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April 11, 2008
Drunks and Lampposts, and Stocks
I've been playing a lot with some Monte Carlos for another project, and along the way I got to messing with the old drunk/gutter/lamppost problem. You know the drill: A drunk starts at a wall X paces from a gutter, with a lamppost half-way between him and the gutter. Assuming he only takes one step at a time, and every step is randomly toward the wall (but not through it) or toward the gutter, how long does it take him to get to the gutter, on average?
Long story short, the graphs of his staggering progress are good fun, reminding me an awful lot of a typical public equity. That point was driven home recently when I had one of these graphs up on my screen and a colleague had to be convinced that it wasn't a stock.
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