What is a coherent risk measure?

A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance . Consider a random outcome viewed as an element of a linear space of measurable functions, defined on an appropriate probability space.

Is 95% VaR a coherent risk measure?

However if we held a portfolio that consisted of 50% of each bond by value then the 95% VaR is 35% (= 0.5*0.7 + 0.5*0) since the probability of at least one of the bonds defaulting is 7.84% (= 1 - 0.96*0.96) which exceeds 5%. This violates the sub-additivity property showing that VaR is not a coherent risk measure.

Is the tail value at risk a coherent risk measure?

The tail value at risk (or tail conditional expectation) is a coherent risk measure only when the underlying distribution is continuous . The Wang transform function (distortion function) for the tail value at risk is . The concavity of proves the coherence of this risk measure in the case of continuous distribution.

Is entropic value at risk a coherent risk measure?

The average value at risk (sometimes called expected shortfall or conditional value-at-risk or ) is a coherent risk measure, even though it is derived from Value at Risk which is not. The domain can be extended for more general Orlitz Hearts from the more typical Lp spaces. The entropic value at risk is a coherent risk measure.