hard · FRM Part 1 Valuation and Risk Models
A bank is calculating the 99% Expected Shortfall (ES) for a $10 million portfolio under the assumption of normality, where the daily volatility is 2.5%. Given that the standard normal density at the 99% quantile is φ(2.326) ≈ 0.02665, calculate the ES and compare it to the 99% Value-at-Risk (VaR).
- ES = $266,500, which is lower than the true 99% VaR
- ES = $750,000, based on an overly conservative 3-sigma assumption
- ES = $666,250, which is higher than the VaR of $581,500
- ES = $581,500, which is exactly equal to VaR
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