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 Merck & Co. Inc. common stock.
Rates of Return
Merck & Co. Inc., monthly rates of return
| Merck & Co. Inc. (MRK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceMRK,t1 | DividendMRK,t1 | RMRK,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2021 | $77.07 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $72.62 | -5.77% | 3,811.15 | 2.61% | |
| 2. | Mar 31, 2021 | $77.09 | $0.65 | 7.05% | 3,972.89 | 4.24% |
| 3. | Apr 30, 2021 | $74.50 | -3.36% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | $104.83 | 21.92% | 6,849.09 | 0.13% | |
| 59. | Dec 31, 2025 | $105.26 | $0.85 | 1.22% | 6,845.50 | -0.05% |
| Average (R): | 1.08% | 1.14% | ||||
| Standard deviation: | 6.75% | 4.37% | ||||
| Merck & Co. Inc. (MRK) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceMRK,t1 | DividendMRK,t1 | RMRK,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2021 | $77.07 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $72.62 | -5.77% | 3,811.15 | 2.61% | |
| 2. | Mar 31, 2021 | $77.09 | $0.65 | 7.05% | 3,972.89 | 4.24% |
| 3. | Apr 30, 2021 | $74.50 | -3.36% | 4,181.17 | 5.24% | |
| 4. | May 31, 2021 | $75.89 | 1.87% | 4,204.11 | 0.55% | |
| 5. | Jun 30, 2021 | $77.77 | $3.75 | 7.42% | 4,297.50 | 2.22% |
| 6. | Jul 31, 2021 | $76.87 | -1.16% | 4,395.26 | 2.27% | |
| 7. | Aug 31, 2021 | $76.29 | -0.75% | 4,522.68 | 2.90% | |
| 8. | Sep 30, 2021 | $75.11 | $0.65 | -0.69% | 4,307.54 | -4.76% |
| 9. | Oct 31, 2021 | $88.05 | 17.23% | 4,605.38 | 6.91% | |
| 10. | Nov 30, 2021 | $74.91 | -14.92% | 4,567.00 | -0.83% | |
| 11. | Dec 31, 2021 | $76.64 | $0.69 | 3.23% | 4,766.18 | 4.36% |
| 12. | Jan 31, 2022 | $81.48 | 6.32% | 4,515.55 | -5.26% | |
| 13. | Feb 28, 2022 | $76.58 | -6.01% | 4,373.94 | -3.14% | |
| 14. | Mar 31, 2022 | $82.05 | $0.69 | 8.04% | 4,530.41 | 3.58% |
| 15. | Apr 30, 2022 | $88.69 | 8.09% | 4,131.93 | -8.80% | |
| 16. | May 31, 2022 | $92.03 | 3.77% | 4,132.15 | 0.01% | |
| 17. | Jun 30, 2022 | $91.17 | $0.69 | -0.18% | 3,785.38 | -8.39% |
| 18. | Jul 31, 2022 | $89.34 | -2.01% | 4,130.29 | 9.11% | |
| 19. | Aug 31, 2022 | $85.36 | -4.45% | 3,955.00 | -4.24% | |
| 20. | Sep 30, 2022 | $86.12 | $0.69 | 1.70% | 3,585.62 | -9.34% |
| 21. | Oct 31, 2022 | $101.20 | 17.51% | 3,871.98 | 7.99% | |
| 22. | Nov 30, 2022 | $110.12 | 8.81% | 4,080.11 | 5.38% | |
| 23. | Dec 31, 2022 | $110.95 | $0.73 | 1.42% | 3,839.50 | -5.90% |
| 24. | Jan 31, 2023 | $107.41 | -3.19% | 4,076.60 | 6.18% | |
| 25. | Feb 28, 2023 | $106.24 | -1.09% | 3,970.15 | -2.61% | |
| 26. | Mar 31, 2023 | $106.39 | $0.73 | 0.83% | 4,109.31 | 3.51% |
