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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?

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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).

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  • $\begingroup$ Sure, but 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? $\endgroup$
    – PalimPalim
    Commented May 16, 2017 at 9:13
  • $\begingroup$ Then try to decrease your confidence level in order to observe exceedances for both of the sVaR. The one yielding to less exceedances will be the best. $\endgroup$
    – JejeBelfort
    Commented May 16, 2017 at 9:17
  • $\begingroup$ But, than it would just mean you are looking for the most conservative model. I am not really happy with that. 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. $\endgroup$
    – PalimPalim
    Commented May 16, 2017 at 9:27
  • $\begingroup$ Usually conservativeness is an important feature of your model as I guess you are concerned about being regulatory compliant. If it is not your main focus, then what about qualitative aspects of your backtests? Is there evidence that one is more stable than the other? Otherwise the approach you proposed seems suitable. $\endgroup$
    – JejeBelfort
    Commented May 16, 2017 at 9:41

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