Table 1. Betas of different companies according to different sources
AT&T Boeing CocaCola Date
Yahoo 0.61 0.46 0.29 12-Feb-03
Multex 0.87 0.66 0.42 12-Feb-03
Quicken 1.14 0.66 0.41 12-Feb-03
Reuters 0.87 0.68 0.42 12-Feb-03
Bloomberg 1.00 1.07 0.64 12-Feb-03
Datastream 1.10 1.10 0.37 12-Feb-03
Buy&hold 0.84 0.66 0.41 14-Feb-03
Max 1.14 1.10 0.64min 0.61 0.46 0.29
Table 2. Historical betas of the 3,813 companies in our sample with respect to the S&P 500
Market Cap. Market Cap.
Number % $ bn % Number % $ bn % Number
All betas > 0 2,780 73% 11,956 93% 404 90% 8,980 93% 28 93%
Average beta > 1 1,242 33% 5,758 45% 157 35% 4,273 44% 13 43%
All betas > 1 434 11% 3,116 24% 71 16% 2,574 27% 7 23%
Average beta < 0 124 3% 132 1% 10 2% 102 1% 0 0%
All betas < 0 2 0% 97 1% 0 0% 0% 0 0%
Abs(Beta max/beta min) > 2 2,927 77% 6,417 50% 235 52% 4,484 47% 12 40%
Total 3,813 100% 12,886 100% 450 100% 9,638 100% 30 100%
Full sample S&P 500
Companies Companies Companies
Market Cap. Market Cap.Number % $ bn % Number % $ bn %
All betas > 0 98 97% 12,747 99% 95 94% 12,450 129%Average beta > 1 20 20% 3,630 28% 26 26% 5,381 56%All betas > 1 12 12% 2,665 21% 18 18% 3,714 39%Average beta < 0 1 1% 18 0% 0 0% 0%All betas < 0 0 0% 0% 0 0% 0%Abs(Beta max/beta min) > 2 25 25% 1,337 10% 31 31% 3,545 37%Total 101 100% 12,886 100% 101 100% 9,638 100%
Industries IndustriesIndustry weighted betas Industry unweighted betas
Market Cap.
% $ bn %
93% 3,223 94%
43% 1,839 54%
23% 1,372 40%
0% 0%
0% 0%
40% 1,225 36%
100% 3,425 100%
DJIA 30
Companies
Market Cap. Market Cap.Number % $ bn % Number % $ bn %
All betas > 0 98 97% 12,747 99% 95 94% 12,450 129%Average beta > 1 20 20% 3,630 28% 26 26% 5,381 56%All betas > 1 12 12% 2,665 21% 18 18% 3,714 39%Average beta < 0 1 1% 18 0% 0 0% 0%All betas < 0 0 0% 0% 0 0% 0%Abs(Beta max/beta min) > 2 25 25% 1,337 10% 31 31% 3,545 37%Total 101 100% 12,886 100% 101 100% 9,638 100%
Industries IndustriesIndustry weighted betas Industry unweighted betas
Company betas Industry betas
Full sample S&P 500 DJIA 30 Weighted Unweighted
Median 0.72 0.82 0.88 0.84 0.74
Beta average Average 0.83 0.91 0.94 0.88 0.79
Maximum 4.46 3.13 1.66 2.78 1.98
minimum -1.43 -0.17 0.12 0.06 -0.05
Median 0.88 0.63 0.53 0.41 0.35
Max - Min Average 1.05 0.68 0.53 0.45 0.38
Maximum 3.99 2.17 0.94 1.02 1.23
minimum 0.12 0.21 0.27 0.14 0.15
Median 3.07 2.11 1.77 1.64 1.52
Abs (Max / Min) Average 15.7 4.76 2.72 2.72 2.57
Maximum 10116.62 251.72 23.58 35.47 42.03
minimum 0.1 0.12 1.25 1.12 0.95
Median 1.31 0.76 0.52 0.49 0.44
(MAX-Min) / Average 6.72 2.32 0.76 1.26 0.71
Abs (Beta December 31) Maximum 2997.32 240.01 3.36 55.62 6.77
minimum 0.21 0.21 0.24 0.12 0.19
