Enterprise Risk Management (ERM) Practice Questions - Enterprise Risk Management (ERM) - Actuaries Institute Fellowship Program Exam

Why is standard Value at Risk (VaR) at confidence level α NOT a coherent risk measure in the general case?

It fails the subadditivity axiom for non-elliptical loss distributions with heavy tails It violates positive homogeneity when portfolio sizes are scaled by a constant factor It fails monotonicity when losses are strictly non-negative It cannot be computed for normally distributed financial asset returns

Correct Answer:

It fails the subadditivity axiom for non-elliptical loss distributions with heavy tails

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