Stock Analysis on Net

YUM! Brands Inc. (NYSE:YUM)

This company has been moved to the archive! The financial data has not been updated since October 11, 2016.

Capital Asset Pricing Model (CAPM)

Microsoft Excel

Rates of Return

YUM! Brands Inc., monthly rates of return

Microsoft Excel
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, 2011 $46.76 1,286.12
1. Feb 28, 2011 $50.33 7.63% 1,327.22 3.20%
2. Mar 31, 2011 $51.38 2.09% 1,325.83 -0.10%
3. Apr 30, 2011 $53.64 $0.25 4.89% 1,363.61 2.85%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2015 $72.51 2.26% 2,080.41 0.05%
59. Dec 31, 2015 $73.05 0.74% 2,043.94 -1.75%
Average (R): 1.10% 0.84%
Standard deviation: 5.95% 3.40%
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, 2011 $46.76 1,286.12
1. Feb 28, 2011 $50.33 7.63% 1,327.22 3.20%
2. Mar 31, 2011 $51.38 2.09% 1,325.83 -0.10%
3. Apr 30, 2011 $53.64 $0.25 4.89% 1,363.61 2.85%
4. May 31, 2011 $55.32 3.13% 1,345.20 -1.35%
5. Jun 30, 2011 $55.24 -0.14% 1,320.64 -1.83%
6. Jul 31, 2011 $52.82 $0.25 -3.93% 1,292.28 -2.15%
7. Aug 31, 2011 $54.37 2.93% 1,218.89 -5.68%
8. Sep 30, 2011 $49.39 -9.16% 1,131.42 -7.18%
9. Oct 31, 2011 $53.57 $0.285 9.04% 1,253.30 10.77%
10. Nov 30, 2011 $56.04 4.61% 1,246.96 -0.51%
11. Dec 31, 2011 $59.01 5.30% 1,257.60 0.85%
12. Jan 31, 2012 $63.33 $0.285 7.80% 1,312.41 4.36%
13. Feb 29, 2012 $66.24 4.59% 1,365.68 4.06%
14. Mar 31, 2012 $71.18 7.46% 1,408.47 3.13%
15. Apr 30, 2012 $72.73 $0.285 2.58% 1,397.91 -0.75%
16. May 31, 2012 $70.36 -3.26% 1,310.33 -6.27%
17. Jun 30, 2012 $64.42 -8.44% 1,362.16 3.96%
18. Jul 31, 2012 $64.84 $0.285 1.09% 1,379.32 1.26%
19. Aug 31, 2012 $63.72 -1.73% 1,406.58 1.98%
20. Sep 30, 2012 $66.34 4.11% 1,440.67 2.42%
21. Oct 31, 2012 $70.11 $0.335 6.19% 1,412.16 -1.98%
22. Nov 30, 2012 $67.08 -4.32% 1,416.18 0.28%
23. Dec 31, 2012 $66.40 -1.01% 1,426.19 0.71%
24. Jan 31, 2013 $64.94 $0.335 -1.69% 1,498.11 5.04%
25. Feb 28, 2013 $65.48 0.83% 1,514.68 1.11%
26. Mar 31, 2013 $71.94 9.87% 1,569.19 3.60%
27. Apr 30, 2013 $68.12 $0.335 -4.84% 1,597.57 1.81%
28. May 31, 2013 $67.75 -0.54% 1,630.74 2.08%
29. Jun 30, 2013 $69.34 2.35% 1,606.28 -1.50%
30. Jul 31, 2013 $72.92 $0.335 5.65% 1,685.73 4.95%
31. Aug 31, 2013 $70.02 -3.98% 1,632.97 -3.13%
32. Sep 30, 2013 $71.39 1.96% 1,681.55 2.97%
33. Oct 31, 2013 $67.62 $0.37 -4.76% 1,756.54 4.46%
34. Nov 30, 2013 $77.68 14.88% 1,805.81 2.80%
35. Dec 31, 2013 $75.61 -2.66% 1,848.36 2.36%
36. Jan 31, 2014 $67.15 $0.37 -10.70% 1,782.59 -3.56%
37. Feb 28, 2014 $74.08 10.32% 1,859.45 4.31%
38. Mar 31, 2014 $75.39 1.77% 1,872.34 0.69%
39. Apr 30, 2014 $76.99 $0.37 2.61% 1,883.95 0.62%
40. May 31, 2014 $77.31 0.42% 1,923.57 2.10%
41. Jun 30, 2014 $81.20 5.03% 1,960.23 1.91%
42. Jul 31, 2014 $69.40 $0.37 -14.08% 1,930.67 -1.51%
43. Aug 31, 2014 $72.43 4.37% 2,003.37 3.77%
44. Sep 30, 2014 $71.98 -0.62% 1,972.29 -1.55%
45. Oct 31, 2014 $71.83 $0.41 0.36% 2,018.05 2.32%
46. Nov 30, 2014 $77.25 7.55% 2,067.56 2.45%
47. Dec 31, 2014 $72.85 -5.70% 2,058.90 -0.42%
48. Jan 31, 2015 $72.28 $0.41 -0.22% 1,994.99 -3.10%
49. Feb 28, 2015 $81.11 12.22% 2,104.50 5.49%
50. Mar 31, 2015 $78.72 -2.95% 2,067.89 -1.74%
51. Apr 30, 2015 $85.96 $0.41 9.72% 2,085.51 0.85%
52. May 31, 2015 $90.11 4.83% 2,107.39 1.05%
53. Jun 30, 2015 $90.08 -0.03% 2,063.11 -2.10%
54. Jul 31, 2015 $87.76 $0.41 -2.12% 2,103.84 1.97%
55. Aug 31, 2015 $79.77 -9.10% 1,972.18 -6.26%
56. Sep 30, 2015 $79.95 0.23% 1,920.03 -2.64%
57. Oct 31, 2015 $70.91 $0.46 -10.73% 2,079.36 8.30%
58. Nov 30, 2015 $72.51 2.26% 2,080.41 0.05%
59. Dec 31, 2015 $73.05 0.74% 2,043.94 -1.75%
Average (R): 1.10% 0.84%
Standard deviation: 5.95% 3.40%

