Capital Asset Pricing Model (CAPM)

Difficulty level: Medium

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Coca-Cola's 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, 2009 21.36 825.88
1. Feb 28, 2009 20.43 -4.35% 735.09 -10.99%
2. Mar 31, 2009 21.98 0.205 8.59% 797.87 8.54%
3. Apr 30, 2009 21.53 -2.05% 872.81 9.39%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2013 40.19 0.28 2.27% 1,805.81 2.80%
59. Dec 31, 2013 41.31 2.79% 1,848.36 2.36%
Average: 1.46% 1.47%
Standard Deviation: 4.37% 4.42%
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, 2009 21.36 825.88
1. Feb 28, 2009 20.43 -4.35% 735.09 -10.99%
2. Mar 31, 2009 21.98 0.205 8.59% 797.87 8.54%
3. Apr 30, 2009 21.53 -2.05% 872.81 9.39%
4. May 31, 2009 24.58 14.17% 919.14 5.31%
5. Jun 30, 2009 24.00 0.205 -1.53% 919.32 0.02%
6. Jul 31, 2009 24.92 3.83% 987.48 7.41%
7. Aug 31, 2009 24.39 -2.13% 1,020.62 3.36%
8. Sep 30, 2009 26.85 0.205 10.93% 1,057.08 3.57%
9. Oct 31, 2009 26.66 -0.71% 1,036.19 -1.98%
10. Nov 30, 2009 28.60 0.205 8.05% 1,095.63 5.74%
11. Dec 31, 2009 28.50 -0.35% 1,115.10 1.78%
12. Jan 31, 2010 27.13 -4.81% 1,073.87 -3.70%
13. Feb 28, 2010 26.36 -2.84% 1,104.49 2.85%
14. Mar 31, 2010 27.50 0.22 5.16% 1,169.43 5.88%
15. Apr 30, 2010 26.73 -2.80% 1,186.69 1.48%
16. May 31, 2010 25.70 -3.85% 1,089.41 -8.20%
17. Jun 30, 2010 25.06 0.22 -1.63% 1,030.71 -5.39%
18. Jul 31, 2010 27.56 9.98% 1,101.60 6.88%
19. Aug 31, 2010 27.94 1.38% 1,049.33 -4.74%
20. Sep 30, 2010 29.26 0.22 5.51% 1,141.20 8.76%
21. Oct 31, 2010 30.66 4.78% 1,183.26 3.69%
22. Nov 30, 2010 31.59 0.22 3.75% 1,180.55 -0.23%
23. Dec 31, 2010 32.89 4.12% 1,257.64 6.53%
24. Jan 31, 2011 31.43 -4.44% 1,286.12 2.26%
25. Feb 28, 2011 31.96 1.69% 1,327.22 3.20%
26. Mar 31, 2011 33.17 0.235 4.52% 1,325.83 -0.10%
27. Apr 30, 2011 33.73 1.69% 1,363.61 2.85%
28. May 31, 2011 33.41 -0.95% 1,345.20 -1.35%
29. Jun 30, 2011 33.65 0.235 1.42% 1,320.64 -1.83%
30. Jul 31, 2011 34.01 1.07% 1,292.28 -2.15%
31. Aug 31, 2011 35.23 3.59% 1,218.89 -5.68%
32. Sep 30, 2011 33.78 0.235 -3.45% 1,131.42 -7.18%
33. Oct 31, 2011 34.16 1.12% 1,253.30 10.77%
34. Nov 30, 2011 33.62 0.235 -0.89% 1,246.96 -0.51%
35. Dec 31, 2011 34.99 4.07% 1,257.60 0.85%
36. Jan 31, 2012 33.77 -3.50% 1,312.41 4.36%
37. Feb 29, 2012 34.93 3.45% 1,365.68 4.06%
38. Mar 31, 2012 37.01 0.225 6.58% 1,408.47 3.13%
39. Apr 30, 2012 38.16 3.12% 1,397.91 -0.75%
40. May 31, 2012 37.37 -2.08% 1,310.33 -6.27%
41. Jun 30, 2012 39.10 0.225 5.23% 1,362.16 3.96%
42. Jul 31, 2012 40.40 3.34% 1,379.32 1.26%
43. Aug 31, 2012 37.40 -7.43% 1,406.58 1.98%
44. Sep 30, 2012 37.93 0.225 2.02% 1,440.67 2.42%
45. Oct 31, 2012 37.18 -1.98% 1,412.16 -1.98%
46. Nov 30, 2012 37.92 0.225 2.60% 1,416.18 0.28%
47. Dec 31, 2012 36.25 -4.40% 1,426.19 0.71%
48. Jan 31, 2013 37.24 2.73% 1,498.11 5.04%
49. Feb 28, 2013 38.72 3.97% 1,514.68 1.11%
50. Mar 31, 2013 40.44 0.28 5.17% 1,569.19 3.60%
51. Apr 30, 2013 42.33 4.67% 1,597.57 1.81%
52. May 31, 2013 39.99 -5.53% 1,630.74 2.08%
53. Jun 30, 2013 40.11 0.28 1.00% 1,606.28 -1.50%
54. Jul 31, 2013 40.08 -0.07% 1,685.73 4.95%
55. Aug 31, 2013 38.18 -4.74% 1,632.97 -3.13%
56. Sep 30, 2013 37.88 0.28 -0.05% 1,681.55 2.97%
57. Oct 31, 2013 39.57 4.46% 1,756.54 4.46%
58. Nov 30, 2013 40.19 0.28 2.27% 1,805.81 2.80%
59. Dec 31, 2013 41.31 2.79% 1,848.36 2.36%
Average: 1.46% 1.47%
Standard Deviation: 4.37% 4.42%

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 KO during period t

3 Rate of return on S&P 500 (the market portfolio proxy) during period t

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Systematic Risk (β) Estimation

 
VarianceKO 19.10
VarianceS&P 500 19.58
CovarianceKO, S&P 500 9.14
Correlation CoefficientKO, S&P 5001 0.47
βKO2 0.47
αKO3 0.77

Calculations

1 CovarianceKO, S&P 500 ÷ (Standard DeviationKO × Standard DeviationS&P 500)
= 9.14 ÷ (4.37 × 4.42)

2 CovarianceKO, S&P 500 ÷ VarianceS&P 500
= 9.14 ÷ 19.58

3 AverageKO – βKO × AverageS&P 500
= 1.46 – 0.47 × 1.47

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Expected Rate of Return

 
Assumptions
Rate of return on LT Treasury Composite1 RF 2.53%
Expected rate of return on market portfolio2 E(RM) 13.54%
Systematic risk (β) of Coca-Cola's common stock βKO 0.47
Expected rate of return on Coca-Cola's common stock3 E(RKO) 7.67%

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(RKO) = RF + βKO [E(RM) – RF]
= 2.53% + 0.47 [13.54% – 2.53%]
= 7.67%

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