자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다 NXP.
수익률
NXP Semiconductors N.V., 월별 수익률
| NXP Semiconductors N.V. (NXPI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NXPI,t1 | 피제수NXPI,t1 | RNXPI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $97.85 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $102.81 | 5.07% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $103.50 | 0.67% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $105.75 | 2.17% | 2,384.20 | 0.91% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | $223.36 | 11.20% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $227.78 | $0.5625 | 2.23% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.93% | 1.36% | ||||
| 표준 편차: | 9.12% | 4.48% | ||||
| NXP Semiconductors N.V. (NXPI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값NXPI,t1 | 피제수NXPI,t1 | RNXPI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 1. 31. | $97.85 | 2,278.87 | ||||
| 1. | 2017. 2. 28. | $102.81 | 5.07% | 2,363.64 | 3.72% | |
| 2. | 2017. 3. 31. | $103.50 | 0.67% | 2,362.72 | -0.04% | |
| 3. | 2017. 4. 30. | $105.75 | 2.17% | 2,384.20 | 0.91% | |
| 4. | 2017. 5. 31. | $109.90 | 3.92% | 2,411.80 | 1.16% | |
| 5. | 2017. 6. 30. | $109.45 | -0.41% | 2,423.41 | 0.48% | |
| 6. | 2017. 7. 31. | $110.33 | 0.80% | 2,470.30 | 1.93% | |
| 7. | 2017. 8. 31. | $112.96 | 2.38% | 2,471.65 | 0.05% | |
| 8. | 2017. 9. 30. | $113.09 | 0.12% | 2,519.36 | 1.93% | |
| 9. | 2017. 10. 31. | $117.05 | 3.50% | 2,575.26 | 2.22% | |
| 10. | 2017. 11. 30. | $113.39 | -3.13% | 2,647.58 | 2.81% | |
| 11. | 2017. 12. 31. | $117.09 | 3.26% | 2,673.61 | 0.98% | |
| 12. | 2018. 1. 31. | $120.32 | 2.76% | 2,823.81 | 5.62% | |
| 13. | 2018. 2. 28. | $124.66 | 3.61% | 2,713.83 | -3.89% | |
| 14. | 2018. 3. 31. | $117.00 | -6.14% | 2,640.87 | -2.69% | |
| 15. | 2018. 4. 30. | $104.90 | -10.34% | 2,648.05 | 0.27% | |
| 16. | 2018. 5. 31. | $114.00 | 8.67% | 2,705.27 | 2.16% | |
| 17. | 2018. 6. 30. | $109.27 | -4.15% | 2,718.37 | 0.48% | |
| 18. | 2018. 7. 31. | $95.34 | -12.75% | 2,816.29 | 3.60% | |
| 19. | 2018. 8. 31. | $93.14 | -2.31% | 2,901.52 | 3.03% | |
| 20. | 2018. 9. 30. | $85.50 | $0.25 | -7.93% | 2,913.98 | 0.43% |
| 21. | 2018. 10. 31. | $74.99 | -12.29% | 2,711.74 | -6.94% | |
| 22. | 2018. 11. 30. | $83.37 | 11.17% | 2,760.17 | 1.79% | |
| 23. | 2018. 12. 31. | $73.28 | $0.25 | -11.80% | 2,506.85 | -9.18% |
| 24. | 2019. 1. 31. | $87.03 | 18.76% | 2,704.10 | 7.87% | |
| 25. | 2019. 2. 28. | $91.32 | 4.93% | 2,784.49 | 2.97% | |
| 26. | 2019. 3. 31. | $88.39 | $0.25 | -2.93% | 2,834.40 | 1.79% |
