Higher High, Lower Low?

Using the Yahoo! historical database of SPY,  I tried to categorize the likelihood of achieving various price points based on the prior day’s range.  On any given day, what are the chances that of a higher high or lower low?  What about crossing the prior day’s high or low? Pivot (high + low + close ) / 3?  Using the prior day’s range, what are the chances it will cross a point that is 33% of the range below the prior days low, cross the prior day’s low, cross 33% above the prior day’s high, 66% of the range above the low, the prior day’s high, 33% of the range above the prior day’s high?

Also, what is the chance the next day will have a higher high or a lower low, or both, or neither?

Looking back over the past 1000 days, here are is what I found:

price point percent achieving
cross -33% 30.00%
cross low 45.20%
cross 33% 56.50%
cross mid 56.70%
cross 66% 58.70%
cross high 48.20%
cross 133 27.00%
cross pivot 63.80%
higher high 51.50%
lower low 47.60%
either 89.00%
both (outside day) 10.10%

At this point this is more food for the thought, but at least it gives some idea of what the next day will look like – there is about 10% chance (1 day in 2 weeks) that both the prior day’s high and prior day’s low will be exceeded, and similarly 10% chance that the neither will be exceeded. Of any particular price point, it is most likely the pivot point will be hit (a bit better than 60% of the time). You have a little less than 50% chance that either the low or the high will be crossed – but 90% chance that at least one of them will be crossed. Comparing the higher high with the cross of the high implies that about 4% of the time there will be a gap higher (about once month). On the other hand the likelihood of a gap lower is less likely ( lower low 47% vs 45% cross low, about 2% of the time).

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