Capital Asset Pricing Model (CAPM)
Difficulty: Intermediate
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Colgate'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, 2013 | 53.69 | 1,498.11 | ||||
| 1. | Feb 28, 2013 | 57.22 | 6.57% | 1,514.68 | 1.11% | |
| 2. | Mar 31, 2013 | 59.02 | 3.15% | 1,569.19 | 3.60% | |
| 3. | Apr 30, 2013 | 59.71 | 0.34 | 1.75% | 1,597.57 | 1.81% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2017 | 72.45 | 2.84% | 2,647.58 | 2.81% | |
| 59. | Dec 31, 2017 | 75.45 | 4.14% | 2,673.61 | 0.98% | |
| Average: | 0.83% | 1.02% | ||||
| Standard Deviation: | 3.93% | 2.71% | ||||
| 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, 2013 | 53.69 | 1,498.11 | ||||
| 1. | Feb 28, 2013 | 57.22 | 6.57% | 1,514.68 | 1.11% | |
| 2. | Mar 31, 2013 | 59.02 | 3.15% | 1,569.19 | 3.60% | |
| 3. | Apr 30, 2013 | 59.71 | 0.34 | 1.75% | 1,597.57 | 1.81% |
| 4. | May 31, 2013 | 57.84 | -3.13% | 1,630.74 | 2.08% | |
| 5. | Jun 30, 2013 | 57.29 | -0.95% | 1,606.28 | -1.50% | |
| 6. | Jul 31, 2013 | 59.87 | 0.34 | 5.10% | 1,685.73 | 4.95% |
| 7. | Aug 31, 2013 | 57.77 | -3.51% | 1,632.97 | -3.13% | |
| 8. | Sep 30, 2013 | 59.30 | 2.65% | 1,681.55 | 2.97% | |
| 9. | Oct 31, 2013 | 64.73 | 0.34 | 9.73% | 1,756.54 | 4.46% |
| 10. | Nov 30, 2013 | 65.81 | 1.67% | 1,805.81 | 2.80% | |
| 11. | Dec 31, 2013 | 65.21 | -0.91% | 1,848.36 | 2.36% | |
| 12. | Jan 31, 2014 | 61.23 | 0.34 | -5.58% | 1,782.59 | -3.56% |
| 13. | Feb 28, 2014 | 62.83 | 2.61% | 1,859.45 | 4.31% | |
| 14. | Mar 31, 2014 | 64.87 | 3.25% | 1,872.34 | 0.69% | |
| 15. | Apr 30, 2014 | 67.30 | 0.36 | 4.30% | 1,883.95 | 0.62% |
| 16. | May 31, 2014 | 68.40 | 1.63% | 1,923.57 | 2.10% | |
| 17. | Jun 30, 2014 | 68.18 | -0.32% | 1,960.23 | 1.91% | |
| 18. | Jul 31, 2014 | 63.40 | 0.36 | -6.48% | 1,930.67 | -1.51% |
| 19. | Aug 31, 2014 | 64.73 | 2.10% | 2,003.37 | 3.77% | |
| 20. | Sep 30, 2014 | 65.22 | 0.76% | 1,972.29 | -1.55% | |
| 21. | Oct 31, 2014 | 66.88 | 0.36 | 3.10% | 2,018.05 | 2.32% |
| 22. | Nov 30, 2014 | 69.59 | 4.05% | 2,067.56 | 2.45% | |
| 23. | Dec 31, 2014 | 69.19 | -0.57% | 2,058.90 | -0.42% | |
| 24. | Jan 31, 2015 | 67.52 | 0.36 | -1.89% | 1,994.99 | -3.10% |
| 25. | Feb 28, 2015 | 70.82 | 4.89% | 2,104.50 | 5.49% | |
| 26. | Mar 31, 2015 | 69.34 | -2.09% | 2,067.89 | -1.74% | |
| 27. | Apr 30, 2015 | 67.28 | 0.38 | -2.42% | 2,085.51 | 0.85% |
| 28. | May 31, 2015 | 66.79 | -0.73% | 2,107.39 | 1.05% | |
| 29. | Jun 30, 2015 | 65.41 | -2.07% | 2,063.11 | -2.10% | |
| 30. | Jul 31, 2015 | 68.02 | 0.38 | 4.57% | 2,103.84 | 1.97% |
| 31. | Aug 31, 2015 | 62.81 | -7.66% | 1,972.18 | -6.26% | |
| 32. | Sep 30, 2015 | 63.46 | 1.03% | 1,920.03 | -2.64% | |
