자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 ServiceNow보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
ServiceNow Inc., 월별 수익률
| ServiceNow Inc. (NOW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NOW,t1 | 피제수NOW,t1 | RNOW,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $108.63 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $106.69 | -1.79% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $100.02 | -6.25% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $101.27 | 1.25% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | $162.48 | -11.63% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $153.19 | -5.72% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.93% | 1.14% | ||||
| 표준 편차: | 8.56% | 4.37% | ||||
| ServiceNow Inc. (NOW) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NOW,t1 | 피제수NOW,t1 | RNOW,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2021. 1. 31. | $108.63 | 3,714.24 | ||||
| 1. | 2021. 2. 28. | $106.69 | -1.79% | 3,811.15 | 2.61% | |
| 2. | 2021. 3. 31. | $100.02 | -6.25% | 3,972.89 | 4.24% | |
| 3. | 2021. 4. 30. | $101.27 | 1.25% | 4,181.17 | 5.24% | |
| 4. | 2021. 5. 31. | $94.78 | -6.41% | 4,204.11 | 0.55% | |
| 5. | 2021. 6. 30. | $109.91 | 15.96% | 4,297.50 | 2.22% | |
| 6. | 2021. 7. 31. | $117.58 | 6.98% | 4,395.26 | 2.27% | |
| 7. | 2021. 8. 31. | $128.73 | 9.48% | 4,522.68 | 2.90% | |
| 8. | 2021. 9. 30. | $124.45 | -3.32% | 4,307.54 | -4.76% | |
| 9. | 2021. 10. 31. | $139.55 | 12.13% | 4,605.38 | 6.91% | |
| 10. | 2021. 11. 30. | $129.54 | -7.17% | 4,567.00 | -0.83% | |
| 11. | 2021. 12. 31. | $129.82 | 0.22% | 4,766.18 | 4.36% | |
| 12. | 2022. 1. 31. | $117.16 | -9.75% | 4,515.55 | -5.26% | |
| 13. | 2022. 2. 28. | $115.98 | -1.01% | 4,373.94 | -3.14% | |
| 14. | 2022. 3. 31. | $111.38 | -3.97% | 4,530.41 | 3.58% | |
| 15. | 2022. 4. 30. | $95.62 | -14.15% | 4,131.93 | -8.80% | |
| 16. | 2022. 5. 31. | $93.49 | -2.23% | 4,132.15 | 0.01% | |
| 17. | 2022. 6. 30. | $95.10 | 1.72% | 3,785.38 | -8.39% | |
| 18. | 2022. 7. 31. | $89.33 | -6.07% | 4,130.29 | 9.11% | |
| 19. | 2022. 8. 31. | $86.92 | -2.70% | 3,955.00 | -4.24% | |
| 20. | 2022. 9. 30. | $75.52 | -13.12% | 3,585.62 | -9.34% | |
| 21. | 2022. 10. 31. | $84.15 | 11.43% | 3,871.98 | 7.99% | |
| 22. | 2022. 11. 30. | $83.26 | -1.06% | 4,080.11 | 5.38% | |
| 23. | 2022. 12. 31. | $77.65 | -6.74% | 3,839.50 | -5.90% | |
| 24. | 2023. 1. 31. | $91.03 | 17.23% | 4,076.60 | 6.18% | |
| 25. | 2023. 2. 28. | $86.43 | -5.05% | 3,970.15 | -2.61% | |
| 26. | 2023. 3. 31. | $92.94 | 7.53% | 4,109.31 | 3.51% | |
