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 Coca-Cola Co. common stock.
Rates of Return
Coca-Cola Co., monthly rates of return
| Coca-Cola Co. (KO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceKO,t1 | DividendKO,t1 | RKO,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2019 | $48.13 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $45.34 | -5.80% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $46.86 | $0.40 | 4.23% | 2,834.40 | 1.79% |
| 3. | Apr 30, 2019 | $49.06 | 4.69% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | $58.44 | $0.46 | 4.27% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $58.93 | 0.84% | 4,769.83 | 4.42% | |
| Average (R): | 0.75% | 1.11% | ||||
| Standard deviation: | 5.33% | 5.31% | ||||
| Coca-Cola Co. (KO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceKO,t1 | DividendKO,t1 | RKO,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2019 | $48.13 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $45.34 | -5.80% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $46.86 | $0.40 | 4.23% | 2,834.40 | 1.79% |
| 3. | Apr 30, 2019 | $49.06 | 4.69% | 2,945.83 | 3.93% | |
| 4. | May 31, 2019 | $49.13 | 0.14% | 2,752.06 | -6.58% | |
| 5. | Jun 30, 2019 | $50.92 | $0.40 | 4.46% | 2,941.76 | 6.89% |
| 6. | Jul 31, 2019 | $52.63 | 3.36% | 2,980.38 | 1.31% | |
| 7. | Aug 31, 2019 | $55.04 | 4.58% | 2,926.46 | -1.81% | |
| 8. | Sep 30, 2019 | $54.44 | $0.40 | -0.36% | 2,976.74 | 1.72% |
| 9. | Oct 31, 2019 | $54.43 | -0.02% | 3,037.56 | 2.04% | |
| 10. | Nov 30, 2019 | $53.40 | $0.40 | -1.16% | 3,140.98 | 3.40% |
| 11. | Dec 31, 2019 | $55.35 | 3.65% | 3,230.78 | 2.86% | |
| 12. | Jan 31, 2020 | $58.40 | 5.51% | 3,225.52 | -0.16% | |
| 13. | Feb 29, 2020 | $53.49 | -8.41% | 2,954.22 | -8.41% | |
| 14. | Mar 31, 2020 | $44.25 | $0.41 | -16.51% | 2,584.59 | -12.51% |
| 15. | Apr 30, 2020 | $45.89 | 3.71% | 2,912.43 | 12.68% | |
| 16. | May 31, 2020 | $46.68 | 1.72% | 3,044.31 | 4.53% | |
| 17. | Jun 30, 2020 | $44.68 | $0.41 | -3.41% | 3,100.29 | 1.84% |
| 18. | Jul 31, 2020 | $47.24 | 5.73% | 3,271.12 | 5.51% | |
| 19. | Aug 31, 2020 | $49.53 | 4.85% | 3,500.31 | 7.01% | |
| 20. | Sep 30, 2020 | $49.37 | $0.41 | 0.50% | 3,363.00 | -3.92% |
| 21. | Oct 31, 2020 | $48.06 | -2.65% | 3,269.96 | -2.77% | |
| 22. | Nov 30, 2020 | $51.60 | $0.41 | 8.22% | 3,621.63 | 10.75% |
| 23. | Dec 31, 2020 | $54.84 | 6.28% | 3,756.07 | 3.71% | |
| 24. | Jan 31, 2021 | $48.15 | -12.20% | 3,714.24 | -1.11% | |
| 25. | Feb 28, 2021 | $48.99 | 1.74% | 3,811.15 | 2.61% | |
| 26. | Mar 31, 2021 | $52.71 | $0.42 | 8.45% | 3,972.89 | 4.24% |
