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 3.06%
Expected rate of return on market portfolio2 E(RM) 13.43%
Systematic risk (β) of YUM's common stock βYUM 0.77
Expected rate of return on YUM's common stock3 E(RYUM) 11.01%

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]
= 3.06% + 0.77 [13.43% – 3.06%]
= 11.01%

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