| 27. | 2023. 4. 30. | $91.88 | -1.14% | 4,169.48 | 1.46% | |
| 28. | 2023. 5. 31. | $108.96 | 18.59% | 4,179.83 | 0.25% | |
| 29. | 2023. 6. 30. | $112.39 | 3.15% | 4,376.86 | 4.71% | |
| 30. | 2023. 7. 31. | $116.60 | 3.75% | 4,588.96 | 4.85% | |
| 31. | 2023. 8. 31. | $117.77 | 1.00% | 4,507.66 | -1.77% | |
| 32. | 2023. 9. 30. | $111.79 | -5.08% | 4,288.05 | -4.87% | |
| 33. | 2023. 10. 31. | $116.37 | 4.10% | 4,193.80 | -2.20% | |
| 34. | 2023. 11. 30. | $137.15 | 17.86% | 4,567.80 | 8.92% | |
| 35. | 2023. 12. 31. | $141.30 | 3.03% | 4,769.83 | 4.42% | |
| 36. | 2024. 1. 31. | $153.08 | 8.34% | 4,845.65 | 1.59% | |
| 37. | 2024. 2. 29. | $154.27 | 0.78% | 5,096.27 | 5.17% | |
| 38. | 2024. 3. 31. | $152.48 | -1.16% | 5,254.35 | 3.10% | |
| 39. | 2024. 4. 30. | $138.67 | -9.06% | 5,035.69 | -4.16% | |
| 40. | 2024. 5. 31. | $131.39 | -5.25% | 5,277.51 | 4.80% | |
| 41. | 2024. 6. 30. | $157.33 | 19.74% | 5,460.48 | 3.47% | |
| 42. | 2024. 7. 31. | $162.88 | 3.53% | 5,522.30 | 1.13% | |
| 43. | 2024. 8. 31. | $171.00 | 4.99% | 5,648.40 | 2.28% | |
| 44. | 2024. 9. 30. | $178.88 | 4.61% | 5,762.48 | 2.02% | |
| 45. | 2024. 10. 31. | $186.60 | 4.32% | 5,705.45 | -0.99% | |
| 46. | 2024. 11. 30. | $209.89 | 12.48% | 6,032.38 | 5.73% | |
| 47. | 2024. 12. 31. | $212.02 | 1.01% | 5,881.63 | -2.50% | |
| 48. | 2025. 1. 31. | $203.68 | -3.93% | 6,040.53 | 2.70% | |
| 49. | 2025. 2. 28. | $185.95 | -8.70% | 5,954.50 | -1.42% | |
| 50. | 2025. 3. 31. | $159.23 | -14.37% | 5,611.85 | -5.75% | |
| 51. | 2025. 4. 30. | $191.00 | 19.95% | 5,569.06 | -0.76% | |
| 52. | 2025. 5. 31. | $202.22 | 5.87% | 5,911.69 | 6.15% | |
| 53. | 2025. 6. 30. | $205.62 | 1.68% | 6,204.95 | 4.96% | |
| 54. | 2025. 7. 31. | $188.62 | -8.27% | 6,339.39 | 2.17% | |
| 55. | 2025. 8. 31. | $183.49 | -2.72% | 6,460.26 | 1.91% | |
| 56. | 2025. 9. 30. | $184.06 | 0.31% | 6,688.46 | 3.53% | |
| 57. | 2025. 10. 31. | $183.86 | -0.11% | 6,840.20 | 2.27% | |
| 58. | 2025. 11. 30. | $162.48 | -11.63% | 6,849.09 | 0.13% | |
| 59. | 2025. 12. 31. | $153.19 | -5.72% | 6,845.50 | -0.05% | |
| 평균의 (R): | 0.93% | 1.14% | ||||
| 표준 편차: | 8.56% | 4.37% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 NOW의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
ServiceNow Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RNOW,t | RS&P 500,t | (RNOW,t–RNOW)2 | (RS&P 500,t–RS&P 500)2 | (RNOW,t–RNOW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -1.79% | 2.61% | 7.40 | 2.17 | -4.01 |
| 2. | 2021. 3. 31. | -6.25% | 4.24% | 51.63 | 9.66 | -22.33 |
