hard · Quantitative Finance
A risk manager uses Value at Risk (VaR) at the 99% confidence level.
If the returns are normally distributed with mean 0 and standard deviation σ, what is the relationship between VaR and Expected Shortfall (ES)?
- ES is always smaller than VaR.
- The ratio of ES to VaR depends only on the mean of the distribution.
- ES and VaR are equal if the distribution is symmetric.
- ES is approximately 1.15 times larger than VaR at high confidence levels for normal distributions.
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