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It seems that some tail-risk centric groups are bent on using Paretian and t-distributions to account for tail risk when fitting log-returns. It has been observed, however, that with and without filtering log-returns with ARMA/GARCH, fitting ecdf's to cdf's still results in better Laplace and logistic distribution fits when compared with stable, normal, or Student's t. Given this, is there a reason why the bulk of the data and its best fitting distribution is not identified first, followed by consideration of tails? If the focus is mostly tails, then the Cauchy is not bad, and a Cauchy with heavy tails could be realized by a stable distribution. Independent of the infinite variance problem, why the constraint for mostly t-distributions?

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Check: quant.stackexchange.com/a/10319/3015 –  Quartz Feb 21 at 17:01

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