| 27. | Apr 30, 2021 | $53.98 | 2.41% | 4,181.17 | 5.24% | |
| 28. | May 31, 2021 | $55.29 | 2.43% | 4,204.11 | 0.55% | |
| 29. | Jun 30, 2021 | $54.11 | $0.42 | -1.37% | 4,297.50 | 2.22% |
| 30. | Jul 31, 2021 | $57.03 | 5.40% | 4,395.26 | 2.27% | |
| 31. | Aug 31, 2021 | $56.31 | -1.26% | 4,522.68 | 2.90% | |
| 32. | Sep 30, 2021 | $52.47 | $0.42 | -6.07% | 4,307.54 | -4.76% |
| 33. | Oct 31, 2021 | $56.37 | 7.43% | 4,605.38 | 6.91% | |
| 34. | Nov 30, 2021 | $52.45 | $0.42 | -6.21% | 4,567.00 | -0.83% |
| 35. | Dec 31, 2021 | $59.21 | 12.89% | 4,766.18 | 4.36% | |
| 36. | Jan 31, 2022 | $61.01 | 3.04% | 4,515.55 | -5.26% | |
| 37. | Feb 28, 2022 | $62.24 | 2.02% | 4,373.94 | -3.14% | |
| 38. | Mar 31, 2022 | $62.00 | $0.44 | 0.32% | 4,530.41 | 3.58% |
| 39. | Apr 30, 2022 | $64.61 | 4.21% | 4,131.93 | -8.80% | |
| 40. | May 31, 2022 | $63.38 | -1.90% | 4,132.15 | 0.01% | |
| 41. | Jun 30, 2022 | $62.91 | $0.44 | -0.05% | 3,785.38 | -8.39% |
| 42. | Jul 31, 2022 | $64.17 | 2.00% | 4,130.29 | 9.11% | |
| 43. | Aug 31, 2022 | $61.71 | -3.83% | 3,955.00 | -4.24% | |
| 44. | Sep 30, 2022 | $56.02 | $0.44 | -8.51% | 3,585.62 | -9.34% |
| 45. | Oct 31, 2022 | $59.85 | 6.84% | 3,871.98 | 7.99% | |
| 46. | Nov 30, 2022 | $63.61 | $0.44 | 7.02% | 4,080.11 | 5.38% |
| 47. | Dec 31, 2022 | $63.61 | 0.00% | 3,839.50 | -5.90% | |
| 48. | Jan 31, 2023 | $61.32 | -3.60% | 4,076.60 | 6.18% | |
| 49. | Feb 28, 2023 | $59.51 | -2.95% | 3,970.15 | -2.61% | |
| 50. | Mar 31, 2023 | $62.03 | $0.46 | 5.01% | 4,109.31 | 3.51% |
| 51. | Apr 30, 2023 | $64.15 | 3.42% | 4,169.48 | 1.46% | |
| 52. | May 31, 2023 | $59.66 | -7.00% | 4,179.83 | 0.25% | |
| 53. | Jun 30, 2023 | $60.22 | $0.46 | 1.71% | 4,376.86 | 4.71% |
| 54. | Jul 31, 2023 | $61.93 | 2.84% | 4,588.96 | 4.85% | |
| 55. | Aug 31, 2023 | $59.83 | -3.39% | 4,507.66 | -1.77% | |
| 56. | Sep 30, 2023 | $55.98 | $0.46 | -5.67% | 4,288.05 | -4.87% |
| 57. | Oct 31, 2023 | $56.49 | 0.91% | 4,193.80 | -2.20% | |
| 58. | Nov 30, 2023 | $58.44 | $0.46 | 4.27% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $58.93 | 0.84% | 4,769.83 | 4.42% | |
| Average (R): | 0.75% | 1.11% | ||||
| Standard deviation: | 5.33% | 5.31% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of KO during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Coca-Cola Co., calculation of variance and covariance of returns
| t | Date | RKO,t | RS&P 500,t | (RKO,t–RKO)2 | (RS&P 500,t–RS&P 500)2 | (RKO,t–RKO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2019 | -5.80% | 2.97% | 42.91 | 3.49 | -12.23 |
| 2. | Mar 31, 2019 | 4.23% | 1.79% | 12.11 | 0.47 | 2.39 |
