*probability of touching*calculations. The analysis tab on the ThinkOrSwim trading platform knows from implied volatility what the chances are of a distant stop price randomly coming up in the next day. This is determined by calculating where your stop price falls on a normal distribution curve and summing the area under the curve. If your stop is far way then there is a very high probability that the market will

*not*randomly encounter your stop price on the next roll, er, day.

*not*getting stopped out tomorrow with the probability of

*not*getting stopped out on the day after. This calculation is easily extended to any number of days in the future by raising the probability of

*not*getting stopped out tomorrow to the power of the desired number of days. This result gets exponentially smaller the more times you repeat the multiplication and therefore the probability of random fluctuations stopping you out becomes a near certainty over time. Try multiplying .9 by itself a number of times on a calculator. How many times does it take for the result to become less than .5? less than .05?

*There are about 250 trading days in year, and raising almost any fraction to the 250th power is going to be a number very close to zero.*

You see you can always find a time period for which the probability of randomly touching almost any price is almost certain. This is because the normal distribution curve never intersects with the zero line - it extends infinitely to the plus and minus and only approaches zero asymptotically. Thus any price you care to name has a non-zero probabililty of occuring randomly for any stock. One minus a small number is still less than one and if you multiply any such near-one number against itself enough times you will always be able to reduce the result to near zero. This just says that if you wait long enough random fluctuations will produce your price.

This is absurd, of course, because it says that all stocks will encounter a very large range of prices in a relatively short amount of time.

__The fact that stock prices don't range widely in the universe of numbers proves that stock prices are not the product of a pure random walk.__

At some point human beings step in to confine the range of prices. Within the range, random fluctuations abound as the market attempts to discover valuation. Outside of the range, human emotions of fear and greed intervene to push the price in a non-random direction - back towards the mean.

*of*10 on the next roll is 3 out of 36, or 1/12. Another way to think of this is that there is a 11/12 (0.917) chance of 10

*not*coming up on the next roll. In the next eight rolls the chance of 10

*not*coming up is .917 raised to the power 8, a number around 1/2.

_