자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Motorola Solutions의 보통주와 같은 위험 자산에 대한 기대 또는 필요한 수익률을 나타냅니다.
수익률
Motorola Solutions Inc., 월별 수익률
| Motorola Solutions Inc. (MSI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MSI,t1 | 피제수MSI,t1 | RMSI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $116.91 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $143.12 | 22.42% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $140.42 | $0.57 | -1.49% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $144.91 | 3.20% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | $322.87 | 15.95% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $313.09 | $0.98 | -2.73% | 4,769.83 | 4.42% |
| 평균의 (R): | 2.08% | 1.11% | ||||
| 표준 편차: | 7.42% | 5.31% | ||||
| Motorola Solutions Inc. (MSI) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값MSI,t1 | 피제수MSI,t1 | RMSI,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2019. 1. 31. | $116.91 | 2,704.10 | ||||
| 1. | 2019. 2. 28. | $143.12 | 22.42% | 2,784.49 | 2.97% | |
| 2. | 2019. 3. 31. | $140.42 | $0.57 | -1.49% | 2,834.40 | 1.79% |
| 3. | 2019. 4. 30. | $144.91 | 3.20% | 2,945.83 | 3.93% | |
| 4. | 2019. 5. 31. | $149.95 | 3.48% | 2,752.06 | -6.58% | |
| 5. | 2019. 6. 30. | $166.73 | $0.57 | 11.57% | 2,941.76 | 6.89% |
| 6. | 2019. 7. 31. | $165.96 | -0.46% | 2,980.38 | 1.31% | |
| 7. | 2019. 8. 31. | $180.91 | 9.01% | 2,926.46 | -1.81% | |
| 8. | 2019. 9. 30. | $170.41 | $0.57 | -5.49% | 2,976.74 | 1.72% |
| 9. | 2019. 10. 31. | $166.32 | -2.40% | 3,037.56 | 2.04% | |
| 10. | 2019. 11. 30. | $167.30 | 0.59% | 3,140.98 | 3.40% | |
| 11. | 2019. 12. 31. | $161.14 | $0.64 | -3.30% | 3,230.78 | 2.86% |
| 12. | 2020. 1. 31. | $177.00 | 9.84% | 3,225.52 | -0.16% | |
| 13. | 2020. 2. 29. | $165.68 | -6.40% | 2,954.22 | -8.41% | |
| 14. | 2020. 3. 31. | $132.92 | $0.64 | -19.39% | 2,584.59 | -12.51% |
| 15. | 2020. 4. 30. | $143.81 | 8.19% | 2,912.43 | 12.68% | |
| 16. | 2020. 5. 31. | $135.33 | -5.90% | 3,044.31 | 4.53% | |
| 17. | 2020. 6. 30. | $140.13 | $0.64 | 4.02% | 3,100.29 | 1.84% |
| 18. | 2020. 7. 31. | $139.80 | -0.24% | 3,271.12 | 5.51% | |
| 19. | 2020. 8. 31. | $154.75 | 10.69% | 3,500.31 | 7.01% | |
| 20. | 2020. 9. 30. | $156.81 | $0.64 | 1.74% | 3,363.00 | -3.92% |
| 21. | 2020. 10. 31. | $158.06 | 0.80% | 3,269.96 | -2.77% | |
| 22. | 2020. 11. 30. | $171.53 | 8.52% | 3,621.63 | 10.75% | |
| 23. | 2020. 12. 31. | $170.06 | $0.71 | -0.44% | 3,756.07 | 3.71% |
| 24. | 2021. 1. 31. | $167.55 | -1.48% | 3,714.24 | -1.11% | |
