A risk measure that satisfies monotonicity, translation invariance, positive homogeneity and subadditivity. VaR fails subadditivity in general; expected shortfall meets all four.
Where you will meet it
Coherent risk measure comes up in 12 learning outcome notes across the FRM syllabus.
A few of them:
Enterprise Risk Management and Future Trends FRM Part I · Foundations of risk management
“A stress test applies a severe but plausible adverse scenario, usually a coherent set of macroeconomic and market shocks over several periods, and projects its effect on losses, earnings, risk-weighted assets, liquidity and capital.”
Fundamentals of Probability FRM Part I · Quantitative analysis
“To be coherent it must contain the sample space itself.”
Measures of Financial Risk FRM Part I · Valuation and risk models
“A coherent risk measure, ρ, satisfies four properties.”
The Evolution of Stress Testing Counterparty Exposures FRM Part II · Credit risk measurement and management
“A full test shocks both sides, preferably in one coherent scenario, because the two interact multiplicatively and may be wrong-way correlated.”
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