2. | 2018. 3. 31. | $107.39 | 8.56% | 2,640.87 | -2.69% | |
| 3. | 2018. 4. 30. | $114.21 | 6.35% | 2,648.05 | 0.27% | |
| 4. | 2018. 5. 31. | $105.47 | -7.65% | 2,705.27 | 2.16% | |
| 5. | 2018. 6. 30. | $98.83 | -6.30% | 2,718.37 | 0.48% | |
| 6. | 2018. 7. 31. | $106.25 | 7.51% | 2,816.29 | 3.60% | |
| 7. | 2018. 8. 31. | $155.12 | 46.00% | 2,901.52 | 3.03% | |
| 8. | 2018. 9. 30. | $155.41 | 0.19% | 2,913.98 | 0.43% | |
| 9. | 2018. 10. 31. | $125.20 | -19.44% | 2,711.74 | -6.94% | |
| 10. | 2018. 11. 30. | $132.77 | 6.05% | 2,760.17 | 1.79% | |
| 11. | 2018. 12. 31. | $122.45 | -7.77% | 2,506.85 | -9.18% | |
| 12. | 2019. 1. 31. | $148.24 | 21.06% | 2,704.10 | 7.87% | |
| 13. | 2019. 2. 28. | $181.73 | 22.59% | 2,784.49 | 2.97% | |
| 14. | 2019. 3. 31. | $189.13 | 4.07% | 2,834.40 | 1.79% | |
| 15. | 2019. 4. 30. | $202.53 | 7.09% | 2,945.83 | 3.93% | |
| 16. | 2019. 5. 31. | $212.10 | 4.73% | 2,752.06 | -6.58% | |
| 17. | 2019. 6. 30. | $226.72 | 6.89% | 2,941.76 | 6.89% | |
| 18. | 2019. 7. 31. | $240.75 | 6.19% | 2,980.38 | 1.31% | |
| 19. | 2019. 8. 31. | $250.12 | 3.89% | 2,926.46 | -1.81% | |
| 20. | 2019. 9. 30. | $209.49 | -16.24% | 2,976.74 | 1.72% | |
| 21. | 2019. 10. 31. | $211.53 | 0.97% | 3,037.56 | 2.04% | |
| 22. | 2019. 11. 30. | $276.81 | 30.86% | 3,140.98 | 3.40% | |
| 23. | 2019. 12. 31. | $264.76 | -4.35% | 3,230.78 | 2.86% | |
| 24. | 2020. 1. 31. | $318.16 | 20.17% | 3,225.52 | -0.16% | |
| 25. | 2020. 2. 29. | $282.65 | -11.16% | 2,954.22 | -8.41% | |
| 26. | 2020. 3. 31. | $202.01 | -28.53% | 2,584.59 | -12.51% | |
| 27. | 2020. 4. 30. | $261.02 | 29.21% | 2,912.43 | 12.68% | |
| 28. | 2020. 5. 31. | $297.23 | 13.87% | 3,044.31 | 4.53% | |
| 29. | 2020. 6. 30. | $309.73 | 4.21% | 3,100.29 | 1.84% | |
| 30. | 2020. 7. 31. | $284.37 | -8.19% | 3,271.12 | 5.51% | |
| 31. | 2020. 8. 31. | $299.46 | 5.31% | 3,500.31 | 7.01% | |
| 32. | 2020. 9. 30. | $311.30 | 3.95% | 3,363.00 | -3.92% | |
| 33. | 2020. 10. 31. | $364.09 | 16.96% | 3,269.96 | -2.77% | |
| 34. | 2020. 11. 30. | $417.08 | 14.55% | 3,621.63 | 10.75% | |
| 35. | 2020. 12. 31. | $452.25 | 8.43% | 3,756.07 | 3.71% | |
| 36. | 2021. 1. 31. | $379.74 | -16.03% | 3,714.24 | -1.11% | |
| 37. | 2021. 2. 28. | $374.24 | -1.45% | 3,811.15 | 2.61% | |
| 38. | 2021. 3. 31. | $370.06 | -1.12% | 3,972.89 | 4.24% | |
