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Answer: For the same confidence level, ES is always greater than VaR.
A is correct. Expected shortfall (ES) is always greater than or equal to Value at Risk (VaR) for a given confidence level \( a \), since VaR measures the minimum loss in case the worst \( a \) percentage probability event happens, while ES accounts for the severity of expected losses beyond VaR. This means that ES provides a more comprehensive view of risk by considering not just the threshold of loss but also the potential magnitude of losses that could occur if the market moves unfavorably beyond the VaR level. B is incorrect because the acceptance of a VaR backtest does not ensure the accuracy of the ES calculation. C is incorrect because VaR is not subadditive, meaning that the risk of a combined portfolio can be greater than the sum of the risks of its individual positions, whereas ES is subadditive and thus provides a more accurate representation of the combined risk. D is incorrect because backtesting ES is more complex due to the need to consider not only the number of VaR breaches but also the size of those breaches, which adds an additional layer of complexity to the process.
Author: LeetQuiz Editorial Team
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To enhance your understanding before modifying the existing risk assessment strategies at an investment bank that currently utilizes Value at Risk (VaR), what key concepts and details regarding both VaR and Expected Shortfall (ES) should you be aware of?
A
For the same confidence level, ES is always greater than VaR.
B
If a VaR backtest at a specified confidence level is accepted, then the corresponding ES will always be accepted.
C
While VaR ensures that the estimate of portfolio risk is less than or equal to the sum of the risks of that portfolio's positions, ES does not.
D
While ES is more complicated to calculate than VaR, it is easier to backtest than VaR.
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