| 3. | 2021. 4. 30. | 1.25% | 5.24% | 0.10 | 16.86 | 1.30 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2025. 11. 30. | -11.63% | 0.13% | 157.81 | 1.01 | 12.64 |
| 59. | 2025. 12. 31. | -5.72% | -0.05% | 44.24 | 1.41 | 7.91 |
| 합계 (Σ): | 4,253.18 | 1,108.23 | 1,091.71 | |||
| t | 날짜 | RNOW,t | RS&P 500,t | (RNOW,t–RNOW)2 | (RS&P 500,t–RS&P 500)2 | (RNOW,t–RNOW)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2021. 2. 28. | -1.79% | 2.61% | 7.40 | 2.17 | -4.01 |
| 2. | 2021. 3. 31. | -6.25% | 4.24% | 51.63 | 9.66 | -22.33 |
| 3. | 2021. 4. 30. | 1.25% | 5.24% | 0.10 | 16.86 | 1.30 |
| 4. | 2021. 5. 31. | -6.41% | 0.55% | 53.91 | 0.35 | 4.31 |
| 5. | 2021. 6. 30. | 15.96% | 2.22% | 225.88 | 1.18 | 16.31 |
| 6. | 2021. 7. 31. | 6.98% | 2.27% | 36.54 | 1.30 | 6.88 |
| 7. | 2021. 8. 31. | 9.48% | 2.90% | 73.09 | 3.11 | 15.07 |
| 8. | 2021. 9. 30. | -3.32% | -4.76% | 18.14 | 34.73 | 25.10 |
| 9. | 2021. 10. 31. | 12.13% | 6.91% | 125.43 | 33.39 | 64.71 |
| 10. | 2021. 11. 30. | -7.17% | -0.83% | 65.72 | 3.88 | 15.97 |
| 11. | 2021. 12. 31. | 0.22% | 4.36% | 0.52 | 10.40 | -2.31 |
| 12. | 2022. 1. 31. | -9.75% | -5.26% | 114.19 | 40.89 | 68.33 |
| 13. | 2022. 2. 28. | -1.01% | -3.14% | 3.77 | 18.25 | 8.29 |
| 14. | 2022. 3. 31. | -3.97% | 3.58% | 24.01 | 5.96 | -11.96 |
| 15. | 2022. 4. 30. | -14.15% | -8.80% | 227.52 | 98.64 | 149.81 |
| 16. | 2022. 5. 31. | -2.23% | 0.01% | 9.99 | 1.28 | 3.58 |
| 17. | 2022. 6. 30. | 1.72% | -8.39% | 0.62 | 90.79 | -7.51 |
| 18. | 2022. 7. 31. | -6.07% | 9.11% | 49.02 | 63.61 | -55.84 |
| 19. | 2022. 8. 31. | -2.70% | -4.24% | 13.19 | 28.95 | 19.54 |
| 20. | 2022. 9. 30. | -13.12% | -9.34% | 197.39 | 109.74 | 147.18 |
| 21. | 2022. 10. 31. | 11.43% | 7.99% | 110.11 | 46.93 | 71.88 |
| 22. | 2022. 11. 30. | -1.06% | 5.38% | 3.97 | 17.97 | -8.44 |
| 23. | 2022. 12. 31. | -6.74% | -5.90% | 58.86 | 49.47 | 53.96 |
| 24. | 2023. 1. 31. | 17.23% | 6.18% | 265.60 | 25.39 | 82.12 |
| 25. | 2023. 2. 28. | -5.05% | -2.61% | 35.85 | 14.04 | 22.44 |
| 26. | 2023. 3. 31. | 7.53% | 3.51% | 43.54 | 5.61 | 15.63 |
| 27. | 2023. 4. 30. | -1.14% | 1.46% | 4.30 | 0.11 | -0.68 |
| 28. | 2023. 5. 31. | 18.59% | 0.25% | 311.72 | 0.79 | -15.68 |
| 29. | 2023. 6. 30. | 3.15% | 4.71% | 4.90 | 12.80 | 7.92 |
| 30. | 2023. 7. 31. | 3.75% | 4.85% | 7.91 | 13.76 | 10.43 |
| 31. | 2023. 8. 31. | 1.00% | -1.77% | 0.00 | 8.46 | -0.20 |
| 32. | 2023. 9. 30. | -5.08% | -4.87% | 36.14 | 36.10 | 36.12 |
| 33. | 2023. 10. 31. | 4.10% | -2.20% | 10.01 | 11.12 | -10.55 |
| 34. | 2023. 11. 30. | 17.86% | 8.92% | 286.39 | 60.56 | 131.69 |
