자본 자산 가격 책정 모델 (CAPM)
자본 자산 가격 책정 모델(CAPM)은 Synopsys보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.
수익률
Synopsys Inc., 월별 수익률
| Synopsys Inc. (SNPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SNPS,t1 | 피제수SNPS,t1 | RSNPS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 11. 30. | $90.38 | 2,647.58 | ||||
| 1. | 2017. 12. 31. | $85.24 | -5.69% | 2,673.61 | 0.98% | |
| 2. | 2018. 1. 31. | $92.61 | 8.65% | 2,823.81 | 5.62% | |
| 3. | 2018. 2. 28. | $84.67 | -8.57% | 2,713.83 | -3.89% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 9. 30. | $458.97 | 0.02% | 4,288.05 | -4.87% | |
| 71. | 2023. 10. 31. | $469.44 | 2.28% | 4,193.80 | -2.20% | |
| 평균의 (R): | 2.68% | 0.78% | ||||
| 표준 편차: | 8.38% | 5.13% | ||||
| Synopsys Inc. (SNPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | 날짜 | 값SNPS,t1 | 피제수SNPS,t1 | RSNPS,t2 | 값S&P 500,t | RS&P 500,t3 |
| 2017. 11. 30. | $90.38 | 2,647.58 | ||||
| 1. | 2017. 12. 31. | $85.24 | -5.69% | 2,673.61 | 0.98% | |
| 2. | 2018. 1. 31. | $92.61 | 8.65% | 2,823.81 | 5.62% | |
| 3. | 2018. 2. 28. | $84.67 | -8.57% | 2,713.83 | -3.89% | |
| 4. | 2018. 3. 31. | $83.24 | -1.69% | 2,640.87 | -2.69% | |
| 5. | 2018. 4. 30. | $85.51 | 2.73% | 2,648.05 | 0.27% | |
| 6. | 2018. 5. 31. | $88.07 | 2.99% | 2,705.27 | 2.16% | |
| 7. | 2018. 6. 30. | $85.57 | -2.84% | 2,718.37 | 0.48% | |
| 8. | 2018. 7. 31. | $89.43 | 4.51% | 2,816.29 | 3.60% | |
| 9. | 2018. 8. 31. | $102.14 | 14.21% | 2,901.52 | 3.03% | |
| 10. | 2018. 9. 30. | $98.61 | -3.46% | 2,913.98 | 0.43% | |
| 11. | 2018. 10. 31. | $89.53 | -9.21% | 2,711.74 | -6.94% | |
| 12. | 2018. 11. 30. | $91.94 | 2.69% | 2,760.17 | 1.79% | |
| 13. | 2018. 12. 31. | $84.24 | -8.38% | 2,506.85 | -9.18% | |
| 14. | 2019. 1. 31. | $93.35 | 10.81% | 2,704.10 | 7.87% | |
| 15. | 2019. 2. 28. | $101.68 | 8.92% | 2,784.49 | 2.97% | |
| 16. | 2019. 3. 31. | $115.15 | 13.25% | 2,834.40 | 1.79% | |
| 17. | 2019. 4. 30. | $121.08 | 5.15% | 2,945.83 | 3.93% | |
| 18. | 2019. 5. 31. | $116.44 | -3.83% | 2,752.06 | -6.58% | |
| 19. | 2019. 6. 30. | $128.69 | 10.52% | 2,941.76 | 6.89% | |
| 20. | 2019. 7. 31. | $132.76 | 3.16% | 2,980.38 | 1.31% | |
| 21. | 2019. 8. 31. | $141.81 | 6.82% | 2,926.46 | -1.81% | |
| 22. | 2019. 9. 30. | $137.25 | -3.22% | 2,976.74 | 1.72% | |
| 23. | 2019. 10. 31. | $135.75 | -1.09% | 3,037.56 | 2.04% | |
| 24. | 2019. 11. 30. | $141.04 | 3.90% | 3,140.98 | 3.40% | |
| 25. | 2019. 12. 31. | $139.20 | -1.30% | 3,230.78 | 2.86% | |
| 26. | 2020. 1. 31. | $147.51 | 5.97% | 3,225.52 | -0.16% | |
| 27. | 2020. 2. 29. | $137.93 | -6.49% | 2,954.22 | -8.41% | |
| 28. | 2020. 3. 31. | $128.79 | -6.63% | 2,584.59 | -12.51% | |
| 29. | 2020. 4. 30. | $157.12 | 22.00% | 2,912.43 | 12.68% | |
