Daily Speculations

The Web Site of Victor Niederhoffer & Laurel Kenner

Dedicated to the scientific method, free markets, deflating ballyhoo, creating value, and laughter;  a forum for us to use our meager abilities to make the world of specinvestments a better place.

 

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2/1/2005
The January Effect, by Victor, Alex And Steve

Around January each year, a bunch of amiable idiots start transmitting data on the January baromoter. If it looks like January is down, then all the chronic bears of the world and more pessimist followers of the abelprechtensteins can be counted on rubbing their hands with glee to predict a imminent dow of 5000. But of course when January is up, the whole year is likely to be up. and when January is down,the chances are reduced. And of course you can play with various starting points , indexes, changes in regime with lame ducks et al to make the numbers of rises and declines, look alluring, especially when you're dealing with a 8% a year drift and 0.6 chance of any month being up. In any case, doc castaldo and boss wiz here respecitiveloy computed the theoretical correlations assuming randomness and compared it to actuality with the guaranteed to happen result of a bullseye at 29%. All other exercises will result in similar bulleyes consistent with multiple comparisons. When will these orgie ofsuperstitions go out of style? Never of course, because otherwise the public couldnt always be counted on to be on the wrong foot.

2/1/2005
Part Whole Correlation, by Alex Castaldo

PWC is a dangerous fallacy which often affects people at this time of the year.

Suppose x is the amount by which the S&P rises in January and y is the amount by which it rises in the remaining 11 months of the year.  Then there will be a correlation between x and x+y, that is between January and the whole year.  And this will be "discovered" empirically and reported in newsletters and research reports.

Let us estimate this spurious correlation:

Corr(x, x+y) = Covar(x,x+y) / SQRT[ Var(x) Var(x+y) ]   /* by definition */

Assuming that x and y are not related, i.e. Covar(x,y) = 0 this reduces to

Var(x) / SQRT[ Var(x) (Var(x)+Var(y)) ]

If all months are equally volatile and serially independent, then the monthly variances add and so  Var(y) = 11 Var (x).  So we get

1 / SQRT[ 1 + 11 ] = 0.288675

So we expect a nearly 30% correlation even if January has no predictive value for the rest of the year.

2/1/2005
The Numbers, An Empirical Check, by Steve Wisdom

An empirical check, SPX from 1970 till Feb-2004, with each month's
log-change aligned with the log-change of the full year starting with that
month.  "As predicted" the corr is 30%'ish

