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 Colgate-Palmolive Co. 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, 2018 | $74.24 | 2,823.81 | ||||
| 1. | Feb 28, 2018 | $68.97 | -7.10% | 2,713.83 | -3.89% | |
| 2. | Mar 31, 2018 | $71.68 | 3.93% | 2,640.87 | -2.69% | |
| 3. | Apr 30, 2018 | $65.23 | $0.42 | -8.41% | 2,648.05 | 0.27% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2022 | $77.48 | 4.93% | 4,080.11 | 5.38% | |
| 59. | Dec 31, 2022 | $78.79 | 1.69% | 3,839.50 | -5.90% | |
| Average (R): | 0.42% | 0.67% | ||||
| Standard deviation: | 5.07% | 5.40% | ||||
| 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, 2018 | $74.24 | 2,823.81 | ||||
| 1. | Feb 28, 2018 | $68.97 | -7.10% | 2,713.83 | -3.89% | |
| 2. | Mar 31, 2018 | $71.68 | 3.93% | 2,640.87 | -2.69% | |
| 3. | Apr 30, 2018 | $65.23 | $0.42 | -8.41% | 2,648.05 | 0.27% |
| 4. | May 31, 2018 | $63.09 | -3.28% | 2,705.27 | 2.16% | |
| 5. | Jun 30, 2018 | $64.81 | 2.73% | 2,718.37 | 0.48% | |
| 6. | Jul 31, 2018 | $67.01 | $0.42 | 4.04% | 2,816.29 | 3.60% |
| 7. | Aug 31, 2018 | $66.41 | -0.90% | 2,901.52 | 3.03% | |
| 8. | Sep 30, 2018 | $66.95 | 0.81% | 2,913.98 | 0.43% | |
| 9. | Oct 31, 2018 | $59.55 | $0.42 | -10.43% | 2,711.74 | -6.94% |
| 10. | Nov 30, 2018 | $63.52 | 6.67% | 2,760.17 | 1.79% | |
| 11. | Dec 31, 2018 | $59.52 | -6.30% | 2,506.85 | -9.18% | |
| 12. | Jan 31, 2019 | $64.68 | $0.42 | 9.38% | 2,704.10 | 7.87% |
| 13. | Feb 28, 2019 | $65.87 | 1.84% | 2,784.49 | 2.97% | |
| 14. | Mar 31, 2019 | $68.54 | 4.05% | 2,834.40 | 1.79% | |
| 15. | Apr 30, 2019 | $72.79 | $0.43 | 6.83% | 2,945.83 | 3.93% |
| 16. | May 31, 2019 | $69.62 | -4.35% | 2,752.06 | -6.58% | |
| 17. | Jun 30, 2019 | $71.67 | 2.94% | 2,941.76 | 6.89% | |
| 18. | Jul 31, 2019 | $71.74 | $0.43 | 0.70% | 2,980.38 | 1.31% |
| 19. | Aug 31, 2019 | $74.15 | 3.36% | 2,926.46 | -1.81% | |
| 20. | Sep 30, 2019 | $73.51 | -0.86% | 2,976.74 | 1.72% | |
| 21. | Oct 31, 2019 | $68.60 | $0.43 | -6.09% | 3,037.56 | 2.04% |
| 22. | Nov 30, 2019 | $67.82 | -1.14% | 3,140.98 | 3.40% | |
| 23. | Dec 31, 2019 | $68.84 | 1.50% | 3,230.78 | 2.86% | |
| 24. | Jan 31, 2020 | $73.78 | $0.43 | 7.80% | 3,225.52 | -0.16% |
| 25. | Feb 29, 2020 | $67.57 | -8.42% | 2,954.22 | -8.41% | |
| 26. | Mar 31, 2020 | $66.36 | -1.79% | 2,584.59 | -12.51% | |
| 27. | Apr 30, 2020 | $70.27 | $0.44 | 6.56% | 2,912.43 | 12.68% |
| 28. | May 31, 2020 | $72.33 | 2.93% | 3,044.31 | 4.53% | |
