# Another Round, by Kim Zussman

February 11, 2010 |

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
```

///////////

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.

///////////////

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
```

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