"You're all blind, and going to eyell at me because I told you, your returns are mostly random."
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The Efficient Market Hypothesis is built on the premise that the market's return / price movement is random. This allows the practitioner to use the Normal Distribution - where the math is easy. In a Gaussian / Normal Distribution, there's a mean, mode, median, variance and standard deviation.
In reality, the market price movement
does not conform to a Gaussian / ND. The only way to arrive at a Gaussian Dsitribution is to throw out outliers and pretend they never happened. The odds of an event such as August of 1998 is 1 in 500 billion; Crash of '87 is 1 in 10^50. In a ND, they should have never have happened. But they did. And as much as you'd like to pretend they had never occured, and I know of some people who love that to happen, they did and that's reality.
If the markets are truely random, how is it that the Hurst Coefficient is never 1/2, as it would for a random market? The only time it is 1/2 is when it moves form above it to below it. But it is never exactly 1/2. How is it that the skewness and kurtosis is never zero?
But again, except when they move from above to below zero...
In reality, the market conforms to a Stable Pareto Levy distribution. In a SPL, there are no mean, mode, median, variance or standard deviation. At this point the math gets hard. You'd have to find a location parameter M, scale parameter C, 3rd and / or 4th moment about the mean (and mean in this sense is not the average.).
Just a side note, the father of EMH, Eugene Fama, based his work on a paper written by Louis Bachelier on French bonds for his PhD. His work was critique by Bernard Levy (of the Stable Pareto Levy Dsitribution) and Henri Poincare. His work was found to be of high honor, not of highest honor. In other words, it was found wanting by 2 of the most eminent mathematicians in history.
So, EMH was built on a foundation of sand.