| 30. | 2020. 5. 31. | $180.91 | 15.14% | 3,044.31 | 4.53% | |
| 31. | 2020. 6. 30. | $195.00 | 7.79% | 3,100.29 | 1.84% | |
| 32. | 2020. 7. 31. | $199.22 | 2.16% | 3,271.12 | 5.51% | |
| 33. | 2020. 8. 31. | $221.30 | 11.08% | 3,500.31 | 7.01% | |
| 34. | 2020. 9. 30. | $213.98 | -3.31% | 3,363.00 | -3.92% | |
| 35. | 2020. 10. 31. | $213.86 | -0.06% | 3,269.96 | -2.77% | |
| 36. | 2020. 11. 30. | $227.50 | 6.38% | 3,621.63 | 10.75% | |
| 37. | 2020. 12. 31. | $259.24 | 13.95% | 3,756.07 | 3.71% | |
| 38. | 2021. 1. 31. | $255.45 | -1.46% | 3,714.24 | -1.11% | |
| 39. | 2021. 2. 28. | $245.21 | -4.01% | 3,811.15 | 2.61% | |
| 40. | 2021. 3. 31. | $247.78 | 1.05% | 3,972.89 | 4.24% | |
| 41. | 2021. 4. 30. | $247.06 | -0.29% | 4,181.17 | 5.24% | |
| 42. | 2021. 5. 31. | $254.34 | 2.95% | 4,204.11 | 0.55% | |
| 43. | 2021. 6. 30. | $275.79 | 8.43% | 4,297.50 | 2.22% | |
| 44. | 2021. 7. 31. | $287.99 | 4.42% | 4,395.26 | 2.27% | |
| 45. | 2021. 8. 31. | $332.24 | 15.37% | 4,522.68 | 2.90% | |
| 46. | 2021. 9. 30. | $299.41 | -9.88% | 4,307.54 | -4.76% | |
| 47. | 2021. 10. 31. | $333.18 | 11.28% | 4,605.38 | 6.91% | |
| 48. | 2021. 11. 30. | $341.00 | 2.35% | 4,567.00 | -0.83% | |
| 49. | 2021. 12. 31. | $368.50 | 8.06% | 4,766.18 | 4.36% | |
| 50. | 2022. 1. 31. | $310.50 | -15.74% | 4,515.55 | -5.26% | |
| 51. | 2022. 2. 28. | $312.39 | 0.61% | 4,373.94 | -3.14% | |
| 52. | 2022. 3. 31. | $333.27 | 6.68% | 4,530.41 | 3.58% | |
| 53. | 2022. 4. 30. | $286.79 | -13.95% | 4,131.93 | -8.80% | |
| 54. | 2022. 5. 31. | $319.20 | 11.30% | 4,132.15 | 0.01% | |
| 55. | 2022. 6. 30. | $303.70 | -4.86% | 3,785.38 | -8.39% | |
| 56. | 2022. 7. 31. | $367.50 | 21.01% | 4,130.29 | 9.11% | |
| 57. | 2022. 8. 31. | $346.02 | -5.84% | 3,955.00 | -4.24% | |
| 58. | 2022. 9. 30. | $305.51 | -11.71% | 3,585.62 | -9.34% | |
| 59. | 2022. 10. 31. | $292.55 | -4.24% | 3,871.98 | 7.99% | |
| 60. | 2022. 11. 30. | $339.54 | 16.06% | 4,080.11 | 5.38% | |
| 61. | 2022. 12. 31. | $319.29 | -5.96% | 3,839.50 | -5.90% | |
| 62. | 2023. 1. 31. | $353.75 | 10.79% | 4,076.60 | 6.18% | |
| 63. | 2023. 2. 28. | $363.76 | 2.83% | 3,970.15 | -2.61% | |
| 64. | 2023. 3. 31. | $386.25 | 6.18% | 4,109.31 | 3.51% | |
| 65. | 2023. 4. 30. | $371.32 | -3.87% | 4,169.48 | 1.46% | |
| 66. | 2023. 5. 31. | $454.96 | 22.53% | 4,179.83 | 0.25% | |
| 67. | 2023. 6. 30. | $435.41 | -4.30% | 4,376.86 | 4.71% | |
| 68. | 2023. 7. 31. | $451.80 | 3.76% | 4,588.96 | 4.85% | |
| 69. | 2023. 8. 31. | $458.89 | 1.57% | 4,507.66 | -1.77% | |
| 70. | 2023. 9. 30. | $458.97 | 0.02% | 4,288.05 | -4.87% | |
| 71. | 2023. 10. 31. | $469.44 | 2.28% | 4,193.80 | -2.20% | |
| 평균의 (R): | 2.68% | 0.78% | ||||
| 표준 편차: | 8.38% | 5.13% | ||||
모두 표시
1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.
