# Difference between revisions of "Expected Loss versus Unexpected Loss"

From Open Risk Manual

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− | \begin{ | + | \begin{align} |

− | \mbox{EL} & = | + | \mbox{EL} & = E[R] \\ |

− | \mbox{UL} & = | + | \mbox{UL} & = \sqrt(Var[R]) |

− | \end{ | + | \end{align} |

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## Revision as of 16:15, 11 September 2019

## Expected Loss versus Unexpected Loss

**Expected Loss versus Unexpected Loss** highlights a very general (and sometimes confusing) strategy in Quantitative Risk Management to *decompose* estimates of potential future Loss into an *expected* component (EL, Expected Loss)) and an uncertain element (UL, Unexpected Loss).

In the simplest case where risk is represented by a Random Variable, the decomposition has an natural mathematical correspondence:

## Issues and Challenges

A number of confusions may emerge from informal or ambiguous use of language

- The 'expectation' in Expected Loss does not imply a
*certain*outcome - The
*expectation*in Expected Loss does not mean the most likely outcome but the scenario average - The
*unexpected*in Unexpected Loss can be captured by many different measures (e.g, quantile or other tail Risk Measure)

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