Most investment banks calculate daily 95% or 99% confidence interval VaR figures. To do this they look at a discrete distribution of simulated revenues. Some methods to estimate VaR relay on a single historic observation date and therefore can exhibit high variability. This both reduces its efficiency and provides little information about the distribution of losses around the tail.

The process of risk management requires not only estimating the VaR but also examining the sensitivity of its positions comprising the portfolio. Taking a single order statistic may be inadequate for this purpose. Computing a weighted average of the dates in the tail will produce more robust risk analysis.

We discuss the use of the Expected Shortfall under certain distribution assumptions and the Harrell-Davis estimator as alternative approaches to estimating VaR and examine their reliability for risk management purposes.

1. FULLTEXT: On the Expected Shortfall and the Harrell-Davis Estimator of the Tail Loss, Microsoft Office Document, 0.1MB

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