2 기간 t 동안 SNPS의 보통주 수익률.
3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.
분산과 공분산
Synopsys Inc., 수익률의 분산 및 공분산 계산
| t | 날짜 | RSNPS,t | RS&P 500,t | (RSNPS,t–RSNPS)2 | (RS&P 500,t–RS&P 500)2 | (RSNPS,t–RSNPS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 12. 31. | -5.69% | 0.98% | 70.05 | 0.04 | -1.69 |
| 2. | 2018. 1. 31. | 8.65% | 5.62% | 35.57 | 23.40 | 28.85 |
| 3. | 2018. 2. 28. | -8.57% | -3.89% | 126.70 | 21.86 | 52.63 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 2023. 9. 30. | 0.02% | -4.87% | 7.10 | 31.95 | 15.06 |
| 71. | 2023. 10. 31. | 2.28% | -2.20% | 0.16 | 8.87 | 1.20 |
| 합계 (Σ): | 4,909.89 | 1,843.80 | 2,089.57 | |||
| t | 날짜 | RSNPS,t | RS&P 500,t | (RSNPS,t–RSNPS)2 | (RS&P 500,t–RS&P 500)2 | (RSNPS,t–RSNPS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 2017. 12. 31. | -5.69% | 0.98% | 70.05 | 0.04 | -1.69 |
| 2. | 2018. 1. 31. | 8.65% | 5.62% | 35.57 | 23.40 | 28.85 |
| 3. | 2018. 2. 28. | -8.57% | -3.89% | 126.70 | 21.86 | 52.63 |
| 4. | 2018. 3. 31. | -1.69% | -2.69% | 19.11 | 12.04 | 15.17 |
| 5. | 2018. 4. 30. | 2.73% | 0.27% | 0.00 | 0.26 | -0.02 |
| 6. | 2018. 5. 31. | 2.99% | 2.16% | 0.10 | 1.90 | 0.43 |
| 7. | 2018. 6. 30. | -2.84% | 0.48% | 30.48 | 0.09 | 1.64 |
| 8. | 2018. 7. 31. | 4.51% | 3.60% | 3.34 | 7.96 | 5.16 |
| 9. | 2018. 8. 31. | 14.21% | 3.03% | 132.93 | 5.04 | 25.89 |
| 10. | 2018. 9. 30. | -3.46% | 0.43% | 37.68 | 0.12 | 2.16 |
| 11. | 2018. 10. 31. | -9.21% | -6.94% | 141.38 | 59.62 | 91.81 |
| 12. | 2018. 11. 30. | 2.69% | 1.79% | 0.00 | 1.01 | 0.01 |
| 13. | 2018. 12. 31. | -8.38% | -9.18% | 122.27 | 99.17 | 110.12 |
| 14. | 2019. 1. 31. | 10.81% | 7.87% | 66.13 | 50.24 | 57.64 |
| 15. | 2019. 2. 28. | 8.92% | 2.97% | 38.95 | 4.81 | 13.68 |
| 16. | 2019. 3. 31. | 13.25% | 1.79% | 111.62 | 1.02 | 10.69 |
| 17. | 2019. 4. 30. | 5.15% | 3.93% | 6.09 | 9.93 | 7.77 |
| 18. | 2019. 5. 31. | -3.83% | -6.58% | 42.44 | 54.15 | 47.94 |
| 19. | 2019. 6. 30. | 10.52% | 6.89% | 61.43 | 37.36 | 47.91 |
| 20. | 2019. 7. 31. | 3.16% | 1.31% | 0.23 | 0.28 | 0.26 |
| 21. | 2019. 8. 31. | 6.82% | -1.81% | 17.09 | 6.71 | -10.71 |