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1 Data in US$ 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


Variance and Covariance

YUM! Brands Inc., calculation of variance and covariance of returns

Microsoft Excel
t Date RYUM,t RS&P 500,t (RYUM,tRYUM)2 (RS&P 500,tRS&P 500)2 (RYUM,tRYUM)×(RS&P 500,tRS&P 500)
1. Feb 28, 2011 7.63% 3.20% 42.76 5.53 15.37
2. Mar 31, 2011 2.09% -0.10% 0.98 0.90 -0.94
3. Apr 30, 2011 4.89% 2.85% 14.36 4.02 7.60
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2015 2.26% 0.05% 1.35 0.63 -0.92
59. Dec 31, 2015 0.74% -1.75% 0.12 6.75 0.91
Total (Σ): 2,050.05 670.89 470.80
t Date RYUM,t RS&P 500,t (RYUM,tRYUM)2 (RS&P 500,tRS&P 500)2 (RYUM,tRYUM)×(RS&P 500,tRS&P 500)
1. Feb 28, 2011 7.63% 3.20% 42.76 5.53 15.37
2. Mar 31, 2011 2.09% -0.10% 0.98 0.90 -0.94
3. Apr 30, 2011 4.89% 2.85% 14.36 4.02 7.60
4. May 31, 2011 3.13% -1.35% 4.15 4.82 -4.47
5. Jun 30, 2011 -0.14% -1.83% 1.54 7.13 3.31
6. Jul 31, 2011 -3.93% -2.15% 25.24 8.95 15.03
7. Aug 31, 2011 2.93% -5.68% 3.38 42.56 -12.00
8. Sep 30, 2011 -9.16% -7.18% 105.17 64.34 82.26
9. Oct 31, 2011 9.04% 10.77% 63.11 98.56 78.87
10. Nov 30, 2011 4.61% -0.51% 12.35 1.82 -4.75
11. Dec 31, 2011 5.30% 0.85% 17.67 0.00 0.04
12. Jan 31, 2012 7.80% 4.36% 45.00 12.35 23.57
13. Feb 29, 2012 4.59% 4.06% 12.24 10.33 11.25
14. Mar 31, 2012 7.46% 3.13% 40.47 5.24 14.56
15. Apr 30, 2012 2.58% -0.75% 2.20 2.54 -2.36
16. May 31, 2012 -3.26% -6.27% 18.96 50.55 30.96
17. Jun 30, 2012 -8.44% 3.96% 90.98 9.68 -29.67
18. Jul 31, 2012 1.09% 1.26% 0.00 0.17 0.00
19. Aug 31, 2012 -1.73% 1.98% 7.97 1.28 -3.19
20. Sep 30, 2012 4.11% 2.42% 9.10 2.49 4.76
21. Oct 31, 2012 6.19% -1.98% 25.93 7.97 -14.38
22. Nov 30, 2012 -4.32% 0.28% 29.35 0.31 3.03
23. Dec 31, 2012 -1.01% 0.71% 4.45 0.02 0.29
24. Jan 31, 2013 -1.69% 5.04% 7.78 17.62 -11.71
25. Feb 28, 2013 0.83% 1.11% 0.07 0.07 -0.07
26. Mar 31, 2013 9.87% 3.60% 76.91 7.58 24.15
27. Apr 30, 2013 -4.84% 1.81% 35.29 0.93 -5.73
28. May 31, 2013 -0.54% 2.08% 2.69 1.52 -2.02
29. Jun 30, 2013 2.35% -1.50% 1.57 5.50 -2.93
30. Jul 31, 2013 5.65% 4.95% 20.70 16.82 18.66
31. Aug 31, 2013 -3.98% -3.13% 25.73 15.80 20.16
32. Sep 30, 2013 1.96% 2.97% 0.74 4.54 1.83
33. Oct 31, 2013 -4.76% 4.46% 34.32 13.07 -21.18
34. Nov 30, 2013 14.88% 2.80% 189.93 3.84 27.01
35. Dec 31, 2013 -2.66% 2.36% 14.14 2.28 -5.68