Date         SPX   Ln    LnChg01  LnChg12 Corr
 1/30/1970   85.02 4.44 -0.0796   0.0010  0.2983
 2/27/1970   89.50 4.49  0.0514   0.1202
 3/31/1970   89.63 4.50  0.0015   0.0779
 4/30/1970   81.52 4.40 -0.0948   0.1126
 5/29/1970   76.55 4.34 -0.0629   0.2431
 6/30/1970   72.72 4.29 -0.0513   0.2635
 7/31/1970   78.05 4.36  0.0707   0.3155
 8/31/1970   81.52 4.40  0.0435   0.2026
 9/30/1970   84.21 4.43  0.0325   0.1946
10/30/1970   83.25 4.42 -0.0115   0.1551
11/30/1970   87.20 4.47  0.0464   0.1239
12/31/1970   92.15 4.52  0.0552   0.0750
 1/29/1971   95.88 4.56  0.0397   0.1024
 2/26/1971   96.75 4.57  0.0090   0.0807
 3/31/1971  100.31 4.61  0.0361   0.0967
 4/30/1971  103.95 4.64  0.0356   0.0664
 5/31/1971   99.63 4.60 -0.0424   0.0352
 6/30/1971   99.70 4.60  0.0007   0.0947
 7/30/1971   95.58 4.56 -0.0422   0.0720
 8/31/1971   99.03 4.60  0.0355   0.1165
 9/30/1971   98.34 4.59 -0.0070   0.1149
10/29/1971   94.23 4.55 -0.0427   0.1170
11/30/1971   93.99 4.54 -0.0026   0.1690
12/31/1971  102.09 4.63  0.0827   0.2162
 1/31/1972  103.94 4.64  0.0180   0.1453
 2/29/1972  106.57 4.67  0.0250   0.1100
 3/31/1972  107.20 4.67  0.0059   0.0468
 4/28/1972  107.67 4.68  0.0044   0.0395
 5/31/1972  109.53 4.70  0.0171  -0.0065
 6/30/1972  107.14 4.67 -0.0221  -0.0427
 7/31/1972  107.39 4.68  0.0023  -0.0272
 8/31/1972  111.09 4.71  0.0339   0.0077
 9/29/1972  110.55 4.71 -0.0049  -0.0635
10/31/1972  111.58 4.71  0.0093  -0.0194
11/30/1972  116.67 4.76  0.0446  -0.0299
12/29/1972  118.05 4.77  0.0118  -0.1954
 1/31/1973  116.03 4.75 -0.0173  -0.1907
 2/28/1973  111.68 4.72 -0.0382  -0.1836
 3/30/1973  111.52 4.71 -0.0014  -0.1490
 4/30/1973  106.97 4.67 -0.0417  -0.1711
 5/31/1973  104.95 4.65 -0.0191  -0.1693
 6/29/1973  104.26 4.65 -0.0066  -0.1844
 7/31/1973  108.22 4.68  0.0373  -0.1925
 8/31/1973  104.25 4.65 -0.0374  -0.3108
 9/28/1973  108.43 4.69  0.0393  -0.3680
10/31/1973  108.29 4.68 -0.0013  -0.5344
11/30/1973   95.96 4.56 -0.1209  -0.3821
12/31/1973   97.55 4.58  0.0164  -0.3159
 1/31/1974   96.57 4.57 -0.0101  -0.3527
 2/28/1974   96.22 4.57 -0.0036  -0.2267
 3/29/1974   93.98 4.54 -0.0236  -0.1649
 4/30/1974   90.31 4.50 -0.0398  -0.1199
 5/31/1974   87.28 4.47 -0.0341  -0.0339
 6/28/1974   86.00 4.45 -0.0148   0.0434
 7/31/1974   79.31 4.37 -0.0810   0.1015
 8/30/1974   72.15 4.28 -0.0946   0.1125
 9/30/1974   63.54 4.15 -0.1271   0.1858
10/31/1974   73.90 4.30  0.1510   0.2776
11/29/1974   69.97 4.25 -0.0546   0.1864
12/31/1974   68.56 4.23 -0.0204   0.2654
 1/31/1975   76.98 4.34  0.1158   0.2742
 2/28/1975   81.59 4.40  0.0582   0.2702
 3/31/1975   83.36 4.42  0.0215   0.2006
 4/30/1975   87.30 4.47  0.0462   0.2093
 5/30/1975   91.15 4.51  0.0432   0.1521
 6/30/1975   95.19 4.56  0.0434   0.0945
 7/31/1975   88.75 4.49 -0.0701   0.0912
