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 Eli Lilly & Co. common stock.
Rates of Return
Eli Lilly & Co., monthly rates of return
| Eli Lilly & Co. (LLY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceLLY,t1 | DividendLLY,t1 | RLLY,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2021 | $207.97 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $204.89 | $0.85 | -1.07% | 3,811.15 | 2.61% |
| 2. | Mar 31, 2021 | $186.82 | -8.82% | 3,972.89 | 4.24% | |
| 3. | Apr 30, 2021 | $182.77 | -2.17% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | $1,075.47 | $1.50 | 24.81% | 6,849.09 | 0.13% |
| 59. | Dec 31, 2025 | $1,074.68 | -0.07% | 6,845.50 | -0.05% | |
| Average (R): | 3.31% | 1.14% | ||||
| Standard deviation: | 9.12% | 4.37% | ||||
| Eli Lilly & Co. (LLY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceLLY,t1 | DividendLLY,t1 | RLLY,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2021 | $207.97 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $204.89 | $0.85 | -1.07% | 3,811.15 | 2.61% |
| 2. | Mar 31, 2021 | $186.82 | -8.82% | 3,972.89 | 4.24% | |
| 3. | Apr 30, 2021 | $182.77 | -2.17% | 4,181.17 | 5.24% | |
| 4. | May 31, 2021 | $199.74 | $0.85 | 9.75% | 4,204.11 | 0.55% |
| 5. | Jun 30, 2021 | $229.52 | 14.91% | 4,297.50 | 2.22% | |
| 6. | Jul 31, 2021 | $243.50 | 6.09% | 4,395.26 | 2.27% | |
| 7. | Aug 31, 2021 | $258.29 | $0.85 | 6.42% | 4,522.68 | 2.90% |
| 8. | Sep 30, 2021 | $231.05 | -10.55% | 4,307.54 | -4.76% | |
| 9. | Oct 31, 2021 | $254.76 | 10.26% | 4,605.38 | 6.91% | |
| 10. | Nov 30, 2021 | $248.04 | $0.85 | -2.30% | 4,567.00 | -0.83% |
| 11. | Dec 31, 2021 | $276.22 | 11.36% | 4,766.18 | 4.36% | |
| 12. | Jan 31, 2022 | $245.39 | -11.16% | 4,515.55 | -5.26% | |
| 13. | Feb 28, 2022 | $249.95 | $0.98 | 2.26% | 4,373.94 | -3.14% |
| 14. | Mar 31, 2022 | $286.37 | 14.57% | 4,530.41 | 3.58% | |
| 15. | Apr 30, 2022 | $292.13 | 2.01% | 4,131.93 | -8.80% | |
| 16. | May 31, 2022 | $313.44 | $0.98 | 7.63% | 4,132.15 | 0.01% |
| 17. | Jun 30, 2022 | $324.23 | 3.44% | 3,785.38 | -8.39% | |
| 18. | Jul 31, 2022 | $329.69 | 1.68% | 4,130.29 | 9.11% | |
| 19. | Aug 31, 2022 | $301.23 | $0.98 | -8.34% | 3,955.00 | -4.24% |
| 20. | Sep 30, 2022 | $323.35 | 7.34% | 3,585.62 | -9.34% | |
| 21. | Oct 31, 2022 | $362.09 | 11.98% | 3,871.98 | 7.99% | |
| 22. | Nov 30, 2022 | $371.08 | $0.98 | 2.75% | 4,080.11 | 5.38% |
| 23. | Dec 31, 2022 | $365.84 | -1.41% | 3,839.50 | -5.90% | |
| 24. | Jan 31, 2023 | $344.15 | -5.93% | 4,076.60 | 6.18% | |
| 25. | Feb 28, 2023 | $311.22 | $1.13 | -9.24% | 3,970.15 | -2.61% |
| 26. | Mar 31, 2023 | $343.42 | 10.35% | 4,109.31 | 3.51% | |