| 25. | 2021. 2. 28. | $175.48 | 4.73% | 3,811.15 | 2.61% | |
| 26. | 2021. 3. 31. | $188.05 | $0.71 | 7.57% | 3,972.89 | 4.24% |
| 27. | 2021. 4. 30. | $188.30 | 0.13% | 4,181.17 | 5.24% | |
| 28. | 2021. 5. 31. | $205.31 | 9.03% | 4,204.11 | 0.55% | |
| 29. | 2021. 6. 30. | $216.85 | $0.71 | 5.97% | 4,297.50 | 2.22% |
| 30. | 2021. 7. 31. | $223.92 | 3.26% | 4,395.26 | 2.27% | |
| 31. | 2021. 8. 31. | $244.22 | 9.07% | 4,522.68 | 2.90% | |
| 32. | 2021. 9. 30. | $232.32 | $0.71 | -4.58% | 4,307.54 | -4.76% |
| 33. | 2021. 10. 31. | $248.59 | 7.00% | 4,605.38 | 6.91% | |
| 34. | 2021. 11. 30. | $253.18 | 1.85% | 4,567.00 | -0.83% | |
| 35. | 2021. 12. 31. | $271.70 | $0.79 | 7.63% | 4,766.18 | 4.36% |
| 36. | 2022. 1. 31. | $231.94 | -14.63% | 4,515.55 | -5.26% | |
| 37. | 2022. 2. 28. | $220.43 | -4.96% | 4,373.94 | -3.14% | |
| 38. | 2022. 3. 31. | $242.20 | $0.79 | 10.23% | 4,530.41 | 3.58% |
| 39. | 2022. 4. 30. | $213.69 | -11.77% | 4,131.93 | -8.80% | |
| 40. | 2022. 5. 31. | $219.74 | 2.83% | 4,132.15 | 0.01% | |
| 41. | 2022. 6. 30. | $209.60 | $0.79 | -4.26% | 3,785.38 | -8.39% |
| 42. | 2022. 7. 31. | $238.59 | 13.83% | 4,130.29 | 9.11% | |
| 43. | 2022. 8. 31. | $243.41 | 2.02% | 3,955.00 | -4.24% | |
| 44. | 2022. 9. 30. | $223.97 | $0.79 | -7.66% | 3,585.62 | -9.34% |
| 45. | 2022. 10. 31. | $249.71 | 11.49% | 3,871.98 | 7.99% | |
| 46. | 2022. 11. 30. | $272.20 | 9.01% | 4,080.11 | 5.38% | |
| 47. | 2022. 12. 31. | $257.71 | $0.88 | -5.00% | 3,839.50 | -5.90% |
| 48. | 2023. 1. 31. | $257.01 | -0.27% | 4,076.60 | 6.18% | |
| 49. | 2023. 2. 28. | $262.81 | 2.26% | 3,970.15 | -2.61% | |
| 50. | 2023. 3. 31. | $286.13 | $0.88 | 9.21% | 4,109.31 | 3.51% |
| 51. | 2023. 4. 30. | $291.40 | 1.84% | 4,169.48 | 1.46% | |
| 52. | 2023. 5. 31. | $281.92 | -3.25% | 4,179.83 | 0.25% | |
| 53. | 2023. 6. 30. | $293.28 | $0.88 | 4.34% | 4,376.86 | 4.71% |
| 54. | 2023. 7. 31. | $286.63 | -2.27% | 4,588.96 | 4.85% | |
| 55. | 2023. 8. 31. | $283.57 | -1.07% | 4,507.66 | -1.77% | |
| 56. | 2023. 9. 30. | $272.24 | $0.88 | -3.69% | 4,288.05 | -4.87% |
| 57. | 2023. 10. 31. | $278.46 | 2.28% | 4,193.80 | -2.20% | |
| 58. | 2023. 11. 30. | $322.87 | 15.95% | 4,567.80 | 8.92% | |
| 59. | 2023. 12. 31. | $313.09 | $0.98 | -2.73% | 4,769.83 | 4.42% |
| 평균의 (R): | 2.08% | 1.11% | ||||
| 표준 편차: | 7.42% | 5.31% | ||||
모두 보기
1 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.
2 기간 t 동안 MSI의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.
