A fat-tailed distribution is one of the so-called heavy-tailed statistical distributions that describe the probability of certain events. Fat tails have a sharp bell shape which leads to the term leptokurtosis, another name for a fat tailed distribution.
A probability distribution with fat tails would be one in which moderately extreme outcomes were more likely than you might have expected. Strictly speaking this differs from a long tailed distribution in would be one in which very very extreme outcomes have non negligible probabilities.
Fat-tail and long-tail probability analysis is used in financial risk management, but it would seem that statisticians and investment professionals would sometimes disagree on what constitues a fat tail and what is a long tail. See the two diagrams below.
The diagram to the left is the one usually referred to by statisticians but the distance of the ends of the long tails above the base line leads to some confusion. See the diagram provided by Pimco to explain tail risk to investors below.
In April 2012, Martin Wolf, chief economic commentator at the FT, considered the arguments of Paul McCulley, former managing director of Pimco and Zoltan Pozsar, formerly at the Federal Reserve Bank of New York. In a paper they co-authored they put the case for aggressive fiscal policy. They argued that fiscal austerity does not work in a liquidity trap and makes as much sense "as putting an anorexic on a diet". They argue that "in a liquidity trap, the fat-tail risk of inflation is replaced by the fat-tail risk of deflation".