Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Diageo PLC common stock.
Rates of Return
Diageo PLC (DEO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceDEO,t1 | DividendDEO,t1 | RDEO,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2008 | $70.38 | 1,267.38 | ||||
1. | Aug 31, 2008 | $74.40 | 5.71% | 1,282.83 | 1.22% | |
2. | Sep 30, 2008 | $68.86 | $1.5526 | -5.36% | 1,166.36 | -9.08% |
3. | Oct 31, 2008 | $62.19 | -9.69% | 968.75 | -16.94% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | May 31, 2014 | $128.79 | 4.89% | 1,923.57 | 2.10% | |
71. | Jun 30, 2014 | $127.27 | -1.18% | 1,960.23 | 1.91% | |
Average (R): | 1.25% | 0.74% | ||||
Standard deviation: | 5.38% | 5.02% |
Diageo PLC (DEO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceDEO,t1 | DividendDEO,t1 | RDEO,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2008 | $70.38 | 1,267.38 | ||||
1. | Aug 31, 2008 | $74.40 | 5.71% | 1,282.83 | 1.22% | |
2. | Sep 30, 2008 | $68.86 | $1.5526 | -5.36% | 1,166.36 | -9.08% |
3. | Oct 31, 2008 | $62.19 | -9.69% | 968.75 | -16.94% | |
4. | Nov 30, 2008 | $56.37 | -9.36% | 896.24 | -7.48% | |
5. | Dec 31, 2008 | $56.74 | 0.66% | 903.25 | 0.78% | |
6. | Jan 31, 2009 | $54.34 | -4.23% | 825.88 | -8.57% | |
7. | Feb 28, 2009 | $46.49 | -14.45% | 735.09 | -10.99% | |
8. | Mar 31, 2009 | $44.75 | $0.792 | -2.04% | 797.87 | 8.54% |
9. | Apr 30, 2009 | $47.85 | 6.93% | 872.81 | 9.39% | |
10. | May 31, 2009 | $54.56 | 14.02% | 919.14 | 5.31% | |
11. | Jun 30, 2009 | $57.25 | 4.93% | 919.32 | 0.02% | |
12. | Jul 31, 2009 | $62.38 | 8.96% | 987.48 | 7.41% | |
13. | Aug 31, 2009 | $62.04 | -0.55% | 1,020.62 | 3.36% | |
14. | Sep 30, 2009 | $61.49 | $1.4453 | 1.44% | 1,057.08 | 3.57% |
15. | Oct 31, 2009 | $65.02 | 5.74% | 1,036.19 | -1.98% | |
16. | Nov 30, 2009 | $67.61 | 3.98% | 1,095.63 | 5.74% | |
17. | Dec 31, 2009 | $69.41 | 2.66% | 1,115.10 | 1.78% | |
18. | Jan 31, 2010 | $67.19 | -3.20% | 1,073.87 | -3.70% | |
19. | Feb 28, 2010 | $65.28 | -2.84% | 1,104.49 | 2.85% | |
20. | Mar 31, 2010 | $67.45 | $0.9161 | 4.73% | 1,169.43 | 5.88% |
21. | Apr 30, 2010 | $68.14 | 1.02% | 1,186.69 | 1.48% | |
22. | May 31, 2010 | $61.28 | -10.07% | 1,089.41 | -8.20% | |
23. | Jun 30, 2010 | $62.74 | 2.38% | 1,030.71 | -5.39% | |
24. | Jul 31, 2010 | $69.88 | 11.38% | 1,101.60 | 6.88% | |
