Capital Asset Pricing Model (CAPM)
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Synopsys Inc. common stock.
Rates of Return
Synopsys Inc., monthly rates of return
| Synopsys Inc. (SNPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceSNPS,t1 | DividendSNPS,t1 | RSNPS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Nov 30, 2018 | $91.94 | 2,760.17 | ||||
| 1. | Dec 31, 2018 | $84.24 | -8.38% | 2,506.85 | -9.18% | |
| 2. | Jan 31, 2019 | $93.35 | 10.81% | 2,704.10 | 7.87% | |
| 3. | Feb 28, 2019 | $101.68 | 8.92% | 2,784.49 | 2.97% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Sep 30, 2024 | $506.39 | -2.54% | 5,762.48 | 2.02% | |
| 71. | Oct 31, 2024 | $513.61 | 1.43% | 5,705.45 | -0.99% | |
| Average (R): | 2.79% | 1.16% | ||||
| Standard deviation: | 8.36% | 5.15% | ||||
| Synopsys Inc. (SNPS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceSNPS,t1 | DividendSNPS,t1 | RSNPS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Nov 30, 2018 | $91.94 | 2,760.17 | ||||
| 1. | Dec 31, 2018 | $84.24 | -8.38% | 2,506.85 | -9.18% | |
| 2. | Jan 31, 2019 | $93.35 | 10.81% | 2,704.10 | 7.87% | |
| 3. | Feb 28, 2019 | $101.68 | 8.92% | 2,784.49 | 2.97% | |
| 4. | Mar 31, 2019 | $115.15 | 13.25% | 2,834.40 | 1.79% | |
| 5. | Apr 30, 2019 | $121.08 | 5.15% | 2,945.83 | 3.93% | |
| 6. | May 31, 2019 | $116.44 | -3.83% | 2,752.06 | -6.58% | |
| 7. | Jun 30, 2019 | $128.69 | 10.52% | 2,941.76 | 6.89% | |
| 8. | Jul 31, 2019 | $132.76 | 3.16% | 2,980.38 | 1.31% | |
| 9. | Aug 31, 2019 | $141.81 | 6.82% | 2,926.46 | -1.81% | |
| 10. | Sep 30, 2019 | $137.25 | -3.22% | 2,976.74 | 1.72% | |
| 11. | Oct 31, 2019 | $135.75 | -1.09% | 3,037.56 | 2.04% | |
| 12. | Nov 30, 2019 | $141.04 | 3.90% | 3,140.98 | 3.40% | |
| 13. | Dec 31, 2019 | $139.20 | -1.30% | 3,230.78 | 2.86% | |
| 14. | Jan 31, 2020 | $147.51 | 5.97% | 3,225.52 | -0.16% | |
| 15. | Feb 29, 2020 | $137.93 | -6.49% | 2,954.22 | -8.41% | |
| 16. | Mar 31, 2020 | $128.79 | -6.63% | 2,584.59 | -12.51% | |
| 17. | Apr 30, 2020 | $157.12 | 22.00% | 2,912.43 | 12.68% | |
| 18. | May 31, 2020 | $180.91 | 15.14% | 3,044.31 | 4.53% | |
| 19. | Jun 30, 2020 | $195.00 | 7.79% | 3,100.29 | 1.84% | |
| 20. | Jul 31, 2020 | $199.22 | 2.16% | 3,271.12 | 5.51% | |
| 21. | Aug 31, 2020 | $221.30 | 11.08% | 3,500.31 | 7.01% | |
| 22. | Sep 30, 2020 | $213.98 | -3.31% | 3,363.00 | -3.92% | |
