Why VaR Backtests Can Pass at 5% but Fail at 1%

Summary

The document asks why volatility models used to estimate Value at Risk may pass a backtest at a 5% confidence tail while failing at a 1% tail. The response says this pattern is common: as the tail becomes more extreme, the assumed return distribution matters more, making accurate forecasts harder. At a less extreme threshold, a wider range of distributional assumptions can appear adequate.

The answer also emphasizes that forecast horizon affects difficulty. It reports that, in the responder’s experience, extending VaR to a ten-day horizon demands especially strong models and can be more challenging than moving from a 5% to a 1% tail area. This is qualitative guidance, not a comparison of the questioner’s specific models or a formal result from their backtest. The document does not discuss sample size, test power, or which backtesting procedure was used, so a pass or failure at either level should be interpreted in light of those omitted details.

Key ideas

• VaR model performance can differ between 5% and 1% tail levels.
• More extreme tail forecasts are more sensitive to distributional assumptions.
• A model that works at a moderate tail threshold may not describe rare losses well.
• Longer VaR horizons can increase model sensitivity and forecasting difficulty.
• The answer is general guidance and does not diagnose the specific backtest or its statistical power.

Tags

# Value at Risk backtesting (kupiec)


# Value at Risk backtesting (kupiec)












I m doing my research on estimating Value at risk using different assumptions on volatility and then compare my results based on backtesting. I obtained results and just on question based on my results.

The different models estimates accurately in 5% confidence level rather than 1%.. Is it common result? Because the same model rejected in 1% but accepted in 5%..

Thanks in advance

## Answer by Patrick Burns (score 5)

https://quant.stackexchange.com/a/1831

It is common.

The smaller the tail area you are considering the harder it is to be right because the effect of the assumption on the distribution becomes more important. Think about it in the other direction: if your level is 50%, then pretty much any distributional assumption will do.

The other issue is the length of the time horizon. As the horizon expands practical amounts, there is even more sensitivity to the model. What I found in http://www.burns-stat.com/pages/Working/varunigar.pdf was that 10 day horizons demand exceptionally good models -- moving from 1 day to 10 days is much harder than moving from 5% to 1% tail areas.

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