| 29. | Jun 30, 2020 | $73.26 | 1.29% | 3,100.29 | 1.84% | |
| 30. | Jul 31, 2020 | $77.20 | $0.44 | 5.98% | 3,271.12 | 5.51% |
| 31. | Aug 31, 2020 | $79.26 | 2.67% | 3,500.31 | 7.01% | |
| 32. | Sep 30, 2020 | $77.15 | -2.66% | 3,363.00 | -3.92% | |
| 33. | Oct 31, 2020 | $78.89 | $0.44 | 2.83% | 3,269.96 | -2.77% |
| 34. | Nov 30, 2020 | $85.64 | 8.56% | 3,621.63 | 10.75% | |
| 35. | Dec 31, 2020 | $85.51 | -0.15% | 3,756.07 | 3.71% | |
| 36. | Jan 31, 2021 | $78.00 | $0.44 | -8.27% | 3,714.24 | -1.11% |
| 37. | Feb 28, 2021 | $75.20 | -3.59% | 3,811.15 | 2.61% | |
| 38. | Mar 31, 2021 | $78.83 | 4.83% | 3,972.89 | 4.24% | |
| 39. | Apr 30, 2021 | $80.70 | $0.45 | 2.94% | 4,181.17 | 5.24% |
| 40. | May 31, 2021 | $83.78 | 3.82% | 4,204.11 | 0.55% | |
| 41. | Jun 30, 2021 | $81.35 | -2.90% | 4,297.50 | 2.22% | |
| 42. | Jul 31, 2021 | $79.50 | $0.45 | -1.72% | 4,395.26 | 2.27% |
| 43. | Aug 31, 2021 | $77.95 | -1.95% | 4,522.68 | 2.90% | |
| 44. | Sep 30, 2021 | $75.58 | -3.04% | 4,307.54 | -4.76% | |
| 45. | Oct 31, 2021 | $76.19 | $0.45 | 1.40% | 4,605.38 | 6.91% |
| 46. | Nov 30, 2021 | $75.02 | -1.54% | 4,567.00 | -0.83% | |
| 47. | Dec 31, 2021 | $85.34 | 13.76% | 4,766.18 | 4.36% | |
| 48. | Jan 31, 2022 | $82.45 | $0.45 | -2.86% | 4,515.55 | -5.26% |
| 49. | Feb 28, 2022 | $76.95 | -6.67% | 4,373.94 | -3.14% | |
| 50. | Mar 31, 2022 | $75.83 | -1.46% | 4,530.41 | 3.58% | |
| 51. | Apr 30, 2022 | $77.05 | $0.47 | 2.23% | 4,131.93 | -8.80% |
| 52. | May 31, 2022 | $78.81 | 2.28% | 4,132.15 | 0.01% | |
| 53. | Jun 30, 2022 | $80.14 | 1.69% | 3,785.38 | -8.39% | |
| 54. | Jul 31, 2022 | $78.74 | $0.47 | -1.16% | 4,130.29 | 9.11% |
| 55. | Aug 31, 2022 | $78.21 | -0.67% | 3,955.00 | -4.24% | |
| 56. | Sep 30, 2022 | $70.25 | -10.18% | 3,585.62 | -9.34% | |
| 57. | Oct 31, 2022 | $73.84 | $0.47 | 5.78% | 3,871.98 | 7.99% |
| 58. | Nov 30, 2022 | $77.48 | 4.93% | 4,080.11 | 5.38% | |
| 59. | Dec 31, 2022 | $78.79 | 1.69% | 3,839.50 | -5.90% | |
| Average (R): | 0.42% | 0.67% | ||||
| Standard deviation: | 5.07% | 5.40% | ||||
Show all
1 Data in US$ 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 28, 2018 | -7.10% | -3.89% | 56.55 | 20.81 | 34.30 |
| 2. | Mar 31, 2018 | 3.93% | -2.69% | 12.31 | 11.26 | -11.77 |
| 3. | Apr 30, 2018 | -8.41% | 0.27% | 78.03 | 0.16 | 3.49 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2022 | 4.93% | 5.38% | 20.33 | 22.17 | 21.23 |
| 59. | Dec 31, 2022 | 1.69% | -5.90% | 1.61 | 43.08 | -8.33 |