분산과 공분산
Motorola Solutions Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RMSI,t | RS&P 500,t | (RMSI,t–RMSI)2 | (RS&P 500,t–RS&P 500)2 | (RMSI,t–RMSI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 22.42% | 2.97% | 413.82 | 3.49 | 37.98 |
| 2. | 2019. 3. 31. | -1.49% | 1.79% | 12.71 | 0.47 | -2.45 |
| 3. | 2019. 4. 30. | 3.20% | 3.93% | 1.26 | 7.98 | 3.17 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 2023. 11. 30. | 15.95% | 8.92% | 192.44 | 61.03 | 108.37 |
| 59. | 2023. 12. 31. | -2.73% | 4.42% | 23.06 | 11.00 | -15.93 |
| 합계 (Σ): | 3,191.39 | 1,634.30 | 1,502.06 | |||
| t | 날짜 | RMSI,t | RS&P 500,t | (RMSI,t–RMSI)2 | (RS&P 500,t–RS&P 500)2 | (RMSI,t–RMSI)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2019. 2. 28. | 22.42% | 2.97% | 413.82 | 3.49 | 37.98 |
| 2. | 2019. 3. 31. | -1.49% | 1.79% | 12.71 | 0.47 | -2.45 |
| 3. | 2019. 4. 30. | 3.20% | 3.93% | 1.26 | 7.98 | 3.17 |
| 4. | 2019. 5. 31. | 3.48% | -6.58% | 1.96 | 59.04 | -10.77 |
| 5. | 2019. 6. 30. | 11.57% | 6.89% | 90.14 | 33.49 | 54.94 |
| 6. | 2019. 7. 31. | -0.46% | 1.31% | 6.44 | 0.04 | -0.53 |
| 7. | 2019. 8. 31. | 9.01% | -1.81% | 48.05 | 8.50 | -20.21 |
| 8. | 2019. 9. 30. | -5.49% | 1.72% | 57.23 | 0.37 | -4.63 |
| 9. | 2019. 10. 31. | -2.40% | 2.04% | 20.04 | 0.88 | -4.20 |
| 10. | 2019. 11. 30. | 0.59% | 3.40% | 2.21 | 5.28 | -3.42 |
| 11. | 2019. 12. 31. | -3.30% | 2.86% | 28.90 | 3.07 | -9.42 |
| 12. | 2020. 1. 31. | 9.84% | -0.16% | 60.31 | 1.61 | -9.85 |
| 13. | 2020. 2. 29. | -6.40% | -8.41% | 71.77 | 90.57 | 80.62 |
| 14. | 2020. 3. 31. | -19.39% | -12.51% | 460.66 | 185.44 | 292.28 |
| 15. | 2020. 4. 30. | 8.19% | 12.68% | 37.41 | 134.06 | 70.82 |
| 16. | 2020. 5. 31. | -5.90% | 4.53% | 63.57 | 11.71 | -27.29 |
| 17. | 2020. 6. 30. | 4.02% | 1.84% | 3.78 | 0.54 | 1.42 |
| 18. | 2020. 7. 31. | -0.24% | 5.51% | 5.34 | 19.40 | -10.18 |
| 19. | 2020. 8. 31. | 10.69% | 7.01% | 74.26 | 34.82 | 50.85 |
| 20. | 2020. 9. 30. | 1.74% | -3.92% | 0.11 | 25.29 | 1.67 |
| 21. | 2020. 10. 31. | 0.80% | -2.77% | 1.64 | 15.00 | 4.95 |
| 22. | 2020. 11. 30. | 8.52% | 10.75% | 41.55 | 93.10 | 62.19 |
| 23. | 2020. 12. 31. | -0.44% | 3.71% | 6.35 | 6.79 | -6.57 |
| 24. | 2021. 1. 31. | -1.48% | -1.11% | 12.62 | 4.93 | 7.88 |
| 25. | 2021. 2. 28. | 4.73% | 2.61% | 7.06 | 2.26 | 3.99 |
| 26. | 2021. 3. 31. | 7.57% | 4.24% | 30.16 | 9.85 | 17.23 |
| 27. | 2021. 4. 30. | 0.13% | 5.24% | 3.78 | 17.11 | -8.04 |
| 28. | 2021. 5. 31. | 9.03% | 0.55% | 48.40 | 0.31 | -3.88 |
| 29. | 2021. 6. 30. | 5.97% | 2.22% | 15.13 | 1.24 | 4.34 |
| 30. | 2021. 7. 31. | 3.26% | 2.27% | 1.40 | 1.37 | 1.38 |
| 31. | 2021. 8. 31. | 9.07% | 2.90% | 48.85 | 3.22 | 12.53 |
| 32. | 2021. 9. 30. | -4.58% | -4.76% | 44.33 | 34.37 | 39.04 |