| 35. | 2023. 12. 31. | 3.03% | 4.42% | 4.38 | 10.80 | 6.88 |
| 36. | 2024. 1. 31. | 8.34% | 1.59% | 54.80 | 0.21 | 3.36 |
| 37. | 2024. 2. 29. | 0.78% | 5.17% | 0.02 | 16.29 | -0.63 |
| 38. | 2024. 3. 31. | -1.16% | 3.10% | 4.39 | 3.86 | -4.12 |
| 39. | 2024. 4. 30. | -9.06% | -4.16% | 99.82 | 28.06 | 52.93 |
| 40. | 2024. 5. 31. | -5.25% | 4.80% | 38.24 | 13.44 | -22.67 |
| 41. | 2024. 6. 30. | 19.74% | 3.47% | 353.77 | 5.43 | 43.84 |
| 42. | 2024. 7. 31. | 3.53% | 1.13% | 6.73 | 0.00 | -0.01 |
| 43. | 2024. 8. 31. | 4.99% | 2.28% | 16.41 | 1.32 | 4.65 |
| 44. | 2024. 9. 30. | 4.61% | 2.02% | 13.50 | 0.78 | 3.25 |
| 45. | 2024. 10. 31. | 4.32% | -0.99% | 11.44 | 4.52 | -7.19 |
| 46. | 2024. 11. 30. | 12.48% | 5.73% | 133.34 | 21.10 | 53.05 |
| 47. | 2024. 12. 31. | 1.01% | -2.50% | 0.01 | 13.21 | -0.29 |
| 48. | 2025. 1. 31. | -3.93% | 2.70% | 23.69 | 2.45 | -7.62 |
| 49. | 2025. 2. 28. | -8.70% | -1.42% | 92.91 | 6.56 | 24.68 |
| 50. | 2025. 3. 31. | -14.37% | -5.75% | 234.19 | 47.48 | 105.45 |
| 51. | 2025. 4. 30. | 19.95% | -0.76% | 361.70 | 3.60 | -36.11 |
| 52. | 2025. 5. 31. | 5.87% | 6.15% | 24.41 | 25.16 | 24.78 |
| 53. | 2025. 6. 30. | 1.68% | 4.96% | 0.56 | 14.63 | 2.86 |
| 54. | 2025. 7. 31. | -8.27% | 2.17% | 84.67 | 1.06 | -9.48 |
| 55. | 2025. 8. 31. | -2.72% | 1.91% | 13.35 | 0.59 | -2.82 |
| 56. | 2025. 9. 30. | 0.31% | 3.53% | 0.39 | 5.74 | -1.49 |
| 57. | 2025. 10. 31. | -0.11% | 2.27% | 1.09 | 1.28 | -1.18 |
| 58. | 2025. 11. 30. | -11.63% | 0.13% | 157.81 | 1.01 | 12.64 |
| 59. | 2025. 12. 31. | -5.72% | -0.05% | 44.24 | 1.41 | 7.91 |
| 합계 (Σ): | 4,253.18 | 1,108.23 | 1,091.71 | |||
모두 보기
분산NOW = Σ(RNOW,t–RNOW)2 ÷ (59 – 1)
= 4,253.18 ÷ (59 – 1)
= 73.33
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
공분산NOW, S&P 500 = Σ(RNOW,t–RNOW)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,091.71 ÷ (59 – 1)
= 18.82
체계적인 위험 추정 (β)
| 분산NOW | 73.33 |
| 분산S&P 500 | 19.11 |
| 공분산NOW, S&P 500 | 18.82 |
| 상관 계수NOW, S&P 5001 | 0.50 |
| βNOW2 | 0.99 |
| αNOW3 | -0.19% |
계산
1 상관 계수NOW, S&P 500
= 공분산NOW, S&P 500 ÷ (표준 편차NOW × 표준 편차S&P 500)
= 18.82 ÷ (8.56% × 4.37%)
= 0.50
2 βNOW
= 공분산NOW, S&P 500 ÷ 분산S&P 500
= 18.82 ÷ 19.11
= 0.99
3 αNOW
= 평균의NOW – βNOW × 평균의S&P 500
= 0.93% – 0.99 × 1.14%
= -0.19%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.95% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 17.36% |
| 보통주의 체계적 위험ServiceNow | βNOW | 0.99 |
| ServiceNow 보통주에 대한 예상 수익률3 | E(RNOW) | 17.17% |
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(RNOW) = RF + βNOW [E(RM) – RF]
= 4.95% + 0.99 [17.36% – 4.95%]
= 17.17%