| 39. | 2021. 4. 30. | $384.41 | 3.88% | 4,181.17 | 5.24% | |
| 40. | 2021. 5. 31. | $329.60 | -14.26% | 4,204.11 | 0.55% | |
| 41. | 2021. 6. 30. | $363.47 | 10.28% | 4,297.50 | 2.22% | |
| 42. | 2021. 7. 31. | $400.00 | 10.05% | 4,395.26 | 2.27% | |
| 43. | 2021. 8. 31. | $488.90 | 22.23% | 4,522.68 | 2.90% | |
| 44. | 2021. 9. 30. | $495.75 | 1.40% | 4,307.54 | -4.76% | |
| 45. | 2021. 10. 31. | $547.85 | 10.51% | 4,605.38 | 6.91% | |
| 46. | 2021. 11. 30. | $437.48 | -20.15% | 4,567.00 | -0.83% | |
| 47. | 2021. 12. 31. | $415.19 | -5.10% | 4,766.18 | 4.36% | |
| 48. | 2022. 1. 31. | $335.30 | -19.24% | 4,515.55 | -5.26% | |
| 49. | 2022. 2. 28. | $339.21 | 1.17% | 4,373.94 | -3.14% | |
| 50. | 2022. 3. 31. | $346.38 | 2.11% | 4,530.41 | 3.58% | |
| 51. | 2022. 4. 30. | $281.47 | -18.74% | 4,131.93 | -8.80% | |
| 52. | 2022. 5. 31. | $284.34 | 1.02% | 4,132.15 | 0.01% | |
| 53. | 2022. 6. 30. | $280.12 | -1.48% | 3,785.38 | -8.39% | |
| 54. | 2022. 7. 31. | $330.49 | 17.98% | 4,130.29 | 9.11% | |
| 55. | 2022. 8. 31. | $351.20 | 6.27% | 3,955.00 | -4.24% | |
| 56. | 2022. 9. 30. | $329.99 | -6.04% | 3,585.62 | -9.34% | |
| 57. | 2022. 10. 31. | $346.00 | 4.85% | 3,871.98 | 7.99% | |
| 58. | 2022. 11. 30. | $339.10 | -1.99% | 4,080.11 | 5.38% | |
| 59. | 2022. 12. 31. | $310.31 | -8.49% | 3,839.50 | -5.90% | |
| 평균의 (R): | 2.98% | 0.67% | ||||
| 표준 편차: | 13.66% | 5.40% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 t 기간 동안 PAYC의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Paycom Software Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RPAYC,t | RS&P 500,t | (RPAYC,t–RPAYC)2 | (RS&P 500,t–RS&P 500)2 | (RPAYC,t–RPAYC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 7.94% | -3.89% | 24.68 | 20.81 | -22.66 |
| 2. | 2018. 3. 31. | 8.56% | -2.69% | 31.20 | 11.26 | -18.74 |
| 3. | 2018. 4. 30. | 6.35% | 0.27% | 11.38 | 0.16 | -1.33 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2022. 11. 30. | -1.99% | 5.38% | 24.71 | 22.17 | -23.41 |
| 59. | 2022. 12. 31. | -8.49% | -5.90% | 131.48 | 43.08 | 75.26 |
| 합계 (Σ): | 10,822.04 | 1,691.48 | 2,299.49 | |||
| t | 날짜 | RPAYC,t | RS&P 500,t | (RPAYC,t–RPAYC)2 | (RS&P 500,t–RS&P 500)2 | (RPAYC,t–RPAYC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2018. 2. 28. | 7.94% | -3.89% | 24.68 | 20.81 | -22.66 |
| 2. | 2018. 3. 31. | 8.56% | -2.69% | 31.20 | 11.26 | -18.74 |
