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, 2020 | $139.64 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $126.13 | $0.74 | -9.14% | 2,954.22 | -8.41% |
| 2. | Mar 31, 2020 | $138.72 | 9.98% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $154.64 | 11.48% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | $795.35 | $1.30 | -3.99% | 6,032.38 | 5.73% |
| 59. | Dec 31, 2024 | $772.00 | -2.94% | 5,881.63 | -2.50% | |
| Average (R): | 3.44% | 1.16% | ||||
| Standard deviation: | 9.02% | 5.28% | ||||
| 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, 2020 | $139.64 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $126.13 | $0.74 | -9.14% | 2,954.22 | -8.41% |
| 2. | Mar 31, 2020 | $138.72 | 9.98% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $154.64 | 11.48% | 2,912.43 | 12.68% | |
| 4. | May 31, 2020 | $152.95 | $0.74 | -0.61% | 3,044.31 | 4.53% |
| 5. | Jun 30, 2020 | $164.18 | 7.34% | 3,100.29 | 1.84% | |
| 6. | Jul 31, 2020 | $150.29 | -8.46% | 3,271.12 | 5.51% | |
| 7. | Aug 31, 2020 | $148.39 | $0.74 | -0.77% | 3,500.31 | 7.01% |
| 8. | Sep 30, 2020 | $148.02 | -0.25% | 3,363.00 | -3.92% | |
| 9. | Oct 31, 2020 | $130.46 | -11.86% | 3,269.96 | -2.77% | |
| 10. | Nov 30, 2020 | $145.65 | $0.74 | 12.21% | 3,621.63 | 10.75% |
| 11. | Dec 31, 2020 | $168.84 | 15.92% | 3,756.07 | 3.71% | |
| 12. | Jan 31, 2021 | $207.97 | 23.18% | 3,714.24 | -1.11% | |
| 13. | Feb 28, 2021 | $204.89 | $0.85 | -1.07% | 3,811.15 | 2.61% |
| 14. | Mar 31, 2021 | $186.82 | -8.82% | 3,972.89 | 4.24% | |
| 15. | Apr 30, 2021 | $182.77 | -2.17% | 4,181.17 | 5.24% | |
| 16. | May 31, 2021 | $199.74 | $0.85 | 9.75% | 4,204.11 | 0.55% |
| 17. | Jun 30, 2021 | $229.52 | 14.91% | 4,297.50 | 2.22% | |
| 18. | Jul 31, 2021 | $243.50 | 6.09% | 4,395.26 | 2.27% | |
| 19. | Aug 31, 2021 | $258.29 | $0.85 | 6.42% | 4,522.68 | 2.90% |
| 20. | Sep 30, 2021 | $231.05 | -10.55% | 4,307.54 | -4.76% | |
| 21. | Oct 31, 2021 | $254.76 | 10.26% | 4,605.38 | 6.91% | |
| 22. | Nov 30, 2021 | $248.04 | $0.85 | -2.30% | 4,567.00 | -0.83% |
| 23. | Dec 31, 2021 | $276.22 | 11.36% | 4,766.18 | 4.36% | |
| 24. | Jan 31, 2022 | $245.39 | -11.16% | 4,515.55 | -5.26% | |
| 25. | Feb 28, 2022 | $249.95 | $0.98 | 2.26% | 4,373.94 | -3.14% |
| 26. | Mar 31, 2022 | $286.37 | 14.57% | 4,530.41 | 3.58% | |
| 27. | Apr 30, 2022 | $292.13 | 2.01% | 4,131.93 | -8.80% | |
| 28. | May 31, 2022 | $313.44 | $0.98 | 7.63% | 4,132.15 | 0.01% |
| 29. | Jun 30, 2022 | $324.23 | 3.44% | 3,785.38 | -8.39% | |
