Distribution of Random Market TICKs

So, based on my TICK article, one would guess that the majority of randomly-chosen market situations would have low TICK values (since there are so many more ways to get a low TICK than a high TICK).

But, how low is “random low”? If you chose 1 million random markets, and calculated their TICKs, what percentage of them would have a TICK of 1000? 500? 300? Since we are talking about random selection, there is a non-zero probability that you’d hit the maximum value. But, I wouldn’t hold my breath…

Knowing where the distribution of random TICKs trails off would be valuable, since it would make a sensible absolute lower threshold for paying attention to the indicator in actual trading. I mean, you really only want to pay attention when the TICK is pointing out a non-random situation!

Today, since I didn’t have any trading prospects, I thought I’d take a minute and find out what that level might be. Here is the distribution of TICKs for 1 million randomly generated 3000-stock markets. The raw result:

… and the prettier histogram version:

As you can see, the vast majority of answers came out in the +/-150 range, while some answers ventured out toward +/-220. None of the million markets got a value in the 300 range. Of course, if I generated enough markets, eventually I’d make one with a TICK of 3000, but due to the normal-looking distribution in the histogram, that would take a long, long time.

So, no matter what, never base any decisions on TICKs smaller than 250. Maybe, if you are trading the index that underlies the TICK, you could justify watching values in the 300 to 500 range. If your position is in a single sector or stock, then it still makes sense to me that values in the 500 to 600 range are the first notable TICKs (because there has to be a broader market force at work to really affect you).

If you are curious, you can check out the html version of the Mathematica document I made. Mathematica’s great for playing around with little ideas like this.