Why can expected shortfall move a lot even when VaR barely changes?
I saw two portfolios with almost the same 99% VaR, but one had a much worse expected shortfall. I thought similar VaR meant similar downside risk.
VaR and expected shortfall look at different parts of the loss distribution.
- VaR asks for the cutoff.
- Expected shortfall asks for the average loss after the cutoff has already been breached.
So two portfolios can share the same 99% VaR and still have very different tail shapes beyond that point.
Example:
- Portfolio A:
99%VaR =$4.8 million, ES =$5.4 million - Portfolio B:
99%VaR =$4.9 million, ES =$9.7 million
Portfolio B has a much fatter or more asymmetric extreme tail. That often happens with short-convexity exposures, concentrated credit, or structures that gap when liquidity disappears.
The exam takeaway is that VaR does not tell you how severe the bad 1% outcomes are on average. Expected shortfall does. That is why ES is often better for comparing portfolios whose worst-case region deepens very differently once the threshold is crossed.
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