1. If the payout is convex, you don't care about the average; you care about the second order effects.
If you're concave, over a long enough time span, you will go bust. If you're convex, over a long enough time span, you will hit a fat-tailed payoff.
Pre-COVID, there were likely hundreds of metrics that correlated closely with the unemployment rate. Almost all of these correlations were broken over the past 6 months.
A normal distribution CANNOT masquerade as a fat-tailed distribution.
Thus, unless there's a strong logical reason for why a distribution is not fat-tailed, the default assumption should be it is fat-tailed.