| 27. | Apr 30, 2023 | $115.47 | 8.53% | 4,169.48 | 1.46% | |
| 28. | May 31, 2023 | $110.41 | -4.38% | 4,179.83 | 0.25% | |
| 29. | Jun 30, 2023 | $115.39 | $0.73 | 5.17% | 4,376.86 | 4.71% |
| 30. | Jul 31, 2023 | $106.65 | -7.57% | 4,588.96 | 4.85% | |
| 31. | Aug 31, 2023 | $108.98 | 2.18% | 4,507.66 | -1.77% | |
| 32. | Sep 30, 2023 | $102.95 | $0.73 | -4.86% | 4,288.05 | -4.87% |
| 33. | Oct 31, 2023 | $102.70 | -0.24% | 4,193.80 | -2.20% | |
| 34. | Nov 30, 2023 | $102.48 | -0.21% | 4,567.80 | 8.92% | |
| 35. | Dec 31, 2023 | $109.02 | $0.77 | 7.13% | 4,769.83 | 4.42% |
| 36. | Jan 31, 2024 | $120.78 | 10.79% | 4,845.65 | 1.59% | |
| 37. | Feb 29, 2024 | $127.15 | 5.27% | 5,096.27 | 5.17% | |
| 38. | Mar 31, 2024 | $131.95 | $0.77 | 4.38% | 5,254.35 | 3.10% |
| 39. | Apr 30, 2024 | $129.22 | -2.07% | 5,035.69 | -4.16% | |
| 40. | May 31, 2024 | $125.54 | -2.85% | 5,277.51 | 4.80% | |
| 41. | Jun 30, 2024 | $123.80 | $0.77 | -0.77% | 5,460.48 | 3.47% |
| 42. | Jul 31, 2024 | $113.13 | -8.62% | 5,522.30 | 1.13% | |
| 43. | Aug 31, 2024 | $118.45 | 4.70% | 5,648.40 | 2.28% | |
| 44. | Sep 30, 2024 | $113.56 | $0.77 | -3.48% | 5,762.48 | 2.02% |
| 45. | Oct 31, 2024 | $102.32 | -9.90% | 5,705.45 | -0.99% | |
| 46. | Nov 30, 2024 | $101.64 | -0.66% | 6,032.38 | 5.73% | |
| 47. | Dec 31, 2024 | $99.48 | $0.81 | -1.33% | 5,881.63 | -2.50% |
| 48. | Jan 31, 2025 | $98.82 | -0.66% | 6,040.53 | 2.70% | |
| 49. | Feb 28, 2025 | $92.25 | -6.65% | 5,954.50 | -1.42% | |
| 50. | Mar 31, 2025 | $89.76 | $0.81 | -1.82% | 5,611.85 | -5.75% |
| 51. | Apr 30, 2025 | $85.20 | -5.08% | 5,569.06 | -0.76% | |
| 52. | May 31, 2025 | $76.84 | -9.81% | 5,911.69 | 6.15% | |
| 53. | Jun 30, 2025 | $79.16 | $0.81 | 4.07% | 6,204.95 | 4.96% |
| 54. | Jul 31, 2025 | $78.12 | -1.31% | 6,339.39 | 2.17% | |
| 55. | Aug 31, 2025 | $84.12 | 7.68% | 6,460.26 | 1.91% | |
| 56. | Sep 30, 2025 | $83.93 | $0.81 | 0.74% | 6,688.46 | 3.53% |
| 57. | Oct 31, 2025 | $85.98 | 2.44% | 6,840.20 | 2.27% | |
| 58. | Nov 30, 2025 | $104.83 | 21.92% | 6,849.09 | 0.13% | |
| 59. | Dec 31, 2025 | $105.26 | $0.85 | 1.22% | 6,845.50 | -0.05% |
| Average (R): | 1.08% | 1.14% | ||||
| Standard deviation: | 6.75% | 4.37% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of MRK during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Merck & Co. Inc., calculation of variance and covariance of returns
| t | Date | RMRK,t | RS&P 500,t | (RMRK,t–RMRK)2 | (RS&P 500,t–RS&P 500)2 | (RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2021 | -5.77% | 2.61% | 46.96 | 2.17 | -10.09 |
| 2. | Mar 31, 2021 | 7.05% | 4.24% | 35.66 | 9.66 | 18.56 |