25. | Aug 31, 2010 | $65.50 | -6.27% | 1,049.33 | -4.74% | |
26. | Sep 30, 2010 | $69.01 | $1.4638 | 7.59% | 1,141.20 | 8.76% |
27. | Oct 31, 2010 | $74.00 | 7.23% | 1,183.26 | 3.69% | |
28. | Nov 30, 2010 | $71.66 | -3.16% | 1,180.55 | -0.23% | |
29. | Dec 31, 2010 | $74.33 | 3.73% | 1,257.64 | 6.53% | |
30. | Jan 31, 2011 | $76.80 | 3.32% | 1,286.12 | 2.26% | |
31. | Feb 28, 2011 | $78.26 | 1.90% | 1,327.22 | 3.20% | |
32. | Mar 31, 2011 | $76.22 | $0.996 | -1.33% | 1,325.83 | -0.10% |
33. | Apr 30, 2011 | $81.37 | 6.76% | 1,363.61 | 2.85% | |
34. | May 31, 2011 | $85.09 | 4.57% | 1,345.20 | -1.35% | |
35. | Jun 30, 2011 | $81.87 | -3.78% | 1,320.64 | -1.83% | |
36. | Jul 31, 2011 | $81.24 | -0.77% | 1,292.28 | -2.15% | |
37. | Aug 31, 2011 | $80.26 | -1.21% | 1,218.89 | -5.68% | |
38. | Sep 30, 2011 | $75.93 | $1.6309 | -3.36% | 1,131.42 | -7.18% |
39. | Oct 31, 2011 | $82.88 | 9.15% | 1,253.30 | 10.77% | |
40. | Nov 30, 2011 | $85.61 | 3.29% | 1,246.96 | -0.51% | |
41. | Dec 31, 2011 | $87.42 | 2.11% | 1,257.60 | 0.85% | |
42. | Jan 31, 2012 | $88.59 | 1.34% | 1,312.41 | 4.36% | |
43. | Feb 29, 2012 | $95.56 | $1.0482 | 9.05% | 1,365.68 | 4.06% |
44. | Mar 31, 2012 | $96.50 | 0.98% | 1,408.47 | 3.13% | |
45. | Apr 30, 2012 | $101.12 | 4.79% | 1,397.91 | -0.75% | |
46. | May 31, 2012 | $95.34 | -5.72% | 1,310.33 | -6.27% | |
47. | Jun 30, 2012 | $103.07 | 8.11% | 1,362.16 | 3.96% | |
48. | Jul 31, 2012 | $106.90 | 3.72% | 1,379.32 | 1.26% | |
49. | Aug 31, 2012 | $109.22 | 2.17% | 1,406.58 | 1.98% | |
50. | Sep 30, 2012 | $112.73 | $1.7084 | 4.78% | 1,440.67 | 2.42% |
51. | Oct 31, 2012 | $114.24 | 1.34% | 1,412.16 | -1.98% | |
52. | Nov 30, 2012 | $119.57 | 4.67% | 1,416.18 | 0.28% | |
53. | Dec 31, 2012 | $116.58 | -2.50% | 1,426.19 | 0.71% | |
54. | Jan 31, 2013 | $119.30 | 2.33% | 1,498.11 | 5.04% | |
55. | Feb 28, 2013 | $119.71 | $1.1272 | 1.29% | 1,514.68 | 1.11% |
56. | Mar 31, 2013 | $125.84 | 5.12% | 1,569.19 | 3.60% | |
57. | Apr 30, 2013 | $122.20 | -2.89% | 1,597.57 | 1.81% | |
58. | May 31, 2013 | $118.26 | -3.22% | 1,630.74 | 2.08% | |
59. | Jun 30, 2013 | $114.95 | -2.80% | 1,606.28 | -1.50% | |
60. | Jul 31, 2013 | $125.33 | 9.03% | 1,685.73 | 4.95% | |
61. | Aug 31, 2013 | $122.68 | $1.7925 | -0.68% | 1,632.97 | -3.13% |
