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The Levy distribution is the actual distribution of prices in a market. The variance is infinite and the mean undefined. Per the Pareto principle only a small number of trades contribute to significant movement. Spread around the median is less than that expressed in the normal distribution.

Comments

Blue DonkeyBlue Donkey
@thedirector 
What about distribution of SPX volatility? 11/30/16
The JokerThe Joker
Will discuss. Volatility affects the downsloping of the stable Levy distribution. Fat tails apply at all times (governed by power law decay, not exponential decay) 11/30/16
DinkDink
Yes! Power laws are the dominant statistical odds in markets. That is why I always laugh when some genius charging money for subscription service claims "the market is now 3 standard deviations above its 20 day MA, so look out below!" The only problem is the market doesn't follow a normal distribution, it follows pareto/power law. 12/1/16
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