- 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.