62. | Sep 30, 2013 | $127.08 | 3.59% | 1,681.55 | 2.97% | |
63. | Oct 31, 2013 | $127.59 | 0.40% | 1,756.54 | 4.46% | |
64. | Nov 30, 2013 | $127.67 | 0.06% | 1,805.81 | 2.80% | |
65. | Dec 31, 2013 | $132.42 | 3.72% | 1,848.36 | 2.36% | |
66. | Jan 31, 2014 | $120.05 | -9.34% | 1,782.59 | -3.56% | |
67. | Feb 28, 2014 | $125.71 | $1.2986 | 5.80% | 1,859.45 | 4.31% |
68. | Mar 31, 2014 | $124.59 | -0.89% | 1,872.34 | 0.69% | |
69. | Apr 30, 2014 | $122.78 | -1.45% | 1,883.95 | 0.62% | |
70. | May 31, 2014 | $128.79 | 4.89% | 1,923.57 | 2.10% | |
71. | Jun 30, 2014 | $127.27 | -1.18% | 1,960.23 | 1.91% | |
Average (R): | 1.25% | 0.74% | ||||
Standard deviation: | 5.38% | 5.02% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of DEO during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RDEO,t | RS&P 500,t | (RDEO,t–RDEO)2 | (RS&P 500,t–RS&P 500)2 | (RDEO,t–RDEO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2008 | 5.71% | 1.22% | 19.87 | 0.23 | 2.12 |
2. | Sep 30, 2008 | -5.36% | -9.08% | 43.74 | 96.49 | 64.96 |
3. | Oct 31, 2008 | -9.69% | -16.94% | 119.69 | 312.80 | 193.50 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | May 31, 2014 | 4.89% | 2.10% | 13.26 | 1.85 | 4.95 |
71. | Jun 30, 2014 | -1.18% | 1.91% | 5.93 | 1.35 | -2.83 |
Total (Σ): | 2,025.99 | 1,765.03 | 1,405.57 |
t | Date | RDEO,t | RS&P 500,t | (RDEO,t–RDEO)2 | (RS&P 500,t–RS&P 500)2 | (RDEO,t–RDEO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2008 | 5.71% | 1.22% | 19.87 | 0.23 | 2.12 |
2. | Sep 30, 2008 | -5.36% | -9.08% | 43.74 | 96.49 | 64.96 |
3. | Oct 31, 2008 | -9.69% | -16.94% | 119.69 | 312.80 | 193.50 |
4. | Nov 30, 2008 | -9.36% | -7.48% | 112.63 | 67.71 | 87.33 |
5. | Dec 31, 2008 | 0.66% | 0.78% | 0.36 | 0.00 | -0.02 |
6. | Jan 31, 2009 | -4.23% | -8.57% | 30.07 | 86.67 | 51.05 |
7. | Feb 28, 2009 | -14.45% | -10.99% | 246.50 | 137.75 | 184.27 |
8. | Mar 31, 2009 | -2.04% | 8.54% | 10.85 | 60.79 | -25.68 |
9. | Apr 30, 2009 | 6.93% | 9.39% | 32.19 | 74.80 | 49.07 |
10. | May 31, 2009 | 14.02% | 5.31% | 163.04 | 20.83 | 58.28 |
11. | Jun 30, 2009 | 4.93% | 0.02% | 13.51 | 0.52 | -2.66 |
12. | Jul 31, 2009 | 8.96% | 7.41% | 59.39 | 44.49 | 51.41 |
13. | Aug 31, 2009 | -0.55% | 3.36% | 3.24 | 6.82 | -4.70 |
14. | Sep 30, 2009 | 1.44% | 3.57% | 0.04 | 8.00 | 0.53 |
