A classic problem in physics is the origin of fat tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags $tau.$ We find that destroying all correlations without changing the $tau = 1$ d distribution, by shuffling the order of the daily returns, causes the fat tails almost to vanish for $tau>1$ d. We argue that the fat tails are caused by known long-range volatility correlations. Indeed, destroying only sign correlations, by shuffling the order of only the signs (but not the absolute values) of the daily returns, allows the fat tails to persist for $tau >1$ d.
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