Why is Expected Shortfall harder to estimate by simulation than VaR in heavy-tailed portfolios?

Question

AcadiFi · Accepted Answer

Expected Shortfall is harder because it depends on the severity of tail losses, not just the cutoff. VaR needs the location of a quantile. ES averages losses beyond that quantile, so the estimate is driven by a small number of extreme scenarios. In heavy-tailed portfolios, those extreme scenarios can vary dramatically across simulation runs.

Suppose Crestline Risk Lab simulates 100,000 losses for a credit portfolio with jump risk. The 99 percent VaR uses the loss around the 1,000th worst scenario. The 99 percent ES averages the worst 1,000 scenarios. If a few very large simulated defaults appear in one run but not another, ES can move materially even when VaR looks stable.

The solution is not to abandon ES. It is to improve estimation discipline. Use enough scenarios, test convergence, consider variance reduction, and check whether the tail model is plausible. For very heavy-tailed exposures, plain Monte Carlo may require a large simulation budget. FRM questions often reward the insight that tail averages need more care than tail cutoffs because they are sensitive to the magnitude of rare losses. On the exam, also state the horizon, confidence level, data source, modeling assumption, and validation step, because those choices usually explain why two reasonable VaR answers differ materially. Practice more in our FRM question bank.

Why is Expected Shortfall harder to estimate by simulation than VaR in heavy-tailed portfolios?

Master Part I with our FRM Course

Related Questions

Practice Questions