| 3. | 2018. 4. 30. | 6.35% | 0.27% | 11.38 | 0.16 | -1.33 |
| 4. | 2018. 5. 31. | -7.65% | 2.16% | 112.98 | 2.23 | -15.88 |
| 5. | 2018. 6. 30. | -6.30% | 0.48% | 85.97 | 0.03 | 1.69 |
| 6. | 2018. 7. 31. | 7.51% | 3.60% | 20.53 | 8.62 | 13.30 |
| 7. | 2018. 8. 31. | 46.00% | 3.03% | 1,850.61 | 5.57 | 101.51 |
| 8. | 2018. 9. 30. | 0.19% | 0.43% | 7.78 | 0.06 | 0.66 |
| 9. | 2018. 10. 31. | -19.44% | -6.94% | 502.45 | 57.87 | 170.51 |
| 10. | 2018. 11. 30. | 6.05% | 1.79% | 9.42 | 1.25 | 3.44 |
| 11. | 2018. 12. 31. | -7.77% | -9.18% | 115.55 | 96.91 | 105.82 |
| 12. | 2019. 1. 31. | 21.06% | 7.87% | 327.07 | 51.87 | 130.25 |
| 13. | 2019. 2. 28. | 22.59% | 2.97% | 384.76 | 5.32 | 45.24 |
| 14. | 2019. 3. 31. | 4.07% | 1.79% | 1.20 | 1.27 | 1.23 |
| 15. | 2019. 4. 30. | 7.09% | 3.93% | 16.88 | 10.66 | 13.41 |
| 16. | 2019. 5. 31. | 4.73% | -6.58% | 3.06 | 52.48 | -12.67 |
| 17. | 2019. 6. 30. | 6.89% | 6.89% | 15.34 | 38.77 | 24.39 |
| 18. | 2019. 7. 31. | 6.19% | 1.31% | 10.32 | 0.42 | 2.08 |
| 19. | 2019. 8. 31. | 3.89% | -1.81% | 0.84 | 6.13 | -2.27 |
| 20. | 2019. 9. 30. | -16.24% | 1.72% | 369.44 | 1.11 | -20.21 |
| 21. | 2019. 10. 31. | 0.97% | 2.04% | 4.01 | 1.89 | -2.76 |
| 22. | 2019. 11. 30. | 30.86% | 3.40% | 777.54 | 7.50 | 76.35 |
| 23. | 2019. 12. 31. | -4.35% | 2.86% | 53.72 | 4.81 | -16.07 |
| 24. | 2020. 1. 31. | 20.17% | -0.16% | 295.59 | 0.69 | -14.26 |
| 25. | 2020. 2. 29. | -11.16% | -8.41% | 199.87 | 82.40 | 128.34 |
| 26. | 2020. 3. 31. | -28.53% | -12.51% | 992.66 | 173.67 | 415.21 |
| 27. | 2020. 4. 30. | 29.21% | 12.68% | 688.27 | 144.43 | 315.28 |
| 28. | 2020. 5. 31. | 13.87% | 4.53% | 118.72 | 14.91 | 42.08 |
| 29. | 2020. 6. 30. | 4.21% | 1.84% | 1.51 | 1.37 | 1.44 |
| 30. | 2020. 7. 31. | -8.19% | 5.51% | 124.64 | 23.46 | -54.07 |
| 31. | 2020. 8. 31. | 5.31% | 7.01% | 5.43 | 40.19 | 14.77 |
| 32. | 2020. 9. 30. | 3.95% | -3.92% | 0.95 | 21.06 | -4.48 |
| 33. | 2020. 10. 31. | 16.96% | -2.77% | 195.48 | 11.79 | -48.00 |
| 34. | 2020. 11. 30. | 14.55% | 10.75% | 134.04 | 101.77 | 116.79 |
| 35. | 2020. 12. 31. | 8.43% | 3.71% | 29.77 | 9.28 | 16.62 |
| 36. | 2021. 1. 31. | -16.03% | -1.11% | 361.37 | 3.17 | 33.84 |
| 37. | 2021. 2. 28. | -1.45% | 2.61% | 19.58 | 3.77 | -8.60 |
| 38. | 2021. 3. 31. | -1.12% | 4.24% | 16.76 | 12.80 | -14.64 |