| 30. | Jul 31, 2022 | $329.69 | 1.68% | 4,130.29 | 9.11% | |
| 31. | Aug 31, 2022 | $301.23 | $0.98 | -8.34% | 3,955.00 | -4.24% |
| 32. | Sep 30, 2022 | $323.35 | 7.34% | 3,585.62 | -9.34% | |
| 33. | Oct 31, 2022 | $362.09 | 11.98% | 3,871.98 | 7.99% | |
| 34. | Nov 30, 2022 | $371.08 | $0.98 | 2.75% | 4,080.11 | 5.38% |
| 35. | Dec 31, 2022 | $365.84 | -1.41% | 3,839.50 | -5.90% | |
| 36. | Jan 31, 2023 | $344.15 | -5.93% | 4,076.60 | 6.18% | |
| 37. | Feb 28, 2023 | $311.22 | $1.13 | -9.24% | 3,970.15 | -2.61% |
| 38. | Mar 31, 2023 | $343.42 | 10.35% | 4,109.31 | 3.51% | |
| 39. | Apr 30, 2023 | $395.86 | 15.27% | 4,169.48 | 1.46% | |
| 40. | May 31, 2023 | $429.46 | $1.13 | 8.77% | 4,179.83 | 0.25% |
| 41. | Jun 30, 2023 | $468.98 | 9.20% | 4,376.86 | 4.71% | |
| 42. | Jul 31, 2023 | $454.55 | -3.08% | 4,588.96 | 4.85% | |
| 43. | Aug 31, 2023 | $554.20 | $1.13 | 22.17% | 4,507.66 | -1.77% |
| 44. | Sep 30, 2023 | $537.13 | -3.08% | 4,288.05 | -4.87% | |
| 45. | Oct 31, 2023 | $553.93 | 3.13% | 4,193.80 | -2.20% | |
| 46. | Nov 30, 2023 | $591.04 | $1.13 | 6.90% | 4,567.80 | 8.92% |
| 47. | Dec 31, 2023 | $582.92 | -1.37% | 4,769.83 | 4.42% | |
| 48. | Jan 31, 2024 | $645.61 | 10.75% | 4,845.65 | 1.59% | |
| 49. | Feb 29, 2024 | $753.68 | $1.30 | 16.94% | 5,096.27 | 5.17% |
| 50. | Mar 31, 2024 | $777.96 | 3.22% | 5,254.35 | 3.10% | |
| 51. | Apr 30, 2024 | $781.10 | 0.40% | 5,035.69 | -4.16% | |
| 52. | May 31, 2024 | $820.34 | $1.30 | 5.19% | 5,277.51 | 4.80% |
| 53. | Jun 30, 2024 | $905.38 | 10.37% | 5,460.48 | 3.47% | |
| 54. | Jul 31, 2024 | $804.27 | -11.17% | 5,522.30 | 1.13% | |
| 55. | Aug 31, 2024 | $960.02 | $1.30 | 19.53% | 5,648.40 | 2.28% |
| 56. | Sep 30, 2024 | $885.94 | -7.72% | 5,762.48 | 2.02% | |
| 57. | Oct 31, 2024 | $829.74 | -6.34% | 5,705.45 | -0.99% | |
| 58. | Nov 30, 2024 | $795.35 | $1.30 | -3.99% | 6,032.38 | 5.73% |
| 59. | Dec 31, 2024 | $772.00 | -2.94% | 5,881.63 | -2.50% | |
| Average (R): | 3.44% | 1.16% | ||||
| Standard deviation: | 9.02% | 5.28% | ||||
Show all
1 Data in US$ 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 29, 2020 | -9.14% | -8.41% | 158.40 | 91.63 | 120.47 |
| 2. | Mar 31, 2020 | 9.98% | -12.51% | 42.79 | 186.96 | -89.44 |
| 3. | Apr 30, 2020 | 11.48% | 12.68% | 64.57 | 132.78 | 92.60 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | -3.99% | 5.73% | 55.19 | 20.87 | -33.94 |
| 59. | Dec 31, 2024 | -2.94% | -2.50% | 40.66 | 13.40 | 23.34 |
| Total (Σ): | 4,719.33 | 1,618.62 | 651.19 | |||
