Capital Asset Pricing Model (CAPM)
Intermediate level
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Colgate-Palmolive Co.’s common stock.
Rates of Return
Colgate-Palmolive Co., monthly rates of return
| Colgate-Palmolive Co. (CL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCL,t1 | DividendCL,t1 | RCL,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2016 | $67.53 | 1,940.24 | ||||
| 1. | Feb 29, 2016 | $65.64 | -2.80% | 1,932.23 | -0.41% | |
| 2. | Mar 31, 2016 | $70.65 | 7.63% | 2,059.74 | 6.60% | |
| 3. | Apr 30, 2016 | $70.92 | $0.39 | 0.93% | 2,065.30 | 0.27% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2020 | $85.64 | 8.56% | 3,621.63 | 10.75% | |
| 59. | Dec 31, 2020 | $85.51 | -0.15% | 3,756.07 | 3.71% | |
| Average (R): | 0.70% | 1.22% | ||||
| Standard deviation: | 4.77% | 4.36% | ||||
| Colgate-Palmolive Co. (CL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCL,t1 | DividendCL,t1 | RCL,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2016 | $67.53 | 1,940.24 | ||||
| 1. | Feb 29, 2016 | $65.64 | -2.80% | 1,932.23 | -0.41% | |
| 2. | Mar 31, 2016 | $70.65 | 7.63% | 2,059.74 | 6.60% | |
| 3. | Apr 30, 2016 | $70.92 | $0.39 | 0.93% | 2,065.30 | 0.27% |
| 4. | May 31, 2016 | $70.41 | -0.72% | 2,096.95 | 1.53% | |
| 5. | Jun 30, 2016 | $73.20 | 3.96% | 2,098.86 | 0.09% | |
| 6. | Jul 31, 2016 | $74.43 | $0.39 | 2.21% | 2,173.60 | 3.56% |
| 7. | Aug 31, 2016 | $74.34 | -0.12% | 2,170.95 | -0.12% | |
| 8. | Sep 30, 2016 | $74.14 | -0.27% | 2,168.27 | -0.12% | |
| 9. | Oct 31, 2016 | $71.36 | $0.39 | -3.22% | 2,126.15 | -1.94% |
| 10. | Nov 30, 2016 | $65.23 | -8.59% | 2,198.81 | 3.42% | |
| 11. | Dec 31, 2016 | $65.44 | 0.32% | 2,238.83 | 1.82% | |
| 12. | Jan 31, 2017 | $64.58 | $0.39 | -0.72% | 2,278.87 | 1.79% |
| 13. | Feb 28, 2017 | $72.98 | 13.01% | 2,363.64 | 3.72% | |
| 14. | Mar 31, 2017 | $73.19 | 0.29% | 2,362.72 | -0.04% | |
| 15. | Apr 30, 2017 | $72.04 | $0.40 | -1.02% | 2,384.20 | 0.91% |
| 16. | May 31, 2017 | $76.36 | 6.00% | 2,411.80 | 1.16% | |
| 17. | Jun 30, 2017 | $74.13 | -2.92% | 2,423.41 | 0.48% | |
| 18. | Jul 31, 2017 | $72.20 | $0.40 | -2.06% | 2,470.30 | 1.93% |
| 19. | Aug 31, 2017 | $71.64 | -0.78% | 2,471.65 | 0.05% | |
| 20. | Sep 30, 2017 | $72.85 | 1.69% | 2,519.36 | 1.93% | |
| 21. | Oct 31, 2017 | $70.45 | $0.40 | -2.75% | 2,575.26 | 2.22% |
| 22. | Nov 30, 2017 | $72.45 | 2.84% | 2,647.58 | 2.81% | |
| 23. | Dec 31, 2017 | $75.45 | 4.14% | 2,673.61 | 0.98% | |
| 24. | Jan 31, 2018 | $74.24 | $0.40 | -1.07% | 2,823.81 | 5.62% |
| 25. | Feb 28, 2018 | $68.97 | -7.10% | 2,713.83 | -3.89% | |
| 26. | Mar 31, 2018 | $71.68 | 3.93% | 2,640.87 | -2.69% | |