| 27. | Apr 30, 2023 | $395.86 | 15.27% | 4,169.48 | 1.46% | |
| 28. | May 31, 2023 | $429.46 | $1.13 | 8.77% | 4,179.83 | 0.25% |
| 29. | Jun 30, 2023 | $468.98 | 9.20% | 4,376.86 | 4.71% | |
| 30. | Jul 31, 2023 | $454.55 | -3.08% | 4,588.96 | 4.85% | |
| 31. | Aug 31, 2023 | $554.20 | $1.13 | 22.17% | 4,507.66 | -1.77% |
| 32. | Sep 30, 2023 | $537.13 | -3.08% | 4,288.05 | -4.87% | |
| 33. | Oct 31, 2023 | $553.93 | 3.13% | 4,193.80 | -2.20% | |
| 34. | Nov 30, 2023 | $591.04 | $1.13 | 6.90% | 4,567.80 | 8.92% |
| 35. | Dec 31, 2023 | $582.92 | -1.37% | 4,769.83 | 4.42% | |
| 36. | Jan 31, 2024 | $645.61 | 10.75% | 4,845.65 | 1.59% | |
| 37. | Feb 29, 2024 | $753.68 | $1.30 | 16.94% | 5,096.27 | 5.17% |
| 38. | Mar 31, 2024 | $777.96 | 3.22% | 5,254.35 | 3.10% | |
| 39. | Apr 30, 2024 | $781.10 | 0.40% | 5,035.69 | -4.16% | |
| 40. | May 31, 2024 | $820.34 | $1.30 | 5.19% | 5,277.51 | 4.80% |
| 41. | Jun 30, 2024 | $905.38 | 10.37% | 5,460.48 | 3.47% | |
| 42. | Jul 31, 2024 | $804.27 | -11.17% | 5,522.30 | 1.13% | |
| 43. | Aug 31, 2024 | $960.02 | $1.30 | 19.53% | 5,648.40 | 2.28% |
| 44. | Sep 30, 2024 | $885.94 | -7.72% | 5,762.48 | 2.02% | |
| 45. | Oct 31, 2024 | $829.74 | -6.34% | 5,705.45 | -0.99% | |
| 46. | Nov 30, 2024 | $795.35 | $1.30 | -3.99% | 6,032.38 | 5.73% |
| 47. | Dec 31, 2024 | $772.00 | -2.94% | 5,881.63 | -2.50% | |
| 48. | Jan 31, 2025 | $811.08 | 5.06% | 6,040.53 | 2.70% | |
| 49. | Feb 28, 2025 | $920.63 | $1.50 | 13.69% | 5,954.50 | -1.42% |
| 50. | Mar 31, 2025 | $825.91 | -10.29% | 5,611.85 | -5.75% | |
| 51. | Apr 30, 2025 | $898.95 | 8.84% | 5,569.06 | -0.76% | |
| 52. | May 31, 2025 | $737.67 | $1.50 | -17.77% | 5,911.69 | 6.15% |
| 53. | Jun 30, 2025 | $779.53 | 5.67% | 6,204.95 | 4.96% | |
| 54. | Jul 31, 2025 | $740.07 | -5.06% | 6,339.39 | 2.17% | |
| 55. | Aug 31, 2025 | $732.58 | $1.50 | -0.81% | 6,460.26 | 1.91% |
| 56. | Sep 30, 2025 | $763.00 | 4.15% | 6,688.46 | 3.53% | |
| 57. | Oct 31, 2025 | $862.86 | 13.09% | 6,840.20 | 2.27% | |
| 58. | Nov 30, 2025 | $1,075.47 | $1.50 | 24.81% | 6,849.09 | 0.13% |
| 59. | Dec 31, 2025 | $1,074.68 | -0.07% | 6,845.50 | -0.05% | |
| Average (R): | 3.31% | 1.14% | ||||
| Standard deviation: | 9.12% | 4.37% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of LLY during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Eli Lilly & Co., calculation of variance and covariance of returns
| t | Date | RLLY,t | RS&P 500,t | (RLLY,t–RLLY)2 | (RS&P 500,t–RS&P 500)2 | (RLLY,t–RLLY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2021 | -1.07% | 2.61% | 19.21 | 2.17 | -6.46 |
| 2. | Mar 31, 2021 | -8.82% | 4.24% | 147.13 | 9.66 | -37.70 |