 8/29/1975   86.88 4.46 -0.0213   0.1532
 9/30/1975   83.87 4.43 -0.0353   0.1693
10/31/1975   89.04 4.49  0.0598   0.2270
11/28/1975   91.24 4.51  0.0244   0.1447
12/31/1975   90.19 4.50 -0.0116   0.1125
 1/30/1976  100.86 4.61  0.1118   0.1752
 2/27/1976   99.71 4.60 -0.0115   0.0115
 3/31/1976  102.77 4.63  0.0302   0.0011
 4/30/1976  101.64 4.62 -0.0111  -0.0432
 5/31/1976  100.18 4.61 -0.0145  -0.0320
 6/30/1976  104.28 4.65  0.0401  -0.0414
 7/30/1976  103.44 4.64 -0.0081  -0.0371
 8/31/1976  102.91 4.63 -0.0051  -0.0454
 9/30/1976  105.24 4.66  0.0224  -0.0615
10/29/1976  102.90 4.63 -0.0225  -0.0864
11/30/1976  102.10 4.63 -0.0078  -0.1083
12/31/1976  107.46 4.68  0.0512  -0.0739
 1/31/1977  102.03 4.63 -0.0519  -0.1222
 2/28/1977   99.82 4.60 -0.0219  -0.1338
 3/31/1977   98.42 4.59 -0.0141  -0.1370
 4/29/1977   98.44 4.59  0.0002  -0.0983
 5/31/1977   96.12 4.57 -0.0238  -0.0165
 6/30/1977  100.48 4.61  0.0444   0.0121
 7/29/1977   98.85 4.59 -0.0164  -0.0505
 8/31/1977   96.77 4.57 -0.0213   0.0183
 9/30/1977   96.53 4.57 -0.0025   0.0652
10/31/1977   92.34 4.53 -0.0444   0.0604
11/30/1977   94.83 4.55  0.0266   0.0087
12/30/1977   95.10 4.55  0.0028  -0.0014
 1/31/1978   89.25 4.49 -0.0635   0.0106
 2/28/1978   87.04 4.47 -0.0251   0.1130
 3/31/1978   89.21 4.49  0.0246   0.1009
 4/28/1978   96.83 4.57  0.0820   0.1300
 5/31/1978   97.29 4.58  0.0047   0.0497
 6/30/1978   95.53 4.56 -0.0183   0.0182
 7/31/1978  100.68 4.61  0.0525   0.0744
 8/31/1978  103.29 4.64  0.0256   0.0306
 9/29/1978  102.54 4.63 -0.0073   0.0567
10/31/1978   93.15 4.53 -0.0960   0.0640
11/30/1978   94.70 4.55  0.0165   0.0890
12/29/1978   96.11 4.57  0.0148   0.1142
 1/31/1979   99.93 4.60  0.0390   0.1161
 2/28/1979   96.28 4.57 -0.0372   0.1331
 3/30/1979  101.59 4.62  0.0537   0.1660
 4/30/1979  101.76 4.62  0.0017   0.0049
 5/31/1979   99.08 4.60 -0.0267   0.0436
 6/29/1979  102.91 4.63  0.0379   0.1158
 7/31/1979  103.81 4.64  0.0087   0.1044
 8/31/1979  109.32 4.69  0.0517   0.1588
 9/28/1979  109.32 4.69  0.0000   0.1129
10/31/1979  101.82 4.62 -0.0711   0.1377
11/30/1979  106.16 4.66  0.0417   0.2247
12/31/1979  107.94 4.68  0.0166   0.2804
 1/31/1980  114.16 4.74  0.0560   0.2293
 2/29/1980  113.66 4.73 -0.0044   0.1265
 3/31/1980  102.09 4.63 -0.1074   0.1440
 4/30/1980  106.29 4.67  0.0403   0.2868
 5/30/1980  111.24 4.71  0.0455   0.2227
 6/30/1980  114.24 4.74  0.0266   0.1756
 7/31/1980  121.67 4.80  0.0630   0.1385
 8/29/1980  122.38 4.81  0.0058   0.0733
 9/30/1980  125.46 4.83  0.0249   0.0033
10/31/1980  127.47 4.85  0.0159  -0.0768
11/28/1980  140.52 4.95  0.0975  -0.0448
12/31/1980  135.76 4.91 -0.0345  -0.1063
 1/30/1981  129.55 4.86 -0.0468  -0.1024
 2/27/1981  131.27 4.88  0.0132  -0.0732
 3/31/1981  136.00 4.91  0.0354  -0.1489
 4/30/1981  132.81 4.89 -0.0237  -0.1945
