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# What is a spectral risk measure?

A spectral risk measure (SRM) is a risk measure that is calculated as a weighted average of outcomes, the weights of which depend on the user’s risk aversion. Unlike value at risk (VaR), for example, it is an example of a ‘coherent risk measure’ as described in the field of mathematical finance.

## Where have you heard about a spectral risk measure?

As a private investor, you probably won’t have heard of spectral risk measures. They remain an esoteric part of theoretical mathematical finance that is largely discussed in academic papers. Some hedge funds are incorporating the measures into their risk analysis to avoid the shortcomings of models such as VaR.

## What you need to know about a spectral risk measure.

After the 2008 financial crisis, risk measurement tools such as VaR were found to be often unsuitable for purpose, so mathematical academics and market professionals looked to develop new methods. The concept of ‘coherent risk measures’ was developed in a research paper by Artzner et al in 1999 and began to be revisited. Coherent measures must exhibit four properties: monotonicity, sub-additivity, positive homogeneity and translational invariance. VaR does not satisfy the requirement for sub-additivity. The sub-category of spectral risk measures utilises the four properties to construct a model that associates the risk measure with the user’s own attitude toward risk.

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