| 3. | Apr 30, 2021 | -2.17% | 5.24% | 30.01 | 16.86 | -22.50 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | 24.81% | 0.13% | 462.40 | 1.01 | -21.64 |
| 59. | Dec 31, 2025 | -0.07% | -0.05% | 11.45 | 1.41 | 4.02 |
| Total (Σ): | 4,825.10 | 1,108.23 | 410.84 | |||
| t | Date | RLLY,t | RS&P 500,t | (RLLY,t–RLLY)2 | (RS&P 500,t–RS&P 500)2 | (RLLY,t–RLLY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2021 | -1.07% | 2.61% | 19.21 | 2.17 | -6.46 |
| 2. | Mar 31, 2021 | -8.82% | 4.24% | 147.13 | 9.66 | -37.70 |
| 3. | Apr 30, 2021 | -2.17% | 5.24% | 30.01 | 16.86 | -22.50 |
| 4. | May 31, 2021 | 9.75% | 0.55% | 41.47 | 0.35 | -3.78 |
| 5. | Jun 30, 2021 | 14.91% | 2.22% | 134.53 | 1.18 | 12.59 |
| 6. | Jul 31, 2021 | 6.09% | 2.27% | 7.73 | 1.30 | 3.17 |
| 7. | Aug 31, 2021 | 6.42% | 2.90% | 9.69 | 3.11 | 5.49 |
| 8. | Sep 30, 2021 | -10.55% | -4.76% | 192.01 | 34.73 | 81.66 |
| 9. | Oct 31, 2021 | 10.26% | 6.91% | 48.32 | 33.39 | 40.17 |
| 10. | Nov 30, 2021 | -2.30% | -0.83% | 31.52 | 3.88 | 11.06 |
| 11. | Dec 31, 2021 | 11.36% | 4.36% | 64.81 | 10.40 | 25.96 |
| 12. | Jan 31, 2022 | -11.16% | -5.26% | 209.43 | 40.89 | 92.54 |
| 13. | Feb 28, 2022 | 2.26% | -3.14% | 1.11 | 18.25 | 4.50 |
| 14. | Mar 31, 2022 | 14.57% | 3.58% | 126.80 | 5.96 | 27.49 |
| 15. | Apr 30, 2022 | 2.01% | -8.80% | 1.69 | 98.64 | 12.90 |
| 16. | May 31, 2022 | 7.63% | 0.01% | 18.66 | 1.28 | -4.88 |
| 17. | Jun 30, 2022 | 3.44% | -8.39% | 0.02 | 90.79 | -1.26 |
| 18. | Jul 31, 2022 | 1.68% | 9.11% | 2.65 | 63.61 | -12.97 |
| 19. | Aug 31, 2022 | -8.34% | -4.24% | 135.62 | 28.95 | 62.65 |
| 20. | Sep 30, 2022 | 7.34% | -9.34% | 16.26 | 109.74 | -42.25 |
| 21. | Oct 31, 2022 | 11.98% | 7.99% | 75.18 | 46.93 | 59.39 |
| 22. | Nov 30, 2022 | 2.75% | 5.38% | 0.31 | 17.97 | -2.36 |
| 23. | Dec 31, 2022 | -1.41% | -5.90% | 22.30 | 49.47 | 33.22 |
| 24. | Jan 31, 2023 | -5.93% | 6.18% | 85.36 | 25.39 | -46.56 |
| 25. | Feb 28, 2023 | -9.24% | -2.61% | 157.52 | 14.04 | 47.03 |
| 26. | Mar 31, 2023 | 10.35% | 3.51% | 49.50 | 5.61 | 16.67 |
| 27. | Apr 30, 2023 | 15.27% | 1.46% | 143.03 | 0.11 | 3.92 |
| 28. | May 31, 2023 | 8.77% | 0.25% | 29.84 | 0.79 | -4.85 |
| 29. | Jun 30, 2023 | 9.20% | 4.71% | 34.71 | 12.80 | 21.08 |
| 30. | Jul 31, 2023 | -3.08% | 4.85% | 40.80 | 13.76 | -23.70 |
| 31. | Aug 31, 2023 | 22.17% | -1.77% | 355.73 | 8.46 | -54.84 |
| 32. | Sep 30, 2023 | -3.08% | -4.87% | 40.84 | 36.10 | 38.39 |
| 33. | Oct 31, 2023 | 3.13% | -2.20% | 0.03 | 11.12 | 0.61 |
| 34. | Nov 30, 2023 | 6.90% | 8.92% | 12.91 | 60.56 | 27.96 |
| 35. | Dec 31, 2023 | -1.37% | 4.42% | 21.94 | 10.80 | -15.40 |
| 36. | Jan 31, 2024 | 10.75% | 1.59% | 55.41 | 0.21 | 3.38 |