 5/29/1981  132.59 4.89 -0.0017  -0.1315
 6/30/1981  131.21 4.88 -0.0105  -0.1698
 7/31/1981  130.92 4.87 -0.0022  -0.1799
 8/31/1981  122.79 4.81 -0.0641  -0.2009
 9/30/1981  116.18 4.76 -0.0553  -0.0271
10/30/1981  121.89 4.80  0.0480   0.0358
11/30/1981  126.35 4.84  0.0359   0.0926
12/31/1981  122.55 4.81 -0.0305   0.0921
 1/29/1982  120.40 4.79 -0.0177   0.1377
 2/26/1982  113.11 4.73 -0.0625   0.1880
 3/31/1982  111.96 4.72 -0.0102   0.2693
 4/30/1982  116.44 4.76  0.0392   0.3120
 5/31/1982  111.88 4.72 -0.0399   0.3450
 6/30/1982  109.61 4.70 -0.0205   0.3726
 7/30/1982  107.09 4.67 -0.0233   0.4277
 8/31/1982  119.51 4.78  0.1097   0.4174
 9/30/1982  120.42 4.79  0.0076   0.3189
10/29/1982  133.71 4.90  0.1047   0.3214
11/30/1982  138.54 4.93  0.0355   0.2014
12/31/1982  140.64 4.95  0.0150   0.1832
 1/31/1983  145.30 4.98  0.0326   0.1593
 2/28/1983  148.06 5.00  0.0188   0.1175
 3/31/1983  152.96 5.03  0.0326   0.0590
 4/29/1983  164.42 5.10  0.0722   0.0399
 5/31/1983  162.39 5.09 -0.0124  -0.0269
 6/30/1983  168.11 5.12  0.0346  -0.0757
 7/29/1983  162.56 5.09 -0.0336  -0.0930
 8/31/1983  164.40 5.10  0.0113  -0.0760
 9/30/1983  166.07 5.11  0.0101   0.0138
10/31/1983  163.55 5.10 -0.0153   0.0002
11/30/1983  166.40 5.11  0.0173   0.0154
12/30/1983  164.93 5.11 -0.0089  -0.0171
 1/31/1984  163.41 5.10 -0.0093   0.0139
 2/29/1984  157.06 5.06 -0.0396   0.0946
 3/30/1984  159.18 5.07  0.0134   0.1429
 4/30/1984  160.05 5.08  0.0055   0.1266
 5/31/1984  150.55 5.01 -0.0612   0.1165
 6/29/1984  153.18 5.03  0.0173   0.2304
 7/31/1984  150.66 5.02 -0.0166   0.2251
 8/31/1984  166.68 5.12  0.1011   0.2368
 9/28/1984  166.10 5.11 -0.0035   0.1237
10/31/1984  166.09 5.11 -0.0001   0.0919
11/30/1984  163.58 5.10 -0.0152   0.1335
12/31/1984  167.24 5.12  0.0221   0.2118
 1/31/1985  179.63 5.19  0.0715   0.2338
 2/28/1985  181.18 5.20  0.0086   0.1646
 3/29/1985  180.66 5.20 -0.0029   0.2251
 4/30/1985  179.83 5.19 -0.0046   0.2794
 5/31/1985  189.55 5.24  0.0526   0.2698
 6/28/1985  191.85 5.26  0.0121   0.2662
 7/31/1985  190.92 5.25 -0.0049   0.2681
 8/30/1985  188.63 5.24 -0.0121   0.2125
 9/30/1985  182.08 5.20 -0.0353   0.2933
10/31/1985  189.82 5.25  0.0416   0.2394
11/29/1985  202.17 5.31  0.0630   0.2510
12/31/1985  211.28 5.35  0.0441   0.2092
 1/31/1986  211.78 5.36  0.0024   0.1365
 2/28/1986  226.92 5.42  0.0690   0.2579
 3/31/1986  238.90 5.48  0.0514   0.2251
 4/30/1986  235.52 5.46 -0.0142   0.1997
 5/30/1986  247.35 5.51  0.0490   0.2024
 6/30/1986  250.84 5.52  0.0140   0.1594
 7/31/1986  236.12 5.46 -0.0605   0.1922
 8/29/1986  252.93 5.53  0.0688   0.2998
 9/30/1986  231.32 5.44 -0.0893   0.2654
10/31/1986  243.98 5.50  0.0533   0.3302
11/28/1986  249.22 5.52  0.0212   0.0315
12/31/1986  242.17 5.49 -0.0287  -0.0790
