medium · FRM Part 1 Valuation and Risk Models
An analyst is comparing two risk measures: 95% Value-at-Risk (VaR) and 95% Expected Shortfall (ES).
For a portfolio with a normal distribution of returns (mean 0, standard deviation σ), what is the relationship between the two metrics?
- VaR will be greater than ES because it represents the maximum possible loss.
- VaR is a coherent risk measure, while ES is not.
- ES will always be greater than VaR.
- ES and VaR are equal for symmetrical distributions like the normal distribution.
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