Table 3. Summary statistics of the historical betas of the 3,813 companies in our sample with respect to the S&P 500
Table 4. Historical betas of the 3813 companies in our sample with respect to the S&P 500
Maximum Beta - Minimum Beta
# companies 3 - 3.99 2 - 2.99 1 - 1.99 0.5 - 0.99 0.2 - 0.49
3813 Full sample 65 268 1246 1574 653
450 S&P 500 0 1 56 250 143
3363 Not in the S&P 500 65 267 1190 1324 510
30 DJIA 0 0 6 16 8
101 Industry weighted 0 0 1 37 59
101 Industry unweighted 0 0 1 15 77
(Maximum Beta - Minimum Beta)/Abs(Beta December 31)
# companies > 3 2 - 2.99 1 - 1.99 0.5 - 0.99 0.2 - 0.49
3813 Full sample 800 425 1208 1125 255
450 S&P 500 36 23 95 190 106
3363 Not in the S&P 500 764 402 1113 935 149
30 DJIA 1 1 3 11 14
101 Industry weighted 3 2 12 31 51
101 Industry unweighted 2 3 10 24 61
Maximum Beta - Minimum Beta
< 0.2 average
7 1.05
0 0.68
7 1.10
0 0.53
4 0.45
8 0.38
(Maximum Beta - Minimum Beta)/Abs(Beta December 31)
< 0.2 average
0 6.72
0 2.32
0 7.31
0 0.76
2 1.26
1 0.71
Correlation Company volatility / Market volatility
Average Max min Max/min Average Max
3M Co. 0.38 0.50 0.23 2.12 1.51 1.69
Alcoa 0.37 0.53 0.21 2.55 2.13 2.47
American Express 0.78 0.83 0.70 1.18 1.88 2.17
AT&T 0.34 0.44 0.14 3.11 2.22 2.57
Boeing 0.45 0.54 0.27 1.97 2.13 2.40
Caterpillar 0.40 0.52 0.31 1.65 1.93 2.15
Citigroup 0.80 0.85 0.71 1.19 2.07 2.32
Coca Cola 0.46 0.61 0.32 1.92 1.73 1.95
Du Pont 0.43 0.55 0.31 1.78 1.75 1.97
Eastman Kodak 0.28 0.35 0.18 1.97 1.98 2.25
Exxon Mobil 0.40 0.58 0.24 2.39 1.06 1.18
General Electric 0.79 0.83 0.74 1.11 1.59 1.72
Hewlett-Packard 0.53 0.68 0.39 1.76 2.55 2.90
Home Depot 0.62 0.71 0.50 1.43 2.01 2.28
Honeywell Intl. 0.50 0.59 0.42 1.40 2.44 2.76
IBM 0.56 0.66 0.36 1.83 2.11 2.30
Intel 0.57 0.64 0.50 1.28 2.72 3.09
Intl.Paper 0.38 0.48 0.29 1.67 1.90 2.15
Johnson & Johnson 0.37 0.53 0.25 2.14 1.29 1.50
J P Morgan Chase 0.72 0.77 0.66 1.18 2.21 2.50
McDonalds 0.41 0.49 0.30 1.64 1.60 1.85
Merck 0.36 0.55 0.14 4.02 1.67 1.89
Microsoft 0.60 0.66 0.52 1.26 2.55 3.10
Philip Morris 0.07 0.25 -0.07 3.67 1.96 2.20
SBC Comm. 0.30 0.47 0.15 3.16 1.62 1.83
United Technologies 0.64 0.72 0.56 1.28 1.89 2.12
Wal Mart Stores 0.56 0.67 0.46 1.45 1.78 2.06
General Motors 0.52 0.58 0.44 1.31 1.95 2.16
Procter & Gamble 0.24 0.45 -0.02 20.37 1.83 2.12
Walt Disney 0.55 0.70 0.43 1.61 1.90 2.07
Average 0.48 0.59 0.35 2.51 1.93 2.19
Max 0.80 0.85 0.74 20.37 2.72 3.10
Min 0.07 0.25 -0.07 1.11 1.06 1.18
Table 5. Some statistics of the correlation and of the company volatility divided by the market volatility of the S&P 500 for the 30 companies in the DJIA in the two-month period of December 2001 and January 2002.
