Stocks and Random Walks Now we come to a well known inference based on the lack of correlation between price movements separated by short times. Because the price of a stock moves up and down in this way, the price as a function of time is exactly equivalent to a random walk, described earlier in section 1.7. That is at one time the stock price will move up or down, and the direction of one step is uncorrelated (i.e. independent) of the preceding step. Of course to attribute this random walk behavior to drink would be a clear mistake. (Well, OK, the occasional beer after lunch probably doesn't hurt.) But seriously, the reason is due to the extremely competitive nature of the business, that as we just saw, sucks away any predictability after a few seconds. A lot of Wall St. runs on the assumption of random walk statistics. Pricing of derivative securities, such as options, are done using mathematics, in particular stochastic processes, that assume underlying random walk behavior of stocks.