# Unexpected Loss

## Definition

**Unexpected Loss** (UL). The worst-case financial loss and/or impact that a business could incur due to a particular Loss event or Risk realization. The unexpected loss is calculated as the Expected Loss plus the potential adverse volatility.

Unexpected Loss is a formal Risk Measure that was introduced as part of the Basel II regulatory reforms. It is used primarily in the context of estimating Risk Capital using internal models and it aims to explicitly separate the related Expected Loss concept, (the idea being that expected losses are provisioned for and unexpected losses must be explicitly insured against with other forms of capital).

Unexpected losses correspond to the unpredictable/unforeseeable losses that have a lower probability of occurrence but may nevertheless occur. Statistically, for a given confidence interval of the Loss Distribution Function, unexpected losses (UL) correspond to the difference between the maximum loss incurred and expected losses (EL).

## Issues and Challenges

- The original usage of the UL term was based on a volatility measure, this was gradually replaced by a quantile based measure
- The quantile to which unexpected losses are computed is not consistent (or even explicit) throughout the regulatory framework
- The numerical outcome is subject to substantial Model Risk as the calculation depends not only in individual risk assessment but also assumption about correlations / dependencies