Company volatility / Market volatility
min Max/min
1.39 1.22
1.91 1.29
1.71 1.27
1.98 1.29
1.92 1.25
1.74 1.24
1.89 1.23
1.46 1.33
1.56 1.26
1.67 1.35
0.90 1.31
1.46 1.18
2.23 1.30
1.82 1.25
2.29 1.20
1.89 1.22
2.43 1.27
1.65 1.30
1.10 1.37
1.89 1.32
1.50 1.23
1.42 1.33
2.24 1.38
1.66 1.32
1.36 1.35
1.70 1.25
1.62 1.27
1.78 1.22
1.58 1.34
1.69 1.22
1.71 1.28
2.43 1.38
0.90 1.18
Table 5. Some statistics of the correlation and of the company volatility divided by the market volatility of the S&P 500 for the 30 companies in the DJIA in the two-month period of December 2001 and January 2002.
Table 6. Percentage days or months that the share price and the S&P 500 move in the same direction
(1/1/1997-31/12/2001)
All companies 30 companies DJIA
Percentage range Monthly data Daily data Monthly data Daily data
0 - 10% 0 10
10% - 20% 4 32
20% - 30% 7 126
30% - 40% 23 598
40% - 50% 404 1138
50% - 60% 2037 1406 2
60% - 70% 1227 474 16 24
70% - 80% 107 29 11 6
80% - 90% 4 0 1
90% - 100% 0 0
Number of companies 3813 3813 30 30
Average 58.0% 48.7% 68.3% 65.9%
Median 58.1% 50.0% 66.9% 64.5%
Number of misallocated portfolios on the 62 days of the following two months.
Date
December: 10 and 16.
December: 12, 13, 14 and 15. January: 12, 13, 15 and 16.
January: 14.
December: 17 and 19.
December: 8 and 21. January: 8, 10, 17 and 19.
December: 18. January: 18, 20 and 21.
December: 5, 6, 7, 9, 11, 20 and 22. January: 5, 6, 7, 9, 11 and 22.
December: 3, 4, 23, 24, 27, 28, 29, 30 and 31. January: 3, 4, 23, 24, 27, 28, 29 and 30.
9 days
Table 7. Twenty portfolios ranked by decreasing beta on December 1, 2001
misallocated portfolios
13
11
10
9
8
6
4
2
0
All Low-ß ß-2 ß-3 ß-4 ß-5 ß-6 ß-7
All 71.3% 52.8% 71.9% 78.2% 82.5% 79.3% 80.6% 82.8%
Small-ME 74.7% 61.5% 77.8% 76.9% 83.8% 86.3% 79.5% 82.9%
ME-2 73.3% 62.5% 73.4% 79.7% 87.5% 78.1% 78.1% 78.1%
ME-3 73.1% 52.6% 76.3% 76.3% 81.6% 81.6% 86.8% 89.5%
ME-4 72.9% 62.5% 75.0% 87.5% 71.9% 68.8% 81.3% 93.8%
ME-5 66.6% 51.7% 65.5% 72.4% 82.8% 72.4% 75.9% 86.2%
ME-6 68.4% 47.6% 61.9% 81.0% 85.7% 90.5% 76.2% 66.7%
ME-7 62.6% 19.0% 42.9% 61.9% 81.0% 71.4% 90.5% 85.7%
ME-8 65.4% 31.6% 73.7% 84.2% 78.9% 63.2% 78.9% 78.9%
ME-9 67.5% 26.3% 63.2% 84.2% 78.9% 84.2% 84.2% 84.2%
Large-ME 66.1% 41.2% 76.5% 82.4% 82.4% 70.6% 82.4% 76.5%
Panel B. Portfolio weighted Beta December, 1 - Portfolio weighted Beta December, 15
All Low-ß ß-2 ß-3 ß-4 ß-5 ß-6 ß-7
All -0.34 -0.22 -0.17 -0.20 -0.09 -0.09 -0.03
Small-ME -0.09 -0.42 -0.22 -0.17 -0.17 -0.10 -0.13 0.04
ME-2 -0.11 -0.36 -0.24 -0.21 -0.20 -0.07 -0.14 -0.14
ME-3 -0.11 -0.29 -0.29 -0.23 -0.26 -0.09 -0.13 -0.18
ME-4 -0.11 -0.48 -0.25 -0.22 -0.17 -0.12 -0.09 -0.03
ME-5 -0.06 -0.35 -0.26 -0.17 -0.26 0.01 -0.04 -0.04
ME-6 -0.06 -0.27 -0.16 -0.16 -0.12 -0.17 -0.02 0.00