| Total (Σ): | 1,488.93 | 1,691.48 | 881.07 | |||
| 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 28, 2018 | -7.10% | -3.89% | 56.55 | 20.81 | 34.30 |
| 2. | Mar 31, 2018 | 3.93% | -2.69% | 12.31 | 11.26 | -11.77 |
| 3. | Apr 30, 2018 | -8.41% | 0.27% | 78.03 | 0.16 | 3.49 |
| 4. | May 31, 2018 | -3.28% | 2.16% | 13.70 | 2.23 | -5.53 |
| 5. | Jun 30, 2018 | 2.73% | 0.48% | 5.31 | 0.03 | -0.42 |
| 6. | Jul 31, 2018 | 4.04% | 3.60% | 13.12 | 8.62 | 10.63 |
| 7. | Aug 31, 2018 | -0.90% | 3.03% | 1.73 | 5.57 | -3.11 |
| 8. | Sep 30, 2018 | 0.81% | 0.43% | 0.15 | 0.06 | -0.09 |
| 9. | Oct 31, 2018 | -10.43% | -6.94% | 117.65 | 57.87 | 82.51 |
| 10. | Nov 30, 2018 | 6.67% | 1.79% | 39.01 | 1.25 | 6.99 |
| 11. | Dec 31, 2018 | -6.30% | -9.18% | 45.14 | 96.91 | 66.14 |
| 12. | Jan 31, 2019 | 9.38% | 7.87% | 80.17 | 51.87 | 64.48 |
| 13. | Feb 28, 2019 | 1.84% | 2.97% | 2.01 | 5.32 | 3.27 |
| 14. | Mar 31, 2019 | 4.05% | 1.79% | 13.19 | 1.27 | 4.09 |
| 15. | Apr 30, 2019 | 6.83% | 3.93% | 41.05 | 10.66 | 20.92 |
| 16. | May 31, 2019 | -4.35% | -6.58% | 22.81 | 52.48 | 34.60 |
| 17. | Jun 30, 2019 | 2.94% | 6.89% | 6.37 | 38.77 | 15.71 |
| 18. | Jul 31, 2019 | 0.70% | 1.31% | 0.08 | 0.42 | 0.18 |
| 19. | Aug 31, 2019 | 3.36% | -1.81% | 8.63 | 6.13 | -7.27 |
| 20. | Sep 30, 2019 | -0.86% | 1.72% | 1.65 | 1.11 | -1.35 |
| 21. | Oct 31, 2019 | -6.09% | 2.04% | 42.45 | 1.89 | -8.97 |
| 22. | Nov 30, 2019 | -1.14% | 3.40% | 2.43 | 7.50 | -4.27 |
| 23. | Dec 31, 2019 | 1.50% | 2.86% | 1.17 | 4.81 | 2.37 |
| 24. | Jan 31, 2020 | 7.80% | -0.16% | 54.46 | 0.69 | -6.12 |
| 25. | Feb 29, 2020 | -8.42% | -8.41% | 78.11 | 82.40 | 80.23 |
| 26. | Mar 31, 2020 | -1.79% | -12.51% | 4.89 | 173.67 | 29.15 |
| 27. | Apr 30, 2020 | 6.56% | 12.68% | 37.63 | 144.43 | 73.72 |
| 28. | May 31, 2020 | 2.93% | 4.53% | 6.30 | 14.91 | 9.69 |
| 29. | Jun 30, 2020 | 1.29% | 1.84% | 0.75 | 1.37 | 1.01 |
| 30. | Jul 31, 2020 | 5.98% | 5.51% | 30.89 | 23.46 | 26.92 |
| 31. | Aug 31, 2020 | 2.67% | 7.01% | 5.05 | 40.19 | 14.25 |
| 32. | Sep 30, 2020 | -2.66% | -3.92% | 9.51 | 21.06 | 14.15 |
| 33. | Oct 31, 2020 | 2.83% | -2.77% | 5.78 | 11.79 | -8.26 |
| 34. | Nov 30, 2020 | 8.56% | 10.75% | 66.18 | 101.77 | 82.07 |
| 35. | Dec 31, 2020 | -0.15% | 3.71% | 0.33 | 9.28 | -1.74 |
| 36. | Jan 31, 2021 | -8.27% | -1.11% | 75.50 | 3.17 | 15.47 |
| 37. | Feb 28, 2021 | -3.59% | 2.61% | 16.09 | 3.77 | -7.79 |
| 38. | Mar 31, 2021 | 4.83% | 4.24% | 19.41 | 12.80 | 15.76 |
