Comparing VaR and Expected Shortfall Backtests

Summary

The document raises the problem of determining empirically whether Expected Shortfall (ES, also called CVaR) is a better risk measure than Value at Risk (VaR). It notes that the measures capture different aspects of tail risk and that their backtests commonly evaluate them separately, making their results difficult to compare directly.

It asks whether a statistical framework could assess both measures using a shared success criterion, across choices of assumed return distribution, confidence level, sample size, and asset class. The text offers no proposed method, data, or empirical findings, so it serves as a research question rather than a worked comparison. Any conclusion would depend on a clearly defined evaluation objective and comparable test setup.

Key ideas

• VaR and ES describe risk differently, so their backtests are not directly interchangeable.
• Separate tests for each measure do not by themselves establish which is superior.
• A comparison needs a common evaluation criterion and a controlled test design.
• The document poses this methodological question but supplies no answer or empirical evidence.

Tags

# Comparing Backtests of Value-at-Risk and Expected Shortfall


# Comparing Backtests of Value-at-Risk and Expected Shortfall












My goal is to test if ES (CVaR) empirically is a better risk measure than VaR for a set of given variables (assumed underlying distribution, confidence level, sample size) for different asset classes.

As VaR and ES are like apples and oranges, they can not be compared directly. Most backtesting frameworks that I have found test explicitly VaR or ES (I am aware of the difficulties of backtesting ES) and these backtests are not comparable and it is seems hard to infer if e.g ES is superior to VaR from given samples. I assume there must be involved some function that include a common success factor.

Based on this, I am wondering if there are any known approaches for statistically testing (backtests) and comparing VaR and ES?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.