ME-7 -0.03 -0.20 -0.17 -0.11 -0.24 -0.08 -0.01 -0.01
ME-8 0.01 -0.13 -0.17 -0.06 -0.18 -0.09 -0.03 0.08
ME-9 -0.01 -0.22 -0.14 -0.16 -0.15 -0.16 -0.08 0.12
Large-ME -0.01 -0.19 -0.18 -0.06 -0.24 -0.07 0.06 -0.03
Table 8. Percentage of the companies in each portfolio formed on December 1 that change portfolio if portfolios formed on December 15, 2001. Change in the betas of each portfolio from December 1 to December 15, 2001. Portfolios formed according to Fama and French (1992).
Panel A. Percentage of the companies in each portfolio formed on December 1 that change portfolio if portfolios formed on December 15.
ß-8 ß-9 High-ß
76.1% 71.1% 39.5%
77.8% 76.9% 45.2%
81.3% 65.6% 48.4%
84.2% 65.8% 40.9%
75.0% 68.8% 45.5%
62.1% 69.0% 31.3%
81.0% 66.7% 30.4%
71.4% 76.2% 27.3%
68.4% 68.4% 30.0%
68.4% 84.2% 26.1%
70.6% 58.8% 22.2%
Panel B. Portfolio weighted Beta December, 1 - Portfolio weighted Beta December, 15
ß-8 ß-9 High-ß
0.04 0.04 0.27
0.06 -0.03 0.20
-0.05 0.06 0.26
0.07 0.04 0.19
-0.03 -0.12 0.42
0.05 0.15 0.30
0.03 0.00 0.25
0.10 0.24 0.19
0.21 0.09 0.41
0.05 0.13 0.42
0.08 0.22 0.34
the companies in each portfolio formed on December 1 that change portfolio if portfolios formed on December 15, 2001. Change in the betas of each portfolio from December 1 to December 15, 2001. Portfolios formed according to Fama and French (1992).
the companies in each portfolio formed on December 1 that change portfolio if portfolios formed on December 15.
Table 9. Historical relative betas of the 30 companies in the Dow Jones Industrial Average Index
Beta S&P 500 / Beta DJ IND Beta S&P 500 / Beta W 5000
Max min average max/min Max min average
3M Co. 0.76 0.51 0.65 1.51 2.02 1.00 1.20
Alcoa 0.86 0.46 0.66 1.86 1.22 0.94 1.03
American Express 1.10 0.89 0.99 1.23 1.16 1.04 1.10
AT&T 2.57 1.19 1.66 2.15 1.09 0.92 1.00
Boeing 0.84 0.55 0.74 1.51 1.11 0.99 1.05
Caterpillar 0.78 0.48 0.66 1.62 1.37 1.10 1.21
Citigroup 1.18 0.96 1.05 1.24 1.16 1.02 1.09
Coca Cola 1.02 0.80 0.90 1.26 1.30 1.07 1.17
Du Pont 0.81 0.54 0.70 1.51 1.75 1.09 1.26
Eastman Kodak 0.90 0.56 0.75 1.60 1.24 0.92 1.10
Exxon Mobil 0.91 0.69 0.80 1.32 1.38 0.97 1.14
General Electric 1.23 1.00 1.10 1.23 1.21 1.07 1.12
Hewlett-Packard 1.33 1.06 1.19 1.26 1.01 0.85 0.93
Home Depot 1.30 1.00 1.15 1.30 1.18 0.99 1.08
Honeywell Intl. 0.87 0.68 0.80 1.29 1.31 1.09 1.18
IBM 1.10 0.80 0.98 1.38 1.10 0.99 1.05
Intel 1.38 1.06 1.24 1.30 1.04 0.95 1.00
Intl.Paper 0.80 0.49 0.66 1.62 1.41 1.10 1.22
Johnson & Johnson 1.12 0.60 0.90 1.86 1.90 1.22 1.40
J P Morgan Chase 1.24 1.02 1.11 1.21 1.08 0.96 1.04
McDonalds 1.12 0.73 0.93 1.53 1.81 1.19 1.36
Merck 1.29 0.70 1.06 1.84 2.67 1.27 1.54
Microsoft 1.55 1.02 1.34 1.52 1.09 0.99 1.04
Philip Morris 12.10 -28.10 -0.07 0.43 27.10 -2.86 1.80
