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Backtesting and Comparing Stressed VaR Models

Article Quant Q&A · Author: PalimPalim
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Summary

The document asks how to compare stressed Value at Risk estimates for a portfolio and whether standard VaR backtests, such as coverage and independence tests, remain suitable. Its answer treats stressed VaR as VaR calculated from returns during a stress period, so conventional VaR statistical tests can be applied to its exceedances. It also expects stressed VaR to be more conservative than ordinary VaR, producing fewer violations.

The discussion raises a practical comparison problem: two models may both pass coverage and independence tests while one gives larger estimates. It proposes evaluating predictions against a historical crisis, but the answer does not assess that proposal or explain how to rank models with similar test outcomes. No empirical results or detailed comparison procedure are provided, so the guidance is limited to the applicability of standard VaR tests.

Key ideas

  • Stressed VaR applies VaR methods to returns drawn from stressed market conditions.
  • Coverage and independence tests used for ordinary VaR can also assess stressed VaR exceedances.
  • A stressed VaR model is expected to produce fewer violations than a normal VaR model.
  • Passing the same tests does not, by itself, resolve which of two differently conservative estimates is preferable.

Tags

Risk managementStatisticsBacktestingEquities
Full text
# testing stressed VaR


# testing stressed VaR












How can you compare stressed VaR estimates?

What are statistical tests for assessing the quality of stressed VaR estimates?

I think the VaR Coverage test for example by Christoffersen (1988) would still be aplicable.

I will build different models for calculating stressed VaR for a portfolio long in the MSCI. I am unsure how I can compare the estimates from different models.

Additional Question Say, I am comparing two sVar estimates X,Y. Both yield less than by VaR expected exceedences. X is more conservative than Y. They both perform equally well on test such as Unconditional Coverage and Independence. Which is better?

I thought about backtesting it on a historical stressfull period such as the financial crisis and than look for a model which predicted exceedences are as close as possible to real exceedences. Does this make sense?

## Answer by JejeBelfort (score 0, accepted)

https://quant.stackexchange.com/a/34231

Stress VaR is a particular case of the VaR as being computed on stressed returns.

Therefore, any suitable statistical test (including Christoffersen test) applicable to VaR would fit for purpose for stress VaR.

Of course, you should expect this measure to be more conservative than normal VaR, by finding a better coverage (less VaR violations).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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