| 27. | 2019. 4. 30. | $105.62 | 19.49% | 2,945.83 | 3.93% | |
| 28. | 2019. 5. 31. | $88.16 | -16.53% | 2,752.06 | -6.58% | |
| 29. | 2019. 6. 30. | $97.61 | $0.25 | 11.00% | 2,941.76 | 6.89% |
| 30. | 2019. 7. 31. | $103.39 | 5.92% | 2,980.38 | 1.31% | |
| 31. | 2019. 8. 31. | $102.14 | -1.21% | 2,926.46 | -1.81% | |
| 32. | 2019. 9. 30. | $109.12 | $0.375 | 7.20% | 2,976.74 | 1.72% |
| 33. | 2019. 10. 31. | $113.68 | 4.18% | 3,037.56 | 2.04% | |
| 34. | 2019. 11. 30. | $115.58 | 1.67% | 3,140.98 | 3.40% | |
| 35. | 2019. 12. 31. | $127.26 | $0.375 | 10.43% | 3,230.78 | 2.86% |
| 36. | 2020. 1. 31. | $126.86 | -0.31% | 3,225.52 | -0.16% | |
| 37. | 2020. 2. 29. | $113.69 | -10.38% | 2,954.22 | -8.41% | |
| 38. | 2020. 3. 31. | $82.93 | $0.375 | -26.73% | 2,584.59 | -12.51% |
| 39. | 2020. 4. 30. | $99.57 | 20.07% | 2,912.43 | 12.68% | |
| 40. | 2020. 5. 31. | $96.10 | -3.48% | 3,044.31 | 4.53% | |
| 41. | 2020. 6. 30. | $114.04 | $0.375 | 19.06% | 3,100.29 | 1.84% |
| 42. | 2020. 7. 31. | $117.53 | 3.06% | 3,271.12 | 5.51% | |
| 43. | 2020. 8. 31. | $125.76 | 7.00% | 3,500.31 | 7.01% | |
| 44. | 2020. 9. 30. | $124.81 | $0.375 | -0.46% | 3,363.00 | -3.92% |
| 45. | 2020. 10. 31. | $135.12 | 8.26% | 3,269.96 | -2.77% | |
| 46. | 2020. 11. 30. | $158.42 | 17.24% | 3,621.63 | 10.75% | |
| 47. | 2020. 12. 31. | $159.01 | $0.375 | 0.61% | 3,756.07 | 3.71% |
| 48. | 2021. 1. 31. | $160.47 | 0.92% | 3,714.24 | -1.11% | |
| 49. | 2021. 2. 28. | $182.55 | 13.76% | 3,811.15 | 2.61% | |
| 50. | 2021. 3. 31. | $201.34 | $0.5625 | 10.60% | 3,972.89 | 4.24% |
| 51. | 2021. 4. 30. | $192.51 | -4.39% | 4,181.17 | 5.24% | |
| 52. | 2021. 5. 31. | $211.42 | 9.82% | 4,204.11 | 0.55% | |
| 53. | 2021. 6. 30. | $205.72 | $0.5625 | -2.43% | 4,297.50 | 2.22% |
| 54. | 2021. 7. 31. | $206.39 | 0.33% | 4,395.26 | 2.27% | |
| 55. | 2021. 8. 31. | $215.13 | 4.23% | 4,522.68 | 2.90% | |
| 56. | 2021. 9. 30. | $195.87 | $0.5625 | -8.69% | 4,307.54 | -4.76% |
| 57. | 2021. 10. 31. | $200.86 | 2.55% | 4,605.38 | 6.91% | |
| 58. | 2021. 11. 30. | $223.36 | 11.20% | 4,567.00 | -0.83% | |
| 59. | 2021. 12. 31. | $227.78 | $0.5625 | 2.23% | 4,766.18 | 4.36% |
| 평균의 (R): | 1.93% | 1.36% | ||||
| 표준 편차: | 9.12% | 4.48% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 NXPI의 보통주에 대한 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
NXP Semiconductors N.V., 수익률의 분산 및 공분산 계산
| t | 날짜 | RNXPI,t | RS&P 500,t | (RNXPI,t–RNXPI)2 | (RS&P 500,t–RS&P 500)2 | (RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 5.07% | 3.72% | 9.86 | 5.58 | 7.41 |