 1/30/1987  274.08 5.61  0.1238   0.0201
 2/27/1987  284.20 5.65  0.0363  -0.0641
 3/31/1987  291.70 5.68  0.0260  -0.0594
 4/30/1987  288.36 5.66 -0.0115  -0.1193
 5/29/1987  290.10 5.67  0.0060  -0.0984
 6/30/1987  304.00 5.72  0.0468  -0.1013
 7/31/1987  318.66 5.76  0.0471  -0.1057
 8/31/1987  329.80 5.80  0.0344  -0.1582
 9/30/1987  321.83 5.77 -0.0245  -0.2320
10/30/1987  251.79 5.53 -0.2454  -0.1686
11/30/1987  230.30 5.44 -0.0892   0.1025
12/31/1987  247.08 5.51  0.0703   0.1726
 1/29/1988  257.07 5.55  0.0396   0.1169
 2/29/1988  267.82 5.59  0.0410   0.1460
 3/31/1988  258.89 5.56 -0.0339   0.0756
 4/29/1988  261.33 5.57  0.0094   0.1301
 5/31/1988  262.16 5.57  0.0032   0.1696
 6/30/1988  273.50 5.61  0.0423   0.2010
 7/29/1988  272.02 5.61 -0.0054   0.1507
 8/31/1988  261.52 5.57 -0.0394   0.2408
 9/30/1988  271.91 5.61  0.0390   0.2956
10/31/1988  278.97 5.63  0.0256   0.2500
11/30/1988  273.70 5.61 -0.0191   0.1989
12/30/1988  277.72 5.63  0.0146   0.2344
 1/31/1989  297.47 5.70  0.0687   0.2410
 2/28/1989  288.86 5.67 -0.0294   0.1010
 3/31/1989  294.87 5.69  0.0206   0.1389
 4/28/1989  309.64 5.74  0.0489   0.1422
 5/31/1989  320.52 5.77  0.0345   0.0661
 6/30/1989  317.98 5.76 -0.0080   0.1196
 7/31/1989  346.08 5.85  0.0847   0.1186
 8/31/1989  351.45 5.86  0.0154   0.0287
 9/29/1989  349.15 5.86 -0.0066  -0.0858
10/31/1989  340.36 5.83 -0.0255  -0.1318
11/30/1989  345.99 5.85  0.0164  -0.1130
12/29/1989  353.40 5.87  0.0212  -0.0712
 1/31/1990  329.08 5.80 -0.0713  -0.0678
 2/28/1990  331.89 5.80  0.0085   0.0441
 3/30/1990  339.94 5.83  0.0240   0.1007
 4/30/1990  330.80 5.80 -0.0273   0.0987
 5/31/1990  361.23 5.89  0.0880   0.1263
 6/29/1990  358.02 5.88 -0.0089   0.0762
 7/31/1990  356.15 5.88 -0.0052   0.0360
 8/31/1990  322.56 5.78 -0.0991   0.0852
 9/28/1990  306.05 5.72 -0.0525   0.2037
10/31/1990  304.00 5.72 -0.0067   0.2369
11/30/1990  322.22 5.78  0.0582   0.2554
12/31/1990  330.22 5.80  0.0245   0.1523
 1/31/1991  343.93 5.84  0.0407   0.2335
 2/28/1991  367.07 5.91  0.0651   0.1728
 3/29/1991  375.22 5.93  0.0220   0.1172
 4/30/1991  375.34 5.93  0.0003   0.0731
 5/31/1991  389.83 5.97  0.0379   0.1003
 6/28/1991  371.16 5.92 -0.0491   0.0634
 7/31/1991  387.81 5.96  0.0439   0.0950
 8/30/1991  395.43 5.98  0.0195   0.0897
 9/30/1991  387.86 5.96 -0.0193   0.0460
10/31/1991  392.45 5.97  0.0118   0.0744
11/29/1991  375.22 5.93 -0.0449   0.0647
12/31/1991  417.09 6.03  0.1058   0.1394
 1/31/1992  408.79 6.01 -0.0201   0.0437
 2/28/1992  412.70 6.02  0.0095   0.0708
 3/31/1992  403.69 6.00 -0.0221   0.0717
 4/30/1992  414.95 6.03  0.0275   0.1123
 5/29/1992  415.35 6.03  0.0010   0.0590
 6/30/1992  408.14 6.01 -0.0175   0.0805
 7/31/1992  424.22 6.05  0.0386   0.0988
 8/31/1992  414.03 6.03 -0.0243   0.0548
 9/30/1992  417.80 6.04  0.0091   0.1130
