Distribution of Stock Price Movements

So maybe this will be a boring post, maybe not. I found it interesting as I'd tried to google information on this subject before and had been unable much that was useful.

My basic question was "what is the distribution of stock price movements?" (what % of the time do they go up, down, and by how much when they do?)

I didn't really feel like a "normal" distribution made sense as down moves "seem" larger and more violent than upward movements in stock prices. (A normal distribution is the normal "bell shaped" distribution we've all come to "assume" in many cases so we can use basic statistical tools such as standard deviations and allows us to constrain probabilities - example if a normal distribution applied we could assume 95% of price movements would fall within +or- 2 standard deviations of the mean of the distribution. This is particularly useful understanding risk).

Well, I was reading Jack Schwager's "The New Market Wizards" this morning - the chapter on trader William Eckhardt and the topic comes up, and when asked about statistics and stock price movements - and he is talking about only using "blunt statistical instruments" and says "I believe that price distributions are pathological." Ha. I kindof cracked up when I read it, but he goes on to talk about fractals and the problem seems to be that sample variance increases as data increases when you look at stock price movement. The more you look at, the more weird, unusual, unexpected moves you find... The implication of this being "it means that lurking somewhere out there are more extreme scenarios than you might imagine". This book came out in 1992, so the term "black swan" wasn't used then, but what he was talking about is the "black swan" concept that's so popular now after the financial collapse of 2008. Market outcomes that you think might be so highly improbable as to not exist might in reality be far more likely than we expect.

By now I've read alot of the stories of these traders in both "Market Wizards" and "The New Market Wizards" and one theme that they keep coming back to is cut your losses fast - and keep your risk small so that no one event can wipe you out. It seems the field is littered with traders who can make money for years but then "blow up" when they run into something unexpected and haven't properly respected risk. Assume risk is much larger than you expect it is, because how you manage risk makes the difference between surviving and getting wiped out.