Are Beautiful Market Patterns Overly Symmetric? from Kim Zussman

July 20, 2010 |

One important aspect of beauty is symmetry. SPY daily closes (1993-present) were checked for local 21day minima, defined as the lowest close centered between 20 days into the future and into the past. Once located, calculated the mean daily drop for the 10-days before and the rising 10-days after each minimum, as a test for velocity of drop vs (respective) velocity of gain. For each respective minimum, used paired t-test to compare the mean after-min rise with mean pre-min decline (ie, changed sign for the mean drop to positive, as a means to compare the rate of drop to the rate of rise for each minimum. A better way would be to regress both sides to fit an OLS slope, or a non-linear function-fit, but no do).

Here is comparison of mean after-min rise with mean pre-min decline :

Paired T-Test and CI: up avg, |dn avg|

Paired T for up avg - |dn avg|

N      Mean     StDev   SE Mean
up avg       141  0.00395  0.00324  0.00027
|dn avg|      141  0.00346  0.00345  0.00029
Difference  141  0.00048  0.00343  0.00028  T=1.7, P=0.098

>>For all 21 day minima, subsequent up averages were greater (faster), though not quite significantly.

However as Tim recently proved, not all beauties are the same. Isolating on those which go down fast (mean daily drops worse than -0.5% per day) gave different results:

Paired T for up avg_1 - |dn avg|_1

N       Mean     StDev   SE Mean
up avg_1    29   0.00585  0.00504  0.00093
|dn avg|_1  29   0.00874  0.00392  0.00073
Difference  29  -0.00289  0.00441  0.00082  T=-3.5

>>For fast declines, the subsequent rise was significantly slower.

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