SBC Comm. 1.94 0.98 1.46 1.97 1.74 1.07 1.26
United Technologies 0.92 0.77 0.86 1.19 1.23 1.07 1.14
Wal Mart Stores 1.25 0.96 1.10 1.31 1.31 1.11 1.22
General Motors 1.07 0.85 0.98 1.26 1.07 0.95 1.01
Procter & Gamble 1.00 -0.16 0.63 6.22 3.09 0.49 1.49
Walt Disney 1.21 0.90 1.05 1.33 1.14 0.96 1.06
Average 1.52 0.80 0.97 1.59 2.28 1.01 1.18
Median 1.11 0.79 0.96 1.36 1.23 1.00 1.13
Beta S&P 500 / Beta W 5000
max/min
2.02
1.30
1.11
1.19
1.13
1.24
1.13
1.21
1.60
1.35
1.43
1.13
1.19
1.19
1.20
1.12
1.09
1.29
1.56
1.12
1.51
2.11
1.10
9.47
1.62
1.15
1.18
1.13
6.34
1.18
1.75
1.19
Table 10. Change in beta ranking order in the month of December, 2001. Statistics of the difference Maximum beta ranking - minimum beta ranking.
Maximum ranking - minimum ranking Full sample S&P 500 DJIA 30
MAX 3760 2592 2041
Min 15 74 467
Average 1542 1154 1001
Median 1391 1126 908
Number of companies 3813 450 30
Table 10. Change in beta ranking order in the month of December, 2001. Statistics of the difference Maximum beta ranking - minimum beta ranking.
Table 11. Calculated betas as of December 31, 2001 of the 30 companies in the Dow Jones Industrial Average Index
12/31/2001 Beta S&P 500 Beta DJ IND Beta W 5000
PHILIP MORRIS MO 0.232 0.378 0.149
PROCTER & GAMBLE PG 0.281 0.460 0.244
EXXON MOBIL XOM 0.358 0.480 0.329
SBC COMMUNICATIONS SBC 0.460 0.367 0.322
MERCK MRK 0.483 0.528 0.299
3M CO. MMM 0.488 0.778 0.464
JOHNSON & JOHNSON JNJ 0.488 0.578 0.363
EASTMAN KODAK EK 0.590 0.791 0.522
COCA COLA KO 0.654 0.775 0.530
MCDONALDS MCD 0.677 0.769 0.500
CATERPILLAR CAT 0.731 1.104 0.633
DU PONT DD 0.771 1.019 0.700
BOEING BA 0.807 1.178 0.744
WAL MART STORES WMT 0.917 1.104 0.749
WALT DISNEY DIS 0.928 1.022 0.844
AT&T T 0.959 1.104 0.942
INTL.PAPER IP 1.011 1.323 0.877
GENERAL MOTORS GM 1.129 1.167 1.087
HOME DEPOT HD 1.130 1.104 1.143
GENERAL ELECTRIC GE 1.163 1.104 1.063
HONEYWELL INTL. HON 1.176 1.564 1.016
ALCOA AA 1.219 1.487 1.209
IBM IBM 1.234 1.196 1.171
AMERICAN EXPRESS AXP 1.245 1.374 1.120
UNITED TECHNOLOGIES UTX 1.323 1.488 1.207
CITIGROUP C 1.459 1.525 1.320
HEWLETT-PACKARD HPQ 1.489 1.270 1.639
J P MORGAN CHASE & CO. JPM 1.518 1.431 1.458
INTEL @INTC 1.696 1.434 1.632
MICROSOFT @MSFT 1.823 1.379 1.716
average average 0.948 1.043 0.866
Table 11. Calculated betas as of December 31, 2001 of the 30 companies in the Dow Jones Industrial Average Index
Max-min
0.229
0.216
0.151
0.138
0.229
0.314
0.215
0.269
0.245
0.269
0.471
0.319
0.434
0.355
0.178
0.162
0.446
0.080
0.039
0.100
0.548
0.278
0.063
0.254
0.281
0.205
0.369
0.087
0.262
0.4440.255
Table 12. Portfolios of 200 companies sorted by realized return. Correlation of the portfolio return with the beta calculated on December 1, 2001
CORRELATION REALIZED RETURN - BETA.
