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Returns are almost always long tailed distributions. Depending on the circumstances, they can have negative long tail (the ‘famous’ lognormal fat tails in risk analysis), positive long tails or both.

If you don’t have the experience or the expertise, handling all these variations can be quite a challenge. For small samples I have observed many times people ignore the tails – i.e. the justification is that these outliers are ‘infrequent’ and due to some other unknown process (a nice way to say “I don’t want to trouble myself”) – and then fit a reasonable normal distribution.

Another problem I have observed with small samples  is that the distribution can change markedly from sample to sample. This can be a severe problem. The concern here is, if you don’t know the true population distribution, how do you model it correctly? I don’t know how others treat this if they do or if they just ignore the whole thing and assume normality.

Note: depending on the data even 100 data points can be considered small.

One important reason why normal can be used. If you are measuring the average of many small samples, than normal gives a good fit. You have to make the distinction that you are working with averages and not the return statistic itself but I find that when this happens many times people don’t. 

Disclosure: I’m a capitalist too, and my musings & opinions on this blog are for informational/educational purposes and part of my efforts to learn from the mistakes of other people. Hope you do, too. These musings are not to be taken as financial advise, and are based on data that is assumed to be correct. Therefore, my opinions are subject to change without notice. This blog is not intended to either negate or advocate any persons, entity, product, services or political position.

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  1. […] View original post here: The Statistical Distribution of Returns « QuantumRisk – Management … […]

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