| 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 29, 2020 | -9.14% | -8.41% | 158.40 | 91.63 | 120.47 |
| 2. | Mar 31, 2020 | 9.98% | -12.51% | 42.79 | 186.96 | -89.44 |
| 3. | Apr 30, 2020 | 11.48% | 12.68% | 64.57 | 132.78 | 92.60 |
| 4. | May 31, 2020 | -0.61% | 4.53% | 16.44 | 11.34 | -13.65 |
| 5. | Jun 30, 2020 | 7.34% | 1.84% | 15.22 | 0.46 | 2.64 |
| 6. | Jul 31, 2020 | -8.46% | 5.51% | 141.63 | 18.91 | -51.76 |
| 7. | Aug 31, 2020 | -0.77% | 7.01% | 17.75 | 34.17 | -24.62 |
| 8. | Sep 30, 2020 | -0.25% | -3.92% | 13.62 | 25.85 | 18.76 |
| 9. | Oct 31, 2020 | -11.86% | -2.77% | 234.21 | 15.43 | 60.11 |
| 10. | Nov 30, 2020 | 12.21% | 10.75% | 76.91 | 92.03 | 84.13 |
| 11. | Dec 31, 2020 | 15.92% | 3.71% | 155.78 | 6.51 | 31.84 |
| 12. | Jan 31, 2021 | 23.18% | -1.11% | 389.47 | 5.18 | -44.90 |
| 13. | Feb 28, 2021 | -1.07% | 2.61% | 20.37 | 2.10 | -6.53 |
| 14. | Mar 31, 2021 | -8.82% | 4.24% | 150.31 | 9.50 | -37.79 |
| 15. | Apr 30, 2021 | -2.17% | 5.24% | 31.46 | 16.66 | -22.89 |
| 16. | May 31, 2021 | 9.75% | 0.55% | 39.81 | 0.38 | -3.87 |
| 17. | Jun 30, 2021 | 14.91% | 2.22% | 131.53 | 1.12 | 12.16 |
| 18. | Jul 31, 2021 | 6.09% | 2.27% | 7.02 | 1.24 | 2.95 |
| 19. | Aug 31, 2021 | 6.42% | 2.90% | 8.89 | 3.02 | 5.18 |
| 20. | Sep 30, 2021 | -10.55% | -4.76% | 195.64 | 35.02 | 82.78 |
| 21. | Oct 31, 2021 | 10.26% | 6.91% | 46.53 | 33.10 | 39.24 |
| 22. | Nov 30, 2021 | -2.30% | -0.83% | 33.00 | 3.98 | 11.46 |
| 23. | Dec 31, 2021 | 11.36% | 4.36% | 62.73 | 10.24 | 25.35 |
| 24. | Jan 31, 2022 | -11.16% | -5.26% | 213.22 | 41.21 | 93.74 |
| 25. | Feb 28, 2022 | 2.26% | -3.14% | 1.40 | 18.47 | 5.08 |
| 26. | Mar 31, 2022 | 14.57% | 3.58% | 123.88 | 5.84 | 26.89 |
| 27. | Apr 30, 2022 | 2.01% | -8.80% | 2.04 | 99.14 | 14.23 |
| 28. | May 31, 2022 | 7.63% | 0.01% | 17.55 | 1.34 | -4.84 |
| 29. | Jun 30, 2022 | 3.44% | -8.39% | 0.00 | 91.26 | -0.02 |
| 30. | Jul 31, 2022 | 1.68% | 9.11% | 3.09 | 63.21 | -13.97 |
| 31. | Aug 31, 2022 | -8.34% | -4.24% | 138.67 | 29.22 | 63.65 |
| 32. | Sep 30, 2022 | 7.34% | -9.34% | 15.23 | 110.27 | -40.98 |
| 33. | Oct 31, 2022 | 11.98% | 7.99% | 72.93 | 46.58 | 58.29 |
| 34. | Nov 30, 2022 | 2.75% | 5.38% | 0.47 | 17.76 | -2.90 |
| 35. | Dec 31, 2022 | -1.41% | -5.90% | 23.55 | 49.82 | 34.25 |
| 36. | Jan 31, 2023 | -5.93% | 6.18% | 87.79 | 25.14 | -46.98 |
| 37. | Feb 28, 2023 | -9.24% | -2.61% | 160.80 | 14.23 | 47.84 |
| 38. | Mar 31, 2023 | 10.35% | 3.51% | 47.69 | 5.49 | 16.19 |