| 39. | Apr 30, 2021 | 2.94% | 5.24% | 6.36 | 20.94 | 11.54 |
| 40. | May 31, 2021 | 3.82% | 0.55% | 11.53 | 0.01 | -0.40 |
| 41. | Jun 30, 2021 | -2.90% | 2.22% | 11.03 | 2.42 | -5.16 |
| 42. | Jul 31, 2021 | -1.72% | 2.27% | 4.59 | 2.59 | -3.44 |
| 43. | Aug 31, 2021 | -1.95% | 2.90% | 5.62 | 4.98 | -5.29 |
| 44. | Sep 30, 2021 | -3.04% | -4.76% | 11.98 | 29.42 | 18.77 |
| 45. | Oct 31, 2021 | 1.40% | 6.91% | 0.96 | 39.03 | 6.13 |
| 46. | Nov 30, 2021 | -1.54% | -0.83% | 3.83 | 2.25 | 2.94 |
| 47. | Dec 31, 2021 | 13.76% | 4.36% | 177.83 | 13.65 | 49.27 |
| 48. | Jan 31, 2022 | -2.86% | -5.26% | 10.76 | 35.11 | 19.44 |
| 49. | Feb 28, 2022 | -6.67% | -3.14% | 50.29 | 14.46 | 26.97 |
| 50. | Mar 31, 2022 | -1.46% | 3.58% | 3.52 | 8.47 | -5.46 |
| 51. | Apr 30, 2022 | 2.23% | -8.80% | 3.27 | 89.54 | -17.10 |
| 52. | May 31, 2022 | 2.28% | 0.01% | 3.47 | 0.44 | -1.23 |
| 53. | Jun 30, 2022 | 1.69% | -8.39% | 1.60 | 82.06 | -11.47 |
| 54. | Jul 31, 2022 | -1.16% | 9.11% | 2.50 | 71.32 | -13.36 |
| 55. | Aug 31, 2022 | -0.67% | -4.24% | 1.20 | 24.11 | 5.37 |
| 56. | Sep 30, 2022 | -10.18% | -9.34% | 112.34 | 100.12 | 106.05 |
| 57. | Oct 31, 2022 | 5.78% | 7.99% | 28.71 | 53.58 | 39.22 |
| 58. | Nov 30, 2022 | 4.93% | 5.38% | 20.33 | 22.17 | 21.23 |
| 59. | Dec 31, 2022 | 1.69% | -5.90% | 1.61 | 43.08 | -8.33 |
| Total (Σ): | 1,488.93 | 1,691.48 | 881.07 | |||
Show all
VarianceCL = Σ(RCL,t–RCL)2 ÷ (59 – 1)
= 1,488.93 ÷ (59 – 1)
= 25.67
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianceCL, S&P 500 = Σ(RCL,t–RCL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 881.07 ÷ (59 – 1)
= 15.19
Systematic Risk (β) Estimation
| VarianceCL | 25.67 |
| VarianceS&P 500 | 29.16 |
| CovarianceCL, S&P 500 | 15.19 |
| Correlation coefficientCL, S&P 5001 | 0.56 |
| βCL2 | 0.52 |
| αCL3 | 0.07% |
Calculations
1 Correlation coefficientCL, S&P 500
= CovarianceCL, S&P 500 ÷ (Standard deviationCL × Standard deviationS&P 500)
= 15.19 ÷ (5.07% × 5.40%)
= 0.56
2 βCL
= CovarianceCL, S&P 500 ÷ VarianceS&P 500
= 15.19 ÷ 29.16
= 0.52
3 αCL
= AverageCL – βCL × AverageS&P 500
= 0.42% – 0.52 × 0.67%
= 0.07%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.68% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk (β) of Colgate-Palmolive Co. common stock | βCL | 0.52 |
| Expected rate of return on Colgate-Palmolive Co. common stock3 | E(RCL) | 9.42% |
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]
= 4.68% + 0.52 [13.79% – 4.68%]
= 9.42%