Expected Shortfall: Historical and Normal-Model Estimation
Summary
Expected Shortfall (ES), also called Conditional Value at Risk, measures the average loss in the tail beyond a chosen Value at Risk (VaR) threshold. The article explains the distinction: VaR identifies a loss cutoff at a confidence level, while ES estimates the average severity of losses beyond that cutoff. It presents ES as a more informative view of tail risk and notes its coherent-risk property.
Two estimation approaches are described. The historical method first finds VaR from observed data, then averages losses worse than that threshold. The parametric method estimates the loss distribution’s parameters and calculates ES from them; the article illustrates this under a normality assumption. Its portfolio example reports that the historical estimate is higher than the normal-model estimate, with both exceeding VaR. The comparison is illustrative, not evidence that either approach forecasts future losses reliably. ES estimates depend on the selected confidence level, data coverage, tail modeling, and distribution assumptions, and sparse extreme observations can make estimates unstable.
Key ideas
- Expected Shortfall estimates the average loss beyond a VaR threshold at a selected confidence level.
- A historical estimate averages observed losses that exceed the empirical VaR cutoff.
- A parametric estimate uses an assumed loss distribution and estimated parameters.
- The example produces different historical and normal-model estimates, showing sensitivity to method.
- Tail data scarcity and model misspecification can undermine ES estimates.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.