| 23. | Oct 31, 2020 | $213.86 | -0.06% | 3,269.96 | -2.77% | |
| 24. | Nov 30, 2020 | $227.50 | 6.38% | 3,621.63 | 10.75% | |
| 25. | Dec 31, 2020 | $259.24 | 13.95% | 3,756.07 | 3.71% | |
| 26. | Jan 31, 2021 | $255.45 | -1.46% | 3,714.24 | -1.11% | |
| 27. | Feb 28, 2021 | $245.21 | -4.01% | 3,811.15 | 2.61% | |
| 28. | Mar 31, 2021 | $247.78 | 1.05% | 3,972.89 | 4.24% | |
| 29. | Apr 30, 2021 | $247.06 | -0.29% | 4,181.17 | 5.24% | |
| 30. | May 31, 2021 | $254.34 | 2.95% | 4,204.11 | 0.55% | |
| 31. | Jun 30, 2021 | $275.79 | 8.43% | 4,297.50 | 2.22% | |
| 32. | Jul 31, 2021 | $287.99 | 4.42% | 4,395.26 | 2.27% | |
| 33. | Aug 31, 2021 | $332.24 | 15.37% | 4,522.68 | 2.90% | |
| 34. | Sep 30, 2021 | $299.41 | -9.88% | 4,307.54 | -4.76% | |
| 35. | Oct 31, 2021 | $333.18 | 11.28% | 4,605.38 | 6.91% | |
| 36. | Nov 30, 2021 | $341.00 | 2.35% | 4,567.00 | -0.83% | |
| 37. | Dec 31, 2021 | $368.50 | 8.06% | 4,766.18 | 4.36% | |
| 38. | Jan 31, 2022 | $310.50 | -15.74% | 4,515.55 | -5.26% | |
| 39. | Feb 28, 2022 | $312.39 | 0.61% | 4,373.94 | -3.14% | |
| 40. | Mar 31, 2022 | $333.27 | 6.68% | 4,530.41 | 3.58% | |
| 41. | Apr 30, 2022 | $286.79 | -13.95% | 4,131.93 | -8.80% | |
| 42. | May 31, 2022 | $319.20 | 11.30% | 4,132.15 | 0.01% | |
| 43. | Jun 30, 2022 | $303.70 | -4.86% | 3,785.38 | -8.39% | |
| 44. | Jul 31, 2022 | $367.50 | 21.01% | 4,130.29 | 9.11% | |
| 45. | Aug 31, 2022 | $346.02 | -5.84% | 3,955.00 | -4.24% | |
| 46. | Sep 30, 2022 | $305.51 | -11.71% | 3,585.62 | -9.34% | |
| 47. | Oct 31, 2022 | $292.55 | -4.24% | 3,871.98 | 7.99% | |
| 48. | Nov 30, 2022 | $339.54 | 16.06% | 4,080.11 | 5.38% | |
| 49. | Dec 31, 2022 | $319.29 | -5.96% | 3,839.50 | -5.90% | |
| 50. | Jan 31, 2023 | $353.75 | 10.79% | 4,076.60 | 6.18% | |
| 51. | Feb 28, 2023 | $363.76 | 2.83% | 3,970.15 | -2.61% | |
| 52. | Mar 31, 2023 | $386.25 | 6.18% | 4,109.31 | 3.51% | |
| 53. | Apr 30, 2023 | $371.32 | -3.87% | 4,169.48 | 1.46% | |
| 54. | May 31, 2023 | $454.96 | 22.53% | 4,179.83 | 0.25% | |
| 55. | Jun 30, 2023 | $435.41 | -4.30% | 4,376.86 | 4.71% | |
| 56. | Jul 31, 2023 | $451.80 | 3.76% | 4,588.96 | 4.85% | |
| 57. | Aug 31, 2023 | $458.89 | 1.57% | 4,507.66 | -1.77% | |
| 58. | Sep 30, 2023 | $458.97 | 0.02% | 4,288.05 | -4.87% | |
| 59. | Oct 31, 2023 | $469.44 | 2.28% | 4,193.80 | -2.20% | |
| 60. | Nov 30, 2023 | $543.23 | 15.72% | 4,567.80 | 8.92% | |
| 61. | Dec 31, 2023 | $514.91 | -5.21% | 4,769.83 | 4.42% | |