| 27. | Apr 30, 2018 | $65.23 | $0.42 | -8.41% | 2,648.05 | 0.27% |
| 28. | May 31, 2018 | $63.09 | -3.28% | 2,705.27 | 2.16% | |
| 29. | Jun 30, 2018 | $64.81 | 2.73% | 2,718.37 | 0.48% | |
| 30. | Jul 31, 2018 | $67.01 | $0.42 | 4.04% | 2,816.29 | 3.60% |
| 31. | Aug 31, 2018 | $66.41 | -0.90% | 2,901.52 | 3.03% | |
| 32. | Sep 30, 2018 | $66.95 | 0.81% | 2,913.98 | 0.43% | |
| 33. | Oct 31, 2018 | $59.55 | $0.42 | -10.43% | 2,711.74 | -6.94% |
| 34. | Nov 30, 2018 | $63.52 | 6.67% | 2,760.17 | 1.79% | |
| 35. | Dec 31, 2018 | $59.52 | -6.30% | 2,506.85 | -9.18% | |
| 36. | Jan 31, 2019 | $64.68 | $0.42 | 9.38% | 2,704.10 | 7.87% |
| 37. | Feb 28, 2019 | $65.87 | 1.84% | 2,784.49 | 2.97% | |
| 38. | Mar 31, 2019 | $68.54 | 4.05% | 2,834.40 | 1.79% | |
| 39. | Apr 30, 2019 | $72.79 | $0.43 | 6.83% | 2,945.83 | 3.93% |
| 40. | May 31, 2019 | $69.62 | -4.35% | 2,752.06 | -6.58% | |
| 41. | Jun 30, 2019 | $71.67 | 2.94% | 2,941.76 | 6.89% | |
| 42. | Jul 31, 2019 | $71.74 | $0.43 | 0.70% | 2,980.38 | 1.31% |
| 43. | Aug 31, 2019 | $74.15 | 3.36% | 2,926.46 | -1.81% | |
| 44. | Sep 30, 2019 | $73.51 | -0.86% | 2,976.74 | 1.72% | |
| 45. | Oct 31, 2019 | $68.60 | $0.43 | -6.09% | 3,037.56 | 2.04% |
| 46. | Nov 30, 2019 | $67.82 | -1.14% | 3,140.98 | 3.40% | |
| 47. | Dec 31, 2019 | $68.84 | 1.50% | 3,230.78 | 2.86% | |
| 48. | Jan 31, 2020 | $73.78 | $0.43 | 7.80% | 3,225.52 | -0.16% |
| 49. | Feb 29, 2020 | $67.57 | -8.42% | 2,954.22 | -8.41% | |
| 50. | Mar 31, 2020 | $66.36 | -1.79% | 2,584.59 | -12.51% | |
| 51. | Apr 30, 2020 | $70.27 | $0.44 | 6.56% | 2,912.43 | 12.68% |
| 52. | May 31, 2020 | $72.33 | 2.93% | 3,044.31 | 4.53% | |
| 53. | Jun 30, 2020 | $73.26 | 1.29% | 3,100.29 | 1.84% | |
| 54. | Jul 31, 2020 | $77.20 | $0.44 | 5.98% | 3,271.12 | 5.51% |
| 55. | Aug 31, 2020 | $79.26 | 2.67% | 3,500.31 | 7.01% | |
| 56. | Sep 30, 2020 | $77.15 | -2.66% | 3,363.00 | -3.92% | |
| 57. | Oct 31, 2020 | $78.89 | $0.44 | 2.83% | 3,269.96 | -2.77% |
| 58. | Nov 30, 2020 | $85.64 | 8.56% | 3,621.63 | 10.75% | |
| 59. | Dec 31, 2020 | $85.51 | -0.15% | 3,756.07 | 3.71% | |
| Average (R): | 0.70% | 1.22% | ||||
| Standard deviation: | 4.77% | 4.36% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of CL during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Colgate-Palmolive Co., calculation of variance and covariance of returns
| t | Date | RCL,t | RS&P 500,t | (RCL,t–RCL)2 | (RS&P 500,t–RS&P 500)2 | (RCL,t–RCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2016 | -2.80% | -0.41% | 12.26 | 2.67 | 5.72 |
| 2. | Mar 31, 2016 | 7.63% | 6.60% | 48.02 | 28.93 | 37.27 |
