hard · Quantitative Finance
An analyst estimates the 1-day 99% Expected Shortfall (ES) for a portfolio with normal losses having mean μ_L and standard deviation σ_L.
Compared to the 99% Value-at-Risk (VaR), which of the following is true?
- ES is smaller than VaR because it is a conditional expectation which 'smooths' the extreme outliers.
- ES is equal to VaR for the normal distribution because the distribution is symmetric.
- ES cannot be compared to VaR because ES is not a subadditive measure.
- ES is always greater than VaR because it averages all losses in the tail beyond the VaR threshold.
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