| 3. | Apr 30, 2019 | 4.69% | 3.93% | 15.53 | 7.98 | 11.13 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | 4.27% | 8.92% | 12.34 | 61.03 | 27.44 |
| 59. | Dec 31, 2023 | 0.84% | 4.42% | 0.01 | 11.00 | 0.28 |
| Total (Σ): | 1,647.38 | 1,634.30 | 964.04 | |||
| t | Date | RKO,t | RS&P 500,t | (RKO,t–RKO)2 | (RS&P 500,t–RS&P 500)2 | (RKO,t–RKO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2019 | -5.80% | 2.97% | 42.91 | 3.49 | -12.23 |
| 2. | Mar 31, 2019 | 4.23% | 1.79% | 12.11 | 0.47 | 2.39 |
| 3. | Apr 30, 2019 | 4.69% | 3.93% | 15.53 | 7.98 | 11.13 |
| 4. | May 31, 2019 | 0.14% | -6.58% | 0.37 | 59.04 | 4.70 |
| 5. | Jun 30, 2019 | 4.46% | 6.89% | 13.72 | 33.49 | 21.43 |
| 6. | Jul 31, 2019 | 3.36% | 1.31% | 6.78 | 0.04 | 0.54 |
| 7. | Aug 31, 2019 | 4.58% | -1.81% | 14.63 | 8.50 | -11.15 |
| 8. | Sep 30, 2019 | -0.36% | 1.72% | 1.25 | 0.37 | -0.68 |
| 9. | Oct 31, 2019 | -0.02% | 2.04% | 0.60 | 0.88 | -0.72 |
| 10. | Nov 30, 2019 | -1.16% | 3.40% | 3.65 | 5.28 | -4.39 |
| 11. | Dec 31, 2019 | 3.65% | 2.86% | 8.40 | 3.07 | 5.08 |
| 12. | Jan 31, 2020 | 5.51% | -0.16% | 22.62 | 1.61 | -6.03 |
| 13. | Feb 29, 2020 | -8.41% | -8.41% | 83.94 | 90.57 | 87.19 |
| 14. | Mar 31, 2020 | -16.51% | -12.51% | 297.97 | 185.44 | 235.07 |
| 15. | Apr 30, 2020 | 3.71% | 12.68% | 8.72 | 134.06 | 34.18 |
| 16. | May 31, 2020 | 1.72% | 4.53% | 0.94 | 11.71 | 3.31 |
| 17. | Jun 30, 2020 | -3.41% | 1.84% | 17.31 | 0.54 | -3.05 |
| 18. | Jul 31, 2020 | 5.73% | 5.51% | 24.76 | 19.40 | 21.91 |
| 19. | Aug 31, 2020 | 4.85% | 7.01% | 16.76 | 34.82 | 24.15 |
| 20. | Sep 30, 2020 | 0.50% | -3.92% | 0.06 | 25.29 | 1.25 |
| 21. | Oct 31, 2020 | -2.65% | -2.77% | 11.61 | 15.00 | 13.20 |
| 22. | Nov 30, 2020 | 8.22% | 10.75% | 55.72 | 93.10 | 72.03 |
| 23. | Dec 31, 2020 | 6.28% | 3.71% | 30.53 | 6.79 | 14.40 |
| 24. | Jan 31, 2021 | -12.20% | -1.11% | 167.79 | 4.93 | 28.75 |
| 25. | Feb 28, 2021 | 1.74% | 2.61% | 0.98 | 2.26 | 1.49 |
| 26. | Mar 31, 2021 | 8.45% | 4.24% | 59.24 | 9.85 | 24.15 |
| 27. | Apr 30, 2021 | 2.41% | 5.24% | 2.74 | 17.11 | 6.85 |
| 28. | May 31, 2021 | 2.43% | 0.55% | 2.80 | 0.31 | -0.93 |
| 29. | Jun 30, 2021 | -1.37% | 2.22% | 4.53 | 1.24 | -2.37 |
| 30. | Jul 31, 2021 | 5.40% | 2.27% | 21.55 | 1.37 | 5.43 |
| 31. | Aug 31, 2021 | -1.26% | 2.90% | 4.07 | 3.22 | -3.62 |
| 32. | Sep 30, 2021 | -6.07% | -4.76% | 46.62 | 34.37 | 40.03 |
| 33. | Oct 31, 2021 | 7.43% | 6.91% | 44.61 | 33.74 | 38.79 |
| 34. | Nov 30, 2021 | -6.21% | -0.83% | 48.48 | 3.76 | 13.50 |
| 35. | Dec 31, 2021 | 12.89% | 4.36% | 147.24 | 10.60 | 39.50 |
| 36. | Jan 31, 2022 | 3.04% | -5.26% | 5.23 | 40.51 | -14.55 |