| 3. | Apr 30, 2016 | 0.93% | 0.27% | 0.05 | 0.90 | -0.22 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2020 | 8.56% | 10.75% | 61.67 | 90.91 | 74.88 |
| 59. | Dec 31, 2020 | -0.15% | 3.71% | 0.73 | 6.21 | -2.13 |
| Total (Σ): | 1,320.08 | 1,103.45 | 680.03 | |||
| t | Date | RCL,t | RS&P 500,t | (RCL,t–RCL)2 | (RS&P 500,t–RS&P 500)2 | (RCL,t–RCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2016 | -2.80% | -0.41% | 12.26 | 2.67 | 5.72 |
| 2. | Mar 31, 2016 | 7.63% | 6.60% | 48.02 | 28.93 | 37.27 |
| 3. | Apr 30, 2016 | 0.93% | 0.27% | 0.05 | 0.90 | -0.22 |
| 4. | May 31, 2016 | -0.72% | 1.53% | 2.02 | 0.10 | -0.44 |
| 5. | Jun 30, 2016 | 3.96% | 0.09% | 10.62 | 1.27 | -3.68 |
| 6. | Jul 31, 2016 | 2.21% | 3.56% | 2.28 | 5.48 | 3.53 |
| 7. | Aug 31, 2016 | -0.12% | -0.12% | 0.68 | 1.80 | 1.11 |
| 8. | Sep 30, 2016 | -0.27% | -0.12% | 0.95 | 1.81 | 1.31 |
| 9. | Oct 31, 2016 | -3.22% | -1.94% | 15.42 | 10.00 | 12.42 |
| 10. | Nov 30, 2016 | -8.59% | 3.42% | 86.37 | 4.83 | -20.42 |
| 11. | Dec 31, 2016 | 0.32% | 1.82% | 0.15 | 0.36 | -0.23 |
| 12. | Jan 31, 2017 | -0.72% | 1.79% | 2.02 | 0.32 | -0.81 |
| 13. | Feb 28, 2017 | 13.01% | 3.72% | 151.39 | 6.25 | 30.76 |
| 14. | Mar 31, 2017 | 0.29% | -0.04% | 0.17 | 1.59 | 0.52 |
| 15. | Apr 30, 2017 | -1.02% | 0.91% | 2.99 | 0.10 | 0.54 |
| 16. | May 31, 2017 | 6.00% | 1.16% | 28.02 | 0.00 | -0.33 |
| 17. | Jun 30, 2017 | -2.92% | 0.48% | 13.13 | 0.55 | 2.68 |
| 18. | Jul 31, 2017 | -2.06% | 1.93% | 7.66 | 0.51 | -1.98 |
| 19. | Aug 31, 2017 | -0.78% | 0.05% | 2.19 | 1.36 | 1.72 |
| 20. | Sep 30, 2017 | 1.69% | 1.93% | 0.97 | 0.50 | 0.70 |
| 21. | Oct 31, 2017 | -2.75% | 2.22% | 11.89 | 1.00 | -3.44 |
| 22. | Nov 30, 2017 | 2.84% | 2.81% | 4.56 | 2.52 | 3.39 |
| 23. | Dec 31, 2017 | 4.14% | 0.98% | 11.82 | 0.06 | -0.81 |
| 24. | Jan 31, 2018 | -1.07% | 5.62% | 3.16 | 19.34 | -7.81 |
| 25. | Feb 28, 2018 | -7.10% | -3.89% | 60.87 | 26.16 | 39.90 |
| 26. | Mar 31, 2018 | 3.93% | -2.69% | 10.41 | 15.28 | -12.61 |
| 27. | Apr 30, 2018 | -8.41% | 0.27% | 83.09 | 0.90 | 8.64 |
| 28. | May 31, 2018 | -3.28% | 2.16% | 15.87 | 0.89 | -3.75 |
| 29. | Jun 30, 2018 | 2.73% | 0.48% | 4.09 | 0.54 | -1.49 |
| 30. | Jul 31, 2018 | 4.04% | 3.60% | 11.15 | 5.67 | 7.96 |
| 31. | Aug 31, 2018 | -0.90% | 3.03% | 2.56 | 3.26 | -2.89 |
| 32. | Sep 30, 2018 | 0.81% | 0.43% | 0.01 | 0.63 | -0.09 |
| 33. | Oct 31, 2018 | -10.43% | -6.94% | 123.85 | 66.59 | 90.82 |
| 34. | Nov 30, 2018 | 6.67% | 1.79% | 35.56 | 0.32 | 3.37 |
| 35. | Dec 31, 2018 | -6.30% | -9.18% | 49.00 | 108.11 | 72.79 |
| 36. | Jan 31, 2019 | 9.38% | 7.87% | 75.20 | 44.20 | 57.65 |
