Coherent risk measure

What it means

A risk measure satisfying monotonicity, subadditivity, positive homogeneity and translation invariance.

The exam angle

Subadditivity is the one VaR fails — and it is the property that says diversification should never increase measured risk.

Where it appears in the syllabus

• Foundations of Risk ManagementFRM Part I · exam weight 20% · Risk taxonomy, governance, CAPM, multifactor models, financial disasters.
• Market Risk Measurement & ManagementFRM Part II · exam weight 20% · VaR and ES estimation, backtesting, EVT, GARCH, copulas, FRTB.

See it worked through

• Expected shortfall versus VaR: what changes in the tailWhy regulators moved from 99% VaR to 97.5% expected shortfall, with normal and fat-tailed numbers.

There is also a short video: watch it on YouTube.

Related terms

• BacktestingComparing realised losses with the VaR forecasts that preceded them, to check that breaches occur about as often as…
• Expected shortfallThe average loss in the cases where the VaR threshold is breached — the expected size of a bad day, given that it is a…
• Stress testingRevaluing a portfolio under severe but plausible scenarios, rather than under the distribution of ordinary days.
• Value at RiskThe loss that will not be exceeded over a stated horizon with a stated confidence — for example, a 1-day 99% VaR of…
• Adverse selectionThe problem that arises when the party with better information self-selects into a transaction, leaving the…
• Agency problemThe conflict that arises when managers act in their own interest rather than that of the owners who employ them.