| 37. | Feb 28, 2022 | 2.02% | -3.14% | 1.59 | 17.99 | -5.35 |
| 38. | Mar 31, 2022 | 0.32% | 3.58% | 0.19 | 6.11 | -1.07 |
| 39. | Apr 30, 2022 | 4.21% | -8.80% | 11.94 | 98.04 | -34.22 |
| 40. | May 31, 2022 | -1.90% | 0.01% | 7.06 | 1.21 | 2.92 |
| 41. | Jun 30, 2022 | -0.05% | -8.39% | 0.64 | 90.21 | 7.61 |
| 42. | Jul 31, 2022 | 2.00% | 9.11% | 1.56 | 64.09 | 10.00 |
| 43. | Aug 31, 2022 | -3.83% | -4.24% | 21.05 | 28.62 | 24.54 |
| 44. | Sep 30, 2022 | -8.51% | -9.34% | 85.78 | 109.11 | 96.74 |
| 45. | Oct 31, 2022 | 6.84% | 7.99% | 37.00 | 47.34 | 41.85 |
| 46. | Nov 30, 2022 | 7.02% | 5.38% | 39.23 | 18.23 | 26.74 |
| 47. | Dec 31, 2022 | 0.00% | -5.90% | 0.57 | 49.04 | 5.28 |
| 48. | Jan 31, 2023 | -3.60% | 6.18% | 18.96 | 25.70 | -22.07 |
| 49. | Feb 28, 2023 | -2.95% | -2.61% | 13.73 | 13.82 | 13.77 |
| 50. | Mar 31, 2023 | 5.01% | 3.51% | 18.09 | 5.76 | 10.21 |
| 51. | Apr 30, 2023 | 3.42% | 1.46% | 7.09 | 0.13 | 0.95 |
| 52. | May 31, 2023 | -7.00% | 0.25% | 60.11 | 0.74 | 6.65 |
| 53. | Jun 30, 2023 | 1.71% | 4.71% | 0.91 | 13.02 | 3.45 |
| 54. | Jul 31, 2023 | 2.84% | 4.85% | 4.35 | 13.99 | 7.80 |
| 55. | Aug 31, 2023 | -3.39% | -1.77% | 17.18 | 8.28 | 11.93 |
| 56. | Sep 30, 2023 | -5.67% | -4.87% | 41.22 | 35.73 | 38.38 |
| 57. | Oct 31, 2023 | 0.91% | -2.20% | 0.02 | 10.92 | -0.52 |
| 58. | Nov 30, 2023 | 4.27% | 8.92% | 12.34 | 61.03 | 27.44 |
| 59. | Dec 31, 2023 | 0.84% | 4.42% | 0.01 | 11.00 | 0.28 |
| Total (Σ): | 1,647.38 | 1,634.30 | 964.04 | |||
Show all
VarianceKO = Σ(RKO,t–RKO)2 ÷ (59 – 1)
= 1,647.38 ÷ (59 – 1)
= 28.40
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceKO, S&P 500 = Σ(RKO,t–RKO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 964.04 ÷ (59 – 1)
= 16.62
Systematic Risk (β) Estimation
| VarianceKO | 28.40 |
| VarianceS&P 500 | 28.18 |
| CovarianceKO, S&P 500 | 16.62 |
| Correlation coefficientKO, S&P 5001 | 0.59 |
| βKO2 | 0.59 |
| αKO3 | 0.10% |
Calculations
1 Correlation coefficientKO, S&P 500
= CovarianceKO, S&P 500 ÷ (Standard deviationKO × Standard deviationS&P 500)
= 16.62 ÷ (5.33% × 5.31%)
= 0.59
2 βKO
= CovarianceKO, S&P 500 ÷ VarianceS&P 500
= 16.62 ÷ 28.18
= 0.59
3 αKO
= AverageKO – βKO × AverageS&P 500
= 0.75% – 0.59 × 1.11%
= 0.10%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.86% |
| Expected rate of return on market portfolio2 | E(RM) | 13.52% |
| Systematic risk (β) of Coca-Cola Co. common stock | βKO | 0.59 |
| Expected rate of return on Coca-Cola Co. common stock3 | E(RKO) | 9.97% |
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(RKO) = RF + βKO [E(RM) – RF]
= 4.86% + 0.59 [13.52% – 4.86%]
= 9.97%