| 2. | 2017. 3. 31. | 0.67% | -0.04% | 1.58 | 1.95 | 1.76 |
| 3. | 2017. 4. 30. | 2.17% | 0.91% | 0.06 | 0.20 | -0.11 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2021. 11. 30. | 11.20% | -0.83% | 85.97 | 4.80 | -20.32 |
| 59. | 2021. 12. 31. | 2.23% | 4.36% | 0.09 | 9.02 | 0.90 |
| 합계 (Σ): | 4,825.79 | 1,164.17 | 1,605.82 | |||
| t | 날짜 | RNXPI,t | RS&P 500,t | (RNXPI,t–RNXPI)2 | (RS&P 500,t–RS&P 500)2 | (RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 2. 28. | 5.07% | 3.72% | 9.86 | 5.58 | 7.41 |
| 2. | 2017. 3. 31. | 0.67% | -0.04% | 1.58 | 1.95 | 1.76 |
| 3. | 2017. 4. 30. | 2.17% | 0.91% | 0.06 | 0.20 | -0.11 |
| 4. | 2017. 5. 31. | 3.92% | 1.16% | 3.98 | 0.04 | -0.40 |
| 5. | 2017. 6. 30. | -0.41% | 0.48% | 5.47 | 0.77 | 2.05 |
| 6. | 2017. 7. 31. | 0.80% | 1.93% | 1.27 | 0.33 | -0.65 |
| 7. | 2017. 8. 31. | 2.38% | 0.05% | 0.21 | 1.70 | -0.59 |
| 8. | 2017. 9. 30. | 0.12% | 1.93% | 3.29 | 0.33 | -1.04 |
| 9. | 2017. 10. 31. | 3.50% | 2.22% | 2.47 | 0.74 | 1.35 |
| 10. | 2017. 11. 30. | -3.13% | 2.81% | 25.57 | 2.10 | -7.33 |
| 11. | 2017. 12. 31. | 3.26% | 0.98% | 1.78 | 0.14 | -0.50 |
| 12. | 2018. 1. 31. | 2.76% | 5.62% | 0.69 | 18.15 | 3.53 |
| 13. | 2018. 2. 28. | 3.61% | -3.89% | 2.81 | 27.59 | -8.81 |
| 14. | 2018. 3. 31. | -6.14% | -2.69% | 65.20 | 16.37 | 32.67 |
| 15. | 2018. 4. 30. | -10.34% | 0.27% | 150.59 | 1.18 | 13.33 |
| 16. | 2018. 5. 31. | 8.67% | 2.16% | 45.50 | 0.64 | 5.42 |
| 17. | 2018. 6. 30. | -4.15% | 0.48% | 36.95 | 0.76 | 5.31 |
| 18. | 2018. 7. 31. | -12.75% | 3.60% | 215.44 | 5.04 | -32.94 |
| 19. | 2018. 8. 31. | -2.31% | 3.03% | 17.95 | 2.78 | -7.07 |
| 20. | 2018. 9. 30. | -7.93% | 0.43% | 97.30 | 0.86 | 9.16 |
| 21. | 2018. 10. 31. | -12.29% | -6.94% | 202.27 | 68.86 | 118.02 |
| 22. | 2018. 11. 30. | 11.17% | 1.79% | 85.47 | 0.18 | 3.96 |
| 23. | 2018. 12. 31. | -11.80% | -9.18% | 188.58 | 111.00 | 144.68 |
| 24. | 2019. 1. 31. | 18.76% | 7.87% | 283.38 | 42.39 | 109.60 |
| 25. | 2019. 2. 28. | 4.93% | 2.97% | 9.00 | 2.61 | 4.84 |
| 26. | 2019. 3. 31. | -2.93% | 1.79% | 23.66 | 0.19 | -2.11 |
| 27. | 2019. 4. 30. | 19.49% | 3.93% | 308.48 | 6.62 | 45.20 |
| 28. | 2019. 5. 31. | -16.53% | -6.58% | 340.80 | 62.97 | 146.50 |
| 29. | 2019. 6. 30. | 11.00% | 6.89% | 82.32 | 30.64 | 50.22 |
| 30. | 2019. 7. 31. | 5.92% | 1.31% | 15.93 | 0.00 | -0.18 |
| 31. | 2019. 8. 31. | -1.21% | -1.81% | 9.85 | 10.03 | 9.94 |
| 32. | 2019. 9. 30. | 7.20% | 1.72% | 27.79 | 0.13 | 1.90 |
| 33. | 2019. 10. 31. | 4.18% | 2.04% | 5.06 | 0.47 | 1.54 |
| 34. | 2019. 11. 30. | 1.67% | 3.40% | 0.07 | 4.19 | -0.53 |