1996-2001 1997 1998 1999 2000 2001
Slope -0.07 0.23 0.64 1.68 -1.00 -0.26
standard error slope 0.076 0.032 0.038 0.013 0.009 0.023
0.0002 0.0145 0.0728 0.8155 0.7667 0.0347
F statistic 0.8 53.2 282.6 15917.3 11835.9 129.4
intercept 0.54 0.02 -0.61 -1.25 1.10 0.43
Returns:
S&P 500 66.2% 33.4% 28.6% 21.0% -9.1% -11.9%
DOW JONES IND. 68.8% 24.9% 18.1% 26.7% -4.5% -5.4%
WILSHIRE 5000 48.8% 29.2% 21.7% 22.0% -11.8% -12.1%
R2
Table 12. Portfolios of 200 companies sorted by realized return. Correlation of the portfolio return with the beta calculated on December 1, 2001
Table A.1. Main findings of Fama and French’s article (1992)
Size Annual Beta Annual
of the Average average of the Average average Price /
companies beta return companies beta return book value
1 (biggest) 0.93 10.7% 1 (high) 1.68 15.1% 1 (high)
2 1.02 11.4% 2 1.52 16.0% 2
3 1.08 13.2% 3 1.41 14.8% 3
4 1.16 12.8% 4 1.32 14.8% 4
5 1.22 14.0% 5 1.26 15.6% 5
6 1.24 15.5% 6 1.19 15.6% 6
7 1.33 15.0% 7 1.13 15.7% 7
8 1.34 14.9% 8 1.04 15.1% 8
9 1.39 15.5% 9 0.92 15.8% 9
10 (smallest) 1.44 18.2% 10 (low) 0.80 14.4% 10 (low)
Annual
Average average
beta return
1.35 5.9%
1.32 10.4%
1.30 11.6%
1.28 12.5%
1.27 14.0%
1.27 15.6%
1.27 17.3%
1.27 18.0%
1.29 19.1%
1.34 22.6%
Appendix 2. Summary statistics of the historical betas of the 30 companies in the Dow Jones Industrial Average Index with respect to the S&P 500, the DJIA and the W 5000.
