Explanation:
Unlike VAR, the expected shortfall is a coherent risk measure that satisfies all four of the required conditions: monotonicity, translation invariance, homogeneity, and subadditivity. The axiom that is not always satisfied by the VaR is subadditivity, which stipulates that a risk measure of a combination of two or more portfolios should never be greater than the sum of the risk measures of each portfolio component. This principle is sometimes violated for the VaR, but never for the expected shortfall.
Statement A is correct. The expected shortfall provides a coherent measure of risk that considers the correlation between various positions in a portfolio.
Statements B and C are correct. One of the disadvantages of the VaR is that it tells us nothing about the size of the loss related to the extreme data points or the tail of the probability distribution. For example, the 99% VaR tells us nothing about the size of the loss in 1% of the cases where the loss can be greater than the calculated figure. On the other hand, the expected shortfall, which by definition is the average of losses beyond the VaR, does give us an idea of how bad the loss might be.
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Q.32 Which of the following statements about expected shortfall (ES) is most likely incorrect?
A
The expected shortfall provides a coherent risk measure across different positions and takes account of correlations.
B
The expected shortfall tells us what to expect in bad states: It gives an idea of how bad the portfolio payoff can be if the portfolio has a bad outcome.
C
The expected shortfall is better at capturing tail risk than the VaR.
D
Like the VAR, the expected shortfall does not always satisfy the subadditivity principle.
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