36. Jan 31, 2014 -10.70% -3.56% 139.13 19.39 51.94
37. Feb 28, 2014 10.32% 4.31% 85.09 12.02 31.98
38. Mar 31, 2014 1.77% 0.69% 0.45 0.02 -0.10
39. Apr 30, 2014 2.61% 0.62% 2.30 0.05 -0.34
40. May 31, 2014 0.42% 2.10% 0.46 1.58 -0.86
41. Jun 30, 2014 5.03% 1.91% 15.49 1.13 4.18
42. Jul 31, 2014 -14.08% -1.51% 230.20 5.54 35.70
43. Aug 31, 2014 4.37% 3.77% 10.69 8.53 9.55
44. Sep 30, 2014 -0.62% -1.55% 2.95 5.74 4.11
45. Oct 31, 2014 0.36% 2.32% 0.54 2.18 -1.08
46. Nov 30, 2014 7.55% 2.45% 41.60 2.59 10.38
47. Dec 31, 2014 -5.70% -0.42% 46.13 1.60 8.58
48. Jan 31, 2015 -0.22% -3.10% 1.73 15.59 5.19
49. Feb 28, 2015 12.22% 5.49% 123.67 21.57 51.65
50. Mar 31, 2015 -2.95% -1.74% 16.34 6.68 10.45
51. Apr 30, 2015 9.72% 0.85% 74.34 0.00 0.06
52. May 31, 2015 4.83% 1.05% 13.93 0.04 0.76
53. Jun 30, 2015 -0.03% -2.10% 1.27 8.68 3.33
54. Jul 31, 2015 -2.12% 1.97% 10.34 1.28 -3.63
55. Aug 31, 2015 -9.10% -6.26% 104.04 50.45 72.45
56. Sep 30, 2015 0.23% -2.64% 0.76 12.17 3.04
57. Oct 31, 2015 -10.73% 8.30% 139.89 55.56 -88.16
58. Nov 30, 2015 2.26% 0.05% 1.35 0.63 -0.92
59. Dec 31, 2015 0.74% -1.75% 0.12 6.75 0.91
Total (Σ): 2,050.05 670.89 470.80

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VarianceYUM = Σ(RYUM,tRYUM)2 ÷ (59 – 1)
= 2,050.05 ÷ (59 – 1)
= 35.35

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 670.89 ÷ (59 – 1)
= 11.57

CovarianceYUM, S&P 500 = Σ(RYUM,tRYUM)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 470.80 ÷ (59 – 1)
= 8.12


Systematic Risk (β) Estimation

Microsoft Excel
VarianceYUM 35.35
VarianceS&P 500 11.57
CovarianceYUM, S&P 500 8.12
Correlation coefficientYUM, S&P 5001 0.40
βYUM2 0.70
αYUM3 0.50%

Calculations

1 Correlation coefficientYUM, S&P 500
= CovarianceYUM, S&P 500 ÷ (Standard deviationYUM × Standard deviationS&P 500)
= 8.12 ÷ (5.95% × 3.40%)
= 0.40

2 βYUM
= CovarianceYUM, S&P 500 ÷ VarianceS&P 500
= 8.12 ÷ 11.57
= 0.70

3 αYUM
= AverageYUM – βYUM × AverageS&P 500
= 1.10%0.70 × 0.84%
= 0.50%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.42%
Expected rate of return on market portfolio2 E(RM) 13.60%
Systematic risk (β) of YUM! Brands Inc. common stock βYUM 0.70
 
Expected rate of return on YUM! Brands Inc. common stock3 E(RYUM) 10.86%

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).

2 See details »

3 E(RYUM) = RF + βYUM [E(RM) – RF]
= 4.42% + 0.70 [13.60%4.42%]
= 10.86%