| 39. | Apr 30, 2023 | 15.27% | 1.46% | 139.93 | 0.09 | 3.58 |
| 40. | May 31, 2023 | 8.77% | 0.25% | 28.44 | 0.83 | -4.87 |
| 41. | Jun 30, 2023 | 9.20% | 4.71% | 33.20 | 12.62 | 20.47 |
| 42. | Jul 31, 2023 | -3.08% | 4.85% | 42.48 | 13.58 | -24.02 |
| 43. | Aug 31, 2023 | 22.17% | -1.77% | 350.84 | 8.60 | -54.94 |
| 44. | Sep 30, 2023 | -3.08% | -4.87% | 42.52 | 36.40 | 39.34 |
| 45. | Oct 31, 2023 | 3.13% | -2.20% | 0.10 | 11.28 | 1.05 |
| 46. | Nov 30, 2023 | 6.90% | 8.92% | 11.99 | 60.17 | 26.86 |
| 47. | Dec 31, 2023 | -1.37% | 4.42% | 23.18 | 10.64 | -15.70 |
| 48. | Jan 31, 2024 | 10.75% | 1.59% | 53.49 | 0.18 | 3.13 |
| 49. | Feb 29, 2024 | 16.94% | 5.17% | 182.25 | 16.09 | 54.14 |
| 50. | Mar 31, 2024 | 3.22% | 3.10% | 0.05 | 3.77 | -0.43 |
| 51. | Apr 30, 2024 | 0.40% | -4.16% | 9.22 | 28.33 | 16.17 |
| 52. | May 31, 2024 | 5.19% | 4.80% | 3.06 | 13.26 | 6.37 |
| 53. | Jun 30, 2024 | 10.37% | 3.47% | 47.97 | 5.32 | 15.97 |
| 54. | Jul 31, 2024 | -11.17% | 1.13% | 213.41 | 0.00 | 0.43 |
| 55. | Aug 31, 2024 | 19.53% | 2.28% | 258.77 | 1.26 | 18.05 |
| 56. | Sep 30, 2024 | -7.72% | 2.02% | 124.48 | 0.74 | -9.58 |
| 57. | Oct 31, 2024 | -6.34% | -0.99% | 95.73 | 4.63 | 21.05 |
| 58. | Nov 30, 2024 | -3.99% | 5.73% | 55.19 | 20.87 | -33.94 |
| 59. | Dec 31, 2024 | -2.94% | -2.50% | 40.66 | 13.40 | 23.34 |
| Total (Σ): | 4,719.33 | 1,618.62 | 651.19 | |||
Show all
VarianceLLY = Σ(RLLY,t–RLLY)2 ÷ (59 – 1)
= 4,719.33 ÷ (59 – 1)
= 81.37
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
CovarianceLLY, S&P 500 = Σ(RLLY,t–RLLY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 651.19 ÷ (59 – 1)
= 11.23
Systematic Risk (β) Estimation
| VarianceLLY | 81.37 |
| VarianceS&P 500 | 27.91 |
| CovarianceLLY, S&P 500 | 11.23 |
| Correlation coefficientLLY, S&P 5001 | 0.24 |
| βLLY2 | 0.40 |
| αLLY3 | 2.97% |
Calculations
1 Correlation coefficientLLY, S&P 500
= CovarianceLLY, S&P 500 ÷ (Standard deviationLLY × Standard deviationS&P 500)
= 11.23 ÷ (9.02% × 5.28%)
= 0.24
2 βLLY
= CovarianceLLY, S&P 500 ÷ VarianceS&P 500
= 11.23 ÷ 27.91
= 0.40
3 αLLY
= AverageLLY – βLLY × AverageS&P 500
= 3.44% – 0.40 × 1.16%
= 2.97%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.78% |
| Expected rate of return on market portfolio2 | E(RM) | 14.43% |
| Systematic risk (β) of Eli Lilly & Co. common stock | βLLY | 0.40 |
| Expected rate of return on Eli Lilly & Co. common stock3 | E(RLLY) | 8.66% |
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]
= 4.78% + 0.40 [14.43% – 4.78%]
= 8.66%