Beta S&P 500 Beta DJIA
1/12/01 -31/1/02 Max min average max/min Max min average max/min
MMM 0.79 0.36 0.57 0.76 2.22 1.09 0.69 0.87 0.46 1.58
AA 1.22 0.45 0.78 0.99 2.73 1.49 0.96 1.18 0.45 1.55
AXP 1.76 1.24 1.46 0.36 1.42 1.75 1.33 1.48 0.28 1.32
T 1.02 0.32 0.77 0.91 3.16 0.75 0.15 0.48 1.24 4.94
BA 1.22 0.57 0.95 0.68 2.14 1.60 1.00 1.28 0.47 1.59
CAT 1.04 0.60 0.78 0.58 1.75 1.36 0.96 1.18 0.34 1.41
C 1.96 1.45 1.66 0.31 1.35 1.71 1.49 1.58 0.14 1.15
KO 1.11 0.55 0.80 0.70 2.02 1.18 0.67 0.88 0.58 1.76
DD 0.87 0.54 0.74 0.45 1.62 1.19 0.93 1.07 0.25 1.28
EK 0.70 0.37 0.56 0.60 1.92 0.93 0.61 0.75 0.42 1.51
XOM 0.67 0.24 0.43 1.00 2.81 0.79 0.34 0.54 0.85 2.35
GE 1.39 1.12 1.25 0.22 1.25 1.35 0.94 1.14 0.36 1.43
HPQ 1.69 0.94 1.34 0.56 1.80 1.36 0.86 1.13 0.44 1.58
HD 1.44 0.99 1.24 0.36 1.45 1.23 0.89 1.08 0.31 1.38
HON 1.42 1.03 1.22 0.32 1.39 1.74 1.26 1.52 0.32 1.39
IBM 1.36 0.76 1.18 0.51 1.79 1.45 0.92 1.19 0.45 1.58
@INTC 1.85 1.25 1.55 0.39 1.48 1.53 0.92 1.25 0.49 1.66
IP 1.02 0.49 0.73 0.73 2.09 1.33 0.93 1.10 0.37 1.43
JNJ 0.75 0.33 0.47 0.89 2.26 0.71 0.41 0.52 0.56 1.70
JPM 1.93 1.38 1.59 0.34 1.39 1.76 1.25 1.44 0.36 1.41
MCD 0.81 0.48 0.66 0.50 1.70 0.90 0.53 0.72 0.51 1.68
MRK 0.95 0.24 0.61 1.18 4.04 0.80 0.31 0.56 0.88 2.58
@MSFT 1.91 1.27 1.53 0.42 1.51 1.43 0.82 1.15 0.54 1.76
MO 0.42 -0.15 0.12 4.70 0.59 -0.01 0.31 1.93
SBC 0.82 0.23 0.48 1.23 3.59 0.52 0.18 0.33 1.04 2.97
UTX 1.39 0.98 1.20 0.35 1.43 1.65 1.09 1.40 0.40 1.52
WMT 1.20 0.77 0.99 0.43 1.55 1.11 0.67 0.90 0.49 1.66
GM 1.20 0.78 1.01 0.41 1.52 1.22 0.88 1.03 0.33 1.38
PG 0.91 -0.04 0.45 2.10 1.07 0.24 0.66 1.26 4.49
DIS 1.37 0.84 1.05 0.51 1.63 1.28 0.81 1.00 0.47 1.58
Average of (+) 1.21 0.68 0.94 0.78 1.96 1.23 0.77 0.99 0.57 1.85
(max-min)/ average
(max-min)/ average
Appendix 2. Summary statistics of the historical betas of the 30 companies in the Dow Jones Industrial Average Index with respect to the S&P 500, the DJIA and the W 5000.
Beta W 5000 Volatility
Max min average max/min Max min average max/min
0.69 0.18 0.49 1.06 3.93 0.31 0.25 0.27 0.23 1.25
1.21 0.44 0.77 1.00 2.72 0.42 0.36 0.38 0.17 1.19
1.62 1.11 1.33 0.38 1.46 0.39 0.29 0.34 0.29 1.34
1.03 0.35 0.77 0.87 2.92 0.45 0.36 0.40 0.24 1.26
1.17 0.54 0.91 0.69 2.15 0.44 0.35 0.38 0.23 1.25
0.85 0.49 0.64 0.56 1.74 0.38 0.31 0.35 0.18 1.20
1.79 1.31 1.52 0.32 1.37 0.43 0.34 0.37 0.24 1.26
0.97 0.44 0.68 0.78 2.21 0.34 0.27 0.31 0.22 1.25
0.76 0.38 0.60 0.63 2.00 0.35 0.28 0.31 0.25 1.28