| 37. | Feb 28, 2019 | 1.84% | 2.97% | 1.29 | 3.07 | 1.99 |
| 38. | Mar 31, 2019 | 4.05% | 1.79% | 11.22 | 0.33 | 1.92 |
| 39. | Apr 30, 2019 | 6.83% | 3.93% | 37.52 | 7.35 | 16.61 |
| 40. | May 31, 2019 | -4.35% | -6.58% | 25.58 | 60.81 | 39.44 |
| 41. | Jun 30, 2019 | 2.94% | 6.89% | 5.02 | 32.18 | 12.72 |
| 42. | Jul 31, 2019 | 0.70% | 1.31% | 0.00 | 0.01 | 0.00 |
| 43. | Aug 31, 2019 | 3.36% | -1.81% | 7.06 | 9.18 | -8.05 |
| 44. | Sep 30, 2019 | -0.86% | 1.72% | 2.45 | 0.25 | -0.78 |
| 45. | Oct 31, 2019 | -6.09% | 2.04% | 46.21 | 0.68 | -5.60 |
| 46. | Nov 30, 2019 | -1.14% | 3.40% | 3.39 | 4.77 | -4.02 |
| 47. | Dec 31, 2019 | 1.50% | 2.86% | 0.64 | 2.69 | 1.31 |
| 48. | Jan 31, 2020 | 7.80% | -0.16% | 50.38 | 1.91 | -9.82 |
| 49. | Feb 29, 2020 | -8.42% | -8.41% | 83.17 | 92.76 | 87.84 |
| 50. | Mar 31, 2020 | -1.79% | -12.51% | 6.22 | 188.57 | 34.25 |
| 51. | Apr 30, 2020 | 6.56% | 12.68% | 34.25 | 131.43 | 67.09 |
| 52. | May 31, 2020 | 2.93% | 4.53% | 4.97 | 10.94 | 7.37 |
| 53. | Jun 30, 2020 | 1.29% | 1.84% | 0.34 | 0.38 | 0.36 |
| 54. | Jul 31, 2020 | 5.98% | 5.51% | 27.83 | 18.40 | 22.63 |
| 55. | Aug 31, 2020 | 2.67% | 7.01% | 3.86 | 33.48 | 11.37 |
| 56. | Sep 30, 2020 | -2.66% | -3.92% | 11.32 | 26.45 | 17.31 |
| 57. | Oct 31, 2020 | 2.83% | -2.77% | 4.51 | 15.89 | -8.46 |
| 58. | Nov 30, 2020 | 8.56% | 10.75% | 61.67 | 90.91 | 74.88 |
| 59. | Dec 31, 2020 | -0.15% | 3.71% | 0.73 | 6.21 | -2.13 |
| Total (Σ): | 1,320.08 | 1,103.45 | 680.03 | |||
Show all
VarianceCL = Σ(RCL,t–RCL)2 ÷ (59 – 1)
= 1,320.08 ÷ (59 – 1)
= 22.76
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,103.45 ÷ (59 – 1)
= 19.02
CovarianceCL, S&P 500 = Σ(RCL,t–RCL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 680.03 ÷ (59 – 1)
= 11.72
Systematic Risk (β) Estimation
| VarianceCL | 22.76 |
| VarianceS&P 500 | 19.02 |
| CovarianceCL, S&P 500 | 11.72 |
| Correlation coefficientCL, S&P 5001 | 0.56 |
| βCL2 | 0.62 |
| αCL3 | -0.05% |
Calculations
1 Correlation coefficientCL, S&P 500
= CovarianceCL, S&P 500 ÷ (Standard deviationCL × Standard deviationS&P 500)
= 11.72 ÷ (4.77% × 4.36%)
= 0.56
2 βCL
= CovarianceCL, S&P 500 ÷ VarianceS&P 500
= 11.72 ÷ 19.02
= 0.62
3 αCL
= AverageCL – βCL × AverageS&P 500
= 0.70% – 0.62 × 1.22%
= -0.05%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 2.08% |
| Expected rate of return on market portfolio2 | E(RM) | 12.39% |
| Systematic risk (β) of Colgate-Palmolive Co.’s common stock | βCL | 0.62 |
| Expected rate of return on Colgate-Palmolive Co.’s common stock3 | E(RCL) | 8.43% |
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(RCL) = RF + βCL [E(RM) – RF]
= 2.08% + 0.62 [12.39% – 2.08%]
= 8.43%