10/30/1992  418.68 6.04  0.0021   0.0939
11/30/1992  431.35 6.07  0.0298   0.1110
12/31/1992  435.71 6.08  0.0101   0.0682
 1/29/1993  438.78 6.08  0.0070   0.0682
 2/26/1993  443.38 6.09  0.0104   0.0931
 3/31/1993  451.67 6.11  0.0185   0.0522
 4/30/1993  440.19 6.09 -0.0257  -0.0131
 5/31/1993  450.19 6.11  0.0225   0.0241
 6/30/1993  450.53 6.11  0.0008   0.0139
 7/30/1993  448.13 6.11 -0.0053  -0.0140
 8/31/1993  463.56 6.14  0.0339   0.0224
 9/30/1993  458.93 6.13 -0.0100   0.0254
10/29/1993  467.83 6.15  0.0192   0.0082
11/30/1993  461.79 6.14 -0.0130   0.0096
12/31/1993  466.45 6.15  0.0100  -0.0177
 1/31/1994  481.61 6.18  0.0320  -0.0155
 2/28/1994  467.14 6.15 -0.0305  -0.0235
 3/31/1994  445.77 6.10 -0.0468   0.0424
 4/29/1994  450.91 6.11  0.0115   0.1162
 5/31/1994  456.51 6.12  0.0123   0.1323
 6/30/1994  444.27 6.10 -0.0272   0.1557
 7/29/1994  458.26 6.13  0.0310   0.2039
 8/31/1994  475.50 6.16  0.0369   0.2042
 9/30/1994  462.71 6.14 -0.0273   0.1669
10/31/1994  472.35 6.16  0.0206   0.2335
11/30/1994  453.69 6.12 -0.0403   0.2079
12/30/1994  459.27 6.13  0.0122   0.2884
 1/31/1995  470.42 6.15  0.0240   0.2935
 2/28/1995  487.39 6.19  0.0354   0.3016
 3/31/1995  500.71 6.22  0.0270   0.2731
 4/28/1995  514.71 6.24  0.0276   0.2540
 5/31/1995  533.40 6.28  0.0357   0.2398
 6/30/1995  544.75 6.30  0.0211   0.2267
 7/31/1995  562.06 6.33  0.0313   0.2079
 8/31/1995  561.88 6.33 -0.0003   0.1298
 9/29/1995  584.41 6.37  0.0393   0.1487
10/31/1995  581.50 6.37 -0.0050   0.1622
11/30/1995  605.37 6.41  0.0402   0.1930
12/29/1995  615.93 6.42  0.0173   0.2235
 1/31/1996  636.02 6.46  0.0321   0.1845
 2/29/1996  640.43 6.46  0.0069   0.2119
 3/29/1996  645.50 6.47  0.0079   0.2109
 4/30/1996  654.17 6.48  0.0133   0.1595
 5/31/1996  669.12 6.51  0.0226   0.2029
 6/28/1996  670.63 6.51  0.0023   0.2372
 7/31/1996  639.95 6.46 -0.0468   0.2775
 8/30/1996  651.99 6.48  0.0186   0.3996
 9/30/1996  687.31 6.53  0.0528   0.3218
10/31/1996  705.27 6.56  0.0258   0.3208
11/29/1996  757.02 6.63  0.0708   0.2599
12/31/1996  740.74 6.61 -0.0217   0.2327
 1/31/1997  786.16 6.67  0.0595   0.2701
 2/28/1997  790.82 6.67  0.0059   0.2207
 3/31/1997  757.12 6.63 -0.0435   0.2828
 4/30/1997  801.34 6.69  0.0568   0.3751
 5/30/1997  848.28 6.74  0.0569   0.3274
 6/30/1997  885.14 6.79  0.0425   0.2515
 7/31/1997  954.29 6.86  0.0752   0.2476
 8/29/1997  899.47 6.80 -0.0592   0.1607
 9/30/1997  947.28 6.85  0.0518   0.0623
10/31/1997  914.62 6.82 -0.0351   0.0710
11/28/1997  955.40 6.86  0.0436   0.1833
12/31/1997  970.43 6.88  0.0156   0.1972
 1/30/1998  980.28 6.89  0.0101   0.2364
 2/27/1998 1049.34 6.96  0.0681   0.2665
 3/31/1998 1101.75 7.00  0.0487   0.1656
 4/30/1998 1111.75 7.01  0.0090   0.1549
 5/29/1998 1090.82 6.99 -0.0190   0.1831