| 62. | Jan 31, 2024 | $533.35 | 3.58% | 4,845.65 | 1.59% | |
| 63. | Feb 29, 2024 | $573.73 | 7.57% | 5,096.27 | 5.17% | |
| 64. | Mar 31, 2024 | $571.50 | -0.39% | 5,254.35 | 3.10% | |
| 65. | Apr 30, 2024 | $530.59 | -7.16% | 5,035.69 | -4.16% | |
| 66. | May 31, 2024 | $560.80 | 5.69% | 5,277.51 | 4.80% | |
| 67. | Jun 30, 2024 | $595.06 | 6.11% | 5,460.48 | 3.47% | |
| 68. | Jul 31, 2024 | $558.32 | -6.17% | 5,522.30 | 1.13% | |
| 69. | Aug 31, 2024 | $519.58 | -6.94% | 5,648.40 | 2.28% | |
| 70. | Sep 30, 2024 | $506.39 | -2.54% | 5,762.48 | 2.02% | |
| 71. | Oct 31, 2024 | $513.61 | 1.43% | 5,705.45 | -0.99% | |
| Average (R): | 2.79% | 1.16% | ||||
| Standard deviation: | 8.36% | 5.15% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of SNPS during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Synopsys Inc., calculation of variance and covariance of returns
| t | Date | 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. | Dec 31, 2018 | -8.38% | -9.18% | 124.57 | 106.87 | 115.38 |
| 2. | Jan 31, 2019 | 10.81% | 7.87% | 64.45 | 45.00 | 53.86 |
| 3. | Feb 28, 2019 | 8.92% | 2.97% | 37.67 | 3.29 | 11.13 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Sep 30, 2024 | -2.54% | 2.02% | 28.35 | 0.74 | -4.58 |
| 71. | Oct 31, 2024 | 1.43% | -0.99% | 1.85 | 4.62 | 2.92 |
| Total (Σ): | 4,895.70 | 1,859.93 | 2,005.29 | |||
| t | Date | 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. | Dec 31, 2018 | -8.38% | -9.18% | 124.57 | 106.87 | 115.38 |
| 2. | Jan 31, 2019 | 10.81% | 7.87% | 64.45 | 45.00 | 53.86 |
| 3. | Feb 28, 2019 | 8.92% | 2.97% | 37.67 | 3.29 | 11.13 |
| 4. | Mar 31, 2019 | 13.25% | 1.79% | 109.44 | 0.40 | 6.62 |
| 5. | Apr 30, 2019 | 5.15% | 3.93% | 5.59 | 7.68 | 6.55 |
| 6. | May 31, 2019 | -3.83% | -6.58% | 43.80 | 59.87 | 51.21 |
| 7. | Jun 30, 2019 | 10.52% | 6.89% | 59.82 | 32.87 | 44.34 |
| 8. | Jul 31, 2019 | 3.16% | 1.31% | 0.14 | 0.02 | 0.06 |
| 9. | Aug 31, 2019 | 6.82% | -1.81% | 16.25 | 8.82 | -11.97 |
| 10. | Sep 30, 2019 | -3.22% | 1.72% | 36.02 | 0.31 | -3.35 |
| 11. | Oct 31, 2019 | -1.09% | 2.04% | 15.05 | 0.78 | -3.43 |
| 12. | Nov 30, 2019 | 3.90% | 3.40% | 1.23 | 5.04 | 2.49 |
| 13. | Dec 31, 2019 | -1.30% | 2.86% | 16.73 | 2.89 | -6.95 |
| 14. | Jan 31, 2020 | 5.97% | -0.16% | 10.14 | 1.75 | -4.21 |
| 15. | Feb 29, 2020 | -6.49% | -8.41% | 86.13 | 91.60 | 88.82 |