| 33. | Oct 31, 2015 | 66.35 | 0.38 | 5.15% | 2,079.36 | 8.30% |
| 34. | Nov 30, 2015 | 65.68 | -1.01% | 2,080.41 | 0.05% | |
| 35. | Dec 31, 2015 | 66.62 | 1.43% | 2,043.94 | -1.75% | |
| 36. | Jan 31, 2016 | 67.53 | 0.38 | 1.94% | 1,940.24 | -5.07% |
| 37. | Feb 29, 2016 | 65.64 | -2.80% | 1,932.23 | -0.41% | |
| 38. | Mar 31, 2016 | 70.65 | 7.63% | 2,059.74 | 6.60% | |
| 39. | Apr 30, 2016 | 70.92 | 0.39 | 0.93% | 2,065.30 | 0.27% |
| 40. | May 31, 2016 | 70.41 | -0.72% | 2,096.95 | 1.53% | |
| 41. | Jun 30, 2016 | 73.20 | 3.96% | 2,098.86 | 0.09% | |
| 42. | Jul 31, 2016 | 74.43 | 0.39 | 2.21% | 2,173.60 | 3.56% |
| 43. | Aug 31, 2016 | 74.34 | -0.12% | 2,170.95 | -0.12% | |
| 44. | Sep 30, 2016 | 74.14 | -0.27% | 2,168.27 | -0.12% | |
| 45. | Oct 31, 2016 | 71.36 | 0.39 | -3.22% | 2,126.15 | -1.94% |
| 46. | Nov 30, 2016 | 65.23 | -8.59% | 2,198.81 | 3.42% | |
| 47. | Dec 31, 2016 | 65.44 | 0.32% | 2,238.83 | 1.82% | |
| 48. | Jan 31, 2017 | 64.58 | 0.39 | -0.72% | 2,278.87 | 1.79% |
| 49. | Feb 28, 2017 | 72.98 | 13.01% | 2,363.64 | 3.72% | |
| 50. | Mar 31, 2017 | 73.19 | 0.29% | 2,362.72 | -0.04% | |
| 51. | Apr 30, 2017 | 72.04 | 0.40 | -1.02% | 2,384.20 | 0.91% |
| 52. | May 31, 2017 | 76.36 | 6.00% | 2,411.80 | 1.16% | |
| 53. | Jun 30, 2017 | 74.13 | -2.92% | 2,423.41 | 0.48% | |
| 54. | Jul 31, 2017 | 72.20 | 0.40 | -2.06% | 2,470.30 | 1.93% |
| 55. | Aug 31, 2017 | 71.64 | -0.78% | 2,471.65 | 0.05% | |
| 56. | Sep 30, 2017 | 72.85 | 1.69% | 2,519.36 | 1.93% | |
| 57. | Oct 31, 2017 | 70.45 | 0.40 | -2.75% | 2,575.26 | 2.22% |
| 58. | Nov 30, 2017 | 72.45 | 2.84% | 2,647.58 | 2.81% | |
| 59. | Dec 31, 2017 | 75.45 | 4.14% | 2,673.61 | 0.98% | |
| Average: | 0.83% | 1.02% | ||||
| Standard Deviation: | 3.93% | 2.71% | ||||
Show All
1 Data in USD $ 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
Systematic Risk (β) Estimation
| VarianceCL | 15.47 |
| VarianceS&P 500 | 7.32 |
| CovarianceCL, S&P 500 | 5.95 |
| Correlation CoefficientCL, S&P 5001 | 0.56 |
| βCL2 | 0.81 |
| αCL3 | 0.00 |
Calculations
1 CovarianceCL, S&P 500 ÷ (Standard DeviationCL × Standard DeviationS&P 500)
= 5.95 ÷ (3.93 × 2.71)
2 CovarianceCL, S&P 500 ÷ VarianceS&P 500
= 5.95 ÷ 7.32
3 AverageCL – βCL × AverageS&P 500
= 0.83 – 0.81 × 1.02
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 3.32% |
| Expected rate of return on market portfolio2 | E(RM) | 12.28% |
| Systematic risk (β) of Colgate's common stock | βCL | 0.81 |
| Expected rate of return on Colgate's common stock3 | E(RCL) | 10.60% |
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).
Calculations
3 E(RCL) = RF + βCL [E(RM) – RF]
= 3.32% + 0.81 [12.28% – 3.32%]
= 10.60%