are stock market returns normally distributed?

Question

Many models assume they are. What have the empirical studies shown?

Answer 1

Empirical studies have shown market return distributions to have fat tails. Way too many outliers to fit a normal distribution.

Answer 2

Hi!

In a low frequency data base, stocks do follow a normal distribution. However, in high frequency, they definitively do not follow a normal distribution.

Recent research indicates that stocks in the very short term follow a Pareto-like distribution.

It is true, stocks distributions have fat tails. But how model them, it is still an on-going research. Extreme Value Theory and Copulas are very helpful to construct portfolios, for example, based on non-normal worlds and non-normal measures of dependence.

Nevertheless, many models assume a normal distribution because one can easily obtain an analytical solution. For non-normal distributions, one usually need to approximate solutions based on numerical optimization techniques.

I hope this helps!

Pedro N.

Answer 3

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Answer 4

They are not, further the mean cannot be estimated nor can the variance as they do not converge.

Answer 5

Not always!