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The Chairman
Victor Niederhoffer

3/1/05
Power Laws, by Victor Niederhoffer

Power laws are used by chronic bears to show that a stock market earthquake is bound to occur, and that distributions of prices are fat tailed, and that buying volatility works.

My favorite discussion of how to deal with such laws simply: [ f(x) = x to -a power ] ( where x is something like the number of people or stocks with income greater than x ) is in Harold Thayer Davis' The Analysis of Economic Time Series.

Take log of both sides to get a straight line relation [ log (f(x) = -a log x ] they liked to deal with things simply in those days as did Pareto when he discovered it in the 19th century.

During the last two years, there has not been one decline or rise or more than 1.5% . How long does it take before people will begin saying that prices are narrow tailed? The answer is never, because power laws are one of those useless descriptive things that explains everything and makes one look sapient, and encourages people with money or respect to part with it, while aggrandizing and legitimizing your hatred of individual differences.

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