When events with low probability occur, people tend to overestimate the chance that they will occur again. For example, if an earthquake strikes the number of people who buy earthquake insurance goes up even though the likelihood of another earthquake happening remains unchanged. The fat tail is the new red subjective probability where the black line is the old objective probability. This shows the increased felling that low-probability events will happen more often. As time passes the subjective probability should return to match the objective probability.
The fat tail idea is one originated by Robert Barro. He says people go to government bonds “just in case” the worst thing possible happens. In this highly unlikely situation, the stock markets would be thrown into chaos (default) but the government would hold steady (at least enough to pay back the held bonds). One has to acknowledge it’s an untestable theory because we have yet to experience this doomsday scenario that would screw the world for twenty years (the "Great" Depression didn’t even last that long).