There is no doubt that the way our stock markets and other financial markets behave is largely governed by the statistical concepts such as the Central Limit Theorem, or the law of large numbers. According to the Central Limit Theorem, the mean of a large number of independent random variables will be approximately close to a normal distribution, or the traditional bell curve. And this is quite possible because of the random nature of the activity that takes place in the stock markets. In fact, such normal distribution is observed quite commonly in various places in science.
However, in reality, our stock markets constantly depart from this normal behaviour and exhibit high kurtosis, fat tails, etc.
To understand, why markets depart from the normal distribution let’s first understand why they have the normal property in the first place. A key assumption in Central Limit Theorem is that the random variables are statistically independent, that is, one does not influence the occurrence of the other. The same can be observed in the stock markets. There are thousands (or even more) of independent buy and sell decisions made every day that influence the demand and supply and all this activity is reflected in how the prices move. If all these individual buy/sell calls and related decisions were truly independent, then the stock markets will exhibit a normal distribution.
However, all these millions of decisions are not always independent, even though they seem to be. The decisions that investors and traders make are highly influenced by the flow of information, news, and events. For example, when a large event occurs such as a fall of a political party, a grim announcement by the central bank, or a natural disaster, the decisions made by many will not really be independent, but will follow a trend based on a shared view of the market. This is enough for the markets to move away from normality.