Explanation:
Statement I is correct: Value at Risk (VaR) is not a coherent risk measure because it fails the subadditivity property. Expected Shortfall (ES), however, satisfies all four axioms of coherence (monotonicity, subadditivity, positive homogeneity, and translation invariance). Statement II is incorrect: Expected Shortfall measures the expected value of all losses that exceed the VaR threshold. It does not provide a narrower range of expected losses; rather, it accounts for the entire tail risk beyond the VaR level.
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Q.74 Which of the following statements is (are) accurate?
I. VaR is not a coherent risk measure while Expected Shortfall is
II. Although the calculation of Expected Shortfall is more difficult, it provides a narrower range of expected losses than VaR does under the same significance level
A
Both I and II
B
I only
C
II only
D
None of the above