| 3. | Apr 30, 2021 | -3.36% | 5.24% | 19.70 | 16.86 | -18.22 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | 21.92% | 0.13% | 434.52 | 1.01 | -20.97 |
| 59. | Dec 31, 2025 | 1.22% | -0.05% | 0.02 | 1.41 | -0.17 |
| Total (Σ): | 2,638.75 | 1,108.23 | 288.27 | |||
| t | Date | RMRK,t | RS&P 500,t | (RMRK,t–RMRK)2 | (RS&P 500,t–RS&P 500)2 | (RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2021 | -5.77% | 2.61% | 46.96 | 2.17 | -10.09 |
| 2. | Mar 31, 2021 | 7.05% | 4.24% | 35.66 | 9.66 | 18.56 |
| 3. | Apr 30, 2021 | -3.36% | 5.24% | 19.70 | 16.86 | -18.22 |
| 4. | May 31, 2021 | 1.87% | 0.55% | 0.62 | 0.35 | -0.46 |
| 5. | Jun 30, 2021 | 7.42% | 2.22% | 40.20 | 1.18 | 6.88 |
| 6. | Jul 31, 2021 | -1.16% | 2.27% | 5.00 | 1.30 | -2.55 |
| 7. | Aug 31, 2021 | -0.75% | 2.90% | 3.36 | 3.11 | -3.23 |
| 8. | Sep 30, 2021 | -0.69% | -4.76% | 3.14 | 34.73 | 10.45 |
| 9. | Oct 31, 2021 | 17.23% | 6.91% | 260.81 | 33.39 | 93.32 |
| 10. | Nov 30, 2021 | -14.92% | -0.83% | 256.06 | 3.88 | 31.52 |
| 11. | Dec 31, 2021 | 3.23% | 4.36% | 4.63 | 10.40 | 6.94 |
| 12. | Jan 31, 2022 | 6.32% | -5.26% | 27.42 | 40.89 | -33.49 |
| 13. | Feb 28, 2022 | -6.01% | -3.14% | 50.30 | 18.25 | 30.30 |
| 14. | Mar 31, 2022 | 8.04% | 3.58% | 48.52 | 5.96 | 17.00 |
| 15. | Apr 30, 2022 | 8.09% | -8.80% | 49.20 | 98.64 | -69.66 |
| 16. | May 31, 2022 | 3.77% | 0.01% | 7.22 | 1.28 | -3.04 |
| 17. | Jun 30, 2022 | -0.18% | -8.39% | 1.60 | 90.79 | 12.04 |
| 18. | Jul 31, 2022 | -2.01% | 9.11% | 9.52 | 63.61 | -24.61 |
| 19. | Aug 31, 2022 | -4.45% | -4.24% | 30.62 | 28.95 | 29.77 |
| 20. | Sep 30, 2022 | 1.70% | -9.34% | 0.38 | 109.74 | -6.50 |
| 21. | Oct 31, 2022 | 17.51% | 7.99% | 270.01 | 46.93 | 112.56 |
| 22. | Nov 30, 2022 | 8.81% | 5.38% | 59.84 | 17.97 | 32.79 |
| 23. | Dec 31, 2022 | 1.42% | -5.90% | 0.11 | 49.47 | -2.38 |
| 24. | Jan 31, 2023 | -3.19% | 6.18% | 18.23 | 25.39 | -21.51 |
| 25. | Feb 28, 2023 | -1.09% | -2.61% | 4.70 | 14.04 | 8.12 |
| 26. | Mar 31, 2023 | 0.83% | 3.51% | 0.06 | 5.61 | -0.59 |
| 27. | Apr 30, 2023 | 8.53% | 1.46% | 55.59 | 0.11 | 2.45 |
| 28. | May 31, 2023 | -4.38% | 0.25% | 29.82 | 0.79 | 4.85 |
| 29. | Jun 30, 2023 | 5.17% | 4.71% | 16.75 | 12.80 | 14.64 |
| 30. | Jul 31, 2023 | -7.57% | 4.85% | 74.87 | 13.76 | -32.10 |
| 31. | Aug 31, 2023 | 2.18% | -1.77% | 1.22 | 8.46 | -3.22 |
| 32. | Sep 30, 2023 | -4.86% | -4.87% | 35.30 | 36.10 | 35.70 |
| 33. | Oct 31, 2023 | -0.24% | -2.20% | 1.75 | 11.12 | 4.41 |
| 34. | Nov 30, 2023 | -0.21% | 8.92% | 1.67 | 60.56 | -10.06 |
| 35. | Dec 31, 2023 | 7.13% | 4.42% | 36.66 | 10.80 | 19.90 |
| 36. | Jan 31, 2024 | 10.79% | 1.59% | 94.26 | 0.21 | 4.40 |