| 22. | 2019. 9. 30. | -3.22% | 1.72% | 34.79 | 0.88 | -5.53 |
| 23. | 2019. 10. 31. | -1.09% | 2.04% | 14.25 | 1.59 | -4.77 |
| 24. | 2019. 11. 30. | 3.90% | 3.40% | 1.47 | 6.89 | 3.19 |
| 25. | 2019. 12. 31. | -1.30% | 2.86% | 15.90 | 4.32 | -8.29 |
| 26. | 2020. 1. 31. | 5.97% | -0.16% | 10.81 | 0.89 | -3.10 |
| 27. | 2020. 2. 29. | -6.49% | -8.41% | 84.22 | 84.49 | 84.35 |
| 28. | 2020. 3. 31. | -6.63% | -12.51% | 86.66 | 176.70 | 123.74 |
| 29. | 2020. 4. 30. | 22.00% | 12.68% | 373.05 | 141.70 | 229.91 |
| 30. | 2020. 5. 31. | 15.14% | 4.53% | 155.22 | 14.04 | 46.69 |
| 31. | 2020. 6. 30. | 7.79% | 1.84% | 26.07 | 1.12 | 5.40 |
| 32. | 2020. 7. 31. | 2.16% | 5.51% | 0.27 | 22.37 | -2.45 |
| 33. | 2020. 8. 31. | 11.08% | 7.01% | 70.57 | 38.76 | 52.30 |
| 34. | 2020. 9. 30. | -3.31% | -3.92% | 35.88 | 22.12 | 28.18 |
| 35. | 2020. 10. 31. | -0.06% | -2.77% | 7.50 | 12.58 | 9.71 |
| 36. | 2020. 11. 30. | 6.38% | 10.75% | 13.66 | 99.48 | 36.86 |
| 37. | 2020. 12. 31. | 13.95% | 3.71% | 126.99 | 8.59 | 33.03 |
| 38. | 2021. 1. 31. | -1.46% | -1.11% | 17.18 | 3.59 | 7.85 |
| 39. | 2021. 2. 28. | -4.01% | 2.61% | 44.77 | 3.34 | -12.23 |
| 40. | 2021. 3. 31. | 1.05% | 4.24% | 2.67 | 11.99 | -5.66 |
| 41. | 2021. 4. 30. | -0.29% | 5.24% | 8.84 | 19.91 | -13.27 |
| 42. | 2021. 5. 31. | 2.95% | 0.55% | 0.07 | 0.05 | -0.06 |
| 43. | 2021. 6. 30. | 8.43% | 2.22% | 33.08 | 2.08 | 8.29 |
| 44. | 2021. 7. 31. | 4.42% | 2.27% | 3.03 | 2.23 | 2.60 |
| 45. | 2021. 8. 31. | 15.37% | 2.90% | 160.85 | 4.49 | 26.87 |
| 46. | 2021. 9. 30. | -9.88% | -4.76% | 157.85 | 30.67 | 69.57 |
| 47. | 2021. 10. 31. | 11.28% | 6.91% | 73.90 | 37.62 | 52.73 |
| 48. | 2021. 11. 30. | 2.35% | -0.83% | 0.11 | 2.61 | 0.54 |
| 49. | 2021. 12. 31. | 8.06% | 4.36% | 28.97 | 12.82 | 19.27 |
| 50. | 2022. 1. 31. | -15.74% | -5.26% | 339.37 | 36.47 | 111.26 |
| 51. | 2022. 2. 28. | 0.61% | -3.14% | 4.30 | 15.34 | 8.12 |
| 52. | 2022. 3. 31. | 6.68% | 3.58% | 16.01 | 7.82 | 11.19 |
| 53. | 2022. 4. 30. | -13.95% | -8.80% | 276.53 | 91.71 | 159.25 |
| 54. | 2022. 5. 31. | 11.30% | 0.01% | 74.28 | 0.60 | -6.68 |
