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Black Swans Fat Tails and Financial Markets

May 25, 2008
The mathematical models used by hedge funds, money center banks, and big investment banks, like even the smart boys at Goldman Sacks, seem to have the evaluation of risks and the frequency at which "rare" statistically almost impossible to occur events actually do occur all wrong.

A black swan is an event that is truly disastrous when it does occur but fortunately, according to the investment models, will occur very rarely. So rarely, in fact, that it makes no sense to worry about it. A recent black swan that has hit the stock markets of the world squarely between the eyes and is still flying wildly about, is the subprime mortgage market meltdown.

Mathematical models discounted the percentage of mortgages that could go bad to such a low number that the effect of just a few going bad from time to time was expected to have little effect on the overall mortgage portfolio. Obviously, given the events of the past year, something very wrong was build into the mathematical models.

A fat tail is an event or serious of events that are considered to be well outside the range of what is consider normal. A bell curve is usually used to demonstrate the distribution of events. If we plot events to a graph, since normal events occur most of the time the largest number of events would be as expected , at or very near the center of the curve.

Events which occur slightly less than normal would be plotted a bit further away from the center, until finally rare events would be plotted at the far end of the graph. Once plotted to a chart the graph would have the shape of a bell, thus the name bell curve.

The financial house statisticians placed in their models certain events likelihood of occurring way at the end of the bell curve. Often so many standard deviations away from the norm that the events were expected to occur once in a hundred thousand years, if at all. Imagine their surprise and disbelieve when a number of these events occurred one after the other giving their bell curve an unexpected fat tail.

What when wrong? How could so many very smart people come up with investment risk models that have proven to be so mismatched with real world events? How could have so many of Wall Streets brightest con men, eeerrrrr, sorry, financial managers, chairman, and CEO's, expand their businesses into such risky areas as repackaging loans make to people who don't have the ability to repay into investment packages that carry a AAA rating? How indeed?

A good summary of the black swan and fat tail problem is this quote: "It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so" (Mark Twain?).

The mathematical models may work fine in a theoretical world. In that world economists, mathematicians, and investment bank analysis, buy into the theory that human beings are rational creatures and will always take actions that are in their own self interests. They also buy into the nonsense that markets are always right, that the current price for a security must be the correct price because at that point in time the market says so.

Unfortunately human beings are often not rational at all. They have a marked tendency to follow each other around. The herd instinct is strong. Humans can stampede one after the other in one direction and then let's say a black swan event occurs, like two hijacked planes slamming into the World Trade center twin towers, and almost immediately the herd reverses course and charges off in the opposite direction.

Alas, the mathematical models used by the big boys to identify and rate risk just can't get a grip on human emotions and behavior. Fear can turn into greed and greed into fear quicker than you can say buy or sell. In financial markets, be they stocks, bonds, commodities, or forex, the effects of fear are often multiplied many times over because of the financial leverage that many investors use in structuring their investments.

Under extreme stress black swans and fat tails seem to flourish. Events that according to the models should only happen once in a million years may happen several times in one week. Perhaps the big smart boys aren't nearly as smart as they think they are. Do they really deserve to pay themselves millions of dollars a year in bonuses on top of multi million dollar salaries? Is this what late stage rape and pillage the average investor capitalism has come to?
About the Author
Gerald "Taipan" Greene is a retired forex trader and portfolio manager who worked in Asia for over 20 years. The nickname was acquired in Hong Kong and is now used for a number of financial, political, and Internet business related blogs. One of them is at Bold Messenger
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