| 33. | 2021. 10. 31. | 7.00% | 6.91% | 24.28 | 33.74 | 28.62 |
| 34. | 2021. 11. 30. | 1.85% | -0.83% | 0.05 | 3.76 | 0.45 |
| 35. | 2021. 12. 31. | 7.63% | 4.36% | 30.81 | 10.60 | 18.07 |
| 36. | 2022. 1. 31. | -14.63% | -5.26% | 279.23 | 40.51 | 106.35 |
| 37. | 2022. 2. 28. | -4.96% | -3.14% | 49.54 | 17.99 | 29.86 |
| 38. | 2022. 3. 31. | 10.23% | 3.58% | 66.56 | 6.11 | 20.16 |
| 39. | 2022. 4. 30. | -11.77% | -8.80% | 191.75 | 98.04 | 137.11 |
| 40. | 2022. 5. 31. | 2.83% | 0.01% | 0.57 | 1.21 | -0.83 |
| 41. | 2022. 6. 30. | -4.26% | -8.39% | 40.09 | 90.21 | 60.13 |
| 42. | 2022. 7. 31. | 13.83% | 9.11% | 138.18 | 64.09 | 94.11 |
| 43. | 2022. 8. 31. | 2.02% | -4.24% | 0.00 | 28.62 | 0.30 |
| 44. | 2022. 9. 30. | -7.66% | -9.34% | 94.83 | 109.11 | 101.72 |
| 45. | 2022. 10. 31. | 11.49% | 7.99% | 88.67 | 47.34 | 64.79 |
| 46. | 2022. 11. 30. | 9.01% | 5.38% | 48.03 | 18.23 | 29.59 |
| 47. | 2022. 12. 31. | -5.00% | -5.90% | 50.07 | 49.04 | 49.56 |
| 48. | 2023. 1. 31. | -0.27% | 6.18% | 5.51 | 25.70 | -11.90 |
| 49. | 2023. 2. 28. | 2.26% | -2.61% | 0.03 | 13.82 | -0.67 |
| 50. | 2023. 3. 31. | 9.21% | 3.51% | 50.86 | 5.76 | 17.11 |
| 51. | 2023. 4. 30. | 1.84% | 1.46% | 0.05 | 0.13 | -0.08 |
| 52. | 2023. 5. 31. | -3.25% | 0.25% | 28.40 | 0.74 | 4.57 |
| 53. | 2023. 6. 30. | 4.34% | 4.71% | 5.13 | 13.02 | 8.17 |
| 54. | 2023. 7. 31. | -2.27% | 4.85% | 18.87 | 13.99 | -16.25 |
| 55. | 2023. 8. 31. | -1.07% | -1.77% | 9.88 | 8.28 | 9.05 |
| 56. | 2023. 9. 30. | -3.69% | -4.87% | 33.19 | 35.73 | 34.44 |
| 57. | 2023. 10. 31. | 2.28% | -2.20% | 0.04 | 10.92 | -0.69 |
| 58. | 2023. 11. 30. | 15.95% | 8.92% | 192.44 | 61.03 | 108.37 |
| 59. | 2023. 12. 31. | -2.73% | 4.42% | 23.06 | 11.00 | -15.93 |
| 합계 (Σ): | 3,191.39 | 1,634.30 | 1,502.06 | |||
모두 보기
분산MSI = Σ(RMSI,t–RMSI)2 ÷ (59 – 1)
= 3,191.39 ÷ (59 – 1)
= 55.02
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
공분산MSI, S&P 500 = Σ(RMSI,t–RMSI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,502.06 ÷ (59 – 1)
= 25.90
체계적인 위험 추정 (β)
| 분산MSI | 55.02 |
| 분산S&P 500 | 28.18 |
| 공분산MSI, S&P 500 | 25.90 |
| 상관 계수MSI, S&P 5001 | 0.66 |
| βMSI2 | 0.92 |
| αMSI3 | 1.06% |
계산
1 상관 계수MSI, S&P 500
= 공분산MSI, S&P 500 ÷ (표준 편차MSI × 표준 편차S&P 500)
= 25.90 ÷ (7.42% × 5.31%)
= 0.66
2 βMSI
= 공분산MSI, S&P 500 ÷ 분산S&P 500
= 25.90 ÷ 28.18
= 0.92
3 αMSI
= 평균의MSI – βMSI × 평균의S&P 500
= 2.08% – 0.92 × 1.11%
= 1.06%
기대 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.91% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 14.72% |
| 보통주의 체계적 위험Motorola Solutions | βMSI | 0.92 |
| Motorola Solutions 보통주에 대한 예상 수익률3 | E(RMSI) | 13.92% |
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(RMSI) = RF + βMSI [E(RM) – RF]
= 4.91% + 0.92 [14.72% – 4.91%]
= 13.92%