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 YUM's common stock.


Rates of Return

YUM! Brands Inc., monthly rates of return

 
YUM! Brands Inc. (YUM) Standard & Poor's 500 (S&P 500)
t Date PriceYUM,t1 DividendYUM,t1 RYUM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2009 28.62 825.88
1. Feb 28, 2009 26.28 -8.18% 735.09 -10.99%
2. Mar 31, 2009 27.48 4.57% 797.87 8.54%
3. Apr 30, 2009 33.35 0.19 22.05% 872.81 9.39%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2013 77.68 14.88% 1,805.81 2.80%
59. Dec 31, 2013 75.61 -2.66% 1,848.36 2.36%
Average: 2.00% 1.47%
Standard Deviation: 6.08% 4.42%
YUM! Brands Inc. (YUM) Standard & Poor's 500 (S&P 500)
t Date PriceYUM,t1 DividendYUM,t1 RYUM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2009 28.62 825.88
1. Feb 28, 2009 26.28 -8.18% 735.09 -10.99%
2. Mar 31, 2009 27.48 4.57% 797.87 8.54%
3. Apr 30, 2009 33.35 0.19 22.05% 872.81 9.39%
4. May 31, 2009 34.63 3.84% 919.14 5.31%
5. Jun 30, 2009 33.34 -3.73% 919.32 0.02%
6. Jul 31, 2009 35.46 0.19 6.93% 987.48 7.41%
7. Aug 31, 2009 34.25 -3.41% 1,020.62 3.36%
8. Sep 30, 2009 33.76 -1.43% 1,057.08 3.57%
9. Oct 31, 2009 32.95 0.21 -1.78% 1,036.19 -1.98%
10. Nov 30, 2009 35.27 7.04% 1,095.63 5.74%
11. Dec 31, 2009 34.97 -0.85% 1,115.10 1.78%
12. Jan 31, 2010 34.21 0.21 -1.57% 1,073.87 -3.70%
13. Feb 28, 2010 33.72 -1.43% 1,104.49 2.85%
14. Mar 31, 2010 38.33 13.67% 1,169.43 5.88%
15. Apr 30, 2010 42.42 0.21 11.22% 1,186.69 1.48%
16. May 31, 2010 40.95 -3.47% 1,089.41 -8.20%
17. Jun 30, 2010 39.04 -4.66% 1,030.71 -5.39%
18. Jul 31, 2010 41.30 0.21 6.33% 1,101.60 6.88%
19. Aug 31, 2010 41.70 0.97% 1,049.33 -4.74%
20. Sep 30, 2010 46.06 10.46% 1,141.20 8.76%
21. Oct 31, 2010 49.56 0.25 8.14% 1,183.26 3.69%
22. Nov 30, 2010 50.08 1.05% 1,180.55 -0.23%
23. Dec 31, 2010 49.05 -2.06% 1,257.64 6.53%
24. Jan 31, 2011 46.76 0.25 -4.16% 1,286.12 2.26%
25. Feb 28, 2011 50.33 7.63% 1,327.22 3.20%
26. Mar 31, 2011 51.38 2.09% 1,325.83 -0.10%
27. Apr 30, 2011 53.64 0.25 4.89% 1,363.61 2.85%
28. May 31, 2011 55.32 3.13% 1,345.20 -1.35%
29. Jun 30, 2011 55.24 -0.14% 1,320.64 -1.83%
30. Jul 31, 2011 52.82 0.25 -3.93% 1,292.28 -2.15%
31. Aug 31, 2011 54.37 2.93% 1,218.89 -5.68%
32. Sep 30, 2011 49.39 -9.16% 1,131.42 -7.18%
33. Oct 31, 2011 53.57 0.285 9.04% 1,253.30 10.77%
34. Nov 30, 2011 56.04 4.61% 1,246.96 -0.51%
35. Dec 31, 2011 59.01 5.30% 1,257.60 0.85%
36. Jan 31, 2012 63.33 0.285 7.80% 1,312.41 4.36%
37. Feb 29, 2012 66.24 4.59% 1,365.68 4.06%
38. Mar 31, 2012 71.18 7.46% 1,408.47 3.13%
39. Apr 30, 2012 72.73 0.285 2.58% 1,397.91 -0.75%
40. May 31, 2012 70.36 -3.26% 1,310.33 -6.27%
41. Jun 30, 2012 64.42 -8.44% 1,362.16 3.96%
42. Jul 31, 2012 64.84 0.285 1.09% 1,379.32 1.26%
43. Aug 31, 2012 63.72 -1.73% 1,406.58 1.98%
44. Sep 30, 2012 66.34 4.11% 1,440.67 2.42%
45. Oct 31, 2012 70.11 0.335 6.19% 1,412.16 -1.98%
46. Nov 30, 2012 67.08 -4.32% 1,416.18 0.28%
47. Dec 31, 2012 66.40 -1.01% 1,426.19 0.71%
48. Jan 31, 2013 64.94 0.335 -1.69% 1,498.11 5.04%
49. Feb 28, 2013 65.48 0.83% 1,514.68 1.11%
50. Mar 31, 2013 71.94 9.87% 1,569.19 3.60%
51. Apr 30, 2013 68.12 0.335 -4.84% 1,597.57 1.81%
52. May 31, 2013 67.75 -0.54% 1,630.74 2.08%
53. Jun 30, 2013 69.34 2.35% 1,606.28 -1.50%
54. Jul 31, 2013 72.92 0.335 5.65% 1,685.73 4.95%
55. Aug 31, 2013 70.02 -3.98% 1,632.97 -3.13%
56. Sep 30, 2013 71.39 1.96% 1,681.55 2.97%
57. Oct 31, 2013 67.62 0.37 -4.76% 1,756.54 4.46%
58. Nov 30, 2013 77.68 14.88% 1,805.81 2.80%
59. Dec 31, 2013 75.61 -2.66% 1,848.36 2.36%
Average: 2.00% 1.47%
Standard Deviation: 6.08% 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 YUM 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

 
VarianceYUM 36.99
VarianceS&P 500 19.58
CovarianceYUM, S&P 500 15.01
Correlation CoefficientYUM, S&P 5001 0.56
βYUM2 0.77
αYUM3 0.87

Calculations

1 CovarianceYUM, S&P 500 ÷ (Standard DeviationYUM × Standard DeviationS&P 500)
= 15.01 ÷ (6.08 × 4.42)

2 CovarianceYUM, S&P 500 ÷ VarianceS&P 500
= 15.01 ÷ 19.58

3 AverageYUM – βYUM × AverageS&P 500
= 2.00 – 0.77 × 1.47

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Expected Rate of Return

 
Assumptions
Rate of return on LT Treasury Composite1 RF 2.70%
Expected rate of return on market portfolio2 E(RM) 13.62%
Systematic risk (β) of YUM's common stock βYUM 0.77
Expected rate of return on YUM's common stock3 E(RYUM) 11.07%

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(RYUM) = RF + βYUM [E(RM) – RF]
= 2.70% + 0.77 [13.62% – 2.70%]
= 11.07%

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