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.

MIssissippi River Flooding and Hurricanes

I work in the insurance industry and a couple weeks ago the issue of this year's hurricane forecasting came up. At the time we were going through some of the worst MS river flooding in years, perhaps back to 1927. My thought is that MS river flooding should be correlated with hurricane activity as the MS river dumps so much water into the Gulf of Mexico - a major storm path for the hurricanes. My initial thought was this should impact hurricane activity because the temperature of water in the gulf is associated with hurricane severity and formation. If the MS river is dumping alot of excess "cooler" water into the gulf it should be associated with lowered hurricane activity.

Average year: From what I can tell an "average" year for storm activity is "The official NHC seasonal averages are 11 named storms, 6 hurricanes, and 2 major hurricanes." I think the 11 named storms include tropical storms, not just hurricanes. Recently it seems almost all forecasts have been higher than this, but I guess the above are much longer term averages.

I didn't investigate any of this throughly, mostly just quickly looked some stuff up - but thought it was interesting non-the-less. MS river flooding does seem correlated with below average storm and hurricane activity - at least from what I can tell - I'd be betting the "under".

Bad MS flooding years:

1927: I started by looking at 1927 hurricane data - because 1927 was the worst year for MS river flooding in U.S. history. I honestly didn't know if they even kept hurricane records back then, but they did have records. The hurricanes didn't have names, but they did show tracks... we had 4 hurricanes that year, and interestingly all of the hurricanes stayed in the Atlantic / not entering the gulf of Mexico.

1951: A "moderately active" hurricane year. This is apparently the most active hurricane year of the MS river flood years looked at - 8 hurricanes in all, but interestingly none of the hurricanes made landfall in the US as a hurricane. Strong "stay in the Atlantic" tendencies here too.

1973: The 1973 flooding of the MS was some of the worst in U.S. history so I also looked there. Interestingly only 4 hurricanes that year also - although 1 did reach strong category 3 status out in the Atlantic. Like in 1927 there was a strong tendency for storms to stay in the Atlantic.


1983: 1983 MS river flooding was charactarized as the 2nd worst MS river flooding in the past century, so we look here also. Similar trends arise. 3 hurricanes that year - and the "lowest accumulated cyclone energy count since 1950". 2 of the 3 hurricanes did enter the gulf that year though.

1993: Another bad MS river flooding year per Wikipedia. 4 hurricanes that year with tendency to stay out in the Atlantic again.


Atlantic Hurricane Seasons

1927 4 hurricanes
1951 8 hurricanes
1973 4 hurricanes
1983 3 hurricanes
1993 4 hurricanes
2011 ?

1927 Wikipedia entry
1951 Wikipedia entry
1973 Wikipedia entry
1983 Wikipedia entry
1993 Wikipedia entry