0.70 0.31 0.51 0.77 2.27 0.40 0.31 0.35 0.24 1.28
0.61 0.22 0.38 1.05 2.82 0.22 0.17 0.19 0.28 1.31
1.25 0.97 1.11 0.25 1.29 0.31 0.26 0.28 0.20 1.22
1.74 0.98 1.43 0.53 1.78 0.50 0.41 0.46 0.19 1.21
1.39 0.85 1.15 0.47 1.64 0.41 0.33 0.36 0.24 1.27
1.28 0.79 1.04 0.47 1.62 0.48 0.41 0.44 0.16 1.17
1.33 0.73 1.12 0.53 1.82 0.44 0.34 0.38 0.25 1.27
1.86 1.30 1.55 0.36 1.43 0.55 0.42 0.49 0.26 1.30
0.88 0.40 0.60 0.81 2.23 0.38 0.30 0.34 0.23 1.25
0.56 0.18 0.34 1.11 3.17 0.27 0.20 0.23 0.32 1.37
1.92 1.32 1.54 0.39 1.46 0.45 0.34 0.40 0.27 1.32
0.68 0.27 0.50 0.83 2.55 0.31 0.27 0.29 0.14 1.15
0.71 0.09 0.42 1.47 8.10 0.33 0.27 0.30 0.21 1.24
1.78 1.22 1.47 0.38 1.46 0.52 0.39 0.46 0.28 1.32
0.31 -0.25 0.00 474.83 0.39 0.30 0.35 0.24 1.28
0.75 0.14 0.40 1.54 5.37 0.34 0.24 0.29 0.33 1.40
1.25 0.84 1.06 0.39 1.49 0.37 0.30 0.34 0.19 1.21
1.04 0.60 0.82 0.54 1.75 0.36 0.28 0.32 0.26 1.30
1.18 0.75 1.00 0.43 1.58 0.38 0.33 0.35 0.14 1.15
0.61 -0.08 0.33 2.06 0.38 0.28 0.33 0.30 1.35
1.30 0.80 0.99 0.50 1.61 0.38 0.31 0.34 0.22 1.24
1.11 0.59 0.85 16.53 2.35 0.39 0.31 0.35 0.23 1.26
(max-min)/ average
(max-min)/ average
31/12/1996-31/5/2002 1/1/2001-31/5/2002
Max min average max/min Max min
Volatility
S&P 500 0.20 0.07 0.14 0.89 2.62 0.20 0.14 0.17
DOW JONES IND. 0.20 0.09 0.14 0.78 2.30 0.20 0.14 0.18
WILSHIRE 5000 0.20 0.08 0.14 0.88 2.58 0.20 0.15 0.18
Beta S&P 500
DOW JONES IND. 1.08 0.79 0.96 0.30 1.37 0.98 0.79 0.91
WILSHIRE 5000 1.06 0.92 1.00 0.14 1.15 1.06 0.95 1.01
Beta DJ IND
S&P 500 0.99 0.72 0.86 0.31 1.37 0.93 0.80 0.88
WILSHIRE 5000 1.01 0.71 0.84 0.36 1.42 0.95 0.74 0.86
Beta W 5000
S&P 500 1.04 0.89 0.95 0.16 1.17 0.98 0.89 0.94
DOW JONES IND. 1.08 0.70 0.90 0.43 1.55 0.90 0.70 0.82
correlation
S&P 500 -DJ IND 0.96 0.82 0.91 0.15 1.17 0.93 0.82 0.89
S&P 500 -W 5000 0.99 0.95 0.98 0.04 1.04 0.99 0.96 0.97
DJ IND -W 5000 0.93 0.76 0.87 0.20 1.23 0.89 0.76 0.84
Appendix 3. Statistics of the indexes
(max-min)/ average
average
1/12/01-31/1/02
max/min Max min average max/min
0.30 1.37 0.19 0.17 0.18 0.14 1.15
0.32 1.41 0.19 0.17 0.18 0.13 1.14
0.28 1.34 0.20 0.17 0.19 0.15 1.16
0.21 1.24 0.97 0.85 0.92 0.13 1.14
0.11 1.12 1.05 0.98 1.02 0.07 1.07
0.15 1.17 0.92 0.82 0.88 0.11 1.12
0.25 1.29 0.94 0.78 0.87 0.19 1.21
0.10 1.10 0.97 0.91 0.94 0.06 1.07
0.24 1.28 0.89 0.78 0.84 0.13 1.14
0.12 1.13 0.93 0.88 0.90 0.06 1.06
0.03 1.03 0.99 0.96 0.98 0.02 1.02
0.15 1.16 0.89 0.81 0.85 0.09 1.09
(max-min)/ average
(max-min)/ average