15. | Oct 31, 2009 | 5.74% | -1.98% | 20.13 | 7.40 | -12.20 |
16. | Nov 30, 2009 | 3.98% | 5.74% | 7.45 | 24.93 | 13.63 |
17. | Dec 31, 2009 | 2.66% | 1.78% | 1.98 | 1.07 | 1.46 |
18. | Jan 31, 2010 | -3.20% | -3.70% | 19.83 | 19.72 | 19.77 |
19. | Feb 28, 2010 | -2.84% | 2.85% | 16.78 | 4.44 | -8.63 |
20. | Mar 31, 2010 | 4.73% | 5.88% | 12.06 | 26.38 | 17.84 |
21. | Apr 30, 2010 | 1.02% | 1.48% | 0.05 | 0.54 | -0.17 |
22. | May 31, 2010 | -10.07% | -8.20% | 128.18 | 79.95 | 101.23 |
23. | Jun 30, 2010 | 2.38% | -5.39% | 1.27 | 37.60 | -6.92 |
24. | Jul 31, 2010 | 11.38% | 6.88% | 102.54 | 37.63 | 62.11 |
25. | Aug 31, 2010 | -6.27% | -4.74% | 56.58 | 30.13 | 41.29 |
26. | Sep 30, 2010 | 7.59% | 8.76% | 40.19 | 64.18 | 50.79 |
27. | Oct 31, 2010 | 7.23% | 3.69% | 35.72 | 8.65 | 17.58 |
28. | Nov 30, 2010 | -3.16% | -0.23% | 19.50 | 0.95 | 4.30 |
29. | Dec 31, 2010 | 3.73% | 6.53% | 6.11 | 33.48 | 14.30 |
30. | Jan 31, 2011 | 3.32% | 2.26% | 4.28 | 2.31 | 3.15 |
31. | Feb 28, 2011 | 1.90% | 3.20% | 0.42 | 6.01 | 1.59 |
32. | Mar 31, 2011 | -1.33% | -0.10% | 6.70 | 0.72 | 2.20 |
33. | Apr 30, 2011 | 6.76% | 2.85% | 30.28 | 4.43 | 11.59 |
34. | May 31, 2011 | 4.57% | -1.35% | 11.01 | 4.38 | -6.95 |
35. | Jun 30, 2011 | -3.78% | -1.83% | 25.39 | 6.60 | 12.95 |
36. | Jul 31, 2011 | -0.77% | -2.15% | 4.10 | 8.36 | 5.85 |
37. | Aug 31, 2011 | -1.21% | -5.68% | 6.05 | 41.25 | 15.80 |
38. | Sep 30, 2011 | -3.36% | -7.18% | 21.32 | 62.73 | 36.57 |
39. | Oct 31, 2011 | 9.15% | 10.77% | 62.39 | 100.57 | 79.22 |
40. | Nov 30, 2011 | 3.29% | -0.51% | 4.16 | 1.56 | -2.55 |
41. | Dec 31, 2011 | 2.11% | 0.85% | 0.74 | 0.01 | 0.09 |
42. | Jan 31, 2012 | 1.34% | 4.36% | 0.01 | 13.07 | 0.30 |
43. | Feb 29, 2012 | 9.05% | 4.06% | 60.79 | 10.99 | 25.85 |
44. | Mar 31, 2012 | 0.98% | 3.13% | 0.07 | 5.71 | -0.65 |
45. | Apr 30, 2012 | 4.79% | -0.75% | 12.48 | 2.23 | -5.28 |
46. | May 31, 2012 | -5.72% | -6.27% | 48.58 | 49.12 | 48.85 |
47. | Jun 30, 2012 | 8.11% | 3.96% | 46.97 | 10.32 | 22.01 |
48. | Jul 31, 2012 | 3.72% | 1.26% | 6.06 | 0.27 | 1.27 |
49. | Aug 31, 2012 | 2.17% | 1.98% | 0.84 | 1.52 | 1.13 |
50. | Sep 30, 2012 | 4.78% | 2.42% | 12.42 | 2.82 | 5.92 |
51. | Oct 31, 2012 | 1.34% | -1.98% | 0.01 | 7.41 | -0.23 |
52. | Nov 30, 2012 | 4.67% | 0.28% | 11.64 | 0.21 | -1.57 |
53. | Dec 31, 2012 | -2.50% | 0.71% | 14.10 | 0.00 | 0.14 |
