I'm not very good at this stuff, but I don't see anything wrong with the graph. It hovers around 0. A Brownian motion starting which starts at 0, will, at time T be normally distributed with mean 0 and variance T.

http://en.wikipedia.org/wiki/File:Random_Walk_example.svg

Some of them go up, some go down, but all will cross 0 infinitely many times, and all the paths averaged will equal 0.