Microsoft Excel LibreOffice Calc

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

Microsoft Excel LibreOffice Calc
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

Microsoft Excel LibreOffice Calc
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
= 0.830.81 × 1.02


Expected Rate of Return

Microsoft Excel LibreOffice Calc
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

2 See Details »

3 E(RCL) = RF + βCL [E(RM) – RF]
= 3.32% + 0.81 [12.28% – 3.32%]
= 10.60%