| 37. | Feb 29, 2024 | 5.27% | 5.17% | 17.60 | 16.29 | 16.93 |
| 38. | Mar 31, 2024 | 4.38% | 3.10% | 10.90 | 3.86 | 6.49 |
| 39. | Apr 30, 2024 | -2.07% | -4.16% | 9.91 | 28.06 | 16.67 |
| 40. | May 31, 2024 | -2.85% | 4.80% | 15.42 | 13.44 | -14.39 |
| 41. | Jun 30, 2024 | -0.77% | 3.47% | 3.43 | 5.43 | -4.31 |
| 42. | Jul 31, 2024 | -8.62% | 1.13% | 94.04 | 0.00 | 0.04 |
| 43. | Aug 31, 2024 | 4.70% | 2.28% | 13.13 | 1.32 | 4.16 |
| 44. | Sep 30, 2024 | -3.48% | 2.02% | 20.76 | 0.78 | -4.03 |
| 45. | Oct 31, 2024 | -9.90% | -0.99% | 120.48 | 4.52 | 23.33 |
| 46. | Nov 30, 2024 | -0.66% | 5.73% | 3.04 | 21.10 | -8.01 |
| 47. | Dec 31, 2024 | -1.33% | -2.50% | 5.79 | 13.21 | 8.75 |
| 48. | Jan 31, 2025 | -0.66% | 2.70% | 3.03 | 2.45 | -2.73 |
| 49. | Feb 28, 2025 | -6.65% | -1.42% | 59.71 | 6.56 | 19.78 |
| 50. | Mar 31, 2025 | -1.82% | -5.75% | 8.41 | 47.48 | 19.98 |
| 51. | Apr 30, 2025 | -5.08% | -0.76% | 37.93 | 3.60 | 11.69 |
| 52. | May 31, 2025 | -9.81% | 6.15% | 118.61 | 25.16 | -54.63 |
| 53. | Jun 30, 2025 | 4.07% | 4.96% | 8.97 | 14.63 | 11.45 |
| 54. | Jul 31, 2025 | -1.31% | 2.17% | 5.72 | 1.06 | -2.47 |
| 55. | Aug 31, 2025 | 7.68% | 1.91% | 43.59 | 0.59 | 5.09 |
| 56. | Sep 30, 2025 | 0.74% | 3.53% | 0.12 | 5.74 | -0.82 |
| 57. | Oct 31, 2025 | 2.44% | 2.27% | 1.86 | 1.28 | 1.54 |
| 58. | Nov 30, 2025 | 21.92% | 0.13% | 434.52 | 1.01 | -20.97 |
| 59. | Dec 31, 2025 | 1.22% | -0.05% | 0.02 | 1.41 | -0.17 |
| Total (Σ): | 2,638.75 | 1,108.23 | 288.27 | |||
Show all
VarianceMRK = Σ(RMRK,t–RMRK)2 ÷ (59 – 1)
= 2,638.75 ÷ (59 – 1)
= 45.50
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
CovarianceMRK, S&P 500 = Σ(RMRK,t–RMRK)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 288.27 ÷ (59 – 1)
= 4.97
Systematic Risk (β) Estimation
| VarianceMRK | 45.50 |
| VarianceS&P 500 | 19.11 |
| CovarianceMRK, S&P 500 | 4.97 |
| Correlation coefficientMRK, S&P 5001 | 0.17 |
| βMRK2 | 0.26 |
| αMRK3 | 0.78% |
Calculations
1 Correlation coefficientMRK, S&P 500
= CovarianceMRK, S&P 500 ÷ (Standard deviationMRK × Standard deviationS&P 500)
= 4.97 ÷ (6.75% × 4.37%)
= 0.17
2 βMRK
= CovarianceMRK, S&P 500 ÷ VarianceS&P 500
= 4.97 ÷ 19.11
= 0.26
3 αMRK
= AverageMRK – βMRK × AverageS&P 500
= 1.08% – 0.26 × 1.14%
= 0.78%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.94% |
| Expected rate of return on market portfolio2 | E(RM) | 17.36% |
| Systematic risk (β) of Merck & Co. Inc. common stock | βMRK | 0.26 |
| Expected rate of return on Merck & Co. Inc. common stock3 | E(RMRK) | 8.17% |
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(RMRK) = RF + βMRK [E(RM) – RF]
= 4.94% + 0.26 [17.36% – 4.94%]
= 8.17%