Distribution of Random TICKs

Let's start with a definition of a single tick value... we'll make a randum integer between -1 and 1.  Obviously,  -1 will represent a downtick, 1 will represent an uptick, and 0 will represent a zero-tick.

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Now, we need a way to generate a market full of single ticks, of any size we want....

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Ok, now let's generate the TICK for a market, which is just the sum of the single ticks (Total[] in Mathematica parlance)...

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Alright, now let's compute 1 million ticks for random markets with 3000 stocks....

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Alright, what were the maximum and minimum TICK values in our million markets?

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How did the ticks end up distributed?  Let's plot them raw...

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It's obvious that the majority of the values fell between -150 and 150.  If we sort the values prior to plotting, this will become more clear....

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We can draw a histogram, to see the distribution:

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Created by Mathematica  (January 24, 2007)