| 37. | Feb 29, 2024 | 16.94% | 5.17% | 185.78 | 16.29 | 55.01 |
| 38. | Mar 31, 2024 | 3.22% | 3.10% | 0.01 | 3.86 | -0.17 |
| 39. | Apr 30, 2024 | 0.40% | -4.16% | 8.45 | 28.06 | 15.40 |
| 40. | May 31, 2024 | 5.19% | 4.80% | 3.53 | 13.44 | 6.89 |
| 41. | Jun 30, 2024 | 10.37% | 3.47% | 49.79 | 5.43 | 16.45 |
| 42. | Jul 31, 2024 | -11.17% | 1.13% | 209.62 | 0.00 | 0.06 |
| 43. | Aug 31, 2024 | 19.53% | 2.28% | 262.98 | 1.32 | 18.61 |
| 44. | Sep 30, 2024 | -7.72% | 2.02% | 121.59 | 0.78 | -9.74 |
| 45. | Oct 31, 2024 | -6.34% | -0.99% | 93.20 | 4.52 | 20.52 |
| 46. | Nov 30, 2024 | -3.99% | 5.73% | 53.27 | 21.10 | -33.53 |
| 47. | Dec 31, 2024 | -2.94% | -2.50% | 39.02 | 13.21 | 22.71 |
| 48. | Jan 31, 2025 | 5.06% | 2.70% | 3.07 | 2.45 | 2.74 |
| 49. | Feb 28, 2025 | 13.69% | -1.42% | 107.77 | 6.56 | -26.58 |
| 50. | Mar 31, 2025 | -10.29% | -5.75% | 184.93 | 47.48 | 93.71 |
| 51. | Apr 30, 2025 | 8.84% | -0.76% | 30.62 | 3.60 | -10.51 |
| 52. | May 31, 2025 | -17.77% | 6.15% | 444.56 | 25.16 | -105.77 |
| 53. | Jun 30, 2025 | 5.67% | 4.96% | 5.59 | 14.63 | 9.04 |
| 54. | Jul 31, 2025 | -5.06% | 2.17% | 70.10 | 1.06 | -8.63 |
| 55. | Aug 31, 2025 | -0.81% | 1.91% | 16.97 | 0.59 | -3.17 |
| 56. | Sep 30, 2025 | 4.15% | 3.53% | 0.71 | 5.74 | 2.02 |
| 57. | Oct 31, 2025 | 13.09% | 2.27% | 95.60 | 1.28 | 11.07 |
| 58. | Nov 30, 2025 | 24.81% | 0.13% | 462.40 | 1.01 | -21.64 |
| 59. | Dec 31, 2025 | -0.07% | -0.05% | 11.45 | 1.41 | 4.02 |
| Total (Σ): | 4,825.10 | 1,108.23 | 410.84 | |||
Show all
VarianceLLY = Σ(RLLY,t–RLLY)2 ÷ (59 – 1)
= 4,825.10 ÷ (59 – 1)
= 83.19
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
CovarianceLLY, S&P 500 = Σ(RLLY,t–RLLY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 410.84 ÷ (59 – 1)
= 7.08
Systematic Risk (β) Estimation
| VarianceLLY | 83.19 |
| VarianceS&P 500 | 19.11 |
| CovarianceLLY, S&P 500 | 7.08 |
| Correlation coefficientLLY, S&P 5001 | 0.18 |
| βLLY2 | 0.37 |
| αLLY3 | 2.89% |
Calculations
1 Correlation coefficientLLY, S&P 500
= CovarianceLLY, S&P 500 ÷ (Standard deviationLLY × Standard deviationS&P 500)
= 7.08 ÷ (9.12% × 4.37%)
= 0.18
2 βLLY
= CovarianceLLY, S&P 500 ÷ VarianceS&P 500
= 7.08 ÷ 19.11
= 0.37
3 αLLY
= AverageLLY – βLLY × AverageS&P 500
= 3.31% – 0.37 × 1.14%
= 2.89%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.84% |
| Expected rate of return on market portfolio2 | E(RM) | 17.37% |
| Systematic risk (β) of Eli Lilly & Co. common stock | βLLY | 0.37 |
| Expected rate of return on Eli Lilly & Co. common stock3 | E(RLLY) | 9.48% |
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(RLLY) = RF + βLLY [E(RM) – RF]
= 4.84% + 0.37 [17.37% – 4.84%]
= 9.48%