Mildenhall 3.6.2 Risk Measures - Tail Risk

I don’t understand the illustrative example for Tail. “An outcome of winning 1M or 3M has variability, but much less tail risk for most people than the possibility of gaining or losing 1M. The variability of the two is the same but the tail risk is different”. Isn’t this an example of “Volume” since the first scenario is always as good or better than the second scenario. I don’t see how it touches on probability of extreme outcomes at all.

The description of Tail talks about a “lower likelihood” of extreme outcomes but in the example scenario is it not implied that the probability of the less favorable outcome is the same, the only difference is the amount?

I haven’t read that source.

But usually when i hear about tail risk, it is defining risk only as a loss.

Sometimes i also see “risk” defined as synonymous with variability. This is usually in more theoretical works.

Tail risk is one sided and looking at the downside risk compared to base.

Scenario 1 is all upside risk: Either gaining 1M or 3M. I’d love to take that bet.

Scenario 2 has both upside and downside risk: Either gaining 1M or losing 1M. That has significant tail risk even though the variance is the same.