| 35. | 2019. 12. 31. | 10.43% | 2.86% | 72.26 | 2.25 | 12.76 |
| 36. | 2020. 1. 31. | -0.31% | -0.16% | 5.04 | 2.31 | 3.41 |
| 37. | 2020. 2. 29. | -10.38% | -8.41% | 151.57 | 95.43 | 120.27 |
| 38. | 2020. 3. 31. | -26.73% | -12.51% | 821.16 | 192.37 | 397.45 |
| 39. | 2020. 4. 30. | 20.07% | 12.68% | 328.89 | 128.29 | 205.41 |
| 40. | 2020. 5. 31. | -3.48% | 4.53% | 29.32 | 10.05 | -17.17 |
| 41. | 2020. 6. 30. | 19.06% | 1.84% | 293.39 | 0.23 | 8.24 |
| 42. | 2020. 7. 31. | 3.06% | 5.51% | 1.28 | 17.24 | 4.69 |
| 43. | 2020. 8. 31. | 7.00% | 7.01% | 25.73 | 31.91 | 28.65 |
| 44. | 2020. 9. 30. | -0.46% | -3.92% | 5.70 | 27.89 | 12.60 |
| 45. | 2020. 10. 31. | 8.26% | -2.77% | 40.08 | 17.01 | -26.11 |
| 46. | 2020. 11. 30. | 17.24% | 10.75% | 234.53 | 88.30 | 143.90 |
| 47. | 2020. 12. 31. | 0.61% | 3.71% | 1.74 | 5.54 | -3.11 |
| 48. | 2021. 1. 31. | 0.92% | -1.11% | 1.02 | 6.11 | 2.50 |
| 49. | 2021. 2. 28. | 13.76% | 2.61% | 139.95 | 1.57 | 14.80 |
| 50. | 2021. 3. 31. | 10.60% | 4.24% | 75.20 | 8.33 | 25.03 |
| 51. | 2021. 4. 30. | -4.39% | 5.24% | 39.88 | 15.09 | -24.53 |
| 52. | 2021. 5. 31. | 9.82% | 0.55% | 62.30 | 0.65 | -6.39 |
| 53. | 2021. 6. 30. | -2.43% | 2.22% | 19.01 | 0.75 | -3.76 |
| 54. | 2021. 7. 31. | 0.33% | 2.27% | 2.57 | 0.84 | -1.47 |
| 55. | 2021. 8. 31. | 4.23% | 2.90% | 5.31 | 2.38 | 3.55 |
| 56. | 2021. 9. 30. | -8.69% | -4.76% | 112.80 | 37.39 | 64.95 |
| 57. | 2021. 10. 31. | 2.55% | 6.91% | 0.38 | 30.87 | 3.43 |
| 58. | 2021. 11. 30. | 11.20% | -0.83% | 85.97 | 4.80 | -20.32 |
| 59. | 2021. 12. 31. | 2.23% | 4.36% | 0.09 | 9.02 | 0.90 |
| 합계 (Σ): | 4,825.79 | 1,164.17 | 1,605.82 | |||
모두 표시
분산NXPI = Σ(RNXPI,t–RNXPI)2 ÷ (59 – 1)
= 4,825.79 ÷ (59 – 1)
= 83.20
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07
공분산NXPI, S&P 500 = Σ(RNXPI,t–RNXPI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,605.82 ÷ (59 – 1)
= 27.69
체계적인 위험 추정 (β)
| 분산NXPI | 83.20 |
| 분산S&P 500 | 20.07 |
| 공분산NXPI, S&P 500 | 27.69 |
| 상관 계수NXPI, S&P 5001 | 0.68 |
| βNXPI2 | 1.38 |
| αNXPI3 | 0.06% |
계산
1 상관 계수NXPI, S&P 500
= 공분산NXPI, S&P 500 ÷ (표준 편차NXPI × 표준 편차S&P 500)
= 27.69 ÷ (9.12% × 4.48%)
= 0.68
2 βNXPI
= 공분산NXPI, S&P 500 ÷ 분산S&P 500
= 27.69 ÷ 20.07
= 1.38
3 αNXPI
= 평균의NXPI – βNXPI × 평균의S&P 500
= 1.93% – 1.38 × 1.36%
= 0.06%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.86% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.54% |
| 보통주 NXP 의 체계적인 리스크 | βNXPI | 1.38 |
| NXP 보통주에 대한 예상 수익률3 | E(RNXPI) | 16.83% |
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(RNXPI) = RF + βNXPI [E(RM) – RF]
= 4.86% + 1.38 [13.54% – 4.86%]
= 16.83%