Expected shortfall

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Expected shortfall is a measure of financial portfolio risk. It requires a quantile-level q, and is defined to be the expected loss of portfolio value given that the loss is occurring at or below the q-quantile.

For example, if we believe our average loss on the worst 5% of the possible outcomes for our portfolio is EUR 1000, then we could say our expected shortfall is EUR 1000 for the 5% tail.

Mathematically:

E(x | x > μ) where μ is the threshold.

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