| 16. | Mar 31, 2020 | -6.63% | -12.51% | 88.60 | 186.92 | 128.69 |
| 17. | Apr 30, 2020 | 22.00% | 12.68% | 369.06 | 132.81 | 221.40 |
| 18. | May 31, 2020 | 15.14% | 4.53% | 152.65 | 11.35 | 41.62 |
| 19. | Jun 30, 2020 | 7.79% | 1.84% | 25.02 | 0.46 | 3.40 |
| 20. | Jul 31, 2020 | 2.16% | 5.51% | 0.39 | 18.92 | -2.71 |
| 21. | Aug 31, 2020 | 11.08% | 7.01% | 68.84 | 34.18 | 48.51 |
| 22. | Sep 30, 2020 | -3.31% | -3.92% | 37.14 | 25.83 | 30.97 |
| 23. | Oct 31, 2020 | -0.06% | -2.77% | 8.08 | 15.42 | 11.16 |
| 24. | Nov 30, 2020 | 6.38% | 10.75% | 12.90 | 92.06 | 34.46 |
| 25. | Dec 31, 2020 | 13.95% | 3.71% | 124.67 | 6.51 | 28.50 |
| 26. | Jan 31, 2021 | -1.46% | -1.11% | 18.05 | 5.17 | 9.66 |
| 27. | Feb 28, 2021 | -4.01% | 2.61% | 46.17 | 2.10 | -9.85 |
| 28. | Mar 31, 2021 | 1.05% | 4.24% | 3.02 | 9.51 | -5.36 |
| 29. | Apr 30, 2021 | -0.29% | 5.24% | 9.47 | 16.67 | -12.56 |
| 30. | May 31, 2021 | 2.95% | 0.55% | 0.03 | 0.37 | -0.10 |
| 31. | Jun 30, 2021 | 8.43% | 2.22% | 31.89 | 1.13 | 5.99 |
| 32. | Jul 31, 2021 | 4.42% | 2.27% | 2.68 | 1.24 | 1.83 |
| 33. | Aug 31, 2021 | 15.37% | 2.90% | 158.23 | 3.02 | 21.88 |
| 34. | Sep 30, 2021 | -9.88% | -4.76% | 160.47 | 35.01 | 74.95 |
| 35. | Oct 31, 2021 | 11.28% | 6.91% | 72.13 | 33.11 | 48.87 |
| 36. | Nov 30, 2021 | 2.35% | -0.83% | 0.19 | 3.97 | 0.88 |
| 37. | Dec 31, 2021 | 8.06% | 4.36% | 27.86 | 10.25 | 16.90 |
| 38. | Jan 31, 2022 | -15.74% | -5.26% | 343.20 | 41.20 | 118.90 |
| 39. | Feb 28, 2022 | 0.61% | -3.14% | 4.74 | 18.46 | 9.35 |
| 40. | Mar 31, 2022 | 6.68% | 3.58% | 15.19 | 5.84 | 9.42 |
| 41. | Apr 30, 2022 | -13.95% | -8.80% | 279.99 | 99.11 | 166.58 |
| 42. | May 31, 2022 | 11.30% | 0.01% | 72.50 | 1.33 | -9.83 |
| 43. | Jun 30, 2022 | -4.86% | -8.39% | 58.40 | 91.24 | 73.00 |
| 44. | Jul 31, 2022 | 21.01% | 9.11% | 332.02 | 63.23 | 144.89 |
| 45. | Aug 31, 2022 | -5.84% | -4.24% | 74.49 | 29.20 | 46.64 |
| 46. | Sep 30, 2022 | -11.71% | -9.34% | 210.06 | 110.24 | 152.17 |
| 47. | Oct 31, 2022 | -4.24% | 7.99% | 49.40 | 46.60 | -47.98 |
| 48. | Nov 30, 2022 | 16.06% | 5.38% | 176.25 | 17.77 | 55.96 |
| 49. | Dec 31, 2022 | -5.96% | -5.90% | 76.56 | 49.80 | 61.75 |
| 50. | Jan 31, 2023 | 10.79% | 6.18% | 64.10 | 25.15 | 40.16 |
| 51. | Feb 28, 2023 | 2.83% | -2.61% | 0.00 | 14.22 | -0.16 |
| 52. | Mar 31, 2023 | 6.18% | 3.51% | 11.54 | 5.50 | 7.97 |
| 53. | Apr 30, 2023 | -3.87% | 1.46% | 44.24 | 0.09 | -2.02 |