54. | Jan 31, 2013 | 2.33% | 5.04% | 1.16 | 18.48 | 4.64 |
55. | Feb 28, 2013 | 1.29% | 1.11% | 0.00 | 0.13 | 0.01 |
56. | Mar 31, 2013 | 5.12% | 3.60% | 14.95 | 8.15 | 11.04 |
57. | Apr 30, 2013 | -2.89% | 1.81% | 17.20 | 1.13 | -4.42 |
58. | May 31, 2013 | -3.22% | 2.08% | 20.06 | 1.78 | -5.97 |
59. | Jun 30, 2013 | -2.80% | -1.50% | 16.43 | 5.03 | 9.09 |
60. | Jul 31, 2013 | 9.03% | 4.95% | 60.46 | 17.66 | 32.68 |
61. | Aug 31, 2013 | -0.68% | -3.13% | 3.76 | 15.00 | 7.51 |
62. | Sep 30, 2013 | 3.59% | 2.97% | 5.44 | 4.98 | 5.20 |
63. | Oct 31, 2013 | 0.40% | 4.46% | 0.73 | 13.81 | -3.17 |
64. | Nov 30, 2013 | 0.06% | 2.80% | 1.42 | 4.25 | -2.46 |
65. | Dec 31, 2013 | 3.72% | 2.36% | 6.08 | 2.60 | 3.98 |
66. | Jan 31, 2014 | -9.34% | -3.56% | 112.27 | 18.51 | 45.58 |
67. | Feb 28, 2014 | 5.80% | 4.31% | 20.63 | 12.73 | 16.21 |
68. | Mar 31, 2014 | -0.89% | 0.69% | 4.60 | 0.00 | 0.11 |
69. | Apr 30, 2014 | -1.45% | 0.62% | 7.33 | 0.02 | 0.33 |
70. | May 31, 2014 | 4.89% | 2.10% | 13.26 | 1.85 | 4.95 |
71. | Jun 30, 2014 | -1.18% | 1.91% | 5.93 | 1.35 | -2.83 |
Total (Σ): | 2,025.99 | 1,765.03 | 1,405.57 |
Show all
VarianceDEO = Σ(RDEO,t–RDEO)2 ÷ (71 – 1)
= 2,025.99 ÷ (71 – 1)
= 28.94
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,765.03 ÷ (71 – 1)
= 25.21
CovarianceDEO, S&P 500 = Σ(RDEO,t–RDEO)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,405.57 ÷ (71 – 1)
= 20.08
Systematic Risk (β) Estimation
VarianceDEO | 28.94 |
VarianceS&P 500 | 25.21 |
CovarianceDEO, S&P 500 | 20.08 |
Correlation coefficientDEO, S&P 5001 | 0.74 |
βDEO2 | 0.80 |
αDEO3 | 0.66% |
Calculations
1 Correlation coefficientDEO, S&P 500
= CovarianceDEO, S&P 500 ÷ (Standard deviationDEO × Standard deviationS&P 500)
= 20.08 ÷ (5.38% × 5.02%)
= 0.74
2 βDEO
= CovarianceDEO, S&P 500 ÷ VarianceS&P 500
= 20.08 ÷ 25.21
= 0.80
3 αDEO
= AverageDEO – βDEO × AverageS&P 500
= 1.25% – 0.80 × 0.74%
= 0.66%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.86% |
Expected rate of return on market portfolio2 | E(RM) | 13.52% |
Systematic risk (β) of Diageo PLC common stock | βDEO | 0.80 |
Expected rate of return on Diageo PLC common stock3 | E(RDEO) | 11.76% |
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).
3 E(RDEO) = RF + βDEO [E(RM) – RF]
= 4.86% + 0.80 [13.52% – 4.86%]
= 11.76%