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According to the Efficient Market hypothesis: 

a) investors have all the information available to them and they independently make rational decisions using this information

b) the market reacts to all the information available reaching equilibrium quickly

c) in this equilibrium state the market essentially follows a random walk, which means, the probability distributions (histograms) of stock market returns are normal (Gaussian)

In such a system, extreme changes such as crashes and bubbles are very rare. 


a) Market dynamics is the result of decisions by interacting agents (e.g., herding behavior), traders who speculate and/or act impulsively on little news, etc.

b) This collective/chaotic behavior can lead to wild swings in the market, driving it away from equilibrium into the realm of non-linearity, resulting in a variety of interesting phenomena such as bubbles, crashes and so on.

c) Lastly, a look at the probability distributions of market returns show that they are not Gaussian distributions at all.

The following figure shows a comparison of the distributions of true market returns with the corresponding Gaussian distributions. The true distributions have fat tails and narrower peaks which are not shown by model distributions.



Comparison of Market distributions with Gaussian distributions for daily and monthly percent returns.    (a) S&P 500 (b) Nasdaq (1990 - 2019)

Comparison of data and Gaussian distributions
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