| 55. | 2022. 6. 30. | -4.86% | -8.39% | 56.83 | 84.14 | 69.15 |
| 56. | 2022. 7. 31. | 21.01% | 9.11% | 335.81 | 69.40 | 152.66 |
| 57. | 2022. 8. 31. | -5.84% | -4.24% | 72.72 | 25.25 | 42.85 |
| 58. | 2022. 9. 30. | -11.71% | -9.34% | 207.07 | 102.42 | 145.63 |
| 59. | 2022. 10. 31. | -4.24% | 7.99% | 47.95 | 51.92 | -49.90 |
| 60. | 2022. 11. 30. | 16.06% | 5.38% | 179.02 | 21.11 | 61.47 |
| 61. | 2022. 12. 31. | -5.96% | -5.90% | 74.76 | 44.59 | 57.74 |
| 62. | 2023. 1. 31. | 10.79% | 6.18% | 65.78 | 29.10 | 43.75 |
| 63. | 2023. 2. 28. | 2.83% | -2.61% | 0.02 | 11.51 | -0.50 |
| 64. | 2023. 3. 31. | 6.18% | 3.51% | 12.25 | 7.42 | 9.54 |
| 65. | 2023. 4. 30. | -3.87% | 1.46% | 42.87 | 0.47 | -4.48 |
| 66. | 2023. 5. 31. | 22.53% | 0.25% | 393.73 | 0.28 | -10.57 |
| 67. | 2023. 6. 30. | -4.30% | 4.71% | 48.71 | 15.47 | -27.45 |
| 68. | 2023. 7. 31. | 3.76% | 4.85% | 1.17 | 16.53 | 4.40 |
| 69. | 2023. 8. 31. | 1.57% | -1.77% | 1.24 | 6.51 | 2.84 |
| 70. | 2023. 9. 30. | 0.02% | -4.87% | 7.10 | 31.95 | 15.06 |
| 71. | 2023. 10. 31. | 2.28% | -2.20% | 0.16 | 8.87 | 1.20 |
| 합계 (Σ): | 4,909.89 | 1,843.80 | 2,089.57 | |||
모두 표시
분산SNPS = Σ(RSNPS,t–RSNPS)2 ÷ (71 – 1)
= 4,909.89 ÷ (71 – 1)
= 70.14
분산S&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,843.80 ÷ (71 – 1)
= 26.34
공분산SNPS, S&P 500 = Σ(RSNPS,t–RSNPS)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,089.57 ÷ (71 – 1)
= 29.85
체계적인 위험 추정 (β)
| 분산SNPS | 70.14 |
| 분산S&P 500 | 26.34 |
| 공분산SNPS, S&P 500 | 29.85 |
| 상관 계수SNPS, S&P 5001 | 0.69 |
| βSNPS2 | 1.13 |
| αSNPS3 | 1.80% |
계산
1 상관 계수SNPS, S&P 500
= 공분산SNPS, S&P 500 ÷ (표준 편차SNPS × 표준 편차S&P 500)
= 29.85 ÷ (8.38% × 5.13%)
= 0.69
2 βSNPS
= 공분산SNPS, S&P 500 ÷ 분산S&P 500
= 29.85 ÷ 26.34
= 1.13
3 αSNPS
= 평균의SNPS – βSNPS × 평균의S&P 500
= 2.68% – 1.13 × 0.78%
= 1.80%
예상 수익률
| 가정 | ||
| LT Treasury Composite의 수익률1 | RF | 4.56% |
| 시장 포트폴리오에 대한 예상 수익률2 | E(RM) | 13.77% |
| 보통주의 체계적 위험Synopsys | βSNPS | 1.13 |
| Synopsys 보통주에 대한 예상 수익률3 | E(RSNPS) | 14.99% |
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(RSNPS) = RF + βSNPS [E(RM) – RF]
= 4.56% + 1.13 [13.77% – 4.56%]
= 14.99%