 6/30/1998 1133.84 7.03  0.0387   0.1768
 7/31/1998 1120.67 7.02 -0.0117   0.1912
 8/31/1998  957.28 6.86 -0.1576   0.1703
 9/30/1998 1017.01 6.92  0.0605   0.3216
10/30/1998 1098.67 7.00  0.0772   0.2321
11/30/1998 1163.63 7.06  0.0574   0.2155
12/31/1998 1229.23 7.11  0.0548   0.1770
 1/29/1999 1279.64 7.15  0.0402   0.1784
 2/26/1999 1238.33 7.12 -0.0328   0.0859
 3/31/1999 1286.37 7.16  0.0381   0.0984
 4/30/1999 1335.18 7.20  0.0372   0.1527
 5/31/1999 1301.84 7.17 -0.0253   0.0842
 6/30/1999 1372.71 7.22  0.0530   0.0873
 7/30/1999 1328.72 7.19 -0.0326   0.0579
 8/31/1999 1320.41 7.19 -0.0063   0.0740
 9/30/1999 1282.71 7.16 -0.0290   0.1392
10/29/1999 1362.93 7.22  0.0607   0.1132
11/30/1999 1388.91 7.24  0.0189   0.0476
12/31/1999 1469.25 7.29  0.0562  -0.0547
 1/31/2000 1394.46 7.24 -0.0522  -0.1069
 2/29/2000 1366.42 7.22 -0.0203  -0.0206
 3/31/2000 1498.58 7.31  0.0923  -0.0971
 4/28/2000 1452.43 7.28 -0.0313  -0.2558
 5/31/2000 1420.60 7.26 -0.0222  -0.1505
 6/30/2000 1454.60 7.28  0.0237  -0.1233
 7/31/2000 1430.83 7.27 -0.0165  -0.1723
 8/31/2000 1517.68 7.32  0.0589  -0.1666
 9/29/2000 1436.51 7.27 -0.0550  -0.2918
10/31/2000 1429.40 7.27 -0.0050  -0.3221
11/30/2000 1314.95 7.18 -0.0835  -0.2992
12/29/2000 1320.28 7.19  0.0040  -0.1433
 1/31/2001 1366.01 7.22  0.0341  -0.1398
 2/28/2001 1239.94 7.12 -0.0968  -0.1895
 3/30/2001 1160.33 7.06 -0.0664  -0.1137
 4/30/2001 1249.46 7.13  0.0740  -0.0112
 5/31/2001 1255.82 7.14  0.0051  -0.1486
 6/29/2001 1224.42 7.11 -0.0253  -0.1628
 7/31/2001 1211.23 7.10 -0.0108  -0.2127
 8/31/2001 1133.58 7.03 -0.0663  -0.2842
 9/28/2001 1040.94 6.95 -0.0853  -0.2130
10/31/2001 1059.78 6.97  0.0179  -0.2443
11/30/2001 1139.45 7.04  0.0725  -0.1794
12/31/2001 1148.08 7.05  0.0075  -0.1964
 1/31/2002 1130.20 7.03 -0.0157  -0.2661
 2/28/2002 1106.73 7.01 -0.0210  -0.2782
 3/29/2002 1147.39 7.05  0.0361  -0.2744
 4/30/2002 1076.92 6.98 -0.0634  -0.3022
 5/31/2002 1067.14 6.97 -0.0091  -0.1608
 6/28/2002  989.82 6.90 -0.0752  -0.1021
 7/31/2002  911.62 6.82 -0.0823  -0.0156
 8/30/2002  916.07 6.82  0.0049   0.0828
 9/30/2002  815.28 6.70 -0.1166   0.0956
10/31/2002  885.76 6.79  0.0829   0.2002
11/29/2002  936.31 6.84  0.0555   0.1708
12/31/2002  879.82 6.78 -0.0622   0.1224
 1/31/2003  855.70 6.75 -0.0278   0.2341
 2/28/2003  841.15 6.73 -0.0171   0.2791
 3/31/2003  848.18 6.74  0.0083   0.3083
 4/30/2003  916.92 6.82  0.0779   0.2835
 5/30/2003  963.59 6.87  0.0496   0.1887
 6/30/2003  974.50 6.88  0.0113   0.1510
 7/31/2003  990.31 6.90  0.0161   0.1576
 8/29/2003 1008.01 6.92  0.0177   0.1066
 9/30/2003  995.97 6.90 -0.0120   0.0912
10/31/2003 1050.71 6.96  0.0535   0.1125
11/28/2003 1058.20 6.96  0.0071   0.0729
12/31/2003 1111.92 7.01  0.0495   0.1037
 1/30/2004 1131.13 7.03  0.0171   0.0861
 2/27/2004 1144.94 7.04  0.0121   0.0434