My favorite example is J.C. Penney. Yes, I have picked on this company several times in the past, but it arguably poses one of the greatest fat tail conundrum risks in recent memory. Management has been battling bankruptcy concerns for several years but eventually staved it off with a complete restructuring plan and a huge influx of capital represented by an intra-day jump of more than 25%. Based on this one giant up-day alone, JCP managed to eek out a +2.54% valuation advantage despite an implied probability disadvantage of -2.44% for calendar year 2014.
How did the valuation potential go positive when the probability of the market went negative? It's all thanks to the fat tail! Removing this obscene outlier nets a valuation disadvantage of -13.3%, which matches the downbeat sentiment evident in the market's probability. Outside of this one-off event, the implied regression for JCP's stock price is $5.18 at the end of 2014. Including the fat tail, implied regression skyrockets to $9.43.
Of course, regression is a target based on probabilities ; there's no guarantee that JCP's stock will hit a number within the previously discussed range, or even anywhere close to it. But the longer an asset is held, the more likely the asset will regress to established baseline probabilities ; since JCP has a historical baseline that is not "buyer favorable," or less than 50/50 odds, the chance that new buyers will lose faith is relatively high. This then poses a risk to the fundamental turnaround story, which in and of itself has very substantial headwind.
The moral of the story? Don't bite on the fat tail...it just might bite you back at a very inopportune moment.