A risk measure is coherent if it satisfies certain simple, mathematical properties. One of these properties, which some popular measures do not possess is sub-additivity, that adding together two risky portfolios cannot increase the measure of risk.
Which risk measures are coherent?
A functional → is said to be coherent risk measure for if it satisfies the following properties:
- Normalized.
- Monotonicity.
- Sub-additivity.
- Positive homogeneity.
- Translation invariance.
- Convex risk measures.
- Value at risk.
- Average value at risk.
Which four conditions should a risk measure satisfy to be seen as a coherent risk measure?
A risk measure satisfying the four axioms of translation invariance, subadditivity, positive homogeneity, and monotonicity is called coherent.
