Another Round, by Kim Zussman
DJIA has recently been near the 10,000 level again (first time in 1999). Checking DJIA closes +/-1% from "round numbers" (ie, 8000,9000,10000,..), I found the most frequent near-round closes were at 11,000, followed by 10,000 (data not shown). In a way, 10,000 is more round than 11,000, but that is more a problem for numerologists.
Another check on possible trading effects related to round numbers was done by looking at days (c-c) which transitioned from below 10,000 to above (and from above to below). And a good control for comparison is the adjacent, non-roundish transition from below 10,500 to above 10,500 (and from above to below).
First is comparison of below to above for 10K and 10.5K:
Two-sample T for XUP10 vs XUP105
N Mean StDev SE Mean
XUP10 30 0.01418 0.00761 0.0014 T- 0.69
XUP105 59 0.01279 0.00951 0.0012
>> the mean moves from below to above 10,000 are bigger than those from below to
above 10,500, but the difference is N.S.
Now the same for down moves:
Two-Sample T-Test and CI: XDN10, XDN105
Two-sample T for XDN10 vs XDN105
N Mean StDev SE Mean
XDN10 29 -0.01419 0.00837 0.0016 T=0.18
XDN105 59 -0.0146 0.0121 0.0016
about the same
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So the size of moves up through the round and down through the round are not different from similar moves through an adjacent non-round.
Is there more variation? The same data was used to compare variance for up moves through 10,000 with up moves through 10,500:
Test for Equal Variances: XUP10, XUP105
95% Bonferroni confidence intervals for standard deviations
N Lower StDev Upper
XUP10 30 0.0058 0.0076 0.0107
XUP105 59 0.0078 0.0095 0.0119
F-Test (normal distribution)
Test statistic = 0.64, p-value = 0.194
The variance was a little less for up moves through 10,000 than
10,500, but the difference was N.S. Here is the check on variance of
down-moves:
Test for Equal Variances: XDN10, XDN105
95% Bonferroni confidence intervals for standard deviations
N Lower StDev Upper
XDN10 29 0.00643 0.00836 0.01185
XDN105 59 0.00997 0.01205 0.01518
F-Test (normal distribution)
Test statistic = 0.48, p-value = 0.037
>> Assuming a normal distribution, the variance associated with down moves
across 10,500 was significantly greater than those going below 10,000.
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What about days after crossing above/below 10,000 vs 10,500?
Two-Sample T-Test and CI: XUP10N, XUP105N
Two-sample T for XUP10N vs XUP105N
N Mean StDev SE Mean
XUP10N 30 -0.0002 0.0127 0.0023 T=0.23
XUP105N 59 0.00040 0.00845 0.0011
Two-Sample T-Test and CI: XDN10N, XDN105N
Two-sample T for XDN10N vs XDN105N
N Mean StDev SE Mean
XDN10N 29 0.0002 0.0148 0.0028 T=-0.43
XDN105N 59 0.0015 0.0131 0.0017
>> No significant differences in mean day return after crossing above or below 10,000 vs 10.500