| 39. | 2021. 4. 30. | 3.88% | 5.24% | 0.81 | 20.94 | 4.12 |
| 40. | 2021. 5. 31. | -14.26% | 0.55% | 297.04 | 0.01 | 2.03 |
| 41. | 2021. 6. 30. | 10.28% | 2.22% | 53.28 | 2.42 | 11.35 |
| 42. | 2021. 7. 31. | 10.05% | 2.27% | 50.04 | 2.59 | 11.38 |
| 43. | 2021. 8. 31. | 22.23% | 2.90% | 370.50 | 4.98 | 42.97 |
| 44. | 2021. 9. 30. | 1.40% | -4.76% | 2.48 | 29.42 | 8.54 |
| 45. | 2021. 10. 31. | 10.51% | 6.91% | 56.74 | 39.03 | 47.06 |
| 46. | 2021. 11. 30. | -20.15% | -0.83% | 534.65 | 2.25 | 34.68 |
| 47. | 2021. 12. 31. | -5.10% | 4.36% | 65.15 | 13.65 | -29.82 |
| 48. | 2022. 1. 31. | -19.24% | -5.26% | 493.65 | 35.11 | 131.65 |
| 49. | 2022. 2. 28. | 1.17% | -3.14% | 3.28 | 14.46 | 6.88 |
| 50. | 2022. 3. 31. | 2.11% | 3.58% | 0.74 | 8.47 | -2.51 |
| 51. | 2022. 4. 30. | -18.74% | -8.80% | 471.59 | 89.54 | 205.48 |
| 52. | 2022. 5. 31. | 1.02% | 0.01% | 3.83 | 0.44 | 1.29 |
| 53. | 2022. 6. 30. | -1.48% | -8.39% | 19.90 | 82.06 | 40.41 |
| 54. | 2022. 7. 31. | 17.98% | 9.11% | 225.15 | 71.32 | 126.72 |
| 55. | 2022. 8. 31. | 6.27% | -4.24% | 10.82 | 24.11 | -16.16 |
| 56. | 2022. 9. 30. | -6.04% | -9.34% | 81.29 | 100.12 | 90.21 |
| 57. | 2022. 10. 31. | 4.85% | 7.99% | 3.52 | 53.58 | 13.73 |
| 58. | 2022. 11. 30. | -1.99% | 5.38% | 24.71 | 22.17 | -23.41 |
| 59. | 2022. 12. 31. | -8.49% | -5.90% | 131.48 | 43.08 | 75.26 |
| 합계 (Σ): | 10,822.04 | 1,691.48 | 2,299.49 | |||
모두 표시
분산PAYC = Σ(RPAYC,t–RPAYC)2 ÷ (59 – 1)
= 10,822.04 ÷ (59 – 1)
= 186.59
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
공분산PAYC, S&P 500 = Σ(RPAYC,t–RPAYC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,299.49 ÷ (59 – 1)
= 39.65
체계적인 위험 추정 (β)
| 분산PAYC | 186.59 |
| 분산S&P 500 | 29.16 |
| 공분산PAYC, S&P 500 | 39.65 |
| 상관 계수PAYC, S&P 5001 | 0.54 |
| βPAYC2 | 1.36 |
| αPAYC3 | 2.07% |
계산
1 상관 계수PAYC, S&P 500
= 공분산PAYC, S&P 500 ÷ (표준 편차PAYC × 표준 편차S&P 500)
= 39.65 ÷ (13.66% × 5.40%)
= 0.54
2 βPAYC
= 공분산PAYC, S&P 500 ÷ 분산S&P 500
= 39.65 ÷ 29.16
= 1.36
3 αPAYC
= 평균의PAYC – βPAYC × 평균의S&P 500
= 2.98% – 1.36 × 0.67%
= 2.07%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.62% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.69% |
| 보통주의 체계적 위험 Paycom | βPAYC | 1.36 |
| Paycom 보통주의 예상 수익률3 | E(RPAYC) | 16.95% |
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(RPAYC) = RF + βPAYC [E(RM) – RF]
= 4.62% + 1.36 [13.69% – 4.62%]
= 16.95%