| 54. | May 31, 2023 | 22.53% | 0.25% | 389.62 | 0.83 | -18.00 |
| 55. | Jun 30, 2023 | -4.30% | 4.71% | 50.17 | 12.63 | -25.17 |
| 56. | Jul 31, 2023 | 3.76% | 4.85% | 0.96 | 13.59 | 3.61 |
| 57. | Aug 31, 2023 | 1.57% | -1.77% | 1.48 | 8.59 | 3.57 |
| 58. | Sep 30, 2023 | 0.02% | -4.87% | 7.67 | 36.38 | 16.70 |
| 59. | Oct 31, 2023 | 2.28% | -2.20% | 0.25 | 11.28 | 1.70 |
| 60. | Nov 30, 2023 | 15.72% | 8.92% | 167.25 | 60.19 | 100.33 |
| 61. | Dec 31, 2023 | -5.21% | 4.42% | 63.99 | 10.65 | -26.10 |
| 62. | Jan 31, 2024 | 3.58% | 1.59% | 0.63 | 0.18 | 0.34 |
| 63. | Feb 29, 2024 | 7.57% | 5.17% | 22.90 | 16.10 | 19.20 |
| 64. | Mar 31, 2024 | -0.39% | 3.10% | 10.08 | 3.77 | -6.17 |
| 65. | Apr 30, 2024 | -7.16% | -4.16% | 98.89 | 28.32 | 52.92 |
| 66. | May 31, 2024 | 5.69% | 4.80% | 8.45 | 13.27 | 10.59 |
| 67. | Jun 30, 2024 | 6.11% | 3.47% | 11.04 | 5.32 | 7.67 |
| 68. | Jul 31, 2024 | -6.17% | 1.13% | 80.29 | 0.00 | 0.25 |
| 69. | Aug 31, 2024 | -6.94% | 2.28% | 94.57 | 1.26 | -10.93 |
| 70. | Sep 30, 2024 | -2.54% | 2.02% | 28.35 | 0.74 | -4.58 |
| 71. | Oct 31, 2024 | 1.43% | -0.99% | 1.85 | 4.62 | 2.92 |
| Total (Σ): | 4,895.70 | 1,859.93 | 2,005.29 | |||
Show all
VarianceSNPS = Σ(RSNPS,t–RSNPS)2 ÷ (71 – 1)
= 4,895.70 ÷ (71 – 1)
= 69.94
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,859.93 ÷ (71 – 1)
= 26.57
CovarianceSNPS, S&P 500 = Σ(RSNPS,t–RSNPS)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,005.29 ÷ (71 – 1)
= 28.65
Systematic Risk (β) Estimation
| VarianceSNPS | 69.94 |
| VarianceS&P 500 | 26.57 |
| CovarianceSNPS, S&P 500 | 28.65 |
| Correlation coefficientSNPS, S&P 5001 | 0.66 |
| βSNPS2 | 1.08 |
| αSNPS3 | 1.54% |
Calculations
1 Correlation coefficientSNPS, S&P 500
= CovarianceSNPS, S&P 500 ÷ (Standard deviationSNPS × Standard deviationS&P 500)
= 28.65 ÷ (8.36% × 5.15%)
= 0.66
2 βSNPS
= CovarianceSNPS, S&P 500 ÷ VarianceS&P 500
= 28.65 ÷ 26.57
= 1.08
3 αSNPS
= AverageSNPS – βSNPS × AverageS&P 500
= 2.79% – 1.08 × 1.16%
= 1.54%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.83% |
| Expected rate of return on market portfolio2 | E(RM) | 14.44% |
| Systematic risk (β) of Synopsys Inc. common stock | βSNPS | 1.08 |
| Expected rate of return on Synopsys Inc. common stock3 | E(RSNPS) | 15.19% |
1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).
3 E(RSNPS) = RF + βSNPS [E(RM) – RF]
= 4.83% + 1.08 [14.44% – 4.83%]
= 15.19%